original_text,compressed_text,prompt_tokens,compressed_tokens,tokens_saved,compression_time,compression_ratio,runtime_date,gpt_o1_saving,avg_distance_interrogative_words,compression_ratio_normalized,memory_used_kb
"Incremental class learning involves sequentially learning classes in bursts of examples from the same class. This violates the assumptions that underlie  methods for training standard deep neural networks, and will cause them to suffer from catastrophic forgetting. Arguably, the best method for incremental class learning is iCaRL, but it requires storing  training examples for each class, making it challenging to scale. Here, we propose FearNet for incremental class learning. FearNet is a generative model that does not store previous examples, making it memory efficient. FearNet uses a brain-inspired dual-memory system in which new memories are consolidated from a network for recent memories inspired by the mammalian hippocampal complex to a network for long-term storage inspired by medial prefrontal cortex. Memory consolidation is inspired by mechanisms that occur during sleep. FearNet also uses a module inspired by the basolateral amygdala for determining which memory system to use for recall.   FearNet achieves state-of-the-art performance at incremental class learning on image (CIFAR-100, CUB-200) and audio classification (AudioSet) benchmarks.
 In incremental classification, an agent must sequentially learn to classify training examples, without necessarily having the ability to re-study previously seen examples. While deep neural networks (DNNs) have revolutionized machine perception BID26 , off-the-shelf DNNs cannot incrementally learn classes due to catastrophic forgetting. Catastrophic forgetting is a phenomenon in which a DNN completely fails to learn new data without forgetting much of its previously learned knowledge BID29 . While methods have been developed to try and mitigate catastrophic forgetting, as shown in BID23 , these methods are not sufficient and perform poorly on larger datasets. In this paper, we propose FearNet, a brain-inspired system for incrementally learning categories that significantly outperforms previous methods.The standard way for dealing with catastrophic forgetting in DNNs is to avoid it altogether by mixing new training examples with old ones and completely re-training the model offline. For large datasets, this may require weeks of time, and it is not a scalable solution. An ideal incremental learning system would be able to assimilate new information without the need to store the entire training dataset. A major application for incremental learning includes real-time operation on-board embedded platforms that have limited computing power, storage, and memory, e.g., smart toys, smartphone applications, and robots. For example, a toy robot may need to learn to recognize objects within its local environment and of interest to its owner. Using cloud computing to overcome these resource limitations may pose privacy risks and may not be scalable to a large number of embedded devices. A better solution is on-device incremental learning, which requires the model to use less storage and computational power.In this paper, we propose an incremental learning framework called FearNet (see Fig. 1 ). FearNet has three brain-inspired sub-systems: 1) a recent memory system for quick recall, 2) a memory system for long-term storage, and 3) a sub-system that determines which memory system to use for a particular example. FearNet mitigates catastrophic forgetting by consolidating recent memories into long-term storage using pseudorehearsal BID34 . Pseudorehearsal allows the network to revisit previous memories during incremental training without the need to store previous training examples, which is more memory efficient.Figure 1: FearNet consists of three braininspired modules based on 1) mPFC (longterm storage), 2) HC (recent storage), and 3) BLA for determining whether to use mPFC or HC for recall.Problem Formulation: Here, incremental class learning consists of T study-sessions. At time t, the learner receives a batch of data B t , which contains N t labeled training samples, i.e., B t = {(x j , y j )} Nt j=1 , where x j ∈ R d is the input feature vector to be classified and y j is its corresponding label. The number of training samples N t may vary between sessions, and the data inside a study-session is not assumed to be independent and identically distributed (iid). During a study session, the learner only has access to its current batch, but it may use its own memory to store information from prior study sessions. We refer to the first session as the model's ""base-knowledge,"" which contains exemplars from M ≥ 1 classes. The batches learned in all subsequent sessions contain only one class, i.e., all y j will be identical within those sessions.Novel Contributions: Our contributions include:1. FearNet's architecture includes three neural networks: one inspired by the hippocampal complex (HC) for recent memories, one inspired by the medial prefrontal cortex (mPFC) for long-term storage, and one inspired by the basolateral amygdala (BLA) that determines whether to use HC or mPFC for recall.2. Motivated by memory replay during sleep, FearNet employs a generative autoencoder for pseudorehearsal, which mitigates catastrophic forgetting by generating previously learned examples that are replayed alongside novel information during consolidation. This process does not involve storing previous training data.3. FearNet achieves state-of-the-art results on large image and audio datasets with a relatively small memory footprint, demonstrating how dual-memory models can be scaled. FearNet's mPFC is trained to both discriminate examples and also generate new examples. While the main use of mPFC's generative abilities is to enable psuedorehearsal, this ability may also help make the model more robust to catastrophic forgetting. BID18 observed that unsupervised networks are more robust (but not immune) to catastrophic forgetting because there are no target outputs to be forgotten. Since the pseudoexample generator is learned as a unsupervised reconstruction task, this could explain why FearNet is slow to forget old information. Table 5 : Memory requirements to train CIFAR-100 and the amount of memory that would be required if these models were trained up to 1,000 classes. Table 5 shows the memory requirements for each model in Sec. 6.1 for learning CIFAR-100 and a hypothetical extrapolation for learning 1,000 classes. This chart accounts for a fixed model capacity and storage of any data or class statistics. FearNet's memory footprint is comparatively small because it only stores class statistics rather than some or all of the raw training data, which makes it better suited for deployment.An open question is how to deal with storage and updating of class statistics if classes are seen in more than one study sessions. One possibility is to use a running update for the class means and covariances, but it may be better to favor the data from the most recent study session due to learning in the autoencoder.FearNet assumed that the output of the mPFC encoder was normally distributed for each class, which may not be the case. It would be interesting to consider modeling the classes with a more complex model, e.g., a Gaussian Mixture Model. BID34 showed that pseudorehearsal worked reasonably well with randomly generated vectors because they were associated with the weights of a given class. Replaying these vectors strengthened their corresponding weights, which could be what is happening with the pseudo-examples generated by FearNet's decoder. The largest impact on model size is the stored covariance matrix Σ c for each class. We tested a variant of FearNet that used a diagonal Σ c instead of a full covariance matrix. TAB5 shows that performance degrades, but FearNet still works.FearNet can be adapted to other paradigms, such as unsupervised learning and regression. For unsupervised learning, FearNet's mPFC already does a form of it implicitly. For regression, this would require changing mPFC's loss function and may require grouping input feature vectors into similar collections. FearNet could also be adapted to perform the supervised data permutation experiment performed by BID20 and BID24 . This would likely require storing statistics from previous permutations and classes. FearNet would sleep between learning different permutations; however, if the number of classes was high, recent recall may suffer. In this paper, we proposed a brain-inspired framework capable of incrementally learning data with different modalities and object classes. FearNet outperforms existing methods for incremental class learning on large image and audio classification benchmarks, demonstrating that FearNet is capable of recalling and consolidating recently learned information while also retaining old information. In addition, we showed that FearNet is more memory efficient, making it ideal for platforms where size, weight, and power requirements are limited. Future work will include 1) integrating BLA directly into the model (versus training it independently); 2) replacing HC with a semi-parametric model; 3) learning the feature embedding from raw inputs; and 4) replacing the pseduorehearsal mechanism with a generative model that does not require the storage of class statistics, which would be more memory efficient.A SUPPLEMENTAL MATERIAL A.1 MODEL HYPERPARAMETERS TAB1 shows the training parameters for the FearNet model for each dataset. We also experimented with various dropout rates, weight decay, and various activation functions; however, weight decay did not work well with FearNet's mPFC. TAB1 : FearNet Training Parameters TAB2 shows the training parameters for the iCaRL framework used in this paper. We adapted the code from the author's GitHub page for our own experiments. The ResNet-18 convolutional neural network was replaced with a fully-connected neural network. We experimented with various regularization strategies to increase the initial base-knowledge accuracy with weight decay working the best. The values that are given as a range of values are the hyperparameter search spaces. TAB9 shows the training parameters for GeppNet and GeppNet+STM. Parameters not listed here are the default parameters defined by BID17 . The values that are given as a range of values are the hyperparameter search spaces. A.3 BLA VARIANTS Our BLA model is a classifier that determines whether a prediction should be made using HC (recent memory) or mPFC (remote memory). An alternative approach would be to use an outlier detection algorithm that determines whether the data being processed by a sub-network is an outlier for that sub-network and should therefore be processed by the other sub-network. To explore this alternative BLA formulation, we experimented with three outlier detection algorithms: 1) one-class support vector machine (SVM) BID36 , 2) determining if the data fits into a Gaussian distribution using a minimum covariance determinant estimation (i.e., elliptical envelope) (Rousseeuw BID35 , and 3) the isolation forest BID27 . All three of these methods set a rejection criterion for if the test sample exists in HC; whereas the binary MLP reports a probability on how likely the test sample resides in HC. TAB5 : Performance of different BLA variants.","Incremental class learning involves sequentially learning classes bursts examples class. violates assumptions underlie methods training standard deep neural networks will cause suffer catastrophic forgetting. Arguably best method incremental class learning is iCaRL which requires storing training examples class making challenging scale. propose FearNet incremental class learning. FearNet is a generative model does not store previous examples making memory efficient. FearNet uses brain-inspired dual-memory system which new memories are consolidated network recent memories inspired mammalian hippocampal complex network long-term storage inspired medial prefrontal cortex. Memory consolidation is inspired mechanisms occur sleep. FearNet also uses module inspired basolateral amygdala determining which memory system use recall. FearNet achieves state-of-the-art performance incremental class learning image CIFAR-100 CUB-200 audio classification AudioSet benchmarks. incremental classification agent must sequentially learn classify training examples without necessarily ability re-study previously seen examples. deep neural networks DNNs have revolutionized machine perception BID26 off-the-shelf DNNs cannot incrementally learn classes due catastrophic forgetting. Catastrophic forgetting is a phenomenon which a DNN completely fails learn new data without forgetting much previously learned knowledge BID29. methods have been developed try mitigate catastrophic forgetting shown BID23 methods are not sufficient perform poorly larger datasets. paper propose FearNet brain-inspired system incrementally learning categories significantly outperforms previous methods.The standard way dealing catastrophic forgetting DNNs is to avoid altogether mixing new training examples old ones completely re-training model offline. large datasets may require weeks time is scalable solution. ideal incremental learning system would able assimilate new information without need store entire training dataset. major application incremental learning includes real-time operation on-board embedded platforms have limited computing power storage which is more memory e.g smart toys smartphone applications robots. example toy robot may need learn recognize objects within local environment interest owner. Using cloud computing overcome resource limitations may pose privacy risks may scalable large number embedded devices. better solution is on-device incremental learning which requires model use less storage computational power.In paper propose incremental learning framework called FearNet see Fig. 1 FearNet has three three brain-inspired sub-systems1 recent memory system quick recall 2 memory system long-term storage 3 sub-system determines which memory system use particular example. FearNet mitigates catastrophic forgetting consolidating recent memories long-term storage using pseudorehearsal BID34. Pseudorehearsal allows network revisit previous memories incremental training without need store previous training examples which is more memory efficient.Figure1:FearNet consists three braininspired modules based 1 mPFC longterm storage 2 HC recent storage 3 BLA determining whether use mPFC HC recall.Problem Formulation:incremental class learning consists study-sessions time learner receives batch dataB which containsN labeled training samples.e B xj j Nt j=1 wherexj∈R is the input feature vector classified j is its corresponding label. number training samplesN may vary sessions data inside study-session is not assumed independent identically distributed iid study session learner has access current batch may use memory store information prior study sessions. refer first session model's base-knowledge which contains exemplars ≥ 1 classes. batches learned subsequent sessions contain one class.e j will be identical within sessions.Novel Contributions:contributions include:1 FearNet's architecture includes three neural networks:one inspired hippocampal complex HC recent memories one inspired medial prefrontal cortex mPFC long-term storage one inspired basolateral amygdala BLA determines whether useHC mPFC recall.2 Motivated memory replay sleep FearNet employs generative autoencoder pseudorehearsal which mitigates catastrophic forgetting generating previously learned examples are replayed alongside novel information consolidation. process does not involve storing previous training data.3 FearNet achieves state-of-the-art results large image audio datasets relatively small memory footprint demonstrating how dual-memory models can be scaled. FearNet's mPFC is trained discriminate examples also generate new examples. main use mPFC's generative abilities is to enable psuedorehearsal ability may also help make model robust catastrophic forgetting. BID18 observed unsupervised networks are more robust immune catastrophic forgetting are no target outputs forgotten. Since pseudoexample generator is learned unsupervised reconstruction task could explain why FearNet is slow forget old information. Table5:Memory requirements train CIFAR-100 amount memory would required if these models were trained 1,000 classes. Table 5 shows memory requirements model Sec. 6.1 learning CIFAR-100 hypothetical extrapolation learning 1,000 classes. chart accounts fixed model capacity storage data class statistics. FearNet's memory footprint is comparatively small stores class statistics rather raw training data which makes better suited deployment.An open question is how to deal storage updating class statistics if classes are seen one study sessions. One possibility is to use running update class means covariances may better favor data recent study session due learning autoencoder.FearNet assumed output mPFC encoder was normally distributed class may case. would interesting consider modeling classes complex model e.g Gaussian Mixture Model. BID34 showed pseudorehearsal worked reasonably well randomly generated vectors were associated weights given class. Replaying vectors strengthened corresponding weights could what is happening pseudo-examples generated FearNet's decoder. largest impact model size is the stored covariance matrixΣ c class. tested variant FearNet used diagonal Σ c instead full covariance matrix. TAB5 shows performance degrades FearNet still works.FearNet can be adapted paradigms unsupervised learning regression. unsupervised learning FearNet's mPFC already does a form implicitly. regression would require changing mPFC's loss function may require grouping input feature vectors similar collections. FearNet could also adapted perform supervised data permutation experiment performed BID20 BID24. would likely require storing statistics previous permutations classes. FearNet would sleep learning different permutations;however if the number classes was high recent recall may suffer. paper proposed brain-inspired framework capable incrementally learning data different modalities object classes. FearNet outperforms existing methods incremental class learning large image audio classification benchmarks demonstrating FearNet is capable recalling consolidating recently learned information also retaining old information. addition showed FearNet is more memory efficient making ideal platforms where size weight power requirements are limited. Future work will include1 integrating BLA directly model versus training independently 2 replacingHC semi-parametric model;3 learning feature embedding raw inputs;4 replacing pseduorehearsal mechanism generative model does not require storage class statistics would memory efficient.A SUPPLEMENTAL MATERIAL A.1 MODEL HYPERPARAMETERS TAB1 shows training parameters FearNet model dataset. also experimented various dropout rates weight decay various activation functions;however weight decay did not work well FearNet's mPFC. TAB1:FearNet Training Parameters TAB2 shows training parameters iCaRL framework used paper. adapted code author's GitHub page experiments. ResNet-18 convolutional neural network was replaced fully-connected neural network. experimented various regularization strategies increase initial base-knowledge accuracy weight decay working best. values are given range values are the hyperparameter search spaces. TAB9 shows training parameters GeppNet GeppNet+STM. Parameters listed are the default parameters defined BID17. values are given range values are the hyperparameter search spaces. A.3 BLA VARIANTS BLA model is a classifier determines whether prediction should be made usingHC recent memory mPFC remote memory alternative approach would use outlier detection algorithm determines whether data processed sub-network is an outlier sub-network should therefore processed sub-network explore alternative BLA formulation experimented three outlier detection algorithms:1 one-class support vector machine SVM BID36 2 determining if the data fits Gaussian distribution using minimum covariance determinant estimation.e elliptical envelope Rousseeuw BID35 3 isolation forest BID27. three methods set rejection criterion if the test sample exists HC;whereas binary MLP reports probability how likely test sample resides HC. TAB5:Performance different BLA variants.",2233,1598,635,0.024,1.397,2025/11/05 17:18:52,0.01,1.514,0.2087227414330216,795.157
"Multi-view learning can provide self-supervision when different views are available of the same data. Distributional hypothesis provides another form of useful self-supervision from adjacent sentences which are plentiful in large unlabelled corpora. Motivated by the asymmetry in the two hemispheres of the human brain as well as the observation that different learning architectures tend to emphasise different aspects of sentence meaning, we present two multi-view frameworks for learning sentence representations in an unsupervised fashion. One framework uses a generative objective and the other a discriminative one. In both frameworks, the final representation is an ensemble of two views, in which, one view encodes the input sentence with a Recurrent Neural Network (RNN), and the other view encodes it with a simple linear model. We show that, after learning, the vectors produced by our multi-view frameworks provide improved representations over their single-view learnt counterparts, and the combination of different views gives representational improvement over each view and demonstrates solid transferability on standard downstream tasks. Multi-view learning methods provide the ability to extract information from different views of the data and enable self-supervised learning of useful features for future prediction when annotated data is not available BID16 . Minimising the disagreement among multiple views helps the model to learn rich feature representations of the data and, also after learning, the ensemble of the feature vectors from multiple views can provide an even stronger generalisation ability.Distributional hypothesis BID22 noted that words that occur in similar contexts tend to have similar meaning BID51 , and distributional similarity BID19 consolidated this idea by stating that the meaning of a word can be determined by the company it has. The hypothesis has been widely used in machine learning community to learn vector representations of human languages. Models built upon distributional similarity don't explicitly require humanannotated training data; the supervision comes from the semantic continuity of the language data.Large quantities of annotated data are usually hard and costly to obtain, thus it is important to study unsupervised and self-supervised learning. Our goal is to propose learning algorithms built upon the ideas of multi-view learning and distributional hypothesis to learn from unlabelled data. We draw inspiration from the lateralisation and asymmetry in information processing of the two hemispheres of the human brain where, for most adults, sequential processing dominates the left hemisphere, and the right hemisphere has a focus on parallel processing BID9 , but both hemispheres have been shown to have roles in literal and non-literal language comprehension BID15 BID14 .Our proposed multi-view frameworks aim to leverage the functionality of both RNN-based models, which have been widely applied in sentiment analysis tasks BID57 , and the linear/loglinear models, which have excelled at capturing attributional similarities of words and sentences BID5 BID24 BID51 for learning sentence representations. Previous work on unsupervised sentence representation learning based on distributional hypothesis can be roughly categorised into two types:Generative objective: These models generally follow the encoder-decoder structure. The encoder learns to produce a vector representation for the current input, and the decoder learns to generate sentences in the adjacent context given the produced vector BID24 BID20 BID50 . The idea is straightforward, yet its scalability for very large corpora is hindered by the slow decoding process that dominates training time, and also the decoder in each model is discarded after learning as the quality of generated sequences is not the main concern, which is a waste of parameters and learning effort.Our first multi-view framework has a generative objective and uses an RNN as the encoder and an invertible linear projection as the decoder. The training time is drastically reduced as the decoder is simple, and the decoder is also utilised after learning. A regularisation is applied on the linear decoder to enforce invertibility, so that after learning, the inverse of the decoder can be applied as a linear encoder in addition to the RNN encoder.Discriminative Objective: In these models, a classifier is learnt on top of the encoders to distinguish adjacent sentences from those that are not BID31 BID26 BID40 BID33 ; these models make a prediction using a predefined differentiable similarity function on the representations of the input sentence pairs or triplets.Our second multi-view framework has a discriminative objective and uses an RNN encoder and a linear encoder; it learns to maximise agreement among adjacent sentences. Compared to earlier work on multi-view learning BID16 BID17 BID52 that takes data from various sources or splits data into disjoint populations, our framework processes the exact same data in two distinctive ways. The two distinctive information processing views tend to encode different aspects of an input sentence; forcing agreement/alignment between these views encourages each view to be a better representation, and is beneficial to the future use of the learnt representations.Our contribution is threefold:• Two multi-view frameworks for learning sentence representations are proposed, in which one framework uses a generative objective and the other one adopts a discriminative objective. Two encoding functions , an RNN and a linear model, are learnt in both frameworks.• The results show that in both frameworks, aligning representations from two views gives improved performance of each individual view on all evaluation tasks compared to their single-view trained counterparts, and furthermore ensures that the ensemble of two views provides even better results than each improved view alone.• Models trained under our proposed frameworks achieve good performance on the unsupervised tasks, and overall outperform existing unsupervised learning models, and armed with various pooling functions, they also show solid results on supervised tasks, which are either comparable to or better than those of the best unsupervised transfer model. It is shown BID24 that the consistency between supervised and unsupervised evaluation tasks is much lower than that within either supervised or unsupervised evaluation tasks alone and that a model that performs well on supervised evaluation tasks may fail on unsupervised tasks. It is subsequently showed BID13 BID48 ) that, with large-scale labelled training corpora, the resulting representations of the sentences from the trained model excel in both supervised and unsupervised tasks, while the labelling process is costly. Our model is able to achieve good results on both groups of tasks without labelled information. In both frameworks, RNN encoder and linear encoder perform well on all tasks, and generative objective and discriminative objective give similar performance. We proposed multi-view sentence representation learning frameworks with generative and discriminative objectives; each framework combines an RNN-based encoder and an average-on-wordvectors linear encoder and can be efficiently trained within a few hours on a large unlabelled corpus. The experiments were conducted on three large unlabelled corpora, and meaningful comparisons were made to demonstrate the generalisation ability and transferability of our learning frameworks and consolidate our claim. The produced sentence representations outperform existing unsupervised transfer methods on unsupervised evaluation tasks, and match the performance of the best unsupervised model on supervised evaluation tasks.Our experimental results support the finding BID24 ) that linear/log-linear models (g in our frameworks) tend to work better on the unsupervised tasks, while RNN-based models (f in our frameworks) generally perform better on the supervised tasks. As presented in our experiments, multi-view learning helps align f and g to produce better individual representations than when they are learned separately. In addition, the ensemble of both views leveraged the advantages of both, and provides rich semantic information of the input sentence. Future work should explore the impact of having various encoding architectures and learning under the multi-view framework.Our multi-view learning frameworks were inspired by the asymmetric information processing in the two hemispheres of the human brain, in which the left hemisphere is thought to emphasise sequential processing and the right one more parallel processing BID9 . Our experimental results raise an intriguing hypothesis about how these two types of information processing may complementarily help learning.","Multi-view learning can provide self-supervision when different views are available data. Distributional hypothesis provides another form useful self-supervision adjacent sentences which are plentiful large unlabelled corpora. Motivated asymmetry two hemispheres human brain well observation different learning architectures tend emphasise different aspects sentence meaning present two multi-view frameworks learning sentence representations unsupervised fashion. One framework uses generative objective discriminative one. frameworks final representation is an ensemble two views which,which one view encodes input sentence Recurrent Neural Network RNN view encodes simple linear model. show learning vectors produced multi-view frameworks provide improved representations single-view learnt counterparts combination different views gives representational improvement view demonstrates solid transferability standard downstream tasks. Multi-view learning methods provide ability extract information different views data enable self-supervised learning useful features future prediction when annotated data is not available BID16. Minimising disagreement among multiple views helps model learn rich feature representations data also learning ensemble feature vectors multiple views can provide even stronger generalisation ability.Distributional hypothesis BID22 noted words occur similar contexts tend have similar meaning BID51 distributional similarity BID19 consolidated idea stating meaning word can be determined company has. hypothesis has been widely used machine learning community learn vector representations human languages. Models built upon distributional similarity explicitly require humanannotated training data;supervision comes semantic continuity language data.Large quantities annotated data are usually hard costly obtain thus is important study unsupervised self-supervised learning. goal is to propose learning algorithms built upon ideas multi-view learning distributional hypothesis learn unlabelled data. draw inspiration lateralisation asymmetry information processing two hemispheres human brain where,for most adults sequential processing dominates left hemisphere right hemisphere has a focus parallel processing BID9 hemispheres have been shown have roles literal non-literal language comprehension BID15 BID14.Our proposed multi-view frameworks aim leverage functionality RNN-based models which have been widely applied sentiment analysis tasks BID57 linear/loglinear models which have excelled capturing attributional similarities words sentences BID5 BID24 BID51 learning sentence representations. Previous work unsupervised sentence representation learning based distributional hypothesis can be roughly categorised two types:Generative objective:models generally follow encoder-decoder structure. encoder learns produce vector representation current input decoder learns generate sentences adjacent context given produced vector BID24 BID20 BID50. idea is straightforward yet scalability large corpora is hindered slow decoding process dominates training time also decoder model is discarded learning quality generated sequences is not the main concern which is a waste parameters learning effort.Our first multi-view framework has a generative objective uses RNN encoder invertible linear projection decoder. training time is drastically reduced decoder is simple decoder is also utilised learning. regularisation is applied linear decoder enforce invertibility learning inverse decoder can be applied linear encoder addition RNN encoder.Discriminative Objective:models classifier is learnt top encoders distinguish adjacent sentences are BID31 BID26 BID40 BID33;models make prediction using predefined differentiable similarity function representations input sentence pairs triplets.Our second multi-view framework has a discriminative objective uses RNN encoder linear encoder;learns maximise agreement among adjacent sentences. Compared earlier work multi-view learning BID16 BID17 BID52 takes data various sources splits data disjoint populations framework processes exact data two distinctive ways. two distinctive information processing views tend encode different aspects input sentence;forcing agreement/alignment views encourages view better representation is beneficial future use learnt representations.Our contribution is threefold:• Two multi-view frameworks learning sentence representations are proposed which,which one framework uses generative objective one adopts discriminative objective. Two encoding functions RNN linear model are learnt frameworks.• results show frameworks aligning representations two views gives improved performance individual view evaluation tasks compared single-view trained counterparts furthermore ensures ensemble two views provides even better results improved view alone.• Models trained proposed frameworks achieve good performance unsupervised tasks overall outperform existing unsupervised learning models armed various pooling functions also show solid results supervised tasks which are either comparable better best unsupervised transfer model. is shown BID24 consistency supervised unsupervised evaluation tasks is much lower within either supervised unsupervised evaluation tasks alone model performs well supervised evaluation tasks may fail unsupervised tasks. is subsequently showed BID13 BID48 large-scale labelled training corpora resulting representations sentences trained model excel supervised unsupervised tasks labelling process is costly. model is able achieve good results groups tasks without labelled information. frameworks RNN encoder linear encoder perform well tasks generative objective discriminative objective give similar performance. proposed multi-view sentence representation learning frameworks generative discriminative objectives;framework combines RNN-based encoder average-on-wordvectors linear encoder can be efficiently trained within hours large unlabelled corpus. experiments were conducted three large unlabelled corpora meaningful comparisons were made demonstrate generalisation ability transferability learning frameworks consolidate claim. produced sentence representations outperform existing unsupervised transfer methods unsupervised evaluation tasks match performance best unsupervised model supervised evaluation tasks.Our experimental results support finding BID24 linear/log-linear models g frameworks tend work better unsupervised tasks RNN-based models f frameworks generally perform better supervised tasks. presented experiments multi-view learning helps align f g produce better individual representations when they are learned separately. addition ensemble views leveraged advantages provides rich semantic information input sentence. Future work should explore impact various encoding architectures learning multi-view framework.Our multi-view learning frameworks were inspired asymmetric information processing two hemispheres human brain which the left hemisphere is thought emphasise sequential processing right one parallel processing BID9. experimental results raise intriguing hypothesis how these two types information processing may complementarily help learning.",1560,1095,465,0.016,1.425,2025/11/05 17:18:52,0.01,1.527,0.2959501557632398,468.553
"We show how discrete objects can be learnt in an unsupervised fashion from pixels, and how to perform reinforcement learning using this object representation.

 More precisely, we construct a differentiable mapping from an image to a discrete tabular list of objects, where each object consists of a differentiable position, feature vector, and scalar presence value that allows the representation to be learnt using an attention mechanism.

 Applying this mapping to Atari games, together with an interaction net-style architecture for calculating quantities from objects, we construct agents that can play Atari games using objects learnt in an unsupervised fashion. During training, many natural objects emerge, such as the ball and paddles in Pong, and the submarine and fish in Seaquest.

 This gives the first reinforcement learning agent for Atari with an interpretable object representation, and opens the avenue for agents that can conduct object-based exploration and generalization. Humans are able to parse the world as a collection of objects, that are discrete, persistent, and can be interacted with. Humans can use this representation for planning, reasoning, and exploration. When playing a game such as Montezuma's Revenge in Atari, a human can identify the different objects, such as an avatar that moves in a 2-D plane, a rolling skull, and a key. Even if they do not know initially what to do, they can explore the state space using the prior knowledge that objects persist, move around contiguously, and can interact with other objects in local proximity.This explicit representation of objects and prior knowledge is missing from artificial reinforcement learning agents, such as DQN BID11 ). Although architectures such as DQN attain superhuman performance on many games, in particular those whose reward signal is dense (see e.g., BID1 ), its performance on games with sparse rewards, or greater planning complexity, is often below that of humans. Perhaps explicit object knowledge is one missing ingredient, which would allow for more powerful exploration than existing epsilon-greedy methods (that simply execute a random walk in action space).In this paper we set forth a method to learn objects from pixels in an unsupervised manner. By an object representation, we mean a ""tabular"" representation, where there is a list of objects, and each object has a position and a set of features (represented by a vector).Learning such a representation from input pixels is a non-trivial challenge. The space of possible inputs is a connected manifold, but the space of object representations is disconnected; for example, there is no continuous transformation from 4 objects to 5. We address this challenge by introducing an object presence value between 0 and 1, which is a continuous relaxation of whether an object is present or not.We give a method of tracking the same object across multiple frames (object persistence), and give an architecture that can perform calculations using the object representation. We test this model in the Atari domain, and show that it is possible to do reinforcement learning on a learnt object representation. Objects such as the ball and paddles in Pong, and the submarine and fish in Seaquest, emerge naturally without supervision. We give results and insights into how best to calculate global values from a collection of objects using an ""interaction net"" style architecture, where calculations are invariant to object order.","show how discrete objects can be learnt unsupervised fashion pixels how to perform reinforcement learning using object representation. precisely construct differentiable mapping image discrete tabular list objects where each object consists differentiable position feature vector scalar presence value allows representation learnt using attention mechanism. Applying mapping Atari games together interaction net-style architecture calculating quantities objects construct agents can play Atari games using objects learnt unsupervised fashion. training many natural objects emerge ball paddles Pong submarine fish Seaquest. gives first reinforcement learning agent Atari interpretable object representation opens avenue agents can conduct object-based exploration generalization. Humans are able parse world collection objects are discrete persistent can be interacted with. Humans can use representation planning reasoning exploration. When playing game Montezuma's Revenge Atari human can identify different objects avatar moves 2-D plane rolling skull key. Even if they do not know initially whattodo,can explore state space using prior knowledge objects persist move around contiguously can interact objects local proximity.This explicit representation objects prior knowledge is missing artificial reinforcement learning agents DQN BID11 Although architectures DQN attain superhuman performance many games particular whose reward signal is dense seee.g BID1 performance games sparse rewards greater planning complexity is often humans. Perhaps explicit object knowledge is one missing ingredient would allow powerful exploration existing epsilon-greedy methods simply execute random walk action space.In paper set forth method learn objects pixels unsupervised manner. object representation mean tabular representation where thereis list objects where each object has a position set features represented vector.Learning representation input pixels is a non-trivial challenge. space possible inputs is a connected manifold space object representations is disconnected;example is no which is a continuous transformation 4 objects 5. address challenge introducing object presence value 0 1 is no which is a continuous relaxation whether object is present not.We give method tracking object across multiple frames object persistence give architecture can perform calculations using object representation. test model Atari domain show is possible do reinforcement learning learnt object representation. Objects ball paddles Pong submarine fish Seaquest emerge naturally without supervision. give results insights how best calculate global values collection objects using interaction net style architecture where calculations are invariant object order.",654,424,230,0.007,1.542,2025/11/05 17:18:52,0.0,1.529,0.660436137071651,255.044
"Most recent gains in visual recognition have originated from the inclusion of attention mechanisms in deep convolutional networks (DCNs). Because these networks are optimized for object recognition, they learn where to attend using only a weak form of supervision derived from image class labels. Here, we demonstrate the benefit of using stronger supervisory signals by teaching DCNs to attend to image regions that humans deem important for object recognition. We first describe a large-scale online experiment (ClickMe) used to supplement ImageNet with nearly half a million human-derived ""top-down"" attention maps. Using human psychophysics, we confirm that the identified top-down features from ClickMe are more diagnostic than ""bottom-up"" saliency features for rapid image categorization. As a proof of concept, we extend a state-of-the-art attention network and demonstrate that adding ClickMe supervision significantly improves its accuracy and yields visual features that are more interpretable and more similar to those used by human observers. Attention has become the subject of intensive research within the deep learning community. While biology is sometimes mentioned as a source of inspiration BID34 BID23 BID2 You et al., 2016; BID3 BID41 BID1 , the attentional mechanisms that have been considered remain limited in comparison to the rich and diverse array of processes used by the human visual system (see BID15 , for a review). In addition, whereas human attention is controlled by varying task demands, attention networks used in computer vision are solely optimized for object recognition. This means that, unlike infants who can rely on a myriad of visual cues and supervision to learn to focus their attention BID15 , DCNs must solve this challenging problem with weak supervisory signals derived from statistical associations between image pixels and class labels. Here, we investigate how explicit human supervision -teaching DCNs what and where to attend -affects their performance and interpretability. We have described the ClickMe dataset, which is aimed at supplementing ImageNet with nearly a half-million human-derived attention maps. The approach was validated with human psychophysics, which indicated the sufficiency of ClickMe features for rapid visual categorization. When participants viewed images that were masked to reveal commonly selected ClickMe map locations, they reached ceiling recognition accuracy when only 6% of image pixels were visible. By comparison, participants viewing images masked according to bottom-up saliency map locations did not reach ceiling performance until the full image was visible. These results indicate that ClickMe.ai may also provide novel insights into human vision with a measure of feature diagnosticity that goes beyond classic bottom-up saliency measures. While a detailed analysis of the ClickMe features falls outside the scope of the present study, we expect a more systematic analysis of this data, including the timecourse of feature selection BID4 BID11 , will aid our understanding of the different attention mechanisms responsible for the selection of diagnostic image features.We also extended the squeeze-and-excitation (SE) module which constituted the building block of the winning architecture in the ILSVRC17 challenge. We trained an SE-ResNet-50 on a reduced amount of data (∼ 300K samples) and found that the architecture overfits compared to a standard ResNet-50. We described a novel global-and-local attention (GALA) module and found that the proposed GALA-ResNet-50, however, significantly increases accuracy in this regime and cuts down top-5 error by ∼ 25% over both . In addition, we described an approach to co-train GALA using ClickMe supervision and cue the network to attend to image regions that are diagnostic to humans for object recognition. The routine casts ClickMe map prediction as an auxiliary task that can be combined with a primary visual categorization task. We found a trade-off between learning visual representations that are more similar to those used by human observers vs. learning visual representations that are more optimal for ILSVRC. The proper trade-off resulted in a model with better classification accuracy and more interpretable visual representations (both qualitatively and according to quantitative experiments on the ClickMe dataset and Microsoft COCO images).While recent advancements in DCNs have led to models that perform on par with human observers in basic visual recognition tasks, there is also growing evidence of qualitative differences in the visual strategies that they employ BID30 BID38 BID8 BID22 . It is not known whether these discrepancies arise because of differences in mechanisms for visual inference or fundamentally different training routines. However , our success in encouraging DCNs to learn more human-like representations with ClickMe map supervision suggests that improved training regimens can help close this gap. In particular , DCNs lack explicit mechanisms for perceptual grouping and figure-ground segmentation which are known to play a key role in the development of our visual system BID18 BID27 ) by simplifying the process of discarding background clutter. In the absence of figure-ground mechanisms, DCNs are compelled to associate foreground objects and their context as single perceptual units. This leads to DCN representations that are significantly more distributed compared to those used by humans BID22 . We hope that this work will help catalyze interest in the development of novel training paradigms that leverage combinations of visual cues (depth, motion, etc) for figure-ground segregation in order to substitute for the human supervision used here for co-training GALA.",recent gains visual recognition have originated inclusion attention mechanisms deep convolutional networks DCNs networks are optimized object recognition learn where to attend using weak form supervision derived image class labels. demonstrate benefit using stronger supervisory signals teaching DCNs attend image regions humans deem important object recognition. first describe large-scale online experiment ClickMe used supplement ImageNet nearly half million human-derived top-down attention maps. Using human psychophysics confirm identified top-down features ClickMe are more diagnostic bottom-up saliency features rapid image categorization. proof concept extend state-of-the-art attention network demonstrate adding ClickMe supervision significantly improves accuracy yields visual features are more interpretable similar used human observers. Attention has become subject intensive research within deep learning community. biology is sometimes mentioned source inspiration BID34 BID23 BID2 etal. 2016;BID3 BID41 BID1 attentional mechanisms have been considered remain limited comparison rich diverse array processes used human visual system see BID15 review addition whereas human attention is controlled varying task demands attention networks used computer vision are solely optimized object recognition. means unlike infants who can rely myriad visual cues supervision learn focus attention BID15 DCNs must solve challenging problem weak supervisory signals derived statistical associations image pixels class labels. investigate how explicit human supervision -teaching DCNs what and where to attend -affects performance interpretability. have described ClickMe dataset which is aimed supplementing ImageNet nearly half-million human-derived attention maps. approach was validated human psychophysics which indicated sufficiency ClickMe features rapid visual categorization. When participants viewed images were masked reveal commonly selected ClickMe map locations reached ceiling recognition accuracy when only6% image pixels were visible. comparison participants viewing images masked according bottom-up saliency map locations did not reach ceiling performance full image was visible. results indicate ClickMe.ai may also provide novel insights human vision measure feature diagnosticity goes beyond classic bottom-up saliency measures. detailed analysis ClickMe features falls outside scope present study expect systematic analysis data including timecourse feature selection BID4 BID11 will aid understanding different attention mechanisms responsible selection diagnostic image features.We also extended squeeze-and-excitation SE module which constituted building block winning architecture ILSVRC17 challenge. trained SE-ResNet-50 reduced amount data ∼ 300K samples found architecture overfits compared standard ResNet-50 have described novel global-and-local attention GALA module found proposed GALA-ResNet-50 however significantly increases accuracy regime cuts top-5 error ∼25% both. addition described approach co-train GALA using ClickMe supervision cue network attend image regions are diagnostic humans object recognition. routine casts ClickMe map prediction auxiliary task can be combined primary visual categorization task. found trade-off learning visual representations are more similar used human observersvs. learning visual representations are more optimal ILSVRC. proper trade-off resulted model better classification accuracy interpretable visual representations qualitatively according quantitative experiments ClickMe dataset Microsoft COCO images.While recent advancements DCNs have led models perform par human observers basic visual recognition tasks is also growing evidence qualitative differences visual strategies employ BID30 BID38 BID8 BID22. is not known whether discrepancies arise differences mechanisms visual inference fundamentally different training routines. However success encouraging DCNs learn human-like representations ClickMe map supervision suggests improved training regimens can help close gap. particular DCNs lack explicit mechanisms perceptual grouping figure-ground segmentation which are known play key role development visual system BID18 BID27 simplifying process discarding background clutter. absence figure-ground mechanisms DCNs are compelled associate foreground objects context single perceptual units. leads DCN representations are significantly distributed compared used humans BID22. hope work will help catalyze interest development novel training paradigms leverage combinations visual cues depth motion etc figure-ground segregation order substitute human supervision used co-training GALA.,1060,745,315,0.01,1.423,2025/11/05 17:18:52,0.0,1.432,0.2897196261682242,323.191
"In recent years, deep neural networks have demonstrated outstanding performancein many machine learning tasks. However, researchers have discovered that thesestate-of-the-art models are vulnerable to adversarial examples:  legitimate examples added by small perturbations which are unnoticeable to human eyes. Adversarial training, which augments the training data with adversarial examples duringthe training process,  is a well known defense to improve the robustness of themodel against adversarial attacks.   However, this robustness is only effective tothe same attack method used for adversarial training.   Madry et al. (2017) suggest that effectiveness of iterative multi-step adversarial attacks and particularlythat projected gradient descent (PGD) may be considered the universal first order adversary and applying the adversarial training with PGD implies resistanceagainst many other first order attacks.    However,  the computational cost of theadversarial training with PGD and other multi-step adversarial examples is muchhigher than that of the adversarial training with other simpler attack techniques. In this paper, we show how strong adversarial examples can be generated only ata cost similar to that of two runs of the fast gradient sign method (FGSM), allowing defense against adversarial attacks with a robustness level comparable to thatof the adversarial training with multi-step adversarial examples.   We empiricallydemonstrate the effectiveness of the proposed two-step defense approach againstdifferent attack methods and its improvements over existing defense strategies. Despite the fact that deep neural networks demonstrate outstanding performance for many machine learning tasks, researchers have found that they are susceptible to attacks by adversarial examples BID18 ; BID2 ). Adversarial examples which are generated by adding crafted perturbations to legitimate input samples are indistinguishable to human eyes. For classification tasks, these perturbations may cause the legitimate samples to be misclassified by the model at the inference time. While there exists no widely agreed conclusion, several studies attempted to explain the underlying causes of the susceptibility of deep neural networks toward adversarial examples. The vulnerability is ascribed to the linearity of the model BID2 ), low flexibility BID1 ), or the flatness/curvedness of the decision boundaries BID10 ), but a more general cause is still under research. The recent literature considered two types of threat models: black-box and white-box attacks. In black-box attacks, the attacker is assumed to have no access to the architecture and parameters of the model, whereas in white-box attacks, the attacker has complete access to such information. Several white-box attack methods were proposed BID2 , BID12 , BID17 , BID0 , BID9 ). In response, several defenses have been proposed to mitigate the effect of adversarial attacks. These defenses were developed along three main directions: (1) expanding the training data to make the classifier more robustly learn the underlying function, e.g., by adversarial training which augments the training data set with adversarial examples generated by certain attack methods BID18 , BID2 , BID5 ); (2) modifying the training procedure to reduce the gradients of the model w.r.t. the input such that the classifier becomes more robust to input perturbations, e.g., via input gradient regularization BID15 , or defensive distillation BID14 ; and (3) using external models as network add-ons when classifying unseen examples (feature squeezing BID19 , MagNet BID8 , and Defense-GAN) BID16 ).Adversarial training, a simple but effective method to improve the robustness of a deep neural network against white-box adversarial attacks, uses the same white-box attack mechanism to generate adversarial examples for augmenting the training data set. However, if the attacker applies a different attack strategy, adversarial training does not work well due to gradient masking BID13 . BID7 have suggested the effectiveness of iterative multi-step adversarial attacks. In particular, it was suggested that projected gradient descent (PGD) PGD may be considered the strongest first-order attack so that the adversarial training with PGD can boost the resistance against many other first-order attacks. However, in the literature a large number (e.g. 40) of steps of back propagation are typically used in the iterative attack method of PGD or its closely related variant iterative fast gradient (IFGSM) BID5 to find strong adversarial examples to be used in each adversarial training step, incurring a prohibitively high computational complexity particularly for large DNNs or training datasets.In this paper, we propose an efficient two-step adversarial defense technique, called e2SAD, to facilitate defense against multiple types of whitebox and blackbox attacks with a quality on a par with the expensive adversarial training using the well-known multi-step attack the iterative fast gradient method (IFGSM) BID5 . The first step of e2SAD is similar to the basic adversarial training, where an adversarial example is generated by applying a simple one-step attack method such as the fast gradient sign method (FGSM). Then in the second step, e2SAD attemps to generate a second adversarial example at which the vulnerability of the current model is maximally revealed such that the resulting defense is at the same quality level of the much more expensive IFGSMbased adversarial training. Finally, the two adversarial examples are taken into consideration in the proposed loss function according to which a more robust model is trained, resulting strong defense to both one-step and multi-step iterative attacks with a training time much less less than that of the adversarial training using IFGSM. The main contributions of this paper are as follows:• We propose a computationally efficient method to generate two adversarial examples per input example while effectively revealing the vulnerability of the learned classifier in the neighborhood of each clean data point;• We show that by considering the generated adversarial examples as part of a well-designed final loss function, the resulting model is robust to both one-step and iterative white box attacks;• We further demonstrate that by adopting other techniques in our two-step approach like the use of soft labels and hyper parameter tuning, robust defense against black box attacks can be achieved. We have aimed to improve the robustness of deep neural networks by presenting an efficient twostep adversarial defense technique e2SAD, particularly w.r.t to strong iterative multi-step attacks. This objective is achieved by finding a combination of two adversarial points to best reveal the vulnerability of the model around each clean input. In particular, we have demonstrated that using a dissimilarity measure between the first and second adversarial examples we are able to appropriately locate the second adversary in a way such that including both types of adversaries in the final training loss function leads to improved robustness against multi-step adversarial attacks. We have demonstrated the effectiveness of e2SAD in terms of defense against while-box one-step FGSM and multi-step IFGSM attacks and black-box IFGSM attacks under various settings.e2SAD provides a general mechanism for defending both one-step and multiple attacks and for balancing between these two defense needs, the latter of which can be achieved by properly tuning the corresponding weight hyperparameters in the training loss function. In the future work, we will explore hyperparameter tuning and other new techniques to provide a more balanced or further improved defense quality for a wider range of white and black box attacks.",recent years deep neural networks have demonstrated outstanding performancein many machine learning tasks. However researchers have discovered thesestate-of-the-art models are vulnerable adversarial examples:legitimate examples added small perturbations which are unnoticeable human eyes. Adversarial training which augments training data adversarial examples duringthe training process is a well known defense improve robustness themodel adversarial attacks. However robustness is only effective tothe attack method used adversarial training. Madryetal. 2017 suggest effectiveness iterative multi-step adversarial attacks particularlythat projected gradient descent PGD may considered universal first order adversary applying adversarial training PGD implies resistanceagainst many first order attacks. However computational cost theadversarial training PGD multi-step adversarial examples is muchhigher adversarial training simpler attack techniques. paper show how strong adversarial examples can be generated ata cost similar two runs fast gradient sign method FGSM allowing defense adversarial attacks robustness level comparable thatof adversarial training multi-step adversarial examples. empiricallydemonstrate effectiveness proposed two-step defense approach againstdifferent attack methods improvements existing defense strategies. Despite fact deep neural networks demonstrate outstanding performance many machine learning tasks researchers have found are susceptible attacks adversarial examples BID18;BID2 Adversarial examples which are generated adding crafted perturbations legitimate input samples are indistinguishable human eyes. classification tasks perturbations may cause legitimate samples misclassified model inference time. exists widely agreed conclusion several studies attempted explain underlying causes susceptibility deep neural networks toward adversarial examples. vulnerability is ascribed linearity model BID2 low flexibility BID1 flatness/curvedness decision boundaries BID10 general cause is still research. recent literature considered two types threat models:black-box white-box attacks. black-box attacks if the attacker is assumed have no access architecture parameters model whereas white-box attacks if the attacker has complete access information. Several white-box attack methods were proposed BID2 BID12 BID17 BID0 BID9 response several defenses have been proposed mitigate effect adversarial attacks. defenses were developed along three main directions:1 expanding training data make classifier robustly learn underlying function e.g where an adversarial training which augments training data set adversarial examples generated certain attack methods BID18 BID2 BID5 2 modifying training procedure reduce gradients modelw.r.t input classifier becomes robust input perturbations e.g via input gradient regularization BID15 defensive distillation BID14;3 using external models network add-ons when classifying unseen examples feature squeezing BID19 MagNet BID8 Defense-GAN BID16.Adversarial training simple effective method improve robustness deep neural network white-box adversarial attacks uses white-box attack mechanism generate adversarial examples augmenting training data set. However if the attacker applies different attack strategy where an adversarial training does not work well due gradient masking BID13. BID7 have suggested effectiveness iterative multi-step adversarial attacks. particular was suggested projected gradient descent PGD PGD may considered strongest first-order attack adversarial training PGD can boost resistance many first-order attacks. However literature large number e.g40 steps back propagation are typically used iterative attack method PGD closely related variant iterative fast gradient IFGSM BID5 find strong adversarial examples used adversarial training step incurring prohibitively high computational complexity particularly large DNNs training datasets.In paper propose efficient two-step adversarial defense technique called e2SAD facilitate defense multiple types whitebox blackbox attacks quality par expensive adversarial training using well-known multi-step attack iterative fast gradient method IFGSM BID5. first step e2SAD is similar basic adversarial training where an adversarial example is generated applying simple one-step attack method fast gradient sign method FGSM second step e2SAD attemps generate second adversarial example which the vulnerability current model is maximally revealed resulting defense is at the same quality level much expensive IFGSMbased adversarial training. Finally two adversarial examples are taken consideration proposed loss function according which a more robust model is trained resulting strong defense one-step multi-step iterative attacks training time much less less adversarial training using IFGSM. main contributions paper are as follows:• propose computationally efficient method generate two adversarial examples per input example effectively revealing vulnerability learned classifier neighborhood clean data point;• show considering generated adversarial examples part well-designed final loss function resulting model is robust one-step iterative white box attacks;• demonstrate adopting techniques two-step approach like use soft labels hyper parameter tuning robust defense black box attacks can be achieved. have aimed improve robustness deep neural networks presenting efficient twostep adversarial defense technique e2SAD particularlyw.r.t strong iterative multi-step attacks. objective is achieved finding combination two adversarial points best reveal vulnerability model around clean input. particular have demonstrated using dissimilarity measure first second adversarial examples are able appropriately locate second adversary way including types adversaries final training loss function leads improved robustness multi-step adversarial attacks. have demonstrated effectiveness e2SAD terms defense while-box one-step FGSM multi-step IFGSM attacks black-box IFGSM attacks various settings.e2SAD provides general mechanism defending one-step multiple attacks balancing two defense needs latter which can be achieved properly tuning corresponding weight hyperparameters training loss function. future work will explore hyperparameter tuning new techniques provide balanced improved defense quality wider range white black box attacks.,1474,1049,425,0.015,1.405,2025/11/05 17:18:52,0.01,1.408,0.233644859813084,454.386
"Recently several different deep learning architectures have been proposed that take a string of characters as the raw input signal and automatically derive features for text classification. Little studies are available that compare the effectiveness of these approaches for character based text classification with each other. In this paper we perform such an empirical comparison for the important cybersecurity problem of DGA detection: classifying domain names as either benign vs. produced by malware (i.e., by a Domain Generation Algorithm). Training and evaluating on a dataset with 2M domain names shows that there is surprisingly little difference between various convolutional neural network (CNN) and recurrent neural network (RNN) based architectures in terms of accuracy, prompting a preference for the simpler architectures, since they are faster to train and less prone to overfitting. Malware is software that infects computers in order to perform unauthorized malicious activities. In order to successfully achieve its goals, the malware needs to be able to connect to a command and control (C&C) center. To this end, both the controller behind the C&C center (hereafter called botmaster) and the malware on the infected machines can run a Domain Generation Algorithm (DGA) that generates hundreds or even thousands of domains automatically. The malware then attempts at resolving each one of these domains with its local DNS server. The botmaster will have registered one or a few of these automatically generated domains. For these domains that have been actually registered, the malware will obtain a valid IP address and will be able to communicate with the C&C center.The binary text classification task that we address in this paper is: given a domain name string as input, classify it as either malicious, i.e. generated by a DGA, or as benign. Deep neural networks have recently appeared in the literature on DGA detection ; BID8 ; BID15 . They significantly outperform traditional machine learning methods in accuracy, at the price of increasing the complexity of training the model and requiring larger datasets. Independent of the work on deep networks for DGA detection, other deep learning approaches for character based text classification have recently been proposed, including deep neural network architectures designed for processing and classification of tweets BID2 ; BID11 ) as well as general natural language text BID16 ). No systematic study is available that compares the predictive accuracy of all these different character based deep learning architectures, leaving one to wonder which one works best for DGA detection.To answer this open question, in this paper we compare the performance of five different deep learning architectures for character based text classification (see TAB0 ) for the problem of detecting DGAs. They all rely on character-level embeddings, and they all use a deep learning architecture based on convolutional neural network (CNN) layers, recurrent neural network (RNN) layers, or a combination of both. Our most important finding is that for DGA detection, which can be thought of as classification of short character strings, despite of vast differences in the deep network architectures, there is remarkably little difference among the methods in terms of accuracy and false positive rates, while they all comfortably outperform a random forest trained on human engineered features. This finding is of practical value for the design of deep neural network based classifiers for short text classification in industry and academia: it provides evidence that one can select an architecture that BID16 is faster to train, without loss of accuracy. In the context of DGA detection, optimizing the training time is of particular importance, as the models need to be retrained on a regular basis to stay current with respect to new, emerging malware. DGA detection, i.e. the classification task of distinguishing between benign domain names and those generated by malware (Domain Generation Algorithms), has become a central topic in information security. In this paper we have compared five different deep neural network architectures that perform this classification task based purely on the domain name string, given as a raw input signal at character level. All five models, i.e. two RNN based architectures, two CNN based architectures, and one hybrid RNN/CNN architecture perform equally well, catching around 97-98% of malicious domain names against a false positive rate of 0.001. This roughly means that for every 970 malicious domain names that the deep networks catch, they flag only one benign domain name erroneously as malicious. A Random Forest based on human defined linguistic features achieves a recall of only 83% against the same 0.001 false positive rate when trained and tested on the same data that was used for the deep networks. The use of a deep neural network that automatically learns features is attractive in a cybersecurity setting because it is a lot harder to craft malware to avoid detection by a system that relies on automatically learned features instead of on human engineered features. An interesting direction for future work is to test the trained deep networks more extensively on domain names generated by new and previously unseen malware families.A KERAS CODE FOR DEEP NETWORKS main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) lstm = LSTM(128, return sequences=False)(embedding) drop = Dropout(0.5) (lstm) output = Dense(1, activation ='sigmoid') (drop) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam')Listing 1: Endgame model with single LSTM layer, adapted from main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) bi lstm = Bidirectional ( layer =LSTM(64, return sequences=False), merge mode='concat')(embedding) output = Dense(1, activation ='sigmoid') ( bi lstm ) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 2: CMU model with bidirectional LSTM, adapted from BID2 main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) conv1 = Conv1D( filters =128, kernel size =3, padding='same', strides =1)(embedding) thresh1 = ThresholdedReLU(1e−6)(conv1) max pool1 = MaxPooling1D(pool size=2, padding='same')(thresh1 ) conv2 = Conv1D( filters =128, kernel size =2, padding='same', strides =1)(max pool1) thresh2 = ThresholdedReLU(1e−6)(conv2) max pool2 = MaxPooling1D(pool size=2, padding='same')(thresh2 ) flatten = Flatten () (max pool2) fc = Dense(64)( flatten ) thresh fc = ThresholdedReLU(1e−6)(fc) drop = Dropout(0.5) ( thresh fc ) output = Dense(1, activation ='sigmoid') (drop) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 3: NYU model with stacked CNN layers, adapted from BID16 def getconvmodel( self , kernel size , filters ) : model = Sequential () model.add( Conv1D( filters = filters , input shape =(128, 128), kernel size = kernel size , padding='same', activation =' relu ', strides =1)) model.add(Lambda(lambda x: K.sum(x, axis=1), output shape =( filters , ) ) ) model.add(Dropout(0.5) ) return model main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) conv1 = getconvmodel(2, 256)(embedding) conv2 = getconvmodel(3, 256)(embedding) conv3 = getconvmodel(4, 256)(embedding) conv4 = getconvmodel(5, 256)(embedding) merged = Concatenate () ([ conv1, conv2, conv3, conv4] ) middle = Dense(1024, activation =' relu ') (merged) middle = Dropout(0.5) (middle) middle = Dense(1024, activation =' relu ') (middle) middle = Dropout(0.5) (middle) output = Dense(1, activation ='sigmoid') (middle) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 4: Invincea CNN model with parallel CNN layers, adapted from BID8 main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) conv = Conv1D( filters =128, kernel size =3, padding='same', activation =' relu ', strides =1)(embedding) max pool = MaxPooling1D(pool size=2, padding='same')(conv) encode = LSTM(64, return sequences=False) (max pool) output = Dense(1, activation ='sigmoid') (encode) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 5: MIT model with a stacked CNN and LSTM layer, adapted from BID11 main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) flatten = Flatten () (embedding) output = Dense(1, activation ='sigmoid') ( flatten ) model = Model(inputs=main input, outputs =output) print (model.summary()) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 6: Baseline Model with only Embedding Layer main input = Input (shape=(11, ) , name='main input') dense = Dense(128, activation =' relu ') ( main input ) output = Dense(1, activation ='sigmoid') (dense) model = Model(inputs=main input, outputs =output) print (model.summary()) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 7: MLP Model with 128 Nodes Dense Layer",Recently several different deep learning architectures have been proposed take string characters raw input signal automatically derive features text classification. Little studies are available compare effectiveness approaches character based text classification other. paper perform empirical comparison important cybersecurity problem DGA detection:classifying domain names either benignvs. produced malware.e Domain Generation Algorithm Training evaluating dataset 2M domain names shows is surprisingly little difference various convolutional neural network CNN recurrent neural network RNN based architectures terms accuracy prompting preference simpler architectures since are faster train less prone overfitting. Malware is software infects computers order perform unauthorized malicious activities. order successfully achieve goals malware needs able connect command control C C center. end controller behind C C center hereafter called botmaster malware infected machines can run Domain Generation Algorithm DGA generates hundreds even thousands domains automatically. malware attempts resolving one domains local DNS server. botmaster will have registered one automatically generated domains. domains have been actually registered malware will obtain valid IP address will be able communicate C C center.The binary text classification task address paper is:given domain name string input classify either malicious.e generated DGA benign. Deep neural networks have recently appeared literature DGA detection;BID8;BID15. significantly outperform traditional machine learning methods accuracy price increasing complexity training model requiring larger datasets. Independent work deep networks DGA detection deep learning approaches character based text classification have recently proposed including deep neural network architectures designed processing classification tweets BID2;BID11 well general natural language text BID16 systematic study is available compares predictive accuracy different character based deep learning architectures leaving one wonder which one works best DGA detection.To answer open question paper compare performance five different deep learning architectures character based text classification see TAB0 problem detecting DGAs. rely character-level embeddings use deep learning architecture based convolutional neural network CNN layers recurrent neural network RNN layers combination both. important finding is that for DGA detection which can be thought classification short character strings despite vast differences deep network architectures is remarkably little difference among methods terms accuracy false positive rates comfortably outperform random forest trained human engineered features. finding is of practical value design deep neural network based classifiers short text classification industry academia:provides evidence one can select architecture BID16 is faster train without loss accuracy. context DGA detection optimizing training time is of particular importance models need retrained regular basis stay current respect new emerging malware. DGA detection.e classification task distinguishing benign domain names generated malware Domain Generation Algorithms has become central topic information security. paper have compared five different deep neural network architectures perform classification task based purely domain name string given raw input signal character level. five models.e two RNN based architectures two CNN based architectures one hybrid RNN/CNN architecture perform equally well catching around 97-98 malicious domain names false positive rate 0.001 roughly means every 970 malicious domain names deep networks catch flag one benign domain name erroneously malicious. Random Forest based human defined linguistic features achieves recall 83% 0.001 false positive rate when trained tested data was used deep networks. use deep neural network automatically learns features is attractive cybersecurity setting is a lot harder craft malware avoid detection system relies automatically learned features instead human engineered features. interesting direction future work is to test trained deep networks extensively domain names generated new previously unseen malware families.A KERAS CODE DEEP NETWORKS main input Input shape= 75 dtype='int32 name='main input' embedding Embedding input dim=128 output dim=128 input length =75 main input lstm LSTM 128 return sequences=False embedding drop Dropout 0.5 lstm output Dense 1 activation ='sigmoid' drop model Model inputs=main input outputs =output model.compile loss =' binary crossentropy optimizer ='adam' Listing1:Endgame model single LSTM layer adapted main input Input shape= 75 dtype='int32 name='main input' embedding Embedding input dim=128 output dim=128 input length =75 main input bi lstm Bidirectional layer =LSTM 64 return sequences=False merge mode='concat' embedding output Dense 1 activation ='sigmoid' bi lstm model Model inputs=main input outputs =output model.compile loss =' binary crossentropy optimizer ='adam' Listing2:CMU model bidirectional LSTM adapted BID2 main input Input shape= 75 dtype='int32 name='main input' embedding Embedding input dim=128 output dim=128 input length =75 main input conv1 Conv1D filters =128 kernel size=3 padding='same' strides=1 embedding thresh1 ThresholdedReLU 1e−6 conv1 max pool1 MaxPooling1D pool size=2 padding='same' thresh1 conv2 Conv1D filters =128 kernel size=2 padding='same' strides=1 max pool1 thresh2 ThresholdedReLU 1e−6 conv2 max pool2 MaxPooling1D pool size=2 padding='same' thresh2 flatten Flatten max pool2 fc Dense 64 flatten threshfc ThresholdedReLU 1e−6 fc drop Dropout 0.5 threshfc output Dense 1 activation ='sigmoid' drop model Model inputs=main input outputs =output model.compile loss =' binary crossentropy optimizer ='adam' Listing3:NYU model stacked CNN layers adapted BID16 def getconvmodel self kernel size filters model Sequential model.add Conv1D filters filters input shape 128 128 kernel size kernel size padding='same' activation =' relu strides=1 model.add Lambda lambdax:K.sum x axis=1 output shape filters model.add Dropout 0.5 return model main input Input shape= 75 dtype='int32 name='main input' embedding Embedding input dim=128 output dim=128 input length =75 main input conv1 getconvmodel 2 256 embedding conv2 getconvmodel 3 256 embedding conv3 getconvmodel 4 256 embedding conv4 getconvmodel 5 256 embedding merged Concatenate conv1 conv2 conv3 conv4 middle Dense 1024 activation =' relu merged middle Dropout 0.5 middle middle Dense 1024 activation =' relu middle middle Dropout 0.5 middle output Dense 1 activation ='sigmoid' middle model Model inputs=main input outputs =output model.compile loss =' binary crossentropy optimizer ='adam' Listing4:Invincea CNN model parallel CNN layers adapted BID8 main input Input shape= 75 dtype='int32 name='main input' embedding Embedding input dim=128 output dim=128 input length =75 main input conv Conv1D filters =128 kernel size=3 padding='same' activation =' relu strides=1 embedding max pool MaxPooling1D pool size=2 padding='same' conv encode LSTM 64 return sequences=False max pool output Dense 1 activation ='sigmoid' encode model Model inputs=main input outputs =output model.compile loss =' binary crossentropy optimizer ='adam' Listing5:MIT model stacked CNN LSTM layer adapted BID11 main input Input shape= 75 dtype='int32 name='main input' embedding Embedding input dim=128 output dim=128 input length =75 main input flatten Flatten embedding output Dense 1 activation ='sigmoid' flatten model Model inputs=main input outputs =output print model.summary model.compile loss =' binary crossentropy optimizer ='adam' Listing6:Baseline Model Embedding Layer main input Input shape= 11 name='main input' dense Dense 128 activation =' relu main input output Dense 1 activation ='sigmoid' dense model Model inputs=main input outputs =output print model.summary model.compile loss =' binary crossentropy optimizer ='adam' Listing7:MLP Model 128 Nodes Dense Layer,2178,1542,636,0.042,1.412,2025/11/05 17:18:52,0.01,1.444,0.2554517133956382,764.57
"Recognizing the relationship between two texts is an important aspect of natural language understanding (NLU), and a variety of neural network models have been proposed for solving NLU tasks. Unfortunately, recent work showed that the datasets these models are trained on often contain biases that allow models to achieve non-trivial performance without possibly learning the relationship between the two texts. We propose a framework for building robust models by using adversarial learning to encourage models to learn latent, bias-free representations. We test our approach in a Natural Language Inference (NLI) scenario, and show that our adversarially-trained models learn robust representations that ignore known dataset-specific biases. Our experiments demonstrate that our models are more robust to new NLI datasets. Recognizing the relationship between two texts is a significant aspect of general natural language understanding (NLU) BID2 . Natural Language Inference (NLI) is often used to gauge a model's ability to understand such a relationship between two texts BID11 BID12 . In NLI, a model is tasked with determining whether a hypothesis (the animal moved) would likely be inferred from a premise (a black cat ran). The development of new large-scale datasets has led to a flurry of various neural network architectures for solving NLI. However, recent work has found that many NLI datasets contain biases that enable hypothesis-only models -models that are given access to the hypothesis alone -to perform surprisingly well without possibly learning the relationship between two texts. For instance, annotation artifacts and statistical irregularities in the popular Stanford Natural Language Inference dataset (SNLI) BID5 allowed hypothesis-only models to perform at double the majority class baseline, and at least 5 other recent NLI datasets contain similar biases BID21 BID43 BID54 . We will use the terms ""artifacts"" and ""biases"" interchangeably.The existence of annotation artifacts in large-scale NLI datasets is detrimental for making progress in deep learning research for NLU. How can we trust the performance of top models if it is possible to infer the relationship without even looking at the premise? Solutions to this concern are so far unsatisfactory: constructing new datasets BID50 ) is costly and may still result in other artifacts; filtering ""easy"" examples and defining a harder subset is useful for evaluation purposes BID21 , but difficult to do on a large scale that will enable training; and compiling adversarial examples BID18 ) is informative but again limited by scale or diversity. Furthermore, these solutions do not address a lingering question: can we develop models that will generalize well despite many NLI datasets containing specific hypothesis-only biases?Inspired by domain-adversarial training of neural networks BID16 BID17 , we propose two architectures (Figure 1 ) that enable a model to perform well on other NLI datasets regardless of what annotation artifacts exist in the training corpus's hypotheses. While learning to classify the relationship between two texts, we simultaneously use adversarial learning to discourage our model from using dataset-specific biases.In this way, the resulting representations contain fewer biases, and the model is encouraged to learn the relationship between the two texts. Our experiments demonstrate that our architectures generate sentence representations that are more robust to annotation artifacts, and also transfer better: when trained on one dataset and evaluated on another, they perform better than a non-adversarial model in 9 out of 12 target datasets. The methodology can also be extended to other NLU tasks, and we outline the necessary changes to our architectures in the conclusion. To our knowledge , this is the first study that explores methods to ignore hypothesis-only biases when training NLI models. Biases in annotations are a major source of concern for the quality of NLI datasets and systems. In this paper, we presented a solution for combating annotation biases based on adversarial learning. We designed two architectures that discourage the hypothesis encoder from learning the biases, and instead obtain a more unbiased representation. We empirically evaluated our approach in a transfer learning scenario, where we found our models to perform better than a non-adversarial baseline on a range of datasets. We also investigated what biases remain in the latent representations.The methodology developed in this work can be extended to deal with biases in other NLU tasks, where one is concerned with finding the relationship between two objects. For example, in Reading Comprehension, a question is being asked about a passage; in story cloze completion, an ending is judged with respect to a context; and in Visual Question Answering, a question is asked about an image. In all these cases, the second element (question, ending, and question, respectively) may contain biases. Our adversarial architectures naturally apply to any model that relies on encoding this biased element, and may help remove such biases from the latent representation. We hope to encourage such investigation in the broader research community. TAB1 we consider the range {1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0}. In each dataset, we choose the best-performing model on the development set and report its quality on the test set.We follow the InferSent training regime, using SGD with an initial learning rate of 0.1. See BID9 for details.",Recognizing relationship two texts is an important aspect natural language understanding NLU variety neural network models have been proposed solving NLU tasks. Unfortunately recent work showed datasets models are trained often contain biases allow models achieve non-trivial performance without possibly learning relationship two texts. propose framework building robust models using adversarial learning encourage models learn latent bias-free representations. test approach Natural Language Inference NLI scenario show adversarially-trained models learn robust representations ignore known dataset-specific biases. experiments demonstrate models are more robust new NLI datasets. Recognizing relationship two texts is a significant aspect general natural language understanding NLU BID2. Natural Language Inference NLI is often used gauge model's ability understand relationship two texts BID11 BID12. NLI model is tasked determining whether hypothesis animal moved would likely inferred premise black cat ran development new large-scale datasets has led flurry various neural network architectures solving NLI. However recent work has found many NLI datasets contain biases will enable hypothesis-only models -models are given access hypothesis alone -to perform surprisingly well without possibly learning relationship two texts. instance annotation artifacts statistical irregularities popular Stanford Natural Language Inference dataset SNLI BID5 allowed hypothesis-only models perform double majority class baseline least5 recent NLI datasets contain similar biases BID21 BID43 BID54. will use terms artifacts biases interchangeably.The existence what annotation artifacts large-scale NLI datasets is detrimental making progress deep learning research NLU. How can we trust performance top models if it is possible infer relationship without even looking premise? Solutions concern are so far unsatisfactory:constructing new datasets BID50 is costly may still result artifacts;filtering easy examples defining harder subset is useful evaluation purposes BID21 difficult do on a large scale will enable training;compiling adversarial examples BID18 is informative limited scale diversity. Furthermore solutions do not address lingering question:can we develop models will generalize well despite many NLI datasets containing specific hypothesis-only biases? Inspired domain-adversarial training neural networks BID16 BID17 propose two architectures Figure1 enable model perform well NLI datasets regardless what annotation artifacts exist training corpus's hypotheses. learning classify relationship two texts simultaneously use adversarial learning discourage model using dataset-specific biases.In way resulting representations contain fewer biases model is encouraged learn relationship two texts. experiments demonstrate architectures generate sentence representations are more robust annotation artifacts also transfer better:when trained one dataset evaluated another perform better non-adversarial model 9 12 target datasets. methodology can also extended NLU tasks outline necessary changes architectures conclusion. knowledge is the first study explores methods ignore hypothesis-only biases when training NLI models. Biases annotations are a major source concern quality NLI datasets systems. paper presented solution combating annotation biases based adversarial learning. designed two architectures discourage hypothesis encoder learning biases instead obtain unbiased representation. empirically evaluated approach transfer learning scenario where we found models perform better non-adversarial baseline range datasets. also investigated what biases remain latent representations.The methodology developed work can be extended deal biases NLU tasks where one is concerned finding relationship two objects. example Reading Comprehension question is being is asked passage;story cloze completion ending is judged respect context;Visual Question Answering question is being is asked image. cases second element question ending question respectively may contain biases. adversarial architectures naturally apply model relies encoding biased element may help remove biases latent representation. hope encourage investigation broader research community. TAB1 consider range 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 dataset choose best-performing model development set report quality test set.We follow InferSent training regime using SGD initial learning rate 0.1 See BID9 details.,1059,735,324,0.011,1.441,2025/11/05 17:18:52,0.0,1.487,0.3457943925233644,327.5
"We study the problem of learning representations of entities and relations in knowledge graphs for predicting missing links. The success of such a task heavily relies on the ability of modeling and inferring the patterns of (or between) the relations. In this paper, we present a new approach for knowledge graph embedding called RotatE, which is able to model and infer various relation patterns including: symmetry/antisymmetry, inversion, and composition. Specifically, the RotatE model defines each relation as a rotation from the source entity to the target entity in the complex vector space. In addition, we propose a novel self-adversarial negative sampling technique for efficiently and effectively training the RotatE model. Experimental results on multiple benchmark knowledge graphs show that the proposed RotatE model is not only scalable, but also able to infer and model various relation patterns and significantly outperform existing state-of-the-art models for link prediction. Knowledge graphs are collections of factual triplets, where each triplet (h, r, t) represents a relation r between a head entity h and a tail entity t. Examples of real-world knowledge graphs include Freebase BID0 , Yago (Suchanek et al., 2007) , and WordNet (Miller, 1995) . Knowledge graphs are potentially useful to a variety of applications such as question-answering BID10 , information retrieval BID30 , recommender systems BID34 , and natural language processing BID31 . Research on knowledge graphs is attracting growing interests in both academia and industry communities.Since knowledge graphs are usually incomplete, a fundamental problem for knowledge graph is predicting the missing links. Recently, extensive studies have been done on learning low-dimensional representations of entities and relations for missing link prediction (a.k.a., knowledge graph embedding) BID3 BID28 BID7 . These methods have been shown to be scalable and effective. The general intuition of these methods is to model and infer the connectivity patterns in knowledge graphs according to the observed knowledge facts. For example, some relations are symmetric (e.g., marriage) while others are antisymmetric (e.g., filiation); some relations are the inverse of other relations (e.g., hypernym and hyponym); and some relations may be composed by others (e.g., my mother's husband is my father). It is critical to find ways to model and infer these patterns, i.e., symmetry/antisymmetry, inversion, and composition, from the observed facts in order to predict missing links.Indeed, many existing approaches have been trying to either implicitly or explicitly model one or a few of the above relation patterns BID3 BID29 BID17 Table 1: The score functions f r (h, t) of several knowledge graph embedding models, where · denotes the generalized dot product, • denotes the Hadamard product, ⊗ denotes circular correlation, σ denotes activation function and * denotes 2D convolution. · denotes conjugate for complex vectors, and 2D reshaping for real vectors in ConvE model. TransX represents a wide range of TransE's variants, such as TransH BID29 , TransR BID17 , and STransE BID23 , where g r,i (·) denotes a matrix multiplication with respect to relation r. BID32 BID28 . For example, the TransE model BID2 , which represents relations as translations, aims to model the inversion and composition patterns; the DisMult model BID32 , which models the three-way interactions between head entities, relations, and tail entities, aims to model the symmetry pattern. However, none of existing models is capable of modeling and inferring all the above patterns. Therefore, we are looking for an approach that is able to model and infer all the three types of relation patterns.In this paper, we propose such an approach called RotatE for knowledge graph embedding. Our motivation is from Euler's identity e iθ = cos θ + i sin θ, which indicates that a unitary complex number can be regarded as a rotation in the complex plane. Specifically, the RotatE model maps the entities and relations to the complex vector space and defines each relation as a rotation from the source entity to the target entity. Given a triplet (h, r, t), we expect that t = h • r, where h, r, t ∈ C k are the embeddings, the modulus |r i | = 1 and • denotes the Hadamard (element-wise) product. Specifically, for each dimension in the complex space, we expect that:t i = h i r i , where h i , r i , t i ∈ C and |r i | = 1.It turns out that such a simple operation can effectively model all the three relation patterns: symmetric/antisymmetric, inversion, and composition. For example, a relation r is symmetric if and only if each element of its embedding r, i.e. r i , satisfies r i = e 0/iπ = ±1; two relations r 1 and r 2 are inverse if and only if their embeddings are conjugates: r 2 =r 1 ; a relation r 3 = e iθ3 is a combination of other two relations r 1 = e iθ1 and r 2 = e iθ2 if and only if r 3 = r 1 • r 2 (i.e. θ 3 = θ 1 + θ 2 ). Moreover, the RotatE model is scalable to large knowledge graphs as it remains linear in both time and memory.To effectively optimizing the RotatE, we further propose a novel self-adversarial negative sampling technique, which generates negative samples according to the current entity and relation embeddings. The proposed technique is very general and can be applied to many existing knowledge graph embedding models. We evaluate the RotatE on four large knowledge graph benchmark datasets including FB15k BID3 , WN18 BID3 ), FB15k-237 (Toutanova & Chen, 2015 and WN18RR BID7 . Experimental results show that the RotatE model significantly outperforms existing state-of-the-art approaches. In addition, RotatE also outperforms state-of-the-art models on Countries BID4 , a benchmark explicitly designed for composition pattern inference and modeling. To the best of our knowledge, RotatE is the first model that achieves state-of-the-art performance on all the benchmarks. 2 The p-norm of a complex vector v is defined as v p = p |vi| p . We use L1-norm for all distancebased models in this paper and drop the subscript of · 1 for brevity. We have proposed a new knowledge graph embedding method called RotatE, which represents entities as complex vectors and relations as rotations in complex vector space. In addition, we propose a novel self-adversarial negative sampling technique for efficiently and effectively training the RotatE model. Our experimental results show that the RotatE model outperforms all existing state-of-theart models on four large-scale benchmarks. Moreover, RotatE also achieves state-of-the-art results on a benchmark that is explicitly designed for composition pattern inference and modeling. A deep investigation into RotatE relation embeddings shows that the three relation patterns are implicitly represented in the relation embeddings. In the future, we plan to evaluate the RotatE model on more datasets and leverage a probabilistic framework to model the uncertainties of entities and relations. No existing models are capable of modeling all the three relation patterns. For example, TransE cannot model the symmetry pattern because it would yield r = 0 for symmetric relations; TransX can infer and model the symmetry/antisymmetry pattern when g r,1 = g r,2 , e.g. in TransH BID29 , but cannot infer inversion and composition as g r,1 and g r,2 are invertible matrix multiplications; due to its symmetric nature, DistMult is difficult to model the asymmetric and inversion pattern; ComplEx addresses the problem of DisMult and is able to infer both the symmetry and asymmetric patterns with complex embeddings. Moreover, it can infer inversion rules because the complex conjugate of the solution to arg max r Re( x, r, y ) is exactly the solution to arg max r Re( y, r, x ). However, ComplEx cannot infer composition rules, since it does not model a bijection mapping from h to t via relation r. These concerns are summarized in TAB0 .B PROOF OF LEMMA 1Proof. if r(x, y) and r(y, x) hold, we have y = r • x ∧ x = r • y ⇒ r • r = 1 Otherwise, if r(x, y) and ¬r(y, x) hold, we have DISPLAYFORM0 Proof. if r 1 (x, y) and r 2 (y, x) hold, we have DISPLAYFORM1 Proof. if r 1 (x, z) , r 2 (x, y ) and r 3 (y, z) hold, we have DISPLAYFORM2","study problem learning representations entities relations knowledge graphs predicting missing links. success task heavily relies ability modeling inferring patterns relations. paper present new approach knowledge graph embedding called RotatE which is able model infer various relation patterns including:symmetry/antisymmetry inversion composition. Specifically RotatE model defines relation rotation source entity target entity complex vector space. addition propose novel self-adversarial negative sampling technique efficiently effectively training RotatE model. Experimental results multiple benchmark knowledge graphs show proposed RotatE model is not only is scalable also able infer model various relation patterns significantly outperform existing state-of-the-art models link prediction. Knowledge graphs are collections factual triplets where each triplet h haveyifr which represents relationr head entityh tail entity t. Examples real-world knowledge graphs include Freebase BID0 Yago Suchaneketal. 2007 WordNet Miller 1995 Knowledge graphs are potentially useful variety applications question-answering BID10 information retrieval BID30 recommender systems BID34 natural language processing BID31. Research knowledge graphs is attracting growing interests academia industry communities.Since knowledge graphs are usually incomplete fundamental problem knowledge graph is predicting missing links. Recently extensive studies have been done learning low-dimensional representations entities relations missing link prediction.k.a knowledge graph embedding BID3 BID28 BID7. methods have been shown scalable effective. general intuition methods is to model infer connectivity patterns knowledge graphs according observed knowledge facts. example relations are symmetric e.g marriage others are antisymmetric e.g filiation relations are the are inverse relations e.g hypernym hyponym relations may composed others e.g mother's husband is my father is critical find ways model infer patterns.e symmetry/antisymmetry inversion composition observed facts order predict missing links.Indeed many existing approaches have been trying either implicitly explicitly model one relation patterns BID3 BID29 BID17 Table1:score functionsfr h several knowledge graph embedding models where · denotes generalized dot product • denotes Hadamard product ⊗ denotes circular correlation σ denotes activation function * denotes 2D convolution. · denotes conjugate complex vectors 2D reshaping real vectors ConvE model. TransX represents wide range TransE's variants TransH BID29 TransR BID17 STransE BID23 wheregr where· denotes matrix multiplication respect relationr. BID32 BID28. example TransE model BID2 which represents relations translations aims model inversion composition patterns;DisMult model BID32 which models three-way interactions head entities relations tail entities aims model symmetry pattern. However none existing models is capable modeling inferring patterns. Therefore are looking approach is able model infer three types relation patterns.In paper propose approach called RotatE knowledge graph embedding. motivation is from Euler's identityeiθ cosθ+sinθ which indicates unitary complex number can be regarded rotation complex plane. Specifically RotatE model maps entities relations complex vector space defines relation rotation source entity target entity. Given triplet h haveyifr expect h•r whereh haveyifr ∈Ck are the embeddings modulus|r 1 • denotes Hadamard element-wise product. Specifically dimension complex space expect that:h r whereh r ∈C |r 1.It turns simple operation can effectively model three relation patterns:symmetric/antisymmetric inversion composition. example relationr is symmetric if and onlyif element embeddingr.er satisfiesr e0/iπ ±1 two relationsr 1 r2 are the are inverse if and onlyif embeddings are conjugates:r2=r1;relationr3 e iθ3 is a combination two relationsr1 e iθ1 r2 e iθ2 if and onlyififr3 r1•r 2.eθ3 θ1+θ 2 Moreover RotatE model is not only is scalable large knowledge graphs remains linear time memory.To effectively optimizing RotatE propose novel self-adversarial negative sampling technique which generates negative samples according current entity relation embeddings. proposed technique is very general can be applied many existing knowledge graph embedding models. evaluate RotatE four large knowledge graph benchmark datasets including FB15k BID3 WN18 BID3 FB15k-237 Toutanova Chen 2015 WN18RR BID7. Experimental results show RotatE model significantly outperforms existing state-of-the-art approaches. addition RotatE also outperforms state-of-the-art models Countries BID4 benchmark explicitly designed composition pattern inference modeling. best knowledge RotatE is the first model achieves state-of-the-art performance benchmarks. 2 p-norm complex vectorv is defined vp p |vi|p. use L1-norm distancebased models paper drop subscript ·1 brevity. have proposed new knowledge graph embedding method called RotatE which represents entities complex vectors relations rotations complex vector space. addition propose novel self-adversarial negative sampling technique efficiently effectively training RotatE model. experimental results show RotatE model outperforms existing state-of-theart models four large-scale benchmarks. Moreover RotatE also achieves state-of-the-art results benchmark is explicitly designed composition pattern inference modeling. deep investigation RotatE relation embeddings shows three relation patterns are implicitly represented relation embeddings. future plan evaluate RotatE model datasets leverage probabilistic framework model uncertainties entities relations. existing models are capable modeling three relation patterns. example TransE cannot model symmetry pattern would yieldr 0 symmetric relations;TransX can infer model symmetry/antisymmetry pattern when g r,1 g r,2 e.g TransH BID29 cannot infer inversion composition g r,1 g r,2 are invertible matrix multiplications;due symmetric nature DistMult is difficult model asymmetric inversion pattern;ComplEx addresses problem DisMult is able infer symmetry asymmetric patterns complex embeddings. Moreover can infer inversion rules complex conjugate solution arg maxr x haveyifr is exactly solution arg maxr r x However ComplEx cannot infer composition rules since does not model bijection mapping h via relationr. concerns are summarized TAB0.B PROOF LEMMA 1Proof. if and onlyififr x haveyifr x hold haveyif r•x∧ x r• ⇒r•r 1 Otherwise haveyifr x ¬r x hold have DISPLAYFORM0 Proof. if and onlyififr1 x haveyifr2 x hold have DISPLAYFORM1 Proof. if and onlyififr1 x z r2 x haveyifr3 z hold have DISPLAYFORM2",1844,1274,570,0.022,1.447,2025/11/05 17:18:52,0.01,1.444,0.3644859813084112,537.3
"Deep learning algorithms have been known to be vulnerable to adversarial perturbations in various tasks such as image classification. This problem was addressed by employing several defense methods for detection and rejection of particular types of attacks. However, training and manipulating networks according to particular defense schemes increases computational complexity of the learning algorithms. In this work, we propose a simple yet effective method to improve robustness of convolutional neural networks (CNNs) to adversarial attacks by using data dependent adaptive convolution kernels. To this end, we propose a new type of HyperNetwork in order to employ statistical properties of input data and features for computation of statistical adaptive maps. Then, we filter convolution weights of CNNs with the learned statistical maps to compute dynamic kernels. Thereby, weights and kernels are collectively optimized for learning of image classification models robust to
 adversarial attacks without employment of additional target detection and rejection algorithms.
 We empirically demonstrate that the proposed method enables CNNs to spontaneously defend against different types of attacks, e.g. attacks generated by Gaussian noise, fast gradient sign methods (Goodfellow et al., 2014) and a black-box attack (Narodytska & Kasiviswanathan, 2016). Deep convolutional neural networks are powerful and popular algorithms that achieve state-of-the-art performance in various computer vision tasks, such as object recognition. Despite the advances made by the recent architectures BID7 BID16 BID18 BID5 , they are discovered to be fragile to small but carefully directed perturbations of images BID17 , such that the targeted images can be classified to incorrect categories with high confidence, while humans are still able to correctly classify the attacked images, being undisturbed or even unaware of the perturbations. The vulnerability of these networks to these, so called adversarial examples, may lead to undesirable consequences in safety-and security-critical applications. provide an example of misclassification of traffic signs which could be a significant threat for autonomous driving systems that employ deep learning algorithms. Various adversarial attack methods for neural networks have been studied in numerous works. The majority of attack methods can be catalogued in three groups.1. Methods which use unspecific statistical noise: In this group, input images are perturbed using unspecific statistical noise, e.g. Gaussian noise, salt and pepper noise and blurring. Since shape and parameters of distribution functions that are used to generate noise are not determined, it is usually not easy to obtain a highly confident misclassification results with imperceptible perturbations BID17 . 2. Gradient based attack methods: They are used to generate high confidence imperceptible adversarial examples within few steps or one-shot gradient based noise. Some examples of the methods considered in this group are (Iterative) Fast Gradient Sign Method BID3 BID8 , L-BFGS BID19 , Jacobian-based Saliency Map BID12 and DeepFool . These methods require a white-box environment in order to make attacks. In other words, the full network architecture and weights are required to be accessible in order to obtain gradients towards input images.3. Black-box attack methods. These methods assume that only the output of the networks can be accessed. Substitute networks and greedy search of noisy pixels BID11 are considered in this group. It is worth mentioning that, methods such as transferring adversarial examples from another network, which is optimized with a sufficient part or the whole training datasets, are not considered as a genuine black-box method.In this work, inspired by the recent works BID0 BID4 that construct neural networks with data dependent weights, we propose a simple yet effective method to train CNNs by improving their robustness to adversarial perturbations. Our main idea is to adaptively filter convolution weights of CNNs by using statistical properties of input data and features. Concretely, we propose a HyperNetwork to compute statistical adaptive maps using these statistical properties (mean and variance) of input data and features for each input channel. Then, we obtain data dependent kernels for convolution operations by computing Hadamard (element-wise) product of computed maps and convolution weights. Our main contributions can be summarized as follows:1. We propose a new type of CNN architecture that employ HyperNetworks to dynamically generate data dependent convolution kernels with statistical properties of input data and features. 2. We empirically verify the robustness of our proposed models using large scale vision dataset, and demonstrate that their robustness is improved without using additional aforementioned computationally complex defense methods or spending effort to generate adversarial examples for training. In this work, we propose a simple yet effective method to improve robustness of convolutional neural networks (CNNs) to adversarial attacks by training CNNs using data dependent adaptive convolution kernels. To this end, we employ HyperNetworks to dynamically generate data dependent convolution kernels with statistical properties of input data and features. The robustness of our proposed method is verified using 3 different types of attack with state-of-the-art CNN models trained on the ILSVRC-2012 dataset. Moreover, the robustness is obtained spontaneously during a normal training progress without losing any performance in the original tasks. This shed light on building practical deep learning systems that focus on the target without a concern of attacker. On the other hand, there still exists uncertainty on the mechanism of the robustness remains to be solved in the future works. Furthermore, designing of network architectures that employ more powerful HyperNetworks with better adversarial robustness is still an open problem.",Deep learning algorithms have been known vulnerable adversarial perturbations various tasks image classification. problem was addressed employing several defense methods detection rejection particular types attacks. However training manipulating networks according particular defense schemes increases computational complexity learning algorithms. work propose simple yet effective method improve robustness convolutional neural networks CNNs adversarial attacks using data dependent adaptive convolution kernels. end propose new type HyperNetwork order employ statistical properties input data features computation statistical adaptive maps. filter convolution weights CNNs learned statistical maps compute dynamic kernels. Thereby weights kernels are collectively optimized learning image classification models robust adversarial attacks without employment additional target detection rejection algorithms. empirically demonstrate proposed method enables CNNs spontaneously defend different types attacks e.g attacks generated Gaussian noise fast gradient sign methods Goodfellowetal. 2014 black-box attack Narodytska Kasiviswanathan 2016 Deep convolutional neural networks are powerful popular algorithms achieve state-of-the-art performance various computer vision tasks object recognition. Despite advances made recent architectures BID7 BID16 BID18 BID5 are discovered fragile small carefully directed perturbations images BID17 targeted images can be classified incorrect categories high confidence humans are still able correctly classify attacked images undisturbed even unaware perturbations. vulnerability networks called adversarial examples may lead undesirable consequences safety-and security-critical applications. provide example misclassification traffic signs could significant threat autonomous driving systems employ deep learning algorithms. Various adversarial attack methods neural networks have been studied numerous works. majority attack methods can be catalogued three groups.1 Methods which use unspecific statistical noise:group input images are perturbed using unspecific statistical noise e.g Gaussian noise salt pepper noise blurring. Since shape parameters distribution functions are used generate noise are not determined is usually easy obtain highly confident misclassification results imperceptible perturbations BID17. 2. Gradient based attack methods:are used generate high confidence imperceptible adversarial examples within steps one-shot gradient based noise. examples methods considered group are(Iterative Fast Gradient Sign Method BID3 BID8 L-BFGS BID19 Jacobian-based Saliency Map BID12 DeepFool. methods require white-box environment order make attacks. words full network architecture weights are required accessible order obtain gradients towards input images.3 Black-box attack methods. methods assume output networks can be accessed. Substitute networks greedy search noisy pixels BID11 are considered group. is worth mentioning methods transferring adversarial examples another network which is optimized sufficient part whole training datasets are not considered genuine black-box method.In work inspired recent works BID0 BID4 construct neural networks data dependent weights propose simple yet effective method train CNNs improving robustness adversarial perturbations. main idea is to adaptively filter convolution weights CNNs using statistical properties input data features. Concretely propose HyperNetwork compute statistical adaptive maps using statistical properties mean variance input data features input channel. obtain data dependent kernels convolution operations computing Hadamard element-wise product computed maps convolution weights. main contributions can be summarized follows:1 propose new type CNN architecture employ HyperNetworks dynamically generate data dependent convolution kernels statistical properties input data features. 2. empirically verify robustness proposed models using large scale vision dataset demonstrate robustness is improved without using additional aforementioned computationally complex defense methods spending effort generate adversarial examples training. work propose simple yet effective method improve robustness convolutional neural networks CNNs adversarial attacks training CNNs using data dependent adaptive convolution kernels. end employ HyperNetworks dynamically generate data dependent convolution kernels statistical properties input data features. robustness proposed method is verified using 3 different types attack state-of-the-art CNN models trained ILSVRC-2012 dataset. Moreover robustness is obtained spontaneously normal training progress without losing performance original tasks. shed light building practical deep learning systems focus target without concern attacker. hand still exists uncertainty mechanism robustness remains solved future works. Furthermore designing network architectures employ powerful HyperNetworks better adversarial robustness is still open problem.,1081,763,318,0.01,1.417,2025/11/05 17:18:52,0.0,1.393,0.2710280373831775,322.841
"Adapting deep networks to new concepts from a few examples is challenging, due to the high computational requirements of standard fine-tuning procedures.
 Most work on few-shot learning has thus focused on simple learning techniques for adaptation, such as nearest neighbours or gradient descent.
 Nonetheless, the machine learning literature contains a wealth of methods that learn non-deep models very efficiently.
 In this paper, we propose to use these fast convergent methods as the main adaptation mechanism for few-shot learning.
 The main idea is to teach a deep network to use standard machine learning tools, such as ridge regression, as part of its own internal model, enabling it to quickly adapt to novel data.
 This requires back-propagating errors through the solver steps.
 While normally the cost of the matrix operations involved in such a process would be significant, by using the Woodbury identity we can make the small number of examples work to our advantage.
 We propose both closed-form and iterative solvers, based on ridge regression and logistic regression components.
 Our methods constitute a simple and novel approach to the problem of few-shot learning and achieve performance competitive with or superior to the state of the art on three benchmarks. Humans can efficiently perform fast mapping BID7 BID8 , i.e. learning a new concept after a single exposure. By contrast, supervised learning algorithms -and neural networks in particular -typically need to be trained using a vast amount of data in order to generalize well. This requirement is problematic, as the availability of large labelled datasets cannot always be taken for granted. Labels can be costly to acquire: in drug discovery, for instance, campaign budgets often limits researchers to only operate with a small amount of biological data that can be used to form predictions about properties and activities of compounds BID0 . In other circumstances, data itself can be scarce, as it can happen for example with the problem of classifying rare animal species, whose exemplars are not easy to observe. Such a scenario, in which just one or a handful of training examples is provided, is referred to as one-shot or few-shot learning BID28 BID12 BID25 BID18 and has recently seen a tremendous surge in interest within the machine learning community (e.g. ; BID4 ; BID39 ; BID14 ).Currently , most methods tackling few-shot learning operate within the general paradigm of metalearning, which allows one to develop algorithms in which the process of learning can improve with the number of training episodes BID53 BID57 . This can be achieved by distilling and transferring knowledge across episodes. In practice , for the problem of few-shot classification, meta-learning is often implemented using two ""nested training loops"". The base learner works at the level of individual episodes, which correspond to learning problems characterised by having only a small set of labelled training images available. The meta learner , by contrast, learns from a collection of such episodes, with the goal of improving the performance of the base learner across episodes. Episode N Figure 1 : Diagram of the proposed method for one episode, of which several are seen during meta-training. The task is to learn new classes given just a few sample images per class. In this illustrative example, there are 3 classes and 2 samples per class, making each episode a 3-way, 2-shot classification problem. At the base learning level, learning is accomplished by a differentiable ridge regression layer (R.R.), which computes episode-specific weights (referred to as w E in Section 3.1 and as W in Section 3.2). At the meta-training level, by back-propagating errors through many of these small learning problems, we train a network whose weights are shared across episodes, together with the hyper-parameters of the R.R. layer. In this way, the R.R. base learner can improve its learning capabilities as the number of experienced episodes increases.Clearly, in any meta-learning algorithm, it is of paramount importance to choose the base learner carefully. On one side of the spectrum , methods related to nearest-neighbours, such as learning similarity functions BID23 BID48 , are fast but rely solely on the quality of the similarity metric, with no additional data-dependent adaptation at test-time. On the other side of the spectrum , methods that optimize standard iterative learning algorithms, such as backpropagating through gradient descent BID14 BID35 or explicitly learning the learner's update rule BID1 BID39 , are slower but allow more adaptability to different problems/datasets.In this paper, we take a different perspective. As base learners, we propose to adopt simple learning algorithms that admit a closed-form solution such as ridge regression. Crucially, the simplicity and differentiability of these solutions allow us to backpropagate through learning problems. Moreover, these algorithms are particularly suitable for use within a meta-learning framework for few-shot classification for two main reasons. First, their closed-form solution allows learning problems to be solved efficiently. Second, in a data regime characterized by few examples of high dimensionality, the Woodbury's identity (Petersen et al., 2008, Chapter 3.2) can be used to obtain a very significant gain in terms of computational speed.We demonstrate the strength of our approach by performing extensive experiments on Omniglot (Lake et al., 2015), CIFAR-100 BID24 ) (adapted to the few-shot problem) and miniImageNet . Our base learners are fast, simple to implement, and can achieve performance that is competitive with or superior to the state of the art in terms of accuracy. With the aim of allowing efficient adaptation to unseen learning problems, in this paper we explored the feasibility of incorporating fast solvers with closed-form solutions as the base learning component of a meta-learning system. Importantly, the use of the Woodbury identity allows significant computational gains in a scenario presenting only a few samples with high dimensionality, like one-shot of few-shot learning. R2-D2, the differentiable ridge regression base learner we introduce, is almost as fast as prototypical networks and strikes a useful compromise between not performing adaptation for new episodes (like metric-learning-based approaches) and conducting a costly iterative approach (like MAML or LSTM-based meta-learners). In general, we showed that our base learners work remarkably well, with excellent results on few-shot learning benchmarks, generalizing to episodes with new classes that were not seen during training. We believe that our findings point in an exciting direction of more sophisticated yet efficient online adaptation methods, able to leverage the potential of prior knowledge distilled in an offline training phase. In future work, we would like to explore Newton's methods with more complicated second-order structure than ridge regression. Contributions within the few-shot learning paradigm. In this work, we evaluated our proposed methods R2-D2 and LR-D2 in the few-shot learning scenario BID12 BID25 BID39 BID18 , which consists in learning how to discriminate between images given one or very few examples. For methods tackling this problem, it is common practice to organise the training procedure in two nested loops. The inner loop is used to solve the actual few-shot classification problem, while the outer loop serves as a guidance for the former by gradually modifying the inductive bias of the base learner BID57 . Differently from standard classification benchmarks, the few-shot ones enforce that classes are disjoint between dataset splits.In the literature (e.g. ), the very small classification problems with unseen classes solved within the inner loop have often been referred to as episodes or tasks. Considering the general few-shot learning paradigm just described, methods in the recent literature mostly differ for the type of learner they use in the inner loop and the amount of per-episode adaptability they allow. For example, at the one end of the spectrum in terms of ""amount of adaptability"", we can find methods such as MAML Finn et al. (2017) , which learns how to efficiently fine-tune the parameters of a neural-network with few iterations of SGD. On the other end, we have methods based on metric learning such as prototypical networks BID48 and relation network BID50 , which are fast but do not perform adaptation. Note that the amount of adaptation to a new episode (i.e.a new classification problem with unseen classes) is not at all indicative of the performance in few-shot learning benchmarks. As a matter of fact, both BID48 and BID50 achieve higher accuracy than MAML. Nonetheless, adaptability is a desirable property, as it allows more design flexibility.Within this landscape, our work proposes a novel technique (R2-D2) that does allow per-episode adaptation while at the same time being fast TAB6 ) and achieving strong performance TAB0 . The key innovation is to use a simple (and differentiable) solver such as ridge regression within the inner loop, which requires back-propagating through the solution of a learning problem. Crucially, its closed-form solution and the use of the Woodbury identity (particularly advantageous in the low data regime) allow this non-trivial endeavour to be efficient. We further demonstrate that this strategy is not limited to the ridge regression case, but it can also be extended to other solvers (LR-D2) by dividing the problem into a short series of weighted least squares problems ( (Murphy, 2012, Chapter 8.3.4",Adapting deep networks new concepts examples is challenging due high computational requirements standard fine-tuning procedures. work few-shot learning has thus focused simple learning techniques adaptation nearest neighbours gradient descent. Nonetheless machine learning literature contains wealth methods learn non-deep models efficiently. paper propose use fast convergent methods main adaptation mechanism few-shot learning. main idea is to teach deep network use standard machine learning tools ridge regression part internal model enabling quickly adapt novel data. requires back-propagating errors solver steps. normally cost matrix operations involved which the process would significant using Woodbury identity can make small number examples work advantage. propose closed-form iterative solvers based ridge regression logistic regression components. methods constitute simple novel approach problem few-shot learning achieve performance competitive superior state art three benchmarks. Humans can efficiently perform fast mapping BID7 BID8.e learning new concept single exposure. contrast supervised learning algorithms -and neural networks particular -typically need trained using vast amount data order generalize well. requirement is problematic availability large labelled datasets cannot always taken granted. Labels can be costly acquire:drug discovery instance campaign budgets often limits researchers operate small amount biological data can be used form predictions properties activities compounds BID0. circumstances data can be scarce can happen example problem classifying rare animal species whose exemplars are not easy observe. scenario which just one handful training examples is provided is referred one-shot few-shot learning BID28 BID12 BID25 BID18 has recently seen tremendous surge interest within machine learning community e.g BID4;BID39;BID14.Currently have methods tackling few-shot learning operate within general paradigm metalearning which allows one develop algorithms which the process learning can improve number training episodes BID53 BID57. can be achieved distilling transferring knowledge across episodes. practice problem few-shot classification meta-learning is often implemented using two nested training loops. base learner works level individual episodes which correspond learning problems characterised small set labelled training images available. meta learner contrast learns collection episodes goal improving performance base learner across episodes. Episode N Figure1:Diagram proposed method one episode which several are seen meta-training task is to learn new classes given sample images per class. illustrative example are 3 classes 2 samples per class making episode 3-way 2-shot classification problem. base learning level learning is accomplished differentiable ridge regression layer R.R which computes episode-specific weights referred wE Section 3.1 W Section 3.2 meta-training level back-propagating errors many small learning problems train network whose weights are shared across episodes together hyper-parameters R.R layer. way R.R base learner can improve learning capabilities number experienced episodes increases.Clearly meta-learning algorithm is of paramount importance choose base learner carefully. one side spectrum have methods related nearest-neighbours learning similarity functions BID23 BID48 are which are fast rely solely quality similarity metric additional data-dependent adaptation test-time side spectrum have methods optimize standard iterative learning algorithms backpropagating gradient descent BID14 BID35 explicitly learning learner's update rule BID1 BID39 are slower allow adaptability different problems/datasets.In paper take different perspective. base learners propose adopt simple learning algorithms admit closed-form solution ridge regression. Crucially simplicity differentiability solutions allowus backpropagate learning problems. Moreover algorithms are particularly suitable use within meta-learning framework few-shot classification two main reasons. First closed-form solution allows learning problems solved efficiently. Second data regime characterized examples high dimensionality Woodbury's identity Petersenetal. 2008 Chapter 3.2 can be used obtain significant gain terms computational speed.We demonstrate strength approach performing extensive experiments Omniglot Lakeetal. 2015 CIFAR-100 BID24 adapted few-shot problem miniImageNet. base learners are fast simple implement can achieve performance is competitive superior state art terms accuracy. aim allowing efficient adaptation unseen learning problems paper explored feasibility incorporating fast solvers closed-form solutions base learning component meta-learning system. Importantly use Woodbury identity allows significant computational gains scenario presenting samples high dimensionality like one-shot few-shot learning. R2-D2 differentiable ridge regression base learner introduce is almost fast prototypical networks strikes useful compromise performing adaptation new episodes like metric-learning-based approaches conducting costly iterative approach like MAML LSTM-based meta-learners general showed base learners work remarkably well excellent results few-shot learning benchmarks generalizing episodes new classes were not seen training. believe findings point exciting direction sophisticated yet efficient online adaptation methods able leverage potential prior knowledge distilled offline training phase. future work would like explore Newton's methods complicated second-order structure ridge regression. Contributions within few-shot learning paradigm. work evaluated proposed methods R2-D2 LR-D2 few-shot learning scenario BID12 BID25 BID39 BID18 which consists learning how to discriminate images given one examples. methods tackling problem is common practice organise training procedure two nested loops. inner loop is used solve actual few-shot classification problem outer loop serves guidance former gradually modifying inductive bias base learner BID57. Differently standard classification benchmarks few-shot ones enforce classes are disjoint dataset splits.In literature e.g small classification problems unseen classes solved within inner loop have often referred episodes tasks. Considering general few-shot learning paradigm described have methods recent literature mostly differ type learner use inner loop amount per-episode adaptability allow. example which just one end spectrum terms amount adaptability can find methods MAML Finnetal. 2017 which learns how to efficiently fine-tune parameters neural-network iterations SGD. end have methods based metric learning prototypical networks BID48 relation network BID50 are which are fast do not perform adaptation. Note amount adaptation new episode.e.a new classification problem unseen classes is notat indicative performance few-shot learning benchmarks. matter fact BID48 BID50 achieve higher accuracy MAML. Nonetheless adaptability is a desirable property which allows design flexibility.Within landscape work proposes novel technique R2-D2 does allow per-episode adaptation time fast TAB6 achieving strong performance TAB0. key innovation is to use simple differentiable solver ridge regression within inner loop which requires back-propagating solution learning problem. Crucially closed-form solution use Woodbury identity particularly advantageous low data regime does allow non-trivial endeavour efficient. demonstrate strategy is not limited ridge regression case can also extended solvers LR-D2 dividing problem short series weighted least squares problems Murphy 2012 Chapter 8.3.4,1871,1235,636,0.023,1.515,2025/11/05 17:18:52,0.01,1.368,0.5763239875389403,569.456
"While many active learning papers assume that the learner can simply ask for a label and receive it, real annotation often presents a mismatch between the form of a label (say, one among many classes), and the form of an annotation (typically yes/no binary feedback). To annotate examples corpora for multiclass classification, we might need to ask multiple yes/no questions, exploiting a label hierarchy if one is available. To address this more realistic setting, we propose active learning with partial feedback (ALPF), where the learner must actively choose both which example to label and which binary question to ask. At each step, the learner selects an example, asking if it belongs to a chosen (possibly composite) class. Each answer eliminates some classes, leaving the learner with a partial label. The learner may then either ask more questions about the same example (until an exact label is uncovered) or move on immediately, leaving the first example partially labeled. Active learning with partial labels requires (i) a sampling strategy to choose (example, class) pairs, and (ii) learning from partial labels between rounds. Experiments on Tiny ImageNet demonstrate that our most effective method improves 26% (relative) in top-1 classification accuracy compared to i.i.d. baselines and standard active learners given 30% of the annotation budget that would be required (naively) to annotate the dataset. Moreover, ALPF-learners fully annotate TinyImageNet at 42% lower cost. Surprisingly, we observe that accounting for per-example annotation costs can alter the conventional wisdom that active learners should solicit labels for hard examples. Given a large set of unlabeled images, and a budget to collect annotations, how can we learn an accurate image classifier most economically? Active Learning (AL) seeks to increase data efficiency by strategically choosing which examples to annotate. Typically, AL treats the labeling process as atomic: every annotation costs the same and produces a correct label. However, large-scale multi-class annotation is seldom atomic; we can't simply ask a crowd-worker to select one among 1000 classes if they aren't familiar with our ontology. Instead, annotation pipelines typically solicit feedback through simpler mechanisms such as yes/no questions. For example, to construct the 1000-class ImageNet dataset, researchers first filtered candidates for each class via Google Image Search, then asking crowd-workers questions like ""Is there a Burmese cat in this image?"" BID5 . For tasks where the Google trick won't work, we might exploit class hierarchies to drill down to the exact label. Costs scale with the number of questions asked. Thus, real-world annotation costs can vary per example BID24 .We propose Active Learning with Partial Feedback (ALPF), asking, can we cut costs by actively choosing both which examples to annotate, and which questions to ask? Say that for a new image, our current classifier places 99% of the predicted probability mass on various dog breeds. Why start at the top of the tree -""is this an artificial object?"" -when we can cut costs by jumping straight to dog breeds ( FIG0 )? ALPF proceeds as follows: In addition to the class labels, the learner possesses a pre-defined collection of composite classes, e.g. dog ⊃ bulldog, mastiff, .... At each round, the learner selects an (example, class) pair. The annotator responds with binary feedback, leaving the learner with a partial label. If only the atomic class label remains, the learner has obtained an exact label. For simplicity, we focus on hierarchically-organized collections-trees with atomic classes as leaves and composite classes as internal nodes. For this to work, we need a hierarchy of concepts familiar to the annotator. Imagine asking an annotator ""is this a foo?"" where foo represents a category comprised of 500 random ImageNet classes. Determining class membership would be onerous for the same reason that providing an exact label is: It requires the annotator be familiar with an enormous list of seemingly-unrelated options before answering. On the other hand , answering ""is this an animal?"" is easy despite animal being an extremely coarse-grained category -because most people already know what an animal is.We use active questions in a few ways. To start, in the simplest setup, we can select samples at random but then once each sample is selected, choose questions actively until finding the label:ML: ""Is it a dog?"" Human: Yes! ML: ""Is it a poodle ?"" Human: No! ML: ""Is it a hound ?"" Human: Yes! ML: "" Is it a Rhodesian ?"" Human: No! ML: ""Is it a Dachsund ?"" Human: Yes!In ALPF, we go one step further. Since our goal is to produce accurate classifiers on tight budget, should we necessarily label each example to completion? After each question, ALPF learners have the option of choosing a different example for the next binary query. Efficient learning under ALPF requires (i) good strategies for choosing (example , class) pairs, and (ii) techniques for learning from the partially-labeled data that results when labeling examples to completion isn't required.We first demonstrate an effective scheme for learning from partial labels. The predictive distribution is parameterized by a softmax over all classes. On a per-example basis, we convert the multiclass problem to a binary classification problem, where the two classes correspond to the subsets of potential and eliminated classes. We determine the total probability assigned to potential classes by summing over their softmax probabilities. For active learning with partial feedback, we introduce several acquisition functions for soliciting partial labels, selecting questions among all (example, class) pairs. One natural method, expected information gain (EIG) generalizes the classic maximum entropy heuristic to the ALPF setting. Our two other heuristics, EDC and ERC, select based on the number of labels that we expect to see eliminated from and remaining in a given partial label, respectively.We evaluate ALPF learners on CIFAR10, CIFAR100, and Tiny ImageNet datasets. In all cases, we use WordNet to impose a hierarchy on our labels. Each of our experiments simulates rounds of active learning, starting with a small amount of i. 2 ACTIVE LEARNING WITH PARTIAL FEEDBACK By x ∈ R d and y ∈ Y for Y = {{1}, ..., {k}}, we denote feature vectors and labels. Here d is the feature dimension and k is the number of atomic classes . By atomic class, we mean that they are indivisible. As in conventional AL, the agent starts off with an unlabeled training set D = {x 1 , ..., x n }.Composite classes We also consider a pre-specified collection of composite classes C = {c 1 , ..., c m }, where each composite class c i ⊂ {1, ..., k} is a subset of labels such that |c i | ≥ 1. Note that C includes both the atomic and composite classes. In this paper's empirical section, we generate composite classes by imposing an existing lexical hierarchy on the class labels BID19 . Our experiments validate the active learning with partial feedback framework on large-scale classification benchmarks. The best among our proposed ALPF learners fully labels the data with 42% fewer binary questions as compared to traditional active learners. Our diagnostic analysis suggests that in ALPF, it's sometimes more efficient to start with ""easier"" examples that can be cheaply annotated rather than with ""harder"" data as often suggested by traditional active learning.A WARM-STARTING PLOT ALPF -ERC -0% ALPF -ERC -5% ALPF -ERC -10% FIG4 : This plot compares our models under various amounts of warm-starting with pre-labeled i.i.d. data. We find that on the investigated datasets, ERC does benefit from warm-starting. However, absent warm-starting, EIG performs significantly worse and EDC suffers even more. We find that 5% warmstarting helps these two models and that for both, increasing warm-starting from 5% up to 10% does not lead to further improvements.",many active learning papers assume learner can simply ask label receive real annotation often presents mismatch form label say one among many classes form annotation typically yes/binary feedback annotate examples corpora multiclass classification might need ask multiple yes/questions exploiting label hierarchy if one is available. address realistic setting propose active learning partial feedback ALPF where the learner must actively choose which example label which binary question ask. step learner selects example asking if it belongs chosen possibly composite class. answer eliminates classes leaving learner partial label. learner may either ask questions example exact label is uncovered move immediately leaving first example partially labeled. Active learning partial labels requires sampling strategy choose example class pairs ii learning partial labels rounds. Experiments Tiny ImageNet demonstrate effective method improves26% relative top-1 classification accuracy compared.i.d baselines standard active learners given 30% annotation budget would required naively annotate dataset. Moreover ALPF-learners fully annotate TinyImageNet 42% lower cost. Surprisingly observe accounting per-example annotation costs can alter conventional wisdom active learners should solicit labels hard examples. Given large set unlabeled images budget collect annotations how can we learn accurate image classifier economically? Active Learning AL seeks increase data efficiency strategically choosing which examples annotate. Typically AL treats labeling process atomic:every annotation costs produces correct label. However large-scale multi-class annotation is seldom atomic;can't simply ask crowd-worker select one among 1000 classes if they aren't familiar ontology. Instead annotation pipelines typically solicit feedback simpler mechanisms yes/questions. example construct 1000-class ImageNet dataset researchers first filtered candidates class via Google Image Search asking crowd-workers questions like Is there a Burmese cat image? BID5. tasks where the Google trick work might exploit class hierarchies drill exact label. Costs scale number questions asked. Thus real-world annotation costs can vary per example BID24.We propose Active Learning Partial Feedback ALPF asking can we cut costs actively choosing which examples annotate which questions ask? Say new image current classifier places99% predicted probability mass various dog breeds. Why start top tree -is artificial object? -when can cut costs jumping straight dog breeds FIG0 ALPF proceeds follows:addition class labels learner possesses pre-defined collection composite classes e.g dog⊃ bulldog mastiff.... round learner selects example class pair. annotator responds binary feedback leaving learner partial label. If only the atomic class label remains learner has obtained exact label. simplicity focus hierarchically-organized collections-trees atomic classes leaves composite classes internal nodes. work need hierarchy concepts familiar annotator. Imagine asking annotator is this a foo? where foo represents category comprised 500 random ImageNet classes. Determining class membership would onerous reason providing exact label is:requires annotator familiar enormous list seemingly-unrelated options answering. hand answering is this an animal? is easy despite animal extremely coarse-grained category -because people already know what an animal is.We use active questions ways. start simplest setup can select samples random sample is selected choose questions actively finding label:ML:Is it a dog? Human:Yes! ML:Is it a poodle? Human:No! ML:Is it a hound? Human:Yes! ML:Is it a Rhodesian? Human:No! ML:Is it a Dachsund? Human:Yes! ALPF go one step further. Since goal is to produce accurate classifiers tight budget should we necessarily label example completion? question ALPF learners have the option choosing different example next binary query. Efficient learning ALPF requires good strategies choosing example class pairs ii techniques learning partially-labeled data results when labeling examples completion required.We first demonstrate effective scheme learning partial labels. predictive distribution is parameterized softmax classes. per-example basis convert multiclass problem binary classification problem where the two classes correspond subsets potential eliminated classes. determine total probability assigned potential classes summing softmax probabilities. active learning partial feedback introduce several acquisition functions soliciting partial labels selecting questions among example class pairs. One natural method expected information gain EIG generalizes classic maximum entropy heuristic ALPF setting. two heuristics EDC ERC can select based number labels expect see eliminated remaining given partial label respectively.We evaluate ALPF learners CIFAR10 CIFAR100 Tiny ImageNet datasets. cases use WordNet impose hierarchy labels. experiments simulates rounds active learning starting small amount i. 2 ACTIVE LEARNING PARTIAL FEEDBACK x∈R ∈ 1... k denote feature vectors labels. is the feature dimension k is the number atomic classes. atomic class mean are indivisible. conventionalAL agent starts unlabeled training set x1... xn.Composite classes also consider pre-specified collection composite classesC c1... c where composite classc ⊂ 1... k is a subset labels |c ≥1. Note C includes atomic composite classes. paper's empirical section generate composite classes imposing existing lexical hierarchy class labels BID19. experiments validate active learning partial feedback framework large-scale classification benchmarks. best among proposed ALPF learners fully labels data 42% fewer binary questions compared traditional active learners. diagnostic analysis suggests ALPF sometimes efficient start easier examples can be cheaply annotated rather harder data often suggested traditional active learning.A WARM-STARTING PLOT ALPF -ERC -0 ALPF -ERC-5 ALPF -ERC -10 FIG4:plot compares models various amounts warm-starting pre-labeled.i.d data. find investigated datasets ERC does benefit warm-starting However absent warm-starting EIG performs significantly worse EDC suffers even more. find 5% warmstarting helps two models increasing warm-starting 5% 10% does not lead improvements.,1645,1102,543,0.018,1.493,2025/11/05 17:18:52,0.01,1.72,0.5077881619937696,522.27
"Despite their prevalence, Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete probability distributions in a Wasserstein space, endowed with an optimal transport metric. Wasserstein spaces are much larger and more flexible than Euclidean spaces, in that they can successfully embed a wider variety of metric structures. We propose to exploit this flexibility by learning an embedding that captures the semantic information in the Wasserstein distance between embedded distributions. We examine empirically the representational capacity of such learned Wasserstein embeddings, showing that they can embed a wide variety of complex metric structures with smaller distortion than an equivalent Euclidean embedding. We also investigate an application to word embedding, demonstrating a unique advantage of Wasserstein embeddings: we can directly visualize the high-dimensional embedding, as it is a probability distribution on a low-dimensional space. This obviates the need for dimensionality reduction techniques such as t-SNE for visualization. Learned embeddings form the basis for many state-of-the-art learning systems. Word embeddings like word2vec BID34 , GloVe BID42 , fastText BID5 , and ELMo BID43 are ubiquitous in natural language processing, where they are used for tasks like machine translation BID38 , while graph embeddings BID41 like node2vec BID21 are used to represent knowledge graphs and pre-trained image models BID47 appear in many computer vision pipelines.An effective embedding should capture the semantic structure of the data with high fidelity, in a way that is amenable to downstream tasks. This makes the choice of a target space for the embedding important, since different spaces can represent different types of semantic structure. The most common choice is to embed data into Euclidean space, where distances and angles between vectors encode their levels of association BID34 BID56 BID27 BID36 . Euclidean spaces, however, are limited in their ability to represent complex relationships between inputs, since they make restrictive assumptions about neighborhood sizes and connectivity. This drawback has been documented recently for tree-structured data, for example, where spaces of negative curvature are required due to exponential scaling of neighborhood sizes BID39 BID49 .In this paper, we embed input data as probability distributions in a Wasserstein space. Wasserstein spaces endow probability distributions with an optimal transport metric, which measures the distance traveled in transporting the mass in one distribution to match another. Recent theory has shown that Wasserstein spaces are quite flexible-more so than Euclidean spaces-allowing a variety of other metric spaces to be embedded within them while preserving their original distance metrics. As such, they make attractive targets for embeddings in machine learning, where this flexibility might capture complex relationships between objects when other embeddings fail to do so.Unlike prior work on Wasserstein embeddings, which has focused on embedding into Gaussian distributions BID37 BID58 , we embed input data as discrete distributions supported at a fixed number of points. In doing so, we attempt to access the full flexibility of Wasserstein spaces to represent a wide variety of structures.Optimal transport metrics and their gradients are costly to compute, requiring the solution of a linear program. For efficiency , we use an approximation to the Wasserstein distance called the Sinkhorn divergence BID15 , in which the underlying transport problem is regularized to make it more tractable. While less well-characterized theoretically with respect to embedding capacity, the Sinkhorn divergence is computed efficiently by a fixed-point iteration. Moreover, recent work has shown that it is suitable for gradient-based optimization via automatic differentiation BID20 . To our knowledge, our work is the first to explore embedding properties of the Sinkhorn divergence.We empirically investigate two settings for Wasserstein embeddings. First, we demonstrate their representational capacity by embedding a variety of complex networks, for which Wasserstein embeddings achieve higher fidelity than both Euclidean and hyperbolic embeddings. Second, we compute Wasserstein word embeddings , which show retrieval performance comparable to existing methods. One major benefit of our embedding is that the distributions can be visualized directly, unlike most embeddings, which require a dimensionality reduction step such as t-SNE before visualization. We demonstrate the power of this approach by visualizing the learned word embeddings. Several characteristics determine the value and effectiveness of an embedding space for representation learning. The space must be large enough to embed a variety of metrics, while admitting a mathematical description compatible with learning algorithms; additional features, including direct interpretability, make it easier to understand, analyze, and potentially debug the output of a representation learning procedure. Based on their theoretical properties, Wasserstein spaces are strong candidates for representing complex semantic structures, when the capacity of Euclidean space does not suffice. Empirically, entropy-regularized Wasserstein distances are effective for embedding a wide variety of semantic structures, while enabling direct visualization of the embedding.Our work suggests several directions for additional research. Beyond simple extensions like weighting points in the point cloud, one observation is that we can lift nearly any representation space X to distributions over that space W(X ) represented as point clouds; in this paper we focused on the case X = R n . Since X embeds within W(X ) using δ-functions, this might be viewed as a general ""lifting"" procedure increasing the capacity of a representation. We can also consider other tasks, such as co-embedding of different modalities into the same transport space. Additionally, our empirical results suggest that theoretical study of the embedding capacity of Sinkhorn divergences may be profitable. Finally, following recent work on computing geodesics in Wasserstein space BID45 , it may be interesting to invert the learned mappings and use them for interpolation.",Despite prevalence Euclidean embeddings data are fundamentally limited ability capture latent semantic structures which need conform Euclidean spatial assumptions. consider alternative which embeds data discrete probability distributions Wasserstein space endowed optimal transport metric. Wasserstein spaces are much larger flexible Euclidean spaces can successfully embed wider variety metric structures. propose exploit flexibility learning embedding captures semantic information Wasserstein distance embedded distributions. examine empirically representational capacity learned Wasserstein embeddings showing can embed wide variety complex metric structures smaller distortion equivalent Euclidean embedding. can also investigate application word embedding demonstrating unique advantage Wasserstein embeddings:can directly visualize high-dimensional embedding is probability distribution low-dimensional space. obviates need dimensionality reduction techniques t-SNE visualization. Learned embeddings form basis many state-of-the-art learning systems. Word embeddings like word2vec BID34 GloVe BID42 fastText BID5 ELMo BID43 are ubiquitous natural language processing where they are used tasks like machine translation BID38 graph embeddings BID41 like node2vec BID21 are used represent knowledge graphs pre-trained image models BID47 appear many computer vision pipelines.An effective embedding should capture semantic structure data high fidelity way is amenable downstream tasks. makes choice target space embedding important since different spaces can represent different types semantic structure. common choice is to embed data Euclidean space where distances angles vectors encode levels association BID34 BID56 BID27 BID36. Euclidean spaces however are limited ability represent complex relationships inputs since make restrictive assumptions neighborhood sizes connectivity. drawback has been documented recently tree-structured data example where spaces negative curvature are required due exponential scaling neighborhood sizes BID39 BID49.In paper embed input data probability distributions Wasserstein space. Wasserstein spaces endow probability distributions optimal transport metric which measures distance traveled transporting mass one distribution match another. Recent theory has shown Wasserstein spaces are quite flexible-more Euclidean spaces-allowing variety metric spaces embedded within preserving original distance metrics. make attractive targets embeddings machine learning where this flexibility might capture complex relationships objects when other embeddings fail do so.Unlike prior work Wasserstein embeddings which has focused embedding Gaussian distributions BID37 BID58 embed input data discrete distributions supported fixed number points. attempt access full flexibility Wasserstein spaces represent wide variety structures.Optimal transport metrics gradients are costly compute requiring solution linear program. efficiency use approximation Wasserstein distance called Sinkhorn divergence BID15 which the underlying transport problem is regularized make tractable. less well-characterized theoretically respect embedding capacity Sinkhorn divergence is computed efficiently fixed-point iteration. Moreover recent work has shown is suitable gradient-based optimization via automatic differentiation BID20. knowledge work is the first explore embedding properties Sinkhorn divergence.We empirically investigate two settings Wasserstein embeddings. First demonstrate representational capacity embedding variety complex networks which Wasserstein embeddings achieve higher fidelity Euclidean hyperbolic embeddings. Second compute Wasserstein word embeddings which show retrieval performance comparable existing methods. One major benefit embedding is that the distributions can be visualized directly unlike embeddings which require dimensionality reduction step t-SNE visualization. demonstrate power approach visualizing learned word embeddings. Several characteristics determine value effectiveness embedding space representation learning. space must large enough embed variety metrics admitting mathematical description compatible learning algorithms;additional features including direct interpretability make easier understand analyze potentially debug output representation learning procedure. Based theoretical properties which Wasserstein spaces are strong candidates representing complex semantic structures when the capacity Euclidean space does not suffice. Empirically entropy-regularized Wasserstein distances are effective embedding wide variety semantic structures enabling direct visualization embedding.Our work suggests several directions additional research. Beyond simple extensions like weighting points point cloud one observation is that we can lift nearly representation spaceX distributions spaceW X represented point clouds;paper focused caseX Rn. Since X embeds within W X using δ-functions might viewed general lifting procedure increasing capacity representation. can also consider tasks co-embedding different modalities transport space. Additionally empirical results suggest theoretical study embedding capacity Sinkhorn divergences may profitable. Finally following recent work computing geodesics Wasserstein space BID45 may interesting invert learned mappings use interpolation.,1127,786,341,0.011,1.434,2025/11/05 17:18:52,0.01,1.386,0.3239875389408096,346.873
"Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The data is embedded into a lower-dimensional space by a deep autoencoder. The autoencoder is optimized as part of the clustering process. The resulting network produces clustered data. The presented approach does not rely on prior knowledge of the number of ground-truth clusters. Joint nonlinear dimensionality reduction and clustering are formulated as optimization of a global continuous objective. We thus avoid discrete reconfigurations of the objective that characterize prior clustering algorithms. Experiments on datasets from multiple domains demonstrate that the presented algorithm outperforms state-of-the-art clustering schemes, including recent methods that use deep networks. Clustering is a fundamental procedure in machine learning and data analysis. Well-known approaches include center-based methods and their generalizations BID2 BID26 , and spectral methods BID20 BID34 . Despite decades of progress, reliable clustering of noisy high-dimensional datasets remains an open problem. High dimensionality poses a particular challenge because assumptions made by many algorithms break down in high-dimensional spaces BID1 BID3 BID24 .There are techniques that reduce the dimensionality of data by embedding it in a lower-dimensional space . Such general techniques, based on preserving variance or dissimilarity, may not be optimal when the goal is to discover cluster structure. Dedicated algorithms have been developed that combine dimensionality reduction and clustering by fitting low-dimensional subspaces BID14 BID31 . Such algorithms can achieve better results than pipelines that first apply generic dimensionality reduction and then cluster in the reduced space. However, frameworks such as subspace clustering and projected clustering operate on linear subspaces and are therefore limited in their ability to handle datasets that lie on nonlinear manifolds.Recent approaches have sought to overcome this limitation by constructing a nonlinear embedding of the data into a low-dimensional space in which it is clustered BID7 BID36 BID38 . Ultimately, the goal is to perform nonlinear embedding and clustering jointly, such that the embedding is optimized to bring out the latent cluster structure. These works have achieved impressive results. Nevertheless, they are based on classic center-based, divergencebased, or hierarchical clustering formulations and thus inherit some limitations from these classic methods. In particular, these algorithms require setting the number of clusters a priori. And the optimization procedures they employ involve discrete reconfigurations of the objective, such as discrete reassignments of datapoints to centroids or merging of putative clusters in an agglomerative procedure. Thus it is challenging to integrate them with an optimization procedure that modifies the embedding of the data itself.We seek a procedure for joint nonlinear embedding and clustering that overcomes some of the limitations of prior formulations. There are a number of characteristics we consider desirable. First, we wish to express the joint problem as optimization of a single continuous objective. Second, this optimization should be amenable to scalable gradient-based solvers such as modern variants of SGD. Third, the formulation should not require setting the number of clusters a priori, since this number is often not known in advance.While any one of these desiderata can be fulfilled by some existing approaches, the combination is challenging. For example, it has long been known that the k-means objective can be optimized by SGD BID5 . But this family of formulations requires positing the number of clusters k in advance. Furthermore, the optimization is punctuated by discrete reassignments of datapoints to centroids, and is thus hard to integrate with continuous embedding of the data.In this paper, we present a formulation for joint nonlinear embedding and clustering that possesses all of the aforementioned desirable characteristics. Our approach is rooted in Robust Continuous Clustering (RCC), a recent formulation of clustering as continuous optimization of a robust objective BID22 . The basic RCC formulation has the characteristics we seek , such as a clear continuous objective and no prior knowledge of the number of clusters. However, integrating it with deep nonlinear embedding is still a challenge. For example, Shah & Koltun (2017) presented a formulation for joint linear embedding and clustering (RCC-DR), but this formulation relies on a complex alternating optimization scheme with linear least-squares subproblems, and does not apply to nonlinear embeddings.We present an integration of the RCC objective with dimensionality reduction that is simpler and more direct than RCC-DR, while naturally handling deep nonlinear embeddings. Our formulation avoids alternating optimization and the introduction of auxiliary dual variables. A deep nonlinear embedding of the data into a low-dimensional space is optimized while the data is clustered in the reduced space. The optimization is expressed by a global continuous objective and conducted by standard gradient-based solvers.The presented algorithm is evaluated on high-dimensional datasets of images and documents. Experiments demonstrate that our formulation performs on par or better than state-of-the-art clustering algorithms across all datasets. This includes recent approaches that utilize deep networks and rely on prior knowledge of the number of ground-truth clusters. Controlled experiments confirm that joint dimensionality reduction and clustering is more effective than a stagewise approach, and that the high accuracy achieved by the presented algorithm is stable across different dimensionalities of the latent space. We have presented a clustering algorithm that combines nonlinear dimensionality reduction and clustering. Dimensionality reduction is performed by a deep network that embeds the data into a lower-dimensional space. The embedding is optimized as part of the clustering process and the resulting network produces clustered data. The presented algorithm does not rely on a priori knowledge of the number of ground-truth clusters. Nonlinear dimensionality reduction and clustering are performed by optimizing a global continuous objective using scalable gradient-based solvers.B CONVOLUTIONAL NETWORK ARCHITECTURE TAB4 summarizes the architecture of the convolutional encoder used for the convolutional configuration of DCC. Convolutional kernels are applied with a stride of two. The encoder is followed by a fully-connected layer with output dimension d and a convolutional decoder with kernel size that matches the output dimension of conv5. The decoder architecture mirrors the encoder and the output from each layer is appropriately zero-padded to match the input size of the corresponding encoding layer. All convolutional and transposed convolutional layers are followed by batch normalization and rectified linear units BID12 BID18 . C HYPERPARAMETERS DCC uses three hyperparameters: the nearest neighbor graph (mkNN) parameter k, the embedding dimensionality d, and the update period M for graduated nonconvexity. For fair comparison to RCC and RCC-DR, we fix k = 10 (the setting used in BID22 ). The other two hyperparameters were set to d = 10 and M = 20 based on grid search on MNIST. The hyperparameters are fixed at these values across all datasets. No dataset-specific tuning is done. However, note that the hyperparameter M is architecture-specific. We set M = 10 for convolutional autoencoders and it is varied for varying dimensionality d during the controlled experiment reported in FIG1 . The other hyperparameters such as λ, δ i , µ i are set automatically as described in Sections 3.2 and 3.3 and in BID22 . DISPLAYFORM0",Clustering high-dimensional datasets is hard interpoint distances become less informative high-dimensional spaces. present clustering algorithm performs nonlinear dimensionality reduction clustering jointly. data is embedded lower-dimensional space deep autoencoder. autoencoder is optimized part clustering process. resulting network produces clustered data. presented approach does not rely prior knowledge number ground-truth clusters. Joint nonlinear dimensionality reduction clustering are formulated optimization global continuous objective. thus avoid discrete reconfigurations objective characterize prior clustering algorithms. Experiments datasets multiple domains demonstrate presented algorithm outperforms state-of-the-art clustering schemes including recent methods use deep networks. Clustering is a fundamental procedure machine learning data analysis. Well-known approaches include center-based methods generalizations BID2 BID26 spectral methods BID20 BID34. Despite decades progress reliable clustering noisy high-dimensional datasets remains open problem. High dimensionality poses particular challenge assumptions made many algorithms break high-dimensional spaces BID1 BID3 BID24.There are techniques reduce dimensionality data embedding lower-dimensional space. general techniques are based preserving variance dissimilarity may optimal when the goal is to discover cluster structure. Dedicated algorithms have been developed combine dimensionality reduction clustering fitting low-dimensional subspaces BID14 BID31. algorithms can achieve better results pipelines first apply generic dimensionality reduction cluster reduced space. However frameworks subspace clustering projected clustering operate linear subspaces are therefore limited ability handle datasets lie nonlinear manifolds.Recent approaches have sought overcome limitation constructing nonlinear embedding data low-dimensional space which it is clustered BID7 BID36 BID38. Ultimately goal is to perform nonlinear embedding clustering jointly embedding is optimized bring latent cluster structure. works have achieved impressive results. Nevertheless are based classic center-based divergencebased hierarchical clustering formulations thus inherit limitations classic methods. particular algorithms require setting number clusters priori. optimization procedures employ involve discrete reconfigurations objective discrete reassignments datapoints centroids merging putative clusters agglomerative procedure. Thus is challenging integrate optimization procedure modifies embedding data itself.We seek procedure joint nonlinear embedding clustering overcomes limitations prior formulations. are a number characteristics consider desirable. First wish express joint problem optimization single continuous objective. Second optimization should be amenable scalable gradient-based solvers modern variants SGD. Third formulation should not require setting number clusters priori since number is often known advance.While one desiderata can be fulfilled existing approaches combination is challenging. example has long known k-means objective can be optimized SGD BID5. family formulations requires positing number clustersk advance. Furthermore optimization is punctuated discrete reassignments datapoints centroids is thus hard integrate continuous embedding data.In paper present formulation joint nonlinear embedding clustering possesses aforementioned desirable characteristics. approach is rooted Robust Continuous Clustering RCC recent formulation clustering continuous optimization robust objective BID22. basic RCC formulation has the characteristics seek clear continuous objective prior knowledge number clusters. However integrating deep nonlinear embedding is still challenge. example Shah Koltun 2017 presented formulation joint linear embedding clustering RCC-DR formulation relies complex alternating optimization scheme linear least-squares subproblems does not apply nonlinear embeddings.We present integration RCC objective dimensionality reduction is simpler direct RCC-DR naturally handling deep nonlinear embeddings. formulation avoids alternating optimization introduction auxiliary dual variables. deep nonlinear embedding data low-dimensional space is optimized data is clustered reduced space. optimization is expressed global continuous objective conducted standard gradient-based solvers.The presented algorithm is evaluated high-dimensional datasets images documents. Experiments demonstrate formulation performs par better state-of-the-art clustering algorithms across datasets. includes recent approaches utilize deep networks rely prior knowledge number ground-truth clusters. Controlled experiments confirm joint dimensionality reduction clustering is more effective stagewise approach high accuracy achieved presented algorithm is stable across different dimensionalities latent space. have presented clustering algorithm combines nonlinear dimensionality reduction clustering. Dimensionality reduction is performed deep network embeds data lower-dimensional space. embedding is optimized part clustering process resulting network produces clustered data. presented algorithm does not rely priori knowledge number ground-truth clusters. Nonlinear dimensionality reduction clustering are performed optimizing global continuous objective using scalable gradient-based solvers.B CONVOLUTIONAL NETWORK ARCHITECTURE TAB4 summarizes architecture convolutional encoder used convolutional configuration DCC. Convolutional kernels are applied stride two. encoder is followed fully-connected layer output dimension convolutional decoder kernel size matches output dimension conv5. decoder architecture mirrors encoder output layer is appropriately zero-padded match input size corresponding encoding layer. convolutional transposed convolutional layers are followed batch normalization rectified linear units BID12 BID18. C HYPERPARAMETERS DCC uses three hyperparameters:nearest neighbor graph mkNN parameterk embedding dimensionality update period graduated nonconvexity. fair comparison RCC RCC-DR fixk 10 setting used BID22 two hyperparameters were set 10 20 based grid search MNIST. hyperparameters are fixed values across datasets. dataset-specific tuning is done. However note hyperparameter is architecture-specific architecture-specific set 10 convolutional autoencoders is varied varying dimensionality controlled experiment reported FIG1. hyperparameters λ δ µ are set automatically described Sections 3.2 3.3 BID22. DISPLAYFORM0,1433,994,439,0.015,1.442,2025/11/05 17:18:52,0.01,1.333,0.3489096573208719,460.814
"Deep convolutional neural networks (CNNs) are deployed in various applications but demand immense computational requirements. Pruning techniques and Winograd convolution are two typical methods to reduce the CNN computation. However, they cannot be directly combined because Winograd transformation fills in the sparsity resulting from pruning. Li et al. (2017) propose sparse Winograd convolution in which weights are directly pruned in the Winograd domain, but this technique is not very practical because Winograd-domain retraining requires low learning rates and hence significantly longer training time. Besides, Liu et al. (2018) move the ReLU function into the Winograd domain, which can help increase the weight sparsity but requires changes in the network structure. To achieve a high Winograd-domain weight sparsity without changing network structures, we propose a new pruning method, spatial-Winograd pruning. As the first step, spatial-domain weights are pruned in a structured way, which efficiently transfers the spatial-domain sparsity into the Winograd domain and avoids Winograd-domain retraining. For the next step, we also perform pruning and retraining directly in the Winograd domain but propose to use an importance factor matrix to adjust weight importance and weight gradients. This adjustment makes it possible to effectively retrain the pruned Winograd-domain network without changing the network structure. For the three models on the datasets of CIFAR-10, CIFAR-100, and ImageNet, our proposed method can achieve the Winograd-domain sparsities of 63%, 50%, and 74%, respectively. Deep convolutional neural networks (CNNs) have been ubiquitously utilized in various application domains. However, their performance comes at the cost of a significant amount of computation which keeps growing over time. As an example, for the ImageNet challenge BID12 , BID5 proposed AlexNet which requires more than 1.1 × 10 9 multiplications. Later, in 2016, the ResNet-152 model BID3 increased the computation cost to 11.3 × 10 9 multiplications. This high computation cost limits the deployment of larger and deeper CNN models.There are two primary methods to reduce the required computation of CNN models: pruning techniques and Winograd/FFT convolution. Pruning removes redundant weight parameters, inducing sparsity into the network. On the other hand, Winograd convolution BID6 and FFT convolution BID10 transform the computation into different domains. The convolution operations can then be replaced by element-wise multiplications. For the typical convolution kernel size of 3 × 3, Winograd convolution can achieve more than twofold speedup over highly optimized spatial convolution algorithms, and typically requires fewer flops than FFT-based approaches BID7 . Therefore, in this paper, we focus on the Winograd convolution.The pruning techniques and Winograd convolution are not directly compatible with each other. Sparse weight matrices, which are generated by pruning, lose most of the sparsity after the Winograd transformation from the spatial (original) domain to the Winograd domain. The remaining sparsity is much lower than what we need for improving computation performance.To increase the Winograd-domain sparsity, BID7 propose to perform pruning and retraining directly on Winograd-domain weights. However, it requires using an extremely small learning rate, e.g., 200x smaller for AlexNet, in retraining and is difficult to be applied to deep networks. Besides, Winograd-ReLU pruning BID9 moves ReLU function into the Winograd domain, which helps increase Winograd-domain sparsity but requires changes in the network structure.In this paper, to further improve the sparsity of Winograd-domain weights without changing the network structure, we propose a new pruning method, spatial-Winograd pruning. It includes two parts: spatial structured pruning and Winograd direct pruning. In spatial structured pruning, we prune the spatial-domain weights in a structured way, in which the structures are designed to transfer the spatial-domain sparsity into the Winograd domain efficiently. After spatial structured pruning, weights of the pruned layers will be converted to and kept in the Winograd domain. Then, for Winograd direct pruning, we perform pruning and retraining entirely in the Winograd domain to improve the sparsity further. This paper makes the following contributions:• We propose a new pruning method, spatial-Winograd pruning. Without changing the network structure, it can achieve higher sparsity in Winograd-domain weights compared with previous methods.• As the first part of spatial-Winograd pruning, we provide a structured pruning method to transfer the spatial-domain sparsity into the Winograd domain efficiently. It can help avoid Winograd-domain retraining in this part and accelerate the pruning process.• In the second part, to perform pruning directly in the Winograd domain, we present a new approach to measuring the importance of each Winograd-domain weight based on its impact on output activations. Also , we propose to use an importance factor matrix to adjust the gradients of Winograd-domain weights, which makes it much faster to retrain deep networks directly in the Winograd domain without changing the network structure. In this paper, we present a new pruning method, spatial-Winograd pruning, to improve the Winograd-domain weight sparsity without changing network structures. It includes two steps: spatial structured pruning and Winograd direct pruning. In spatial structured pruning, we prune the spatial-domain weights based on the internal structure in the Winograd transformation. It can help efficiently transfer the spatial-domain sparsity into the Winograd domain. For Winograd direct pruning, we perform both pruning and retraining in the Winograd domain. An importance factor matrix is proposed to adjust the weight gradients in Winograd retraining, which makes it possible to effectively retrain the Winograd-domain network to regain the original accuracy without changing the network structure. We evaluate spatial-Winograd pruning on three datasets, CIFAR-10, CIFAR-100, ImageNet, and it can achieve the Winograd-domain sparsities of 63%, 50%, and 74%, respectively.",Deep convolutional neural networks CNNs are deployed various applications demand immense computational requirements. Pruning techniques Winograd convolution are two typical methods reduce CNN computation. However cannot directly combined Winograd transformation fills sparsity resulting pruning. Lietal. 2017 propose sparse Winograd convolution which weights are are not directly pruned Winograd domain technique is not very practical Winograd-domain retraining requires low learning rates hence significantly longer training time. Besides Liuetal. 2018 move ReLU function Winograd domain which can help increase weight sparsity requires changes network structure. achieve high Winograd-domain weight sparsity without changing network structures propose new pruning method spatial-Winograd pruning. first step spatial-domain weights are pruned structured way which efficiently transfers spatial-domain sparsity Winograd domain avoids Winograd-domain retraining. next step also perform pruning retraining directly Winograd domain propose use importance factor matrix adjust weight importance weight gradients. adjustment makes possible effectively retrain pruned Winograd-domain network without changing network structure. three models datasets CIFAR-10 CIFAR-100 ImageNet proposed method can achieve Winograd-domain sparsities 63% 50% 74% respectively. Deep convolutional neural networks CNNs have been ubiquitously utilized various application domains. However performance comes cost significant amount computation which keeps growing time. example ImageNet challenge BID12 BID5 proposed AlexNet which requires 1.1×109 multiplications. Later 2016 ResNet-152 model BID3 increased computation cost 11.3×109 multiplications. high computation cost limits deployment larger deeper CNN models.There are two primary methods reduce required computation CNN models:pruning techniques Winograd/FFT convolution. Pruning removes redundant weight parameters inducing sparsity network. hand Winograd convolution BID6 FFT convolution BID10 transform computation different domains. convolution operations can then be replaced element-wise multiplications. typical convolution kernel size 3×3 Winograd convolution can achieve twofold speedup highly optimized spatial convolution algorithms typically requires fewer flops FFT-based approaches BID7. Therefore paper focus Winograd convolution.The pruning techniques Winograd convolution are are not directly compatible other. Sparse weight matrices which are generated pruning lose sparsity Winograd transformation spatial original domain Winograd domain. remaining sparsity is much lower what we need improving computation performance.To increase Winograd-domain sparsity BID7 propose perform pruning retraining directly Winograd-domain weights. However requires using extremely small learning rate e.g 200x smaller AlexNet retraining is difficult applied deep networks. Besides Winograd-ReLU pruning BID9 moves ReLU function Winograd domain which helps increase Winograd-domain sparsity requires changes network structure.In paper improve sparsity Winograd-domain weights without changing network structure propose new pruning method spatial-Winograd pruning. includes two parts:spatial structured pruning Winograd direct pruning. spatial structured pruning prune spatial-domain weights structured way which the structures are designed transfer spatial-domain sparsity Winograd domain efficiently. spatial structured pruning weights pruned layers will be converted kept Winograd domain. Winograd direct pruning perform pruning retraining entirely Winograd domain improve sparsity further. paper makes following contributions:• propose new pruning method spatial-Winograd pruning. Without changing network structure can can achieve higher sparsity Winograd-domain weights compared previous methods.• first part spatial-Winograd pruning provide structured pruning method transfer spatial-domain sparsity Winograd domain efficiently. can help avoid Winograd-domain retraining part accelerate pruning process.• second part perform pruning directly Winograd domain present new approach measuring importance Winograd-domain weight based impact output activations. Also propose use importance factor matrix adjust gradients Winograd-domain weights which makes much faster retrain deep networks directly Winograd domain without changing network structure. paper present new pruning method spatial-Winograd pruning improve Winograd-domain weight sparsity without changing network structures. includes two steps:spatial structured pruning Winograd direct pruning. spatial structured pruning prune spatial-domain weights based internal structure Winograd transformation. can help efficiently transfer spatial-domain sparsity Winograd domain. Winograd direct pruning perform pruning retraining Winograd domain. importance factor matrix is proposed adjust weight gradients Winograd retraining which makes possible effectively retrain Winograd-domain network regain original accuracy without changing network structure. evaluate spatial-Winograd pruning three datasets CIFAR-10 CIFAR-100 ImageNet can can achieve Winograd-domain sparsities 63% 50% 74% respectively.,1212,877,335,0.012,1.382,2025/11/05 17:18:52,0.01,1.407,0.1619937694704044,343.166
"In federated learning problems, data is scattered across different servers and exchanging or pooling it is often impractical or prohibited. We develop a Bayesian nonparametric framework for federated learning with neural networks. Each data server is assumed to train local neural network weights, which are modeled through our framework. We then develop an inference approach that allows us to synthesize a more expressive global network without additional supervision or data pooling. We then demonstrate the efficacy of our approach on federated learning problems simulated from two popular image classification datasets. The standard machine learning paradigm involves algorithms that learn from centralized data, possibly pooled together from multiple data sources. The computations involved may be done on a single machine or farmed out to a cluster of machines. However, in the real world, data often lives in silos and amalgamating them may be rendered prohibitively expensive by communication costs, time sensitivity, or privacy concerns. Consider, for instance, data recorded from sensors embedded in wearable devices. Such data is inherently private, can be voluminous depending on the sampling rate of the sensing modality, and may be time sensitive depending on the analysis of interest. Pooling data from many users is technically challenging owing to the severe computational burden of moving large amounts of data, and fraught with privacy concerns stemming from potential data breaches that may expose the user's protected health information (PHI).Federated learning avoids these pitfalls by obviating the need for centralized data and instead designs algorithms that learn from sequestered data sources with different data distributions. To be effective , such algorithms must be able to extract and distill important statistical patterns from various independent local learners coherently into an effective global model without centralizing data. This will allow us to avoid the prohibitively expensive cost of data communication. To achieve this , we develop and investigate a probabilistic federated learning framework with a particular emphasis on training and aggregating neural network models on siloed data.We proceed by training local models for each data source, in parallel. We then match the estimated local model parameters (groups of weight vectors in the case of neural networks) across data sources to construct a global network. The matching, to be formally defined later, is governed by the posterior of a Beta-Bernoulli process (BBP) (Thibaux & Jordan, 2007; Yurochkin et al., 2018) , a Bayesian nonparametric model that allows the local parameters to either match existing global ones or create a new global parameter if existing ones are poor matches. Our construction allows the size of the global network to flexibly grow or shrink as needed to best explain the observed data. Crucially, we make no assumptions about how the data is distributed between the different sources or even about the local learning algorithms. These may be adapted as necessary, for instance to account for non-identically distributed data. Further, we only require communication after the local algorithms have converged. This is in contrast with popular distributed training algorithms that rely on frequent communication between the local machines. Our construction also leads to compressed global models with fewer parameters than the set of all local parameters. Unlike naive ensembles of local models, this allows us to store fewer parameters and leads to more efficient inference at test time, requiring only a single forward pass through the compressed model as opposed to J forward passes, once for each local model. While techniques such as distillation allow for the cost of multiple forward passes to be amortized, training the distilled model itself requires access to data pooled across all sources, a luxury unavailable in our federated learning scenario. In summary, the key question we seek to answer in this paper is the following: given pre-trained neural networks trained locally on non-centralized data, can we learn a compressed federated model without accessing the original data, while improving on the performance of the local networks?The remainder of the paper is organized as follows. We briefly introduce the Beta-Bernoulli process in Section 2 before describing our model for federated learning in Section 3. We thoroughly vet the proposed models and demonstrate the utility of the proposed approach in Section 4. Finally, Section 5 discusses limitations and open questions. In this work we have developed models for matching fully connected networks, and experimentally demonstrated the capabilities of our methodology, particularly when prediction time is limited and communication is expensive. We also observed the importance of convergent local neural networks that serve as inputs to our matching algorithms. Poor quality local neural network weights will affect the quality of the master network. In future work we plan to explore more sophisticated ways to account for uncertainty in the weights of small batches. Additionally, our matching approach is completely unsupervised -incorporating some form of supervised signal may help to improve the performance of the global network when local networks are low quality. Finally, it is of interest to extend our modeling framework to other architectures such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). The permutation invariance necessitating matching inference arises in CNNs too -any permutation of the filters results in same output, however additional bookkeeping is needed due to pooling operations.Ohad Shamir, Nati Srebro, and Tong Zhang. Communication-efficient distributed optimization using an approximate newton-type method. In International conference on machine learning, pp. The goal of maximum a posteriori (MAP) estimation is to maximize posterior probability of the latent variables: global atoms DISPLAYFORM0 and assignments of observed neural network weight estimates to global atoms {B j } J j=1 , given estimates of the batch weights DISPLAYFORM1 arg max DISPLAYFORM2 MAP estimates given matching (Proposition 1 in the main text) First we note that given {B j } it is straightforward to find MAP estimates of {✓ i } based on Gaussian-Gaussian conjugacy: DISPLAYFORM3 where L = max{i : DISPLAYFORM4 . . , J} is the number of active global atoms, which is an (unknown) latent random variable identified by {B j }. For simplicity we assume ⌃ 0 = I 2 0 , ⌃ j = I 2 j and µ 0 = 0.Inference of atom assignment. We can now cast optimization corresponding to (1) with respect to only {B j } J j=1 . Taking natural logarithm we obtain: DISPLAYFORM5 Let us first simplify the first term of (3):1 2 DISPLAYFORM6 We consider an iterative optimization approach: fixing all but one B j we find corresponding optimal assignment, then pick a new j at random and proceed until convergence. In the following we will use notation j to say ""all but j"". Let L j = max{i : B j i,l = 1} denote number of active global weights outside of group j. We now rearrange (4) by partitioning it into i = 1, . . . , L j and i = L j + 1, . . . , L j + L j . We are interested in solving for B j , hence we can modify objective function by subtracting terms independent of B j : DISPLAYFORM7 Now observe that P l B j i,l 2 {0, 1}, i.e. it is 1 if some neuron from batch j is matched to global neuron i and 0 otherwise. Due to this we can rewrite (5) as a linear sum assignment problem: DISPLAYFORM8 Now we consider second term of FORMULA12 : DISPLAYFORM9 First, because we are optimizing for B j , we can ignore log P (B j ). Second, due to exchangeability of batches (i.e. customers of the IBP), we can always consider B j to be the last batch (i.e. last customer of the IBP). Let m j i = P j,l B j i,l denote number of times batch weights were assigned to global atom i outside of group j. We now obtain the following: DISPLAYFORM10 We now rearrange (7) as linear sum assignment problem: DISPLAYFORM11 Combining FORMULA20 and FORMULA25 we arrive at the cost specification for finding B j as minimizer of DISPLAYFORM12 , where: DISPLAYFORM13 This completes the proof of Proposition 2 in the main text. FIG3 illustrates the overall multilayer inference procedure visually, and Algorithm 1 provides the details. Nodes in the graphs indicate neurons, neurons of the same color have been matched. On the left, the individual layer matching approach is shown, consisting of using the matching assignments of the next highest layer to convert the neurons in each of the J servers to weight vectors referencing the global previous layer. These weight vectors are then used to form a cost matrix, which the Hungarian algorithm then uses to do the matching. Finally, the matched neurons are then aggregated and averaged to form the new layer of the global model. As shown on the right, in the multilayer setting the resulting global layer is then used to match the next lower layer, etc. until the bottom hidden layer is reached FIG3 ,... in order).",federated learning problems data is scattered across different servers exchanging pooling is often impractical prohibited. develop Bayesian nonparametric framework federated learning neural networks. data server is assumed train local neural network weights which are modeled framework. develop inference approach allowsus synthesize expressive global network without additional supervision data pooling. demonstrate efficacy approach federated learning problems simulated two popular image classification datasets. standard machine learning paradigm involves algorithms learn centralized data possibly pooled together multiple data sources. computations involved may done single machine farmed cluster machines. However real world data often lives silos amalgamating may rendered prohibitively expensive communication costs time sensitivity privacy concerns. Consider instance data recorded sensors embedded wearable devices. data is inherently private can be voluminous depending sampling rate sensing modality may time sensitive depending analysis interest. Pooling data many users is technically challenging owing severe computational burden moving large amounts data fraught privacy concerns stemming potential data breaches may expose user's protected health information PHI.Federated learning avoids pitfalls obviating need centralized data instead designs algorithms learn sequestered data sources different data distributions. effective algorithms must able extract distill important statistical patterns various independent local learners coherently effective global model without centralizing data. will allowus avoid prohibitively expensive cost data communication. achieve develop investigate probabilistic federated learning framework particular emphasis training aggregating neural network models siloed data.We proceed training local models data source parallel. match estimated local model parameters groups weight vectors case neural networks across data sources construct global network. matching formally defined later is governed posterior Beta-Bernoulli process BBP Thibaux Jordan 2007;Yurochkinetal. 2018 Bayesian nonparametric model allows local parameters either match existing global ones create new global parameter if existing ones are poor matches. construction allows size global network flexibly grow shrink needed best explain observed data. Crucially make assumptions how the data is distributed different sources even local learning algorithms. may adapted necessary instance account non-identically distributed data. require communication local algorithms have converged. is in contrast popular distributed training algorithms rely frequent communication local machines. construction also leads compressed global models fewer parameters set local parameters. Unlike naive ensembles local models allowsus store fewer parameters leads efficient inference test time requiring single forward pass compressed model opposed J forward passes local model. techniques distillation allow cost multiple forward passes amortized training distilled model requires access data pooled across sources luxury unavailable federated learning scenario. summary key question seek answer paper is the following:given pre-trained neural networks trained locally non-centralized data can we learn compressed federated model without accessing original data improving performance local networks? remainder paper is organized follows. briefly introduce Beta-Bernoulli process Section2 describing model federated learning Section3. thoroughly vet proposed models demonstrate utility proposed approach Section4. Finally Section 5 discusses limitations open questions. work have developed models matching fully connected networks experimentally demonstrated capabilities methodology particularly when prediction time is limited communication is expensive. also observed importance convergent local neural networks serve inputs do the matching algorithms. Poor quality local neural network weights will affect quality master network. future work plan explore sophisticated ways account uncertainty weights small batches. Additionally matching approach is completely unsupervised -incorporating form supervised signal may help improve performance global network when local networks are low quality. Finally is of interest extend modeling framework architectures Convolutional Neural Networks CNNs Recurrent Neural Networks RNNs permutation invariance necessitating matching inference arises CNNs -any permutation filters results output however additional bookkeeping is needed due pooling operations.Ohad Shamir Nati Srebro Tong Zhang. Communication-efficient distributed optimization using approximate newton-type method. International conference machine learning pp. goal maximum posteriori MAP estimation is to maximize posterior probability latent variables:global atoms DISPLAYFORM0 assignments observed neural network weight estimates global atoms Bj J j=1 given estimates batch weights DISPLAYFORM1 arg max DISPLAYFORM2 MAP estimates given matching Proposition1 main text First note given Bj is straightforward find MAP estimates ✓ based Gaussian-Gaussian conjugacy:DISPLAYFORM3 whereL max i:DISPLAYFORM4. J is the number active global atoms whichisan unknown latent random variable identified Bj simplicity assume⌃0 20 ⌃j 2j µ0 0.Inference atom assignment. can now cast optimization corresponding 1 respect Bj J j=1 Taking natural logarithm obtain:DISPLAYFORM5 Let us first simplify first term 3:1 2 DISPLAYFORM6 consider iterative optimization approach:fixing oneBj find corresponding optimal assignment pick newj random proceed convergence. following will use notationj say j. LetLj max i:Bj l 1 denote number active global weights outside groupj. rearrange 4 partitioning is1 Lj Lj+1 Lj+L j. are interested solving Bj hence can modify objective function subtracting terms independent Bj:DISPLAYFORM7 observe PlBj l2 0 1.e is1 if some neuron batchj is matched global neuron 0 otherwise. Due can rewrite 5 linear sum assignment problem:DISPLAYFORM8 consider second term FORMULA12:DISPLAYFORM9 First are optimizing Bj can ignore logP Bj Second due exchangeability batches.e customers IBP can always considerBj last batch.e last customer IBP Let j Pj lBj l denote number times batch weights were assigned global atom outside groupj. obtain following:DISPLAYFORM10 rearrange 7 linear sum assignment problem:DISPLAYFORM11 Combining FORMULA20 FORMULA25 arrive cost specification findingBj minimizer DISPLAYFORM12 where:DISPLAYFORM13 completes proof Proposition2 main text. FIG3 illustrates overall multilayer inference procedure visually Algorithm 1 provides details. Nodes graphs indicate neurons neurons color have been matched. left individual layer matching approach is shown consisting using matching assignments next highest layer convert neurons J servers weight vectors referencing global previous layer. weight vectors are then used form cost matrix which the Hungarian algorithm uses do the matching. Finally matched neurons are then aggregated averaged form new layer global model. shown right multilayer setting resulting global layer is then used match next lower layer etc. bottom hidden layer is reached FIG3... order,1827,1210,617,0.02,1.51,2025/11/05 17:18:52,0.01,1.358,0.5607476635514017,559.016
"We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution. Our method generalizes Hamiltonian Monte Carlo and is trained to maximize expected squared jumped distance, a proxy for mixing speed. We demonstrate large empirical gains on a collection of simple but challenging distributions, for instance achieving a 106x improvement in effective sample size in one case, and mixing when standard HMC makes no measurable progress in a second. Finally, we show quantitative and qualitative gains on a real-world task: latent-variable generative modeling. Python source code will be open-sourced with the camera-ready paper. High-dimensional distributions that are only analytically tractable up to a normalizing constant are ubiquitous in many fields. For instance, they arise in protein folding BID41 , physics simulations BID37 , and machine learning BID1 . Sampling from such distributions is a critical task for learning and inference BID31 , however it is an extremely hard problem in general.Markov Chain Monte Carlo (MCMC) methods promise a solution to this problem. They operate by generating a sequence of correlated samples that converge in distribution to the target. This convergence is most often guaranteed through detailed balance, a sufficient condition for the chain to have the target equilibrium distribution. In practice, for any proposal distribution, one can ensure detailed balance through a Metropolis-Hastings BID20 accept/reject step.Despite theoretical guarantees of eventual convergence, in practice convergence and mixing speed depend strongly on choosing a proposal that works well for the task at hand. What's more, it is often more art than science to know when an MCMC chain has converged (""burned-in""), and when the chain has produced a new uncorrelated sample (""mixed""). Additionally, the reliance on detailed balance, which assigns equal probability to the forward and reverse transitions, often encourages random-walk behavior and thus slows exploration of the space BID24 .For densities over continuous spaces, Hamiltonian Monte Carlo (HMC; BID12 BID36 introduces independent, auxiliary momentum variables, and computes a new state by integrating Hamiltonian dynamics. This method can traverse long distances in state space with a single Metropolis-Hastings test. This is the state-of-the-art method for sampling in many domains. However , HMC can perform poorly in a number of settings. While HMC mixes quickly spatially, it struggles at mixing across energy levels due to its volume-preserving dynamics. HMC also does not work well with multi-modal distributions, as the probability of sampling a large enough momentum to traverse a very low-density region is negligibly small. Furthermore , HMC struggles with ill-conditioned energy landscapes BID14 and deals poorly with rapidly changing gradients BID44 .Recently, probabilistic models parameterized by deep neural networks have achieved great success at approximately sampling from highly complex, multi-modal empirical distributions BID27 BID39 BID16 . Building on these successes , we present a method that, given an analytically described distribution, automatically returns an exact sampler with good convergence and mixing properties, from a class of highly expressive parametric models. The proposed family of samplers is a generalization of HMC; it transforms the HMC trajectory using parametric functions (deep networks in our experiments), while retaining theoretical guarantees with a tractable Metropolis-Hastings accept/reject step. The sampler is trained to minimize a variation on expected squared jumped distance (similar in spirit to BID38 ). Our parameterization reduces easily to standard HMC. It is further capable of emulating several common extensions of HMC such as withintrajectory tempering BID34 and diagonal mass matrices BID4 .We evaluate our method on distributions where HMC usually struggles, as well as on a the real-world task of training latent-variable generative models.Our contributions are as follows:• We introduce a generic training procedure which takes as input a distribution defined by an energy function, and returns a fast-mixing MCMC kernel.• We show significant empirical gains on various distributions where HMC performs poorly.• We finally evaluate our method on the real-world task of training and sampling from a latent variable generative model, where we show improvement in the model's log-likelihood, and greater complexity in the distribution of posterior samples. In this work, we presented a general method to train expressive MCMC kernels parameterized with deep neural networks. Given a target distribution p, analytically known up to a constant, our method provides a fast-mixing sampler, able to efficiently explore the state space. Our hope is that our method can be utilized in a ""black-box"" manner, in domains where sampling constitutes a huge bottleneck such as protein foldings BID41 or physics simulations BID37 .... DISPLAYFORM0 Figure 4: Diagram of our L2HMC-DGLM model. Nodes are functions of their parents. Round nodes are deterministic , diamond nodes are stochastic and the doubly-circled node is observed.",present general-purpose method train Markov chain Monte Carlo kernels parameterized deep neural networks converge mix quickly have the target distribution. method generalizes Hamiltonian Monte Carlo is trained maximize expected squared jumped distance proxy mixing speed. demonstrate large empirical gains collection simple challenging distributions instance achieving 106x improvement effective sample size one case mixing when standard HMC makes measurable progress second. Finally where we show quantitative qualitative gains real-world task:latent-variable generative modeling. Python source code will be open-sourced camera-ready paper. High-dimensional distributions are only analytically tractable normalizing constant are ubiquitous many fields. instance arise protein folding BID41 physics simulations BID37 machine learning BID1. Sampling distributions is a critical task learning inference BID31 however is an extremely hard problem general.Markov Chain Monte Carlo MCMC methods promise solution problem. operate generating sequence correlated samples converge distribution have the target. convergence is most often guaranteed detailed balance sufficient condition chain have the target equilibrium distribution. practice proposal distribution one can ensure detailed balance Metropolis-Hastings BID20 accept/reject step.Despite theoretical guarantees eventual convergence practice convergence mixing speed depend strongly choosing proposal works well task hand. What's is often art science know when an MCMC chain has converged burned-in when chain has produced new uncorrelated sample mixed Additionally reliance detailed balance which assigns equal probability forward reverse transitions often encourages random-walk behavior thus slows exploration space BID24.For densities continuous spaces Hamiltonian Monte Carlo HMC;BID12 BID36 introduces independent auxiliary momentum variables computes new state integrating Hamiltonian dynamics. method can traverse long distances state space single Metropolis-Hastings test. is the state-of-the-art method sampling many domains. However HMC can perform poorly number settings. HMC mixes quickly spatially struggles mixing across energy levels due volume-preserving dynamics. HMC also does not work well multi-modal distributions probability sampling large enough momentum traverse low-density region is negligibly small. Furthermore HMC struggles ill-conditioned energy landscapes BID14 deals poorly rapidly changing gradients BID44.Recently probabilistic models parameterized deep neural networks have achieved great success approximately sampling highly complex multi-modal empirical distributions BID27 BID39 BID16. Building successes present method given analytically described distribution automatically returns exact sampler good convergence mixing properties class highly expressive parametric models. proposed family samplers is a generalization HMC;transforms HMC trajectory using parametric functions deep networks experiments retaining theoretical guarantees tractable Metropolis-Hastings accept/reject step. sampler is trained minimize variation expected squared jumped distance similar spirit BID38 parameterization reduces easily standard HMC. is further capable emulating several common extensions HMC withintrajectory tempering BID34 diagonal mass matrices BID4.We evaluate method distributions where HMC usually struggles well real-world task training latent-variable generative models.Our contributions are as follows:• introduce generic training procedure which takes input distribution defined energy function returns fast-mixing MCMC kernel.• show significant empirical gains various distributions where HMC performs poorly.• finally evaluate method real-world task training sampling latent variable generative model where we show improvement model's log-likelihood greater complexity distribution posterior samples. work presented general method train expressive MCMC kernels parameterized deep neural networks. Given target distributionp analytically known constant method provides fast-mixing sampler able efficiently explore state space. hope is that our method can be utilized black-box manner domains where sampling constitutes huge bottleneck protein foldings BID41 physics simulations BID37.... DISPLAYFORM0 Figure4:Diagram L2HMC-DGLM model. Nodes are functions parents. Round nodes are deterministic diamond nodes are stochastic doubly-circled node is observed.,989,717,272,0.009,1.379,2025/11/05 17:18:52,0.0,1.444,0.1526479750778814,299.4
"This paper addresses the problem of evaluating learning systems in safety critical domains such as autonomous driving, where failures can have catastrophic consequences. We focus on two problems: searching for scenarios when learned agents fail and assessing their probability of failure. The standard method for agent evaluation in reinforcement learning, Vanilla Monte Carlo, can miss failures entirely, leading to the deployment of unsafe agents. We demonstrate this is an issue for current agents, where even matching the compute used for training is sometimes insufficient for evaluation. To address this shortcoming, we draw upon the rare event probability estimation literature and propose an adversarial evaluation approach. Our approach focuses evaluation on adversarially chosen situations, while still providing unbiased estimates of failure probabilities. The key difficulty is in identifying these adversarial situations -- since failures are rare there is little signal to drive optimization. To solve this we propose a continuation approach that learns failure modes in related but less robust agents. Our approach also allows reuse of data already collected for training the agent. We demonstrate the efficacy of adversarial evaluation on two standard domains: humanoid control and simulated driving. Experimental results show that our methods can find catastrophic failures and estimate failures rates of agents multiple orders of magnitude faster than standard evaluation schemes, in minutes to hours rather than days. How can we ensure machine learning systems do not make catastrophic mistakes? While machine learning systems have shown impressive results across a variety of domains BID6 BID11 BID26 , they may also fail badly on particular inputs, often in unexpected ways BID28 . As we start deploying these systems, it is important that we can reliably evaluate the risk of failure. This is particularly important for safety critical domains like autonomous driving where the negative consequences of a single mistake can overwhelm the positive benefits accrued during typical operation of the system.Limitations of random testing. The key problem we highlight is that for standard statistical evaluation, attaining confidence that the failure rate of a policy is below requires at least 1/ episodes. We now informally summarize this point, which we discuss further in Appendix A. For concreteness, consider a self-driving car company that decides that the cost of a single accident where the car is at fault outweighs the benefits of 100 million miles of faultless operation. The standard approach in machine learning is to estimate the expected return via i.i.d. samples from the data distribution (frequently a test set). For tightly bounded returns, the sample estimate is guaranteed to quickly converge to the true expectation. However, with catastrophic failures, this may be prohibitively inefficient. In our current example, any policy with a failure probability greater than = 10 −8 per mile has negative expected return. In other words, it would be better to not deploy the car. However, to achieve reasonable confidence that the car crashes with probability below 1e-8, the manufacturer would need to test-drive the car for at least 1e8 miles, which may be prohibitively expensive.Our Contributions. To overcome the above-mentioned problems, we develop a novel adversarial evaluation approach. The central motivation behind our algorithmic choices is the fact that realworld evaluation is typically dominated by the cost of running the agent in the real-world and/or human supervision. In the self-driving car example, both issues are present: testing requires both operating a physical car, and a human test driver behind the wheel. The overarching idea is thus to screen out situations that are unlikely to be problematic, and focus evaluation on the most difficult situations. The difficulty arises in identifying these situations -since failures are rare, there is little signal to drive optimization. To address this problem, we introduce a continuation approach to learning a failure probability predictor (AVF), which estimates the probability the agent fails given some initial conditions. The idea is to leverage data from less robust agents, which fail more frequently, to provide a stronger learning signal. In our implementation, this also allows the algorithm to reuse data gathered for training the agent, saving time and resources during evaluation. We note that adversarial testing is a well-established idea (see Section 5), but typically requires either a dense optimization signal or expert domain knowledge. We avoid these stumbling blocks by relying on the learned AVF, which guides the adversarially acting evaluator.We look at two settings where the AVF can be used. In the simplest setting, failure search, the problem is to efficiently find inputs (initial conditions) that cause failures (Section 2.1). This task has several uses. First, an adversary that solves this task efficiently allows one to identify and debug potentially unsafe policies. Second, as has been done previously in the supervised learning literature, efficient adversaries can be used for adversarial training, by folding the states causing failures back into the training algorithm BID9 . The second setting, risk estimation, is the problem of efficiently estimating the failure probability of an agent (Section 2.2), which also has a simple application to efficiently selecting the most reliable agent from a finite set (Section 4.3).Empirically , we demonstrate dramatic improvements in efficiency through adversarial testing on two domains (simulated driving and humanoid locomotion). In summary , we present 3 key contributions:1. We empirically demonstrate the limitations of random testing. We observe that with random testing, the cost of reliably obtaining even a single adversarial input can exceed the entire cost of training. Further, reliably estimating risk can exceed training costs.2. We describe a continuation approach for learning failure probability predictors even when failures are rare. We develop algorithms applying failure probability predictors to failure search, risk estimation, and model selection.3. We extensively evaluate our method on simulated driving and humanoid locomotion domains. Using adversarial evaluation, we find failures with 198 and 3100 times fewer samples respectively. On Humanoid, we bring the cost of reliable risk estimation down from greater than the cost of training to a practical budget. In this work, we argued that standard approaches to evaluating RL agents are highly inefficient in detecting rare, catastrophic failures, which can create a false sense of safety. We believe the approach and results here strongly demonstrate that adversarial testing can play an important role in assessing and improving agents, but are only scratching the surface. We hope this work lays the groundwork for future research into evaluating and developing robust, deployable agents.",paper addresses problem evaluating learning systems safety critical domains autonomous driving where failures can have catastrophic consequences. focus two problems:searching scenarios when learned agents fail assessing probability failure. standard method agent evaluation reinforcement learning Vanilla Monte Carlo can miss failures entirely leading deployment unsafe agents. demonstrate is an issue current agents where even matching compute used training is sometimes insufficient evaluation. address shortcoming draw upon rare event probability estimation literature propose adversarial evaluation approach. approach focuses evaluation adversarially chosen situations still providing unbiased estimates failure probabilities. key difficulty is in identifying adversarial situations since failures are rare is little signal drive optimization. solve propose continuation approach learns failure modes related less robust agents. approach also allows reuse data already collected training agent. demonstrate efficacy adversarial evaluation two standard domains:humanoid control simulated driving. Experimental results show methods can find catastrophic failures estimate failures rates agents multiple orders magnitude faster standard evaluation schemes minutes hours rather days. How can we ensure machine learning systems do not make catastrophic mistakes? machine learning systems have shown impressive results across variety domains BID6 BID11 BID26 may also fail badly particular inputs often unexpected ways BID28. start deploying systems is important can reliably evaluate risk failure. is particularly important safety critical domains like autonomous driving where the negative consequences single mistake can overwhelm positive benefits accrued typical operation system.Limitations random testing. key problem highlight is that for standard statistical evaluation attaining confidence failure rate policy is below requires least 1/episodes. informally summarize point which we discuss Appendix A. concreteness consider self-driving car company decides cost single accident where the car is at fault outweighs benefits 100 million miles faultless operation. standard approach machine learning is to estimate expected return via.i.d samples data distribution frequently test set tightly bounded returns sample estimate is guaranteed quickly converge true expectation. However catastrophic failures may prohibitively inefficient. current example policy failure probability greater 10 −8 per mile has negative expected return. words would better deploy car. However achieve reasonable confidence car crashes probability 1e-8 manufacturer would need test-drive car least 1e8 miles may prohibitively expensive.Our Contributions. overcome above-mentioned problems develop novel adversarial evaluation approach. central motivation behind algorithmic choices is the fact realworld evaluation is typically dominated cost running agent real-world/human supervision. self-driving car example issues are present:testing requires operating physical car human test driver behind wheel. overarching idea is thus screen situations are unlikely problematic focus evaluation difficult situations. difficulty arises identifying situations -since failures are rare is little signal drive optimization. address problem introduce continuation approach learning failure probability predictor AVF which estimates probability agent fails given initial conditions. idea is to leverage data less robust agents which fail frequently provide stronger learning signal. implementation also allows algorithm reuse data gathered training agent saving time resources evaluation. note adversarial testing is a well-established idea see Section5 typically requires either dense optimization signal expert domain knowledge. avoid stumbling blocks relying learned AVF which guides adversarially acting evaluator.We look two settings where the AVF can be used. simplest setting failure search is the problem is to efficiently find inputs initial conditions cause failures Section 2.1 task has several uses. First adversary solves task efficiently allows one identify debug potentially unsafe policies. Second has been done previously supervised learning literature efficient adversaries can be used adversarial training folding states causing failures back training algorithm BID9. second setting risk estimation is the problem efficiently estimating failure probability agent Section 2.2 which also has a simple application efficiently selecting reliable agent finite set Section 4.3.Empirically demonstrate dramatic improvements efficiency adversarial testing two domains simulated driving humanoid locomotion summary present 3 key contributions:1 empirically demonstrate limitations random testing. observe random testing cost reliably obtaining even single adversarial input can exceed can exceed entire cost training. reliably estimating risk can exceed can exceed training costs.2 describe continuation approach learning failure probability predictors even when failures are rare. develop algorithms applying failure probability predictors failure search risk estimation model selection.3 extensively evaluate method simulated driving humanoid locomotion domains. Using adversarial evaluation find failures 198 3100 times fewer samples respectively. Humanoid bring cost reliable risk estimation greater cost training practical budget. work argued standard approaches evaluating RL agents are highly inefficient detecting rare catastrophic failures which can create false sense safety. believe approach results strongly demonstrate adversarial testing can play important role assessing improving agents are only scratching surface. hope work lays groundwork future research evaluating developing robust deployable agents.,1265,878,387,0.014,1.441,2025/11/05 17:18:52,0.01,1.491,0.3457943925233644,424.751
"The variational autoencoder (VAE) is a popular combination of deep latent variable model and accompanying variational learning technique. By using a neural inference network to approximate the model's posterior on latent variables, VAEs efficiently parameterize a lower bound on marginal data likelihood that can be optimized directly via gradient methods. In practice, however, VAE training often results in a degenerate local optimum known as ""posterior collapse"" where the model learns to ignore the latent variable and the approximate posterior mimics the prior. In this paper, we investigate posterior collapse from the perspective of training dynamics. We find that during the initial stages of training the inference network fails to approximate the model's true posterior, which is a moving target. As a result, the model is encouraged to ignore the latent encoding and posterior collapse occurs. Based on this observation, we propose an extremely simple modification to VAE training to reduce inference lag: depending on the model's current mutual information between latent variable and observation, we aggressively optimize the inference network before performing each model update. Despite introducing neither new model components nor significant complexity over basic VAE, our approach is able to avoid the problem of collapse that has plagued a large amount of previous work. Empirically, our approach outperforms strong autoregressive baselines on text and image benchmarks in terms of held-out likelihood, and is competitive with more complex techniques for avoiding collapse while being substantially faster.",variational autoencoder VAE is a popular combination deep latent variable model accompanying variational learning technique. using neural inference network approximate model's posterior latent variables VAEs efficiently parameterize lower bound marginal data likelihood can be optimized directly via gradient methods. practice however VAE training often results degenerate local optimum known posterior collapse where the model learns ignore latent variable approximate posterior mimics prior. paper investigate posterior collapse perspective training dynamics. find initial stages training inference network fails approximate model's true posterior which is a moving target. result model is encouraged ignore latent encoding posterior collapse occurs. Based observation propose extremely simple modification VAE training reduce inference lag:depending model's current mutual information latent variable observation aggressively optimize inference network performing model update. Despite introducing neither new model components significant complexity basic VAE approach is able avoid problem collapse has plagued large amount previous work. Empirically approach outperforms strong autoregressive baselines text image benchmarks terms held-out likelihood is competitive complex techniques avoiding collapse substantially faster.,284,194,90,0.003,1.464,2025/11/05 17:18:52,0.0,1.625,0.4174454828660433,99.403
"Online healthcare services can provide the general public with ubiquitous access to medical knowledge and reduce the information access cost for both individuals and societies. To promote these benefits, it is desired to effectively expand the scale of high-quality yet novel relational medical entity pairs that embody rich medical knowledge in a structured form. To fulfill this goal, we introduce a generative model called Conditional Relationship Variational Autoencoder (CRVAE), which can discover meaningful and novel relational medical entity pairs without the requirement of additional external knowledge. Rather than discriminatively identifying the relationship between two given medical entities in a free-text corpus, we directly model and understand medical relationships from diversely expressed medical entity pairs. The proposed model introduces the generative modeling capacity of variational autoencoder to entity pairs, and has the ability to discover new relational medical entity pairs solely based on the existing entity pairs. Beside entity pairs, relationship-enhanced entity representations are obtained as another appealing benefit of the proposed method. Both quantitative and qualitative evaluations on real-world medical datasets demonstrate the effectiveness of the proposed method in generating relational medical entity pairs that are meaningful and novel. Increasingly, people engage in health services on the Internet BID11 . The healthcare services can provide the general public with ubiquitous access to medical knowledge and reduce the information access cost significantly. The relational medical entity pair, which consists of two medical entities with a semantic connection between them, is an intuitive representation that distills human medical reasoning processes in a structured form. The medical relationships discussed in this paper are binary ones. For example, the Disease Cause − −−− →Symptom relationship indicates a ""Cause"" relationship from a disease entity to a symptom entity that is caused by this disease, such as the medical entity pairs <Synovitis, Joint Pain>. For the relationship Symptom Belongto − −−−−− →Department, we may have a relational medical entity pair such as <Stiffness of a Joint, Orthopedics>.The ability to understand, reason and generalize is central to human intelligence BID27 . However , it possesses significant challenges for machines to understand and reason about the relationships between two entities BID31 . Real-world relational medical entity pairs possess certain challenging properties to deal with: First, as the medical research develops, many medical relationships among medical entities that were once neglected due to the underdeveloped medical knowledge now need to be discovered. An increasing number of relationships will be formed among a large number of medical entities. Also, various linguistic expressions can be used for the same medical entity. For example, Nose Plugged, Blocked Nose and Sinus Congestion are symptom entities that share the same meaning but expressed very differently. Moreover, one medical relationship may instantiate entity pairs with varying granularities or relationship strength. For instance, Disease Cause − −−− →Symptom may include entity pairs like <Rhinitis, Nose Plugged> as a coarse-grained entity pair, while < Acute Rhinitis, Nose Plugged>, <Chronic Rhinitis, Nose Plugged> are considered fine-grained entity pairs. As for the relationship strength, <Cold, Fatigue> has greater relationship strength than <Cold, Ear Infections> as cold rarely cause serious complications such as ear infections.To effectively expand the scale of high-quality yet novel relational medical entity pairs, relation extraction methods BID8 BID2 are proposed to examine whether or not a semantic relationship exists between two given entities given a context. Although the existing relation extraction methods BID1 BID3 BID30 BID39 BID6 BID37 achieve decent performance in identifying the relationship for given entity pairs, those methods require contexts such as sentences retrieved from a large free-text corpus, from existing domain-specific knowledge graphs BID0 , or from web tables and links BID21 . As medical relationships in the real-world are becoming more and more complex and diversely expressed, existing relation extraction methods suffer from the data sparsity problem where it is hard to obtain additional external knowledge that covers all possible entity pairs, e.g. free-text corpus where two entities co-occur in the same sentence with a relationship between them. Therefore, it is crucial and appealing for us to discover meaningful relational medical entity pairs solely based on existing medical entity pairs, without the requirement of a well-maintained context as an additional external knowledge.Furthermore, most relation extraction methods adopt a discriminative approach that learns to distinguish entity pairs of one relationship from the other BID41 BID22 , or to identify meaningful entity pairs from randomly sampled negative entity pairs with no relationships BID4 BID32 . Those methods need to iterate over the combination of all possible entity pairs and check each of them to discover new entity pairs. Such discriminative approach is tedious and labor-intensive. It is challenging yet rewarding for us to understand medical relationships intrinsically from the existing entity pairs. Specifically, in the medical domain, the diversely expressed medical entity pairs offer great advantages for us to ultimately understand medical relationships and discover high-quality relational medical entity pairs solely from existing meaningful medical entity pairs.Problem Studied: We propose a novel research problem called RElational Medical Entity-pair DiscoverY (REMEDY), which aims at modeling relational medical entity pairs solely from the existing entity pairs. Also, it aims to discover meaningful and novel entity pairs pertaining to a certain medical relationship in a generative fashion, without sophisticated feature engineering and the requirement of external knowledge such as free-text corpora.Proposed Model: A generative model named Conditional Relationship Variational Autoencoder (CRVAE) is introduced for relational medical entity pair discovery. It is unlikely to create meaningful, novel relational medical entity pairs without intrinsically understanding each medical relationship, more specifically, understanding the relationships between every two medical entities that instantiate a particular relationship. CRVAE fully explores the generative modeling capacity which roots in Bayesian inference while incorporating deep learning for powerful hands-free feature engineering. CRVAE is trained to encode each relational medical entity pair into a latent space conditioned on the relationship type. The encoding process addresses relationship-enhanced entity representations, interactions between entities as well as expressive latent variables. The latent variables are decoded to reconstruct entity pairs. Once the model is trained, we can sample directly from the distribution of latent variables and decode them into high-quality and novel relational medical entity pairs.Overall, CRVAE has three notable strengths:CRVAE models the intrinsic relations between medical entity pairs directly based on the existing meaningful relational medical entity pairs, without the requirement of additional external contexts for entity pair extraction. Existing relation extraction methods usually rely on the free-text corpus to decide whether a candidate entity pair it mentions is meaningful or not. The CRVAE only utilizes the existing entity pairs and pre-trained word vector as initial entity representations which are trained separately.CRVAE is able to generate entity pairs for a particular relationship, even if it observes existing entity pairs only for that particular relationship. Unlike most discriminative methods which harness discrepancies among different relationships to distinguish the relationship of an entity pair from the other, or from randomly constructed negative entity pairs with no relations. The CRVAE understands the intrinsic medical relation from diversely expressed medical entity pairs and discovers meaningful, novel entity pairs of a particular relationship that we specified.CRVAE generates novel entity pairs by a density-based sampling strategy in the generator. The generator samples directly from the latent space based on the density of hidden parameters. With the hands-free feature engineering by deep neural networks, the model is able to discover meaningful and novel entity pairs which does not exist in the training data.The contributions of this paper can be summarized as follows:• We study the Relational Medical Entity-pair Discovery (REMEDY) problem, which aims to expand the scale of high-quality yet novel relational medical entity pairs without maintaining large-scale context information such as the free-text corpus.• We propose a generative model named Conditional Relationship Variational Autoencoder (CRVAE) that discovers relational medical entity pairs for a given relationship, solely from the diversely expressed entity pairs without sophisticated feature engineering.• We obtain relationship-enhanced entity representations as an appealing benefit of the proposed model. To effectively expand the scale of high-quality relational medical entity pairs which store the medical knowledge, a novel generative model named Conditional Relationship Variational Autoencoder (CRVAE) is introduced for Relational Medical Entity-pair Discovery (REMEDY). The proposed model fully explores the generative modeling ability while incorporates deep learning for powerful hands-free feature engineering. Unlike traditional relation extraction tasks which require additional contexts for extraction and need negative samples for discriminative training, the proposed method learns to intrinsically understand the medical relations from diversely expressed medical entity pairs, without the requirement of external context information. Moreover, it is able to generate meaningful, novel entity pairs for a given type of medical relationship. The relationshipenhanced entity representations have the potential to improve other NLP tasks. The performance of the proposed method is evaluated on real-world medical data both quantitatively and qualitatively.",Online healthcare services can provide general public ubiquitous access medical knowledge reduce information access cost individuals societies. promote benefits is desired effectively expand scale high-quality yet novel relational medical entity pairs embody rich medical knowledge structured form. fulfill goal introduce generative model called Conditional Relationship Variational Autoencoder CRVAE which can discover meaningful novel relational medical entity pairs without requirement additional external knowledge. Rather discriminatively identifying relationship two given medical entities free-text corpus directly model understand medical relationships diversely expressed medical entity pairs. proposed model introduces generative modeling capacity variational autoencoder entity pairs has the ability discover new relational medical entity pairs solely based existing entity pairs. Beside entity pairs relationship-enhanced entity representations are obtained another appealing benefit proposed method. quantitative qualitative evaluations real-world medical datasets demonstrate effectiveness proposed method generating relational medical entity pairs are meaningful novel. Increasingly people engage health services Internet BID11. healthcare services can provide general public ubiquitous access medical knowledge reduce information access cost significantly. relational medical entity pair which consists two medical entities semantic connection is intuitive representation distills human medical reasoning processes structured form. medical relationships discussed paper are binary ones. example Disease Cause − −−− →Symptom relationship indicates Cause relationship disease entity symptom entity is caused disease medical entity pairs Synovitis Joint Pain relationship Symptom Belongto− −−−−− →Department may have a relational medical entity pair Stiffness Joint Orthopedics.The ability understand reason generalize is central human intelligence BID27. However possesses significant challenges machines understand reason relationships two entities BID31. Real-world relational medical entity pairs possess certain challenging properties deal with:First medical research develops many medical relationships among medical entities were once neglected due underdeveloped medical knowledge need discovered. increasing number relationships will be formed among large number medical entities. Also various linguistic expressions can be used medical entity. example Nose Plugged Blocked Nose Sinus Congestion are symptom entities share meaning expressed differently. Moreover one medical relationship may instantiate entity pairs varying granularities relationship strength. instance Disease Cause − −−− →Symptom may include entity pairs like Rhinitis Nose Plugged coarse-grained entity pair Acute Rhinitis Nose Plugged Chronic Rhinitis Nose Plugged are considered fine-grained entity pairs. relationship strength Cold Fatigue has greater relationship strength Cold Ear Infections cold rarely cause serious complications ear infections.To effectively expand scale high-quality yet novel relational medical entity pairs relation extraction methods BID8 BID2 are proposed examine whether semantic relationship exists two given entities given context. Although existing relation extraction methods BID1 BID3 BID30 BID39 BID6 BID37 achieve decent performance identifying relationship given entity pairs methods require contexts sentences retrieved large free-text corpus existing domain-specific knowledge graphs BID0 web tables links BID21. medical relationships real-world are becoming complex diversely expressed existing relation extraction methods suffer data sparsity problem where it is hard obtain additional external knowledge covers possible entity pairs e.g free-text corpus where two entities co-occur sentence relationship them. Therefore is crucial appealing us discover meaningful relational medical entity pairs solely based existing medical entity pairs without requirement well-maintained context additional external knowledge.Furthermore relation extraction methods adopt discriminative approach learns distinguish entity pairs one relationship BID41 BID22 identify meaningful entity pairs randomly sampled negative entity pairs relationships BID4 BID32. methods need iterate combination possible entity pairs check discover new entity pairs. discriminative approach is tedious labor-intensive is challenging yet rewarding us understand medical relationships intrinsically existing entity pairs. Specifically medical domain diversely expressed medical entity pairs offer great advantages us ultimately understand medical relationships discover high-quality relational medical entity pairs solely existing meaningful medical entity pairs.Problem Studied:propose novel research problem called RElational Medical Entity-pair DiscoverY REMEDY which aims modeling relational medical entity pairs solely existing entity pairs. Also which aims discover meaningful novel entity pairs pertaining certain medical relationship generative fashion without sophisticated feature engineering requirement external knowledge free-text corpora.Proposed Model:generative model named Conditional Relationship Variational Autoencoder CRVAE is introduced relational medical entity pair discovery. is unlikely create meaningful novel relational medical entity pairs without intrinsically understanding medical relationship specifically understanding relationships every two medical entities instantiate particular relationship. CRVAE fully explores generative modeling capacity which roots Bayesian inference incorporating deep learning powerful hands-free feature engineering. CRVAE is trained encode relational medical entity pair latent space conditioned relationship type. encoding process addresses relationship-enhanced entity representations interactions entities well expressive latent variables. latent variables are decoded reconstruct entity pairs. model is trained can sample directly distribution latent variables decode high-quality novel relational medical entity pairs.Overall CRVAE has three notable strengths:CRVAE models intrinsic relations medical entity pairs directly based existing meaningful relational medical entity pairs without requirement additional external contexts entity pair extraction. Existing relation extraction methods usually rely free-text corpus decide whether candidate entity pair mentions is meaningful not. CRVAE utilizes existing entity pairs pre-trained word vector initial entity representations which are trained separately.CRVAE is able generate entity pairs particular relationship even if it observes existing entity pairs particular relationship. Unlike discriminative methods which harness discrepancies among different relationships distinguish relationship entity pair randomly constructed negative entity pairs relations. CRVAE understands intrinsic medical relation diversely expressed medical entity pairs discovers meaningful novel entity pairs particular relationship specified.CRVAE generates novel entity pairs density-based sampling strategy generator. generator samples directly latent space based density hidden parameters. hands-free feature engineering deep neural networks model is able discover meaningful novel entity pairs which does not exist training data.The contributions paper can be summarized follows:• study Relational Medical Entity-pair Discovery REMEDY problem which aims expand scale high-quality yet novel relational medical entity pairs without maintaining large-scale context information free-text corpus.• propose generative model named Conditional Relationship Variational Autoencoder CRVAE discovers relational medical entity pairs given relationship solely diversely expressed entity pairs without sophisticated feature engineering.• obtain relationship-enhanced entity representations appealing benefit proposed model. effectively expand scale high-quality relational medical entity pairs which store medical knowledge novel generative model named Conditional Relationship Variational Autoencoder CRVAE is introduced Relational Medical Entity-pair Discovery REMEDY proposed model fully explores generative modeling ability incorporates deep learning powerful hands-free feature engineering. Unlike traditional relation extraction tasks which require additional contexts extraction need negative samples discriminative training proposed method learns intrinsically understand medical relations diversely expressed medical entity pairs without requirement external context information. Moreover is able generate meaningful novel entity pairs given type medical relationship. relationshipenhanced entity representations have the potential improve NLP tasks. performance proposed method is evaluated real-world medical data quantitatively qualitatively.,1781,1291,490,0.018,1.38,2025/11/05 17:18:52,0.01,1.304,0.1557632398753888,510.785
"Although variational autoencoders (VAEs) represent a widely influential deep generative model, many aspects of the underlying energy function remain poorly understood.  In particular, it is commonly believed that Gaussian encoder/decoder assumptions reduce the effectiveness of VAEs in generating realistic samples .  In this regard, we rigorously analyze the VAE objective, differentiating situations where this belief is and is not actually true .  We then leverage the corresponding insights to develop a simple VAE enhancement that requires no additional hyperparameters or sensitive tuning .  Quantitatively, this proposal produces crisp samples and stable FID scores that are actually competitive with a variety of GAN models, all while retaining desirable attributes of the original VAE architecture . The code for our model is available at \url{https://github.com/daib13/TwoStageVAE}. Our starting point is the desire to learn a probabilistic generative model of observable variables x ∈ χ, where χ is a r-dimensional manifold embedded in R d . Note that if r = d, then this assumption places no restriction on the distribution of x ∈ R d whatsoever; however, the added formalism is introduced to handle the frequently encountered case where x possesses low-dimensional structure relative to a high-dimensional ambient space, i.e., r d. In fact, the very utility of generative models of continuous data, and their attendant low-dimensional representations, often hinges on this assumption BID1 . It therefore behooves us to explicitly account for this situation.Beyond this, we assume that χ is a simple Riemannian manifold, which means there exists a diffeomorphism ϕ between χ and R r , or more explicitly, the mapping ϕ : χ → R r is invertible and differentiable. Denote a ground-truth probability measure on χ as µ gt such that the probability mass of an infinitesimal dx on the manifold is µ gt (dx) and χ µ gt (dx) = 1.The variational autoencoder (VAE) BID17 BID28 attempts to approximate this ground-truth measure using a parameterized density p θ (x) defined across all of R d since any underlying generative manifold is unknown in advance. This density is further assumed to admit the latent decomposition p θ (x) = p θ (x|z)p(z)dz, where z ∈ R κ serves as a lowdimensional representation, with κ ≈ r and prior p(z) = N (z|0, I).Ideally we might like to minimize the negative log-likelihood − log p θ (x) averaged across the ground-truth measure µ gt , i.e., solve min θ χ − log p θ (x)µ gt (dx). Unfortunately though, the required marginalization over z is generally infeasible. Instead the VAE model relies on tractable encoder q φ (z|x) and decoder p θ (x|z) distributions, where φ represents additional trainable parameters. The canonical VAE cost is a bound on the average negative log-likelihood given by L(θ, φ) χ {− log p θ (x) + KL [q φ (z|x)||p θ (z|x)]} µ gt (dx) ≥ χ − log p θ (x)µ gt (dx),where the inequality follows directly from the non-negativity of the KL-divergence. Here φ can be viewed as tuning the tightness of bound, while θ dictates the actual estimation of µ gt . Using a few standard manipulations, this bound can also be expressed as DISPLAYFORM0 which explicitly involves the encoder/decoder distributions and is conveniently amenable to SGD optimization of {θ, φ} via a reparameterization trick BID17 BID28 . The first term in (2 ) can be viewed as a reconstruction cost (or a stochastic analog of a traditional autoencoder), while the second penalizes posterior deviations from the prior p(z). Additionally, for any realizable implementation via SGD, the integration over χ must be approximated via a finite sum across training samples {x (i) } n i=1 drawn from µ gt . Nonetheless, examining the true objective L(θ, φ) can lead to important, practically-relevant insights.At least in principle, q φ (z|x) and p θ (x|z) can be arbitrary distributions, in which case we could simply enforce q φ (z|x) = p θ (z|x) ∝ p θ (x|z)p(z) such that the bound from (1) is tight. Unfortunately though, this is essentially always an intractable undertaking. Consequently, largely to facilitate practical implementation, a commonly adopted distributional assumption for continuous data is that both q φ (z|x) and p θ (x|z) are Gaussian. This design choice has previously been cited as a key limitation of VAEs BID5 BID18 , and existing quantitative tests of generative modeling quality thus far dramatically favor contemporary alternatives such as generative adversarial networks (GAN) BID13 . Regardless, because the VAE possesses certain desirable properties relative to GAN models (e.g., stable training BID29 , interpretable encoder/inference network BID4 , outlier-robustness BID9 , etc.), it remains a highly influential paradigm worthy of examination and enhancement.In Section 2 we closely investigate the implications of VAE Gaussian assumptions leading to a number of interesting diagnostic conclusions. In particular, we differentiate the situation where r = d, in which case we prove that recovering the ground-truth distribution is actually possible iff the VAE global optimum is reached, and r < d, in which case the VAE global optimum can be reached by solutions that reflect the ground-truth distribution almost everywhere, but not necessarily uniquely so. In other words, there could exist alternative solutions that both reach the global optimum and yet do not assign the same probability measure as µ gt .Section 3 then further probes this non-uniqueness issue by inspecting necessary conditions of global optima when r < d. This analysis reveals that an optimal VAE parameterization will provide an encoder/decoder pair capable of perfectly reconstructing all x ∈ χ using any z drawn from q φ (z|x). Moreover, we demonstrate that the VAE accomplishes this using a degenerate latent code whereby only r dimensions are effectively active. Collectively, these results indicate that the VAE global optimum can in fact uniquely learn a mapping to the correct ground-truth manifold when r < d, but not necessarily the correct probability measure within this manifold, a critical distinction.Next we leverage these analytical results in Section 4 to motivate an almost trivially-simple, twostage VAE enhancement for addressing typical regimes when r < d. In brief, the first stage just learns the manifold per the allowances from Section 3, and in doing so, provides a mapping to a lower dimensional intermediate representation with no degenerate dimensions that mirrors the r = d regime. The second (much smaller) stage then only needs to learn the correct probability measure on this intermediate representation, which is possible per the analysis from Section 2. Experiments from Sections 5 and 6 empirically corroborate motivational theory and reveal that the proposed two-stage procedure can generate high-quality samples, reducing the blurriness often attributed to VAE models in the past BID11 BID21 . And to the best of our knowledge, this is the first demonstration of a VAE pipeline that can produce stable FID scores, an influential recent metric for evaluating generated sample quality BID16 , that are comparable to GAN models under neutral testing conditions. Moreover, this is accomplished without additional penalties, cost function modifications, or sensitive tuning parameters. Finally, an extended version of this work can be found in BID8 ). There we include additional results, consideration of disentangled representations, as well as a comparative discussion of broader VAE modeling paradigms such as those involving normalizing flows or parameterized families for p(z). It is often assumed that there exists an unavoidable trade-off between the stable training, valuable attendant encoder network, and resistance to mode collapse of VAEs, versus the impressive visual quality of images produced by GANs. While we certainly are not claiming that our two-stage VAE model is superior to the latest and greatest GAN-based architecture in terms of the realism of generated samples, we do strongly believe that this work at least narrows that gap substantially such that VAEs are worth considering in a broader range of applications. For further results and discussion, including consideration of broader VAE modeling paradigms and the identifiability of disentangled representations, please see BID8 .",Although variational autoencoders VAEs represent widely influential deep generative model many aspects underlying energy function remain poorly understood. particular is commonly believed Gaussian encoder/decoder assumptions reduce effectiveness VAEs generating realistic samples. regard rigorously analyze VAE objective differentiating situations where this belief is and is not is actually true. leverage corresponding insights develop simple VAE enhancement requires additional hyperparameters sensitive tuning. Quantitatively proposal produces crisp samples stable FID scores are actually competitive variety GAN models retaining desirable attributes original VAE architecture. code model is available \url https://github.com/daib13/TwoStageVAE starting point is the desire learn probabilistic generative model observable variablesx∈ χ whereχ is a r-dimensional manifold embedded R d. Note ifr assumption places restriction distribution x∈R whatsoever;however added formalism is introduced handle frequently encountered case where x possesses low-dimensional structure relative high-dimensional ambient space.e r d. fact utility generative models continuous data attendant low-dimensional representations often hinges assumption BID1. therefore behoovesus explicitly account situation.Beyond assume χ is a simple Riemannian manifold which means exists diffeomorphismϕ χ Rr explicitly mappingϕ:χ→Rr is invertible differentiable. Denote ground-truth probability measure χ µgt probability mass infinitesimaldx manifold isµgt dx χµgt dx 1.The variational autoencoder VAE BID17 BID28 attempts approximate ground-truth measure using parameterized densitypθ x defined across R since underlying generative manifold is unknown advance. density is further assumed admit latent decompositionpθ x pθ x|z p z dz wherez∈Rκ serves lowdimensional representation κ≈r priorp z N z|0.Ideally might like minimize negative log-likelihood − log pθ x averaged across ground-truth measureµgt.e solve minθχ − logpθ x µgt dx Unfortunately though required marginalization z is generally infeasible. Instead VAE model relies tractable encoderqφ z|x decoderpθ x|z distributions where φ represents additional trainable parameters. canonical VAE cost is a bound average negative log-likelihood given L θ whereφ χ − logpθ x+KL qφ z|x ||pθ z|x µgt dx ≥ χ − log pθ x µgt dx where the inequality follows directly non-negativity KL-divergence φ can be viewed tuning tightness bound θ dictates actual estimation µgt. Using standard manipulations bound can also expressed DISPLAYFORM0 which explicitly involves encoder/decoder distributions is conveniently amenable SGD optimization θ whereφ via reparameterization trick BID17 BID28. first term 2 can be viewed reconstruction cost stochastic analog traditional autoencoder second penalizes posterior deviations priorp z Additionally realizable implementation via SGD integration χ must approximated via finite sum across training samples x n i=1 drawn µgt. Nonetheless examining true objectiveL θ whereφ can lead important practically-relevant insights.At least principle qφ z|x pθ x|z can be arbitrary distributions which case could simply enforceq φ z|x pθ z|x ∝pθ x|z p z bound 1 is tight. Unfortunately though is essentially always intractable undertaking. Consequently largely facilitate practical implementation is commonly adopted distributional assumption continuous data is that bothqφ z|x pθ x|z are Gaussian. design choice has previously cited key limitation VAEs BID5 BID18 existing quantitative tests generative modeling quality thus far dramatically favor contemporary alternatives generative adversarial networks GAN BID13. Regardless VAE possesses certain desirable properties relative GAN models e.g stable training BID29 interpretable encoder/inference network BID4 outlier-robustness BID9 etc. remains highly influential paradigm worthy examination enhancement.In Section2 closely investigate implications VAE Gaussian assumptions leading number interesting diagnostic conclusions. particular differentiate situation wherer which case prove recovering ground-truth distribution is and is not is actually possible iff VAE global optimum is reached r which case VAE global optimum can be reached solutions reflect ground-truth distribution almost everywhere necessarily uniquely so. words could exist alternative solutions reach global optimum yet do not assign probability measure µ gt.Section3 probes non-uniqueness issue inspecting necessary conditions global optima whenr d. analysis reveals optimal VAE parameterization will provide encoder/decoder pair capable perfectly reconstructing x ∈ χ using z drawn qφ z|x Moreover demonstrate VAE accomplishes using degenerate latent code whereby r dimensions are effectively active. Collectively results indicate VAE global optimum can in fact uniquely learn mapping correct ground-truth manifold whenr necessarily correct probability measure within manifold critical distinction.Next leverage analytical results Section4 motivate almost trivially-simple twostage VAE enhancement addressing typical regimes whenr d. brief is the first stage learns manifold per allowances Section3 provides mapping lower dimensional intermediate representation degenerate dimensions mirrors r regime. second much smaller stage needs learn correct probability measure intermediate representation which is possible per analysis Section2. Experiments Sections5 6 empirically corroborate motivational theory reveal proposed two-stage procedure can generate high-quality samples reducing blurriness often attributed VAE models past BID11 BID21. best knowledge is the first demonstration VAE pipeline can produce stable FID scores influential recent metric evaluating generated sample quality BID16 are comparable GAN models neutral testing conditions. Moreover is accomplished without additional penalties cost function modifications sensitive tuning parameters. Finally extended version work can be found BID8 include additional results consideration disentangled representations well comparative discussion broader VAE modeling paradigms involving normalizing flows parameterized families p z is often assumed exists unavoidable trade-off stable training valuable attendant encoder network resistance mode collapse VAEs versus impressive visual quality images produced GANs. certainly are not claiming two-stage VAE model is superior latest greatest GAN-based architecture terms realism generated samples do strongly believe work least narrows gap substantially VAEs are worth considering broader range applications. results discussion including consideration broader VAE modeling paradigms identifiability disentangled representations please see BID8.,1753,1210,543,0.022,1.449,2025/11/05 17:18:52,0.01,1.386,0.3707165109034268,534.855
"We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions.   We focus on the high-dimensional regime where the canonical example is training a neural network with a large number of hyperparameters. The algorithm --- an iterative application of compressed sensing techniques for orthogonal polynomials --- requires only uniform sampling of the hyperparameters and is thus easily parallelizable.
 
 Experiments for training deep neural networks on Cifar-10 show that compared to state-of-the-art tools (e.g., Hyperband and Spearmint), our algorithm finds significantly improved solutions, in some cases better than what is attainable by hand-tuning.   In terms of overall running time (i.e., time required to sample various settings of hyperparameters plus additional computation time), we are at least an order of magnitude faster than Hyperband and Bayesian Optimization.   We also outperform Random Search $8\times$.
   
Our method is inspired by provably-efficient algorithms for learning decision trees using the discrete Fourier transform.   We obtain improved sample-complexty bounds for learning decision trees while matching state-of-the-art bounds on running time (polynomial and quasipolynomial, respectively). Large scale machine learning and optimization systems usually involve a large number of free parameters for the user to fix according to their application. A timely example is the training of deep neural networks for a signal processing application: the ML specialist needs to decide on an architecture, depth of the network, choice of connectivity per layer (convolutional, fully-connected, etc.), choice of optimization algorithm and recursively choice of parameters inside the optimization library itself (learning rate, momentum, etc.).Given a set of hyperparameters and their potential assignments, the naive practice is to search through the entire grid of parameter assignments and pick the one that performed the best, a.k.a. ""grid search"". As the number of hyperparameters increases, the number of possible assignments increases exponentially and a grid search becomes quickly infeasible. It is thus crucial to find a method for automatic tuning of these parameters.This auto-tuning, or finding a good setting of these parameters, is now referred to as hyperparameter optimization (HPO), or simply automatic machine learning (auto-ML). For continuous hyperparameters, gradient descent is usually the method of choice BID25 BID24 BID9 . Discrete parameters , however, such as choice of architecture, number of layers, connectivity and so forth are significantly more challenging. More formally, let DISPLAYFORM0 be a function mapping hyperparameter choices to test error of our model. That is, each dimension corresponds to a certain hyperparameter (number of layers, connectivity, etc.), and for simplicity of illustration we encode the choices for each parameter as binary numbers {−1, 1}. The goal of HPO is to approximate the minimizer x * = arg min x∈{0,1} n f (x) in the following setting:1. Oracle model: evaluation of f for a given choice of hyperparameters is assumed to be very expensive. Such is the case of training a given architecture of a huge dataset.2. Parallelism is crucial: testing several model hyperparameters in parallel is entirely possible in cloud architecture, and dramatically reduces overall optimization time.3. f is structured.The third point is very important since clearly HPO is information-theoretically hard and 2 n evaluations of the function are necessary in the worst case. Different works have considered exploiting one or more of the properties above. The approach of Bayesian optimization BID32 addresses the structure of f , and assumes that a useful prior distribution over the structure of f is known in advance. Multi-armed bandit algorithms BID22 , and Random Search BID2 , exploit computational parallelism very well, but do not exploit any particular structure of f 1 . These approaches are surveyed in more detail later .","give simple fast algorithm hyperparameter optimization inspired techniques analysis Boolean functions. focus high-dimensional regime where the canonical example is is the training neural network large number hyperparameters. algorithm iterative application compressed sensing techniques orthogonal polynomials requires uniform sampling hyperparameters is thus easily parallelizable. Experiments training deep neural networks Cifar-10 show compared state-of-the-art tools e.g Hyperband Spearmint algorithm finds significantly improved solutions cases better what is attainable hand-tuning terms overall running time.e time required sample various settings hyperparameters plus additional computation time are least order magnitude faster Hyperband Bayesian Optimization. also outperform Random Search $8\times$. method is inspired provably-efficient algorithms learning decision trees using discrete Fourier transform. obtain improved sample-complexty bounds learning decision trees matching state-of-the-art bounds running time polynomial quasipolynomial respectively Large scale machine learning optimization systems usually involve large number free parameters user fix according application. timely example is is the training deep neural networks signal processing application:ML specialist needs decide architecture depth network choice connectivity per layer convolutional fully-connected etc. choice optimization algorithm recursively choice parameters inside optimization library learning rate momentum etc. .Given set hyperparameters potential assignments naive practice is to search entire grid parameter assignments pick one performed best.k.a grid search. number hyperparameters increases number possible assignments increases exponentially grid search becomes quickly infeasible. is thus crucial find method automatic tuning parameters.This auto-tuning finding good setting parameters is now referred hyperparameter optimization HPO simply automatic machine learning auto-ML continuous hyperparameters gradient descent is usually method choice BID25 BID24 BID9. Discrete parameters however choice architecture number layers connectivity forth are significantly challenging. formally let DISPLAYFORM0 function mapping hyperparameter choices test error model. is,each dimension corresponds certain hyperparameter number layers connectivity etc. simplicity illustration encode choices parameter binary numbers −1 1 goal HPO is to approximate minimizerx* arg minx∈ 0,1 nf x following setting:1 Oracle model:evaluation f given choice hyperparameters is assumed expensive. is the case training given architecture huge dataset.2 Parallelism is crucial:testing several model hyperparameters parallel is entirely possible cloud architecture dramatically reduces overall optimization time.3f is structured.The third point is very important since clearly HPO is information-theoretically hard 2 n evaluations function are necessary worst case. Different works have considered exploiting one properties above. approach Bayesian optimization BID32 addresses structure f assumes useful prior distribution structure f is known advance. Multi-armed bandit algorithms BID22 Random Search BID2 do not exploit computational parallelism well do not exploit particular structure f1. approaches are surveyed detail later.",773,525,248,0.008,1.472,2025/11/05 17:18:52,0.0,1.423,0.4423676012461057,271.561
"Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collection of new methods for end-to-end learning in such models that approximate discrete maximum-weight matching using the continuous Sinkhorn operator.   Sinkhorn iteration is attractive because it functions as a simple, easy-to-implement analog of the softmax operator. With this, we can define the Gumbel-Sinkhorn method, an extension of the Gumbel-Softmax method (Jang et al. 2016, Maddison2016 et al. 2016) to distributions over latent matchings. We demonstrate the effectiveness of our method by outperforming competitive baselines on a range of qualitatively different tasks: sorting numbers, solving jigsaw puzzles, and identifying neural signals in worms. In principle, deep networks can learn arbitrarily sophisticated mappings from inputs to outputs. However, in practice we must encode specific inductive biases in order to learn accurate models from limit data. In a variety of recent research efforts, practitioners have provided models with the ability to explicitly manipulate latent combinatorial objects such as stacks BID12 BID23 , memory slots BID16 BID45 , mathematical expressions BID33 , program traces BID13 BID6 , and first order logic . Operations on these discrete objects can be approximated using differentiable operations on continuous relaxations of the objects. As such, these operations can be included as modules in neural network models that can be trained end-toend by gradient descent.Matchings and permutations are a fundamental building block in a variety of applications, as they can be used to align, canonicalize, and sort data. Prior work has developed learning algorithms for supervised learning where the training data includes annotated matchings BID36 BID46 . However, we would like to learn models with latent matchings, where the matching is not provided to us as supervision. This is a common and relevant setting. For example, BID30 showed a problem from neuroscience involving the identification of neurons from the worm C. elegans can be cast as the inference of latent permutation on a larger hierarchical structure.Unfortunately, maximizing the marginal likelihood for problems with latent matchings is very challenging. Unlike for problems with categorical latent variables, we cannot obtain unbiased stochastic gradients of the marginal likelihood using the score function estimator BID54 , as computing the probability of a given matching requires computing an intractable partition function for a structured distribution. Instead, we draw on recent work that obtains biased stochastic gradients by relaxing the discrete latent variables into continuous random variables that support the reparametrization trick BID22 BID31 .Our contributions are the following: first, in Section 2 we present a theoretical result showing that the non-differentiable parameterization of a permutation can be approximated in terms of a differentiable relaxation, the so-called Sinkhorn operator. Based on this result, in Section 3 we introduce Sinkhorn networks, which generalize the work of method of BID1 for predicting rankings, and complements the concurrent work by BID9 , by focusing on more fundamental aspects. Further , in Section 4 we introduce the Gumbel-Sinkhorn, an analog of the Gumbel Softmax distribution BID22 BID31 for permutations. This enables optimization of the marginal likelihood by the reparametrization trick. Finally, in Section 5 we demonstrate that our methods outperform strong neural network baselines on the tasks of sorting numbers, solving jigsaw puzzles, and identifying neural signals from C. elegans worms. We have demonstrated Sinkhorn networks are able to learn to find the right permutation in the most elementary cases; where all training samples obey the same sequential structure; e.g., in sorted number and in pieces of faces, as we expect parts of faces occupy similar positions from sample to sample. This is already non-trivial, as indicates one can train a neural network to solve the linear assignment problem.However, the fact that Imagenet represented a much more challenging scenario indicates there are clear limits to our formulation. As the most obvious extension we propose to introduce a sequential stage, in which current solutions are kept on a memory buffer, and improved. One way to achieve this would be by exploring more complex parameterizations for permutations; i.e. replacing M (X) by a quadratic operator that may parameterize a notion of local distance between pieces. Alternatively, one may resort to reinforcement learning techniques, as suggested in BID3 . Either sequential improvement would help solve the ""Order Matters"" problem BID52 , and we deem our elementary work as a significant step in that direction.We have made available Tensorflow code for Gumbel-Sinkhorn networks featuring an implementation of the number sorting experiment at http://github.com/google/gumbel sinkhorn .",Permutations matchings are core building blocks variety latent variable models allowus align canonicalize sort data. Learning models is difficult however exact marginalization combinatorial objects is intractable. response paper introduces collection new methods end-to-end learning models approximate discrete maximum-weight matching using continuous Sinkhorn operator. Sinkhorn iteration is attractive functions simple easy-to-implement analog softmax operator. can define Gumbel-Sinkhorn method extension Gumbel-Softmax method Jangetal. 2016 Maddison2016etal. 2016 distributions latent matchings. demonstrate effectiveness method outperforming competitive baselines range qualitatively different tasks:sorting numbers solving jigsaw puzzles identifying neural signals worms. principle deep networks can learn arbitrarily sophisticated mappings inputs outputs. However practice must encode specific inductive biases order learn accurate models limit data. variety recent research efforts practitioners have provided models ability explicitly manipulate latent combinatorial objects stacks BID12 BID23 memory slots BID16 BID45 mathematical expressions BID33 program traces BID13 BID6 first order logic. Operations discrete objects can be approximated using differentiable operations continuous relaxations objects. operations can be included modules neural network models can be trained end-toend gradient descent.Matchings permutations are a fundamental building block variety applications can used align canonicalize sort data. Prior work has developed learning algorithms supervised learning where the where all training data includes annotated matchings BID36 BID46. However would like learn models latent matchings where the matching is not provided us supervision. is a common relevant setting. example BID30 showed problem neuroscience involving identification neurons wormC. elegans can be cast inference latent permutation larger hierarchical structure.Unfortunately maximizing marginal likelihood problems latent matchings is very challenging. Unlike problems categorical latent variables cannot obtain unbiased stochastic gradients marginal likelihood using score function estimator BID54 computing probability given matching requires computing intractable partition function structured distribution. Instead draw recent work obtains biased stochastic gradients relaxing discrete latent variables continuous random variables support reparametrization trick BID22 BID31.Our contributions are the following:first Section2 present theoretical result showing non-differentiable parameterization permutation can be approximated terms differentiable relaxation so-called Sinkhorn operator. Based result Section3 introduce Sinkhorn networks which generalize work method BID1 predicting rankings complements concurrent work BID9 focusing fundamental aspects. Section4 introduce Gumbel-Sinkhorn analog Gumbel Softmax distribution BID22 BID31 permutations. enables optimization marginal likelihood reparametrization trick. Finally Section5 demonstrate methods outperform strong neural network baselines tasks sorting numbers solving jigsaw puzzles identifying neural signals C. elegans worms. have demonstrated Sinkhorn networks are able learn find right permutation elementary cases;where the where all training samples obey sequential structure;e.g sorted number pieces faces expect parts faces occupy similar positions sample sample. is already non-trivial indicates one can train neural network solve linear assignment problem.However fact Imagenet represented much challenging scenario indicates are clear limits formulation. obvious extension propose introduce sequential stage which current solutions are kept memory buffer improved. One way achieve would exploring complex parameterizations permutations;.e replacing X quadratic operator may parameterize notion local distance pieces. Alternatively one may resort reinforcement learning techniques suggested BID3. Either sequential improvement would help solve Order Matters problem BID52 deem elementary work significant step direction.We have made available Tensorflow code Gumbel-Sinkhorn networks featuring implementation number sorting experiment http://github.com/google/gumbel sinkhorn.,985,676,309,0.009,1.457,2025/11/05 17:18:52,0.0,1.4,0.3956386292834891,296.951
"Recent work in network quantization has substantially reduced the time and space complexity of neural network inference, enabling their deployment on embedded and mobile devices with limited computational and memory resources. However, existing quantization methods often represent all weights and activations with the same precision (bit-width). In this paper, we explore a new dimension of the design space: quantizing different layers with different bit-widths. We formulate this problem as a neural architecture search problem and propose a novel differentiable neural architecture search (DNAS) framework to efficiently explore its exponential search space with gradient-based optimization. Experiments show we surpass the state-of-the-art compression of ResNet on CIFAR-10 and ImageNet. Our quantized models with 21.1x smaller model size or 103.9x lower computational cost can still outperform baseline quantized or even full precision models. Recently, ConvNets have become the de-facto method in a wide range of computer vision tasks, achieving state-of-the-art performance. However, due to high computation complexity, it is nontrivial to deploy ConvNets to embedded and mobile devices with limited computational and storage budgets. In recent years, research efforts in both software and hardware have focused on lowprecision inference of ConvNets. Most of the existing quantization methods use the same precision for all (or most of) the layers of a ConvNet. However, such uniform bit-width assignment can be suboptimal since quantizing different layers can have different impact on the accuracy and efficiency of the overall network. Although mixed precision computation is widely supported in a wide range of hardware platforms such as CPUs, FPGAs, and dedicated accelerators, prior efforts have not thoroughly explored the mixed precision quantization of ConvNets.For a ConvNet with N layers and M candidate precisions in each layer, we want to find an optimal assignment of precisions to minimize the cost in terms of model size, memory footprint or computation, while keeping the accuracy. An exhaustive combinatorial search has exponential time complexity (O(M N )). Therefore, we need a more efficient approach to explore the design space.In this work, we propose a novel, effective, and efficient differentiable neural architecture search (DNAS) framework to solve this problem. The idea is illustrated in FIG0 . The problem of neural architecture search (NAS) aims to find the optimal neural net architecture in a given search space.In the DNAS framework, we represent the architecture search space with a stochastic super net where nodes represent intermediate data tensors of the super net (e.g., feature maps of a ConvNet) and edges represent operators (e.g., convolution layers in a ConvNet). Any candidate architecture can be seen as a child network (sub-graph) of the super net. When executing the super net, edges are executed stochastically and the probability of execution is parameterized by some architecture parameters θ. Under this formulation, we can relax the NAS problem and focus on finding the optimal θ that gives the optimal expected performance of the stochastic super net. The child network can then be sampled from the optimal architecture distribution.We solve for the optimal architecture parameter θ by training the stochastic super net with SGD with respect to both the network's weights and the architecture parameter θ. To compute the gradient of θ, we need to back propagate gradients through discrete random variables that control the stochastic edge execution. To address this, we use the Gumbel SoftMax function BID9 ) to ""soft-control"" the edges. This allows us to directly compute the gradient estimation of θ with a controllable trade-off between bias and variance. Using this technique, the stochastic super net becomes fully differentiable and can be effectively and efficiently solved by SGD. We apply the DNAS framework to solve the mixed precision quantization problem, by constructing a super net whose macro architecture (number of layers, filter size of each layer, etc.) is the same as the target network. Each layer of the super net contains several parallel edges representing convolution operators with quantized weights and activations with different precisions. We show that using DNAS to search for layer-wise precision assignments for ResNet models on CIFAR10 and ImageNet, we surpass the state-of-the-art compression. Our quantized models with 21.1x smaller model size or 103.9x smaller computational cost can still outperform baseline quantized or even full precision models. The DNAS pipeline is very fast, taking less than 5 hours on 8 V100 GPUs to complete a search on ResNet18 for ImageNet, while previous NAS algorithms (such as Zoph & Le (2016)) typically take a few hundred GPUs for several days. Last, but not least, DNAS is a general architecture search framework that can be applied to other problems such as efficient ConvNet-structure discovery. Due to the page limit, we will leave the discussion to future publications. In this work we focus on the problem of mixed precision quantization of a ConvNet to determine its layer-wise bit-widths. We formulate this problem as a neural architecture search (NAS) problem and propose a novel, efficient, and effective differentiable neural architecture search (DNAS) framework to solve it. Under the DNAS framework, we efficiently explore the exponential search space of the NAS problem through gradient based optimization (SGD). We use DNAS to search for layer-wise precision assignment for ResNet on CIFAR10 and ImageNet. Our quantized models with 21.1x smaller model size or 103.9x smaller computational cost can still outperform baseline quantized or even full precision models. DNAS is very efficient, taking less than 5 hours to finish a search on ResNet18 for ImageNet. It is also a general architecture search framework that is not limited to the mixed precision quantization problem. Its other applications will be discussed in future publications. DISPLAYFORM0 w denotes the latent full-precision weight of a network. Q k (·) denotes a k-bit quantization function that quantizes a continuous value w ∈ [0, 1] to its nearest neighbor in { DISPLAYFORM1 To quantize activations, we follow to use a bounded activation function followed by a quantization function as DISPLAYFORM2 Here, x is the full precision activation, y k is the quantized activation. P ACT (·) is a function that bounds the output between [0, α]. α is a learnable upper bound of the activation function.",Recent work network quantization has substantially reduced time space complexity neural network inference enabling deployment embedded mobile devices limited computational memory resources. However existing quantization methods often represent weights activations precision bit-width paper explore new dimension design space:quantizing different layers different bit-widths formulate problem neural architecture search problem propose novel differentiable neural architecture search DNAS framework efficiently explore exponential search space gradient-based optimization. Experiments show surpass state-of-the-art compression ResNet CIFAR-10 ImageNet. quantized models 21.1x smaller model size 103.9x lower computational cost can still outperform baseline quantized even full precision models. Recently ConvNets have become de-facto method wide range computer vision tasks achieving state-of-the-art performance. However due high computation complexity is nontrivial deploy ConvNets embedded mobile devices limited computational storage budgets. recent years research efforts software hardware have focused lowprecision inference ConvNets. existing quantization methods use precision layers ConvNet. However uniform bit-width assignment can be suboptimal since quantizing different layers can have different impact accuracy efficiency overall network. Although mixed precision computation is widely supported wide range hardware platforms CPUs FPGAs dedicated accelerators prior efforts have not thoroughly explored mixed precision quantization ConvNets.For ConvNet N layers candidate precisions layer want find optimal assignment precisions minimize cost terms model size memory footprint computation keeping accuracy. exhaustive combinatorial search has exponential time complexity N Therefore need efficient approach explore design space.In work propose novel effective efficient differentiable neural architecture search DNAS framework solve problem. idea is illustrated FIG0. problem neural architecture search NAS aims find optimal neural net architecture given search space.In DNAS framework represent architecture search space stochastic super net where nodes represent intermediate data tensors super net e.g feature maps ConvNet edges represent operators e.g convolution layers ConvNet candidate architecture can be seen child network sub-graph super net. When executing super net edges are executed stochastically probability execution is parameterized architecture parametersθ. formulation can relax NAS problem focus finding optimalθ gives optimal expected performance stochastic super net. child network can then be sampled optimal architecture distribution.We solve optimal architecture parameterθ training stochastic super net SGD respect network's weights architecture parameterθ. compute gradient θ need back propagate gradients discrete random variables control stochastic edge execution. address use Gumbel SoftMax function BID9 soft-control edges. allowsus directly compute gradient estimation θ controllable trade-off bias variance. Using technique stochastic super net becomes fully differentiable can be effectively efficiently solved SGD. apply DNAS framework solve mixed precision quantization problem constructing super net whose macro architecture number layers filter size layer etc. is the same target network. layer super net contains several parallel edges representing convolution operators quantized weights activations different precisions. show using DNAS search layer-wise precision assignments ResNet models CIFAR10 ImageNet surpass state-of-the-art compression. quantized models 21.1x smaller model size 103.9x smaller computational cost can still outperform baseline quantized even full precision models. DNAS pipeline is very fast taking less 5 hours 8 V100 GPUs complete search ResNet18 ImageNet previous NAS algorithms Zoph Le 2016 typically take hundred GPUs several days. Last least DNAS is a general architecture search framework can be applied problems efficient ConvNet-structure discovery. Due page limit will leave discussion future publications. work focus problem mixed precision quantization ConvNet determine layer-wise bit-widths formulate problem neural architecture search NAS problem propose novel efficient effective differentiable neural architecture search DNAS framework solve it. DNAS framework efficiently explore exponential search space NAS problem gradient based optimization SGD use DNAS search layer-wise precision assignment ResNet CIFAR10 ImageNet. quantized models 21.1x smaller model size 103.9x smaller computational cost can still outperform baseline quantized even full precision models. DNAS is very efficient taking less 5 hours finish search ResNet18 ImageNet. is also general architecture search framework is not limited mixed precision quantization problem. applications will be discussed future publications. DISPLAYFORM0 w denotes latent full-precision weight network. Qk · denotes k-bit quantization function quantizes continuous valuew∈ 0 1 nearest neighbor DISPLAYFORM1 quantize activations follow use bounded activation function followed quantization function DISPLAYFORM2 x is the full precision activation k is the quantized activation. P ACT · is a function bounds output 0 α α is a learnable upper bound activation function.,1302,892,410,0.013,1.46,2025/11/05 17:18:52,0.01,1.594,0.4049844236760122,414.793
"The top-$k$ error is a common measure of performance in machine learning and computer vision. In practice, top-$k$ classification is typically performed with deep neural networks trained with the cross-entropy loss. Theoretical results indeed suggest that cross-entropy is an optimal learning objective for such a task in the limit of infinite data. In the context of limited and noisy data however, the use of a loss function that is specifically designed for top-$k$ classification can bring significant improvements.
 Our empirical evidence suggests that the loss function must be smooth and have non-sparse gradients in order to work well with deep neural networks. Consequently, we introduce a family of smoothed loss functions that are suited to top-$k$ optimization via deep learning. The widely used cross-entropy is a special case of our family. Evaluating our smooth loss functions is computationally challenging: a na{\""i}ve algorithm would require $\mathcal{O}(\binom{n}{k})$ operations, where $n$ is the number of classes. Thanks to a connection to polynomial algebra and a divide-and-conquer approach, we provide an algorithm with a time complexity of $\mathcal{O}(k n)$. Furthermore, we present a novel approximation to obtain fast and stable algorithms on GPUs with single floating point precision. We compare the performance of the cross-entropy loss and our margin-based losses in various regimes of noise and data size, for the predominant use case of $k=5$. Our investigation reveals that our loss is more robust to noise and overfitting than cross-entropy. In machine learning many classification tasks present inherent label confusion. The confusion can originate from a variety of factors, such as incorrect labeling, incomplete annotation, or some fundamental ambiguities that obfuscate the ground truth label even to a human expert. For example, consider the images from the ImageNet data set (Russakovsky et al., 2015) in Figure 1 , which illustrate the aforementioned factors. To mitigate these issues, one may require the model to predict the k most likely labels, where k is typically very small compared to the total number of labels. Then the prediction is considered incorrect if all of its k labels differ from the ground truth, and correct otherwise. This is commonly referred to as the top-k error. Learning such models is a longstanding task in machine learning, and many loss functions for top-k error have been suggested in the literature.In the context of correctly labeled large data, deep neural networks trained with cross-entropy have shown exemplary capacity to accurately approximate the data distribution. An illustration of this phenomenon is the performance attained by deep convolutional neural networks on the ImageNet challenge. Specifically, state-of-the-art models trained with cross-entropy yield remarkable success on the top-5 error, although cross-entropy is not tailored for top-5 error minimization. This phenomenon can be explained by the fact that cross-entropy is top-k calibrated for any k (Lapin et al., 2016) , an asymptotic property which is verified in practice in the large data setting. However, in cases where only a limited amount of data is available, learning large models with cross-entropy can be prone to over-fitting on incomplete or noisy labels.To alleviate the deficiency of cross-entropy, we present a new family of top-k classification loss functions for deep neural networks. Taking inspiration from multi-class SVMs, our loss creates a Figure 1 : Examples of images with label confusion, from the validation set of ImageNet. The top-left image is incorrectly labeled as ""red panda"", instead of ""giant panda"". The bottom-left image is labeled as ""strawberry"", although the categories ""apple"", ""banana"" and ""pineapple"" would be other valid labels. The center image is labeled as ""indigo bunting"", which is only valid for the lower bird of the image. The right-most image is labeled as a cocktail shaker, yet could arguably be a part of a music instrument (for example with label ""cornet, horn, trumpet, trump""). Such examples motivate the need to predict more than a single label per image.margin between the correct top-k predictions and the incorrect ones. Our empirical results show that traditional top-k loss functions do not perform well in combination with deep neural networks. We believe that the reason for this is the lack of smoothness and the sparsity of the derivatives that are used in backpropagation. In order to overcome this difficulty, we smooth the loss with a temperature parameter. The evaluation of the smooth function and its gradient is challenging, as smoothing increases the naïve time complexity from O(n) to O( n k ). With a connection to polynomial algebra and a divide-and-conquer method, we present an algorithm with O(kn) time complexity and training time comparable to cross-entropy in practice. We provide insights for numerical stability of the forward pass. To deal with instabilities of the backward pass, we derive a novel approximation. Our investigation reveals that our top-k loss outperforms cross-entropy in the presence of noisy labels or in the absence of large amounts of data. We further confirm that the difference of performance reduces with large correctly labeled data, which is consistent with known theoretical results. This work has introduced a new family of loss functions for the direct minimization of the top-k error (that is, without the need for fine-tuning). We have empirically shown that non-sparsity is essential for loss functions to work well with deep neural networks. Thanks to a connection to polynomial algebra and a novel approximation, we have presented efficient algorithms to compute the smooth loss and its gradient. The experimental results have demonstrated that our smooth top-5 loss function is more robust to noise and overfitting than cross-entropy when the amount of training data is limited.We have argued that smoothing the surrogate loss function helps the training of deep neural networks. This insight is not specific to top-k classification, and we hope that it will help the design of other surrogate loss functions. In particular, structured prediction problems could benefit from smoothed SVM losses.","top- $k error is a common measure performance machine learning computer vision. practice top- $k classification is typically performed deep neural networks trained cross-entropy loss. Theoretical results indeed suggest cross-entropy is an optimal learning objective task limit infinite data. context limited noisy data however use loss function is specifically designed top- $k classification can bring significant improvements. empirical evidence suggests loss function must smooth have non-sparse gradients order work well deep neural networks. Consequently introduce family smoothed loss functions are suited top- $k optimization via deep learning. widely used cross-entropy is a special case family. Evaluating smooth loss functions is computationally challenging:na \i algorithm would require $\mathcal \binom n k operations where$n$n is the number classes. Thanks connection polynomial algebra divide-and-conquer approach provide algorithm time complexity $\mathcal kn $. Furthermore present novel approximation obtain fast stable algorithms GPUs single floating point precision. compare performance cross-entropy loss margin-based losses various regimes noise data size predominant use case $k=5$. investigation reveals loss is more robust noise overfitting cross-entropy machine learning many classification tasks present inherent label confusion. confusion can originate variety factors incorrect labeling incomplete annotation fundamental ambiguities obfuscate ground truth label even human expert. example consider images ImageNet data set Russakovskyetal. 2015 Figure1 which illustrate aforementioned factors. mitigate issues one may require model predict k likely labels wherek is typically small compared total number labels. prediction is considered incorrect if all of its k labels differ ground truth correct otherwise. is commonly referred top-k error. Learning models is a longstanding task machine learning many loss functions top-k error have been suggested literature.In context correctly labeled large data deep neural networks trained cross-entropy have shown exemplary capacity accurately approximate data distribution. illustration phenomenon is the performance attained deep convolutional neural networks ImageNet challenge. Specifically state-of-the-art models trained cross-entropy yield remarkable success top-5 error although cross-entropy is not tailored top-5 error minimization. phenomenon can be explained fact cross-entropy is top-k calibrated k Lapinetal. 2016 asymptotic property which is verified practice large data setting. However cases where only a limited amount data is available learning large models cross-entropy can be prone over-fitting incomplete noisy labels.To alleviate deficiency cross-entropy present new family top-k classification loss functions deep neural networks. Taking inspiration multi-class SVMs loss creates Figure1:Examples images label confusion validation set ImageNet. top-left image is incorrectly labeled red panda instead giant panda. bottom-left image is labeled strawberry although categories apple banana pineapple would valid labels. center image is labeled indigo bunting which is only valid lower bird image. right-most image is labeled cocktail shaker yet could arguably part music instrument example label cornet horn trumpet trump examples motivate need predict single label per image.margin correct top-k predictions incorrect ones. empirical results show traditional top-k loss functions do not perform well combination deep neural networks. believe reason is the lack smoothness sparsity derivatives are used backpropagation. order overcome difficulty smooth loss temperature parameter. evaluation smooth function gradient is challenging smoothing increases naïve time complexity n nk connection polynomial algebra divide-and-conquer method present algorithm kn time complexity training time comparable cross-entropy practice. provide insights numerical stability forward pass. deal instabilities backward pass derive novel approximation. investigation reveals top-k loss outperforms cross-entropy presence noisy labels absence large amounts data. confirm difference performance reduces large correctly labeled data which is consistent known theoretical results. work has introduced new family loss functions direct minimization top-k error is,without need fine-tuning have empirically shown non-sparsity is essential loss functions work well deep neural networks. Thanks connection polynomial algebra novel approximation have presented efficient algorithms compute smooth loss gradient. experimental results have demonstrated smooth top-5 loss function is more robust noise overfitting cross-entropy when the amount training data is limited.We have argued smoothing surrogate loss function helps training deep neural networks. insight is not specific top-k classification hope will help design surrogate loss functions. particular structured prediction problems could benefit smoothed SVM losses.",1232,823,409,0.013,1.497,2025/11/05 17:18:53,0.01,1.542,0.5202492211838008,373.399
"Designing a molecule with desired properties is one of the biggest challenges in drug development, as it requires optimization of chemical compound structures with respect to many complex properties. To augment the compound design process we introduce Mol-CycleGAN -- a CycleGAN-based model that generates optimized compounds with a chemical scaffold of interest. Namely, given a molecule our model generates a structurally similar one with an optimized value of the considered property. We evaluate the performance of the model on selected optimization objectives related to structural properties (presence of halogen groups, number of aromatic rings) and to a physicochemical property (penalized logP). In the task of optimization of penalized logP of drug-like molecules our model significantly outperforms previous results. The principal goal of the drug design process is to find new chemical compounds that are able to modulate the activity of a given target (typically a protein) in a desired way BID27 ). However, finding such molecules in high-dimensional chemical space of all molecules without any prior knowledge is nearly impossible. In silico methods have been introduced to leverage the existing chemical, pharmacological and biological knowledge, thus forming a new branch of science -computer-aided drug design (CADD) BID26 BID0 . In particular, the recent advancements in deep learning encouraged its application to CADD BID4 . Computer methods are nowadays applied at every stage of drug design pipelines BID26 from the search of new, potentially active compounds BID22 , through optimization of their activity and physicochemical profile BID15 and simulating their scheme of interaction with the target protein BID9 , to assisting in planning the synthesis and evaluation of its difficulty BID30 .In the center of our interest are the hit-to-lead and lead optimization phases of the compound design process. Their goals are to optimize drug-like molecules identified in previous steps in terms of, respectively, the desired activity profile (increased potency towards given target protein and provision of inactivity towards undesired proteins) and the physicochemical and pharmacokinetic properties. The challenge here is to optimize a molecule with respect to multiple properties simultaneously BID15 .Our principal contribution is the introduction of Mol-CycleGAN, a generative model based on CycleGAN BID36 with the goal to augment the compound design process. We show that our model can generate molecules that possess desired properties 1 while retaining their chemical scaffolds. Given a starting molecule, the model generates a similar one but with a desired characteristics. The similarity between the two molecules is important in the context of multiparameter optimization, as it makes it easier to optimize the selected property without spoiling the previously optimized ones. To the best of our knowledge , this is the first approach to molecule generation that uses the CycleGAN architecture. We evaluate our model on its ability to perform structural transformations and molecular optimization. The former indicates that the model is able to do simple structural modifications such as a change in the presence of halogen groups or number of aromatic rings. In the latter, we aim to maximize penalized logP to assess the model's utility for compound design. Penalized logP is a physicochemical property often selected as a testing ground for molecule optimization models BID18 BID35 , as it is relevant in the drug design process. In the optimization of penalized logP for drug-like molecules our model significantly outperforms previous results. In this work, we introduced Mol-CycleGAN -a new model based on CycleGAN that can be used for the de novo generation of molecules. The advantage of the proposed model is the ability to learn transformation rules from the sets of compounds with desired and undesired values of the considered property. The model operates in the latent space trained by another model -in our work we use the latent space of JT-VAE. The model can generate molecules with desired properties -both structural and physicochemical. The generated molecules are close to the starting ones and the degree of similarity can be controlled via a hyperparameter. In the task of constrained optimization of druglike molecules our model significantly outperforms previous results. In future work we will extend the approach to multi-parameter optimization of molecules using StarGAN BID5 . It would also be interesting to test the model on cases where a small structural change leads to a drastic change in the property (e.g. on the so-called activity cliffs), which are hard for other approaches. Another interesting direction is the application of the model to working on text embeddings, where the X and Y sets could be characterized, e.g., by different sentiment.",Designing molecule desired properties is one biggest challenges drug development requires optimization chemical compound structures respect many complex properties. augment compound design process introduce Mol-CycleGAN CycleGAN-based model generates optimized compounds chemical scaffold interest. Namely given molecule model generates structurally similar one optimized value considered property. evaluate performance model selected optimization objectives related structural properties presence halogen groups number aromatic rings physicochemical property penalized logP task optimization penalized logP drug-like molecules model significantly outperforms previous results. principal goal drug design process is to find new chemical compounds are able modulate activity given target typically protein desired way BID27 However finding molecules high-dimensional chemical space molecules without prior knowledge is nearly impossible. silico methods have been introduced leverage existing chemical pharmacological biological knowledge thus forming new branch science -computer-aided drug design CADD BID26 BID0. particular recent advancements deep learning encouraged application CADD BID4. Computer methods are nowadays applied every stage drug design pipelines BID26 search new potentially active compounds BID22 optimization activity physicochemical profile BID15 simulating scheme interaction target protein BID9 assisting planning synthesis evaluation difficulty BID30.In center interest are the hit-to-lead lead optimization phases compound design process. goals are to optimize drug-like molecules identified previous steps terms respectively desired activity profile increased potency towards given target protein provision inactivity towards undesired proteins physicochemical pharmacokinetic properties. challenge is to optimize molecule respect multiple properties simultaneously BID15.Our principal contribution is the introduction Mol-CycleGAN generative model based CycleGAN BID36 goal augment compound design process. show model can generate molecules possess desired properties1 retaining chemical scaffolds. Given starting molecule model generates similar one desired characteristics. similarity two molecules is important context multiparameter optimization makes easier optimize selected property without spoiling previously optimized ones. best knowledge is the first approach molecule generation uses CycleGAN architecture. evaluate model ability perform structural transformations molecular optimization. former indicates model is able do simple structural modifications change presence halogen groups number aromatic rings. latter aim maximize penalized logP assess model's utility compound design. Penalized logP is a physicochemical property often selected testing ground molecule optimization models BID18 BID35 is relevant drug design process. optimization penalized logP drug-like molecules model significantly outperforms previous results. work introduced Mol-CycleGAN -a new model based CycleGAN can be used de novo generation molecules. advantage proposed model is the ability learn transformation rules sets compounds desired undesired values considered property. model operates latent space trained another model -in work use latent space JT-VAE model can generate molecules desired properties -both structural physicochemical. generated molecules are close starting ones degree similarity can be controlled via hyperparameter. task constrained optimization druglike molecules model significantly outperforms previous results. future work will extend approach multi-parameter optimization molecules using StarGAN BID5. would also interesting test model cases where a small structural change leads drastic change property e.g so-called activity cliffs which are hard approaches. Another interesting direction is the application model working text embeddings where theX sets could characterized e.g different sentiment.,902,605,297,0.009,1.491,2025/11/05 17:18:53,0.0,1.577,0.5015576323987541,293.733
"Knowledge distillation is a potential solution for model compression. The idea is to make a small student network imitate the target of a large teacher network, then the student network can be competitive to the teacher one. Most previous studies focus on model distillation in the classification task, where they propose different architectures and initializations for the student network. However, only the classification task is not enough, and other related tasks such as regression and retrieval are barely considered. To solve the problem, in this paper, we take face recognition as a breaking point and propose model distillation with knowledge transfer from face classification to alignment and verification. By selecting appropriate initializations and targets in the knowledge transfer, the distillation can be easier in non-classification tasks. Experiments on the CelebA and CASIA-WebFace datasets demonstrate that the student network can be competitive to the teacher one in alignment and verification, and even surpasses the teacher network under specific compression rates. In addition, to achieve stronger knowledge transfer, we also use a common initialization trick to improve the distillation performance of classification. Evaluations on the CASIA-Webface and large-scale MS-Celeb-1M datasets show the effectiveness of this simple trick. Since the emergence of Alexnet BID12 , larger and deeper networks have shown to be more powerful BID22 . However, as the network going larger and deeper, it becomes difficult to use it in mobile devices. Therefore, model compression has become necessary in compressing the large network into a small one. In recent years, many compression methods have been proposed, including knowledge distillation BID0 BID8 BID19 , weight quantization BID4 BID17 , weight pruning BID6 BID24 and weight decomposition BID2 BID16 . In this paper, we focus on the knowledge distillation, which is a potential approach for model compression.In knowledge distillation, there is usually a large teacher network and a small student one, and the objective is to make the student network competitive to the teacher one by learning specific targets of the teacher network. Previous studies mainly consider the selection of targets in the classification task, e.g., hidden layers BID15 , logits BID0 BID25 BID20 or soft predictions BID8 BID19 . However, only the distillation of the classification task is not enough, and some common tasks such as regression and retrieval should also be considered. In this paper, we take face recognition as a breaking point that we start with the knowledge distillation in face classification, and consider the distillation on two domain-similar tasks, including face alignment and verification. The objective of face alignment is to locate the key-point locations in each image; while in face verification, we have to determine if two images belong to the same identity.For distillation on non-classification tasks, one intuitive idea is to adopt a similar method as in face classification that trains teacher and student networks from scratch. In this way, the distillation on all tasks will be independent, and this is a possible solution. However, this independence cannot give the best distillation performance. There has been strong evidence that in object detection BID18 , object segmentation BID3 and image retrieval BID30 , they all used the pretrained classification model(on ImageNet) as initialization to boost performance. This success comes from the fact that their domains are similar, which makes them transfer a lot from low-level to high-level representation BID29 . Similarly, face classification, alignment and verification also share the similar domain, thus we propose to transfer the distilled knowledge of classification by taking its teacher and student networks to initialize corresponding networks in alignment and verification.Another problem in knowledge transfer is what targets should be used for distillation? In face classification, the knowledge is distilled from the teacher network by learning its soft-prediction, which has been proved to work well BID8 BID19 . However, in face alignment BID27 and verification BID27 , they have additional task-specific targets. As a result, selecting the classification or task-specific target for distillation remains a problem. One intuitive idea is to measure the relevance of objectives between non-classification and classification tasks. For example, it is not obvious to see the relation between face classification and alignment, but the classification can help a lot in verification. Therefore, it seems reasonable that if the tasks are highly related, the classification target is preferred, or the task-specific target is better.Inspired by the above thoughts, in this paper, we propose the model distillation in face alignment and verification by transferring the distilled knowledge from face classification. With appropriate selection of initializations and targets, we show that the distillation performance of alignment and verification on the CelebA and CASIA-WebFace BID28 datasets can be largely improved, and the student network can even exceed the teacher network under specific compression rates. This knowledge transfer is our main contribution. In addition, we realize that in the proposed method, the knowledge transfer depends on the distillation of classification, thus we use a common initialization trick to further boost the distillation performance of classification. Evaluations on the CASIA-WebFace and large-scale MS-Celeb-1M BID5 datasets show that this simple trick can give the best distillation results in the classification task. In this paper, we take face recognition as a breaking point, and propose the knowledge distillation on two non-classification tasks, including face alignment and verification. We extend the previous distillation framework by transferring the distilled knowledge from face classification to face alignment and verification. By selecting appropriate initializations and targets, the distillation on non-classification tasks can be easier. Besides, we also give some guidelines for target selection on non-classification tasks, and we hope these guidelines can be helpful for more tasks. Experiments on the datasets of CASIA-WebFace, CelebA and large-scale MS-Celeb-1M have demonstrated the effectiveness of the proposed method, which gives the student networks that can be competitive or exceed the teacher network under appropriate compression rates. In addition, we use a common initialization trick to further improve the distillation performance of classification, and this can boost the distillation on non-classification tasks. Experiments on CASIA-WebFace have demonstrated the effectiveness of this simple trick.",Knowledge distillation is a potential solution model compression. idea is to make small student network imitate target large teacher network student network can be competitive teacher one. previous studies focus model distillation classification task where they propose different architectures initializations student network. However classification task is not enough related tasks regression retrieval are barely considered. solve problem paper take face recognition breaking point propose model distillation knowledge transfer face classification alignment verification. selecting appropriate initializations targets knowledge transfer distillation can be easier non-classification tasks. Experiments CelebA CASIA-WebFace datasets demonstrate student network can be competitive teacher one alignment verification even surpasses teacher network specific compression rates. addition achieve stronger knowledge transfer also use common initialization trick improve distillation performance classification. Evaluations CASIA-Webface large-scale MS-Celeb-1M datasets show effectiveness simple trick. Since emergence Alexnet BID12 larger deeper networks have shown powerful BID22. However network going larger deeper becomes difficult use mobile devices. Therefore model compression has become necessary compressing large network small one. recent years many compression methods have been proposed including knowledge distillation BID0 BID8 BID19 weight quantization BID4 BID17 weight pruning BID6 BID24 weight decomposition BID2 BID16. paper focus knowledge distillation which is a potential approach model compression.In knowledge distillation is usually large teacher network small student one objective is to make student network competitive teacher one learning specific targets teacher network. Previous studies mainly consider selection targets classification task e.g hidden layers BID15 logits BID0 BID25 BID20 soft predictions BID8 BID19. However distillation classification task is not enough common tasks regression retrieval should also considered. paper take face recognition breaking point start knowledge distillation face classification consider distillation two domain-similar tasks including face alignment verification. objective face alignment is to locate key-point locations image;face verification have to determine if two images belong identity.For distillation non-classification tasks one intuitive idea is to adopt similar method face classification trains teacher student networks scratch. way distillation tasks will be independent is possible solution. However independence cannot give best distillation performance. has been strong evidence object detection BID18 object segmentation BID3 image retrieval BID30 used pretrained classification model ImageNet initialization boost performance. success comes fact domains are similar which makes transfer lot low-level high-level representation BID29. Similarly face classification alignment verification also share similar domain thus propose transfer distilled knowledge classification taking teacher student networks initialize corresponding networks alignment verification.Another problem knowledge transfer is what targets should be used distillation? face classification knowledge is distilled teacher network learning soft-prediction which has been proved work well BID8 BID19. However face alignment BID27 verification BID27 have additional task-specific targets. result selecting classification task-specific target distillation remains problem. One intuitive idea is to measure relevance objectives non-classification classification tasks. example is not obvious see relation face classification alignment classification can help lot verification. Therefore seems reasonable if the tasks are highly related classification target is preferred task-specific target is better.Inspired thoughts paper where they propose model distillation face alignment verification transferring distilled knowledge face classification. appropriate selection initializations targets show distillation performance alignment verification CelebA CASIA-WebFace BID28 datasets can be largely improved student network can even exceed teacher network specific compression rates. knowledge transfer is our main contribution. addition realize proposed method knowledge transfer depends distillation classification thus use common initialization trick boost distillation performance classification. Evaluations CASIA-WebFace large-scale MS-Celeb-1M BID5 datasets show simple trick can give best distillation results classification task. paper take face recognition breaking point where they propose knowledge distillation two non-classification tasks including face alignment verification. extend previous distillation framework transferring distilled knowledge face classification face alignment verification. selecting appropriate initializations targets distillation non-classification tasks can be easier. Besides also give guidelines target selection non-classification tasks hope guidelines can be helpful tasks. Experiments datasets CASIA-WebFace CelebA large-scale MS-Celeb-1M have demonstrated effectiveness proposed method which gives student networks can be competitive exceed teacher network appropriate compression rates. addition use common initialization trick improve distillation performance classification can boost distillation non-classification tasks. Experiments CASIA-WebFace have demonstrated effectiveness simple trick.,1242,841,401,0.015,1.477,2025/11/05 17:18:53,0.01,1.581,0.4579439252336449,382.084
"RNNs have been shown to be excellent models for sequential data and in particular for session-based user behavior. The use of RNNs provides impressive performance benefits over classical methods in session-based recommendations. In this work we introduce a novel ranking loss function tailored for RNNs in recommendation settings. The better performance of such loss over alternatives, along with further tricks and improvements described in this work, allow to achieve an overall improvement of up to 35% in terms of MRR and Recall@20 over previous session-based RNN solutions and up to 51% over classical collaborative filtering approaches. Unlike data augmentation-based improvements, our method does not increase training times significantly. Session-based recommendation is a very common recommendation problem that is encountered in many domains such as e-commerce, classified sites, music and video recommendation. In the session-based setting, past user history logs are typically not available (either because the user is new or not logged-in or not tracked) and recommender systems have to rely only on the actions of the user in the current sessions to provide accurate recommendations. Until recently many of these recommendations tasks were tackled mainly using relatively simple methods such as item-based collaborative filtering BID16 or content-based methods. Recurrent Neural Networks (RNNs) have emerged from the deep learning literature as powerful methods for modeling sequential data. These models have been successfully applied in speech recognition, translation, time series forecasting and signal processing. In recommender systems RNNs have been recently applied to the session-based recommendation setting with impressive results BID7 .The advantage of RNNs over traditional similarity-based methods for recommendation is that they can effectively model the whole session of user interactions (clicks, views, etc.) . By modeling the whole session RNNs can in effect learn the 'theme' of the session and thus provide recommendations with increased accuracy (between 20%-30%) over traditional methods.RNNs in session-based recommendation have been adapted to the task of recommendation. One of the main objectives in recommendation is to rank items by user preference; i.e. the exact ranking or scoring of items in the tail of the item list (items that the user will not like) is not that important, but it is very important to rank correctly the items that the user will like at the top of the list (first 5, 10 or 20 positions). To achieve this with machine learning one has to typically utilize learning to rank techniques(see e.g. BID2 ) and in particular ranking objectives and loss functions. The current session-based RNN approaches use ranking loss functions and, in particular, pairwise ranking loss functions. As in most deep learning approaches the choice of a good ranking loss can have a very significant influence on performance. Since deep learning methods need to propagate gradients over several layers and in the case of RNNs 'back in time' over previous steps, to optimize the model parameters, the quality of these gradients originating from the loss function influences the quality of the optimization and the model parameters. Moreover the nature of the recommendation task, which typically entails large output spaces (due to large number of items), poses unique challenges that have to be taken into account as well when designing a proper ranking loss function. We will see that the way this large output space issue is tackled is very crucial in achieving good performance.In this work we analyze ranking loss functions used in RNNs for session-based recommendations, this analysis leads to a new set of ranking loss functions that increase the performance of the RNN up to 30% over previous commonly used losses without incurring in significant computational overheads. We essentially devise a new class of loss functions that combines learnings from the deep learning and the learning to rank literature. Experimental results on several datasets coming from industry validate these impressive improvements, in terms of Mean Reciprocal Rank (MRR) and Recall@20. With these improvements the difference between RNNs and conventional memory-based collaborative filtering jumps to 51% in terms of MRR and Recall@20 demonstrating the potential that deep learning methods bring to the area of Recommender Systems. We introduced a new class of loss function that together with an improved sampling strategy have provided impressive top-k gains for RNNs for session-based recommendations. We believe that these new losses could be more generally applicable and along with the corresponding sampling strategies also provide top-k gains for different recommendations settings and algorithms such as e.g. matrix factorization or autoencoders. It is also conceivable that these techniques could also provide similar benefits in the area of Natural Language Processing a domain that shares significant similarities to the recommendation domain in terms of machine learning (e.g. ranking, retrieval) and data structure (e.g. sparse large input and output space).",RNNs have been shown excellent models sequential data particular session-based user behavior. use RNNs provides impressive performance benefits classical methods session-based recommendations. work introduce novel ranking loss function tailored RNNs recommendation settings. better performance loss alternatives along tricks improvements described work allow achieve overall improvement 35% terms MRR Recall@20 previous session-based RNN solutions 51% classical collaborative filtering approaches. Unlike data augmentation-based improvements method does not increase training times significantly. Session-based recommendation is a very common recommendation problem is encountered many domains e-commerce classified sites music video recommendation. session-based setting past user history logs are typically available either user is new logged-in tracked recommender systems have to rely actions user current sessions provide accurate recommendations. recently many recommendations tasks were tackled mainly using relatively simple methods item-based collaborative filtering BID16 content-based methods. Recurrent Neural Networks RNNs have emerged deep learning literature powerful methods modeling sequential data. models have been successfully applied speech recognition translation time series forecasting signal processing. recommender systems RNNs have been recently applied session-based recommendation setting impressive results BID7.The advantage RNNs traditional similarity-based methods recommendation is that they can effectively model whole session user interactions clicks views etc. modeling whole session RNNs can in effect learn 'theme' session thus provide recommendations increased accuracy 20%-30 traditional methods.RNNs session-based recommendation have been adapted task recommendation. One main objectives recommendation is to rank items user preference;.e exact ranking scoring items tail item list items user will not will like is not that important is important rank correctly items user will not will like top list first5 10 20 positions achieve machine learning one has to typically utilize learning rank techniques see e.g BID2 particular ranking objectives loss functions. current session-based RNN approaches use ranking loss functions particular pairwise ranking loss functions. deep learning approaches choice good ranking loss can have a very significant influence performance. Since deep learning methods need propagate gradients several layers case RNNs 'back time' previous steps optimize model parameters quality gradients originating loss function influences quality optimization model parameters. Moreover nature recommendation task which typically entails large output spaces due large number items poses unique challenges have to be taken account well when designing proper ranking loss function. will see way large output space issue is tackled is very crucial achieving good performance.In work analyze ranking loss functions used RNNs session-based recommendations analysis leads new set ranking loss functions increase performance RNN 30% previous commonly used losses without incurring significant computational overheads. essentially devise new class loss functions combines learnings deep learning learning rank literature. Experimental results several datasets coming industry validate impressive improvements terms Mean Reciprocal Rank MRR Recall@20 improvements difference RNNs conventional memory-based collaborative filtering jumps 51% terms MRR Recall@20 demonstrating potential deep learning methods bring area Recommender Systems. introduced new class loss function together improved sampling strategy have provided impressive top-k gains RNNs session-based recommendations. believe new losses could generally applicable along corresponding sampling strategies also provide top-k gains different recommendations settings algorithms e.g matrix factorization autoencoders. is also conceivable techniques could also provide similar benefits area Natural Language Processing domain shares significant similarities recommendation domain terms machine learning e.g ranking retrieval data structure e.g sparse large input output space,948,646,302,0.175,1.467,2025/11/05 17:18:53,0.0,1.793,0.4267912772585671,304.359
"In representational lifelong learning an agent aims to continually learn to solve novel tasks while updating its representation in light of previous tasks. Under the assumption that future tasks are related to previous tasks, representations should be learned in such a way that they capture the common structure across learned tasks, while allowing the learner sufficient flexibility to adapt to novel aspects of a new task. We develop a framework for lifelong learning in deep neural networks that is based on generalization bounds, developed within the PAC-Bayes framework. Learning takes place through the construction of a distribution over networks based on the tasks seen so far, and its utilization for learning a new task. Thus, prior knowledge is incorporated through setting a history-dependent prior for novel tasks. We develop a gradient-based algorithm implementing these ideas, based on minimizing an objective function motivated by generalization bounds, and demonstrate its effectiveness through numerical examples. Learning from examples is the process of inferring a general rule from a finite set of examples. It is well known in statistics (e.g., BID7 ) that learning cannot take place without prior assumptions. This idea has led in Machine Learning to the notion of inductive bias BID23 . Recent work in deep neural networks has achieved significant success in using prior knowledge in the implementation of structural constraints, e.g. the use of convolutions and weight sharing as building blocks, capturing the translational invariance of image classification. However, in general the relevant prior information for a given task is not always clear, and there is a need for building prior knowledge through learning from previous interactions with the world.Learning from previous experience can take several forms: Continual learning -a single model is trained to solve a task which changes over time (and hopefully not 'forget' the knowledge from previous times, (e.g., ). Multi-task learning -the goal is to learn how to solve several observed tasks, while exploiting their shared structure. Domain adaptation -the goal is to solve a 'target' learning task using a single 'source' learning task (both are observed, but usually the target has mainly unlabeled data). Lifelong Learning / Meta-Learning / Learning-to-Learnthe goal is to extract knowledge from several observed tasks to be used for future learning on new (not yet observed) learning tasks. In contrast to multi-task learning, the performance is evaluated on the new tasks.We work within the framework of lifelong learning, where an agent learns through interacting with the world, transferring the knowledge acquired along its path to any new task it encounters. This notion has been formulated by BID3 in a clear and simple context of 'task-environment'. In analogy to the standard single-task learning in which data is sampled from an unknown distribution, Baxter suggested to model a lifelong learning setting as if tasks are sampled from an unknown task distribution (environment), so that knowledge acquired from previous tasks can be used in order to improve performance on a novel task. Baxter's work not only provided an interesting and mathematically precise perspective for lifelong learning, but also provided generalization bounds demonstrating the potential improvement in performance due to prior knowledge. Baxter's seminal work, has led to a large number of extensions and developments.In this contribution we work within the framework formulated by BID3 , and, following the setup in BID25 , provide generalization error bounds within the PAC-Bayes framework. These bounds are then used to develop a practical learning algorithm that is applied to neural networks, demonstrating the utility of the approach. The main contributions of this work are the following. (i) An improved and tighter bound in the theoretical framework of BID25 which can utilize different single-task PAC-Bayesian bounds.(ii ) Developing a learning algorithm within this general framework and its implementation using probabilistic feedforward neural networks. This yields transfer of knowledge between tasks through constraining the prior distribution on a learning network. (iii ) Empirical demonstration of the performance enhancement compared to naive approaches and recent methods in this field.As noted above, BID3 provided a basic mathematical formulation and initial results for lifelong learning. While there have been many developments in this field since then (e.g., BID1 ; BID9 BID10 ; BID27 ), most of them were not based on generalization error bounds which is the focus of the present work. An elegant extension of generalization error bounds to lifelong learning was provided by BID25 , mentioned above (more recently extended in BID26 ). Their work , however, did not provide a practical algorithm applicable to deep neural networks. More recently , Dziugaite & Roy (2017) developed a single-task algorithm based on PAC-Bayes bounds that was demonstrated to yield good performance in simple classification tasks. Other recent theoretical approaches to lifelong or multitask learning (e.g. BID0 ; BID20 ) provide increasingly general bounds but have not led directly to practical learning algorithms. We have presented a framework for representational lifelong learning, motivated by PAC-Bayes generalization bounds, and implemented through the adjustment of a learned prior, based on tasks encountered so far. The framework bears conceptual similarity to the empirical Bayes method while not being Bayesian, and is implemented at the level of tasks rather than samples. Combining the general approach with the rich representational structure of deep neural networks, and learning through gradient based methods leads to an efficient procedure for lifelong learning, as motivated theoretically and demonstrated empirically. While our experimental results are preliminary, we believe that our work attests to the utility of using rigorous performance bounds to derive learning algorithms, and demonstrates that tighter bounds indeed lead to improved performance.There are several open issues to consider. First, the current version learns to solve all available tasks in parallel, while a more useful procedure should be sequential in nature. This can be easily incorporated into our framework by updating the prior following each novel task. Second, our method requires training stochastic models which is challenging due to the the high-variance gradients. We we would like to develop new methods within our framework which have more stable convergence and are easier to apply in larger scale problems. Third, there is much current effort in reinforcement learning to augment model free learning with model based components, where some aspects of the latter are often formulated as supervised learning tasks. Incorporating our approach in such a context would be a worthwhile challenge. In fact, a similar framework to ours was recently proposed within an RL setting BID33 , although it was not motivated from performance guarantees as was our approach, but rather from intuitive heuristic arguments.",representational lifelong learning agent aims continually learn solve novel tasks updating representation light previous tasks. assumption future tasks are related previous tasks representations should be learned way capture common structure across learned tasks allowing learner sufficient flexibility adapt novel aspects new task. develop framework lifelong learning deep neural networks is based generalization bounds developed within PAC-Bayes framework. Learning takes place construction distribution networks based tasks seen far utilization learning new task. Thus prior knowledge is incorporated setting history-dependent prior novel tasks. develop gradient-based algorithm implementing ideas based minimizing objective function motivated generalization bounds demonstrate effectiveness numerical examples. Learning examples is the process inferring general rule finite set examples. is well known statistics e.g BID7 learning cannot take place without prior assumptions. idea has led Machine Learning notion inductive bias BID23. Recent work deep neural networks has achieved significant success using prior knowledge implementation structural constraints e.g use convolutions weight sharing building blocks capturing translational invariance image classification. However general relevant prior information given task is not always clear is need building prior knowledge learning previous interactions world.Learning previous experience can take several forms:Continual learning -a single model is trained solve task which changes time hopefully 'forget' knowledge previous times e.g Multi-task learning -the goal is to learn how to solve several observed tasks exploiting shared structure. Domain adaptation -the goal is to solve 'target' learning task using single 'source' learning task are observed usually target has mainly unlabeled data Lifelong Learning/Meta-Learning/Learning-to-Learnthe goal is to extract knowledge several observed tasks used future learning new yet observed learning tasks. contrast multi-task learning performance is evaluated new tasks.We work within framework lifelong learning where an agent learns interacting world transferring knowledge acquired along path new task encounters. notion has been formulated BID3 clear simple context 'task-environment'. analogy standard single-task learning which data is sampled unknown distribution Baxter suggested model lifelong learning setting if tasks are sampled unknown task distribution environment knowledge acquired previous tasks can be used order improve performance novel task. Baxter's work provided interesting mathematically precise perspective lifelong learning also provided generalization bounds demonstrating potential improvement performance due prior knowledge. Baxter's seminal work has led large number extensions developments.In contribution work within framework formulated BID3 following setup BID25 did not provide generalization error bounds within PAC-Bayes framework. bounds are then used develop practical learning algorithm is applied neural networks demonstrating utility approach. main contributions work are the following. improved tighter bound theoretical framework BID25 which can utilize different single-task PAC-Bayesian bounds. ii Developing learning algorithm within general framework implementation using probabilistic feedforward neural networks. yields transfer knowledge tasks constraining prior distribution learning network. iii Empirical demonstration performance enhancement compared naive approaches recent methods field.As noted BID3 provided basic mathematical formulation initial results lifelong learning. have been many developments field since e.g BID1;BID9 BID10;BID27 were not based generalization error bounds which is the focus present work. elegant extension generalization error bounds lifelong learning was provided BID25 mentioned recently extended BID26 work however did not provide practical algorithm applicable deep neural networks. recently Dziugaite Roy 2017 developed single-task algorithm based PAC-Bayes bounds was demonstrated yield good performance simple classification tasks. recent theoretical approaches lifelong multitask learning e.g BID0;BID20 provide increasingly general bounds have not led directly practical learning algorithms. have presented framework representational lifelong learning motivated PAC-Bayes generalization bounds is implemented adjustment learned prior based tasks encountered far. framework bears conceptual similarity empirical Bayes method Bayesian is implemented level tasks rather samples. Combining general approach rich representational structure deep neural networks learning gradient based methods leads efficient procedure lifelong learning motivated theoretically demonstrated empirically. experimental results are preliminary believe work attests utility using rigorous performance bounds derive learning algorithms demonstrates tighter bounds indeed lead improved performance.There are several open issues consider. First current version learns solve available tasks parallel useful procedure should be sequential nature. can be easily incorporated framework updating prior following novel task. Second method requires training stochastic models which is challenging due high-variance gradients. would like develop new methods within framework which have more stable convergence are easier apply larger scale problems. Third is much current effort reinforcement learning augment model free learning model based components where some aspects latter are often formulated supervised learning tasks. Incorporating approach context would worthwhile challenge. fact similar framework was recently proposed within RL setting BID33 although was not motivated performance guarantees was our approach rather intuitive heuristic arguments.,1284,879,405,0.015,1.461,2025/11/05 17:18:53,0.01,1.5,0.4080996884735203,437.319
"Optimization algorithms for training deep models not only affects the convergence rate and stability of the training process, but are also highly related to the generalization performance of trained models. While adaptive algorithms, such as Adam and RMSprop, have shown better optimization performance than stochastic gradient descent (SGD) in many scenarios, they often lead to worse generalization performance than SGD, when used for training deep neural networks (DNNs). In this work, we identify two problems regarding the direction and step size for updating the weight vectors of hidden units, which may degrade the generalization performance of Adam. As a solution, we propose the normalized direction-preserving Adam (ND-Adam) algorithm, which controls the update direction and step size more precisely, and thus bridges the generalization gap between Adam and SGD. Following a similar rationale, we further improve the generalization performance in classification tasks by regularizing the softmax logits. By bridging the gap between SGD and Adam, we also shed some light on why certain optimization algorithms generalize better than others. In contrast with the growing complexity of neural network architectures BID10 BID12 , the training methods remain relatively simple. Most practical optimization methods for deep neural networks (DNNs) are based on the stochastic gradient descent (SGD) algorithm. However, the learning rate of SGD, as a hyperparameter, is often difficult to tune, since the magnitudes of different parameters can vary widely, and adjustment is required throughout the training process.To tackle this problem, several adaptive variants of SGD have been developed, including Adagrad BID6 ), Adadelta (Zeiler, 2012 , RMSprop BID24 , Adam BID15 , etc. These algorithms aim to adapt the learning rate to different parameters automatically, based on the statistics of gradient. Although they usually simplify learning rate settings, and lead to faster convergence, it is observed that their generalization performance tend to be significantly worse than that of SGD in some scenarios BID25 . This intriguing phenomenon may explain why SGD (possibly with momentum) is still prevalent in training state-of-the-art deep models, especially feedforward DNNs BID10 BID12 . Furthermore, recent work has shown that DNNs are capable of fitting noise data BID31 , suggesting that their generalization capabilities are not the mere result of DNNs themselves, but are entwined with optimization BID2 .This work aims to bridge the gap between SGD and Adam in terms of the generalization performance. To this end, we identify two problems that may degrade the generalization performance of Adam, and show how these problems are (partially) avoided by using SGD with L2 weight decay. First, the updates of SGD lie in the span of historical gradients, whereas it is not the case for Adam. This difference has been discussed in rather recent literature BID25 , where the authors show that adaptive methods can find drastically different but worse solutions than SGD. Second, while the magnitudes of Adam parameter updates are invariant to rescaling of the gradient, the effect of the updates on the same overall network function still varies with the magnitudes of parameters. As a result, the effective learning rates of weight vectors tend to decrease during training, which leads to sharp local minima that do not generalize well BID11 .To fix the two problems for Adam, we propose the normalized direction-preserving Adam (NDAdam) algorithm, which controls the update direction and step size more precisely. We show that ND-Adam is able to achieve significantly better generalization performance than vanilla Adam, and matches that of SGD in image classification tasks.We summarize our contributions as follows:• We observe that the directions of Adam parameter updates are different from that of SGD, i.e., Adam does not preserve the directions of gradients as SGD does. We fix the problem by adapting the learning rate to each weight vector, instead of each individual weight, such that the direction of the gradient is preserved.• For both Adam and SGD without L2 weight decay, we observe that the magnitude of each vector's direction change depends on its L2-norm. We show that, using SGD with L2 weight decay implicitly normalizes the weight vectors, and thus remove the dependence in an approximate manner. We fix the problem for Adam by explicitly normalizing each weight vector, and by optimizing only its direction, such that the effective learning rate can be precisely controlled.• We further show that, without proper regularization, the learning signal backpropagated from the softmax layer may vary with the overall magnitude of the logits in an undesirable way. Based on the observation, we apply batch normalization or L2-regularization to the logits, which further improves the generalization performance in classification tasks.In essence, our proposed methods, ND-Adam and regularized softmax, improve the generalization performance of Adam by enabling more precise control over the directions of parameter updates, the learning rates, and the learning signals.",Optimization algorithms training deep models affects convergence rate stability training process are also highly related generalization performance trained models. adaptive algorithms Adam RMSprop have shown better optimization performance stochastic gradient descent SGD many scenarios is often lead worse generalization performance SGD when used training deep neural networks DNNs work identify two problems regarding direction step size updating weight vectors hidden units may degrade generalization performance Adam. solution propose normalized direction-preserving Adam ND-Adam algorithm which controls update direction step size precisely thus bridges generalization gap Adam SGD. Following similar rationale improve generalization performance classification tasks regularizing softmax logits. bridging gap SGD Adam are also shed light why certain optimization algorithms generalize better others. contrast growing complexity neural network architectures BID10 BID12 training methods remain relatively simple. practical optimization methods deep neural networks DNNs are based stochastic gradient descent SGD algorithm. However learning rate SGD hyperparameter is often difficult tune since magnitudes different parameters can vary widely adjustment is required throughout training process.To tackle problem several adaptive variants SGD have been developed including Adagrad BID6 Adadelta Zeiler 2012 RMSprop BID24 Adam BID15 etc. algorithms aim adapt learning rate different parameters automatically based statistics gradient. Although usually simplify learning rate settings lead faster convergence is observed generalization performance tend significantly worse SGD scenarios BID25. intriguing phenomenon may explain why SGD possibly momentum is still prevalent training state-of-the-art deep models especially feedforward DNNs BID10 BID12. Furthermore recent work has shown DNNs are capable fitting noise data BID31 suggesting generalization capabilities are not the mere result DNNs are entwined optimization BID2.This work aims bridge gap SGD Adam terms generalization performance. end identify two problems may degrade generalization performance Adam show how these problems are(partially avoided using SGD L2 weight decay. First updates SGD lie span historical gradients whereas is not the case Adam. difference has been discussed rather recent literature BID25 where the authors show adaptive methods can find drastically different worse solutions SGD. Second magnitudes Adam parameter updates are invariant rescaling gradient effect updates overall network function still varies magnitudes parameters. result effective learning rates weight vectors tend decrease training which leads sharp local minima do not generalize well BID11.To fix two problems Adam propose normalized direction-preserving Adam NDAdam algorithm which controls update direction step size precisely. show ND-Adam is able achieve significantly better generalization performance vanilla Adam matches SGD image classification tasks.We summarize contributions follows:• observe directions Adam parameter updates are different SGD.e Adam does not preserve directions gradients SGD does. fix problem adapting learning rate weight vector instead individual weight direction gradient is preserved.• Adam SGD without L2 weight decay observe magnitude vector's direction change depends L2-norm show using SGD L2 weight decay implicitly normalizes weight vectors thus remove dependence approximate manner. fix problem Adam explicitly normalizing weight vector optimizing direction effective learning rate can be precisely controlled.• show without proper regularization learning signal backpropagated softmax layer may vary overall magnitude logits undesirable way. Based observation apply batch normalization L2-regularization logits which further improves generalization performance classification tasks.In essence proposed methods ND-Adam regularized softmax improve generalization performance Adam enabling precise control directions parameter updates learning rates learning signals.,981,636,345,0.01,1.542,2025/11/05 17:18:53,0.01,1.406,0.660436137071651,323.049
"Options in reinforcement learning allow agents to hierarchically decompose a task into subtasks, having the potential to speed up learning and planning. However, autonomously learning effective sets of options is still a major challenge in the field. In this paper we focus on the recently introduced idea of using representation learning methods to guide the option discovery process. Specifically, we look at eigenoptions, options obtained from representations that encode diffusive information flow in the environment. We extend the existing algorithms for eigenoption discovery to settings with stochastic transitions and in which handcrafted features are not available.   We propose an algorithm that discovers eigenoptions while learning non-linear state representations from raw pixels. It exploits recent successes in the deep reinforcement learning literature and the equivalence between proto-value functions and the successor representation. We use traditional tabular domains to provide intuition about our approach and Atari 2600 games to demonstrate its potential. Sequential decision making usually involves planning, acting, and learning about temporally extended courses of actions over different time scales. In the reinforcement learning framework, options are a well-known formalization of the notion of actions extended in time; and they have been shown to speed up learning and planning when appropriately defined (e.g., BID4 BID9 BID24 . In spite of that, autonomously identifying good options is still an open problem. This problem is known as the problem of option discovery.Option discovery has received ample attention over many years, with varied solutions being proposed (e.g., BID0 BID5 BID20 BID8 BID13 BID20 BID21 . Recently, Machado et al. (2017) and BID31 proposed the idea of learning options that traverse directions of a latent representation of the environment. In this paper we further explore this idea.More specifically, we focus on the concept of eigenoptions BID16 , options learned using a model of diffusive information flow in the environment. They have been shown to improve agents' performance by reducing the expected number of time steps a uniform random policy needs in order to traverse the state space. Eigenoptions are defined in terms of proto-value functions (PVFs; BID18 , basis functions learned from the environment's underlying state-transition graph. PVFs and eigenoptions have been defined and thoroughly evaluated in the tabular case. Currently, eigenoptions can be used in environments where it is infeasible to enumerate states only when a linear representation of these states is known beforehand.In this paper we extend the notion of eigenoptions to stochastic environments with non-enumerated states, which are commonly approximated by feature representations. Despite methods that learn representations generally being more flexible, more scalable, and often leading to better performance, current algorithms for eigenoption discovery cannot be combined with representation learn-ing. We introduce an algorithm that is capable of discovering eigenoptions while learning representations. The learned representations implicitly approximate the model of diffusive information flow (hereafter abbreviated as the DIF model) in the environment. We do so by exploiting the equivalence between PVFs and the successor representation (SR; BID7 . Notably, by using the SR we also start to be able to deal with stochastic transitions naturally, a limitation of previous algorithms.We evaluate our algorithm in a tabular domain as well as on Atari 2600 games. We use the tabular domain to provide intuition about our algorithm and to compare it to the algorithms in the literature. Our evaluation in Atari 2600 games provides promising evidence of the applicability of our algorithm in a setting in which a representation of the agent's observation is learned from raw pixels. In this paper we introduced a new algorithm for eigenoption discovery in RL. Our algorithm uses the successor representation (SR) to estimate the model of diffusive information flow in the environment, leveraging the equivalence between proto-value functions (PVFs) and the SR. This approach circumvents several limitations from previous work: (i) it builds increasingly accurate estimates using a constant-cost update-rule; (ii) it naturally deals with stochastic MDPs; (iii) it does not depend on the assumption that the transition matrix is symmetric; and (iv) it does not depend on handcrafted feature representations. The first three items were achieved by simply using the SR instead of the PVFs, while the latter was achieved by using a neural network to estimate the SR.The proposed framework opens up multiple possibilities for investigation in the future. It would be interesting to evaluate the compositionality of eigenoptions, or how transferable they are between similar environments, such as the different modes of Atari 2600 games BID17 . Finally, now that the fundamental algorithms have been introduced, it would be interesting to investigate whether one can use eigenoptions to accumulate rewards instead of using them for exploration.",Options reinforcement learning allow agents hierarchically decompose task subtasks potential speed learning planning. However autonomously learning effective sets options is still major challenge field. paper focus recently introduced idea using representation learning methods guide option discovery process. Specifically look eigenoptions options obtained representations encode diffusive information flow environment. extend existing algorithms eigenoption discovery settings stochastic transitions which handcrafted features are not available. propose algorithm discovers eigenoptions learning non-linear state representations raw pixels. exploits recent successes deep reinforcement learning literature equivalence proto-value functions successor representation. use traditional tabular domains provide intuition approach Atari 2600 games demonstrate potential. Sequential decision making usually involves planning acting learning temporally extended courses actions different time scales. reinforcement learning framework options are a well-known formalization notion actions extended time;have been shown speed learning planning when appropriately defined e.g BID4 BID9 BID24. spite autonomously identifying good options is still open problem. problem is known problem option discovery.Option discovery has received ample attention many years varied solutions proposed e.g BID0 BID5 BID20 BID8 BID13 BID20 BID21. Recently Machadoetal. 2017 BID31 proposed idea learning options traverse directions latent representation environment. paper explore idea.More specifically focus concept eigenoptions BID16 options learned using model diffusive information flow environment. have been shown improve agents' performance reducing expected number time steps uniform random policy needs order traverse state space. Eigenoptions are defined terms proto-value functions PVFs;BID18 basis functions learned environment's underlying state-transition graph. PVFs eigenoptions have been defined thoroughly evaluated tabular case. Currently eigenoptions can be used environments where it is infeasible enumerate states when a linear representation states is known beforehand.In paper extend notion eigenoptions stochastic environments non-enumerated states which are commonly approximated feature representations. Despite methods learn representations generally flexible scalable often leading better performance current algorithms eigenoption discovery cannot combined representation learn-ing introduce algorithm is capable discovering eigenoptions learning representations. learned representations implicitly approximate model diffusive information flow hereafter abbreviated DIF model environment. do so by exploiting equivalence PVFs successor representation SR;BID7. Notably using SR also start able deal stochastic transitions naturally limitation previous algorithms.We evaluate algorithm tabular domain well Atari 2600 games. use tabular domain provide intuition algorithm compare algorithms literature. evaluation Atari 2600 games provides promising evidence applicability algorithm setting which a representation agent's observation is learned raw pixels. paper introduced new algorithm eigenoption discovery RL. algorithm uses successor representation SR estimate model diffusive information flow environment leveraging equivalence proto-value functions PVFs SR. approach circumvents several limitations previous work:builds increasingly accurate estimates using constant-cost update-rule ii naturally deals stochastic MDPs;iii does not depend assumption transition matrix is symmetric;iv does not depend handcrafted feature representations. first three items were achieved simply using SR instead PVFs latter was achieved using neural network estimate SR.The proposed framework opens multiple possibilities investigation future. would interesting evaluate compositionality eigenoptions how transferable are between similar environments different modes Atari 2600 games BID17. Finally fundamental algorithms have been introduced would interesting investigate whether one can use eigenoptions accumulate rewards instead using exploration.,938,627,311,0.009,1.496,2025/11/05 17:18:53,0.0,1.593,0.5171339563862927,308.591
"One form of characterizing the expressiveness of a piecewise linear neural network is by the number of linear regions, or pieces, of the function modeled. We have observed substantial progress in this topic through lower and upper bounds on the maximum number of linear regions and a counting procedure. However, these bounds only account for the dimensions of the network and the exact counting may take a prohibitive amount of time, therefore making it infeasible to benchmark the expressiveness of networks. In this work, we approximate the number of linear regions of specific rectifier networks with an algorithm for probabilistic lower bounds of mixed-integer linear sets. In addition, we present a tighter upper bound that leverages network coefficients. We test both on trained networks. The algorithm for probabilistic lower bounds is several orders of magnitude faster than exact counting and the values reach similar orders of magnitude, hence making our approach a viable method to compare the expressiveness of such networks. The refined upper bound is particularly stronger on networks with narrow layers.   Neural networks with piecewise linear activations have become increasingly more common along the past decade, in particular since BID40 and BID25 . The simplest and most commonly used among such forms of activation is the Rectifier Linear Unit (ReLU), which outputs the maximum between 0 and its input argument BID30 BID35 . In the functions modeled by these networks, we can associate each part of the domain in which the network corresponds to an affine function with a particular set of units having positive outputs. We say that those are the active units for that part of the domain. Counting these ""pieces"" into which the domain is split, which are often denoted as linear regions or decision regions, is one way to compare the expressiveness of models defined by networks with different configurations or coefficients. The theoretical analysis of the number of input regions in deep learning dates back to at least BID8 , and more recently BID45 have shown empirical evidence that the accuracy of similar rectifier networks can be associated with the number of such regions.From the study of how many linear regions can be defined on such a rectifier network with n ReLUs, we already know that not all configurations -and in some cases none -can reach the ceiling of 2 n regions. We have learned that the number of regions may depend on the dimension of the input as well as on the number of layers and how the units are distributed among these layers. On the one hand, it is possible to obtain neural networks where the number of regions is exponential on network depth . On the other hand, there is a bottleneck effect by which the width of each layer affects how the regions are partitioned by subsequent layers due to the dimension of the space containing the image of the function, up to the point that shallow networks define the largest number of linear regions if the input dimension exceeds n BID45 .The literature on this topic has mainly focused on bounding the maximum number of linear regions. Lower bounds are obtained by constructing networks defining increasingly larger number of linear regions BID2 BID45 . Upper bounds are proven using the theory of hyperplane arrangements by BID54 along with other analytical insights BID44 BID38 BID45 . These bounds are only identical -and thus tight -in the case of one-dimensional inputs BID45 . Both of these lines have explored deepening connections with polyhedral theory, but some of these results have also been recently revisited using tropical algebra BID55 BID13 . In addition , BID45 have shown that the linear regions of a trained network correspond to a set of projected solutions of a Mixed-Integer Linear Program (MILP).Other methods to study neural network expressiveness include universal approximation theory BID16 , VC dimension BID5 , and trajectory length BID44 . Different networks can be compared by transforming one network to another with different number of layers or activation functions. For example, it has been shown that any continuous function can be modeled using a single hidden layer of sigmoid activation functions BID16 . In the context of ReLUs , BID36 have shown that the popular ResNet architecture BID31 with a single ReLU neuron in every hidden layer can be a universal approximator. Furthermore, BID2 have shown that a network with single hidden layer of ReLUs can be trained for global optimality with a runtime polynomial in the data size, but exponential in the input dimension. The use of trajectory length for expressiveness is related to linear regions, i.e., by changing the input along a one dimensional path we study the transition in the linear regions.Certain critical network architectures using leaky ReLUs (f (x) = max(x, αx), α ∈ (0, 1)) are identified to produce connected decision regions BID42 . In order to avoid such degenerate cases, we need to use sufficiently wide hidden layers. However, this result is mainly applicable for leaky ReLUs and not for the standard ReLUs BID7 .Although the number of linear regions has been long conjectured and recently shown to work for comparing similar networks, this metric would only be used in practice if we come up with faster methods to count or reasonably approximate such number. Our approach in this paper consists of introducing empirical upper and lower bounds, both of which based on the weight and bias coefficients of the networks, and thus able to compare networks having the same configuration of layers.In particular, we reframe the problem of determining the potential number of linear regions N of an architecture with that of estimating the representation efficiency η = log 2 N of a network, which can be interpreted as the minimum number of units to define as many linear regions, thereby providing a more practical and interpretable metric for expressiveness. We present the following contributions:(i ) We adapt approximate model counting methods for propositional satisfiability (SAT) to obtain probabilistic bounds on the number of solutions of MILP formulations, which we use to count regions. Interestingly, these methods are particularly simpler and faster when restricted to lower bounds on the order of magnitude. See results in FIG2 and algorithm in Section 5. (ii) We refine the best known upper bound by considering the coefficients of the trained network.With such information, we identify that unit activity further contributes to the bottleneck effect caused by narrow layers BID45 . Furthermore, we are able to compare networks with the same configuration of layers. See results in Table 1 and theory in Section 4. (iii) We also survey and contribute to the literature on MILP formulations of rectifier networks due to the impact of the formulation on obtaining better empirical bounds. See Section 3. This paper introduced methods to obtain upper and lower bounds on a rectifier network. The upper bound refines the best known result for the network configuration by taking into account the coefficients of the network. By analyzing how the network coefficients affect when each unit can be active, we break the commonly used theoretical assumption that the activation hyperplane of each unit intersects every linear region defined by the previous layers. The resulting bound is particularly stronger when the network has a narrow layer, hence evidencing that the bottleneck effected identified by BID45 can be even stronger in those cases. The lower bound is based on extending an approximate model counting algorithm of SAT formulas to MILP formulations, which can then be used on MILP formulations of rectifier networks. The resulting algorithm is orders of magnitude faster than exact counting on networks with a large number of linear regions. The probabilistic bounds obtained can be parameterized for a balance between precision and speed, but it is interesting to observe that the the bounds obtained for different networks preserve a certain ordering in their sizes as we make the estimate more precise. Hence, we have some indication that faster approximations could suffice if we just want to compare networks for their relative expressiveness.Algorithm 1 Computes probabilistic lower bounds on the number of distinct solutions on n binary variables of a formulation F using parity constraints of size k DISPLAYFORM0 end for 6:while Termination criterion not satisfied do 7:F ← F Start over with F as formulation F 8: DISPLAYFORM1 Number of times that we have made F infeasible 9:r ← 0 Number of parity constraints added this time 10:while F has some solution s do 11:repeat 12:Generate parity constraint C of size k among n variables 13: DISPLAYFORM2 r ← r + 1 15: until C removes s This loop is implemented as a lazy cut callback 16: end while 17: DISPLAYFORM3 Number of times that F is feasible after adding j constraints 19:end for 20:end while 21:for j ← 0 → n − 1 do Computes probabilities after last call to the solver 22: BID46 and BID47 used these functions to show that approximate counting can be done in polynomial time with an NP-oracle, whereas BID50 have shown that SAT formulas with unique solution are as hard as those with multiple solutions. Hence, from a theoretical standpoint, such approximations are not much harder than solving for a single solution. DISPLAYFORM4 The seminal work by BID26 introduced the MBound algorithm, where XOR constraints on sets of variables with a fixed size k are used to compute the probability that 2 r is either a lower or an upper bound. These probabilistic lower bounds are always valid but get better as k increases, whereas the probabilistic upper bound is only valid if k = |V |/2. However, BID29 have shown that these lower bounds can be very good in practice for small values of k. The same principles have also been applied to constraint satisfaction problems BID28 .With time, this topic has gradually shifted to more precise estimates and to reducing the value of k needed to obtain valid upper bounds. Some of the subsequent work has been influenced by uniform sampling results from BID27 , where the fixed size k is replaced with an independent probability p of including each variable in each XOR constraint. That work includes the ApproxMC and the WISH algorithms BID10 BID21 , which rely on finding more solutions of the restricted formulas but generate (σ, ) certificates by which, with probability 1 − σ, the result is within (1 ± )|S|. The following work by BID22 and BID56 aimed at providing upper bound guarantees when p < 1/2, showing that the size of those sets can be Θ log(|V |) . Other groups tackled this issue differently. BID11 and BID33 have limited the counting to any set of variables I for which any assignment leads to at most one solution in V , denoting those as minimal independent supports. BID0 and BID1 have broken with the independent probability p by using each variable the same number of times across the r XOR constraints.","One form characterizing expressiveness piecewise linear neural network is by the number linear regions pieces function modeled. have observed substantial progress topic lower upper bounds maximum number linear regions counting procedure. However bounds account dimensions network exact counting may take prohibitive amount time therefore making infeasible benchmark expressiveness networks. work approximate number linear regions specific rectifier networks algorithm probabilistic lower bounds mixed-integer linear sets. addition present tighter upper bound leverages network coefficients. test trained networks. algorithm probabilistic lower bounds is several orders magnitude faster exact counting values reach similar orders magnitude hence making approach viable method compare expressiveness networks. refined upper bound is particularly stronger networks narrow layers. Neural networks piecewise linear activations have become increasingly common along past decade particular since BID40 BID25. simplest commonly used among forms activation is the Rectifier Linear Unit ReLU which outputs maximum 0 input argument BID30 BID35. functions modeled networks can associate part domain which the network corresponds affine function particular set units positive outputs. say are the active units part domain. Counting pieces which the domain is split which are often denoted linear regions decision regions is one way compare expressiveness models defined networks different configurations coefficients. theoretical analysis number input regions deep learning dates back least BID8 recently BID45 have shown empirical evidence accuracy similar rectifier networks can be associated number regions.From study how many linear regions can be defined rectifier network n ReLUs already know configurations -and cases none -can reach ceiling 2 n regions. have learned number regions may depend dimension input well number layers how the units are distributed among layers. one hand is possible obtain neural networks where the number regions is exponential network depth. hand is a bottleneck effect which the width layer affects how the regions are partitioned subsequent layers due dimension space containing image function point shallow networks define largest number linear regions if the input dimension exceedsn BID45.The literature topic has mainly focused bounding maximum number linear regions. Lower bounds are obtained constructing networks defining increasingly larger number linear regions BID2 BID45. Upper bounds are proven using theory hyperplane arrangements BID54 along analytical insights BID44 BID38 BID45. bounds are only identical -and thus tight -in case one-dimensional inputs BID45. lines have explored deepening connections polyhedral theory results have also recently revisited using tropical algebra BID55 BID13. addition BID45 have shown linear regions trained network correspond set projected solutions Mixed-Integer Linear Program MILP.Other methods study neural network expressiveness include universal approximation theory BID16 VC dimension BID5 trajectory length BID44. Different networks can be compared transforming one network another different number layers activation functions. example has been shown continuous function can be modeled using single hidden layer sigmoid activation functions BID16. context ReLUs BID36 have shown popular ResNet architecture BID31 single ReLU neuron every hidden layer can be a universal approximator. Furthermore BID2 have shown network single hidden layer ReLUs can be trained global optimality runtime polynomial data size exponential input dimension. use trajectory length expressiveness is related linear regions.e changing input along one dimensional path study transition linear regions.Certain critical network architectures using leaky ReLUs f x max x αx α∈ 0 1 are identified produce connected decision regions BID42. order avoid degenerate cases need use sufficiently wide hidden layers. However result is mainly applicable leaky ReLUs standard ReLUs BID7.Although number linear regions has been long conjectured recently shown work comparing similar networks metric would used practice if we come faster methods count reasonably approximate number. approach paper consists introducing empirical upper lower bounds which based weight bias coefficients networks thus able compare networks configuration layers.In particular reframe problem determining potential number linear regionsN architecture estimating representation efficiencyη log2N network which can be interpreted minimum number units define many linear regions thereby providing practical interpretable metric expressiveness. present following contributions:adapt approximate model counting methods propositional satisfiability SAT obtain probabilistic bounds number solutions MILP formulations which we use count regions. Interestingly methods are particularly simpler faster when restricted lower bounds order magnitude. See results FIG2 algorithm Section5. ii refine best known upper bound considering coefficients trained network.With information identify unit activity contributes bottleneck effect caused narrow layers BID45. Furthermore are able compare networks configuration layers. See results Table1 theory Section4. iii also survey contribute literature MILP formulations rectifier networks due impact formulation obtaining better empirical bounds. See Section3. paper introduced methods obtain upper lower bounds rectifier network. upper bound refines best known result network configuration taking account coefficients network. analyzing how the network coefficients affect when each unit can be active break commonly used theoretical assumption activation hyperplane unit intersects every linear region defined previous layers. resulting bound is particularly stronger when the network has a narrow layer hence evidencing bottleneck effected identified BID45 can be even stronger cases. lower bound is based extending approximate model counting algorithm SAT formulas MILP formulations which can then used MILP formulations rectifier networks. resulting algorithm is orders magnitude faster exact counting networks large number linear regions. probabilistic bounds obtained can be parameterized balance precision speed is interesting observe bounds obtained different networks preserve certain ordering sizes make estimate precise. Hence have some indication faster approximations could suffice if we just want compare networks relative expressiveness.Algorithm 1 Computes probabilistic lower bounds number distinct solutions n binary variables formulation F using parity constraints size k DISPLAYFORM0 end 6:Termination criterion satisfied do7:F ← F Start F formulationF8:DISPLAYFORM1 Number times have made F infeasible9:r ← 0 Number parity constraints added time10:F has some solution do11:repeat12:Generate parity constraintC size k amongn variables13:DISPLAYFORM2r←r+115:C removes loop is implemented lazy cut callback16:end 17:DISPLAYFORM3 Number times F is feasible adding j constraints19:end 20:end 21:j←0→ n−1 do Computes probabilities last call solver22:BID46 BID47 used functions show approximate counting can be done polynomial time NP-oracle whereas BID50 have shown SAT formulas unique solution are as hard multiple solutions. Hence theoretical standpoint approximations are not much harder solving single solution. DISPLAYFORM4 seminal work BID26 introduced MBound algorithm where XOR constraints sets variables fixed sizek are used compute probability 2r is either lower upper bound. probabilistic lower bounds are always valid get better k increases whereas probabilistic upper bound is only valid ifk |V/2. However BID29 have shown lower bounds can be very good practice small values k. principles have also applied constraint satisfaction problems BID28.With time topic has gradually shifted precise estimates reducing value k needed obtain valid upper bounds. subsequent work has been influenced uniform sampling results BID27 where the fixed sizek is replaced independent probabilityp including variable XOR constraint. work includes ApproxMC WISH algorithms BID10 BID21 which rely finding solutions restricted formulas generate σ certificates which,with probability1−σ result is within 1± |S|. following work BID22 BID56 aimed providing upper bound guarantees whenp 1/2 showing size sets can be Θ log |V groups tackled issue differently. BID11 BID33 have limited counting set variables which any assignment leads one solution V denoting minimal independent supports. BID0 BID1 have broken independent probabilityp using variable number times across r XOR constraints.",2164,1457,707,0.033,1.485,2025/11/05 17:18:53,0.01,1.559,0.4828660436137073,766.237
"The ability to look multiple times through a series of pose-adjusted glimpses is fundamental to human vision. This critical faculty allows us to understand highly complex visual scenes. Short term memory plays an integral role in aggregating the information obtained from these glimpses and informing our interpretation of the scene. Computational models have attempted to address glimpsing and visual attention but have failed to incorporate the notion of memory. We introduce a novel, biologically inspired visual working memory architecture that we term the Hebb-Rosenblatt memory. We subsequently introduce a fully differentiable Short Term Attentive Working Memory model (STAWM) which uses transformational attention to learn a memory over each image it sees. The state of our Hebb-Rosenblatt memory is embedded in STAWM as the weights space of a layer. By projecting different queries through this layer we can obtain goal-oriented latent representations for tasks including classification and visual reconstruction. Our model obtains highly competitive classification performance on MNIST and CIFAR-10. As demonstrated through the CelebA dataset, to perform reconstruction the model learns to make a sequence of updates to a canvas which constitute a parts-based representation. Classification with the self supervised representation obtained from MNIST is shown to be in line with the state of the art models (none of which use a visual attention mechanism). Finally, we show that STAWM can be trained under the dual constraints of classification and reconstruction to provide an interpretable visual sketchpad which helps open the `black-box' of deep learning. Much of the current effort and literature in deep learning focuses on performance from a statistical pattern recognition perspective. In contrast, we go back to a biological motivation and look to build a model that includes aspects of the human visual system. The eminent computational neuroscientist David Marr posited that vision is composed of stages which lead from a two dimensional input to a three dimensional contextual model with an established notion of object BID27 . This higher order model is built up in the visual working memory as a visual sketchpad which integrates notions of pattern and texture with a notion of pose BID3 . Visual attention models often draw inspiration from some of these concepts and perform well at various tasks BID0 BID1 BID12 BID18 BID38 . Inspired by vision in nature, visual attention corresponds to adaptive filtering of the model input, typically, through the use of a glimpsing mechanism which allows the model to select a portion of the image to be processed at each step. Broadly speaking, visual attention models exist at the crux of two key challenges. The first is to separate notions of pose and object from visual features. The second is to effectively model long range dependencies over a sequence of observations.Various models have been proposed and studied which hope to enable deep networks to construct a notion of pose. For example, transformational attention models learn an implicit representation of object pose by applying a series of transforms to an image BID18 BID0 . Other models such as Transformational Autoencoders and Capsule Networks harness an explicit understanding of positional relationships between objects BID16 BID36 . Short term memories have previously been studied as a way of improving the ability of Recurrent Neural Networks (RNNs) to learn long range dependencies. The ubiquitous Long Short-Term Memory (LSTM) network is perhaps the most commonly used example of such a model BID17 . More recently, the fast weights model, proposed by BID2 provides a way of imbuing recurrent networks with an ability to attend to the recent past.From these approaches, it is evident that memory is a central requirement for any method which attempts to augment deep networks with the ability to attend to visual scenes. The core concept which underpins memory in neuroscience is synaptic plasticity, the notion that synaptic efficacy, the strength of a connection, changes as a result of experience BID33 . These changes occur at multiple time scales and, consequently, much of high level cognition can be explained in terms of the interplay between immediate, short and long term memories. An example of this can be found in vision, where each movement of our eyes requires an immediate contextual awareness and triggers a short term change. We then aggregate these changes to make meaningful observations over a long series of glimpses. Fast weights BID2 draw inspiration from the Hebbian theory of learning BID14 which gives a framework for how this plasticity may occur. Furthermore, differentiable plasticity BID28 combines neural network weights with weights updated by a Hebbian rule to demonstrate that backpropagation can be used to learn a substrate over which the plastic network acts as a content-addressable memory.In this paper, we propose augmenting transformational attention models with a visual working memory in order to move towards two key goals. Firstly, we wish to understand if visual attention and working memory provide more than just increased efficiency and enable functions that cannot otherwise be achieved. Secondly, we wish to understand and seek answers to some of the challenges faced when attempting to model such psychophysical concepts in deep networks. We demonstrate classification performance on MNIST (LeCun, 1998) and CIFAR-10 ( BID21 ) that is competitive with the state of the art and vastly superior to previous models of attention, demonstrating the value of a working memory. We then demonstrate that it is possible to learn this memory representation in an unsupervised manner by painting images, similar to the Deep Recurrent Attentive Writer (DRAW) network BID12 . Using this representation, we demonstrate competitive classification performance on MNIST with self supervised features. Furthermore, we demonstrate that the model can learn a disentangled space over the images in CelebA BID25 , shedding light on some of the higher order functions that are enabled by visual attention. Finally, we show that the model can perform multiple tasks in parallel and how a visual sketchpad can be used to produce interpretable classifiers. In this paper we have described a novel, biologically motivated short term attentive working memory model (STAWM) which demonstrates impressive results on a series of tasks and makes a strong case for further study of short term memories in deep networks. As well as demonstrating competitive classification results on MNIST and CIFAR-10, we have shown that the core model can be used for image reconstruction and for disentangling foreground from background in an unsupervised setting with CelebA. Finally, we have given a concrete example of how a model augmented with a visual sketchpad can 'describe what it sees' in a way that is naturally interpretable for humans. It is easy to see how similar systems could be used in future technologies to help open the 'black-box' and understand why a decision was made, through the eyes of the model that made it. Furthermore, we have explored the notion that building up a memory representation over an attention policy, coupled with a smooth changing latent space can result in a movement from simple to complex regions of a scene. This perhaps gives us some insight into how humans learn to attend to their environment when endowed with a highly capable visual memory. Future work will look to see if variants of this model can be used to good effect on higher resolution images. Experimentation and analysis should also be done to further understand the dynamics of the Hebb-Rosenblatt memory and the representation it learns. We further intend to investigate if the memory model can be used for other applications such as fusion of features from multi-modal inputs. Finally, we will look further into the relationship between visual memories and saliency.A STABILISING THE MEMORY The working memory model described in the paper exhibits a potential issue with stability. It is possible for the gradient to explode, causing damaging updates which halt learning and from which the model cannot recover. In this section we will briefly demonstrate some properties of the learning rule in Equation 2 and derive some conditions under which the dynamics are stable. We will broadly follow the method of with minor alterations for our approach. We use the terms stimuli and response to represent input to and output from a neuron respectively. We will consider a sequence of DISPLAYFORM0 Hg×Wg , presented to L I when attending to a single image. ν as the identity input to some ν ∈ L II . We then define γ DISPLAYFORM1 ν , the projection of e (i) through the weights matrix W ∈ R M ×M . The total input to ν if stimulus i is presented to L I at time t is the sum of these two terms given in Equation 9. DISPLAYFORM2 Suppose that a stimulus i is presented at time t 0 for some period ∆t. The subsequent change in the weight, w µν , of some connection is defined in Equation 10, where φ II is a nonlinear activation function of neurons in L II . Note that the change in the matrix W for this step is the learning rule in Equation 2. DISPLAYFORM3 From FORMULA1 and (8) we derive Equation 11 which gives the change in the weighted component γ (q) ν for some query stimulus q over a single time step. We omit the subscript ν for brevity. The response of L II to q is the latent representation derived from the memory during the glimpse sequence. DISPLAYFORM4 The next step in is to define some sequence over the set of possible stimuli to be presented in order. We deviate slightly here as our sequence is not drawn from a bounded set. Instead, as we have seen, each glimpse is a sample from the manifold space of affine transforms over the image. As such, in Equation 12 we generalise Equation 11 to represent the change in the query response for some arbitrary point, n, in the sequence, with stimulus g n at time t + n∆t. Summing over the whole sequence we obtain Equation 13. We can now obtain an expression for the gradient of Equation 13 by dividing by N ∆t in the limit of ∆t → 0 (Equation 14). DISPLAYFORM5 DISPLAYFORM6 Although Equation 14 is only an approximation of the dynamics of the system, we have demonstrated stability under certain conditions: firstly, the input to the memory network must not vary with time. This is satisfied in the case where the feature vector is not dependent on the output of a recurrent network. It is possible to extend this proof to incorporate such networks BID35 , however, that is outside the scope of this paper. Secondly, the activation functions must be nonnegative and have an upper bound (as with ReLU6 or Sigmoid). This introduces an interesting similarity as there is an upper bound to the number of times a real neuron can fire in a given window, governed by its refractory period. Finally, we can observe that Equation 15 is nondecreasing iff η is greater than δ, δ is positive and η and θ are nonnegative.",ability look multiple times series pose-adjusted glimpses is fundamental human vision. critical faculty allowsus understand highly complex visual scenes. Short term memory plays integral role aggregating information obtained glimpses informing interpretation scene. Computational models have attempted address glimpsing how a visual attention have failed incorporate notion memory. introduce novel biologically inspired visual working memory architecture term Hebb-Rosenblatt memory. subsequently introduce fully differentiable Short Term Attentive Working Memory model STAWM which uses transformational attention learn memory image sees. state Hebb-Rosenblatt memory is embedded STAWM weights space layer. projecting different queries layer can obtain goal-oriented latent representations tasks including classification how a visual reconstruction. model obtains highly competitive classification performance MNIST CIFAR-10 demonstrated CelebA dataset perform reconstruction model learns make sequence updates canvas which constitute parts-based representation. Classification self supervised representation obtained MNIST is shown line state art models none which use visual attention mechanism Finally show STAWM can be trained dual constraints classification reconstruction provide interpretable visual sketchpad which helps open black-box' deep learning. Much current effort literature deep learning focuses performance statistical pattern recognition perspective. contrast go back biological motivation look build model includes aspects human visual system. eminent computational neuroscientist David Marr posited vision is composed stages which lead two dimensional input three dimensional contextual model established notion object BID27. higher order model is built visual working memory visual sketchpad which integrates notions pattern texture notion pose BID3. Visual attention models often draw inspiration concepts perform well various tasks BID0 BID1 BID12 BID18 BID38. Inspired vision nature visual attention corresponds adaptive filtering how a model input typically use glimpsing mechanism which allows model select portion image processed step. Broadly speaking visual attention models exist crux two key challenges. first is to separate notions pose object visual features. second is to effectively model long range dependencies sequence observations.Various models have been proposed studied which hope enable deep networks construct notion pose. example transformational attention models learn implicit representation object pose applying series transforms image BID18 BID0. models Transformational Autoencoders Capsule Networks harness explicit understanding positional relationships objects BID16 BID36. Short term memories have previously studied way improving ability Recurrent Neural Networks RNNs learn long range dependencies. ubiquitous Long Short-Term Memory LSTM network is perhaps commonly used example how a model BID17. recently fast weights model proposed BID2 provides way imbuing recurrent networks ability attend recent past.From approaches is evident memory is a central requirement method which attempts augment deep networks ability attend visual scenes. core concept which underpins memory neuroscience is synaptic plasticity notion synaptic efficacy strength connection changes result experience BID33. changes occur multiple time scales consequently much high level cognition can be explained terms interplay immediate short long term memories. example can be found vision where each movement eyes requires immediate contextual awareness triggers short term change. aggregate changes make meaningful observations long series glimpses. Fast weights BID2 draw inspiration Hebbian theory learning BID14 which gives framework how this plasticity may occur. Furthermore differentiable plasticity BID28 combines neural network weights weights updated Hebbian rule demonstrate backpropagation can be used learn substrate which the plastic network acts content-addressable memory.In paper propose augmenting transformational attention models visual working memory order move towards two key goals. Firstly wish understand if visual attention working memory provide increased efficiency enable functions cannot otherwise achieved. Secondly wish understand seek answers challenges faced when attempting model psychophysical concepts deep networks. demonstrate classification performance MNIST LeCun 1998 CIFAR-10 BID21 is competitive state art vastly superior previous models attention demonstrating value working memory. demonstrate is possible learn memory representation unsupervised manner painting images similar Deep Recurrent Attentive Writer DRAW network BID12. Using representation demonstrate competitive classification performance MNIST self supervised features. Furthermore demonstrate model can learn disentangled space images CelebA BID25 shedding light higher order functions are enabled visual attention. Finally show model can perform multiple tasks parallel how a visual sketchpad can be used produce interpretable classifiers. paper have described novel biologically motivated short term attentive working memory model STAWM which demonstrates impressive results series tasks makes strong case study short term memories deep networks. well demonstrating competitive classification results MNIST CIFAR-10 have shown core model can be used image reconstruction disentangling foreground background unsupervised setting CelebA. Finally have given concrete example how a model augmented visual sketchpad can 'describe what it sees' way is naturally interpretable humans. is easy see how similar systems could used future technologies help open 'black-box' understand why a decision was made eyes how a model made it. Furthermore have explored notion building memory representation attention policy coupled smooth changing latent space can result movement simple complex regions scene. perhaps givesus insight how humans learn attend environment when endowed highly capable visual memory. Future work will look see if variants how a model can be used good effect higher resolution images. Experimentation analysis should also done understand dynamics Hebb-Rosenblatt memory representation learns. intend investigate if the memory model can be used applications fusion features multi-modal inputs. Finally will look relationship visual memories saliency.A STABILISING MEMORY working memory model described paper exhibits potential issue stability. is possible gradient explode causing damaging updates which halt learning which the model cannot recover. section will briefly demonstrate properties learning rule Equation2 derive conditions which the dynamics are stable. will broadly follow method minor alterations approach. use terms stimuli response represent input output neuron respectively. will consider sequence DISPLAYFORM0 Hg×Wg presented L when attending single image. ν identity input ν∈LII. define γ DISPLAYFORM1ν projection e weights matrixW∈ R ×M total input ν if stimulus is presented L time is the sum two terms given Equation9. DISPLAYFORM2 Suppose stimulus is presented time 0 period∆t subsequent change weight wµν connection is defined Equation10 whereφII is a nonlinear activation function neurons LII. Note change matrixW step is the learning rule Equation2. DISPLAYFORM3 FORMULA1 8 derive Equation11 which gives change weighted componentγ q ν query stimulusq single time step. omit subscriptν brevity. response LII q is the latent representation derived memory glimpse sequence. DISPLAYFORM4 next step is to define sequence set possible stimuli presented order. deviate slightly sequence is not drawn bounded set. Instead have seen glimpse is a sample manifold space affine transforms image. Equation12 generalise Equation11 represent change query response arbitrary point n sequence stimulusgn time+n∆t Summing whole sequence can obtain Equation13. can now obtain expression gradient Equation13 dividing N∆t limit ∆t→0 Equation14 DISPLAYFORM5 DISPLAYFORM6 Although Equation 14 is only an approximation dynamics system have demonstrated stability certain conditions:firstly input memory network must vary time. is satisfied case where the feature vector is not dependent output recurrent network. is possible extend proof incorporate networks BID35 however is outside scope paper. Secondly activation functions must nonnegative have an upper bound ReLU6 Sigmoid introduces interesting similarity is an upper bound number times real neuron can fire given window governed refractory period. Finally can observe Equation15 is nondecreasing iffη is greater δ δ is positive η θ are nonnegative.,2164,1431,733,0.029,1.512,2025/11/05 17:18:53,0.01,1.323,0.5669781931464173,778.757
"Generative models have been successfully applied to image style transfer and domain translation. However, there is still a wide gap in the quality of results when learning such tasks on musical audio. Furthermore, most translation models only enable one-to-one or one-to-many transfer by relying on separate encoders or decoders and complex, computationally-heavy models. In this paper, we introduce the Modulated Variational auto-Encoders (MoVE) to perform musical timbre transfer. First, we define timbre transfer as applying parts of the auditory properties of a musical instrument onto another. We show that we can achieve and improve this task by conditioning existing domain translation techniques with Feature-wise Linear Modulation (FiLM). Then, by replacing the usual adversarial translation criterion by a Maximum Mean Discrepancy (MMD) objective, we alleviate the need for an auxiliary pair of discriminative networks. This allows a faster and more stable training, along with a controllable latent space encoder. By further conditioning our system on several different instruments, we can generalize to many-to-many transfer within a single variational architecture able to perform multi-domain transfers. Our models map inputs to 3-dimensional representations, successfully translating timbre from one instrument to another and supporting sound synthesis on a reduced set of control parameters. We evaluate our method in reconstruction and generation tasks while analyzing the auditory descriptor distributions across transferred domains. We show that this architecture incorporates generative controls in multi-domain transfer, yet remaining rather light, fast to train and effective on small datasets.",Generative models have been successfully applied image style transfer domain translation. However is still wide gap quality results when learning tasks musical audio. Furthermore translation models enable one-to-one one-to-many transfer relying separate encoders decoders complex computationally-heavy models. paper introduce Modulated Variational auto-Encoders MoVE perform musical timbre transfer. First define timbre transfer applying parts auditory properties musical instrument onto another. show can achieve improve task conditioning existing domain translation techniques Feature-wise Linear Modulation FiLM replacing usual adversarial translation criterion Maximum Mean Discrepancy MMD objective alleviate need auxiliary pair discriminative networks. allows faster stable training along controllable latent space encoder. conditioning system several different instruments can generalize many-to-many transfer within single variational architecture able perform multi-domain transfers. models map inputs 3-dimensional representations successfully translating timbre one instrument another supporting sound synthesis reduced set control parameters. evaluate method reconstruction generation tasks analyzing auditory descriptor distributions across transferred domains. show architecture incorporates generative controls multi-domain transfer yet remaining rather light fast train effective small datasets.,306,209,97,0.003,1.464,2025/11/05 17:18:53,0.0,1.2,0.4174454828660433,101.105
"We study the behavior of weight-tied multilayer vanilla autoencoders under the assumption of random weights. Via an exact characterization in the limit of large dimensions, our analysis reveals interesting phase transition phenomena when the depth becomes large. This, in particular, provides quantitative answers and insights to three questions that were yet fully understood in the literature. Firstly, we provide a precise answer on how the random deep weight-tied autoencoder model performs “approximate inference” as posed by Scellier et al. (2018), and its connection to reversibility considered by several theoretical studies. Secondly, we show that deep autoencoders display a higher degree of sensitivity to perturbations in the parameters, distinct from the shallow counterparts. Thirdly, we obtain insights on pitfalls in training initialization practice, and demonstrate experimentally that it is possible to train a deep autoencoder, even with the tanh activation and a depth as large as 200 layers, without resorting to techniques such as layer-wise pre-training or batch normalization. Our analysis is not specific to any depths or any Lipschitz activations, and our analytical techniques may have broader applicability. The autoencoder is a cornerstone in machine learning, first as a response to the unsupervised learning problem (Rumelhart & Zipser (1985) ), then with applications to dimensionality reduction (Hinton & Salakhutdinov (2006) ), unsupervised pre-training (Erhan et al. (2010) ), and also as a precursor to many modern generative models (Goodfellow et al. (2016) ). Its reconstruction power is well utilized in applications such as anomaly detection (Chandola et al. (2009) ) and image recovery (Mousavi et al. (2015) ). With the surge of deep learning, thousands of papers have studied multilayer variants of this architecture, but theoretical understanding has been limited, since analyzing the learning dynamics of a highly nonlinear structure is typically a difficult problem even for the shallow autoencoder. To get around this, we tackle the task with a critical assumption: the weights are random and the autoencoder is weight-tied. One enjoys much analytical tractability from the randomness assumption, whereas weight tying enforces the random autoencoder to perform ""autoencoding"". We also study this in the high-dimensional setting, where all dimensions are comparably large and ideally jointly approaching infinity. We consider the simplest setting: vanilla autoencoders (i.e., ones with fully connected layers only) and their reconstruction capability. This is done for the sake of understanding the effect of depth, while we note our techniques may have broader applicability.The aforementioned assumptions are not without justifications. There is a growing literature on deep neural networks with random weights, (Li & Saad (2018) ; Giryes et al. (2016) ; Poole et al. (2016) ; Schoenholz et al. (2016) ; Gabrié et al. (2018) ; Amari et al. (2018) ) to name a few, revealing certain properties of deep feedforward networks 1 . Several recent works have also studied random multilayer feedforward networks through the lens of statistical inference (Manoel et al. (2017) ; Reeves (2017); Fletcher et al. (2018) ). The idea of weight tying is considered in the important paper Vincent et al. (2010) with an empirical finding that autoencoders with and without weight tying perform comparably, and has become standard in autoencoders. Similar features of random connection and symmetry also appear in other neural models (Lillicrap et al. (2016) ; Scellier et al. (2018) ). Finally the high-dimensional setting is common in recent statistical learning advances (Bühlmann & Van De Geer (2011) ), and not too far from the actual practice where many large datasets have dimensions of at least a few hundreds and are harnessed by large-scaled models.We seek quantitative answers to three specific questions that are motivated by previous works:• In exactly what way does the (vanilla) random weight-tied autoencoder perform ""approximate inference""? This term is coined in Scellier et al. (2018) in connection with the theoretical results in Arora et al. (2015) , which implicitly studies the said model. In particular, Arora et al. (2015) proves an upper bound on x − x 2 , where x andx are the input and the output of the network, but is limited in the number of layers and specific to the ReLU activation. This direction has been recently extended by Gilbert et al. (2017) . In our work, we establish precisely what this approximate inference is by obtaining a general and asymptotically exact characterization 2 ofx, for any number of layers and any Lipschitz continuous activations (Theorem 1 and Section 3.3). Theorem 1 is the key theoretical result of our work and lays the foundation for all analyses that follow.• In what way is the deep autoencoder different from the shallow counterpart? Li & Saad (2018) ; Poole et al. (2016) reveal this in terms of the candidate function space and expressivity for feedforward networks. It is unclear how these notions are applicable to weighttied autoencoders, which seek replication of the input rather than a generic mapping. In this work, we show that the deep autoencoder exhibits a higher order of sensitivity to perturbations of the parameters (Section 3.4). Burkholz & Dubatovka (2018) demonstrate a connection between the study of random networks, or ones at initialization, and their trainability. Note that these works either do not study weight-tied structures, or assume the analysis of the untying case for weight-tied structures. In our work , we derive and experimentally verify insights on how (not) to initialize deep weight-tied autoencoders, demonstrating that it is possible to train them without resorting to techniques such as greedy layer-wise pretraining, drop-out and batch normalization (Section 3.5). Specifically we experiment with 200-layer autoencoders.No prior works have attempted all three tasks. The quantitative difference between weight-tied and weight-untied networks is in fact not negligible, yet the analysis is non-trivial due to the weight tying constraint (Arora et al. (2015) ; Chen et al. (2018) ). To address this issue and obtain Theorem 1, we apply the Gaussian conditioning technique, which first appears in the studies of TAP equations in spin glass theory (Bolthausen (2014) ) and is extensively used in the approximate message passing algorithm literature (Bayati & Montanari (2011); Javanmard & Montanari (2013) ; Berthier et al. (2017) ). This should be contrasted with untied random networks, whose analysis is typically more straightforward. More importantly , the difference is not only analytical: the overall picture of deep random weight-tied autoencoders is rich and drastically different from that of feedforward networks. An analysis in the limit of infinite depth reveals three fundamental equations governing the picture (Section 3.1), which displays multiple phase transition phenomena (Section 3.2) . Consider the following 2L-layers autoencoder with weight tying: DISPLAYFORM0 Here x ∈ R n0 is the input, W ∈ R n ×n −1 is the weight, b ∈ R n is the encoder bias, and v ∈ R n −1 is the decoder bias, for = 1, ..., L. Also ϕ : R → R and σ : R → R are the activations (where for a vector u ∈ R n and a function ϕ : R → R, we write ϕ (u) to denote the vector (ϕ (u 1 ) , ..., ϕ (u n )) ). It is usually the case in practice that σ 0 (u) = u the identity function. We introduce some convenient quantities inductively: FIG6 of Appendix A.1 for a schematic diagram. We assume weights are random . Specifically we generate the weights and biases according to DISPLAYFORM1 DISPLAYFORM2 independently of each other. The scaling of the variances accords with the literature and actual practice (Glorot & Bengio (2010); Vincent et al. (2010) ). We also consider the asymptotic highdimensional regime, indexed by n: DISPLAYFORM3 Here σ W, , σ b, , σ v, and α are finite constants independent of n. We enforce σ W, > 0, but allow σ b, and σ v, to be zero. We assume that all activations are Lipschitz continuous, and the encoder activations σ 's are non-trivial in the sense that for any τ > 0, E z σ (τ z) This paper has shown quantitative answers to the three questions posed in Section 1. This feat is enabled by an exact analysis via Theorem 1. The theorem is stated in a general setting, allowing varying activations, weight variances, etc, but our analyses in Section 3 have made several simplifications. This leaves a question of whether these simplifications can be relaxed, and how the picture changes accordingly, for instance, when the parameters vary across layers, similar to Yang & Schoenholz (2018) . Many other questions also remain. For example, what would be the covariance structure between the outputs of two distinct inputs? How does the network's Jacobian matrix look like? These questions have been answered in the feedforward case (Poole et al. (2016) ; Pennington et al. FORMULA12 ), but we believe answering them is more technically involved in our case. We have also seen that an autoencoder that shows initial progress may not necessarily produce meaningful reconstruction eventually after training, and hence much more work is needed to understand the training dynamics far beyond initialization. Recent works Mei et al. FORMULA12 In the following, we give an outline of the proof of Theorem 1, and the complete proof. First, we start with a few notations and definitions. DISPLAYFORM0",study behavior weight-tied multilayer vanilla autoencoders assumption random weights. Via exact characterization limit large dimensions analysis reveals interesting phase transition phenomena when the depth becomes large. particular provides quantitative answers insights three questions were yet fully understood literature. Firstly provide precise answer how the random deep weight-tied autoencoder model performs approximate inference posed Scellieretal. 2018 connection reversibility considered several theoretical studies. Secondly show deep autoencoders display higher degree sensitivity perturbations parameters distinct shallow counterparts. Thirdly obtain insights pitfalls training initialization practice demonstrate experimentally is possible train deep autoencoder even tanh activation depth large 200 layers without resorting techniques layer-wise pre-training batch normalization. analysis is not specific depths Lipschitz activations analytical techniques may have broader applicability. autoencoder is a cornerstone machine learning which first response unsupervised learning problem Rumelhart Zipser 1985 applications dimensionality reduction Hinton Salakhutdinov 2006 unsupervised pre-training Erhanetal. 2010 also precursor many modern generative models Goodfellowetal. 2016 reconstruction power is well utilized applications anomaly detection Chandolaetal. 2009 image recovery Mousavietal. 2015 surge deep learning thousands papers have studied multilayer variants architecture theoretical understanding has been limited since analyzing learning dynamics highly nonlinear structure is typically difficult problem even shallow autoencoder. get around tackle task critical assumption:weights are random autoencoder is weight-tied weight-tied One enjoys much analytical tractability randomness assumption whereas weight tying enforces random autoencoder perform autoencoding. have also study high-dimensional setting where all dimensions are comparably large ideally jointly approaching infinity. consider simplest setting:vanilla autoencoders.e ones fully connected layers reconstruction capability. is done sake understanding effect depth note techniques may have broader applicability.The aforementioned assumptions are not without justifications. is a growing literature deep neural networks random weights Li Saad 2018 Giryesetal. 2016 Pooleetal. 2016 Schoenholzetal. 2016 Gabriéetal. 2018 Amarietal. 2018 name revealing certain properties deep feedforward networks1. Several recent works have also studied random multilayer feedforward networks lens statistical inference Manoeletal. 2017 Reeves 2017 Fletcheretal. 2018 idea weight tying is considered important paper Vincentet al. 2010 empirical finding autoencoders without weight tying perform comparably has become standard autoencoders. Similar features random connection symmetry also appear neural models Lillicrapetal. 2016 Scellieretal. 2018 Finally high-dimensional setting is common recent statistical learning advances Bühlmann Van De Geer 2011 far actual practice where many large datasets have dimensions least hundreds are harnessed large-scaled models.We seek quantitative answers three specific questions are motivated previous works:• exactly what way does the(vanilla random weight-tied autoencoder perform approximate inference? term is coined Scellieretal. 2018 connection theoretical results Aroraetal. 2015 which implicitly studies said model. particular Aroraetal. 2015 proves upper bound x−x2 where x andx are the input output network is limited number layers specific ReLU activation. direction has been recently extended Gilbertetal. 2017 work establish precisely what this approximate inference is by obtaining general asymptotically exact characterization2 ofx number layers Lipschitz continuous activations Theorem1 Section 3.3 Theorem1 is the key theoretical result work lays foundation analyses follow.• what way is the deep autoencoder different shallow counterpart? Li Saad 2018 Pooleetal. 2016 reveal terms candidate function space expressivity feedforward networks. is unclear how these notions are applicable weighttied autoencoders which seek replication input rather generic mapping. work show deep autoencoder exhibits higher order sensitivity perturbations parameters Section 3.4 Burkholz Dubatovka 2018 demonstrate connection study random networks ones initialization trainability. Note works either do not study weight-tied structures assume analysis untying case weight-tied structures. work derive experimentally verify insights how(not initialize deep weight-tied autoencoders demonstrating is possible train without resorting techniques greedy layer-wise pretraining drop-out batch normalization Section 3.5 Specifically experiment 200-layer autoencoders.No prior works have attempted three tasks. quantitative difference weight-tied weight-untied networks is in fact negligible yet analysis is non-trivial due weight tying constraint Aroraetal. 2015 Chenetal. 2018 address issue obtain Theorem1 apply Gaussian conditioning technique which first appears studies TAP equations spin glass theory Bolthausen 2014 is extensively used approximate message passing algorithm literature Bayati Montanari 2011 Javanmard Montanari 2013 Berthieretal. 2017 shouldbe contrasted untied random networks whose analysis is typically straightforward. importantly difference is not only analytical:overall picture deep random weight-tied autoencoders is rich drastically different feedforward networks. analysis limit infinite depth reveals three fundamental equations governing picture Section 3.1 which displays multiple phase transition phenomena Section 3.2 Consider following 2L-layers autoencoder weight tying:DISPLAYFORM0 x∈Rn0 is the input W∈Rn ×n−1 is the weight b∈Rn is the encoder bias v∈Rn −1 is the decoder bias 1... L. Alsoϕ:R→R σ:R→R are the activations where for a vectoru∈R n functionϕ:R→R writeϕ u denote vector ϕ u1... ϕ un is usually case practice σ0 u u identity function. introduce convenient quantities inductively:FIG6 Appendix A.1 schematic diagram. assume weights are random. Specifically generate weights biases according DISPLAYFORM1 DISPLAYFORM2 independently other. scaling variances accords literature actual practice Glorot Bengio 2010 Vincentetal. 2010 also consider asymptotic highdimensional regime indexed n:DISPLAYFORM3 σW σb σv α are finite constants independent n. enforceσW 0 allowσb σv zero. assume activations are Lipschitz continuous encoder activationsσ's are non-trivial sense τ 0 Ezσ τz paper has shown quantitative answers three questions posed Section1. feat is enabled exact analysis via Theorem 1. theorem is stated general setting allowing varying activations weight variances etc analyses Section3 have made several simplifications. leaves question whether simplifications can be relaxed how the picture changes accordingly instance when the parameters vary across layers similar Yang Schoenholz 2018 Many questions also remain. example would covariance structure outputs two distinct inputs? How does the network's Jacobian matrix look like? questions have been answered feedforward case Pooleetal. 2016 Penningtonetal. FORMULA12 believe answering is more technically involved case. have also seen autoencoder shows initial progress may necessarily produce meaningful reconstruction eventually training hence much work is needed understand training dynamics far beyond initialization. Recent works Meiet al. FORMULA12 following give outline proof Theorem1 complete proof. First start notations definitions. DISPLAYFORM0,2112,1449,663,0.031,1.458,2025/11/05 17:18:53,0.01,1.513,0.3987538940809966,703.718
"Assessing distance betweeen the true and the sample distribution is a key component of many state of the art generative models, such as Wasserstein Autoencoder (WAE). Inspired by prior work on Sliced-Wasserstein Autoencoders (SWAE) and
 kernel smoothing we construct a new generative model – Cramer-Wold AutoEncoder (CWAE). CWAE cost function, based on introduced Cramer-Wold distance between samples, has a simple closed-form in the case of normal prior. As a consequence, while simplifying the optimization procedure (no need of sampling necessary to evaluate the distance function in the training loop), CWAE performance matches quantitatively and qualitatively that of WAE-MMD (WAE using maximum mean discrepancy based distance function) and often improves upon SWAE. One of the crucial aspects in construction of generative models is devising effective method for computing and minimizing distance between the true and the model distribution. Originally in Variational Autencoder (VAE) BID10 this computation was carried out using variational methods. An important improvement was brought by the introduction of Wasserstein metric BID14 and the construction of WAE-GAN and WAE-MMD models, which relax the need for variational methods. WAE-GAN requires a separate optimization problem to be solved to approximate the used divergence measure, while in WAE-MMD the discriminator has the closed-form obtained from a characteristic kernel, i.e. one that is injective on distributions BID12 . A recent contribution to this trend of simplifying the construction of generative models is Sliced-Wasserstein Autoencoder (SWAE, BID11 ), where a significantly simpler AutoEncoder based model based on Wasserstein distance is proposed. The main innovation of SWAE was the introduction of the sliced-Wasserstein distance -a fast to estimate metric for comparing two distributions, based on the mean Wasserstein distance of one-dimensional projections. However, even in SWAE there is no close analytic formula that would enable computing the distance of the sample from the standard normal distribution. Consequently in SWAE two types of sampling are needed: (i) sampling from the prior distribution and (ii) sampling over one-dimensional projections.Our main contribution is introduction of the CramerWold distance between distributions, which has a closed-form for the distance of a sample from standard multivariate normal distribution. Its important feature is that it is given by a characteristic kernel which has a closed-form given by equation 7 for the product of radial Gaussians 1 . We use it to construct an AutoEncoder based generative model, called Cramer-Wold AutoEncoder (CWAE), in which the cost function, for a normal prior distribution, has a closed analytic formula. Thus In the paper we have presented a new autoencoder based generative model CWAE, which matches results of WAE-MMD, while using a cost function given by a simple closed analytic formula. We hope this result will encourage future work in developing simpler to optimize analogs of strong neural models.Crucial in the construction of CWAE is the use of the developed Cramer-Wold metric between samples and distributions, which can be effectively computed for Gaussian mixtures. As a consequence we obtain a reliable measure of the divergence from normality. Future work could explore use of the Cramer-Wold distance in other settings, in particular in adversarial models.",Assessing distance betweeen true sample distribution is a key component many state art generative models Wasserstein Autoencoder WAE Inspired prior work Sliced-Wasserstein Autoencoders SWAE kernel smoothing construct new generative model– Cramer-Wold AutoEncoder CWAE CWAE cost function based introduced Cramer-Wold distance samples has a simple closed-form case normal prior. consequence simplifying optimization procedure need sampling necessary evaluate distance function training loop CWAE performance matches quantitatively qualitatively WAE-MMD WAE using maximum mean discrepancy based distance function often improves upon SWAE. One crucial aspects construction generative models is devising effective method computing minimizing distance true model distribution. Originally Variational Autencoder VAE BID10 computation was carried using variational methods. important improvement was brought introduction Wasserstein metric BID14 construction WAE-GAN WAE-MMD models which relax need variational methods. WAE-GAN requires separate optimization problem solved approximate used divergence measure WAE-MMD discriminator has the closed-form obtained characteristic kernel.e one is injective distributions BID12. recent contribution trend simplifying construction generative models is Sliced-Wasserstein Autoencoder SWAE BID11 where a significantly simpler AutoEncoder based model based Wasserstein distance is proposed. main innovation SWAE was the introduction sliced-Wasserstein distance -a fast estimate metric comparing two distributions based mean Wasserstein distance one-dimensional projections. However even SWAE is no close analytic formula would enable computing distance sample standard normal distribution. Consequently SWAE two types sampling are needed:sampling prior distribution ii sampling one-dimensional projections.Our main contribution is introduction CramerWold distance distributions which has a closed-form distance sample standard multivariate normal distribution. important feature is given characteristic kernel which has a closed-form given equation7 product radial Gaussians1. use construct AutoEncoder based generative model called Cramer-Wold AutoEncoder CWAE which cost function normal prior distribution has a closed analytic formula. Thus paper have presented new autoencoder based generative model CWAE which matches results WAE-MMD using cost function given simple closed analytic formula. hope result will encourage future work developing simpler optimize analogs strong neural models.Crucial construction CWAE is the use developed Cramer-Wold metric samples distributions which can be effectively computed Gaussian mixtures. consequence obtain reliable measure divergence normality. Future work could explore use Cramer-Wold distance settings particular adversarial models.,679,477,202,0.006,1.423,2025/11/05 17:18:53,0.0,1.56,0.2897196261682242,209.652
"We propose a rejection sampling scheme using the discriminator of a GAN to
 approximately correct errors in the GAN generator distribution. We show that
 under quite strict assumptions, this will allow us to recover the data distribution
 exactly. We then examine where those strict assumptions break down and design a
 practical algorithm—called Discriminator Rejection Sampling (DRS)—that can be
 used on real data-sets. Finally, we demonstrate the efficacy of DRS on a mixture of
 Gaussians and on the state of the art SAGAN model. On ImageNet, we train an
 improved baseline that increases the best published Inception Score from 52.52 to
 62.36 and reduces the Frechet Inception Distance from 18.65 to 14.79. We then use
 DRS to further improve on this baseline, improving the Inception Score to 76.08
 and the FID to 13.75. Generative Adversarial Networks (GANs) BID5 are a powerful tool for image synthesis. They have also been applied successfully to semi-supervised and unsupervised learning BID25 BID20 BID11 , image editing BID31 BID12 , and image style transfer BID2 . Informally, the GAN training procedure pits two neural networks against each other, a generator and a discriminator. The discriminator is trained to distinguish between samples from the target distribution and samples from the generator. The generator is trained to fool the discriminator into thinking its outputs are real. The GAN training procedure is thus a two-player differentiable game, and the game dynamics are largely what distinguishes the study of GANs from the study of other generative models. These game dynamics have well-known and heavily studied stability issues. Addressing these issues is an active area of research BID17 BID7 .However , we are interested in studying something different: Instead of trying to improve the training procedure, we (temporarily) accept its flaws and attempt to improve the quality of trained generators by post-processing their samples using information from the trained discriminator. It's well known that (under certain very strict assumptions) the equilibrium of this training procedure is reached when sampling from the generator is identical to sampling from the target distribution and the discriminator always outputs 1/2. However, these assumptions don't hold in practice. In particular , GANs as presently trained don't learn to reproduce the target distribution BID1 . Moreover, trained GAN discriminators aren't just identically 1/2 -they can even be used to perform chess-type skill ratings of other trained generators .We ask if the information retained in the weights of the discriminator at the end of the training procedure can be used to ""improve"" the generator. At face value, this might seem unlikely. After all, if there is useful information left in the discriminator, why doesn't it find its way into the generator via the training procedure? Further reflection reveals that there are many possible reasons. First, the assumptions made in various analyses of the training procedure surely don't hold in practice (e.g. the discriminator and generator have finite capacity and are optimized in parameter space rather than density-space). Second, due to the concrete realization of the discriminator and the generator as neural networks, it may be that it is harder for the generator to model a given distribution than it is for the discriminator to tell that this distribution is not being modeled precisely. Finally, we may simply not train GANs long enough in practice for computational reasons.In this paper, we focus on using the discriminator as part of a probabilistic rejection sampling scheme. In particular, this paper makes the following contributions:• We propose a rejection sampling scheme using the GAN discriminator to approximately correct errors in the GAN generator distribution.• We show that under quite strict assumptions, this scheme allows us to recover the data distribution exactly.• We then examine where those strict assumptions break down and design a practical algorithm -called DRS -that takes this into account.• We conduct experiments demonstrating the effectiveness of DRS. First, as a baseline, we train an improved version of the Self-Attention GAN, improving its performance from the best published Inception Score of 52.52 up to 62.36, and from a Fréchet Inception Distance of 18.65 down to 14.79. We then show that DRS yields further improvement over this baseline, increasing the Inception Score to 76.08 and decreasing the Fréchet Inception Distance to 13.75. We have proposed a rejection sampling scheme using the GAN discriminator to approximately correct errors in the GAN generator distribution. We've shown that under strict assumptions, we can recover the data distribution exactly. We've also examined where those assumptions break down and Each row shows images synthesized by interpolating in latent space. The color bar above each row represents the acceptance probabilities for each sample: red for high and white for low. Subjective visual quality of samples with high acceptance probability is considerably better: objects are more coherent and more recognizable as belonging to a specific class. There are fewer indistinct textures, and fewer scenes without recognizable objects. • There's no reason that our scheme can only be applied to GAN generators. It seems worth investigating whether rejection sampling can improve e.g. VAE decoders. This seems like it might help, because VAEs may have trouble with ""spreading mass around"" too much.• In one ideal case, the critic used for rejection sampling would be a human. Can we use better proxies for the human visual system to improve rejection sampling's effect on image synthesis models?• It would be interesting to theoretically characterize the efficacy of rejection sampling under the breakdown-of-assumptions that we have described earlier. In addition , we represent Inception score as a function of acceptance rate in FIG5 -left. Different acceptance rates are achieved by changing γ from the 0 th percentile of F (x) (acceptance rate = 100%) to its 90 th percentile (acceptance rate = 14%). Decreasing the acceptance rate filters more non-realistic samples and increases the final Inception score. After an specific rate, rejecting more samples does not gain any benefit in collecting a better pool of samples.Moreover, FIG5 -right shows the correlation between the acceptance probabilities that DRS assigns to the synthesized samples and the recognizability of those samples from the view-point of a pre-trained Inception network. The latter is measured by computing max j p(y j |x i ) which is the probability of sample x i belonging to the category y j from the 1,000 ImageNet classes. As expected, there is a large mass of the recognizable images accepted with high acceptance probabilities on the top right corner. The small mass of images which cannot be easily classified into one of the 1,000 categories while having high acceptance probability scores (the top left corner of the graph) can be due to the non-optimal GAN discriminator in practice. Therefore, we expect that improving the discriminator performance boosts the final inception score even more substantially. , and the acceptance probability assigned to each sample x i by DRS versus the maximum probability of belonging to one of the 1K categories based on a pre-trained Inception network, max j p(y j |x i ) (right).","propose rejection sampling scheme using discriminator GAN approximately correct errors GAN generator distribution. show quite strict assumptions will allowus recover data distribution exactly. examine where those strict assumptions break design practical algorithm called Discriminator Rejection Sampling DRS can be used real data-sets Finally demonstrate efficacy DRS mixture Gaussians state art SAGAN model. ImageNet train improved baseline increases best published Inception Score 52.52 62.36 reduces Frechet Inception Distance 18.65 14.79 use DRS improve baseline improving Inception Score 76.08 FID 13.75 Generative Adversarial Networks GANs BID5 are a powerful tool image synthesis. have also applied successfully semi-supervised unsupervised learning BID25 BID20 BID11 image editing BID31 BID12 image style transfer BID2. Informally GAN training procedure pits two neural networks generator discriminator. discriminator is trained distinguish samples target distribution samples generator. generator is trained fool discriminator thinking outputs are real. GAN training procedure is thus two-player differentiable game game dynamics are largely what distinguishes study GANs study generative models. game dynamics have well-known heavily studied stability issues. Addressing issues is an active area research BID17 BID7.However are interested studying something different:Instead trying improve training procedure temporarily accept flaws attempt improve quality trained generators post-processing samples using information trained discriminator. well known certain strict assumptions equilibrium training procedure is reached when sampling generator is identical sampling target distribution discriminator always outputs1/2. However assumptions hold practice. particular GANs presently trained learn reproduce target distribution BID1. Moreover trained GAN discriminators identically1/2 -they can even used perform chess-type skill ratings trained generators.We ask if the information retained weights discriminator end training procedure can be used improve generator. face value might seem unlikely. if is useful information left discriminator why doesn't it find way generator via training procedure? reflection reveals are many possible reasons. First assumptions made various analyses training procedure surely hold practice e.g discriminator generator have finite capacity are optimized parameter space rather density-space Second due concrete realization discriminator generator neural networks may is harder generator model given distribution is for discriminator tell distribution is not being modeled precisely. Finally may simply train GANs long enough practice computational reasons.In paper focus using discriminator part probabilistic rejection sampling scheme. particular paper makes following contributions:• propose rejection sampling scheme using GAN discriminator approximately correct errors GAN generator distribution.• show quite strict assumptions scheme allowsus recover data distribution exactly.• examine where those strict assumptions break design practical algorithm -called DRS -that takes account.• conduct experiments demonstrating effectiveness DRS. First baseline train improved version Self-Attention GAN improving performance best published Inception Score 52.52 62.36 Fréchet Inception Distance 18.65 14.79 show DRS yields improvement baseline increasing Inception Score 76.08 decreasing Fréchet Inception Distance 13.75 have proposed rejection sampling scheme using GAN discriminator approximately correct errors GAN generator distribution. shown strict assumptions can recover data distribution exactly. also examined where those assumptions break row shows images synthesized interpolating latent space. color bar row represents acceptance probabilities sample:red high white low. Subjective visual quality samples high acceptance probability is considerably better:objects are more coherent recognizable belonging specific class. are fewer indistinct textures fewer scenes without recognizable objects. • There's reason scheme can only be applied GAN generators. seems worth investigating whether rejection sampling can improve improve e.g VAE decoders. seems like might help VAEs may have trouble spreading mass around much.• one ideal case critic used rejection sampling would human. Can we use better proxies human visual system improve rejection sampling's effect image synthesis models? • would interesting theoretically characterize efficacy rejection sampling breakdown-of-assumptions have described earlier. addition represent Inception score function acceptance rate FIG5 -left Different acceptance rates are achieved changingγ 0 th percentile F x acceptance rate 100% 90 th percentile acceptance rate 14% Decreasing acceptance rate filters non-realistic samples increases final Inception score. specific rate rejecting samples does not gain benefit collecting better pool samples.Moreover FIG5 -right shows correlation acceptance probabilities DRS assigns synthesized samples recognizability samples view-point pre-trained Inception network. latter is measured computing maxjp j|x whichis probability samplex belonging category j 1,000 ImageNet classes. expected is a large mass recognizable images accepted high acceptance probabilities top right corner. small mass images which cannot easily classified one 1,000 categories high acceptance probability scores top left corner graph can be due non-optimal GAN discriminator practice. Therefore expect improving discriminator performance boosts final inception score even substantially. acceptance probability assigned samplex DRS versus maximum probability belonging one 1K categories based pre-trained Inception network maxjp j|x right",1453,948,505,0.015,1.533,2025/11/05 17:18:53,0.01,1.457,0.6323987538940806,458.51
"The quality of the features used in visual recognition is of fundamental importance for the overall system. For a long time, low-level hand-designed feature algorithms as SIFT and HOG have obtained the best results on image recognition. Visual features have recently been extracted from trained convolutional neural networks. Despite the high-quality results, one of the main drawbacks of this approach, when compared with hand-designed features, is the training time required during the learning process. In this paper, we propose a simple and fast way to train supervised convolutional models to feature extraction while still maintaining its high-quality. This methodology is evaluated on different datasets and compared with state-of-the-art approaches. The design of high-quality image features is essential to vision recognition related tasks. They are needed to provide high accuracy and scalability on processing large image data. Many approaches to building visual features have been proposed such as dictionary learning that aims to find a sparse representation of the data in the form of a linear combination of fundamental elements called atoms BID5 . Scattering approaches provide mathematical frameworks to build geometric image priors BID11 . Unsupervised bag of words methods identifies object categories using a corpus of unlabeled images BID15 . Unsupervised deep learning techniques are also used to extract features by using neural networks based models with many layers and frequently trained using contrastive divergence algorithms BID6 . All of them have been shown to improve the results of hand-crafted designed feature vectors such as SIFT BID10 or HOG BID1 with promising results BID0 BID11 .Another recent but very successful alternative is to use supervised Convolutional Neural Networks (CNN) to extract high-quality image features BID12 . These models take into consideration that images are symmetrical by a shift in position and therefore weight sharing and selective fields techniques are used to create filter banks that extract geometrically related features from the image dataset. The process is composed hierarchically over many layers to obtain higher level features after each layer. The network is typically trained using gradient backpropagation techniques. After the CNN training, the last layer (usually a fully connected layer) is removed to provide the learned features.A drawback of this approach is the time needed to thoroughly train a CNN to obtain high accuracy results. In this paper , we propose the Simple Fast Convolutional (SFC) feature learning technique to significantly reduce the time required to learning supervised convolutional features without losing much of the representation performance presented by such solutions. To accelerate the training time, we consider few training epochs combined with fast learning decay rate.To evaluate the proposed approach we combined SFC and alternative features methods with classical classifiers such as Support Vector Machines (SVM) BID18 and Extreme Learning Machines (ELM) . The results show that SFC provides better performance than alternative approaches while significantly reduces the training time. We evaluated the alternative feature methods over the MNIST (Lecun & Cortes) , CIFAR-10 and CIFAR-100 BID4 ). In this paper, we showed that convolutional feature learning can be performed in a fast way. Moreover, despite being very fast, it is still capable of generating representations that present better performance than other approaches. The proposed method is also flexible enough since a compromise can be obtained between the speed of the training and the final solution test accuracy. Naturally, the difference in test accuracy presented in this paper could be even greater if more training time is allowed to be used.We emphasize that transfer learning techniques can be used to extend the application of the proposed method. Finally, we show that despite efforts to the contrary, supervised convolutional method still provides state-of-the-art results for image feature generation. Moreover, the experiments showed that a quick change in the learning rate decay is a valid method to speed up the training of deep neural networks significantly.",quality features used visual recognition is of fundamental importance overall system. long time low-level hand-designed feature algorithms SIFT HOG have obtained best results image recognition. Visual features have recently extracted trained convolutional neural networks. Despite high-quality results one main drawbacks approach when compared hand-designed features is the training time required learning process. paper propose simple fast way train supervised convolutional models feature extraction still maintaining high-quality methodology is evaluated different datasets compared state-of-the-art approaches. design high-quality image features is essential vision recognition related tasks. are needed provide high accuracy scalability processing large image data. Many approaches building visual features have been proposed dictionary learning aims find sparse representation data form linear combination fundamental elements called atoms BID5. Scattering approaches provide mathematical frameworks build geometric image priors BID11. Unsupervised bag words methods identifies object categories using corpus unlabeled images BID15. Unsupervised deep learning techniques are also used extract features using neural networks based models many layers frequently trained using contrastive divergence algorithms BID6. have shown improve results hand-crafted designed feature vectors SIFT BID10 HOG BID1 promising results BID0 BID11.Another recent successful alternative is to use supervised Convolutional Neural Networks CNN extract high-quality image features BID12. models take consideration images are symmetrical shift position therefore weight sharing selective fields techniques are used create filter banks extract geometrically related features image dataset. process is composed hierarchically many layers obtain higher level features layer. network is typically trained using gradient backpropagation techniques. CNN training last layer usually fully connected layer is removed provide learned features.A drawback approach is the time needed thoroughly train CNN obtain high accuracy results. paper propose Simple Fast Convolutional SFC feature learning technique significantly reduce time required learning supervised convolutional features without losing much representation performance presented solutions. accelerate training time consider training epochs combined fast learning decay rate.To evaluate proposed approach combined SFC alternative features methods classical classifiers Support Vector Machines SVM BID18 Extreme Learning Machines ELM results show SFC provides better performance alternative approaches significantly reduces training time. evaluated alternative feature methods MNIST Lecun Cortes CIFAR-10 CIFAR-100 BID4 paper showed convolutional feature learning can be performed fast way. Moreover despite fast is still capable generating representations present better performance approaches. proposed method is also flexible enough since compromise can be obtained speed training final solution test accuracy. Naturally difference test accuracy presented paper could even greater if more training time is allowed used.We emphasize transfer learning techniques can be used extend application proposed method. Finally show despite efforts contrary supervised convolutional method still provides state-of-the-art results image feature generation. Moreover experiments showed quick change learning rate decay is a valid method speed training deep neural networks significantly.,752,533,219,0.007,1.411,2025/11/05 17:18:53,0.0,1.385,0.2523364485981307,260.979
"We develop a framework for understanding and improving recurrent neural networks (RNNs) using max-affine spline operators (MASOs). We prove that RNNs using piecewise affine and convex nonlinearities can be written as a simple piecewise affine spline operator. The resulting representation provides several new perspectives for analyzing RNNs, three of which we study in this paper. First, we show that an RNN internally partitions the input space during training and that it builds up the partition through time. Second, we show that the affine slope parameter of an RNN corresponds to an input-specific template, from which we can interpret an RNN as performing a simple template matching (matched filtering) given the input. Third, by carefully examining the MASO RNN affine mapping, we prove that using a random initial hidden state corresponds to an explicit L2 regularization of the affine parameters, which can mollify exploding gradients and improve generalization. Extensive experiments on several datasets of various modalities demonstrate and validate each of the above conclusions. In particular, using a random initial hidden states elevates simple RNNs to near state-of-the-art performers on these datasets. Recurrent neural networks (RNNs) are a powerful class of models for processing sequential inputs and a basic building block for more advanced models that have found success in challenging problems involving sequential data, including sequence classification (e.g., sentiment analysis BID30 , sequence generation (e.g., machine translation BID1 ), speech recognition BID10 , and image captioning BID22 . Despite their success, however, our understanding of how RNNs work remains limited. For instance, an attractive theoretical result is the universal approximation property that states that an RNN can approximate an arbitrary function BID28 BID29 BID11 . These classical theoretical results have been obtained primarily from the dynamical system BID29 BID28 and measure theory BID11 perspectives. These theories provide approximation error bounds but unfortunately limited guidance on applying RNNs and understanding their performance and behavior in practice.In this paper, we provide a new angle for understanding RNNs using max-affine spline operators (MASOs) BID21 BID12 ) from approximation theory. The piecewise affine approximations made by compositions of MASOs provide a new and useful framework to study neural networks. For example, BID4 ; BID2 have provided a detailed analysis in the context of feedforward networks. Here, we go one step further and find new insights and interpretations from the MASO perspective for RNNs. We will see that the input space partitioning and matched filtering links developed in BID4 ; BID2 extend to RNNs and yield interesting insights into their inner workings. Moreover, the MASO formulation of RNNs enables us to theoretically justify the use of a random initial hidden state to improve RNN performance.For concreteness, we focus our analysis on a specific class of simple RNNs BID8 with piecewise affine and convex nonlinearities such as the ReLU BID9 . RNNs with such nonlinearities have recently gained considerable attention due to their ability to combat the exploding gradient problem; with proper initialization BID19 BID33 and clever parametrization of the recurrent weight BID0 BID39 BID16 BID15 BID24 BID13 , these RNNs achieve performance on par with more complex ones such as LSTMs. Below is a summary of our key contributions. Contribution 1. We prove that an RNN with piecewise affine and convex nonlinearities can be rewritten as a composition of MASOs, making it a piecewise affine spline operator with an elegant analytical form (Section 3).Contribution 2. We leverage the partitioning of piecewise affine spline operators to analyze the input space partitioning that an RNN implicitly performs. We show that an RNN calculates a new, high-dimensional representation (the partition code) of the input sequence that captures informative underlying characteristics of the input. We also provide a new perspective on RNN dynamics by visualizing the evolution of the RNN input space partitioning through time (Section 4).Contribution 3. We show the piecewise affine mapping in an RNN associated with a given input sequence corresponds to an input-dependent template, from which we can interpret the RNN as performing greedy template matching (matched filtering) at every RNN cell (Section 5).Contribution 4. We rigorously prove that using a random (rather than zero) initial hidden state in an RNN corresponds to an explicit regularizer that can mollify exploding gradients. We show empirically that such a regularization improves RNN performance (to state-of-the-art) on four datasets of different modalities (Section 6). We have developed and explored a novel perspective of RNNs in terms of max-affine spline operators (MASOs). RNNs with piecewise affine and convex nonlinearities are piecewise affine spline operators with a simple, elegant analytical form. The connections to input space partitioning (vector quantization) and matched filtering followed immediately. The spline viewpoint also suggested that the typical zero initial hidden state be replaced with a random one that mollifies the exploding gradient problem and improves generalization performance.There remain abundant promising research directions. First, we can extend the MASO RNN framework following BID3 to cover more general networks like gated RNNs (e.g, GRUs, LSTMs) that employ the sigmoid nonlinearity, which is neither piecewise affine nor convex. Second, we can apply recent random matrix theory results BID23 to the affine parameter A RNN (e.g., the change of the distribution of its singular values during training) to understand RNN training dynamics. t th time step of a discrete time-serie, DISPLAYFORM0 x Concatenation of the whole length T time-serie: DISPLAYFORM1 Output/prediction associated with input x y n True label (target variable) associated with the nth time-serie example x n . For classification y n ∈ {1, . . . , C}, C > 1; For regression y n ∈ R C , C ≥ 1 DISPLAYFORM2 Output of an RNN cell at layer and time step t; Alternatively, input to an RNN cell at layer + 1 and time step t − 1 DISPLAYFORM3 Concatenation of hidden state h ( ,t) of all time steps at layer : DISPLAYFORM4 Concatenated input to an RNN cell at layer and time step t: DISPLAYFORM5 th layer RNN weight associated with the input h ( ,t−1) from the previous time step: DISPLAYFORM6 th layer RNN weight associated with the input h ( −1,t) from the previous layer: DISPLAYFORM7 Bias of the last fully connected layer: DISPLAYFORM8 Pointwise nonlinearity in an RNN (assumed to be piecewise affine and convex in this paper) σ Standard deviation of noise injected into the initial hidden state h DISPLAYFORM9 MASO formula of the RNN activation σ(·) at layer and time step t: DISPLAYFORM10 MASO parameters of an RNN at layer and time step t: DISPLAYFORM11",develop framework understanding improving recurrent neural networks RNNs using max-affine spline operators MASOs prove RNNs using piecewise affine convex nonlinearities can be written simple piecewise affine spline operator. resulting representation provides several new perspectives analyzing RNNs three which we study paper. First show RNN internally partitions input space training builds partition time. Second show affine slope parameter RNN corresponds input-specific template whichwe can interpret RNN performing simple template matching matched filtering given input. Third carefully examining MASO RNN affine mapping prove using random initial hidden state corresponds explicit L2 regularization affine parameters which can mollify exploding gradients improve generalization. Extensive experiments several datasets various modalities demonstrate validate conclusions. particular using random initial hidden states elevates simple RNNs near state-of-the-art performers datasets. Recurrent neural networks RNNs are a powerful class models processing sequential inputs basic building block advanced models have found success challenging problems involving sequential data including sequence classification e.g sentiment analysis BID30 sequence generation e.g machine translation BID1 speech recognition BID10 image captioning BID22. Despite success however understanding how RNNs work remains limited. instance attractive theoretical result is the universal approximation property states RNN can approximate arbitrary function BID28 BID29 BID11. classical theoretical results have been obtained primarily dynamical system BID29 BID28 measure theory BID11 perspectives. theories provide approximation error bounds unfortunately limited guidance applying RNNs understanding performance behavior practice.In paper provide new angle understanding RNNs using max-affine spline operators MASOs BID21 BID12 approximation theory. piecewise affine approximations made compositions MASOs provide new useful framework study neural networks. example BID4;BID2 have provided detailed analysis context feedforward networks. go one step find new insights interpretations MASO perspective RNNs. will see input space partitioning matched filtering links developed BID4;BID2 extend RNNs yield interesting insights inner workings. Moreover MASO formulation how RNNs enablesus theoretically justify use random initial hidden state improve RNN performance.For concreteness focus analysis specific class simple RNNs BID8 piecewise affine convex nonlinearities ReLU BID9. RNNs nonlinearities have recently gained considerable attention due ability combat exploding gradient problem;proper initialization BID19 BID33 clever parametrization recurrent weight BID0 BID39 BID16 BID15 BID24 BID13 RNNs achieve performance par complex ones LSTMs. is a summary key contributions. Contribution1. prove RNN piecewise affine convex nonlinearities can be rewritten composition MASOs making piecewise affine spline operator elegant analytical form Section3.Contribution2. leverage partitioning piecewise affine spline operators analyze input space partitioning RNN implicitly performs. show RNN calculates new high-dimensional representation partition code input sequence captures informative underlying characteristics input. also provide new perspective RNN dynamics visualizing evolution RNN input space partitioning time Section4.Contribution3. show piecewise affine mapping RNN associated given input sequence corresponds input-dependent template whichwe can interpret RNN performing greedy template matching matched filtering every RNN cell Section5.Contribution4. rigorously prove using random rather zero initial hidden state RNN corresponds explicit regularizer can mollify exploding gradients. show empirically regularization improves RNN performance state-of-the-art four datasets different modalities Section6 have developed explored novel perspective how RNNs terms max-affine spline operators MASOs RNNs piecewise affine convex nonlinearities are piecewise affine spline operators simple elegant analytical form. connections input space partitioning vector quantization matched filtering followed immediately. spline viewpoint also suggested typical zero initial hidden state replaced random one mollifies exploding gradient problem improves generalization performance.There remain abundant promising research directions. First can extend MASO RNN framework following BID3 cover general networks like gated RNNs e.g GRUs LSTMs employ sigmoid nonlinearity which is neither piecewise affine convex. Second can apply recent random matrix theory results BID23 affine parameter RNN e.g change distribution singular values training understand RNN training dynamics. th time step discrete time-serie DISPLAYFORM0 x Concatenation whole length time-serie DISPLAYFORM1 Output/prediction associated inputx n True label target variable associated nth time-serie examplex n. classification n∈ 1 C C 1;regression n∈RC C ≥ 1 DISPLAYFORM2 Output RNN cell layer time step t;Alternatively input RNN cell layer+1 time step − 1 DISPLAYFORM3 Concatenation hidden stateh time steps layer:DISPLAYFORM4 Concatenated input RNN cell layer time step t:DISPLAYFORM5 th layer RNN weight associated inputh t−1 previous time step:DISPLAYFORM6 th layer RNN weight associated inputh −1 previous layer:DISPLAYFORM7 Bias last fully connected layer:DISPLAYFORM8 Pointwise nonlinearity RNN assumed piecewise affine convex paper σ Standard deviation noise injected initial hidden stateh DISPLAYFORM9 MASO formula RNN activationσ · layer time step t:DISPLAYFORM10 MASO parameters RNN layer time step t:DISPLAYFORM11,1435,1014,421,0.014,1.415,2025/11/05 17:18:53,0.01,1.455,0.2647975077881619,412.098
"Reasoning over text and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering.  Transducing text to logical forms which can be operated on is a brittle and error-prone process . Operating directly on text by jointly learning representations and transformations thereof by means of neural architectures that lack the ability to learn and exploit general rules can be very data-inefficient and not generalise correctly . These issues are addressed by Neural Theorem Provers (NTPs) (Rocktäschel & Riedel, 2017), neuro-symbolic systems based on a continuous relaxation of Prolog’s backward chaining algorithm, where symbolic unification between atoms is replaced by a differentiable operator computing the similarity between their embedding representations . In this paper, we first propose Neighbourhood-approximated Neural Theorem Provers (NaNTPs) consisting of two extensions toNTPs, namely a) a method for drastically reducing the previously prohibitive time and space complexity during inference and learning, and b) an attention mechanism for improving the rule learning process, deeming them usable on real-world datasets. Then, we propose a novel approach for jointly reasoning over KB facts and textual mentions, by jointly embedding them in a shared embedding space. The proposed method is able to extract rules and provide explanations—involving both textual patterns and KB relations—from large KBs and text corpora. We show that NaNTPs perform on par with NTPs at a fraction of a cost, and can achieve competitive link prediction results on challenging large-scale datasets, including WN18, WN18RR, and FB15k-237 (with and without textual mentions) while being able to provide explanations for each prediction and extract interpretable rules. The main focus in Artificial Intelligence is building systems that exhibit intelligent behaviour BID38 . In particular, Natural Language Understanding (NLU) and Machine Reading (MR) aim at building models and systems with the ability to read text, extract meaningful knowledge, and actively reason with it BID18 BID45 . This ability enables both the synthesis of new knowledge and the possibility to verify and update a given assertion. For example, given the following statement:The River Thames is in the United Kingdom. NTPs combine the strengths of rule-based and neural models but, so far, they were unable to reason over large KBs, and therefore over natural language.In this paper, we proposed NaNTPs that utilise ANNS and attention as a solution to scaling issues of NTP. By efficiently considering only the subset of proof paths associated with the highest proof scores during the construction of a dynamic computation graph, NaNTPs yield drastic speedups and memory efficiency, while yielding the same or a better predictive accuracy than NTPs. This enables application of NaNTPs to mixed KB and natural language data by embedding logic atoms and textual mentions in a joint embedding space.Albeit results are still slightly lower than those yielded by state-of-the-art Neural Link Predictors on large datasets, NaNTPs is interpretable and is able to provide explanations of its reasoning at scale.",Reasoning text Knowledge Bases KBs is a major challenge Artificial Intelligence applications machine reading dialogue question answering. Transducing text logical forms which can be operated is a brittle error-prone process. Operating directly text jointly learning representations transformations thereof means neural architectures lack ability learn exploit general rules can be very data-inefficient generalise correctly. issues are addressed Neural Theorem Provers NTPs Rocktäschel Riedel 2017 neuro-symbolic systems based continuous relaxation Prologs backward chaining algorithm where symbolic unification atoms is replaced differentiable operator computing similarity embedding representations. paper first propose Neighbourhood-approximated Neural Theorem Provers NaNTPs consisting two extensions toNTPs namely method drastically reducing previously prohibitive time space complexity inference learning b attention mechanism improving rule learning process deeming usable real-world datasets. propose novel approach jointly reasoning KB facts textual mentions jointly embedding shared embedding space. proposed method is able extract rules provide explanations involving textual patterns KB relations large KBs text corpora. show NaNTPs perform par NTPs fraction cost can achieve competitive link prediction results challenging large-scale datasets including WN18 WN18RR FB15k-237 without textual mentions able provide explanations prediction extract interpretable rules. main focus Artificial Intelligence is building systems exhibit intelligent behaviour BID38. particular Natural Language Understanding NLU Machine Reading MR aim building models systems ability read text extract meaningful knowledge actively reason BID18 BID45. ability enables synthesis new knowledge possibility verify update given assertion. example given following statement:River Thames is in the United Kingdom. NTPs combine strengths rule-based neural models far were unable reason large KBs therefore natural language.In paper proposed NaNTPs utilise ANNS attention solution scaling issues NTP. efficiently considering subset proof paths associated highest proof scores construction dynamic computation graph NaNTPs yield drastic speedups memory efficiency yielding better predictive accuracy NTPs. enables application NaNTPs mixedKB natural language data embedding logic atoms textual mentions joint embedding space.Albeit results are still slightly lower yielded state-of-the-art Neural Link Predictors large datasets NaNTPs is interpretable is able provide explanations reasoning scale.,635,429,206,0.006,1.48,2025/11/05 17:18:53,0.0,1.533,0.467289719626168,201.799
"We investigate the methods by which a Reservoir Computing Network (RCN) learns concepts such as 'similar' and 'different' between pairs of images using a small training dataset and generalizes these concepts to previously unseen types of data. Specifically, we show that an RCN trained to identify relationships between image-pairs drawn from a subset of digits from the MNIST database or the depth maps of subset of visual scenes from a moving camera generalizes the learned transformations to images of digits unseen during training or depth maps of different visual scenes. We infer, using Principal Component Analysis, that the high dimensional reservoir states generated from an input image pair with a specific transformation converge over time to a unique relationship. Thus, as opposed to training the entire high dimensional reservoir state, the reservoir only needs to train on these unique relationships, allowing the reservoir to perform well with very few training examples. Thus, generalization of learning to unseen images is interpretable in terms of clustering of the reservoir state onto the attractor corresponding to the transformation in reservoir space. We find that RCNs can identify and generalize linear and non-linear transformations, and combinations of transformations, naturally and be a robust and effective image classifier. Additionally, RCNs perform significantly better than state of the art neural network classification techniques such as deep Siamese Neural Networks (SNNs) in generalization tasks both on the MNIST dataset and more complex depth maps of visual scenes from a moving camera. This work helps bridge the gap between explainable machine learning and biological learning through analogies using small datasets, and points to new directions in the investigation of learning processes. Different types of Artificial Neural Networks (ANNs) have been used through time for the task of object recognition and classification. Feed-forward structures, such as convolutional neural networks, deep learning BID17 , stacked auto encoders etc. have been extensively studied and are the state of the art for classification. These architectures are well understood due to their feed-forward and non-dynamic nature.However, biological systems such as the visual cortex are known to have primarily ( 70 %) recurrent connections BID2 with less than 1 % of the connections being feedforward Da Costa and Martin (2009). RCN's (or closely related models) provides explanations of why biological brains can carry out accurate computations with an 'inaccurate' and noisy physical substrate BID11 , especially accurate timing BID16 , of the way in which visual spatio-temporal information is super-imposed and processed in primary visual cortex Danko Nikoli c and Maas (2006); BID1 . In addition, biological systems learn visual concepts through analogies, using only a handful of examples BID20 . In particular, in BID9 , bees were trained to fly towards the image from a pair of images that looked very similar to a previously displayed base image. On training bees to fly towards the visually similar image, the bees were presented with two scents, one very similar and one different from a base scent. As a consequence of the visual training that induced preference to the very similar category, the bees flew towards the very similar scent. Thus, biological systems have been found to translate learning of concepts of similarity across sensory inputs, leading us to believe that the brain has a common and fundamental mechanism that comprehends through analogies or through concepts of 'similarity'.Deriving inspiration from nature, we hope to develop a biologically plausible learning technique that learns through analogies.In our framework, we refer to generalization as the ability of a system to learn the relationships or transformations, both linear and non-linear, between a pair of images and be able to recognize the same transformation in unseen image-pairs. Feed-forward networks have, to the best of our knowledge, not been successful in developing an explainable model for this type of generalization of learning. In addition, learning of stand-alone images without drawing comparisons isn't biologically plausible. Networks that require large datasets and hence increasingly powerful GPUs do not scale well. It seems reasonable to say that humans learn through comparitively few training examples BID8 . For instance, a child would learn the features of a horse and the difference between a horse and a donkey, simply by observing at a handful of examples, contrary to deep learning. While research in learning from very few images, one shot learning BID23 etc. has gained momentum recently, integrating it with generalization of learning is a relatively unexplored area.In the ground-breaking work of BID12 , the success of Recurrent Neural Networks (RNNs) depend on the existence of attractors. In training, the dynamical system of the RNN is left running until it ends up in one of its several attractors. Similarly, in BID14 , a unique conceptor is found for each input pattern in a driven RNN. However, training of RNNs is difficult due to problems like the vanishing gradient. BID3 showed that much slower dynamics can be introduced in the RNN by using a random network of neurons with short term plasticity, thus allowing the system to work with training of only the output weights. Exploiting this property, Echo State Networks (ESN) BID13 and Liquid State Machine (LSM) BID18 , commonly falling under Reservoir Computing (RC) were introduced. RC is appealing because of its dynamical property and easy scalability since the recurrent connections in the network aren't trained. Applications of RC include many real world phenomena such as weather or stock market prediction, self driven cars, speech processing and language interpretation, gait generation and motion control in robots etc. RCNs and RNNs perform very well for generating chaotic dynamics BID15 . Models of spontaneously active neural circuits typically exhibit chaotic dynamics, as in RCNs BID19 . Such chaotic dynamics is found in spiking models of spontaneous activity in cortical circuits BID21 .In this work, we train RCNs on both the MNIST handwritten digit database as proof of concept as well as depth maps of visual scenes from a moving camera, to study generalization of the learned transformations between pairs of images. We classify pairs of images into very similar, rotated, zoomed , blurred or different. The reservoir activity is then studied to reveal the underlying features of the activity that are responsible for classification. We find that the relationships between reservoirstate pairs corresponding to input image pairs converge for image pairs with a common relationship between them. In other words, the reservoir only learns relationships between the images , not features of the individual images themselves. This allows for generalization of the learned relationships to all image pairs, seen and unseen by the reservoir. Additionally we compare its performance for a generalization task to a pair-based deep siamese neural network (SNN) built on the keras implementation and show that the reservoir performs significantly better, both for simpler MNIST images as well as for depth maps . We also show that the reservoir is able to recognize linear combinations of the individuals transformations it has learned. This work can useful in the field of computer vision to identify similar transformations between images, even if they are non-linear as in a moving camera, in a biological plausible and computationally efficient way. In this paper we have used RCNs to solve a class of image classification problems that generalize learning of relationships between images using a rather small training data. While image classification has been studied extensively before, here we present a biologically plausible method that not only generalizes learning, but also allows us to interpret the results analytically through a dynamical systems lens. We see that the differential reservoir states obtained from input image-pairs with a common transformation have principal components that are aligned closer together. From a dynamical systems perspective, this can be interpreted as the existence of attractors in reservoir space, each corresponding to a given image transformation. Thus, by reducing the dimensionality of the reservoir space, the reservoir as a dynamical system allows us to train on a much smaller training dataset, whereas contemporary methods such as deep learning require much larger datasets due partly to the lack of dynamics. This same property also allows the reservoir to generalizes the relationships learned to images it hasn't seen during training.In a reservoir, the image space is mapped onto the reservoir space in a way as to preserve the locality of common transformations in reservoir space. In addition, the reservoir performs significantly better than a deep SNN for the task of generalization. From a computation perspective, the reservoir is fast since only the output weights are being trained and the reservoir is sparsely connected. Further, we argue that our method is biologically plausible primarily due to the learning technique based on learning using concepts of similarity from a small training, and secondly due to the dynamics of the reservoir that have been shown to resemble neural cortex activity. We conclude that although state of the art machine learning techniques such as SNNs work exceedingly well for image classification, they do not work as well for generalization of learning, for whch RCNs outperform them, due to their ability to function as a dynamical system with 'memory'. Thus, we see the strength of our work as lying in not only its ability to generalize to untrained images, but also our ability to explain this in terms of the reservoir dynamics and PCA. This relates to new ideas in explainable Artificial Intelligence, a topic that continues to receive traction. An interesting direction would be to explore different reservoir architectures that model the human brain better. Another interesting direction would be to use RCNs to study videos which are naturally temporal, and and investigate how the reservoir generalizes in the action domain. Finally, although we get a fairly good performance with a sparse reservoir and few training images, we predict that as the image complexity increases, a more sophisticated reservoir would be required to match performance.","investigate methods which a Reservoir Computing Network RCN learns concepts 'similar' 'different' pairs images using small training dataset generalizes concepts previously unseen types data. Specifically show RCN trained identify relationships image-pairs drawn subset digits MNIST database depth maps subset visual scenes moving camera generalizes learned transformations images digits unseen training depth maps different visual scenes. infer using Principal Component Analysis high dimensional reservoir states generated input image pair specific transformation converge time unique relationship. Thus opposed training entire high dimensional reservoir state reservoir needs train unique relationships allowing reservoir perform well training examples. Thus generalization learning unseen images is interpretable terms clustering reservoir state onto attractor corresponding transformation reservoir space. find RCNs can identify generalize linear non-linear transformations combinations transformations naturally robust effective image classifier. Additionally RCNs perform significantly better state art neural network classification techniques deep Siamese Neural Networks SNNs generalization tasks MNIST dataset complex depth maps visual scenes moving camera. work helps bridge gap explainable machine learning biological learning analogies using small datasets points new directions investigation learning processes. Different types Artificial Neural Networks ANNs have been used time task object recognition classification. Feed-forward structures convolutional neural networks deep learning BID17 stacked auto encoders etc. have been extensively studied are the state art classification. architectures are well understood due feed-forward non-dynamic nature.However biological systems visual cortex are known have primarily 70% recurrent connections BID2 less 1% connections feedforward Da Costa Martin 2009 RCN's closely related models provides explanations why biological brains can carry accurate computations 'inaccurate' noisy physical substrate BID11 especially accurate timing BID16 way which visual spatio-temporal information is super-imposed processed primary visual cortex Danko Nikolic Maas 2006 BID1. addition biological systems learn visual concepts analogies using handful examples BID20. particular BID9 bees were trained fly towards image pair images looked similar previously displayed base image. training bees fly towards visually similar image bees were presented two scents one similar one different base scent. consequence visual training induced preference similar category bees flew towards similar scent. Thus biological systems have been found translate learning concepts similarity across sensory inputs leadingus believe brain has a common fundamental mechanism comprehends analogies concepts 'similarity'.Deriving inspiration nature hope develop biologically plausible learning technique learns analogies.In framework refer generalization ability system learn relationships transformations linear non-linear pair images able recognize transformation unseen image-pairs Feed-forward networks have,to the best knowledge successful developing explainable model type generalization learning. addition learning stand-alone images without drawing comparisons biologically plausible. Networks require large datasets hence increasingly powerful GPUs do not scale well. seems reasonable say humans learn comparitively training examples BID8. instance child would learn features horse difference horse donkey simply observing handful examples contrary deep learning. research learning images one shot learning BID23 etc. has gained momentum recently integrating generalization learning is a relatively unexplored area.In ground-breaking work BID12 success Recurrent Neural Networks RNNs depend existence attractors. training dynamical system RNN is left running ends one several attractors. Similarly BID14 unique conceptor is found input pattern driven RNN. However training RNNs is difficult due problems like vanishing gradient. BID3 showed much slower dynamics can be introduced RNN using random network neurons short term plasticity thus allowing system work training output weights. Exploiting property Echo State Networks ESN BID13 Liquid State Machine LSM BID18 commonly falling Reservoir Computing RC were introduced. RC is appealing dynamical property easy scalability since recurrent connections network trained. Applications RC include many real world phenomena weather stock market prediction self driven cars speech processing language interpretation gait generation motion control robots etc. RCNs RNNs perform well generating chaotic dynamics BID15. Models spontaneously active neural circuits typically exhibit chaotic dynamics RCNs BID19. chaotic dynamics is found spiking models spontaneous activity cortical circuits BID21.In work train RCNs MNIST handwritten digit database proof concept well depth maps visual scenes moving camera study generalization learned transformations pairs images. classify pairs images similar rotated zoomed blurred different. reservoir activity is then studied reveal underlying features activity are responsible classification. find relationships reservoirstate pairs corresponding input image pairs converge image pairs common relationship them. words reservoir learns relationships images features individual images themselves. allows generalization learned relationships image pairs seen unseen reservoir. Additionally compare performance generalization task pair-based deep siamese neural network SNN built keras implementation show reservoir performs significantly better simpler MNIST images well depth maps. also show reservoir is able recognize linear combinations individuals transformations has learned. work can useful field computer vision identify similar transformations images even if they are non-linear moving camera biological plausible computationally efficient way. paper have used RCNs solve class image classification problems generalize learning relationships images using rather small training data. image classification has been studied extensively present biologically plausible method generalizes learning also allowsus interpret results analytically dynamical systems lens. see differential reservoir states obtained input image-pairs common transformation have principal components are aligned closer together. dynamical systems perspective can be interpreted existence attractors reservoir space corresponding given image transformation. Thus reducing dimensionality reservoir space reservoir dynamical system allowsus train much smaller training dataset whereas contemporary methods deep learning require much larger datasets due partly lack dynamics. property also allows reservoir generalizes relationships learned images seen training.In reservoir image space is mapped onto reservoir space way preserve locality common transformations reservoir space. addition reservoir performs significantly better deep SNN task generalization. computation perspective reservoir is fast since output weights are being trained reservoir is sparsely connected. argue method is biologically plausible primarily due learning technique based learning using concepts similarity small training secondly due dynamics reservoir have been shown resemble neural cortex activity. conclude although state art machine learning techniques SNNs work exceedingly well image classification do not work well generalization learning whch RCNs outperform due ability function dynamical system 'memory'. Thus see strength work lying ability generalize untrained images also ability explain terms reservoir dynamics PCA. relates new ideas explainable Artificial Intelligence topic continues receive traction. interesting direction would explore different reservoir architectures model human brain better. Another interesting direction would use RCNs study videos which are naturally temporal investigate how the reservoir generalizes action domain. Finally although get fairly good performance sparse reservoir training images predict image complexity increases sophisticated reservoir would required match performance.",1954,1256,698,0.025,1.556,2025/11/05 17:18:53,0.01,1.468,0.7040498442367601,714.676
"We present Generative Adversarial Privacy and Fairness (GAPF), a data-driven framework for learning private and fair representations of the data. GAPF leverages recent advances in adversarial learning to allow a data holder to learn ""universal"" representations that decouple a set of sensitive attributes from the rest of the dataset. Under GAPF, finding the optimal decorrelation scheme is formulated as a constrained minimax game between a generative decorrelator and an adversary. We show that for appropriately chosen adversarial loss functions, GAPF provides privacy guarantees against strong information-theoretic adversaries and enforces demographic parity. We also evaluate the performance of GAPF on multi-dimensional Gaussian mixture models and real datasets, and show how a designer can certify that representations learned under an adversary with a fixed architecture perform well against more complex adversaries. The use of deep learning algorithms for data analytics has recently seen unprecedented success for a variety of problems such as image classification, natural language processing, and prediction of consumer behavior, electricity use, political preferences, to name a few. The success of these algorithms hinges on the availability of large datasets, that often contain sensitive information, and thus, may facilitate learning models that inherit societal biases leading to unintended algorithmic discrimination on legally protected groups such as race or gender. This, in turn, has led to privacy and fairness concerns and a growing body of research focused on developing representations of the dataset with fairness and/or privacy guarantees. These techniques predominantly involve designing randomizing schemes, and in recent years, distinct approaches with provable statistical privacy or fairness guarantees have emerged.In the context of privacy, preserving the utility of published datasets while simultaneously providing provable privacy guarantees is a well-known challenge. While context-free privacy solutions, such as differential privacy BID10 a; BID7 BID8 , provide strong worst-case privacy guarantees, they often lead to a significant reduction in utility. In contrast, context-aware privacy solutions, e.g., mutual information privacy BID31 BID5 BID33 BID32 BID3 ), achieve improved privacy-utility tradeoff, but assume that the data holder has access to dataset statistics.In the context of fairness, machine learning models seek to maximize predictive accuracy. Fairness concerns arise when models learned from datasets that include patterns of societal bias and discrimination inherit such biases. Thus, there is a need for actively decorrelating sensitive and non-sensitive data. In the context of publishing datasets or meaningful representations that can be ""universally"" used for a variety of learning tasks, modifying the training data is the most appropriate and is the focus of this work. Fairness can then be achieved by carefully designing objective functions which approximate a specific fairness definition while simultaneously ensuring maximal utility (Zemel et al., 2013; BID6 BID16 . This, in turn, requires dataset statistics.Adversarial learning approaches for context-aware privacy and fairness have been studied extensively BID13 BID0 BID30 BID20 BID36 BID4 BID27 Zhang et al., 2018) . They allow the data curator to cleverly decorrelate the sensitive attributes from the rest of the dataset. These approaches overcome the lack of statistical knowledge by taking a data-driven approach that leverages recent advancements in generative adversarial networks (GANs) BID17 BID28 . However, most existing efforts focus on extensive empirical studies without theoretical verification and focus predominantly on providing guarantees for a specific classification task. This work introduces a general framework for context-aware privacy and fairness that we call generative adversarial privacy and fairness (GAPF) (see FIG0 . We provide precise connections to information-theoretic privacy and fairness formulations and derive game-theoretically optimal decorrelation schemes to compare against those learned directly from the data. While our framework can be generalized to learn an arbitrary representation using an encoder-decoder structure, this paper primarily focuses on learning private/fair representations of the data (of the same dimension).Our Contributions. We list our main contributions below.1. We introduce GAPF, a framework for creating private/fair representations of data using an adversarially trained conditional generative model. Unlike existing works, GAPF can create representations that are useful for a variety of classification tasks, without requiring the designer to model these tasks at training time. We validate this observation via experiments on the GENKI (Whitehill & Movellan, 2012) and HAR BID2 datasets.2. We show that via the choice of the adversarial loss function, our framework can capture a rich class of statistical and information-theoretic adversaries. This allows us to compare data-driven approaches directly against strong inferential adversaries (e.g., a maximum a posteriori probability (MAP) adversary with access to dataset statistics). We also show that by carefully designing the loss functions in the GAPF framework, we can enforce demographic parity.3. We make precise comparison between data-driven privacy/fairness methods and the minimax game-theoretic GAPF formulation. For Gaussian mixture data, we derive game-theoretically optimal decorrelation schemes and compare them with those that are directly learned in a datadriven fashion to show that the gap between theory and practice is negligible. Furthermore, we propose using mutual information estimators to verify that no adversary (regardless of their computational power) can reliably infer the sensitive attribute from the learned representation.Related work. In the context of publishing datasets with privacy and utility guarantees, a number of similar approaches have been recently considered. We briefly review them here. A detailed literature review is included in Appendix A. DP-based obfuscators for data publishing have been considered in BID18 BID26 . These novel approaches leverage non-generative minimax filters and deep auto-encoders to allow non-malicious entities to learn some public features from the filtered data, while preventing malicious entities from learning other sensitive features. However, DP can still incur a significant utility loss since it assumes worst-case dataset statistics. Our approach models a rich class of randomization-based schemes via a generative model that allows the generative decorrelator to tailor the noise to the dataset.Our work is closely related to adversarial neural cryptography BID0 , learning censored representations BID13 , privacy preserving image sharing BID30 , privacy-preserving adversarial networks BID36 , and adversarially learning fair representation BID27 in which adversarial learning is used to learn how to protect communications by encryption or hide/remove sensitive information or generate fair representation of the data. Similar to these problems, our model includes a minimax formulation and uses adversarial neural networks to learn decorrelation schemes that prevent an adversary from inferring the sensitive variable. However, most of these papers use non-generative auto-encoders to remove sensitive information. Instead, we use a GANs-like approach to learn decorrelation schemes . We also go beyond in formulating a game-theoretic setting subject to a distortion constraint which allows us to learn private/fair representation for a variety of learning tasks. Enforcing the distortion constraint calls for a new training process that relies on the Penalty method or Augmented Lagrangian method presented in Appendix C. We show that our framework captures a rich class of statistical and information-theoretic adversaries by changing the loss function. We also compare the performance of data-driven privacy/fairness methods and the minimax game-theoretic GAPF.Fair representations using information-theoretic objective functions and constrained optimization have been proposed in BID6 BID16 . However, both approaches require the knowledge of dataset statistics, which is very difficult to obtain for real datasets. We overcome the issue of statistical knowledge by taking a data-driven approach , i.e., learning the representation from the data directly via adversarial models. In contrast to in-processing approaches that modify learning algorithms to ensure fair predictions (e..g, using linear programs in BID11 BID14 or via adversarial learning approach in ( Zhang et al., 2018) ), we focus on a pre-processing approach to ensure fairness for a variety of learning tasks. Using GANs to generate synthetic non-sensitive attributes and labels which ensure fairness while preserving the utility of the data (predicting the label) has been studied in (Xu et al., 2018; BID34 . Rather than using a conditional-generative model to generate synthetic data, we focus on creating fair/private representations of the original data while preserving the utility of the representations for a variety of learning tasks by learning nonlinear compression and noise adding schemes via a generative adversarial model. We have introduced a novel adversarial learning framework for creating private/fair representations of the data with verifiable guarantees. GAPF allows the data holder to learn the decorrelation scheme directly from the dataset (to be published) without requiring access to dataset statistics. Under GAPF, finding the optimal decorrelation scheme is formulated as a game between two players: a generative decorrelator and an adversary. We have shown that for appropriately chosen loss functions, GAPF can provide guarantees against strong information-theoretic adversaries, such as MAP and MI adversaries. It can also enforce fairness, quantified via demographic parity by using the log-loss function. We have also validated the performance of GAPF on Gaussian mixture models and real datasets. There are several fundamental questions that we seek to address. An immediate one is to develop techniques to rigorously benchmark data-driven results for large datasets against computable theoretical guarantees. More broadly, it will be interesting to investigate the robustness and convergence speed of the decorrelation schemes learned in a data-driven fashion. In this paper, we connect our objective function in GAPF with demographic parity. Since there is no single metric for fairness, this leaves room for designing objective functions that link to other fairness metrics such as equalized odds and equal opportunity.",present Generative Adversarial Privacy Fairness GAPF data-driven framework learning private fair representations data. GAPF leverages recent advances which adversarial learning allow data holder learn universal representations decouple set sensitive attributes rest dataset. GAPF finding optimal decorrelation scheme is formulated constrained minimax game generative decorrelator adversary. show appropriately chosen adversarial loss functions GAPF provides privacy guarantees strong information-theoretic adversaries enforces demographic parity. have also evaluate performance GAPF multi-dimensional Gaussian mixture models real datasets show how a designer can certify representations learned adversary fixed architecture perform well complex adversaries. use deep learning algorithms data analytics has recently seen unprecedented success variety problems image classification natural language processing prediction consumer behavior electricity use political preferences name few. success algorithms hinges availability large datasets often contain sensitive information thus may facilitate learning models inherit societal biases leading unintended algorithmic discrimination legally protected groups race gender. turn has led privacy fairness concerns growing body research focused developing representations dataset fairness/privacy guarantees. techniques predominantly involve designing randomizing schemes recent years distinct approaches provable statistical privacy fairness guarantees have emerged.In context privacy preserving utility published datasets simultaneously providing provable privacy guarantees is a well-known challenge. context-free privacy solutions differential privacy BID10 a;BID7 BID8 provide strong worst-case privacy guarantees often lead significant reduction utility. contrast context-aware privacy solutions e.g mutual information privacy BID31 BID5 BID33 BID32 BID3 achieve improved privacy-utility tradeoff assume data holder has access dataset statistics.In context fairness machine learning models seek maximize predictive accuracy. Fairness concerns arise when models learned datasets include patterns societal bias discrimination inherit biases. Thus is a need actively decorrelating sensitive non-sensitive data. context publishing datasets meaningful representations can be universally used variety learning tasks modifying training data is the most appropriate is the focus work. Fairness can then be achieved carefully designing objective functions which approximate specific fairness definition simultaneously ensuring maximal utility Zemeletal. 2013;BID6 BID16. turn requires dataset statistics.Adversarial learning approaches context-aware privacy fairness have been studied extensively BID13 BID0 BID30 BID20 BID36 BID4 BID27 Zhangetal. 2018 allow data curator cleverly decorrelate sensitive attributes rest dataset. approaches overcome lack statistical knowledge taking data-driven approach leverages recent advancements generative adversarial networks GANs BID17 BID28. However existing efforts focus extensive empirical studies without theoretical verification is the focus predominantly providing guarantees specific classification task. work introduces general framework context-aware privacy fairness call generative adversarial privacy fairness GAPF see FIG0. provide precise connections information-theoretic privacy fairness formulations derive game-theoretically optimal decorrelation schemes compare learned directly data. framework can be generalized learn arbitrary representation using encoder-decoder structure paper primarily focuses learning private/fair representations data dimension.Our Contributions. list main contributions below.1 introduce GAPF framework creating private/fair representations data using adversarially trained conditional generative model. Unlike existing works GAPF can create representations are useful variety classification tasks without requiring designer model tasks training time. validate observation via experiments GENKI Whitehill Movellan 2012 HAR BID2 datasets.2 show via choice adversarial loss function framework can capture rich class statistical information-theoretic adversaries. allowsus compare data-driven approaches directly strong inferential adversaries e.g maximum posteriori probability MAP adversary access dataset statistics also show carefully designing loss functions GAPF framework can enforce enforce demographic parity.3 make precise comparison data-driven privacy/fairness methods minimax game-theoretic GAPF formulation. Gaussian mixture data derive game-theoretically optimal decorrelation schemes compare are directly learned datadriven fashion show gap theory practice is negligible. Furthermore propose using mutual information estimators verify adversary regardless computational power can reliably infer sensitive attribute learned representation.Related work. context publishing datasets privacy utility guarantees number similar approaches have been recently considered. briefly review here. detailed literature review is included Appendix A. DP-based obfuscators data publishing have been considered BID18 BID26. novel approaches leverage non-generative minimax filters deep auto-encoders allow non-malicious entities learn public features filtered data preventing malicious entities learning sensitive features. However DP can still incur significant utility loss since assumes worst-case dataset statistics. approach models rich class randomization-based schemes via generative model allows generative decorrelator tailor noise dataset.Our work is closely related adversarial neural cryptography BID0 learning censored representations BID13 privacy preserving image sharing BID30 privacy-preserving adversarial networks BID36 adversarially learning fair representation BID27 which adversarial learning is used learn how to protect communications encryption hide/remove sensitive information generate fair representation data. Similar problems model includes minimax formulation uses adversarial neural networks learn decorrelation schemes prevent adversary inferring sensitive variable. However papers use non-generative auto-encoders remove sensitive information. Instead use GANs-like approach learn decorrelation schemes. have also go beyond formulating game-theoretic setting subject distortion constraint which allowsus learn private/fair representation variety learning tasks. Enforcing distortion constraint calls new training process relies Penalty method Augmented Lagrangian method presented AppendixC. show framework captures rich class statistical information-theoretic adversaries changing loss function. have also compare performance data-driven privacy/fairness methods minimax game-theoretic GAPF.Fair representations using information-theoretic objective functions constrained optimization have been proposed BID6 BID16. However approaches require knowledge dataset statistics which is very difficult obtain real datasets. overcome issue statistical knowledge taking data-driven approach.e learning representation data directly via adversarial models. contrast in-processing approaches modify learning algorithms ensure fair predictions e..g using linear programs BID11 BID14 via adversarial learning approach Zhangetal. 2018 focus pre-processing approach ensure fairness variety learning tasks. Using GANs generate synthetic non-sensitive attributes labels which ensure fairness preserving utility data predicting label has been studied Xuetal. 2018;BID34. Rather using conditional-generative model generate synthetic data focus creating fair/private representations original data preserving utility representations variety learning tasks learning nonlinear compression noise adding schemes via generative adversarial model. have introduced novel adversarial learning framework creating private/fair representations data verifiable guarantees. GAPF allows data holder learn decorrelation scheme directly dataset published without requiring access dataset statistics. GAPF finding optimal decorrelation scheme is formulated game two players:generative decorrelator adversary. have shown appropriately chosen loss functions GAPF can provide guarantees strong information-theoretic adversaries MAP MI adversaries. can also enforce fairness quantified via demographic parity using log-loss function. have also validated performance GAPF Gaussian mixture models real datasets. are several fundamental questions seek address. immediate one is to develop techniques rigorously benchmark data-driven results large datasets computable theoretical guarantees. broadly will be interesting investigate robustness convergence speed decorrelation schemes learned data-driven fashion. paper connect objective function GAPF demographic parity. Since is no single metric fairness leaves room designing objective functions link fairness metrics equalized odds equal opportunity.,1957,1386,571,0.022,1.412,2025/11/05 17:18:53,0.01,1.478,0.2554517133956382,574.419
"Current machine learning algorithms can be easily fooled by adversarial examples. One possible solution path is to make models that use confidence thresholding to avoid making mistakes. Such models refuse to make a prediction when they are not confident of their answer. We propose to evaluate such models in terms of tradeoff curves with the goal of high success rate on clean examples and low failure rate on adversarial examples. Existing untargeted attacks developed for models that do not use confidence thresholding tend to underestimate such models' vulnerability. We propose the MaxConfidence family of attacks, which are optimal in a variety of theoretical settings, including one realistic setting: attacks against linear models. Experiments show the attack attains good results in practice. We show that simple defenses are able to perform well on MNIST but not on CIFAR, contributing further to previous calls that MNIST should be retired as a benchmarking dataset for adversarial robustness research.   We release code for these evaluations as part of the cleverhans (Papernot et al 2018) library  (ICLR reviewers should be careful not to look at who contributed these features to cleverhans to avoid de-anonymizing this submission). We have made the following contributions:• We have shown that adversarial training on one kind of out-of-distribution data can actually worsen performance on other kinds of out-of-distribution data, relative to a baseline that uses confidence thresholding as the only defense.• We have introduced the evaluation methodology of success-fail curves, showing which success rates on clean data and failure rates on adversarial data are feasible for different confidence thresholds.• We have presented an attack that is optimal against a variety of confidence thresholding models. Specifically , it is optimal against linear classifiers and optimal against general models whenever the underlying optimization approximately succeeds.• We have shown an evaluation methodology that maps out an entire success-failure tradeoff curve without needing to re-train the model or re-run the evaluation for different thresholds.• We have shown that confidence thresholding with simple regularization is sufficient to achieve reasonable robustness to L ∞ attacks on MNIST, despite being roughly 40X cheaper to train than adversarial training.• We have shown that confidence thresholding can lead to robustness to a variety of attacks, without needing to anticipate and formally specify each attack type.Overall, we hope that our evaluation methodology will help to design and rigorously test low-cost, versatile defenses against a wide variety of adversarial examples. A set of points that should be equivalent to x. An adversarial example corresponding to x must be drawn from this set. x An adversarial example corresponding to x p model (y | x) The conditional distribution over the classes represented by the model c(x)arg max y p model (y | x), the confidence of the model for input x kThe number of classes tThe confidence threshold used by the model. An input x is covered only if c(x) > t. wThe weight vector for a logistic regression model η A perturbation applied to a clean input x B MODEL A Our ""Model A"" is a simple model that we tuned by trial and error to yield better success-fail curves than the baseline. We do not advocate ""Model A"" as the latest and greatest model that everyone should switch to. It is only included as a test point to show that our evaluation methodology can find interesting differences between models that have similar accuracy at 100% coverage on clean and adversarial data.Our trial-and-error design process was based on performance on clean data and on L ∞ adversarial examples. We did not use information about performance on semantic adversarial examples during the design process, so the defense was not designed in any specific way to handle these examples.The model architecture is straightforward to describe in cleverhans format: Conv2D(nb_filters, (3, 3) , (2, 2), ""SAME""), ReLU(), Add ([Conv2D(nb_filters, (3, 3) , (1, 1), ""SAME""), ReLU(), Conv2D(nb_filters, (3, 3) , (1, 1), ""SAME"")]), Conv2D(nb_filters * 2, (3, 3), (2, 2), ""SAME""), ReLU(), Conv2D(nb_filters * 2, (3, 3), (1, 1), ""VALID""), ReLU(), Flatten(), Linear(nb_classes), Softmax()] DISPLAYFORM0 In other words, it is a simple convolutional network, containing a convolution and 2X downsampling layer, a residual layer, two convolutional layers, and a fully connected layer to output the logits. There are no normalization layers, etc., and all of the hidden units are ReLUs BID9 BID14 BID3 .",Current machine learning algorithms can be easily fooled adversarial examples. One possible solution path is to make models do not use confidence thresholding avoid making mistakes. models refuse make prediction when they are not confident answer. propose evaluate models terms tradeoff curves goal high success rate clean examples low failure rate adversarial examples. Existing untargeted attacks developed models do not use confidence thresholding tend underestimate models' vulnerability. propose MaxConfidence family attacks which are is optimal variety theoretical settings including one realistic setting:attacks linear models. Experiments show attack attains good results practice. show simple defenses are able perform well MNIST CIFAR contributing previous calls MNIST should be retired benchmarking dataset adversarial robustness research. release code evaluations part cleverhans Papernot et al 2018 library ICLR reviewers should be careful look who contributed features cleverhans avoid de-anonymizing submission have made following contributions:• have shown adversarial training one kind out-of-distribution data can actually worsen performance kinds out-of-distribution data relative baseline uses confidence thresholding defense.• have introduced evaluation methodology success-fail curves showing which success rates clean data failure rates adversarial data are feasible different confidence thresholds.• have presented attack is optimal variety confidence thresholding models. Specifically which are is optimal linear classifiers optimal general models whenever underlying optimization approximately succeeds.• have shown evaluation methodology maps entire success-failure tradeoff curve without needing re-train model re-run evaluation different thresholds.• have shown confidence thresholding simple regularization is sufficient achieve reasonable robustness L ∞ attacks MNIST despite roughly 40X cheaper train adversarial training.• have shown confidence thresholding can lead robustness variety attacks without needing anticipate formally specify attack type.Overall hope evaluation methodology will help design rigorously test low-cost versatile defenses wide variety adversarial examples. set points should be equivalent x. adversarial example corresponding x must drawn set. x adversarial example corresponding x p model x conditional distribution classes represented modelc x arg max p model x confidence model input x kThe number classes tThe confidence threshold used model. inputx is covered ifc x t. wThe weight vector logistic regression modelη perturbation applied clean inputxB MODEL Model is a simple model tuned trial error yield better success-fail curves baseline. do not advocate Model latest greatest model everyone should switch to. is only included test point show evaluation methodology can find interesting differences models have similar accuracy 100% coverage clean adversarial data.Our trial-and-error design process was based performance clean data L ∞ adversarial examples. did not use information performance semantic adversarial examples design process defense was not designed specific way handle examples.The model architecture is straightforward describe cleverhans format:Conv2D nb_filters 3 3 2 2 ReLU Add Conv2D nb_filters 3 3 1 1 ReLU Conv2D nb_filters 3 3 1 1 Conv2D nb_filters*2 3 3 2 2 ReLU Conv2D nb_filters*2 3 3 1 1 VALID ReLU Flatten Linear nb_classes Softmax DISPLAYFORM0 words is a simple convolutional network containing convolution 2X downsampling layer residual layer two convolutional layers fully connected layer output logits. are no normalization layers etc. hidden units are ReLUs BID9 BID14 BID3.,969,664,305,0.01,1.459,2025/11/05 17:18:53,0.0,1.459,0.4018691588785047,314.863
"Deep learning has achieved remarkable successes in solving challenging reinforcement learning (RL) problems when dense reward function is provided. However, in sparse reward environment it still often suffers from the need to carefully shape reward function to guide policy optimization. This limits the applicability of RL in the real world since both reinforcement learning and domain-specific knowledge are required. It is therefore of great practical importance to develop algorithms which can learn from a binary signal indicating successful task completion or other unshaped, sparse reward signals. We propose a novel method called competitive experience replay, which efficiently supplements a sparse reward by placing learning in the context of an exploration competition between a pair of agents. Our method complements the recently proposed hindsight experience replay (HER) by inducing an automatic exploratory curriculum. We evaluate our approach on the tasks of reaching various goal locations in an ant maze and manipulating objects with a robotic arm. Each task provides only binary rewards indicating whether or not the goal is achieved. Our method asymmetrically augments these sparse rewards for a pair of agents each learning the same task, creating a competitive game designed to drive exploration. Extensive experiments demonstrate that this method leads to faster converge and improved task performance. Recent progress in deep reinforcement learning has achieved very impressive results in domains ranging from playing games BID28 BID39 BID31 , to high dimensional continuous control , and robotics BID21 BID2 .Despite these successes, in robotics control and many other areas, deep reinforcement learning still suffers from the need to engineer a proper reward function to guide policy optimization (see e.g. BID36 BID29 . In robotic control as stacking bricks, reward function need to be sharped to very complex which consists of multiple terms BID36 . It is extremely hard and not applicable to engineer such reward function for each task in real world since both reinforcement learning expertise and domain-specific knowledge are required. Learning to perform well in environments with sparse rewards remains a major challenge. Therefore, it is of great practical importance to develop algorithms which can learn from binary signal indicating successful task completion or other unshaped reward signal.In environments where dense reward function is not available, only a small fraction of the agents' experiences will be useful to compute gradient to optimize policy, leading to substantial high sample complexity. Providing agents with useful signals to pursue in sparse reward environments becomes crucial in these scenarios.In the domain of goal-directed RL, the recently proposed hindsight experience replay (HER) BID0 addresses the challenge of learning from sparse rewards by re-labelling visited states as goal states during training. However, this technique continues to suffer from sample inefficiency, ostensibly due to difficulties related to exploration. In this work, we address these limitations by introducing a method called Competitive Experience Replay (CER). This technique attempts to emphasize exploration by introducing a competition between two agents attempting to learn the same task. Intuitively, agent A (the agent ultimately used for evaluation) receives a penalty for visiting states that the competitor agent (B) also visits; and B is rewarded for visiting states found by A. Our approach maintains the reward from the original task such that exploration is biased towards the behaviors best suited to accomplishing the task goals. We show that this competition between agents can automatically generate a curriculum of exploration and shape otherwise sparse reward. We jointly train both agents' policies by adopting methods from multi-agent RL. In addition, we propose two versions of CER, independent CER, and interact CER, which differ in the state initialization of agent B: whether it is sampled from the initial state distribution or sampled from off-policy samples of agent A, respectively.Whereas HER re-labels samples based on an agent's individual rollout, our method re-labels samples based on intra-agent behavior; as such, the two methods do not interfere with each other algorithmically and are easily combined during training. We evaluate our method both with and without HER on a variety of reinforcement learning tasks, including navigating an ant agent to reach a goal position and manipulating objects with a robotic arm. For each such task the default reward is sparse, corresponding to a binary indicator of goal completion. Ablation studies show that our method is important for achieving a high success rate and often demonstrates faster convergence. Interestingly, we find that CER and HER are complementary methods and employ both to reach peak efficiency and performance. Furthermore, we observe that, when combined with HER, CER outperforms curiosity-driven exploration. We introduce Competitive Experience Replay, a new and general method for encouraging exploration through implicit curriculum learning in sparse reward settings. We demonstrate an empirical advantage of our technique when combined with existing methods in several challenging RL tasks. In future work, we aim to investigate richer ways to re-label rewards based on intra-agent samples to further harness multi-agent competition, it's interesting to investigate counterfactual inference to promote efficient re-label off-policy samples. We hope that this will facilitate the application of our method to more open-end environments with even more challenging task structures. In addition, future work will explore integrating our method into approaches more closely related to model-based learning, where adequate exposure to the dynamics of the environment is often crucial. As BID0 and BID1 observe (and we also observe), performance depends on the batch size. We leverage this observation to tune the relative strengths of Agents A and B by separately manipulating the batch sizes used for updating each.For simplicity, we control the batch size by changing the number of MPI workers devoted to a particular update. Each MPI worker computes the gradients for a batch size of 256; averaging the gradients from each worker results in an effective batch size of N * 256. For our single-agent baselines, we choose N = 30 workers, and, when using CER, a default of N = 15 for each A and B In the following, AxBy denotes, for agent A, N = x and, for agent B, N = y. These results suggest that, while a sufficiently large batch size is important for achieving the best performance, the optimal configuration occurs when the batch sizes used for the two agents are balanced. Interestingly, we observe that batch size imbalance adversely effects both agents trained during CER.",Deep learning has achieved remarkable successes solving challenging reinforcement learning RL problems when dense reward function is provided. However sparse reward environment still often suffers need carefully shape reward function guide policy optimization. limits applicability RL real world since reinforcement learning domain-specific knowledge are required. is therefore great practical importance develop algorithms which can learn binary signal indicating successful task completion unshaped sparse reward signals. propose novel method called competitive experience replay which efficiently supplements sparse reward placing learning context exploration competition pair agents. method complements recently proposed hindsight experience replay inducing automatic exploratory curriculum. evaluate approach tasks reaching various goal locations ant maze manipulating objects robotic arm. task provides binary rewards indicating whether goal is achieved. method asymmetrically augments sparse rewards pair agents learning task creating competitive game designed drive exploration. Extensive experiments demonstrate method leads faster converge improved task performance. Recent progress deep reinforcement learning has achieved impressive results domains ranging playing games BID28 BID39 BID31 high dimensional continuous control robotics BID21 BID2.Despite successes robotics control many areas deep reinforcement learning still suffers need engineer proper reward function guide policy optimization see e.g BID36 BID29. robotic control stacking bricks reward function need sharped complex which consists multiple terms BID36. is extremely hard applicable engineer reward function task real world since reinforcement learning expertise domain-specific knowledge are required. Learning perform well environments sparse rewards remains major challenge. Therefore is of great practical importance develop algorithms which can learn binary signal indicating successful task completion unshaped reward signal.In environments where dense reward function is not available small fraction agents' experiences will be useful compute gradient optimize policy leading substantial high sample complexity. Providing agents useful signals pursue sparse reward environments becomes crucial scenarios.In domain goal-directedRL recently proposed hindsight experience replay BID0 addresses challenge learning sparse rewards re-labelling visited states goal states training. However technique continues suffer sample inefficiency ostensibly due difficulties related exploration. work address limitations introducing method called Competitive Experience Replay CER technique attempts emphasize exploration introducing competition two agents attempting learn task. Intuitively agent agent ultimately used evaluation receives penalty visiting states competitor agent B also visits;B is rewarded visiting states found A. approach maintains reward original task exploration is biased towards behaviors best suited accomplishing task goals. show competition agents can automatically generate curriculum exploration shape otherwise sparse reward. jointly train agents' policies adopting methods multi-agentRL. addition propose two versions CER independent CER interact CER which differ state initialization agentB:whether is sampled initial state distribution sampled off-policy samples agent respectively.Whereas re-labels samples based agent's individual rollout method re-labels samples based intra-agent behavior;two methods do not interfere algorithmically are easily combined training. evaluate method without variety reinforcement learning tasks including navigating ant agent reach goal position manipulating objects robotic arm. task default reward is sparse corresponding binary indicator goal completion. Ablation studies show method is important achieving high success rate often demonstrates faster convergence. Interestingly find CER are complementary methods employ reach peak efficiency performance. Furthermore observe when combined CER outperforms curiosity-driven exploration. introduce Competitive Experience Replay new general method encouraging exploration implicit curriculum learning sparse reward settings. demonstrate empirical advantage technique when combined existing methods several challenging RL tasks. future work aim investigate richer ways re-label rewards based intra-agent samples harness multi-agent competition interesting investigate counterfactual inference promote efficient re-label off-policy samples. hope will facilitate application method open-end environments even challenging task structures. addition future work will explore integrating method approaches closely related model-based learning where adequate exposure dynamics environment is often crucial. BID0 BID1 observe also observe performance depends batch size. leverage observation tune relative strengths Agents B separately manipulating batch sizes used updating each.For simplicity control batch size changing number MPI workers devoted particular update. MPI worker computes gradients batch size 256;averaging gradients worker results effective batch size N * 256. single-agent baselines chooseN 30 workers when using CER default N 15 B following AxBy denotes agent N x agentB N y. results suggest sufficiently large batch size is important achieving best performance optimal configuration occurs when the batch sizes used two agents are balanced. Interestingly observe batch size imbalance adversely effects agents trained CER.,1216,801,415,0.013,1.518,2025/11/05 17:18:53,0.01,1.182,0.585669781931464,414.214
"This paper proposes a neural end-to-end text-to-speech (TTS) model which can control latent attributes in the generated speech that are rarely annotated in the training data, such as speaking style, accent, background noise, and recording conditions. The model is formulated as a conditional generative model with two levels of hierarchical latent variables. The first level is a categorical variable, which represents attribute groups (e.g. clean/noisy) and provides interpretability. The second level, conditioned on the first, is a multivariate Gaussian variable, which characterizes specific attribute configurations (e.g. noise level, speaking rate) and enables disentangled fine-grained control over these attributes. This amounts to using a Gaussian mixture model (GMM) for the latent distribution. Extensive evaluation demonstrates its ability to control the aforementioned attributes. In particular, it is capable of consistently synthesizing high-quality clean speech regardless of the quality of the training data for the target speaker. Recent development of neural sequence-to-sequence TTS models has shown promising results in generating high fidelity speech without the need of handcrafted linguistic features BID30 BID37 BID2 . These models rely heavily on a encoderdecoder neural network structure BID31 BID5 that maps a text sequence to a sequence of speech frames. Extensions to these models have shown that attributes such as speaker identity can be controlled by conditioning the decoder on additional attribute labels BID3 .There are many speech attributes aside from speaker identity that are difficult to annotate, such as speaking style, prosody, recording channel, and noise levels. ; model such latent attributes through conditional auto-encoding, by extending the decoder inputs to include a vector inferred from the target speech which aims to capture the residual attributes that are not specified by other input streams, in addition to text and a speaker label. These models have shown convincing results in synthesizing speech that resembles the prosody or the noise conditions of the reference speech, which may not have the same text or speaker identity as the target speech.Nevertheless, the presence of multiple latent attributes is common in crowdsourced data such as BID26 , in which prosody, speaker, and noise conditions all vary simultaneously. Using such data , simply copying the latent attributes from a reference is insufficient if one desires to synthesize speech that mimics the prosody of the reference, but is in the same noise condition as another. If the latent representation were disentangled, these generating factors could be controlled independently. Furthermore, it is can useful to construct a systematic method for synthesizing speech with random latent attributes, which would facilitate data augmentation BID33 BID12 BID8 by generating diverse examples. These properties were not explicitly addressed in the previous studies, which model variation of a single latent attribute.Motivated by the applications of sampling, inferring, and independently controlling individual attributes, we build off of and extend Tacotron 2 to model two separate latent spaces: one for labeled (i.e. related to speaker identity) and another for unlabeled attributes. Each latent variable is modeled in a variational autoencoding BID22 ) framework using Gaussian mixture priors. The resulting latent spaces (1) learn disentangled attribute representations, where each dimension controls a different generating factor; (2) discover a set of interpretable clusters, each of which corresponds to a representative mode in the training data (e.g., one cluster for clean speech and another for noisy speech); and (3) provide a systematic sampling mechanism from the learned prior. The proposed model is extensively evaluated on four datasets with subjective and objective quantitative metrics, as well as comprehensive qualitative studies. Experiments confirm that the proposed model is capable of controlling speaker, noise, and style independently, even when variation of all attributes is present but unannotated in the train set.Our main contributions are as follows:• We propose a principled probabilistic hierarchical generative model, which improves (1) sampling stability and disentangled attribute control compared to e.g. the GST model of , and (2) interpretability and quality compared to e.g. BID0 .• The model formulation explicitly factors the latent encoding by using two mixture distributions to separately model supervised speaker attributes and latent attributes in a disentangled fashion. This makes it straightforward to condition the model output on speaker and latent encodings inferred from different reference utterances.• To the best of our knowledge, this work is the first to train a high-quality controllable textto-speech system on real found data containing significant variation in recording condition, speaker identity, as well as prosody and style. Previous results on similar data focused on speaker modeling , and did not explicitly address modeling of prosody and background noise. Leveraging disentangled speaker and latent attribute encodings, the proposed model is capable of inferring the speaker attribute representation from a noisy utterance spoken by a previously unseen speaker, and using it to synthesize high-quality clean speech that approximates the voice of that speaker. We describe GMVAE-Tacotron, a TTS model which learns an interpretable and disentangled latent representation to enable fine-grained control of latent attributes and provides a systematic sampling scheme for them. If speaker labels are available, we demonstrate an extension of the model that learns a continuous space that captures speaker attributes, along with an inference model which enables one-shot learning of speaker attributes from unseen reference utterances.The proposed model was extensively evaluated on tasks spanning a wide range of signal variation. We demonstrated that it can independently control many latent attributes, and is able to cluster them without supervision. In particular, we verified using both subjective and objective tests that the model could synthesize high-quality clean speech for a target speaker even if the quality of data for that speaker does not meet high standard. These experimental results demonstrated the effectiveness of the model for training high-quality controllable TTS systems on large scale training data with rich styles by learning to factorize and independently control latent attributes underlying the speech signal.",paper proposes neural end-to-end text-to-speech TTS model which can control latent attributes generated speech are rarely annotated training data speaking style accent background noise recording conditions. model is formulated conditional generative model two levels hierarchical latent variables. first level is a categorical variable which represents attribute groups e.g clean/noisy provides interpretability. second level conditioned first is a multivariate Gaussian variable which characterizes specific attribute configurations e.g noise level speaking rate enables disentangled fine-grained control attributes. amounts using Gaussian mixture model GMM latent distribution. Extensive evaluation demonstrates ability control aforementioned attributes. particular is capable consistently synthesizing high-quality clean speech regardless quality training data target speaker. Recent development neural sequence-to-sequence TTS models has shown promising results generating high fidelity speech without need handcrafted linguistic features BID30 BID37 BID2. models rely heavily encoderdecoder neural network structure BID31 BID5 maps text sequence sequence speech frames. Extensions models have shown attributes speaker identity can be controlled conditioning decoder additional attribute labels BID3.There are many speech attributes aside speaker identity are difficult annotate speaking style which prosody recording channel is in noise levels. model latent attributes conditional auto-encoding extending decoder inputs include vector inferred target speech which aims capture residual attributes are not specified input streams addition text speaker label. models have shown convincing results synthesizing speech resembles prosody noise conditions reference speech may have the same text speaker identity target speech.Nevertheless presence multiple latent attributes is common crowdsourced data BID26 which prosody speaker is in noise conditions vary simultaneously. Using data simply copying latent attributes reference is insufficient if one desires synthesize speech mimics prosody reference isin noise condition another. If the latent representation were disentangled generating factors could controlled independently. Furthermore is can useful construct systematic method synthesizing speech random latent attributes would facilitate data augmentation BID33 BID12 BID8 generating diverse examples. properties were not explicitly addressed previous studies which model variation single latent attribute.Motivated applications sampling inferring independently controlling individual attributes build extend Tacotron2 model two separate latent spaces:one labeled.e related speaker identity another unlabeled attributes. latent variable is modeled variational autoencoding BID22 framework using Gaussian mixture priors. resulting latent spaces 1 learn disentangled attribute representations where each dimension controls different generating factor;2 discover set interpretable clusters which corresponds representative mode training data e.g one cluster clean speech another noisy speech 3 provide systematic sampling mechanism learned prior. proposed model is extensively evaluated four datasets subjective objective quantitative metrics well comprehensive qualitative studies. Experiments confirm proposed model is capable controlling speaker is in noise style independently even when variation attributes is present unannotated train set.Our main contributions are as follows:• propose principled probabilistic hierarchical generative model which improves 1 sampling stability disentangled attribute control compared e.g GST model 2 interpretability quality compared e.g BID0.• model formulation explicitly factors latent encoding using two mixture distributions separately model supervised speaker attributes latent attributes disentangled fashion. makes straightforward condition model output speaker latent encodings inferred different reference utterances.• best knowledge work is the first train high-quality controllable textto-speech system real found data containing significant variation recording condition speaker identity well prosody style. Previous results similar data focused speaker modeling did not explicitly address modeling prosody background noise. Leveraging disentangled speaker latent attribute encodings proposed model is capable inferring speaker attribute representation noisy utterance spoken previously unseen speaker using synthesize high-quality clean speech approximates voice speaker. describe GMVAE-Tacotron TTS model which learns interpretable disentangled latent representation enable fine-grained control latent attributes provides systematic sampling scheme them. If speaker labels are available demonstrate extension model learns continuous space captures speaker attributes along inference model which enables one-shot learning speaker attributes unseen reference utterances.The proposed model was extensively evaluated tasks spanning wide range signal variation. demonstrated can independently control many latent attributes is able cluster without supervision. particular verified using subjective objective tests model could synthesize high-quality clean speech target speaker even if the quality data speaker does not meet high standard. experimental results demonstrated effectiveness model training high-quality controllable TTS systems large scale training data rich styles learning factorize independently control latent attributes underlying speech signal.,1180,822,358,0.012,1.436,2025/11/05 17:18:53,0.01,1.37,0.3302180685358252,359.867
"Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%. Consider the problem of counting how many cats there are in Figure 1 . Solving this involves several rough steps: understanding what instances of that type can look like, finding them in the image, and adding them up. This is a common task in Visual Question Answering (VQA) -answering questions about images -and is rated as among the tasks requiring the lowest human age to be able to answer (Antol et al., 2015) . However, current models for VQA on natural images struggle to answer any counting questions successfully outside of dataset biases (Jabri et al., 2016) .One reason for this is the presence of a fundamental problem with counting in the widely-used soft attention mechanisms (section 3). Another reason is that unlike standard counting tasks, there is no ground truth labeling of where the objects to count are. Coupled with the fact that models need to be able to count a large variety of objects and that, ideally, performance on non-counting questions should not be compromised, the task of counting in VQA seems very challenging.To make this task easier, we can use object proposals -pairs of a bounding box and object featuresfrom object detection networks as input instead of learning from pixels directly. In any moderately complex scene, this runs into the issue of double-counting overlapping object proposals. This is a problem present in many natural images, which leads to inaccurate counting in real-world scenarios.Our main contribution is a differentiable neural network component that tackles this problem and consequently can learn to count (section 4). Used alongside an attention mechanism, this component avoids a fundamental limitation of soft attention while producing strong counting features. We provide experimental evidence of the effectiveness of this component (section 5). On a toy dataset, we demonstrate that this component enables robust counting in a variety of scenarios. On the number category of the VQA v2 Open-Ended dataset (Goyal et al., 2017) , a relatively simple baseline model using the counting component outperforms all previous models -including large ensembles of state-of-the-art methods -without degrading performance on other categories. 1 2 RELATED WORK Usually, greedy non-maximum suppression (NMS) is used to eliminate duplicate bounding boxes. The main problem with using it as part of a model is that its gradient is piecewise constant. Various differentiable variants such as by Azadi et al. (2017) , Hosang et al. (2017) , and Henderson & Ferrari (2017) exist. The main difference is that, since we are interested in counting, our component does not need to make discrete decisions about which bounding boxes to keep; it outputs counting features, not a smaller set of bounding boxes. Our component is also easily integrated into standard VQA models that utilize soft attention without any need for other network architecture changes and can be used without using true bounding boxes for supervision.On the VQA v2 dataset (Goyal et al., 2017 ) that we apply our method on, only few advances on counting questions have been made. The main improvement in accuracy is due to the use of object proposals in the visual processing pipeline, proposed by BID0 . Their object proposal network is trained with classes in singular and plural forms, for example ""tree"" versus ""trees"", which only allows primitive counting information to be present in the object features after region-of-interest pooling. Our approach differs in the way that instead of relying on counting features being present in the input, we create counting features using information present in the attention map over object proposals. This has the benefit of being able to count anything that the attention mechanism can discriminate instead of only objects that belong to the predetermined set of classes that had plural forms.Using these object proposals, Trott et al. (2018) train a sequential counting mechanism with a reinforcement learning loss on the counting question subsets of VQA v2 and Visual Genome. They achieve a small increase in accuracy and can obtain an interpretable set of objects that their model counted, but it is unclear whether their method can be integrated into traditional VQA models due to their loss not applying to non-counting questions. Since they evaluate on their own dataset, their results can not be easily compared to existing results in VQA.Methods such as by Santoro et al. (2017) and Perez et al. (2017) can count on the synthetic CLEVR VQA dataset BID0 successfully without bounding boxes and supervision of where the objects to count are. They also use more training data (∼250,000 counting questions in the CLEVR training set versus ∼50,000 counting questions in the VQA v2 training set), much simpler objects, and synthetic question structures.More traditional approaches based on Lempitsky & Zisserman (2010) learn to produce a target density map, from which a count is computed by integrating over it. In this setting, Cohen et al. (2017) make use of overlaps of convolutional receptive fields to improve counting performance. Chattopadhyay et al. (2017) use an approach that divides the image into smaller non-overlapping chunks, each of which is counted individually and combined together at the end. In both of these contexts, the convolutional receptive fields or chunks can be seen as sets of bounding boxes with a fixed structure in their positioning. Note that while Chattopadhyay et al. (2017) evaluate their models on a small subset of counting questions in VQA, major differences in training setup make their results not comparable to our work. After understanding why VQA models struggle to count, we designed a counting component that alleviates this problem through differentiable bounding box deduplication. The component can readily be used alongside any future improvements in VQA models, as long as they still use soft attention as all current top models on VQA v2 do. It has uses outside of VQA as well: for many counting tasks, it can allow an object-proposal-based approach to work without ground-truth objects available as long as there is a -possibly learned -per-proposal scoring (for example using a classification score) and a notion of how dissimilar a pair of proposals are. Since each step in the component has a clear purpose and interpretation, the learned weights of the activation functions are also interpretable. The design of the counting component is an example showing how by encoding inductive biases into a deep learning model, challenging problems such as counting of arbitrary objects can be approached when only relatively little supervisory information is available.For future research, it should be kept in mind that VQA v2 requires a versatile skill set that current models do not have. To make progress on this dataset, we advocate focusing on understanding of what the current shortcomings of models are and finding ways to mitigate them.","Visual Question Answering VQA models have struggled counting objects natural images far. identify fundamental problem due soft attention models cause. circumvent problem propose neural network component allows robust counting object proposals. Experiments toy task show effectiveness component can obtain state-of-the-art accuracy number category VQA v2 dataset without negatively affecting categories even outperforming ensemble models single model. difficult balanced pair metric component gives substantial improvement counting strong baseline 6.6%. Consider problem counting how many cats are in Figure1. Solving involves several rough steps:understanding what instances type can look like finding image adding up. is a common task Visual Question Answering VQA -answering questions images -and is rated among tasks requiring lowest human age able answer Antoletal. 2015 However current models VQA natural images struggle answer counting questions successfully outside dataset biases Jabrietal. 2016.One reason is the presence fundamental problem counting widely-used soft attention mechanisms section3 Another reason is that unlike standard counting tasks is no ground truth labeling where the objects count are. Coupled fact models need able count large variety where the objects ideally performance non-counting questions should not be compromised task counting VQA seems challenging.To make task easier can use object proposals -pairs bounding box object featuresfrom object detection networks input instead learning pixels directly. moderately complex scene runs issue double-counting overlapping object proposals. is a problem present many natural images which leads inaccurate counting real-world scenarios.Our main contribution is a differentiable neural network component tackles problem consequently can learn count section4 Used alongside attention mechanism component avoids fundamental limitation soft attention producing strong counting features. provide experimental evidence effectiveness component section5 toy dataset demonstrate component enables robust counting variety scenarios. number category VQA v2 Open-Ended dataset Goyaletal. 2017 relatively simple baseline model using counting component outperforms previous models -including large ensembles state-of-the-art methods -without degrading performance categories. 1 2 RELATED WORK Usually greedy non-maximum suppression NMS is used eliminate duplicate bounding boxes. main problem using part model is that its gradient is piecewise constant. Various differentiable variants Azadietal. 2017 Hosangetal. 2017 Henderson Ferrari 2017 exist. main difference is that,since are interested counting component does not need make discrete decisions which bounding boxes keep;outputs counting features smaller set bounding boxes. component is also easily integrated standard VQA models utilize soft attention without need network architecture changes can be used without using true bounding boxes supervision.On VQA v2 dataset Goyaletal. 2017 apply method advances counting questions have been made. main improvement accuracy is due use object proposals visual processing pipeline proposed BID0. object proposal network is trained classes singular plural forms example tree versus trees which only allows primitive counting information present object features region-of-interest pooling. approach differs way instead relying counting features present input create counting features using information present attention map object proposals. has the benefit able count anything attention mechanism can discriminate instead where the objects belong predetermined set classes had plural forms.Using object proposals Trottetal. 2018 train sequential counting mechanism reinforcement learning loss counting question subsets VQAv2 Visual Genome. achieve small increase accuracy can obtain interpretable set where the objects model counted is unclear whether method can be integrated traditional VQA models due loss applying non-counting questions. Since evaluate dataset results can not be easily compared existing results VQA.Methods Santoroetal. 2017 Perezetal. 2017 can count synthetic CLEVR VQA dataset BID0 successfully without bounding boxes supervision where the objects count are. also use training data ∼250,000 counting questions CLEVR training set versus ∼50,000 counting questions VQA v2 training set much simpler objects synthetic question structures.More traditional approaches based Lempitsky Zisserman 2010 learn produce target density map which a count is computed integrating it. setting Cohenetal. 2017 make use overlaps convolutional receptive fields improve counting performance. Chattopadhyayetal. 2017 use approach divides image smaller non-overlapping chunks which is counted individually combined together end. contexts convolutional receptive fields chunks can be seen sets bounding boxes fixed structure positioning. Note Chattopadhyayetal. 2017 evaluate models small subset counting questions VQA major differences training setup make results comparable work. understanding why VQA models struggle count designed counting component alleviates problem differentiable bounding box deduplication. component can readily used alongside future improvements VQA models long still use soft attention current top models VQAv2 do. has uses outside VQA well:many counting tasks can allow object-proposal-based approach work without ground-truth objects available long is a -possibly learned -per-proposal scoring example using classification score notion how dissimilar pair proposals are. Since step component has a clear purpose interpretation learned weights activation functions are also interpretable. design counting component is an example showing how by encoding inductive biases deep learning model challenging problems counting arbitrary objects can be approached when only relatively little supervisory information is available.For future research should be kept mind VQA v2 requires versatile skill set current models have. make progress dataset advocate focusing understanding what the current shortcomings models are and finding ways mitigate them.",1505,1040,465,0.017,1.447,2025/11/05 17:18:53,0.01,1.559,0.3644859813084112,474.393
"We propose a simple and robust training-free approach for building sentence representations. Inspired by the Gram-Schmidt Process in geometric theory, we build an orthogonal basis of the subspace spanned by a word and its surrounding context in a sentence. We model the semantic meaning of a word in a sentence based on two aspects. One is its relatedness to the word vector subspace already spanned by its contextual words. The other is its novel semantic meaning which shall be introduced as a new basis vector perpendicular to this existing subspace.   Following this motivation, we develop an innovative method based on orthogonal basis to combine pre-trained word embeddings into sentence representation. This approach requires zero training and zero parameters, along with efficient inference performance. We evaluate our approach on 11 downstream NLP tasks. Experimental results show that our model outperforms all existing zero-training alternatives in all the tasks and it is competitive to other approaches relying on either large amounts of labelled data or prolonged training time. The concept of word embeddings has been prevalent in NLP community in recent years, as they can characterize semantic similarity between any pair of words, achieving promising results in a large number of NLP tasks BID14 BID18 BID20 . However, due to the hierarchical nature of human language, it is not sufficient to comprehend text solely based on isolated understanding of each word. This has prompted a recent rise in search for semantically robust embeddings for longer pieces of text, such as sentences and paragraphs.Based on learning paradigms, the existing approaches to sentence embeddings can be categorized into two categories: i) parameterized methods and ii) non-parameterized methods.Parameterized sentence embeddings. These models are parameterized and require training to optimize their parameters. SkipThought BID11 is an encoder-decoder model that predicts adjacent sentences. BID15 proposes an unsupervised model, Sent2Vec, to learn an n-gram feature in a sentence to predict the center word from the surrounding context. Quick thoughts (QT) BID12 replaces the encoder with a classifier to predict context sentences from candidate sequences. BID10 proposesà la carte to learn a linear mapping to reconstruct the center word from its context. BID5 generates the sentence encoder InferSent using Natural Language Inference (NLI) dataset. Universal Sentence Encoder utilizes the transformer BID24 for sentence embeddings. The model is first trained on large scale of unsupervised data from Wikipedia and forums, and then trained on the Stanford Natural Language Inference (SNLI) dataset. BID27 propose the gated recurrent averaging network (GRAN), which is trained on Paraphrase Database (PPDB) and English Wikipedia. BID23 leverages a multi-task learning framework to generate sentence embeddings. BID28 learns the paraphrastic sentence representations as the simple average of updated word embeddings.Non-parameterized sentence embedding. Recent work BID0 shows that, surprisingly, a weighted sum or transformation of word representations can outperform many sophisticated neural network structures in sentence embedding tasks. These methods are parameter-free and require no further training upon pre-trained word vectors. BID0 constructs a sentence embedding called SIF as a sum of pre-trained word embeddings, weighted by reverse document frequency. BID19 concatenates different power mean word embeddings as a sentence vector in p-mean. As these methods do not have a parameterized model, they can be easily adapted to novel text domains with both fast inference speed and high-quality sentence embeddings. In view of this trend, our work aims to further advance the frontier of this group and make its new state-of-the-art.In this paper, we propose a novel sentence embedding algorithm, Geometric Embedding (GEM), based entirely on the geometric structure of word embedding space. Given a d-dim word embedding matrix A ∈ R d×n for a sentence with n words, any linear combination of the sentence's word embeddings lies in the subspace spanned by the n word vectors. We analyze the geometric structure of this subspace in R d . When we consider the words in a sentence one-by-one in order, each word may bring in a novel orthogonal basis to the existing subspace. This new basis can be considered as the new semantic meaning brought in by this word, while the length of projection in this direction can indicate the intensity of this new meaning. It follows that a word with a strong intensity should have a larger influence in the sentence's meaning. Thus, these intensities can be converted into weights to linearly combine all word embeddings to obtain the sentence embedding. In this paper, we theoretically frame the above approach in a QR factorization of the word embedding matrix A. Furthermore, since the meaning and importance of a word largely depends on its close neighborhood, we propose the sliding-window QR factorization method to capture the context of a word and characterize its significance within the context.In the last step, we adapt a similar approach as BID0 to remove top principal vectors before generating the final sentence embedding. This step is to ensure commonly shared background components, e.g. stop words, do not bias sentence similarity comparison. As we build a new orthogonal basis for each sentence, we propose to have disparate background components for each sentence. This motivates us to put forward a sentence-specific principal vector removal method, leading to better empirical results.We evaluate our algorithm on 11 NLP tasks. In all of these tasks, our algorithm outperforms all non-parameterized methods and many parameterized approaches. For example, compared to SIF BID0 , the performance is boosted by 5.5% on STS benchmark dataset, and by 2.5% on SST dataset. Plus, the running time of our model compares favorably with existing models.The rest of this paper is organized as following. In Section 2, we describe our sentence embedding algorithm GEM. We evaluate our model on various tasks in Section 3 and Section 4. Finally, we summarize our work in Section 5. Ablation Study. As shown in in Table 4 , every GEM weight (α n , α s , α u ) and proposed principal components removal methods contribute to the performance. As listed on the left, adding GEM weights improves the score by 8.6% on STS dataset compared with averaging three concatenated word vectors. The sentence-dependent principal component removal (SDR) proposed in GEM improves 0.3% compared to directly removing the top h corpus principal components (SIR). Using GEM weights and SDR together yields an overall improvement of 19.7%. As shown on the right in Table 4 , every weight contributes to the performance of our model. For example, three weights altogether improve the score in SUBJ task by 0.38% compared with only using α n . Sensitivity Study. We evaluate the effect of all four hyper-parameters in our model: the window size m in the contextual window matrix, the number of candidate principal components K, the number of principal components to remove h, and the power of the singular value in coarse sentence embedding, i.e. the power t in f (σ j ) = σ t j in Equation FORMULA9 . We sweep the hyper-parameters and test on STSB dev set, SUBJ, and MPQA. Unspecified parameters are fixed at m = 7, K = 45, h = 17 and t = 3. As shown in Figure 2 , our model is quite robust with respect to hyper-parameters. We proposed a simple non-parameterized method 1 to generate sentence embeddings, based entirely on the geometric structure of the subspace spanned by word embeddings. Our sentence embedding evolves from the new orthogonal basis vector brought in by each word, which represents novel semantic meaning. The evaluation shows that our method not only sets up the new state-of-the-art of non-parameterized models but also performs competitively when compared with models requiring either large amount of training data or prolonged training time. In future work, we plan to consider multi-characters, i.e. subwords, into the model and explore other geometric structures in sentences.",propose simple robust training-free approach building sentence representations. Inspired Gram-Schmidt Process geometric theory build orthogonal basis subspace spanned word surrounding context sentence. model semantic meaning word sentence based two aspects. One is its relatedness word vector subspace already spanned contextual words. is its novel semantic meaning shall introduced new basis vector perpendicular existing subspace. Following motivation develop innovative method based orthogonal basis combine pre-trained word embeddings sentence representation. approach requires zero training zero parameters along efficient inference performance. evaluate approach 11 downstream NLP tasks. Experimental results show model outperforms existing zero-training alternatives tasks is competitive approaches relying either large amounts labelled data prolonged training time. concept word embeddings has been prevalent NLP community recent years can characterize semantic similarity pair words achieving promising results large number NLP tasks BID14 BID18 BID20. However due hierarchical nature human language is not sufficient comprehend text solely based isolated understanding word. has prompted recent rise search semantically robust embeddings longer pieces text sentences paragraphs.Based learning paradigms existing approaches sentence embeddings can be categorized two categories:parameterized methods ii non-parameterized methods.Parameterized sentence embeddings. models are parameterized require training optimize parameters. SkipThought BID11 is an encoder-decoder model predicts adjacent sentences. BID15 proposes unsupervised model Sent2Vec learn n-gram feature sentence predict center word surrounding context. Quick thoughts QT BID12 replaces encoder classifier predict context sentences candidate sequences. BID10 proposesà la carte learn linear mapping reconstruct center word context. BID5 generates sentence encoder InferSent using Natural Language Inference NLI dataset. Universal Sentence Encoder utilizes transformer BID24 sentence embeddings. model is first trained large scale unsupervised data Wikipedia forums trained Stanford Natural Language Inference SNLI dataset. BID27 propose gated recurrent averaging network GRAN which is trained Paraphrase Database PPDB English Wikipedia. BID23 leverages multi-task learning framework generate sentence embeddings. BID28 learns paraphrastic sentence representations simple average updated word embeddings.Non-parameterized sentence embedding. Recent work BID0 shows surprisingly weighted sum transformation word representations can outperform many sophisticated neural network structures sentence embedding tasks. methods are parameter-free require training upon pre-trained word vectors. BID0 constructs sentence embedding called SIF sum pre-trained word embeddings weighted reverse document frequency. BID19 concatenates different power mean word embeddings sentence vector p-mean methods do not have a parameterized model can be easily adapted novel text domains fast inference speed high-quality sentence embeddings. view trend work aims advance frontier group make new state-of-the-art.In paper propose novel sentence embedding algorithm Geometric Embedding GEM based entirely geometric structure word embedding space. Given d-dim word embedding matrix ∈ R d×n sentence n words linear combination sentence's word embeddings lies subspace spanned n word vectors. analyze geometric structure subspace R d. When we consider words sentence one-by-one order word may bring novel orthogonal basis existing subspace. new basis can be considered new semantic meaning brought word length projection direction can indicate intensity new meaning. follows word strong intensity should have a larger influence sentence's meaning. Thus intensities can be converted weights linearly combine word embeddings obtain sentence embedding. paper theoretically frame approach QR factorization word embedding matrix A. Furthermore since meaning importance word largely depends close neighborhood propose sliding-window QR factorization method capture context word characterize significance within context.In last step adapt similar approach BID0 remove top principal vectors generating final sentence embedding. step is to ensure commonly shared background components e.g stop words do not bias sentence similarity comparison. build new orthogonal basis sentence propose have disparate background components sentence. motivatesus put forward sentence-specific principal vector removal method leading better empirical results.We evaluate algorithm 11 NLP tasks. tasks algorithm outperforms non-parameterized methods many parameterized approaches. example compared SIF BID0 performance is boosted 5.5 STS benchmark dataset 2.5 SST dataset. Plus running time model compares favorably existing models.The rest paper is organized following. Section2 describe sentence embedding algorithm GEM. evaluate model various tasks Section3 Section4. Finally summarize work Section5. Ablation Study. shown Table4 every GEM weight αn α αu proposed principal components removal methods contribute performance. listed left adding GEM weights improves score 8.6 STS dataset compared averaging three concatenated word vectors. sentence-dependent principal component removal SDR proposed GEM improves 0.3 compared directly removing top h corpus principal components SIR Using GEM weights SDR together yields overall improvement 19.7%. shown right Table4 every weight contributes performance model. example three weights altogether improve score SUBJ task 0.38 compared usingαn. Sensitivity Study. evaluate effect four hyper-parameters model:window size contextual window matrix number candidate principal componentsK number principal components removeh power singular value coarse sentence embedding.e power f σj σ j Equation FORMULA9. sweep hyper-parameters test STSB dev set SUBJ MPQA. Unspecified parameters are fixed 7 K 45 h 17 3. shown Figure2 model is quite robust respect hyper-parameters proposed simple non-parameterized method1 generate sentence embeddings based entirely geometric structure subspace spanned word embeddings. sentence embedding evolves new orthogonal basis vector brought word which represents novel semantic meaning. evaluation shows method sets new state-of-the-art non-parameterized models also performs competitively when compared models requiring either large amount training data prolonged training time. future work plan consider multi-characters.e subwords model explore geometric structures sentences.,1619,1087,532,0.016,1.489,2025/11/05 17:18:53,0.01,1.6,0.4953271028037385,486.535
"In few-shot classification, we are interested in learning algorithms that train a classifier from only a handful of labeled examples. Recent progress in few-shot classification has featured meta-learning, in which a parameterized model for a learning algorithm is defined and trained on episodes representing different classification problems, each with a small labeled training set and its corresponding test set. In this work, we advance this few-shot classification paradigm towards a scenario where unlabeled examples are also available within each episode. We consider two situations: one where all unlabeled examples are assumed to belong to the same set of classes as the labeled examples of the episode, as well as the more challenging situation where examples from other distractor classes are also provided. To address this paradigm, we propose novel extensions of Prototypical Networks (Snell et al., 2017) that are augmented with the ability to use unlabeled examples when producing prototypes. These models are trained in an end-to-end way on episodes, to learn to leverage the unlabeled examples successfully. We evaluate these methods on versions of the Omniglot and miniImageNet benchmarks, adapted to this new framework augmented with unlabeled examples. We also propose a new split of ImageNet, consisting of a large set of classes, with a hierarchical structure. Our experiments confirm that our Prototypical Networks can learn to improve their predictions due to unlabeled examples, much like a semi-supervised algorithm would. The availability of large quantities of labeled data has enabled deep learning methods to achieve impressive breakthroughs in several tasks related to artificial intelligence, such as speech recognition, object recognition and machine translation. However, current deep learning approaches struggle in tackling problems for which labeled data are scarce. Specifically, while current methods excel at tackling a single problem with lots of labeled data, methods that can simultaneously solve a large variety of problems that each have only a few labels are lacking. Humans on the other hand are readily able to rapidly learn new classes, such as new types of fruit when we visit a tropical country. This significant gap between human and machine learning provides fertile ground for deep learning developments.For this reason, recently there has been an increasing body of work on few-shot learning, which considers the design of learning algorithms that specifically allow for better generalization on problems with small labeled training sets. Here we focus on the case of few-shot classification, where the given classification problem is assumed to contain only a handful of labeled examples per class. One approach to few-shot learning follows a form of meta-learning 1 BID21 BID9 , which performs transfer learning from a pool of various classification problems generated from large quantities of available labeled data, to new classification problems from classes unseen at training time. Meta-learning may take the form of learning a shared metric BID23 BID20 , a common initialization for few-shot classifiers BID16 BID5 or a generic inference network BID19 BID15 . DISPLAYFORM0 Unlabeled Set Support Set Figure 1 : Consider a setup where the aim is to learn a classifier to distinguish between two previously unseen classes, goldfish and shark, given not only labeled examples of these two classes, but also a larger pool of unlabeled examples, some of which may belong to one of these two classes of interest. In this work we aim to move a step closer to this more natural learning framework by incorporating in our learning episodes unlabeled data from the classes we aim to learn representations for (shown with dashed red borders) as well as from distractor classes .These various meta-learning formulations have led to significant progress recently in few-shot classification. However , this progress has been limited in the setup of each few-shot learning episode, which differs from how humans learn new concepts in many dimensions. In this paper we aim to generalize the setup in two ways. First, we consider a scenario where the new classes are learned in the presence of additional unlabeled data. While there have been many successful applications of semisupervised learning to the regular setting of a single classification task BID2 where classes at training and test time are the same, such work has not addressed the challenge of performing transfer to new classes never seen at training time, which we consider here. Second , we consider the situation where the new classes to be learned are not viewed in isolation. Instead , many of the unlabeled examples are from different classes; the presence of such distractor classes introduces an additional and more realistic level of difficulty to the fewshot problem.This work is a first study of this challenging semi-supervised form of few-shot learning. First, we define the problem and propose benchmarks for evaluation that are adapted from the Omniglot and miniImageNet benchmarks used in ordinary few-shot learning. We perform an extensive empirical investigation of the two settings mentioned above, with and without distractor classes. Second, we propose and study three novel extensions of Prototypical Networks BID20 , a state-ofthe-art approach to few-shot learning, to the semi-supervised setting. Finally, we demonstrate in our experiments that our semi-supervised variants successfully learn to leverage unlabeled examples and outperform purely supervised Prototypical Networks. In this work, we propose a novel semi-supervised few-shot learning paradigm, where an unlabeled set is added to each episode. We also extend the setup to more realistic situations where the unlabeled set has novel classes distinct from the labeled classes. To address the problem that current fewshot classification datasets are too small for a labeled vs. unlabeled split and also lack hierarchical levels of labels, we introduce a new dataset, tieredImageNet. We propose several novel extensions of Prototypical Networks, and they show consistent improvements under semi-supervised settings compared to our baselines. As future work, we are working on incorporating fast weights BID0 BID5 into our framework so that examples can have different embedding representations given the contents in the episode.","few-shot classification are interested learning algorithms train classifier handful labeled examples. Recent progress few-shot classification has featured meta-learning which a parameterized model learning algorithm is defined trained episodes representing different classification problems small labeled training set corresponding test set. work advance few-shot classification paradigm towards scenario where where all where the unlabeled examples are also available within episode. consider two situations:one where where all where the unlabeled examples are assumed belong set classes labeled examples episode well challenging situation where examples distractor classes are also provided. address paradigm propose novel extensions Prototypical Networks Snelletal. 2017 are augmented ability use unlabeled examples when producing prototypes. models are trained end-to-end way episodes learn leverage unlabeled examples successfully. evaluate methods versions Omniglot miniImageNet benchmarks adapted new framework augmented unlabeled examples. also propose new split ImageNet consisting large set classes hierarchical structure. experiments confirm Prototypical Networks can learn improve predictions due unlabeled examples much like semi-supervised algorithm would. availability large quantities labeled data has enabled deep learning methods achieve impressive breakthroughs several tasks related artificial intelligence speech recognition object recognition machine translation. However current deep learning approaches struggle tackling problems which labeled data are scarce. Specifically current methods excel tackling single problem lots labeled data methods can simultaneously solve large variety problems have only labels are lacking. Humans hand are readily able rapidly learn new classes new types fruit when we visit tropical country. significant gap human machine learning provides fertile ground deep learning developments.For reason recently has been an increasing body work few-shot learning which considers design learning algorithms specifically allow better generalization problems small labeled training sets. focus case few-shot classification where the given classification problem is assumed contain handful labeled examples per class. One approach few-shot learning follows form meta-learning 1 BID21 BID9 which performs transfer learning pool various classification problems generated large quantities available labeled data new classification problems classes unseen training time. Meta-learning may take form learning shared metric BID23 BID20 common initialization few-shot classifiers BID16 BID5 generic inference network BID19 BID15. DISPLAYFORM0 Unlabeled Set Support Set Figure1:Consider setup where the aim is to learn classifier distinguish two previously unseen classes goldfish shark where the given labeled examples two classes also larger pool unlabeled examples may belong one two classes interest. work aim move step closer natural learning framework incorporating learning episodes unlabeled data classes aim learn representations shown dashed red borders well distractor classes.These various meta-learning formulations have led significant progress recently few-shot classification. However progress has been limited setup few-shot learning episode which differs how humans learn new concepts many dimensions. paper aim generalize setup two ways. First which we consider scenario where the new classes are learned presence additional unlabeled data. have been many successful applications semisupervised learning regular setting single classification task BID2 where classes training test time are the same,work has not addressed challenge performing transfer new classes never seen training time which we consider here. Second which we consider situation where the new classes learned are not viewed isolation. Instead many unlabeled examples are from different classes;presence distractor classes introduces additional realistic level difficulty fewshot problem.This work is a first study challenging semi-supervised form few-shot learning. First define problem propose benchmarks evaluation are adapted Omniglot miniImageNet benchmarks used ordinary few-shot learning. perform extensive empirical investigation two settings mentioned without distractor classes. Second propose study three novel extensions Prototypical Networks BID20 state-ofthe-art approach few-shot learning semi-supervised setting. Finally demonstrate experiments semi-supervised variants successfully learn leverage unlabeled examples outperform purely supervised Prototypical Networks. work propose novel semi-supervised few-shot learning paradigm where an unlabeled set is added episode. also extend setup realistic situations where where all where the unlabeled set has novel classes distinct labeled classes. address problem current fewshot classification datasets are too small which labeledvs. unlabeled split also lack hierarchical levels labels introduce new dataset tieredImageNet. propose several novel extensions Prototypical Networks show consistent improvements semi-supervised settings compared baselines. future work are working incorporating fast weights BID0 BID5 framework examples can have different embedding representations given contents episode.",1174,826,348,0.011,1.421,2025/11/05 17:18:53,0.01,1.48,0.2834890965732086,359.403
"We investigate the properties of multidimensional probability distributions in the context of latent space prior distributions of implicit generative models. Our work revolves around the phenomena arising while decoding linear interpolations between two random latent vectors -- regions of latent space in close proximity to the origin of the space are oversampled, which restricts the usability of linear interpolations as a tool to analyse the latent space. We show that the distribution mismatch can be eliminated completely by a proper choice of the latent probability distribution or using non-linear interpolations. We prove that there is a trade off between the interpolation being linear, and the latent distribution having even the most basic properties required for stable training, such as finite mean. We use the multidimensional Cauchy distribution as an example of the prior distribution, and also provide a general method of creating non-linear interpolations, that is easily applicable to a large family of commonly used latent distributions. Generative latent variable models have grown to be a very popular research topic, with Variational Auto-Encoders (VAEs) BID8 and Generative Adversarial Networks (GANs) BID4 gaining a lot of interest in the last few years. VAEs use a stochastic encoder network to embed input data in a typically lower dimensional space, using a conditional probability distribution p(z|x) over possible latent space codes z ∈ R D . A stochastic decoder network is then used to reconstruct the original sample. GANs, on the other hand, use a generator network that creates data samples from noise z ∼ p(z), where p(z) is a fixed prior distribution, and train a discriminator network jointly to distinguish between real and generated data. Both of these model families require a probability distribution to be defined on the latent space. The most popular variants are the multidimensional normal distribution and the uniform distribution on the zero-centred hypercube. Given a trained model, studying the structure of the latent space is a common way to measure generator capabilities.",investigate properties multidimensional probability distributions context latent space prior distributions implicit generative models. work revolves around phenomena arising decoding linear interpolations two random latent vectors regions latent space close proximity origin space are oversampled which restricts usability linear interpolations tool analyse latent space. show distribution mismatch can be eliminated completely proper choice latent probability distribution using non-linear interpolations. prove is a trade interpolation linear latent distribution even basic properties required stable training finite mean. use multidimensional Cauchy distribution example prior distribution also provide general method creating non-linear interpolations is easily applicable large family commonly used latent distributions. Generative latent variable models have grown popular research topic Variational Auto-Encoders VAEs BID8 Generative Adversarial Networks GANs BID4 gaining lot interest last years. VAEs use stochastic encoder network embed input data typically lower dimensional space using conditional probability distributionp z|x possible latent space codes z∈R D. stochastic decoder network is then used reconstruct original sample. GANs hand use generator network creates data samples noisez∼p z wherep z is a fixed prior distribution train discriminator network jointly distinguish real generated data. model families require probability distribution defined latent space. popular variants are the multidimensional normal distribution uniform distribution zero-centred hypercube. Given trained model studying structure latent space is a common way measure generator capabilities.,392,265,127,0.004,1.479,2025/11/05 17:18:53,0.0,1.545,0.4641744548286605,133.028
"Deep neural networks (DNN) have shown promising performance in computer vision. In medical imaging, encouraging results have been achieved with deep learning for applications such as segmentation, lesion detection and classification. Nearly all of the deep learning based image analysis methods work on reconstructed images, which are obtained from original acquisitions via solving inverse problems (reconstruction). The reconstruction algorithms are designed for human observers, but not necessarily optimized for DNNs which can often observe features that are incomprehensible for human eyes. Hence, it is desirable to train the DNNs directly from the original data which lie in a different domain with the images. In this paper, we proposed an end-to-end DNN for abnormality detection in medical imaging. To align the acquisition with the annotations made by radiologists in the image domain, a DNN was built as the unrolled version of iterative reconstruction algorithms to map the acquisitions to images, and followed by a 3D convolutional neural network (CNN) to detect the abnormality in the reconstructed images. The two networks were trained jointly in order to optimize the entire DNN for the detection task from the original acquisitions. The DNN was implemented for lung nodule detection in low-dose chest computed tomography (CT), where a numerical simulation was done to generate acquisitions from 1,018 chest CT images with radiologists' annotations. The proposed end-to-end DNN demonstrated better sensitivity and accuracy for the task compared to a two-step approach, in which the reconstruction and detection DNNs were trained separately. A significant reduction of false positive rate on suspicious lesions were observed, which is crucial for the known over-diagnosis in low-dose lung CT imaging. The images reconstructed by the proposed end-to-end network also presented enhanced details in the region of interest. Deep neural networks (DNN) have shown promising performance in computer vision for various applications such as segmentation, detection and recognition. In medical imaging, DNNbased computer vision is also desirable because that radiologists' routine work requires handling of large amount of data, and the possibility exists that the intensive labor may lead to misdiagnosis BID14 BID38 . Furthermore, in some radiation related applications such as computed tomography (CT), low-dose scans are always preferred to decrease the potential harm that ionized radiation may do to human body. The increased noise level in lowdose data made it even more challenging for the radiologists to make correct decisions BID19 .Almost all the DNNs in medical image analysis are constructed in the image domain, which is the same domain where radiologists do the observations. However , in most medical imaging modalities, the acquired data are in a different domain from the images, and inverse problems have to be solved to reconstruct the images. For example , magnetic resonance imaging (MRI) acquires data in the Fourier domain, and CT acquires data in the Radon transform domain BID10 . During the reconstruction, there is great possibility of information lost due to the presence of noise in the measurements, especially for low-dose scans BID27 . To compensate for the noise, iterative methods that exploit prior knowledge about human body have been proposed BID11 BID30 . To achieve better representation of the med-ical images, DNN based reconstruction methods were also proposed recently BID36 b; BID12 . However, there is still gap between the objective image quality improvement and its utility in diagnosis, which means that both radiologists and computer aided diagnosis (CAD) systems are working with sub-optimal images.There is an emerging trend on task-based (end-to-end) signal processing with DNNs in recent years, where the decisions were directly made by the DNNs without explicit intermediate representations. BID13 used DNN for speech recognition directly from audio data without and intermediate phonetic representations. BID4 trained a DNN for self-driving cars which learned commands directly from images without recognition of land markers. BID18 used a classification criteria for the colorization of grey-scale images. BID35 detected words directly from scenes without doing a two-step text detection and optical character recognition (OCR). It was demonstrated that end-to-end DNNs had improved performance compared to multiple-step learning in these applications.In this paper, we proposed an end-to-end DNN which predicts the location of abnormalities in the images from the acquisitions. A reconstruction DNN was built first to map the acquired data to the images in order to align the data with annotations made by the radiologists. The DNN approximated a 10-iteration unrolled sequential quadratic surrogates (SQS) algorithm BID11 . A 3D convolutional neural network ( CNN) was used to detect abnormalities from the reconstructed images. The entire DNN was optimized jointly with regard to the total detection cross entropy loss. The method was implemented on The Lung Image Database Consortium image collection (LIDC-IDRI) from The Cancer Image Archive (TCIA), where we simulated ultra low-dose CT scans from the original patients' data BID2 BID8 BID3 . The task of the DNN was lung nodule detection , which is essential for early stage cancer screening (Team et al., 2011) . The performance of the end-to-end method was evaluated with entropy loss and receiver operating characteristic (ROC), and compared to a two-step approach, where the reconstruction DNN was trained first and the detection DNN was trained on the reconstructed images. Furthermore, the intermediate reconstructed images and features from the end-to-end network were studied for more comprehensive understanding of the DNN. In this paper a novel end-to-end DNN was proposed for abnormality detection in medical imaging. A reconstruction network and detection network were trained jointly to maximize the abnormality detection accuracy. We implemented the method on simulated chest CT data and achieved higher non-small lung nodule detection accuracy compared to two-step training scheme. There was significant false positive rate reduction on suspicious lesions (annotated non-nodules), and fair improvement on the overall detection sensitivity and accuracy. The images reconstructed by the end-to-end method resembled ordinary CT images, with more details and increased noise level compared to that from a two-step approach.Among the 102 validation cases, the mean entropy loss of nodule detection of the end-to-end method was smaller or similar than the two-step method for most of the cases, which indicated a statistical improvement on nodule detection from the proposed method. However, there was one case where the end-to-end entropy loss was significantly higher than the two-step loss. We studied the case further and confirmed that it was due to a strong misclassification of the positive samples, which was shown in figure 9(d).Although there was no significant improvement on the total AUC as shown in table 2, the ROC study in FIG4 indicated a significantly improved true positive rate at small false positive rate. The U.S. carried a national lung cancer screening with low-dose CT, which was considered to cause overdiagnosis due to the high false positive rate (Team et al., 2011; BID26 . The sensitivity improvement on the low false positive rate end indicated that the end-to-end DNN had great potential value to cancer screening tasks.There was great difference in the appearance of the reconstructed images from the two methods. The two-step training gave images with smaller overall noise level, but some of the details in lung were smoothed out, which caused misclassification for the detection network, as shown in FIG5 (a) and (b). The end-to-end training revealed more details in lung with higher spatial resolution, and the images were more suitable for the automatic nodule detection task. Though there were some misclassification due to the increased noise level, the overall performance of the nodule detection was improved with the end-to-end training scheme.The analysis on the intermediate results from the reconstruction network further revealed the difference between the two approaches. Whereas both methods kept similar structural component, the end-to-end method had more focus on the edges and tissues inside lung compared to the two-step method. As observed in FIG0 , the structures of the lung tissue were much more clearer in the end-to-end networks. This observation indicated that sharper edge and structures were of more importance for the detection network than the noise level in the reconstructed images, which is in accordance with human perceptions when radiologists perform the same task.Selecting appropriate representations of the data for further tasks such as detection is crucial, and the philosophy in end-to-end training is to leave the representation selection problem to machine rather than hand-crafting it. In this work, we demonstrated the feasibility of the end-to-end DNN for abnormality detection in medical imaging for a specific lung nodule detection problem in chest CT, and concluded that better results can be achieved for CAD systems by doing so. Nowadays most CAD systems are trained on reconstructed images, which are designed and tuned for radiologists rather than machines. By integrating the reconstruction process into the detection pipeline, better detection accuracy could be achieved for the CAD systems, and will increase its value to radiologists.","Deep neural networks DNN have shown promising performance computer vision. medical imaging encouraging results have been achieved deep learning applications segmentation lesion detection classification. Nearly deep learning based image analysis methods work reconstructed images which are obtained original acquisitions via solving inverse problems reconstruction reconstruction algorithms are designed human observers necessarily optimized DNNs which can often observe features are incomprehensible human eyes. Hence is desirable train DNNs directly original data which lie different domain images. paper proposed end-to-end DNN abnormality detection medical imaging. align acquisition annotations made radiologists image domain DNN was built unrolled version iterative reconstruction algorithms map acquisitions images followed 3D convolutional neural network CNN detect abnormality reconstructed images. two networks were trained jointly order optimize entire DNN detection task original acquisitions. DNN was implemented lung nodule detection low-dose chest computed tomography CT where a numerical simulation was done generate acquisitions 1,018 chest CT images radiologists' annotations. proposed end-to-end DNN demonstrated better sensitivity accuracy task compared two-step approach which the where the reconstruction detection DNNs were trained separately. significant reduction false positive rate suspicious lesions were observed which is crucial known over-diagnosis low-dose lung CT imaging. images reconstructed proposed end-to-end network also presented enhanced details region interest. Deep neural networks DNN have shown promising performance computer vision various applications segmentation detection recognition. medical imaging DNNbased computer vision is also desirable radiologists' routine work requires handling large amount data possibility exists intensive labor may lead misdiagnosis BID14 BID38. Furthermore radiation related applications computed tomography CT low-dose scans are always preferred decrease potential harm ionized radiation may do to human body. increased noise level lowdose data made even challenging radiologists make correct decisions BID19.Almost DNNs medical image analysis are constructed image domain which is the domain where radiologists do the observations. However medical imaging modalities acquired data are in a different domain images inverse problems have to be solved reconstruct images. example magnetic resonance imaging MRI acquires data Fourier domain CT acquires data Radon transform domain BID10. reconstruction is great possibility information lost due presence noise measurements especially low-dose scans BID27. compensate noise iterative methods exploit prior knowledge human body have been proposed BID11 BID30. achieve better representation med-ical images DNN based reconstruction methods were also proposed recently BID36 b;BID12. However is still gap objective image quality improvement utility diagnosis which means radiologists computer aided diagnosis CAD systems are working sub-optimal images.There is an emerging trend task-based end-to-end signal processing DNNs recent years where the decisions were directly made DNNs without explicit intermediate representations. BID13 used DNN speech recognition directly audio data without intermediate phonetic representations. BID4 trained DNN self-driving cars which learned commands directly images without recognition land markers. BID18 used classification criteria colorization grey-scale images. BID35 detected words directly scenes without two-step text detection optical character recognition OCR was demonstrated end-to-end DNNs had improved performance compared multiple-step learning applications.In paper proposed end-to-end DNN which predicts location abnormalities images acquisitions. reconstruction DNN was built first map acquired data images order align data annotations made radiologists. DNN approximated 10-iteration unrolled sequential quadratic surrogates SQS algorithm BID11. 3D convolutional neural network CNN was used detect abnormalities reconstructed images. entire DNN was optimized jointly regard total detection cross entropy loss. method was implemented Lung Image Database Consortium image collection LIDC-IDRI Cancer Image Archive TCIA where we simulated ultra low-doseCT scans original patients' data BID2 BID8 BID3. task DNN was lung nodule detection which is essential early stage cancer screening Teametal. 2011 performance end-to-end method was evaluated entropy loss receiver operating characteristic ROC compared two-step approach which the where the reconstruction DNN was trained first detection DNN was trained reconstructed images. Furthermore intermediate reconstructed images features end-to-end network were studied comprehensive understanding DNN. paper novel end-to-end DNN was proposed abnormality detection medical imaging. reconstruction network detection network were trained jointly maximize abnormality detection accuracy. implemented method simulated chest CT data achieved higher non-small lung nodule detection accuracy compared two-step training scheme. was significant false positive rate reduction suspicious lesions annotated non-nodules fair improvement overall detection sensitivity accuracy. images reconstructed end-to-end method resembled ordinary CT images details increased noise level compared two-step approach.Among 102 validation cases mean entropy loss nodule detection end-to-end method was smaller similar two-step method cases which indicated statistical improvement nodule detection proposed method. However was one case where the end-to-end entropy loss was significantly higher two-step loss. studied case confirmed was due strong misclassification positive samples which was shown figure9.Although was no significant improvement total AUC shown table2 ROC study FIG4 indicated significantly improved true positive rate small false positive rate. U.S carried national lung cancer screening low-doseCT which was considered cause overdiagnosis due high false positive rate Teametal. 2011;BID26. sensitivity improvement low false positive rate end indicated end-to-end DNN had great potential value cancer screening tasks.There was great difference appearance reconstructed images two methods. two-step training gave images smaller overall noise level details lung were smoothed which caused misclassification detection network which was shown FIG5 b end-to-end training revealed details lung higher spatial resolution images were more suitable automatic nodule detection task. Though were some misclassification due increased noise level overall performance nodule detection was improved end-to-end training scheme.The analysis intermediate results reconstruction network revealed difference two approaches. Whereas methods kept similar structural component end-to-end method had more focus edges tissues inside lung compared two-step method. observed FIG0 structures lung tissue were much clearer end-to-end networks. observation indicated sharper edge structures were of more importance detection network noise level reconstructed images which is in accordance human perceptions when radiologists perform task.Selecting appropriate representations data tasks detection is crucial philosophy end-to-end training is to leave representation selection problem machine rather hand-crafting it. work demonstrated feasibility end-to-end DNN abnormality detection medical imaging specific lung nodule detection problem chestCT concluded better results can be achieved CAD systems so. Nowadays CAD systems are trained reconstructed images which are designed tuned radiologists rather machines. integrating reconstruction process detection pipeline better detection accuracy could achieved CAD systems will increase value radiologists.",1802,1263,539,0.019,1.427,2025/11/05 17:18:53,0.01,1.447,0.3021806853582554,537.526
"Deep reinforcement learning (DRL) algorithms have demonstrated progress in learning to find a goal in challenging environments. As the title of the paper by Mirowski et al. (2016) suggests, one might assume that DRL-based algorithms are able to “learn to navigate” and are thus ready to replace classical mapping and path-planning algorithms, at least in simulated environments. Yet, from experiments and analysis in this earlier work, it is not clear what strategies are used by these algorithms in navigating the mazes and finding the goal. In this paper, we pose and study this underlying question: are DRL algorithms doing some form of mapping and/or path-planning? Our experiments show that the algorithms are not memorizing the maps of mazes at the testing stage but, rather, at the training stage. Hence, the DRL algorithms fall short of qualifying as mapping or path-planning algorithms with any reasonable definition of mapping. We extend the experiments in Mirowski et al. (2016) by separating the set of training and testing maps and by a more ablative coverage of the space of experiments. Our systematic experiments show that the NavA3C-D1-D2-L algorithm, when trained and tested on the same maps, is able to choose the shorter paths to the goal. However, when tested on unseen maps the algorithm utilizes a wall-following strategy to find the goal without doing any mapping or path planning. Navigation remains a fundamental problem in mobile robotics and artificial intelligence BID14 ; BID2 ). The problem is classically addressed by separating the task of navigation into two steps, exploration and exploitation. In the exploration stage, the environment is represented as some kind of map. In the exploitation stage, the map is used to plan a path to a given destination based on some optimality criterion. This classical approach has been quite successful in navigation using a variety of sensors. However, navigation in general unstructured environments, especially with texture-less BID17 , transparent and reflective surfaces BID5 , remains a challenge.Recently, end-to-end navigation methods-which attempt to solve the navigation problem without breaking it down into separate parts of mapping and path-planning-have gained traction. With the recent advances in Deep Reinforcement Learning (DRL), these end-to-end navigation methods, such as BID10 ; ; BID6 ; BID7 ; BID12 , forego decisions about the details that are required in the intermediate step of mapping. The potential for simpler yet more capable methods is rich; for example, the resulting trained agents can potentially optimize the amount of map information required for navigation tasks. One such algorithm by BID7 has shown promise in exploring and finding the goal efficiently within complex environments. Notably, this is done using only monocular first-person views.Despite such potential advances, DRL-based navigation remains a relatively unexplored field with its own limitations. The black-box nature of these methods make them difficult to study, and the patterns captured by the methods are not well understood. Recent work analyzing neural networks has shown that deep learning-based object detection methods can be easily fooled by introducing noise that is imperceptible to humans BID11 ); this level of sensitivity motivates why it is particularly important to analyze DRL methods across a wide variety of experiments: we need to understand their strengths and limitations. Figure 1 : Snapshots of the path taken by the agent while evaluating the model trained on the same random map with random goal and random spawn. The first row shows the top view of the robot moving through the maze with the goal location marked orange, the agent marked black and the agent's orientation marked red. The second row shows the first person view, which, besides reward, is the only input available to the agent and the top view is available only for human analysis.In this work, we develop a better understanding of recent DRL-based methods. In particular, we thoroughly explore and analyze the state-of-the-art BID7 methods across hundreds of maps with increasing difficulty levels. We set up the environment as a randomly generated map, as shown in Fig 1, with an agent and a goal. The agent is provided only with the first-person view and is tasked to find the goal as many times as possible within a fixed amount of time, re-spawning its location each time it reaches the goal. We train and evaluate the algorithms with increasing difficulty. In the easiest stage, we keep the goal location, spawn location and map constant over the training and testing. We call this set up static goal, static spawn, and static map. To increase the difficulty, we incrementally randomize the spawn locations, goal locations and map structures until all three are random. We discuss the design of experiments in Section 4.1 in more detail. BID7 do train and test their algorithms with randomized goals and spawns and show that their algorithm is able to exploit the knowledge of the goal location at evaluation time to maximize reward. However, following training and testing on constant map structures, this state-ofthe-art result is shown to be successful on only one map, which brings into question the repeatability of the results. It is also unclear whether these results generalize to unseen maps.Although disjoint training and testing sets are standard practice in machine learning, to the best of our knowledge, we are the first to evaluate any DRL-based navigation method on maps with unseen structures. We expand on the analysis in BID7 to address its limitations and ask whether DRL-based algorithms such as NavA3C+D 1 D 2 L perform any mapping followed by shortest path planning. Our experiments show no evidence of mapping in cases where algorithms are evaluated on unseen maps and no evidence of optimal path planning, even when the map is constant and only the goal is randomized.To better understand navigation, we compute attention-maps for models to show which portions of the input image are being used. We find that the models discard most of the image information, focusing attention on a small band in the middle of the image except around junctions, in which case the attention is distributed evenly throughout the image.These findings result from training and testing on multiple maps that were randomly selected from a set of 1100 randomly generated maps. We provide experimental results on ten randomly selected maps and a testing set of 100 unseen maps to ensure results are independent of map choice. We will make our code and data available following the blind review process. In this work, we comprehensively evaluate NavA3C+D 1 D 2 L BID7 ), a DRL-based navigation algorithms, through systematic set of experiments that are repeated over multiple randomly chosen maps. Our experiments show that DRL-based navigation models are able to perform some degree of path-planning and mapping when trained and tested on the same map even when spawn locations and goal locations are randomized. However the large variation in the evaluation metrics show that how such behaviour is not consistent across episodes. We also train and test these methods on disjoint set of maps and show that such trained models fail to perform any form of path-planning or mapping in unseen environments.In this work, we begin by asking: do DRL-based navigation algorithms really ""learn to navigate""? Our results answer this question negatively. At best, we can say that DRL-based algorithms learn to navigate in the exact same environment, rather than general technique of navigation which is what classical mapping and path planning provide. We hope that the systematic approach to the experiments in this work serve as a benchmark for future DRL-based navigation methods.",Deep reinforcement learning DRL algorithms have demonstrated progress learning find goal challenging environments. title paper Mirowskietal. 2016 suggests one might assume DRL-based algorithms are able learn navigate are thus ready replace classical mapping path-planning algorithms least simulated environments. Yet experiments analysis earlier work is not clear what strategies are are being used algorithms navigating mazes finding goal. paper pose study underlying question:are DRL algorithms form mapping/path-planning experiments show algorithms are not memorizing maps mazes testing stage rather training stage. Hence DRL algorithms fall short qualifying mapping path-planning algorithms reasonable definition mapping. extend experiments Mirowskietal. 2016 separating set training testing maps ablative coverage space experiments. systematic experiments show NavA3C-D1-D2-L algorithm when trained tested maps is able choose shorter paths goal. However when tested unseen maps algorithm utilizes wall-following strategy find goal without mapping path planning. Navigation remains fundamental problem mobile robotics artificial intelligence BID14;BID2 problem is classically addressed separating task navigation two steps exploration exploitation. exploration stage environment is represented kind map. exploitation stage map is used plan path given destination based optimality criterion. classical approach has been quite successful navigation using variety sensors. However navigation general unstructured environments especially texture-less BID17 transparent reflective surfaces BID5 remains challenge.Recently end-to-end navigation methods-which attempt solve navigation problem without breaking separate parts mapping path-planning-have gained traction. recent advances Deep Reinforcement Learning DRL end-to-end navigation methods BID10;BID6;BID7;BID12 forego decisions details are required intermediate step mapping. potential simpler yet capable methods is rich;example resulting trained agents can potentially optimize amount map information required navigation tasks. One algorithm BID7 has shown promise exploring finding goal efficiently within complex environments. Notably is done using monocular first-person views.Despite potential advances DRL-based navigation remains relatively unexplored field limitations. black-box nature methods make difficult study patterns captured methods are not well understood. Recent work analyzing neural networks has shown deep learning-based object detection methods can be easily fooled introducing noise is imperceptible humans BID11 level sensitivity motivates why it is particularly important analyze DRL methods across wide variety experiments:need understand strengths limitations. Figure1:Snapshots path taken agent evaluating model trained random map random goal random spawn. first row shows top view robot moving maze goal location marked orange agent marked black agent's orientation marked red. second row shows first person view besides reward is the only input available agent top view is available human analysis.In work develop better understanding recent DRL-based methods. particular thoroughly explore analyze state-of-the-art BID7 methods across hundreds maps increasing difficulty levels. set environment randomly generated map shown Fig1 agent goal. agent is provided first-person view is tasked find goal many times possible within fixed amount time re-spawning location time reaches goal. train evaluate algorithms increasing difficulty. easiest stage keep goal location spawn location map constant training testing. call set static goal static spawn static map. increase difficulty incrementally randomize spawn locations goal locations map structures three are random. discuss design experiments Section 4.1 detail. BID7 do train test algorithms randomized goals spawns show algorithm is able exploit knowledge goal location evaluation time maximize reward. However following training testing constant map structures state-ofthe-art result is shown successful one map which brings question repeatability results. is also unclear whether results generalize unseen maps.Although disjoint training testing sets are standard practice machine learning best knowledge are the first evaluate DRL-based navigation method maps unseen structures. expand analysis BID7 address limitations ask whether DRL-based algorithms NavA3C+1 2 L perform mapping followed shortest path planning. experiments show evidence mapping cases where algorithms are evaluated unseen maps evidence optimal path planning even when the map is constant goal is randomized.To better understand navigation compute attention-maps models show which portions input image are are being used. find models discard image information focusing attention small band middle image except around junctions which case attention is distributed evenly throughout image.These findings result training testing multiple maps were randomly selected set 1100 randomly generated maps. provide experimental results ten randomly selected maps testing set 100 unseen maps ensure results are independent map choice. will make code data available following blind review process. work comprehensively evaluate NavA3C+1 2 L BID7 DRL-based navigation algorithms systematic set experiments are repeated multiple randomly chosen maps. experiments show DRL-based navigation models are able perform degree path-planning mapping when trained tested map even when spawn locations goal locations are randomized. However large variation evaluation metrics show how such behaviour is not consistent across episodes. also train test methods disjoint set maps show trained models fail perform form path-planning mapping unseen environments.In work begin asking:do DRL-based navigation algorithms really learn navigate? results answer question negatively. best can say DRL-based algorithms learn navigate exact environment rather general technique navigation which is what classical mapping path planning provide. hope systematic approach experiments work serve benchmark future DRL-based navigation methods.,1508,1003,505,0.019,1.503,2025/11/05 17:18:53,0.01,1.281,0.5389408099688469,505.521
"In many robotic applications, it is crucial to maintain a belief about the state of 
 a system, like the location of a robot or the pose of an object.
 These state estimates serve as input for planning and decision making and 
 provide feedback during task execution. 
 Recursive Bayesian Filtering algorithms address the state estimation problem,
 but they require a model of the process dynamics and the sensory observations as well as 
 noise estimates that quantify the accuracy of these models. 
 Recently, multiple works have demonstrated that the process and sensor models can be 
 learned by end-to-end training through differentiable versions of Recursive Filtering methods.
 However, even if the predictive models are known, finding suitable noise models 
 remains challenging. Therefore, many practical applications rely on very simplistic noise 
 models. 
 Our hypothesis is that end-to-end training through differentiable Bayesian 
 Filters enables us to learn more complex heteroscedastic noise models for
 the system dynamics. We evaluate learning such models with different types of 
 filtering algorithms and on two different robotic tasks. Our experiments show that especially 
 for sampling-based filters like the Particle Filter, learning heteroscedastic noise 
 models can drastically improve the tracking performance in comparison to using 
 constant noise models. For many real-world systems that we would like to control, we cannot directly observe the current state directly. However, in order to stabilize a system at a goal state or make it track a trajectory, we need to have access to state feedback. An observer provides an estimate of the current system state from sensor measurements. Recursive Bayesian Filtering is a probabilistic approach towards estimating a belief about the current state. The method relies on a process model that predicts how the system behaves over time and an observation model that generates the expected observations given the predicted state. While the approach itself is general and makes few assumptions, the challenge is to formulate the process and observation models and to estimate the noise in these models. Process and observation noise quantify how certain the filter is about either the prediction or the observations. This information is used to determine how much the predicted state is updated based on the observation.Deep neural networks are well suited for tasks that require finding patterns or extracting information from raw, high-dimensional input signals and compressing them into a more compact representation. They have therefore become the method of choice especially in perception problems. For many robotics tasks like modeling dynamics, planning or tracking however, it has been shown that combining prior knowledge in the form of analytical models and/or algorithmic structure with trainable network components leads to better performance and generalizability than trying to learn the complete tasks from scratch BID17 BID11 BID9 BID23 BID19 BID8 BID6 BID12 .Specifically , BID8 BID6 BID9 BID12 have presented differentiable Bayesian Filtering algorithms. The authors focus on learning the observation and dynamics models end-to-end through the filters and demonstrate that the recursive filtering structure improves prediction results over using recurrent neural networks that were trained for the same task.In many robotic applications, it is possible to formulate the process and observation model based on first-order principles. However, finding appropriate values for the process and observation noise is often difficult and despite of much research on identification methods (e.g. BID2 BID25 ) they are often tuned manually. To reduce the tedious tuning effort, the noise models are typically assumed to be a Gaussian with zero mean and constant covariance. Many real systems can however be better modeled with heteroscedastic noise models, where the level of uncertainty depends on the state of the system and/or possible control inputs. Taking heterostochasticity into account has been demonstrated to improve filtering performance in many robotic tasks BID1 BID14 .In this work, we propose a method to learn heteroscedastic noise models from data by optimizing the prediction likelihood end-to-end through differentiable Bayesian Filters. In addition to differentiable Extended Kalman Filters and Particle Filters, which have been proposed in related work, we also propose two different versions of the Unscented Kalman Filter.In our experiments we focus on learning the noise models and therefore assume that observation and process models are known or at least pretrained. We evaluate the performance of the different filters and noise models on two different real-world robotic problems: (i) Visual Odometry for an driving car BID6 BID9 BID4 which has simple smooth dynamics and a low-dimensional state, and (ii) Visual tracking of an object that is pushed by a robot (Yu et al., 2016; BID17 . Planar pushing has challenging, discontinuous dynamics and was shown to have a heteroscedastic noise distribution BID1 . Furthermore, the dimensionality of the state is double of the Visual Odometry task.Our experiments show that using heteroscedastic process noise models drastically improves the tracking performance of the Particle Filter and Unscented Filter variants and facilitated learning as compared to learning a constant process noise model. While learning the noise models can be beneficial for all filters, the tracking performance of the EKF turned out to be least sensitive to the noise models. In comparison to the process noise, learning the observation noise did not improve the results much for the two tasks we evaluated. We proposed to optimize the process and observation noise for Bayesian Filters through end-to-end training and evaluated the method with different filtering algorithms and on two robotic applications. Our experiments showed that learning the process noise is especially important for filters that sample around the mean estimate of the state, like the Particle Filter but also the Unscented Kalman Filters. The Extended Kalman Filter in contrast proved to be most robust to suboptimal choices of the noise models. While this makes it a good choice for problems with simple and smooth dynamics, our experiments on the pushing task demonstrated that the (optimized) Unscented Filters can perform better on problems with more complex and even discontinuous dynamics.Training a state-dependent process noise model instead of a constant one improves the prediction accuracy for dynamic systems that are expected to have heteroscedastic noise. In our experiments, it also facilitated learning in general and lead to faster convergence of the models.We also used a heteroscedastic observation noise model in all our experiments. But different from the results in BID6 , we could not see a large benefit from it: Inspection on the pushing task showed that larger errors in the prediction of the preprocessing networks were not associated with higher observation noise. Identifying inputs that will lead to bad predictions is a difficult task if no obvious problems like occlusions are present to explain such outliers. Developing better methods for communicating uncertainty about the predictions of a neural network would thus be an impotent next step to further improve the performance of differentiable Bayesian Filters. The basic steps of the Extended Kalman Filter can be directly implemented in Tensorflow without any modifications. The only aspect of interest is how to compute the Jacobians of the process and observation model. Tensorflow implements auto differentiation, but has (as of now) no native support for computing Jacobians. While it can be done, it requires looping over the dimensions of the differentiated variable one by one, which we found to be relatively slow, especially during graph-construction. We therefore recommend to manually derive the Jacobians where applicable.",many robotic applications is crucial maintain belief state system like location robot pose object. state estimates serve input planning decision making provide feedback task execution. Recursive Bayesian Filtering algorithms address state estimation problem require model process dynamics sensory observations well noise estimates quantify accuracy models. Recently multiple works have demonstrated process sensor models can be learned end-to-end training differentiable versions Recursive Filtering methods. However even if the predictive models are known finding suitable noise models remains challenging. Therefore many practical applications rely simplistic noise models. hypothesis is that end-to-end training differentiable Bayesian Filters enables us learn complex heteroscedastic noise models system dynamics. evaluate learning models different types filtering algorithms two different robotic tasks. experiments show especially sampling-based filters like Particle Filter learning heteroscedastic noise models can drastically improve tracking performance comparison using constant noise models. many real-world systems would like control cannot directly observe current state directly. However order stabilize system goal state make track trajectory need have access state feedback. observer provides estimate current system state sensor measurements. Recursive Bayesian Filtering is a probabilistic approach towards estimating belief current state. method relies process model predicts how the system behaves time observation model generates expected observations given predicted state. approach is general makes assumptions challenge is to formulate process observation models estimate noise models. Process observation noise quantify how certain filter is about either prediction observations. information is used determine how much predicted state is updated based observation.Deep neural networks are well suited tasks require finding patterns extracting information raw high-dimensional input signals compressing compact representation. have therefore become method choice especially perception problems. many robotics tasks like modeling dynamics planning tracking however has been shown combining prior knowledge form analytical models/algorithmic structure trainable network components leads better performance generalizability trying learn complete tasks scratch BID17 BID11 BID9 BID23 BID19 BID8 BID6 BID12.Specifically BID8 BID6 BID9 BID12 have presented differentiable Bayesian Filtering algorithms. authors focus learning observation dynamics models end-to-end filters demonstrate recursive filtering structure improves prediction results using recurrent neural networks were trained task.In many robotic applications is possible formulate process observation model based first-order principles. However finding appropriate values process observation noise is often difficult despite much research identification methods e.g BID2 BID25 are often tuned manually. reduce tedious tuning effort noise models are typically assumed Gaussian zero mean constant covariance. Many real systems can however better modeled heteroscedastic noise models where the level uncertainty depends state system/possible control inputs. Taking heterostochasticity account has been demonstrated improve filtering performance many robotic tasks BID1 BID14.In work propose method learn heteroscedastic noise models data optimizing prediction likelihood end-to-end differentiable Bayesian Filters. addition differentiable Extended Kalman Filters Particle Filters which have been proposed related work also propose two different versions Unscented Kalman Filter.In experiments focus learning noise models therefore assume observation process models are known least pretrained. evaluate performance different filters noise models two different real-world robotic problems:Visual Odometry driving car BID6 BID9 BID4 which has simple smooth dynamics low-dimensional state ii Visual tracking object is pushed robot Yuetal. 2016;BID17. Planar pushing has challenging discontinuous dynamics was shown have a have heteroscedastic noise distribution BID1. Furthermore dimensionality state is double Visual Odometry task.Our experiments show using heteroscedastic process noise models drastically improves tracking performance Particle Filter Unscented Filter variants facilitated learning compared learning constant process noise model. learning noise models can be beneficial filters tracking performance EKF turned least sensitive noise models. comparison process noise learning observation noise did not improve results much two tasks evaluated. proposed optimize process observation noise Bayesian Filters end-to-end training evaluated method different filtering algorithms two robotic applications. experiments showed learning process noise is especially important filters sample around mean estimate state like Particle Filter also Unscented Kalman Filters. Extended Kalman Filter contrast proved robust suboptimal choices noise models. makes good choice problems simple smooth dynamics experiments pushing task demonstrated optimized Unscented Filters can perform better problems complex even discontinuous dynamics.Training state-dependent process noise model instead constant one improves prediction accuracy dynamic systems are expected have a have heteroscedastic noise. experiments also facilitated learning general lead faster convergence models.We also used heteroscedastic observation noise model experiments. different results BID6 could see large benefit it:Inspection pushing task showed larger errors prediction preprocessing networks were not associated higher observation noise. Identifying inputs will lead bad predictions is a difficult task if no obvious problems like occlusions are present explain outliers. Developing better methods communicating uncertainty predictions neural network would thus impotent next step improve performance differentiable Bayesian Filters. basic steps Extended Kalman Filter can be directly implemented Tensorflow without modifications. aspect interest is how to compute Jacobians process observation model. Tensorflow implements auto differentiation has(native support computing Jacobians. can be done requires looping dimensions differentiated variable one one which we found relatively slow especially graph-construction therefore recommend manually derive Jacobians where applicable.,1434,973,461,0.015,1.474,2025/11/05 17:18:53,0.01,1.472,0.4485981308411212,466.452
"Graph convolutional neural networks have recently shown great potential for the task of zero-shot learning. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, we find that the extensive use of Laplacian smoothing at each layer in current approaches can easily dilute the knowledge from distant nodes and consequently decrease the performance in zero-shot learning. In order to still enjoy the benefit brought by the graph structure while preventing the dilution of knowledge from distant nodes, we propose a Dense Graph Propagation (DGP) module with carefully designed direct links among distant nodes. DGP allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants. A weighting scheme is further used to weigh their contribution depending on the distance to the node. Combined with finetuning of the representations in a two-stage training approach our method outperforms state-of-the-art zero-shot learning approaches. With the ever-growing supply of image data, from an ever-expanding number of classes, there is an increasing need to use prior knowledge to classify images from unseen classes into correct categories based on semantic relationships between seen and unseen classes. This task is called zero-shot image classification. To obtain satisfactory performance on this task, it is crucial to model precise class relationships based on prior class knowledge. Previously prior knowledge has been incorporated in form of semantic descriptions of classes, such as attributes BID0 BID27 BID18 or word embeddings BID29 BID10 , or by using semantic relations such as knowledge graphs BID23 BID26 BID28 BID19 . Approaches that use knowledge graphs are less-explored and generally are based on the assumption that unknown classes can exploit similarity to known classes. Recently the benefit of hybrid approaches that combine knowledge graph and semantic class descriptions has been illustrated BID31 .The current state-of-the-art approach BID31 processes knowledge graphs by making use of recent developments in applying neural network techniques to non-euclidean spaces, such as graph and manifold spaces BID1 . A deep graph convolutional neural network (GCN) BID13 ) is used and the problem is phrased as weight regression, where the GCN is trained to regress classifier weights for each class. GCNs balance model complexity and expressiveness with a simple scalable model relying on the idea of message passing, i.e. nodes pass knowledge to their neighbors. However, these models were originally designed for classification tasks, albeit semi-supervised, an arguably simpler task than regression. In recent work , it has been shown that GCNs perform a form of Laplacian smoothing, where feature representations will become more similar as depth increases leading to easier classification BID16 . In the regression setting, instead, the aim is to exchange information between nodes in the graph and extensive smoothing is not desired as it dilutes information and does not allow for accurate regression. For instance, in a connected graph all features in a GCN with n layers will converge to the same representation as n → ∞ under some conditions, hence washing out all information BID16 . Here, graph propagation represents the knowledge that a node receives in a single layer for previous approaches. b) Proposed dense graph propagation for node 'Cat'. The node receives knowledge from all its descendants during the descendant phase (blue arrows) and its ancestors during the ancestor phase (red arrows). This leads to a densely connected graph where knowledge can directly propagate between related nodes. Weights α k are used to weigh nodes that are k-hops away from a given node.We, therefore, argue that this approach is not ideal for the task of zero-shot learning and that the number of layers in the graph should be small in order to avoid smoothing. We illustrate this phenomenon in practice , by showing that a shallow GCN consistently outperforms previously reported results. We employ a model-of-models framework by training the method to predict a set of logistic regression classifier for each class on top of a set of extracted features produced by a CNN. Choosing a small number of layers, however , has the effect that knowledge will not propagate well through the graph. A 1-layer GCN for instance only considers neighbors that are two hops away in the graph such that only immediate neighbors influence a given node. Thus, we propose a dense connectivity scheme , where nodes are connected directly to descendants/ancestors in order to include distant information. These connections allow us to propagate information without many smoothing operations but leads to the problem that all descendants/ancestors are weighed equally when computing the regression weight vector for a given class. However, intuitively, nodes closer to a given node should have higher importance. To remedy this, we extend this framework by adding a weighting scheme that considers the distance between nodes in order to weigh the contribution of different nodes. Making use of shared weights based on the distance also has the advantage that it only adds a minimal amount of additional parameters, is computationally efficient, and provides a balance between increasing flexibility of the model and keeping it restrictive enough to allow good predictions for the nodes of the unseen classes. FIG0 illustrates the difference in the way knowledge is propagated in this proposed Dense Graph Propagation (DGP) module compared to a GCN layer.To allow the feature extraction stage of the pre-trained CNN to adjust to the newly learned classifiers we propose a two-phase training scheme. In the first step, the DGP is trained to predict the last layer CNN weights. In the second phase, we replace the last layer weights of the CNN with the weights predicted by the DGP, freeze the weights and finetune the remaining weights of the CNN by optimizing the cross entropy classification loss on the seen classes.Our contributions can be summarized as follows. We present• an analysis of our intuitions for zero-shot learning and illustrate how these intuitions can be combined to design a DGP that outperforms previous zero-shot learning results. In contrast to previous approaches using graph convolutional neural networks for zero-shot learning, we illustrate that the task of zero-shot learning benefits from shallow networks. Further, to avoid the lack of information propagation between distant nodes in shallow models, we propose DGP, which exploits the hierarchical structure of the knowledge graph by adding a dense connection scheme. Experiments illustrate the ability of the proposed methods, outperforming previous state-of-the-art methods for zero-shot learning. In future work, we aim to investigate the potential of more advanced weighting mechanisms to further improve the performance of DGP compared to the SGCN. The inclusion of additional semantic information for settings where these are available for a subset of nodes is another future direction.A QUALITATIVE RESULTS Figure 4 and 5 provide further qualitative results of our finetuned Graph Propagation Module GPM and Dense Graph Propagation Module DGP compared to a standard ResNet and GCNZ, our reimplementation of BID31 .upright , grand piano, organ, accordion, barbershop piano, spinet, keyboard instrument, concert grand, baby grand piano, spinet, concert grand, baby grand, keyboard instrument piano, baby grand, concert grand, spinet, keyboard instrument B TWO-PHASE PROPAGATION TAB4 illustrates the benefit of a two-phase directed propagation rule where ancestors and descendants are considered individually compared to two consecutive updates using the full adjacency matrix in the dense method. C ANALYSIS OF NUMBER OF LAYERS TAB5 illustrates the drop in performance that is caused by using additional hidden layers in the GCN for the 2-hops experiment. All hidden layers have dimensionality of 2048 with 0.5 dropout. TAB6 explains the performance difference between our SGCN, our reimplementation of GCNZ and the reported results in BID31 . Note, unless otherwise stated training is performed for 3000 epochs. Non-symmetric normalization (D −1 A) is denoted as non-sym in the normalization column, while a symmetric normalization (D −1/2 AD −1/2 ) is denoted as sym. No finetuning has been performed for SGCN in these results. TAB7 shows the mean and std for 3 runs for the 2-hops and All dataset. It can clearly be observed that as the number of classes increases (2-hops to all), results become more stable.",Graph convolutional neural networks have recently shown great potential task zero-shot learning. models are highly sample efficient related concepts graph structure share statistical strength allowing generalization new classes when faced lack data. However find extensive use Laplacian smoothing layer current approaches can easily dilute knowledge distant nodes consequently decrease performance zero-shot learning. order still enjoy benefit brought graph structure preventing dilution knowledge distant nodes propose Dense Graph Propagation DGP module carefully designed direct links among distant nodes. DGP allowsus exploit hierarchical graph structure knowledge graph additional connections. connections are added based node's relationship ancestors descendants. weighting scheme is further used weigh contribution depending distance node. Combined finetuning representations two-stage training approach method outperforms state-of-the-art zero-shot learning approaches. ever-growing supply image data ever-expanding number classes is an increasing need use prior knowledge classify images unseen classes correct categories based semantic relationships seen unseen classes. task is called zero-shot image classification. obtain satisfactory performance task is crucial model precise class relationships based prior class knowledge. Previously prior knowledge has been incorporated form semantic descriptions classes attributes BID0 BID27 BID18 word embeddings BID29 BID10 using semantic relations knowledge graphs BID23 BID26 BID28 BID19. Approaches use knowledge graphs are less-explored generally are based assumption unknown classes can exploit similarity known classes. Recently benefit hybrid approaches combine knowledge graph semantic class descriptions has been illustrated BID31.The current state-of-the-art approach BID31 processes knowledge graphs making use recent developments applying neural network techniques non-euclidean spaces graph manifold spaces BID1. deep graph convolutional neural network GCN BID13 is used problem is phrased weight regression where the GCN is trained regress classifier weights class. GCNs balance model complexity expressiveness simple scalable model relying idea message passing.e nodes pass knowledge neighbors. However models were originally designed classification tasks albeit semi-supervised arguably simpler task regression. recent work has been shown GCNs perform form Laplacian smoothing where feature representations will become similar depth increases leading easier classification BID16. regression setting instead aim is to exchange information nodes graph extensive smoothing is not desired dilutes information does not allow accurate regression. instance connected graph features GCN n layers will converge representation n→∞ conditions hence washing information BID16. graph propagation represents knowledge node receives single layer previous approaches. b Proposed dense graph propagation node 'Cat'. node receives knowledge descendants descendant phase blue arrows ancestors ancestor phase red arrows leads densely connected graph where knowledge can directly propagate related nodes. Weightsαk are used weigh nodes are k-hops away given node.We therefore argue approach is not ideal task zero-shot learning number layers graph should be small order avoid smoothing. illustrate phenomenon practice showing shallow GCN consistently outperforms previously reported results. employ model-of-models framework training method predict set logistic regression classifier class top set extracted features produced CNN. Choosing small number layers however has the effect knowledge will not propagate well graph. 1-layer GCN instance considers neighbors are two hops away graph immediate neighbors influence given node. Thus propose dense connectivity scheme where nodes are connected directly descendants/ancestors order include distant information. connections allowus propagate information without many smoothing operations leads problem descendants/ancestors are weighed equally when computing regression weight vector given class. However intuitively where nodes closer given node should have higher importance. remedy extend framework adding weighting scheme considers distance nodes order weigh contribution different nodes. Making use shared weights based distance also has the advantage adds minimal amount additional parameters is computationally efficient provides balance increasing flexibility model keeping restrictive enough allow good predictions nodes unseen classes. FIG0 illustrates difference way knowledge is propagated proposed Dense Graph Propagation DGP module compared GCN layer.To allow feature extraction stage pre-trained CNN adjust newly learned classifiers propose two-phase training scheme. first step DGP is trained predict last layer CNN weights. second phase replace last layer weights CNN weights predicted DGP freeze weights finetune remaining weights CNN optimizing cross entropy classification loss seen classes.Our contributions can be summarized follows. present• analysis intuitions zero-shot learning illustrate how these intuitions can be combined design DGP outperforms previous zero-shot learning results. contrast previous approaches using graph convolutional neural networks zero-shot learning illustrate task zero-shot learning benefits shallow networks. avoid lack information propagation distant nodes shallow models propose DGP which exploits hierarchical structure knowledge graph adding dense connection scheme. Experiments illustrate ability proposed methods outperforming previous state-of-the-art methods zero-shot learning. future work aim investigate potential advanced weighting mechanisms improve performance DGP compared SGCN. inclusion additional semantic information settings where these are available subset nodes is another future direction.A QUALITATIVE RESULTS Figure4 5 provide qualitative results finetuned Graph Propagation Module GPM Dense Graph Propagation Module DGP compared standard ResNet GCNZ reimplementation BID31.upright grand piano organ accordion barbershop piano spinet keyboard instrument concert grand baby grand piano spinet concert grand baby grand keyboard instrument piano baby grand concert grand spinet keyboard instrument B TWO-PHASE PROPAGATION TAB4 illustrates benefit two-phase directed propagation rule where ancestors descendants are considered individually compared two consecutive updates using full adjacency matrix dense method. C ANALYSIS NUMBER LAYERS TAB5 illustrates drop performance is caused using additional hidden layers GCN 2-hops experiment. hidden layers have dimensionality 2048 0.5 dropout. TAB6 explains performance difference SGCN reimplementation GCNZ reported results BID31. Note unless otherwise stated training is performed 3000 epochs. Non-symmetric normalization −1 is denoted non-sym normalization column symmetric normalization −1/2AD −1/2 is denoted sym. finetuning has been performed SGCN results. TAB7 shows mean std 3 runs 2-hops dataset. can clearly observed number classes increases 2-hops results become stable.,1680,1153,527,0.017,1.457,2025/11/05 17:18:53,0.01,1.362,0.3956386292834891,538.267
"In this paper, we propose a capsule-based neural network model to solve the semantic segmentation problem. By taking advantage of the extractable part-whole dependencies available in capsule layers, we derive the probabilities of the class labels for individual capsules through a recursive, layer-by-layer procedure. We model this procedure as a traceback pipeline and take it as a central piece to build an end-to-end segmentation network. Under the proposed framework, image-level class labels and object boundaries are jointly sought in an explicit manner, which poses a significant advantage over the state-of-the-art fully convolutional network (FCN) solutions. Experiments conducted on modified MNIST and neuroimages demonstrate that our model considerably enhance the segmentation performance compared to the leading FCN variant.
 An effective segmentation solution should have a well-equipped mechanism to capture both semantic (i.e., what) and location (i.e., where) information. The fully convolutional network (FCN) BID19 and its variants BID24 BID21 BID1 constitute a popular class of solutions for this task, producing state-of-the-art results in a variety of applications. FCN and its variants (FCNs) are commonly constructed with an encoder-decoder architecture. In the encoding path, input images are processed through a number of ""convolution + pooling"" layers to generate high-level latent features, which are then progressively upsampled in the decoder to reconstruct the target pixel labels. The feature maps produced in higher (coarser) layers and those in lower (finer) layers contain complementary information: the former is richer in semantics, while the latter carries more spatial details that define class boundaries.Originated from and constructed upon convolutional neural networks (CNNs) BID13 BID26 , FCNs' encoders inherit some common drawbacks of CNNs, one of which is the lack of an internal mechanism in achieving viewpoint-invariant recognition. Traditional CNNs, as well as FCNs, rely on convolution operations to capture various visual patterns, and utilize poolings to enable multi-scale processing of the input images. Rotation invariance, however, is not readily available in both models. As a result, more data samples or additional network setups BID6 BID7 would be required for objects from different viewpoints to be correctly recognized. The absence of explicit part-whole relationships among objects imposes another limitation for FCNs -without such a mechanism, the rich semantic information residing in the higher layers and the precise boundary information in the lower layers can only be integrated in an implicit manner .Capsule nets BID25 BID10 , operating on a different paradigm, can provide a remedy. Capsule nets are built on capsules, each of which is a group of neurons representing one instance of a visual entity, i.e., an object or one of its parts BID9 . Capsules output both activation probabilities of their presence and the instantiation parameters that describe their properties, such as pose, deformation and texture, relative to a viewer BID9 . During inference propagation, the principle of coincidence filtering is employed to activate higher-level capsules and set up part-whole relationships among capsule entities. Such part-whole hierarchy equips capsule nets with a solid foundation for viewpoint-invariant recognition, which can be implemented through dynamic routing BID25 or EM routing BID10 . The same hierarchy , if properly embedded into a segmentation network, would provide a well-grounded platform to specify contextual constraints and enforce label consistency.With this thought, we develop a capsule-based semantic segmentation solution in this paper. Our approach treats capsule nets as probabilistic graphical models capable of inferring probabilistic dependences among visual entities, through which part-whole relationships can be explicitly constructed. As a concrete implementation , we propose a new operation sequence, which we call traceback pipeline, to capture such part-whole information through a recursive procedure to derive the class memberships for individual pixels. We term our model Tr-CapsNet .The contributions of our Tr-CapsNet can be summarized as:1. In Tr-CapsNet, the class labels for individual spatial coordinates within each capsule layer are analytically derived. The traceback pipeline in our model , taking advantage of the graphical properties of capsule nets, is mathematically rigorous. To the best of our knowledge, this is the first work to explore a capsule traceback approach for image segmentation. In addition, probability maps at each capsule layer are readily available, which makes it convenient to conduct feature visualization and layer interpretation.2. In parallel with segmentation, Tr-CapsNet carries out explicit class recognition at the same time. Such explicitness poses a powerful practical advantage over FCNs.3. The traceback pipeline is designed under a general context, making it applicable to many other potential tasks, including object localization and detection, action localization and network interpretation.",paper propose capsule-based neural network model solve semantic segmentation problem. taking advantage extractable part-whole dependencies available capsule layers derive probabilities class labels individual capsules recursive layer-by-layer procedure. model procedure traceback pipeline take central piece build end-to-end segmentation network. proposed framework image-level class labels object boundaries are jointly sought explicit manner which poses significant advantage state-of-the-art fully convolutional network FCN solutions. Experiments conducted modified MNIST neuroimages demonstrate model considerably enhance segmentation performance compared leading FCN variant. effective segmentation solution should have a well-equipped mechanism capture semantic.e what)and location.e where)information. fully convolutional network FCN BID19 variants BID24 BID21 BID1 constitute popular class solutions task producing state-of-the-art results variety applications. FCN variants FCNs are commonly constructed encoder-decoder architecture. encoding path input images are processed number convolution+pooling layers generate high-level latent features which are then progressively upsampled decoder reconstruct target pixel labels. feature maps produced higher coarser layers lower finer layers contain complementary information:former is richer semantics latter carries spatial details define class boundaries.Originated constructed upon convolutional neural networks CNNs BID13 BID26 FCNs' encoders inherit common drawbacks CNNs one which is the lack internal mechanism achieving viewpoint-invariant recognition. Traditional CNNs well FCNs rely convolution operations capture various visual patterns utilize poolings enable multi-scale processing input images. Rotation invariance however is not readily available models. result data samples additional network setups BID6 BID7 would required objects different viewpoints correctly recognized. absence explicit part-whole relationships among objects imposes another limitation FCNs -without mechanism rich semantic information residing higher layers precise boundary information lower layers can only be integrated implicit manner.Capsule nets BID25 BID10 operating different paradigm can provide remedy. Capsule nets are built capsules which isa group neurons representing one instance visual entity.e object one parts BID9. Capsules output activation probabilities presence instantiation parameters describe properties pose deformation texture relative viewer BID9. inference propagation principle coincidence filtering is employed activate higher-level capsules set part-whole relationships among capsule entities. part-whole hierarchy equips capsule nets solid foundation viewpoint-invariant recognition which can be implemented dynamic routing BID25 EM routing BID10. hierarchy if properly embedded segmentation network would provide well-grounded platform specify contextual constraints enforce label consistency.With thought develop capsule-based semantic segmentation solution paper. approach treats capsule nets probabilistic graphical models capable inferring probabilistic dependences among visual entities which part-whole relationships can be explicitly constructed. concrete implementation propose new operation sequence which we call traceback pipeline capture part-whole information recursive procedure derive class memberships individual pixels. term model Tr-CapsNet.The contributions Tr-CapsNet can be summarized summarized as:1 Tr-CapsNet class labels individual spatial coordinates within capsule layer are analytically derived. traceback pipeline model taking advantage graphical properties capsule nets is mathematically rigorous. best knowledge is the first work explore capsule traceback approach image segmentation. addition probability maps capsule layer are readily available which makes convenient conduct feature visualization layer interpretation.2 parallel segmentation Tr-CapsNet carries explicit class recognition time. explicitness poses powerful practical advantage FCNs.3 traceback pipeline is designed general context making applicable many potential tasks including object localization detection action localization network interpretation.,944,643,301,0.009,1.468,2025/11/05 17:18:53,0.0,1.69,0.4299065420560745,296.977
"Studying the evolution of information theoretic quantities during Stochastic Gradient Descent (SGD) learning of Artificial Neural Networks (ANNs) has gained popularity in recent years. 
 Nevertheless, these type of experiments require estimating mutual information and entropy which becomes intractable for moderately large problems. In this work we propose a framework for understanding SGD learning in the information plane which consists of observing entropy and conditional entropy of the output labels of ANN. Through experimental results and theoretical justifications it is shown that, under some assumptions, the SGD learning trajectories appear to be similar for different ANN architectures. First, the SGD learning is modeled as a Hidden Markov Process (HMP) whose entropy tends to increase to the maximum. Then, it is shown that the SGD learning trajectory appears to move close to the shortest path between the initial and final joint distributions in the space of probability measures equipped with the total variation metric. Furthermore, it is shown that the trajectory of learning in the information plane can provide an alternative for observing the learning process, with potentially richer information about the learning than the trajectories in training and test error. How do information theoretic quantities behave during the training of ANNs? This question was addressed by Shwartz-Ziv & Tishby (2017) in an attempt to explain the learning through the lens of the information bottleneck method (Tishby et al., 1999) . In that work, the layers of an ANNs are considered random variables forming a Markov chain. The authors constructed a 2D information plane by estimating the mutual information values between hidden layers, inputs, and outputs of ANNs. Using this approach it was observed that the information bottleneck method provides an approximate explanation for SGD learning. In addition, their experiments showed the role of compression in learning. That initial paper motivated further work on this line of research BID17 BID9 . The main practical limitation of that type of experiments is that it requires estimating mutual information between high dimensional continuous random variables. This becomes prohibitive as soon we move to moderately large problems, such as the CIFAR-100 dataset, where the large ANNs are employed. Other works dealing with information theoretic quantities tend to have these experimental limitations. For instance, BID16 ; Xu & Raginsky (2017) ; BID3 used generic chaining techniques to show that generalization error can be upper bounded by the mutual information between the training dataset and output of the learning algorithm. Nevertheless, estimating that mutual information to verify those results experimentally becomes intractable. Furthermore, in our previous work BID1 we defined a novel 2D information plane that only requires to estimate information theoretic quantities between the correct and estimated labels. Since these random variables are discrete and one-dimensional, this framework can be used to study learning in large recognition problems as well. Moreover, that work provides a preliminary empirical study on the behavior of those information theoretic quantities during learning along with some connections between error and conditional entropy.In this work, we extend the experiments from BID1 to more general scenarios and aim to characterize the observed behavior of SGD. Our main contributions are as follows:• We define a 2D-information plane, inspired by the works of Shwartz-Ziv & Tishby (2017) , and use it to study the behavior of ANNs during SGD learning. The main quantities are entropy of the output labels and its conditional entropy given true labels.• It is shown that if the learning is done perfectly and under some other mild assumptions, the entropy tends to increase to its maximum.• It is additionally shown that SGD learning trajectory follows approximately the shortest path in the space of probability measures equipped with the total variation metric. The shortest path is characterized well by a Markov chain defined on probabilities of estimate labels conditioned on true labels. To that end we provide theoretical and experimental justifications for constructing a simple Markovian model for learning, and compare it with SGD through experiments. These experiments are conducted using various datasets such as MNIST BID13 , CIFAR-10/ CIFAR-100, spirals BID1 , as well as different ANN architectures like Fully Connected Neural Networks (FCNNs), LeNet-5 (LeCun et al., 1999) , and DenseNet BID11 .• The trajectory, however, is not universal. Through a set of experiments, it is shown that SGD learning trajectory differs significantly for different learning strategies, noisy labels, overfitting, and underfitting. We show examples where this type of trajectories provide a richer view of the learning process than conventional training and test error, which allows us to spot undesired effects such as overfitting and underfitting.The paper is organized as follows: Section 2 introduces the notation as well as elementary notions from information theory. Section 3 formulates learning as a trajectory on the space of probability measures, defines the notion of shortest learning path, and provides a connection to Markov chains. Section 4 constructs a simple Markov chain model for gradient based learning that moves along the shortest learning path. Finally , Section 5 performs an empirical evaluation of the proposed model.",Studying evolution information theoretic quantities Stochastic Gradient Descent SGD learning Artificial Neural Networks ANNs has gained popularity recent years. Nevertheless type experiments require estimating mutual information entropy which becomes intractable moderately large problems. work propose framework understanding SGD learning information plane which consists observing entropy conditional entropy output labels ANN. experimental results theoretical justifications is shown assumptions SGD learning trajectories appear similar different ANN architectures. First SGD learning is modeled Hidden Markov Process HMP whose entropy tends increase maximum. is shown SGD learning trajectory appears move close shortest path initial final joint distributions space probability measures equipped total variation metric. Furthermore is shown trajectory learning information plane can provide alternative observing learning process potentially richer information learning trajectories training test error. How do information theoretic quantities behave training ANNs? question was addressed Shwartz-Ziv Tishby 2017 attempt explain learning lens information bottleneck method Tishbyetal. 1999 work layers ANNs are considered random variables forming Markov chain. authors constructed 2D information plane estimating mutual information values hidden layers inputs outputs ANNs. Using approach was observed information bottleneck method provides approximate explanation SGD learning. addition experiments showed role compression learning. initial paper motivated work line research BID17 BID9. main practical limitation type experiments is that it requires estimating mutual information high dimensional continuous random variables. becomes prohibitive soon move moderately large problems CIFAR-100 dataset where the large ANNs are employed. works dealing information theoretic quantities tend have these experimental limitations. instance BID16;Xu Raginsky 2017 BID3 used generic chaining techniques show generalization error can be upper bounded mutual information training dataset output learning algorithm. Nevertheless estimating mutual information verify results experimentally becomes intractable. Furthermore previous work BID1 defined novel 2D information plane requires estimate information theoretic quantities correct estimated labels. Since random variables are discrete one-dimensional framework can be used study learning large recognition problems well. Moreover work provides preliminary empirical study behavior information theoretic quantities learning along connections error conditional entropy.In work extend experiments BID1 general scenarios aim characterize observed behavior SGD. main contributions are as follows:• define 2D-information plane inspired works Shwartz-Ziv Tishby 2017 use study behavior ANNs SGD learning. main quantities are entropy output labels conditional entropy given true labels.• is shown if the learning is done perfectly mild assumptions entropy tends increase maximum.• is additionally shown SGD learning trajectory follows approximately shortest path space probability measures equipped total variation metric. shortest path is characterized well Markov chain defined probabilities estimate labels conditioned true labels. end provide theoretical experimental justifications constructing simple Markovian model learning compare SGD experiments. experiments are conducted using various datasets MNIST BID13 CIFAR-10/CIFAR-100 spirals BID1 well different ANN architectures like Fully Connected Neural Networks FCNNs LeNet-5 LeCunetal. 1999 DenseNet BID11.• trajectory however is not universal. set experiments is shown SGD learning trajectory differs significantly different learning strategies noisy labels overfitting underfitting. show examples where this type trajectories provide richer view learning process conventional training test error which allowsus spot undesired effects overfitting underfitting.The paper is organized follows:Section 2 introduces notation well elementary notions information theory. Section 3 formulates learning trajectory space probability measures defines notion shortest learning path provides connection Markov chains. Section 4 constructs simple Markov chain model gradient based learning moves along shortest learning path. Finally Section 5 performs empirical evaluation proposed model.,1027,691,336,0.01,1.486,2025/11/05 17:18:53,0.01,1.355,0.4859813084112147,323.409
"Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic model, even a simple modification of the underlying dynamical system requires significant physical intuition. This paper presents the first meta-learning algorithm that allows automated design for the underlying continuous dynamics of an SG-MCMC sampler. The learned sampler generalizes Hamiltonian dynamics with state-dependent drift and diffusion, enabling fast traversal and efficient exploration of energy landscapes. Experiments validate the proposed approach on Bayesian fully connected neural network, Bayesian convolutional neural network and Bayesian recurrent neural network tasks, showing that the learned sampler outperforms generic, hand-designed SG-MCMC algorithms, and generalizes to different datasets and larger architectures. There is a resurgence of research interests in Bayesian deep learning BID8 Blundell et al., 2015; BID10 BID9 BID4 BID33 , which applies Bayesian inference to neural networks for better uncertainty estimation. It is crucial for e.g. better exploration in reinforcement learning (Deisenroth & Rasmussen, 2011; Depeweg et al., 2017) , resisting adversarial attacks BID2 BID19 BID24 and continual learning BID28 . A popular approach to performing Bayesian inference on neural networks is stochastic gradient Markov chain Monte Carlo (SG-MCMC), which adds properly scaled Gaussian noise to a stochastic gradient ascent procedure BID46 . Recent advances in this area further introduced optimization techniques such as pre-conditioning BID1 BID30 , annealing (Ding et al., 2014 ) and adaptive learning rates BID16 Chen et al., 2016) . All these efforts have made SG-MCMC highly scalable to many deep learning tasks, including shape and texture modeling in computer vision BID17 and language modeling with recurrent neural networks BID5 . However, inventing novel dynamics for SG-MCMC requires significant mathematical work to ensure the sampler's stationary distribution is the target distribution, which is less friendly to practitioners. Furthermore, many of these algorithms are designed as a generic sampling procedure, and the associated physical mechanism might not be best suited for sampling neural network weights. This paper aims to automate the SG-MCMC proposal design by introducing meta-learning techniques BID36 Bengio et al., 1992; BID26 BID43 . The general idea is to train a learner on one or multiple tasks in order to acquire common knowledge that generalizes to future tasks. Recent applications of meta-learning include learning to transfer knowledge to unseen few-shot learning tasks BID35 BID32 BID3 , and learning algorithms such as gradient descent (Andrychowicz et al., 2016; BID18 BID47 , Bayesian optimization BID5 and reinforcement learning (Duan et al., 2016; . Unfortunately, these advances cannot be directly transferred to the world of MCMC samplers, as a naive neural network parameterization of the transition kernel does not guarantee the posterior distribution to be the stationary distribution of the sampler.• An SG-MCMC sampler that extends Hamiltonian dynamics with learnable diffusion and curl matrices. Once trained, the sampler can generalize to different datasets and architectures.• Extensive evaluation of the proposed sampler on Bayesian fully connected neural networks, Bayesian convolutional neural networks and Bayesian recurrent neural networks, with comparisons to popular SG-MCMC schemes based on e.g. Hamiltonian Monte Carlo (Chen et al., 2014) and pre-conditioned Langevin dynamics BID16 . We have presented a meta-learning algorithm that can learn an SG-MCMC sampler on simpler tasks and generalizes to more complicated densities in high dimensions. Experiments on Bayesian MLPs, Bayesian CNNs and Bayesian RNNs confirmed the strong generalization of the trained sampler to the long-time horizon as well as across datasets and network architectures. Future work will focus on better designs for both the sampler and the meta-learning procedure. For the former, temperature variable augmentation as well as moving average estimation will be explored. For the latter, better loss functions will be proposed for faster training, e.g. by reducing the unrolling steps of the sampler during training. Finally, the automated design of generic MCMC algorithms that might not be derived from continuous Markov processes remains an open challenge.A COMPARING MOMENTUM SGD AND SGHMC Similar to the relationship between SGLD and SGD, SGHMC is closely related SGD with momentum (SGD-M). First in HMC, the state space is augmented with an additional momentum variable denoted as p p p ∈ R D . We assume an identity mass matrix associated with that momentum term. Then the corresponding drift f f f (θ θ θ, p p p) and diffusion matrix D D D are: DISPLAYFORM0 where C C C is a positive definite matrix called friction coefficient. Thus, HMC's continuous-time dynamics is governed by the following SDE: DISPLAYFORM1 The discretized update rule (with simple Euler discretization) of HMC with step-size η is DISPLAYFORM2 If stochastic gradient ∇Ũ (θ θ θ) is used, we need to replace the covariance matrix of with 2η(C C C −B B B) whereB B B is the variance estimation of the gradients.On the other hand, the update equations of SGD with momentum (SGD-M) are the following: DISPLAYFORM3 where k and l are called momentum discount factor and learning rate, respectively. Also we can rewrite the SGHMC update equations by setting ηp p DISPLAYFORM4 Thus, the discretized SGHMC updates can be viewed as the SGD-M update injected with carefully controlled Gaussian noise. Therefore, the hyperparameter of SGHMC can be heuristically chosen based on the experience of SGD-M and vice versa. BID27 showed that in practice, simple Euler discretization for HMC simulation might cause divergence, therefore advanced discretization schemes such as Leapfrog and modified Euler are recommended. We use modified Euler discretization in our implementation of SGHMC and the meta sampler, resulting in the following update: DISPLAYFORM5 DISPLAYFORM6 Due to the two-stage update of Euler integrator, at time t, we have f DISPLAYFORM7 ), which is not exactly the history from the previous time. Therefore we further approximate it using delayed estimate: DISPLAYFORM8 Similarly, the Γ Γ Γ p p p term expands as DISPLAYFORM9 We further approximate DISPLAYFORM10 ∂U (θ θ θ) by the following DISPLAYFORM11 This only requires the storage of previous Q Q Q matrix. However, DISPLAYFORM12 ∂pi requires one further forward pass to obtainf DISPLAYFORM13 Therefore the proposed finite difference method only requires one more forward passes to computê f f f t−1 φ D and instead, save 3 back-propagations. As back-propagation is typically more expensive than forward pass, our approach reduces running time drastically, especially when the sampler are applied to large neural network.Time complexity figures Every SG-MCMC method (including the meta sampler) requires ∇ θ θ θŨ (θ θ θ). The main burden is the forward pass and back-propagation through the D D D(z z z) and Q Q Q(z z z) matrices, where the latter one has been replaced by the proposed finite difference scheme. The time complexity is O(HD) for both forward pass and finite difference with H the number of hidden units in the neural network of the meta sampler. Parallel computation with GPUs improves real-time speed, indeed in our MNIST experiment the meta sampler spends roughly 1.5x time when compared with SGHMC.",Stochastic gradient Markov chain Monte Carlo SG-MCMC has become increasingly popular simulating posterior samples large-scale Bayesian modeling. However existing SG-MCMC schemes are not tailored specific probabilistic model even simple modification underlying dynamical system requires significant physical intuition. paper presents first meta-learning algorithm allows automated design underlying continuous dynamics SG-MCMC sampler. learned sampler generalizes Hamiltonian dynamics state-dependent drift diffusion enabling fast traversal efficient exploration energy landscapes. Experiments validate proposed approach Bayesian fully connected neural network Bayesian convolutional neural network Bayesian recurrent neural network tasks showing learned sampler outperforms generic hand-designed SG-MCMC algorithms generalizes different datasets larger architectures. is a resurgence research interests Bayesian deep learning BID8 Blundelletal. 2015;BID10 BID9 BID4 BID33 which applies Bayesian inference neural networks better uncertainty estimation. is crucial e.g better exploration reinforcement learning Deisenroth Rasmussen 2011;Depewegetal. 2017 resisting adversarial attacks BID2 BID19 BID24 continual learning BID28. popular approach performing Bayesian inference neural networks is stochastic gradient Markov chain Monte Carlo SG-MCMC which adds properly scaled Gaussian noise stochastic gradient ascent procedure BID46. Recent advances area introduced optimization techniques pre-conditioning BID1 BID30 annealing Dingetal. 2014 adaptive learning rates BID16 Chenetal. 2016 efforts have made SG-MCMC highly scalable many deep learning tasks including shape texture modeling computer vision BID17 language modeling recurrent neural networks BID5. However inventing novel dynamics SG-MCMC requires significant mathematical work ensure sampler's stationary distribution is the target distribution which is less friendly practitioners. Furthermore many algorithms are designed generic sampling procedure associated physical mechanism might best suited sampling neural network weights. paper aims automate SG-MCMC proposal design introducing meta-learning techniques BID36 Bengioetal. 1992;BID26 BID43. general idea is to train learner one multiple tasks order acquire common knowledge generalizes future tasks. Recent applications meta-learning include learning transfer knowledge unseen few-shot learning tasks BID35 BID32 BID3 learning algorithms gradient descent Andrychowiczetal. 2016;BID18 BID47 Bayesian optimization BID5 reinforcement learning Duanetal. 2016;Unfortunately advances cannot directly transferred world MCMC samplers naive neural network parameterization transition kernel does not guarantee posterior distribution stationary distribution sampler.• SG-MCMC sampler extends Hamiltonian dynamics learnable diffusion curl matrices. trained sampler can generalize different datasets architectures.• Extensive evaluation proposed sampler Bayesian fully connected neural networks Bayesian convolutional neural networks Bayesian recurrent neural networks comparisons popular SG-MCMC schemes based e.g Hamiltonian Monte Carlo Chenetal. 2014 pre-conditioned Langevin dynamics BID16. have presented meta-learning algorithm can learn SG-MCMC sampler simpler tasks generalizes complicated densities high dimensions. Experiments Bayesian MLPs Bayesian CNNs Bayesian RNNs confirmed strong generalization trained sampler long-time horizon well across datasets network architectures. Future work will focus better designs sampler meta-learning procedure. former temperature variable augmentation well moving average estimation will be explored. latter better loss functions will be proposed faster training e.g reducing unrolling steps sampler training. Finally automated design generic MCMC algorithms might derived continuous Markov processes remains open challenge.A COMPARING MOMENTUM SGD SGHMC Similar relationship SGLD SGD SGHMC is closely related SGD momentum SGD-M First HMC state space is augmented additional momentum variable denoted ppp∈ R D. assume identity mass matrix associated momentum term. corresponding driftff f θθθ ppp diffusion matrix are:DISPLAYFORM0 whereCCC is a positive definite matrix called friction coefficient. Thus HMC's continuous-time dynamics is governed following SDE:DISPLAYFORM1 discretized update rule simple Euler discretization HMC step-sizeη is DISPLAYFORM2 If stochastic gradient∇Ũ θθθ is used need replace covariance matrix 2η CCC−B BB whereBBB is the variance estimation gradients.On hand update equations SGD momentum SGD-M are the following:DISPLAYFORM3 wherek l are called momentum discount factor learning rate respectively. Also can rewrite SGHMC update equations setting ηp p DISPLAYFORM4 Thus discretized SGHMC updates can be viewed SGD-M update injected carefully controlled Gaussian noise. Therefore hyperparameter SGHMC can be heuristically chosen based experience SGD-M vice versa. BID27 showed practice simple Euler discretization HMC simulation might cause divergence therefore advanced discretization schemes Leapfrog modified Euler are recommended. use modified Euler discretization implementation SGHMC meta sampler resulting following update:DISPLAYFORM5 DISPLAYFORM6 Due two-stage update Euler integrator time have f DISPLAYFORM7 whichis exactly history previous time. Therefore approximate using delayed estimate:DISPLAYFORM8 Similarly ΓΓΓp p p term expands DISPLAYFORM9 approximate DISPLAYFORM10∂U θθθ are the following DISPLAYFORM11 requires storage previousQQQ matrix. However DISPLAYFORM12 ∂pi requires one forward pass obtainf DISPLAYFORM13 Therefore proposed finite difference method requires one forward passes computêfff t−1φ instead save 3 back-propagations back-propagation is typically expensive forward pass approach reduces running time drastically especially when the sampler are applied large neural network.Time complexity figures Every SG-MCMC method including meta sampler requires∇θθ θŨ θθθ main burden is the forward pass back-propagation zzz QQQ zzz matrices where the latter one has been replaced proposed finite difference scheme. time complexity isO(HD forward pass finite difference H number hidden units neural network meta sampler. Parallel computation GPUs improves real-time speed indeed MNIST experiment meta sampler spends roughly 1.5x time when compared SGHMC.,1532,1130,402,0.014,1.356,2025/11/05 17:18:53,0.01,1.444,0.0809968847352025,428.837
"We propose a new, multi-component energy function for energy-based Generative Adversarial Networks (GANs) based on methods from the image quality assessment literature. Our approach expands on the Boundary Equilibrium Generative Adversarial Network (BEGAN) by outlining some of the short-comings of the original energy and loss functions. We address these short-comings by incorporating an l1 score, the Gradient Magnitude Similarity score, and a chrominance score into the new energy function. We then provide a set of systematic experiments that explore its hyper-parameters. We show that each of the energy function's components is able to represent a slightly different set of features, which require their own evaluation criteria to assess whether they have been adequately learned. We show that models using the new energy function are able to produce better image representations than the BEGAN model in predicted ways.",propose new multi-component energy function energy-based Generative Adversarial Networks GANs based methods image quality assessment literature. approach expands Boundary Equilibrium Generative Adversarial Network BEGAN outlining short-comings original energy loss functions. address short-comings incorporating l1 score Gradient Magnitude Similarity score chrominance score new energy function. provide set systematic experiments explore hyper-parameters show energy function's components is able represent slightly different set features which require evaluation criteria assess whether have been adequately learned. show models using new energy function are able produce better image representations BEGAN model predicted ways.,175,117,58,0.002,1.496,2025/11/05 17:18:53,0.0,1.25,0.5171339563862927,72.731
"Momentum is a simple and widely used trick which allows gradient-based optimizers to pick up speed along low curvature directions. Its performance depends crucially on a damping coefficient. Largecamping  coefficients can potentially deliver much larger speedups, but are prone to oscillations and instability; hence one typically resorts to small values such as 0.5 or 0.9. We propose Aggregated Momentum (AggMo), a variant of momentum which combines multiple velocity vectors with different damping coefficients. AggMo is trivial to implement, but significantly dampens oscillations, enabling it to remain stable even for aggressive damping coefficients such as 0.999. We reinterpret Nesterov's accelerated gradient descent as a special case of AggMo and analyze rates of convergence for quadratic objectives. Empirically, we find that AggMo is a suitable drop-in replacement for other momentum methods, and frequently delivers faster convergence with little to no tuning. In spite of a wide range of modern optimization research, gradient descent with momentum and its variants remain the tool of choice in machine learning. Momentum methods can help the optimizer pick up speed along low curvature directions without becoming unstable in high-curvature directions. The simplest of these methods, classical momentum BID24 , has an associated damping coefficient, 0 ≤ β < 1, which controls how quickly the momentum vector decays. The choice of β imposes a tradoff between speed and stability: in directions where the gradient is small but consistent, the terminal velocity is proportional to 1/(1 − β), suggesting that β slightly less than 1 could deliver much improved optimization performance. However, large β values are prone to oscillations and instability BID22 BID3 , requiring a smaller learning rate and hence slower convergence.Finding a way to dampen the oscillations while preserving the high terminal velocity of large beta values could dramatically speed up optimization. BID29 found that Nesterov accelerated gradient descent BID20 , which they reinterpreted as a momentum method, was more stable than classical momentum for large β values and gave substantial speedups for training neural networks. However, the reasons for the improved performance remain somewhat mysterious. O' Donoghue & Candes (2015) proposed to detect oscillations and eliminate them by resetting the velocity vector to zero. But in practice it is difficult to determine an appropriate restart condition.In this work, we introduce Aggregated Momentum (AggMo), a variant of classical momentum which maintains several velocity vectors with different β parameters. AggMo averages the velocity vectors when updating the parameters. We find that this combines the advantages of both small and large β values: the large values allow significant buildup of velocity along low curvature directions, while the small values dampen the oscillations, hence stabilizing the algorithm. AggMo is trivial to implement and incurs almost no computational overhead.We draw inspiration from the physics literature when we refer to our method as a form of passive damping. Resonance occurs when a system is driven at specific frequencies but may be prevented through careful design BID4 . Passive damping can address this in structures by making use of different materials with unique resonant frequencies. This prevents any single frequency from producing catastrophic resonance. By combining several momentum velocities together we achieve a similar effect -no single frequency is driving the system and so oscillation is prevented.In this paper we analyze rates of convergence on quadratic functions. We also provide theoretical convergence analysis showing that AggMo achieves converging average regret in online convex programming BID37 . To evaluate AggMo empirically we compare against other commonly used optimizers on a range of deep learning architectures: deep autoencoders, convolutional networks, and long-term short-term memory (LSTM).In all of these cases, we find that AggMo works as a drop-in replacement for classical momentum, in the sense that it works at least as well for a given β parameter. But due to its stability at higher β values, it often delivers substantially faster convergence than both classical and Nesterov momentum when its maximum β value is tuned.2 Background : momentum-based optimization Classical momentum We consider a function f : R d → R to be minimized with respect to some variable θ. Classical momentum (CM) minimizes this function by taking some initial point θ 0 and running the following iterative scheme, v t = βv t−1 − ∇ θ f (θ t−1 ), DISPLAYFORM0 where γ t denotes a learning rate schedule, β is the damping coefficient and we set v 0 = 0. Momentum can speed up convergence but it is often difficult to choose the right damping coefficient, β. Even with momentum, progress in a low curvature direction may be very slow. If the damping coefficient is increased to overcome this then high curvature directions may cause instability and oscillations.Nesterov momentum Nesterov's Accelerated Gradient BID20 BID21 ) is a modified version of the gradient descent algorithm with improved convergence and stability. It can be written as a momentum-based method BID29 , DISPLAYFORM1 Nesterov momentum seeks to solve stability issues by correcting the error made after moving in the direction of the velocity, v. In fact, it can be shown that for a quadratic function Nesterov momentum adapts to the curvature by effectively rescaling the damping coefficients by the eigenvalues of the quadratic BID29 . Aggregated Momentum is a simple extension to classical momentum which is easy to implement and has negligible computational overhead on modern deep learning tasks. We showed empirically that AggMo is able to remain stable even with large damping coefficients and enjoys faster convergence rates as a consequence of this. Nesterov momentum can be viewed as a special case of AggMo.(Incidentally , we found that despite its lack of adoption by deep learning practitioners, Nesterov momentum also showed substantial advantages compared to classical momentum.) On the tasks we explored, AggMo could be used as a drop-in replacement for existing optimizers with little-to-no additional hyperparameter tuning. But due to its stability at higher β values, it often delivered substantially faster convergence than both classical and Nesterov momentum.",Momentum is a simple widely used trick which allows gradient-based optimizers pick speed along low curvature directions. performance depends crucially damping coefficient. Largecamping coefficients can potentially deliver much larger speedups are prone oscillations instability;hence one typically resorts small values 0.5 0.9 propose Aggregated Momentum AggMo variant momentum which combines multiple velocity vectors different damping coefficients. AggMo is trivial implement significantly dampens oscillations enabling remain stable even aggressive damping coefficients 0.999 reinterpret Nesterov's accelerated gradient descent special case AggMo analyze rates convergence quadratic objectives. Empirically find AggMo is a suitable drop-in replacement momentum methods frequently delivers faster convergence little tuning. spite wide range modern optimization research gradient descent momentum variants remain tool choice machine learning. Momentum methods can help optimizer pick speed along low curvature directions without becoming unstable high-curvature directions. simplest methods classical momentum BID24 has an associated damping coefficient 0≤β 1 which controls how quickly momentum vector decays. choice β imposes tradoff speed stability:directions where the gradient is small consistent terminal velocity is proportional 1/1−β suggesting β slightly less 1 could deliver much improved optimization performance. However large β values are prone oscillations instability BID22 BID3 requiring smaller learning rate hence slower convergence.Finding way dampen oscillations preserving high terminal velocity large beta values could dramatically speed optimization. BID29 found Nesterov accelerated gradient descent BID20 which they reinterpreted momentum method was more stable classical momentum large β values gave substantial speedups training neural networks. However reasons improved performance remain somewhat mysterious. O' Donoghue Candes 2015 proposed detect oscillations eliminate resetting velocity vector zero. practice is difficult determine appropriate restart condition.In work introduce Aggregated Momentum AggMo variant classical momentum which maintains several velocity vectors different β parameters. AggMo averages velocity vectors when updating parameters. find combines advantages small large β values:large values allow significant buildup velocity along low curvature directions small values dampen oscillations hence stabilizing algorithm. AggMo is trivial implement incurs almost computational overhead.We draw inspiration physics literature when we refer method form passive damping. Resonance occurs when a system is driven specific frequencies may prevented careful design BID4. Passive damping can address structures making use different materials unique resonant frequencies. prevents single frequency producing catastrophic resonance. combining several momentum velocities together achieve similar effect -no single frequency is driving system oscillation is prevented.In paper analyze rates convergence quadratic functions. also provide theoretical convergence analysis showing AggMo achieves converging average regret online convex programming BID37. evaluate AggMo empirically compare commonly used optimizers range deep learning architectures:deep autoencoders convolutional networks long-term short-term memory LSTM.In cases find AggMo works drop-in replacement classical momentum sense works least well given β parameter. due stability higher β values often delivers substantially faster convergence classical Nesterov momentum when its maximum β value is tuned.2 Background:momentum-based optimization Classical momentum consider functionf:R →R minimized respect variableθ. Classical momentum CM minimizes function taking initial pointθ0 running following iterative scheme v βv t−1−∇ θf θ t−1 DISPLAYFORM0 whereγ denotes learning rate schedule β is the damping coefficient setv0 0. Momentum can speed convergence is often difficult choose right damping coefficient β. Even momentum progress low curvature direction may slow. If the damping coefficient is increased overcome high curvature directions may cause instability oscillations.Nesterov momentum Nesterov's Accelerated Gradient BID20 BID21 is a modified version gradient descent algorithm improved convergence stability. can be written momentum-based method BID29 DISPLAYFORM1 Nesterov momentum seeks solve stability issues correcting error made moving direction velocity v. fact can be shown quadratic function Nesterov momentum adapts curvature effectively rescaling damping coefficients eigenvalues quadratic BID29. Aggregated Momentum is a simple extension classical momentum which is easy implement has negligible computational overhead modern deep learning tasks. showed empirically AggMo is able remain stable even large damping coefficients enjoys faster convergence rates consequence this. Nesterov momentum can be viewed special case AggMo. Incidentally found despite lack adoption deep learning practitioners Nesterov momentum also showed substantial advantages compared classical momentum. tasks explored AggMo could used drop-in replacement existing optimizers little-to-no additional hyperparameter tuning. due stability higher β values often delivered substantially faster convergence classical Nesterov momentum.,1213,875,338,0.011,1.386,2025/11/05 17:18:53,0.01,1.39,0.1744548286604356,365.557
"Recurrent Neural Networks architectures excel at processing sequences by
 modelling dependencies over different timescales. The recently introduced
 Recurrent Weighted Average (RWA) unit captures long term dependencies
 far better than an LSTM on several challenging tasks. The RWA achieves
 this by applying attention to each input and computing a weighted average
 over the full history of its computations. Unfortunately, the RWA cannot
 change the attention it has assigned to previous timesteps, and so struggles
 with carrying out consecutive tasks or tasks with changing requirements.
 We present the Recurrent Discounted Attention (RDA) unit that builds on
 the RWA by additionally allowing the discounting of the past.
 We empirically compare our model to RWA, LSTM and GRU units on
 several challenging tasks. On tasks with a single output the RWA, RDA and
 GRU units learn much quicker than the LSTM and with better performance.
 On the multiple sequence copy task our RDA unit learns the task three
 times as quickly as the LSTM or GRU units while the RWA fails to learn at
 all. On the Wikipedia character prediction task the LSTM performs best
 but it followed closely by our RDA unit. Overall our RDA unit performs
 well and is sample efficient on a large variety of sequence tasks. Many types of information such as language, music and video can be represented as sequential data. Sequential data often contains related information separated by many timesteps, for instance a poem may start and end with the same line, a scenario which we call long term dependencies. Long term dependencies are difficult to model as we must retain information from the whole sequence and this increases the complexity of the model. A class of model capable of capturing long term dependencies are Recurrent Neural Networks (RNNs). A specific RNN architecture, known as Long Short-Term Memory (LSTM) BID13 , is the benchmark against which other RNNs are compared. LSTMs have been shown to learn many difficult sequential tasks effectively. They store information from the past within a hidden state that is combined with the latest input at each timestep. This hidden state can carry information right from the beginning of the input sequence, which allows long term dependencies to be captured. However, the hidden state tends to focus on the more recent past and while this mostly works well, in tasks requiring equal weighting between old and new information LSTMs can fail to learn.A technique for accessing information from anywhere in the input sequence is known as attention. The attention mechanism was introduced to RNNs by BID2 for neural machine translation. The text to translate is first encoded by a bidirectional-RNN producing a new sequence of encoded state. Different locations within the encoded state are focused on by multiplying each of them by an attention matrix and calculating the weighted average. This attention is calculated for each translated word. Computing the attention matrix for each encoded state and translated word combination provides a great deal of flexibility in choosing where in the sequence to attend to, but the cost of computing these matrices grows as a square of the number of words to translate. This cost limits this method to short sequences, typically only single sentences are processed at a time.The Recurrent Weighted Average (RWA) unit, recently introduced by BID17 , can apply attention to sequences of any length. It does this by only computing the attention for each input once and computing the weighted average by maintaining a running average up to the current timestep. Their experiments show that the RWA performs very well on tasks where information is needed from any point in the input sequence. Unfortunately, as it cannot change the attention it assigns to previous timesteps, it performs poorly when asked to carry out multiple tasks within the same sequence, or when asked to predict the next character in a sample of text, a task in which new information is more important than old.We introduce the Recurrent Discounted Attention (RDA) unit, which extends the RWA by allowing it to discount the attention applied to previous timesteps. As this adjustment is applied to all previous timesteps at once, it continues to be efficient. It performs very well both at tasks requiring equal weighting over all information seen and at tasks in which new information is more important than old.The main contributions of this paper are as follows:1. We analyse the Recurrent Weighted Average unit and show that it cannot output certain simple sequences.2. We propose the Recurrent Discounted Attention unit that extends the Recurrent Weighted Average by allowing it to discount the past.3. We run extensive experiments on the RWA, RDA, LSTM and GRU units and show that the RWA, RDA and GRU units are well suited to tasks with a single output, the RDA performs best on the multiple sequence copy task while the LSTM unit performs better on the Hutter Prize Wikipedia dataset.Our paper is setout as follows: we present the analysis of the RWA (sections 3 and 4) and propose the RDA (section 5). The experimental results (section 6), discussion (section 7) and conclusion follow (section 8). We analysed the Recurrent Weighted Average (RWA) unit and identified its weakness as the inability to forget the past. By adding this ability to forget the past we arrived at the Recurrent Discounted Attention (RDA). We implemented several varieties of the RDA and compared them to the RWA, LSTM and GRU units on several different tasks. We showed that in almost all cases the RDA should be used in preference to the RWA and is a flexible RNN unit that can perform well on all types of tasks.We also determined which types of tasks were more suited to each different RNN unit. For tasks involving a single output the RWA, RDA and GRU units performed best, for the multiple sequence copy task the RDA performed best, while on the Wikipedia character prediction task the LSTM unit performed best. We recommend taking these results into account when choosing a unit for real world applications.",Recurrent Neural Networks architectures excel processing sequences modelling dependencies different timescales. recently introduced Recurrent Weighted Average RWA unit captures long term dependencies far better LSTM several challenging tasks. RWA achieves applying attention input computing weighted average full history computations. Unfortunately RWA cannot change attention has assigned previous timesteps struggles carrying consecutive tasks tasks changing requirements. present Recurrent Discounted Attention RDA unit builds RWA additionally allowing discounting past. empirically compare model RWA LSTM GRU units several challenging tasks. tasks single output RWA RDA GRU units learn much quicker LSTM better performance. multiple sequence copy task RDA unit learns task three times quickly LSTM GRU units RWA fails learn all. Wikipedia character prediction task LSTM performs best followed closely RDA unit. Overall RDA unit performs well is sample efficient large variety sequence tasks. Many types information language music video can be represented sequential data. Sequential data often contains related information separated many timesteps instance poem may start end line scenario which we call long term dependencies. Long term dependencies are difficult model must retain information whole sequence increases complexity model. class model capable capturing long term dependencies are Recurrent Neural Networks RNNs specific RNN architecture known Long Short-Term Memory LSTM BID13 is the benchmark which other RNNs are compared. LSTMs have been shown learn many difficult sequential tasks effectively. store information past within hidden state is combined latest input timestep. hidden state can carry information right beginning input sequence which allows long term dependencies captured. However hidden state tends focus recent past mostly works well tasks requiring equal weighting old new information LSTMs can fail learn.A technique accessing information anywhere input sequence is known attention. attention mechanism was introduced RNNs BID2 neural machine translation. text translate is first encoded bidirectional-RNN producing new sequence encoded state. Different locations within encoded state are focused multiplying attention matrix calculating weighted average. attention is calculated translated word. Computing attention matrix encoded state translated word combination provides great deal flexibility choosing where in the sequence attend cost computing matrices grows square number words translate. cost limits method short sequences typically single sentences are processed time.The Recurrent Weighted Average RWA unit recently introduced BID17 can apply attention sequences length. does thisby computing attention input computing weighted average maintaining running average current timestep. experiments show RWA performs well tasks where information is needed point input sequence. Unfortunately cannot change attention assigns previous timesteps performs poorly when asked carry multiple tasks within sequence when asked predict next character sample text task which new information is more important old.We introduce Recurrent Discounted Attention RDA unit which extends RWA allowing discount attention applied previous timesteps. adjustment is applied previous timesteps continues efficient. performs well tasks requiring equal weighting information seen tasks which new information is more important old.The main contributions paper are as follows:1 follows:1 analyse Recurrent Weighted Average unit show cannot output certain simple sequences.2 propose Recurrent Discounted Attention unit extends Recurrent Weighted Average allowing discount past.3 run extensive experiments RWA RDA LSTM GRU units show RWA RDA GRU units are well suited tasks single output RDA performs best multiple sequence copy task LSTM unit performs better Hutter Prize Wikipedia dataset.Our paper is setout follows:present analysis RWA sections3 4 propose RDA section5 experimental results section6 discussion section7 conclusion follow section8 analysed Recurrent Weighted Average RWA unit identified weakness inability forget past. adding ability forget past arrived Recurrent Discounted Attention RDA implemented several varieties RDA compared RWA LSTM GRU units several different tasks. showed almost cases RDA should be used preference RWA is a flexible RNN unit can perform well types tasks.We also determined which types tasks were more suited different RNN unit. tasks involving single output RWA RDA GRU units performed best multiple sequence copy task RDA performed best Wikipedia character prediction task LSTM unit performed best. recommend taking results account when choosing unit real world applications.,1218,787,431,0.014,1.548,2025/11/05 17:18:53,0.01,1.375,0.6791277258566978,410.805
"Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through test-time averaging. In this paper, we introduce variance layers, a different kind of stochastic layers. Each weight of a variance layer follows a zero-mean distribution and is only parameterized by its variance. It means that each object is represented by a zero-mean distribution in the space of the activations. We show that such layers can learn surprisingly well, can serve as an efficient exploration tool in reinforcement learning tasks and provide a decent defense against adversarial attacks. We also show that a number of conventional Bayesian neural networks naturally converge to such zero-mean posteriors. We observe that in these cases such zero-mean parameterization leads to a much better training objective than more flexible conventional parameterizations where the mean is being learned. Modern deep neural networks are usually trained in a stochastic setting. They use different stochastic layers BID8 ; BID12 ) and stochastic optimization techniques BID14 ; Kingma & Ba (2014) ). Stochastic methods are used to reduce overfitting BID8 ; BID13 ; BID12 ), estimate uncertainty BID5 ; Malinin & Gales (2018) ) and to obtain more efficient exploration for reinforcement learning BID4 ; Plappert et al. (2017) ) algorithms.Bayesian deep learning provides a principled approach to training stochastic models (Kingma & Welling (2013) ; Rezende et al. (2014) ). Several existing stochastic training procedures have been reinterpreted as special cases of particular Bayesian models, including, but not limited to different versions of dropout BID5 ), drop-connect (Kingma et al. (2015) ), and even the stochastic gradient descent itself BID7 ). One way to create a stochastic neural network from an existing deterministic architecture is to replace deterministic weights w ij with random weightsŵ ij ∼ q(ŵ ij | φ ij ) (Hinton & Van Camp (1993) ; BID1 ). During training, a distribution over the weights is learned instead of a single point estimate. Ideally one would want to average the predictions over different samples of such distribution, which is known as test-time averaging, model averaging or ensembling. However, test-time averaging is impractical, so during inference the learned distribution is often discarded, and only the expected values of the weights are used instead. This heuristic is known as mean propagation or the weight scaling rule BID8 ; Goodfellow et al. (2016) ), and is widely and successfully used in practice BID8 ; Kingma et al. (2015) ; Molchanov et al. (2017) ).In our work we study the an extreme case of stochastic neural network where all the weights in one or more layers have zero means and trainable variances, e.g. w ij ∼ N (0, σ 2 ij ). Although no information get stored in the expected values of the weights, these models can learn surprisingly well and achieve competitive performance. Our key results can be summarized as follows:1. We introduce variance layers, a new kind of stochastic layers that store information only in the variances of its weights, keeping the means fixed at zero, and mapping the objects into zero-mean distributions over activations. The variance layer is a simple example when the weight scaling rule BID8 ) fails.2. We draw the connection between neural networks with variance layers (variance networks) and conventional Bayesian deep learning models. We show that several popular Bayesian models (Kingma et al. (2015) ; Molchanov et al. (2017) ) converge to variance networks, and demonstrate a surprising effect -a less flexible posterior approximation may lead to much better values of the variational inference objective (ELBO).3. Finally, we demonstrate that variance networks perform surprisingly well on a number of deep learning problems. They achieve competitive classification accuracy, are more robust to adversarial attacks and provide good exploration in reinforcement learning problems. In this paper we introduce variance networks, surprisingly stable stochastic neural networks that learn only the variances of the weights, while keeping the means fixed at zero in one or several layers.We show that such networks can still be trained well and match the performance of conventional models. Variance networks are more stable against adversarial attacks than conventional ensembling techniques, and can lead to better exploration in reinforcement learning tasks.The success of variance networks raises several counter-intuitive implications about the training of deep neural networks:• DNNs not only can withstand an extreme amount of noise during training, but can actually store information using only the variances of this noise. The fact that all samples from such zero-centered posterior yield approximately the same accuracy also provides additional evidence that the landscape of the loss function is much more complicated than was considered earlier BID6 ).• A popular trick, replacing some random variables in the network with their expected values, can lead to an arbitrarily large degradation of accuracy -up to a random guess quality prediction.• Previous works used the signal-to-noise ratio of the weights or the layer output to prune excessive units BID1 ; Molchanov et al. (2017); Neklyudov et al. (2017) ). However , we show that in a similar model weights or even a whole layer with an exactly zero SNR (due to the zero mean output) can be crucial for prediction and can't be pruned by SNR only.• We show that a more flexible parameterization of the approximate posterior does not necessarily yield a better value of the variational lower bound, and consequently does not necessarily approximate the posterior distribution better.We believe that variance networks may provide new insights on how neural networks learn from data as well as give new tools for building better deep models.A PROOF OF THEOREM 1 DISPLAYFORM0 t,i ) in terms of Maximum Mean Discrepancy: DISPLAYFORM1 Proof. By the definition of the Maximum Mean Discrepancy, we have DISPLAYFORM2 where the supremum is taken over the set of continuous functions, bounded by 1. Let's reparameterize and join the expectations: DISPLAYFORM3 (18) Since linear transformations of the argument do not change neither the norm of the function, nor its continuity, we can hide the component-wise multiplication of ε by √ α t µ t inside the function f (ε).This would not change the supremum. DISPLAYFORM4 There exists a rotation matrix R such that R( DISPLAYFORM5 αt , 0, . . . , 0) . As ε comes from an isotropic Gaussian ε ∼ N (0, I D ), its rotation Rε would follow the same distribution Rε ∼ N (0, I D ). Once again, we can incorporate this rotation into the function f without affecting the supremum. DISPLAYFORM6 Let's consider the integration over ε 1 separately (φ(ε 1 ) denotes the density of the standard Gaussian distribution): DISPLAYFORM7 Next, we view f (ε 1 , . . . ) as a function of ε 1 and denote its antiderivative as F 1 (ε) = f (ε)dε 1 . Note that as f is bounded by 1, hence F 1 is Lipschitz in ε 1 with a Lipschitz constant L = 1. It would allow us to bound its deviation DISPLAYFORM8 Let's use integration by parts: DISPLAYFORM9 The first term is equal to zero, as DISPLAYFORM10 Finally, we can use the Lipschitz property of F 1 (ε) to bound this value: DISPLAYFORM11 Thus, we obtain the following bound on the MMD: DISPLAYFORM12 This bound goes to zero as α t goes to infinity.As the output of a softmax network lies in the interval [0, 1], we obtain the following bound on the deviation of the prediction of the ensemble after applying the zero-mean approximation: Figure 8 : These are the learning curves for VGG-like architectures, trained on CIFAR-10 with layerwise parameterization and with different prior distributions. These plots show that all three priors are equivalent in practice: all three models converge to variance networks. The convergence for the Student 's prior is slower, because in this case the KL-term is estimated using one-sample MC estimate. This makes the stochastic gradient w.r.t. log α very noisy when α is large. DISPLAYFORM13",Ordinary stochastic neural networks mostly rely expected values weights make predictions whereas induced noise is mostly used capture uncertainty prevent overfitting slightly boost performance test-time averaging. paper introduce variance layers different kind stochastic layers. weight variance layer follows zero-mean distribution is only parameterized variance. means object is represented zero-mean distribution space activations. show layers can learn surprisingly well can serve efficient exploration tool reinforcement learning tasks provide decent defense adversarial attacks. also show number conventional Bayesian neural networks naturally converge zero-mean posteriors. observe cases zero-mean parameterization leads much better training objective flexible conventional parameterizations where the mean is being is learned. Modern deep neural networks are usually trained stochastic setting. use different stochastic layers BID8;BID12 stochastic optimization techniques BID14;Kingma Ba 2014 Stochastic methods are used reduce overfitting BID8;BID13;BID12 estimate uncertainty BID5;Malinin Gales 2018 obtain efficient exploration reinforcement learning BID4;Plappertetal. 2017 algorithms.Bayesian deep learning provides principled approach training stochastic models Kingma Welling 2013 Rezendeetal. 2014 Several existing stochastic training procedures have been reinterpreted special cases particular Bayesian models including limited different versions dropout BID5 drop-connect Kingmaetal. 2015 even stochastic gradient descent BID7 One way create stochastic neural network existing deterministic architecture is to replace deterministic weightsw ij random weightsŵij∼ q ŵij φij Hinton Van Camp 1993 BID1 training distribution weights is being is learned instead single point estimate. Ideally one would want average predictions different samples distribution which is known test-time averaging model averaging ensembling. However test-time averaging is impractical inference learned distribution is often discarded expected values weights are used instead. heuristic is known mean propagation weight scaling rule BID8;Goodfellowetal. 2016 is widely successfully used practice BID8;Kingmaetal. 2015 Molchanovetal. 2017.In work study extreme case stochastic neural network where all the weights one layers have zero means trainable variances e.gwij ∼N 0 σ2ij Although information get stored expected values weights models can learn surprisingly well achieve competitive performance. key results can be summarized follows:1 introduce variance layers new kind stochastic layers store information variances weights keeping means fixed zero mapping objects zero-mean distributions activations. variance layer is a simple example when the weight scaling rule BID8 fails.2 draw connection neural networks variance layers variance networks conventional Bayesian deep learning models. show several popular Bayesian models Kingmaetal. 2015 Molchanovetal. 2017 converge variance networks demonstrate surprising effect -a less flexible posterior approximation may lead much better values variational inference objective ELBO .3 Finally demonstrate variance networks perform surprisingly well number deep learning problems. achieve competitive classification accuracy are more robust adversarial attacks provide good exploration reinforcement learning problems. paper introduce variance networks surprisingly stable stochastic neural networks learn variances weights keeping means fixed zero one several layers.We show networks can still trained well match performance conventional models. Variance networks are more stable adversarial attacks conventional ensembling techniques can can lead better exploration reinforcement learning tasks.The success variance networks raises several counter-intuitive implications training deep neural networks:• DNNs can withstand extreme amount noise training can actually store information using variances noise. fact samples zero-centered posterior yield approximately accuracy also provides additional evidence landscape loss function is much complicated was considered earlier BID6.• popular trick replacing random variables network expected values can can lead arbitrarily large degradation accuracy -up random guess quality prediction.• Previous works used signal-to-noise ratio weights layer output prune excessive units BID1;Molchanovetal. 2017 Neklyudovetal. 2017 However show similar model weights even whole layer exactly zero SNR due zero mean output can be crucial prediction can't pruned SNR.• show flexible parameterization approximate posterior does not necessarily yield better value variational lower bound consequently does not necessarily approximate posterior distribution better.We believe variance networks may provide new insights how neural networks learn data well give new tools building better deep models.A PROOF THEOREM 1 DISPLAYFORM0 terms Maximum Mean Discrepancy:DISPLAYFORM1 Proof. definition Maximum Mean Discrepancy have DISPLAYFORM2 where the supremum is taken set continuous functions bounded 1. Let's reparameterize join expectations:DISPLAYFORM3 18 Since linear transformations argument do not change neither norm function continuity can hide component-wise multiplication ε √α µ inside functionf ε.This would change supremum. DISPLAYFORM4 exists rotation matrixR R DISPLAYFORM5αt 0 0 ε comes isotropic Gaussianε∼ N 0 rotation Rε would follow distributionRε∼N 0 can incorporate rotation function f without affecting supremum. DISPLAYFORM6 Let's consider integration ε 1 separately φ ε1 denotes density standard Gaussian distribution DISPLAYFORM7 Next viewf ε1 function ε1 denote antiderivative F1 ε f ε dε1. Note f is bounded 1 henceF1 is Lipschitz ε1 Lipschitz constantL 1. would allowus bound deviation DISPLAYFORM8 Let's use integration parts:DISPLAYFORM9 first term is equal zero DISPLAYFORM10 Finally can use Lipschitz property F1 ε bound value:DISPLAYFORM11 Thus obtain following bound MMD:DISPLAYFORM12 bound goes zero α goes infinity.As output softmax network lies interval 0 1 obtain following bound deviation prediction ensemble applying zero-mean approximation:Figure8:are the learning curves VGG-like architectures trained CIFAR-10 layerwise parameterization different prior distributions. plots show three priors are equivalent practice:three models converge variance networks. convergence Student 's prior is slower case KL-term is estimated using one-sampleMC estimate. makes stochastic gradientw.r.t logα noisy whenα is large. DISPLAYFORM13,1725,1184,541,0.019,1.457,2025/11/05 17:18:53,0.01,1.36,0.3956386292834891,529.788
"Graph Convolutional Networks (GCNs) are a recently proposed architecture which has had success in semi-supervised learning on graph-structured data. At the same time, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper we propose a model, Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-GCN model achieves state-of-the-art performance on all of the challenging node classification tasks we consider: Cora, Citeseer, Pubmed, and PPI. In addition, our proposed method has other desirable properties, including generalization to recently proposed semi-supervised learning methods such as GraphSAGE, allowing us to propose N-SAGE, and resilience to adversarial input perturbations. Semi-supervised learning on graphs is important in many real-world applications, where the goal is to recover labels for all nodes given only a fraction of labeled ones. Some applications include social networks, where one wishes to predict user interests, or in health care, where one wishes to predict whether a patient should be screened for cancer. In many such cases, collecting node labels can be prohibitive. However, edges between nodes can be easier to obtain, either using an explicit graph (e.g. social network) or implicitly by calculating pairwise similarities (e.g. using a patient-patient similarity kernel, BID19 .Convolutional Neural Networks BID16 learn location-invariant hierarchical filters, enabling significant improvements on Computer Vision tasks BID15 BID23 BID12 . This success has motivated researchers BID7 to extend convolutions from spatial (i.e. regular lattice) domains to graph-structured (i.e. irregular) domains, yielding a class of algorithms known as Graph Convolutional Networks (GCNs).Formally, we are interested in semi-supervised learning where we are given a graph G = (V, E) with N = |V| nodes; adjacency matrix A; and matrix X ∈ R N ×F of node features. Labels for only a subset of nodes V L ⊂ V observed. In general, |V L | |V|. Our goal is to recover labels for all unlabeled nodes V U = V − V L , using the feature matrix X, the known labels for nodes in V L , and the graph G. In this setting, one treats the graph as the ""unsupervised"" and labels of V L as the ""supervised"" portions of the data.Depicted in FIG2 , our model for semi-supervised node classification builds on the GCN module proposed by BID14 , which operates on the normalized adjacency matrixÂ, as in GCN(Â), where = D , and D is diagonal matrix of node degrees. Our proposed extension of GCNs is inspired by the recent advancements in random walk based graph embeddings (e.g. BID22 BID9 BID1 . We make a Network of GCN modules (N-GCN), feeding each module a different power ofÂ, as in {GCN( 0 ), GCN( 1 ), GCN( 2 ), . . . }. The k-th power contains statistics from the k-th step of a random walk on the graph. Therefore, our N-GCN model is able to combine information from various step-sizes. We then combine the output of all GCN modules into a classification sub-network, and we jointly train all GCN modules and the classification sub-network on the upstream objective, Model architecture, where is the normalized normalized adjacency matrix, I is the identity matrix, X is node features matrix, and × is matrix-matrix multiply operator. We calculate K powers of the , feeding each power into r GCNs, along with X. The output of all K × r GCNs can be concatenated along the column dimension, then fed into fully-connected layers, outputting C channels per node, where C is size of label space. We calculate cross entropy error , between rows prediction N × C with known labels, and use them to update parameters of classification subnetwork and all GCNs. Right: pre-relu activations after the first fully-connected layer of a 2-layer classification sub-network. Activations are PCA-ed to 50 dimensions then visualized using t-SNE.semi-supervised node classification. Weights of the classification sub-network give us insight on how the N-GCN model works. For instance, in the presence of input perturbations , we observe that the classification sub-network weights shift towards GCN modules utilizing higher powers of the adjacency matrix, effectively widening the ""receptive field"" of the (spectral) convolutional filters. We achieve state-of-the-art on several semi-supervised graph learning tasks, showing that explicit random walks enhance the representational power of vanilla GCN's.The rest of this paper is organized as follows. Section 2 reviews background work that provides the foundation for this paper. In Section 3, we describe our proposed method, followed by experimental evaluation in Section 4. We compare our work with recent closely-related methods in Section 5 . Finally, we conclude with our contributions and future work in Section 6. In this paper, we propose a meta-model that can run arbitrary Graph Convolution models, such as GCN BID14 and SAGE BID10 , on the output of random walks. Traditional Graph Convolution models operate on the normalized adjacency matrix. We make multiple instantiations of such models, feeding each instantiation a power of the adjacency matrix, and then concatenating the output of all instances into a classification sub-network. Our model, Network of GCNs (and similarly, Network of SAGE), is end-to-end trainable, and is able to directly learn information across near or distant neighbors. We inspect the distribution of parameter weights in our classification sub-network, which reveal to us that our model is effectively able to circumvent adversarial perturbations on the input by shifting weights towards model instances consuming higher powers of the adjacency matrix. For future work, we plan to extend our methods to a stochastic implementation and tackle other (larger) graph datasets.",Graph Convolutional Networks GCNs are a recently proposed architecture which has had success semi-supervised learning graph-structured data. time unsupervised learning graph embeddings has benefited information contained random walks. paper propose model Network GCNs N-GCN which marries two lines work. core N-GCN trains multiple instances GCNs node pairs discovered different distances random walks learns combination instance outputs which optimizes classification objective. experiments show proposed N-GCN model achieves state-of-the-art performance challenging node classification tasks consider:Cora Citeseer Pubmed PPI. addition proposed method has other desirable properties including generalization recently proposed semi-supervised learning methods GraphSAGE allowingus propose N-SAGE resilience adversarial input perturbations. Semi-supervised learning graphs is important many real-world applications where the goal is to recover labels nodes given fraction labeled ones. applications include social networks where one wishes predict user interests health care where one wishes predict whether patient should be screened cancer. many cases collecting node labels can be prohibitive. However edges nodes can be easier obtain either using explicit graph e.g social network implicitly calculating pairwise similarities e.g using patient-patient similarity kernel BID19.Convolutional Neural Networks BID16 learn location-invariant hierarchical filters enabling significant improvements Computer Vision tasks BID15 BID23 BID12. success has motivated researchers BID7 extend convolutions spatial.e regular lattice domains graph-structured.e irregular domains yielding class algorithms known Graph Convolutional Networks GCNs.Formally are interested semi-supervised learning where we are given graphG V E N |V| nodes;adjacency matrix A;matrixX∈R N×F node features. Labels subset nodesVL⊂ V observed. general |VL |V|. goal is to recover labels unlabeled nodesVU V−VL using feature matrixX known labels nodes VL graphG. setting where one treats graph unsupervised labels VL supervised portions data.Depicted FIG2 model semi-supervised node classification builds GCN module proposed BID14 which operates normalized adjacency matrix GCN  where is diagonal matrix node degrees. proposed extension GCNs is inspired recent advancements random walk based graph embeddings e.g BID22 BID9 BID1. make Network GCN modules N-GCN feeding module different power of GCN Â0 GCN Â1 GCN Â2 k-th power contains statistics k-th step random walk graph. Therefore N-GCN model is able combine information various step-sizes combine output GCN modules classification sub-network jointly train GCN modules classification sub-network upstream objective Model architecture where is the normalized normalized adjacency matrix is the identity matrix X is node features matrix × is matrix-matrix multiply operator. calculate K powers the feeding power r GCNs along X. output K × r GCNs can be concatenated along column dimension fed fully-connected layers outputting C channels per node whereC is size label space. calculate cross entropy error rows predictionN× C known labels use update parameters classification subnetwork GCNs. Right:pre-relu activations first fully-connected layer 2-layer classification sub-network Activations are PCA-ed 50 dimensions visualized using t-SNE.semi-supervised node classification. Weights classification sub-network giveus insight how the N-GCN model works. instance presence input perturbations observe classification sub-network weights shift towards GCN modules utilizing higher powers adjacency matrix effectively widening receptive field spectral convolutional filters. achieve state-of-the-art several semi-supervised graph learning tasks showing explicit random walks enhance representational power vanilla GCN's.The rest paper is organized follows. Section 2 reviews background work provides foundation paper. Section3 describe proposed method followed experimental evaluation Section4. compare work recent closely-related methods Section5. Finally conclude contributions future work Section6. paper propose meta-model can run arbitrary Graph Convolution models GCN BID14 SAGE BID10 output random walks. Traditional Graph Convolution models operate normalized adjacency matrix. make multiple instantiations models feeding instantiation power adjacency matrix concatenating output instances classification sub-network model Network GCNs similarly Network SAGE is end-to-end trainable is able directly learn information across near distant neighbors. inspect distribution parameter weights classification sub-network which reveal us model is effectively able circumvent adversarial perturbations input shifting weights towards model instances consuming higher powers adjacency matrix. future work plan extend methods stochastic implementation tackle larger graph datasets.,1291,871,420,0.012,1.482,2025/11/05 17:18:53,0.01,1.429,0.4735202492211836,359.417
"Recent DNN pruning algorithms have succeeded in reducing the number of parameters in fully connected layers often with little or no drop in classification accuracy. However most of the existing pruning schemes either have to be applied during training or require a costly retraining procedure after pruning to regain classification accuracy. In this paper we propose a cheap pruning algorithm based on difference of convex (DC) optimisation. We also provide theoretical analysis for the growth in the Generalisation Error (GE) of the new pruned network. Our method can be used with any convex regulariser and allows for a controlled degradation in classification accuracy while being orders of magnitude faster than competing approaches. Experiments on common feedforward neural networks show that for sparsity levels above 90% our method achieves 10% higher classification accuracy compared to Hard Thresholding. Recently, deep neural networks have achieved state-of-the art results in a number of machine learning tasks BID12 . Training such networks is computationally intensive and often requires dedicated and expensive hardware. Furthermore, the resulting networks often require a considerable amount of memory to be stored. Using a Pascal Titan X GPU the popular AlexNet and VGG-16 models require 13 hours and 7 days, respectively, to train, while requiring 200MB and 600MB, respectively, to store. The large memory requirements limit the use of DNNs in embedded systems and portable devices such as smartphones, which are now ubiquitous.A number of approaches have been proposed to reduce the DNN size during training time, often with little or no degradation to classification performance. Approaches include introducing bayesian, sparsity-inducing priors BID13 BID2 BID14 and binarization BID10 BID5 .Other methods include the hashing trick used in BID4 , tensorisation BID17 and efficient matrix factorisations BID11 .However , trained DNN models are used by researchers and developers that do not have dedicated hardware to train them, often as general feature extractors for transfer learning. In such settings it is important to introduce a cheap compression method, i.e., one that can be implemented as a postprocessing step with little or no retraining. Some first work in this direction has been BID11 BID8 BID9 although these still require a lengthy retraining procedure. Closer to our approach recently in BID0 the authors propose a convexified layerwise pruning algorithm termed Net-Trim. Building upon Net-Trim, the authors in BID6 propose LOBS, an algorithm for layerwise pruning by loss function approximation.Pruning a neural network layer introduces a pertubation to the latent signal representations generated by that layer. As the pertubated signal passes through layers of non-linear projections, the pertubation could become arbitrary large. In BID0 and BID6 the authors conduct a theoretical analysis using the Lipschitz properties of DNNs showing the stability of the latent representations, over the training set, after pruning. The methods employed have connections to recent work BID19 BID1 BID15 In this paper we have presented an efficient pruning algorithm for fully connected layers of DNNs, based on difference of convex functions optimisation. Our algorithm is orders of magnitude faster than competing approaches while allowing for a controlled degradation in the Generalization Error.We provided a theoretical analysis of the degradation in GE resulting from our pruning algorithm. This analysis validates the previously observed phenomenon that network layers closer to the input are exponentially less robust to pruning compared to layers close to the output. Our theoretical analysis is of value by itself as it holds for any kind of bounded pertubation to one or multiple hidden DNN layers. Experiments on common feedforward architectures validate our results. Proof. See BID3 for details, the derivation is not entirely trivial due to the nonsmoothness of the rectifier non-linearity. Proof. We see that: DISPLAYFORM0 1+exp(βx) ≤ 1. Therefore the smooth approximation to the rectifier non-linarity is Lipschitz smooth with Lipschitz constant k = 1. Then DISPLAYFORM1 We drop the W i from the layer notation for clarity. Using the triangle inequality DISPLAYFORM2 where we used Lemma 6.1 and Lemma 6.2 in line 5.B. PROOF OF THEOREM 3.2. We will proceed as follows. We first introduce some prior results which hold for the general class of robust classifiers. We will then give specific prior generalization error results for the case of classifiers operating on datapoints from C m -regular manifolds. Afterwards we will provide prior results for the specific case of DNN clasifiers. Finally we will prove our novel generalization error bound and provide a link with prior bounds.We first formalize robustness for generic classifiers g(x ). In the following we assume a loss function l(g(x) , y) that is positive and bounded DISPLAYFORM3 , such that ∀s i ∈ S m , ∀s ∈ S, DISPLAYFORM4 Now letl(·) and l emp (·) denote the expected error and the training error, i.e, DISPLAYFORM5 we can then state the following theorem from Xu & Mannor (2012): Theorem 6.3. If S m consists of m i.i.d. samples, and g(x) is (K, (S m ))-robust, then for any δ > 0, with probability at least 1 − δ, DISPLAYFORM6 The above generic bound can be specified for the case of C m -regular manifolds as in BID19 . We recall the definition of the sample margin γ(s i ) as well as the following theorem:Theorem 6.4. If there exists γ such that DISPLAYFORM7 By direct substitution of the above result and the definiton of a C m -regular manifold into Theorem 6.3 we get: Corollary 6.4.1. Assume that X is a (subset of) C M regular k−dimensional manifold, where DISPLAYFORM8 k . Assume also that classifier g(x) achieves a classification margin γ and take l(g(x), y) to be the 0 − 1 loss. Then for any δ > 0, with probability at least 1 − δ, DISPLAYFORM9 Note that in the above we have used the fact that l(g(x), y) ≤ 1 and therefore M = 1. The above holds for a wide range of algorithms that includes as an example SVMs. We are now ready to specify the above bound for the case of DNNs, adapted from BID19 , Theorem 6.5. Assume that a DNN classifier g(x), as defined in equation 8 , and letx be the training sample with the smallest score o(s) > 0. Then the classification margin is bounded as DISPLAYFORM10 We now prove our main result. We will denote byx = arg min si∈Sm min j =g(xi) v T g(xi)j f (x i ) the training sample with the smallest score. For this training sample we will denote j = arg min j =g(x) v T g(x)j f (x) the second best guess of the classifier g(·). Throughout the proof, we will use the notation DISPLAYFORM11 First we assume the score o 1 (x, g 1 (x)) of the pointx for the original classifier g 1 (x). Then , for the second classifier g 2 (x), we take a point x that lies on the decision boundary between g 2 (x) and j such that o 2 (x , g 2 (x)) = 0. We assume for simplicity that, after pruning, the classification decisions do not change such that g 1 (x) = g 2 (x). We then make the following calculations DISPLAYFORM12 where we used Theorem 3.1 in line 5, since x is not a training sample. From the above we can therefore write o 1 (x, g 1 (x)) − √ C 2 i>i ||W i || 2 DISPLAYFORM13 By following the derivation of the margin from the original paper BID19 and taking into account the definition of the margin we know that DISPLAYFORM14 Therefore we can finally write DISPLAYFORM15 The theorem follows from direct application of Corollary 3.1.1. Note that if γ − √ C2 i>i ||W i||2 i ||W i||2 < 0 the derived bound becomes vacuous, as by definition 0 ≤ γ 2 (x).C. PROOF OF THEOREM 3.3. We start as in theorem 3.2 by assuming the score o 1 (x, g 1 (x)) of the pointx for the original classifier g 1 (x). Then, for the second classifier g 2 (x), we take a point x that lies on the decision boundary between g 2 (x) and j such that o 2 (x , g 2 (x )) = 0. We assume as before that the classification decisions do not change such that g 1 (x) = g 2 ( x). We write DISPLAYFORM16 We can then write DISPLAYFORM17 Then as before DISPLAYFORM18 The theorem follows from direct application of Corollary 3.1.1.",Recent DNN pruning algorithms have succeeded reducing number parameters fully connected layers often little drop classification accuracy. However existing pruning schemes either have to be applied training require costly retraining procedure pruning regain classification accuracy. paper propose cheap pruning algorithm based difference convex DC optimisation. also provide theoretical analysis growth Generalisation Error GE new pruned network. method can be used convex regulariser allows controlled degradation classification accuracy orders magnitude faster competing approaches. Experiments common feedforward neural networks show sparsity levels 90% method achieves10% higher classification accuracy compared Hard Thresholding. Recently deep neural networks have achieved state-of-the art results number machine learning tasks BID12. Training networks is computationally intensive often requires dedicated expensive hardware. Furthermore resulting networks often require considerable amount memory stored. Using Pascal Titan X GPU popular AlexNet VGG-16 models require13 hours 7 days respectively train requiring 200MB 600MB respectively store. large memory requirements limit use DNNs embedded systems portable devices smartphones which are now ubiquitous.A number approaches have been proposed reduce DNN size training time often little degradation classification performance. Approaches include introducing bayesian sparsity-inducing priors BID13 BID2 BID14 binarization BID10 BID5.Other methods include hashing trick used BID4 tensorisation BID17 efficient matrix factorisations BID11.However trained DNN models are used researchers developers do not have dedicated hardware train often general feature extractors transfer learning. settings is important introduce cheap compression method.e one can be implemented postprocessing step little retraining. first work direction has been BID11 BID8 BID9 although still require lengthy retraining procedure. Closer approach recently BID0 authors propose convexified layerwise pruning algorithm termed Net-Trim Building upon Net-Trim authors BID6 propose LOBS algorithm layerwise pruning loss function approximation.Pruning neural network layer introduces pertubation latent signal representations generated layer. pertubated signal passes layers non-linear projections pertubation could become arbitrary large. BID0 BID6 authors conduct theoretical analysis using Lipschitz properties DNNs showing stability latent representations training set pruning. methods employed have connections recent work BID19 BID1 BID15 paper have presented efficient pruning algorithm fully connected layers DNNs based difference convex functions optimisation. algorithm is orders magnitude faster competing approaches allowing controlled degradation Generalization Error.We provided theoretical analysis degradation GE resulting pruning algorithm. analysis validates previously observed phenomenon network layers closer input are exponentially less robust pruning compared layers close output. theoretical analysis is of value holds kind bounded pertubation one multiple hidden DNN layers. Experiments common feedforward architectures validate results. Proof. See BID3 details derivation is not entirely trivial due nonsmoothness rectifier non-linearity Proof. see that:DISPLAYFORM0 1+exp βx ≤1. Therefore smooth approximation rectifier non-linarity is Lipschitz smooth Lipschitz constantk 1. DISPLAYFORM1 drop W layer notation clarity. Using triangle inequality DISPLAYFORM2 where we used Lemma 6.1 Lemma 6.2 line 5.B PROOF THEOREM 3.2 will proceed follows. first introduce prior results which hold general class robust classifiers. will then give specific prior generalization error results case classifiers operating datapoints C -regular manifolds. Afterwards will provide prior results specific case DNN clasifiers. Finally will prove novel generalization error bound provide link prior bounds.We first formalize robustness generic classifiersg x following assume loss functionl g x is positive bounded DISPLAYFORM3 ∀s ∈ ∀s∈ DISPLAYFORM4 letl · l emp · denote expected error training error.e DISPLAYFORM5 can then state following theorem Xu Mannor 2012 Theorem 6.3 If S m consists.i.d samples g x is(K -robust δ 0 probability least1−δ DISPLAYFORM6 generic bound can be specified case C -regular manifolds BID19. recall definition sample marginγ well following theorem:Theorem 6.4 If there existsγ DISPLAYFORM7 direct substitution result definiton C -regular manifold Theorem 6.3 get:Corollary 6.4.1 Assume X is a(subset C regular k−dimensional manifold where DISPLAYFORM8k. Assume also classifierg x achieves classification marginγ takel g x 0 − 1 loss. δ 0 probability least1−δ DISPLAYFORM9 Note have used fact l g x ≤1 therefore 1. holds wide range algorithms includes example SVMs. are now ready specify bound case DNNs adapted BID19 Theorem 6.5 Assume DNN classifierg x defined equation8 letx training sample smallest score 0. classification margin is bounded DISPLAYFORM10 prove main result. will denote byx arg min si∈Sm min j=g xi v g xi jf x training sample smallest score. training sample will denotej arg minj=g x v g x jf x second best guess classifierg · Throughout proof will use notation DISPLAYFORM11 First assume score 1 x g1 x pointx original classifierg1 x second classifierg2 x take pointx lies decision boundary g2 x j 2 x g2 x 0. assume simplicity pruning classification decisions do not change g1 x g2 x make following calculations DISPLAYFORM12 where we used Theorem 3.1 line5 sincex is not a training sample. can therefore write 1 x g1 x −√C2 ||W || 2 DISPLAYFORM13 following derivation margin original paper BID19 taking account definition margin know DISPLAYFORM14 Therefore can finally write DISPLAYFORM15 theorem follows direct application Corollary 3.1.1 Note ifγ−√C2 ||W i||2 ||W i||2 0 derived bound becomes vacuous definition0≤γ 2 x.C PROOF THEOREM 3.3 start theorem 3.2 assuming score 1 x g1 x pointx original classifierg1 x second classifierg2 x take pointx lies decision boundary g2 x j 2 x g2 x 0. assume classification decisions do not change g1 x g2 x write DISPLAYFORM16 can then write DISPLAYFORM17 DISPLAYFORM18 theorem follows direct application Corollary 3.1.1,1914,1258,656,0.037,1.521,2025/11/05 17:18:54,0.01,1.6,0.595015576323987,699.819
"Action segmentation as a milestone towards building automatic systems to understand untrimmed videos has received considerable attention in the recent years. It is typically being modeled as a sequence labeling problem but contains intrinsic and sufficient differences than text parsing or speech processing. In this paper, we introduce a novel hybrid temporal convolutional and recurrent network (TricorNet), which has an encoder-decoder architecture: the encoder consists of a hierarchy of temporal convolutional kernels that capture the local motion changes of different actions; the decoder is a hierarchy of recurrent neural networks that are able to learn and memorize long-term action dependencies after the encoding stage. Our model is simple but extremely effective in terms of video sequence labeling. The experimental results on three public action segmentation datasets have shown that the proposed model achieves superior performance over the state of the art. Action segmentation is a challenging problem in high-level video understanding. In its simplest form, action segmentation aims to segment a temporally untrimmed video by time and label each segmented part with one of k pre-defined action labels. For example, given a video of Making Hotdog (see FIG0 ), we label the first 10 seconds as take bread, and the next 20 seconds as take sausage, and the remaining video as pour ketchup following the procedure dependencies of making a hotdog. The results of action segmentation can be further used as input to various applications, such as video-to-text BID2 and action localization BID14 .Most current approaches for action segmentation BID26 BID19 use features extracted by convolutional neural networks, e.g., two-stream CNNs BID18 or local 3D ConvNets BID23 , at every frame after a downsampling as the input, and apply a one-dimensional sequence prediction model, such as recurrent neural networks, to label actions on frames. Despite the simplicity in handling video data, action segmentation is treated similar to text parsing BID1 , which results the local motion changes in various actions being under-explored. For example , the action pour ketchup may consist of a series of sub-actions, e.g., pick up the ketchup, squeeze and pour, and put down the ketchup. Furthermore , the time duration of performing the same action pour ketchup may vary according to different people and contexts.Indeed, the recent work by BID12 starts to explore the local motion changes in action segmentation. They propose an encoder-decoder framework, similar to the deconvolution networks in image semantic segmentation BID15 , for video sequence labeling. By using a hierarchy of 1D temporal convolutional and deconvolutional kernels in the encoder and decoder networks, respectively, their model is effective in terms of capturing the local motions and achieves state-of-theart performance in various action segmentation datasets. However, one obvious drawback is that it fails to capture the long-term dependencies of different actions in a video due to its fixed-size, local receptive fields. For example, pour ketchup usually happens after both take bread and take sausage for a typically video of Making Hotdog. In addition, a dilated temporal convolutional network, similar to the WavNet for speech processing BID24 , is also tested in BID12 , but has worse performance, which further suggests the existence of differences between video and speech data, despite they are both being represented as sequential features. To overcome the above limitations , we propose a novel hybrid TempoRal COnvolutional and Recurrent Network (TricorNet), that attends to both local motion changes and long-term action dependencies for modeling video action segmentation. TricorNet uses frame-level features as the input to an encoder-decoder architecture. The encoder is a temporal convolutional network that consists of a hierarchy of one-dimensional convolutional kernels, observing that the convolutional kernels are good at encoding the local motion changes; the decoder is a hierarchy of recurrent neural networks, in our case Bi-directional Long Short-Term Memory networks (Bi-LSTMs) BID5 , that are able to learn and memorize long-term action dependencies after the encoding process. Our network is simple but extremely effective in terms of dealing with different time durations of actions and modeling the dependencies among different actions.We conduct extensive experiments on three public action segmentation datasets, where we compare our proposed models with a set of recent action segmentation networks using three different evaluation metrics. The quantitative experimental results show that our proposed TricorNet achieves superior or competitive performance to state of the art on all three datasets. A further qualitative exploration on action dependencies shows that our model is good at capturing long-term action dependencies and produce smoother labeling.For the rest of the paper, we first survey related work in the domain of action segmentation and action detection in Sec. 2. We introduce our hybrid temporal convolutional and recurrent network with some implementation variants in Sec. 3. We present both quantitative and qualitative experimental results in Sec. 4, and conclude the paper in Sec. 5. In this paper, we propose TricorNet, a novel hybrid temporal convolutional and recurrent network for video action segmentation problems. Taking frame-level features as the input to an encoder-decoder architecture, TricorNet uses temporal convolutional kernels to model local motion changes and uses bi-directional LSTM units to learn long-term action dependencies. We provide three model variants to comprehensively evaluate our model design. Despite the simplicity in methods, experimental results on three public action segmentation datasets with different metrics show that our proposed model achieves superior performance over the state of the art. A further qualitative exploration on action dependencies shows that our model is good at capturing long-term action dependencies, which help to produce segmentation in a smoother and preciser manner.Limitations. In experiments we find that all the best results of TricorNet are achieved with number of layers K = 2. It will either over-fit or stuck in local optimum when adding more layers. Considering all three datasets are relatively small with limited training data (despite they are standard in evaluating action segmentation), using more data is likely going to further improve the performance.Future Work. We consider two directions for the future work. Firstly, the proposed TricorNet is good to be evaluated on other action segmentation datasets to further explore its strengths and limitations. Secondly, TricorNet can be extended to solve other video understanding problems, taking advantage of its flexible structural design and superior capability of capturing video information.",Action segmentation milestone towards building automatic systems understand untrimmed videos has received considerable attention recent years. is typically modeled sequence labeling problem contains intrinsic sufficient differences text parsing speech processing. paper introduce novel hybrid temporal convolutional recurrent network TricorNet which has encoder-decoder architecture:encoder consists hierarchy temporal convolutional kernels capture local motion changes different actions;decoder is a hierarchy recurrent neural networks are able learn memorize long-term action dependencies encoding stage. model is simple extremely effective terms video sequence labeling. experimental results three public action segmentation datasets have shown proposed model achieves superior performance state art. Action segmentation is a challenging problem high-level video understanding. simplest form action segmentation aims segment temporally untrimmed video time label segmented part one k pre-defined action labels. example given video Making Hotdog see FIG0 label first 10 seconds take bread next 20 seconds take sausage remaining video pour ketchup following procedure dependencies making hotdog. results action segmentation can be further used input various applications video-to-text BID2 action localization BID14.Most current approaches action segmentation BID26 BID19 use features extracted convolutional neural networks e.g two-stream CNNs BID18 local 3D ConvNets BID23 every frame downsampling input apply one-dimensional sequence prediction model recurrent neural networks label actions frames. Despite simplicity handling video data action segmentation is treated similar text parsing BID1 which results local motion changes various actions under-explored example action pour ketchup may consist series sub-actions e.g pick ketchup squeeze pour put ketchup. Furthermore time duration performing action pour ketchup may vary according different people contexts.Indeed recent work BID12 starts explore local motion changes action segmentation. propose encoder-decoder framework similar deconvolution networks image semantic segmentation BID15 video sequence labeling. using hierarchy 1D temporal convolutional deconvolutional kernels encoder decoder networks respectively model is effective terms capturing local motions achieves state-of-theart performance various action segmentation datasets. However one obvious drawback is that it fails capture long-term dependencies different actions video due fixed-size local receptive fields. example pour ketchup usually happens take bread take sausage typically video Making Hotdog. addition dilated temporal convolutional network similar WavNet speech processing BID24 is also tested BID12 has worse performance which further suggests existence differences video speech data despite are both being represented sequential features. overcome limitations propose novel hybrid TempoRal COnvolutional Recurrent Network TricorNet attends local motion changes long-term action dependencies modeling video action segmentation. TricorNet uses frame-level features input encoder-decoder architecture. encoder is a temporal convolutional network consists hierarchy one-dimensional convolutional kernels observing convolutional kernels are good encoding local motion changes;decoder is a hierarchy recurrent neural networks case Bi-directional Long Short-Term Memory networks Bi-LSTMs BID5 are able learn memorize long-term action dependencies encoding process. network is simple extremely effective terms dealing different time durations actions modeling dependencies among different actions.We conduct extensive experiments three public action segmentation datasets where we compare proposed models set recent action segmentation networks using three different evaluation metrics. quantitative experimental results show proposed TricorNet achieves superior competitive performance state art three datasets. qualitative exploration action dependencies shows model is good capturing long-term action dependencies produce smoother labeling.For rest paper first survey related work domain action segmentation action detection Sec. 2. introduce hybrid temporal convolutional recurrent network implementation variants Sec. 3. present quantitative qualitative experimental results Sec. 4 conclude paper Sec. 5. paper propose TricorNet novel hybrid temporal convolutional recurrent network video action segmentation problems. Taking frame-level features input encoder-decoder architecture TricorNet uses temporal convolutional kernels model local motion changes uses bi-directional LSTM units learn long-term action dependencies. provide three model variants comprehensively evaluate model design. Despite simplicity methods experimental results three public action segmentation datasets different metrics show proposed model achieves superior performance state art. qualitative exploration action dependencies shows model is good capturing long-term action dependencies which help produce segmentation smoother preciser manner.Limitations. experiments find best results TricorNet are achieved number layersK 2. will either over-fit stuck local optimum when adding layers. Considering three datasets are relatively small limited training data despite are standard evaluating action segmentation using data is likely going improve performance.Future Work. consider two directions future work. Firstly proposed TricorNet is good evaluated action segmentation datasets explore strengths limitations. Secondly TricorNet can be extended solve video understanding problems taking advantage flexible structural design superior capability capturing video information.,1267,882,385,0.014,1.437,2025/11/05 17:18:54,0.01,1.433,0.3333333333333333,407.928
"Convolutional Neural Networks (CNNs) become deeper and deeper in recent years, making the study of model acceleration imperative. It is a common practice to employ a shallow network, called student, to learn from a deep one, which is termed as teacher. Prior work made many attempts to transfer different types of knowledge from teacher to student, however, there are two problems remaining unsolved. Firstly, the knowledge used by existing methods is highly dependent on task and dataset, limiting their applications. Secondly, there lacks an effective training scheme for the transfer process, leading to degradation of performance. In this work, we argue that feature is the most important knowledge from teacher. It is sufficient for student to just learn good features regardless of the target task. From this discovery, we further present an efficient learning strategy to mimic features stage by stage. Extensive experiments demonstrate the importance of features and show that the proposed approach significantly narrows down the gap between student and teacher, outperforming the state-of-the-art methods.
 Over the past few years, Convolutional Neural Networks (CNNs) have advanced various tasks in computer vision field, such as image classification BID8 , object detection BID17 , semantic segmentation BID3 , etc. However, along with the architecture growing deeper BID12 BID20 BID5 , the great success of CNN is at the cost of large computational power, which can not be afforded by most devices in practice. Some lightweight models are presented by recent work BID7 to reduce the computing cost especially for mobile devices, but the performance drops severely compared with the state-of-the-art methods. Accordingly, it is crucial to balance the trade-off between efficiency and capability of a CNN model.To tackle this problem, knowledge distillation is introduced in BID6 for model acceleration. The core idea is to train shallow networks (student) to mimic deep ones (teacher) following two folds. First, teacher employs a very deep model to achieve satisfying performance by excavating information (knowledge) from labeled data. Second, student learns the knowledge from teacher with a shallow model to speed up without losing much accuracy. Accordingly, the main challenges, corresponding to the above two steps respectively, lie in (1) what kind of knowledge should be transferred to student, and (2) how to transfer the knowledge from teacher to student as much as possible.For the first issue, previous work usually make student to learn from both teacher and original labeled data. There are mainly two problems in doing so. On one hand, it is very sensitive to tasks and datasets. The hyper-parameters, e.g. the loss weights to balance these two objective functions, require careful adjustment, or otherwise, it may cause severe performance degradation. On the other hand, the purposes to learn from teacher and to learn from ground-truth are not always consistent with each other. For example, teacher model may eliminate some label errors during the training process. In this case, trying to minimize the loss to mimic teacher as well as the loss from target task may cause confusions to student. Furthermore, prior work has also characterized various types of knowledge from teacher model for student to learn, such as attention map BID23 , information flow BID22 , etc. However, all types of knowledge are manually defined, which may not fully conform with the information contained in the teacher network. In other words, teacher is trained independently from these handcraft definitions, but is required to guide the student with such knowledge, which may cause some ambiguities. For the second issue, previous approaches do not solve the problem caused by the gaps between the learning abilities of student and teacher. Intuitively, student model has much less parameters compared to teacher, resulting in lower representation capability. Training it from scratch may always lead to poor performance.In this paper, we address these weaknesses by proposing a task independent knowledge transfer approach, where student is trained to mimic features from teacher stage by stage. Here, for simplicity, we do not distinguish between feature and feature map. It has two appealing properties.First, we isolate the knowledge contained in teacher model from the information provided by ground-truth. This goal is achieved with two phases. In the first phase, student learns knowledge by mimicking the output features of teacher, while in the second phase, student is trained with task dependent objection function based on the features from first phase. In this way, student can focus on acquiring information from only one source in each phase, making the transfer process more accurate. Separating these two phases apart also makes our method more generic to various tasks. Besides, we directly treat features as knowledge in this work. Since teacher model just uses features for inference in practice, they are expected to contain the compete information extracted by teacher from training data.Second, instead of training all parameters of student together, we divide the transfer process into different stages and only train a sub-network at one time. Student network has far more limited representation ability than teacher, resulting in the huge difficulty to mimic the final features directly. To alleviate such obstacle, we let the student to learn from teacher gradually. In other words, both teacher network and student network are separated into sequential parts. Then, in each stage, one part of student will be trained to mimic the output of the corresponding part of teacher with all previous parts fixed. In doing so, the gap between learning powers between student and teacher is narrowed down. As long as each stage is well trained, they will finally collaborate to achieve appealing results.To summarize, the contributions of this work are as follows:• We demonstrate the effectiveness of mimicking features directly in task independent knowledge transfer.• We present a stage-by-stage training strategy to learn features accurately and efficiently.• We show experimentally that our approach surpasses the state-of-the-art methods on various tasks with higher performance and stronger stability. This work presents a stage-by-stage knowledge transfer approach by training student to mimic the output features of teacher network gradually. Compared to prior work, our method pays more attention to the information contained in the model, regardless of what task the model is applied for, making it a generic solution for model acceleration. The progressive training strategy helps reduce the learning difficulties of student in each stage, and all stages cooperate together for a better result.Extensive experimental results suggest that our scheme can significantly improve the performance of student model on various tasks with strong stability.",Convolutional Neural Networks CNNs become deeper deeper recent years making study model acceleration imperative. is a common practice employ shallow network called student learn deep one which is termed teacher. Prior work made many attempts transfer different types knowledge teacher student however are two problems remaining unsolved. Firstly knowledge used existing methods is highly dependent task dataset limiting applications. Secondly lacks effective training scheme transfer process leading degradation performance. work argue feature is the most important knowledge teacher. is sufficient student learn good features regardless target task. discovery present efficient learning strategy mimic features stage stage. Extensive experiments demonstrate importance features show proposed approach significantly narrows gap student teacher outperforming state-of-the-art methods. past years Convolutional Neural Networks CNNs have advanced various tasks computer vision field image classification BID8 object detection BID17 semantic segmentation BID3 etc. However along architecture growing deeper BID12 BID20 BID5 great success CNN is at the cost large computational power which can not afforded devices practice. lightweight models are presented recent work BID7 reduce computing cost especially mobile devices performance drops severely compared state-of-the-art methods. Accordingly is crucial balance trade-off efficiency capability CNN model.To tackle problem knowledge distillation is introduced BID6 model acceleration. core idea is to train shallow networks student mimic deep ones teacher following two folds. First teacher employs deep model achieve satisfying performance excavating information knowledge labeled data. Second where student learns knowledge teacher shallow model speed without losing much accuracy. Accordingly main challenges corresponding two steps respectively lie 1 what kind knowledge should be transferred student 2 how to transfer knowledge teacher student much possible.For first issue previous work usually make student learn teacher original labeled data. are mainly two problems so. one hand is very sensitive tasks datasets. hyper-parameters e.g loss weights balance two objective functions require careful adjustment otherwise may cause severe performance degradation. hand purposes learn teacher learn ground-truth are not always consistent other. example teacher model may eliminate label errors training process. case trying minimize loss mimic teacher well loss target task may cause confusions student. Furthermore prior work has also characterized various types knowledge teacher model student learn attention map BID23 information flow BID22 etc. However types knowledge are manually defined may fully conform information contained teacher network. words teacher is trained independently handcraft definitions is required guide student knowledge may cause ambiguities. second issue previous approaches do not solve problem caused gaps learning abilities student teacher. Intuitively where student model has much less parameters compared teacher resulting lower representation capability. Training scratch may always lead poor performance.In paper address weaknesses proposing task independent knowledge transfer approach where student is trained mimic features teacher stage stage. simplicity do not distinguish feature feature map. has two appealing properties.First isolate knowledge contained teacher model information provided ground-truth goal is achieved two phases. first phase where student learns knowledge mimicking output features teacher second phase where student is trained task dependent objection function based features first phase. way where student can focus acquiring information one source phase making transfer process accurate. Separating two phases apart also makes method generic various tasks. Besides directly treat features knowledge work. Since teacher model uses features inference practice are expected contain compete information extracted teacher training data.Second instead training parameters student together divide transfer process different stages train sub-network one time. Student network has far limited representation ability teacher resulting huge difficulty mimic final features directly. alleviate obstacle let student learn teacher gradually. words teacher network student network are separated sequential parts. stage one part student will be trained mimic output corresponding part teacher previous parts fixed. gap learning powers student teacher is narrowed down. long stage is well trained will finally collaborate achieve appealing results.To summarize contributions work are as follows:• demonstrate effectiveness mimicking features directly task independent knowledge transfer.• present stage-by-stage training strategy learn features accurately efficiently.• show experimentally approach surpasses state-of-the-art methods various tasks higher performance stronger stability. work presents stage-by-stage knowledge transfer approach training student mimic output features teacher network gradually. Compared prior work method pays attention information contained model regardless what task model is applied making generic solution model acceleration. progressive training strategy helps reduce learning difficulties student stage stages cooperate together better result.Extensive experimental results suggest scheme can significantly improve performance student model various tasks strong stability.,1263,819,444,0.017,1.542,2025/11/05 17:18:54,0.01,1.415,0.660436137071651,445.756
"We augment adversarial training (AT) with worst case adversarial training
 (WCAT) which improves adversarial robustness by 11% over the current state-
 of-the-art result in the `2-norm on CIFAR-10. We interpret adversarial training as
 Total Variation Regularization, which is a fundamental tool in mathematical im-
 age processing, and WCAT as Lipschitz regularization, which appears in Image
 Inpainting. We obtain verifiable worst and average case robustness guarantees,
 based on the expected and maximum values of the norm of the gradient of the
 loss. We augment adversarial training (AT) with worst case adversarial training (WCAT) which improves adversarial robustness by 11% over the current state-of-the-art result BID27 in the 2 norm. The method also achieves results comparable to the state-of-the-art results of BID22 in the ∞ norm. Moreover, our adversarial training step uses only one gradient evaluation compared to seven steps in the BID22 work. The worst case adversarial training method is described as follows. During adversarial training, the gradient of the loss is computed for each perturbed image. WCAT records the largest of the gradients norms, and adds a penalty to the loss proportional to this term. In many cases we observe that models trained with AT and WCAT have improved test/validation error over the unregularized model.In §2 we show that the norm of the gradient of the loss of the model is a measure of the robustness of a model to adversarial examples. We obtain verifiable worst and average case robustness guarantees, based on the expected and maximum values of the norm of the gradient of the loss. We then compute these quantities empirically on trained models, and demonstrate that improving these quantities leads to proportional improvements in adversarial robustness.In §3 we interpret adversarial training as Total Variation (TV) Regularization, which is a fundamental tool in mathematical image processing. TV regularization was introduced for image denoising BID29 . It is a measure of the variation of a function, allowing for discontinuities. We also show that WCAT corresponds to Lipschitz regularization, which appears in Image Inpainting BID2 and function approximation BID7 BID25 . Lipschitz regularization was used in a recent proof of generalization of deep neural networks BID26 . Write (x) = • f (x) for the loss of the model. We show that training with AT and WCAT is equivalent to minimizing DISPLAYFORM0 where is the size of the adversarial training perturbation, and λ is the WCAT multiplier. The dual norm · * corresponds to · 1 for attacks measured in ∞ and to · 2 for attacks measured in 2 , 1 see §3.1.",augment adversarial training worst case adversarial training WCAT which improves adversarial robustness 11% current state- of-the-art result 2-norm CIFAR-10 interpret adversarial training Total Variation Regularization which is a fundamental tool mathematical im- age processing WCAT Lipschitz regularization which appears Image Inpainting. obtain verifiable worst average case robustness guarantees based expected maximum values norm gradient loss. augment adversarial training worst case adversarial training WCAT which improves adversarial robustness 11% current state-of-the-art result BID27 2 norm. method also achieves results comparable state-of-the-art results BID22 ∞ norm. Moreover adversarial training step uses one gradient evaluation compared seven steps BID22 work. worst case adversarial training method is described follows. adversarial training gradient loss is computed perturbed image. WCAT records largest gradients norms adds penalty loss proportional term. many cases observe models trained WCAT have improved test/validation error unregularized model.In§2 show norm gradient loss model is a measure robustness model adversarial examples. obtain verifiable worst average case robustness guarantees based expected maximum values norm gradient loss. compute quantities empirically trained models demonstrate improving quantities leads proportional improvements adversarial robustness.In§3 interpret adversarial training Total Variation TV Regularization which is a fundamental tool mathematical image processing. TV regularization was introduced image denoising BID29. is a measure variation function allowing discontinuities. also show WCAT corresponds Lipschitz regularization which appears Image Inpainting BID2 function approximation BID7 BID25. Lipschitz regularization was used recent proof generalization deep neural networks BID26. Write x •f x loss model. show training WCAT is equivalent minimizing DISPLAYFORM0 where is the size adversarial training perturbation λ is the WCAT multiplier. dual norm·* corresponds ·1 attacks measured ∞ ·2 attacks measured 2 1 see §3.1,564,383,181,0.005,1.473,2025/11/05 17:18:54,0.0,1.538,0.4454828660436138,178.709
"The task of Reading Comprehension with Multiple Choice Questions, requires a human (or machine) to read a given \{\textit{passage, question}\} pair and select one of the $n$ given options. The current state of the art model for this task first computes a query-aware representation for the passage and then \textit{selects} the option which has the maximum similarity with this representation. However, when humans perform this task they do not just focus on option selection but use a combination of \textit{elimination} and \textit{selection}. Specifically, a human would first try to eliminate the most irrelevant option and then read the document again in the light of this new information (and perhaps ignore portions corresponding to the eliminated option). This process could be repeated multiple times till the reader is finally ready to select the correct option. We propose \textit{ElimiNet}, a neural network based model which tries to mimic this process. Specifically, it has gates which decide whether an option can be eliminated given the \{\textit{document, question}\} pair and if so it tries to make the document representation orthogonal to this eliminatedd option (akin to ignoring portions of the document corresponding to the eliminated option). The model makes multiple rounds of partial elimination to refine the document representation and finally uses a selection module to pick the best option. We evaluate our model on the recently released large scale RACE dataset and show that it outperforms the current state of the art model on 7 out of the 13 question types in this dataset. Further we show that taking an ensemble of our \textit{elimination-selection} based method with a \textit{selection} based method gives us an improvement of 7\% (relative) over the best reported performance on this dataset.    
 Reading comprehension is the task of answering questions from a given passage. An AI agent which can display such capabilities would be useful in a wide variety of commercial applications such as answering questions from financial reports of a company, troubleshooting using product manuals, answering general knowledge questions from Wikipedia documents, etc. Given its widespread applicability, several variants of this task have been studied in the literature. For example, given a passage and a question, the answer could either (i) match some span in the passage or (ii) be synthesized from the passage or (iii) be one of the n given candidate answers. The last variant is typically used in various high school, middle school and competitive examinations. We refer to this as Reading Comprehension with Multiple Choice Questions (RC-MCQ). There is an increasing interest in building AI agents with deep language understanding capabilities which can perform at par with humans on such competitive tests. For example, recently BID10 have released a large scale dataset for RC-MCQ collected from Chinese high school and middle school English examinations comprising of 28000 passages and 100000 questions. The large size of this dataset makes it possible to train and evaluate complex neural network based models and measure the scientific progress on RC-MCQ.While answering such Multiple Choice Questions (MCQs), humans typically use a combination of option elimination and option selection. More specifically, it makes sense to first try to eliminate options which are completely irrelevant for the given question. While doing so, we may also be able to discard certain portions of the document which are not relevant to the question (because they revolve around the option which has been eliminated). This process can then be repeated multiple times, each time eliminating an option and refining the document (by discarding irrelevant portions). Finally, when it is no longer possible to eliminate any option, we can pick the best option from the remaining options. In contrast, current state of the art models for RC-MCQ focus explicitly on option selection. Specifically, given a question and a passage, they first compute a question aware representation of the passage (say d q ). They then compute a representation for each of the n options and select an option whose representation is closest to d q . There is no iterative process where options get eliminated and the representation of the document gets refined in the light of this elimination.We propose a model which tries to mimic the human process of answering MCQs. Similar to the existing state of the art method BID3 , we first compute a query-aware representation of the document (which essentially tries to retain only those portions of the document which are relevant to the question). We then use an elimination gate which takes a soft decision as to whether an option needs to be eliminated or not. This gate depends on the question, document and option. Next, akin to the human process described above, we would like to discard portions of the document representation which are aligned with this eliminated option. We do this by subtracting the component of the document representation along the option representation (same as Gram-Schmidt orthogonalization). The amount of orthogonalization depends on the soft decision given by the elimination gate. We repeat this process multiple times, during each pass doing a soft elimination of the options and refining the document representation. At the end of a few passes, we expect the document representation to be orthogonal (hence dissimilar) to the irrelevant options. Finally, we use a selection module to select the option which is most similar to the refined document representation. We refer to this model as ElimiNet.We evaluate ElimiNet on the RACE dataset and compare it with Gated Attention Reader (GAR) BID3 which is the current state of the art method on this dataset. We show that of the 13 question types in this dataset our model outperforms GAR on 7 question types. We also visualize the soft elimination probabilities learnt by ElimiNet and observe that it indeed learns to iteratively refine the document representation and push the probability mass towards the correct option. Finally, we show that an ensemble model combining ElimiNet with GAR gives an accuracy of 47.2% which is 7% (relative) better than the best reported performance on this dataset. In this section, we discuss the results of our experiments as described above. We focus on the task of Reading Comprehension with Multiple Choice Questions and propose a model which mimics how humans approach this task. Specifically, the model uses a combination of elimination and selection to arrive at the correct option. This is achieved by introducing an elimination module which takes a soft decision as to whether an option should be eliminated or not. It then modifies the document representation to either align it with uneliminated options or orthogonalize it to eliminated options. The amount of orthogonalization or alignment is determined by two gating functions. This process is repeated multiple times to iteratively refine the document representation. We evaluate our model on the recently released RACE dataset and show that it outperforms current state of the art models on 7 out of 13 question types. Finally, using an ensemble of our eliminationselection approach with a state of the art selection approach, we get an improvement of 7% over the best reported performance on RACE dataset. As future work, instead of soft elimination we would like to use reinforcement learning techniques to learn a policy for hard elimination.",task Reading Comprehension Multiple Choice Questions requires human machine read given \textit passage question pair select one $n given options. current state art model task first computes query-aware representation passage \textit selects option which has the maximum similarity representation. However when humans perform task do not just focus option selection use combination \textit elimination \textit selection Specifically human would first try eliminate irrelevant option read document light new information perhaps ignore portions corresponding eliminated option process could repeated multiple times till reader is finally ready select correct option. propose \textit ElimiNet neural network based model which tries mimic process. Specifically has gates which decide whether option can be eliminated given \textit document question pair if so it tries make document representation orthogonal eliminatedd option akin ignoring portions document corresponding eliminated option model makes multiple rounds partial elimination refine document representation finally uses selection module pick best option. evaluate model recently released large scale RACE dataset show outperforms current state art model 7 13 question types dataset. show taking ensemble \textit elimination-selection based method \textit selection based method givesus improvement 7\ relative best reported performance dataset. Reading comprehension is the task answering questions given passage. AI agent which can display capabilities would useful wide variety commercial applications answering questions financial reports company troubleshooting using product manuals answering general knowledge questions Wikipedia documents etc. Given widespread applicability several variants task have been studied literature. example given passage question answer could either match span passage ii synthesized passage iii one n given candidate answers. last variant is typically used various high school middle school competitive examinations. refer Reading Comprehension Multiple Choice Questions RC-MCQ is increasing interest building AI agents deep language understanding capabilities which can perform par humans competitive tests. example recently BID10 have released large scale dataset RC-MCQ collected Chinese high school middle school English examinations comprising 28000 passages 100000 questions. large size dataset makes possible train evaluate complex neural network based models measure scientific progress RC-MCQ.While answering Multiple Choice Questions MCQs humans typically use combination option elimination option selection. specifically makes sense first try eliminate options which are completely irrelevant given question. may also able discard certain portions document which are not which are relevant question revolve around option which has been eliminated process can then be repeated multiple times time eliminating option refining document discarding irrelevant portions Finally whenitis longer possible eliminate option can pick best option remaining options. contrast current state art models RC-MCQ focus explicitly option selection. Specifically given question passage first compute question aware representation passage say q compute representation n options select option whose representation is closest q. is no iterative process where options get eliminated representation document gets refined light elimination.We propose model which tries mimic human process answering MCQs. Similar existing state art method BID3 first compute query-aware representation document which essentially tries retain portions document which are not which are relevant question use elimination gate which takes soft decision whether option needs eliminated not. gate depends question document option. Next akin human process described would like discard portions document representation which are aligned eliminated option. do this by subtracting component document representation along option representation Gram-Schmidt orthogonalization amount orthogonalization depends soft decision given elimination gate. repeat process multiple times pass soft elimination options refining document representation. end passes expect document representation orthogonal hence dissimilar irrelevant options. Finally use selection module select option which is most similar refined document representation. refer model ElimiNet.We evaluate ElimiNet RACE dataset compare Gated Attention Reader GAR BID3 which is the current state art method dataset. show 13 question types dataset model outperforms GAR 7 question types. also visualize soft elimination probabilities learnt ElimiNet observe indeed learns iteratively refine document representation push probability mass towards correct option. Finally show ensemble model combining ElimiNet GAR gives accuracy 47.2 whichis7% relative better best reported performance dataset. section discuss results experiments described above. focus task Reading Comprehension Multiple Choice Questions propose model which mimics how humans approach task. Specifically model uses combination elimination selection arrive correct option. is achieved introducing elimination module which takes soft decision whether option should be eliminated not. modifies document representation either align uneliminated options orthogonalize eliminated options. amount orthogonalization alignment is determined two gating functions. process is repeated multiple times iteratively refine document representation. evaluate model recently released RACE dataset show outperforms current state art models 7 13 question types. Finally using ensemble eliminationselection approach state art selection approach get improvement 7% best reported performance RACE dataset. future work instead soft elimination would like use reinforcement learning techniques learn policy hard elimination.,1445,905,540,0.018,1.597,2025/11/05 17:18:54,0.01,1.795,0.8317757009345792,488.63
"Humans are capable of attributing latent mental contents such as beliefs, or intentions to others. The social skill is critical in everyday life to reason about the potential consequences of their behaviors so as to plan ahead. It is known that humans use this reasoning ability recursively, i.e. considering what others believe about their own beliefs.   In this paper, we start  from level-$1$ recursion and introduce a probabilistic recursive reasoning (PR2) framework for multi-agent reinforcement learning. Our hypothesis is that it is beneficial for each agent to account for how the opponents would react to its future behaviors. Under the PR2 framework, we adopt variational Bayes methods to approximate the opponents' conditional policy, to which each agent finds the  best response and then improve their own policy. We develop  decentralized-training-decentralized-execution  algorithms, PR2-Q and PR2-Actor-Critic, that are proved to converge in the self-play scenario when there is one Nash equilibrium. Our methods are tested on both the matrix game and the differential game, which have a non-trivial equilibrium where common gradient-based methods fail to converge. Our experiments show that it is critical to reason about how the opponents believe about what the agent believes. We expect our work to contribute a new idea of modeling the opponents to the multi-agent reinforcement learning community.  
",Humans are capable attributing latent mental contents beliefs intentions others. social skill is critical everyday life reason potential consequences behaviors plan ahead. is known humans use reasoning ability recursively.e considering what others believe beliefs. paper start level- $1 recursion introduce probabilistic recursive reasoning PR2 framework multi-agent reinforcement learning. hypothesis is beneficial agent account how the opponents would react future behaviors. PR2 framework adopt variational Bayes methods approximate opponents' conditional policy which each agent finds best response improve policy. develop decentralized-training-decentralized-execution algorithms PR2-Q PR2-Actor-Critic are proved converge self-play scenario when there is one Nash equilibrium. methods are tested matrix game differential game which have a non-trivial equilibrium where common gradient-based methods fail converge. experiments show is critical reason how the opponents believe what the agent believes. expect work contribute new idea modeling opponents multi-agent reinforcement learning community.,270,176,94,0.003,1.534,2025/11/05 17:18:54,0.0,1.533,0.6355140186915887,96.324
"Due to the substantial computational cost, training state-of-the-art deep neural networks for large-scale datasets often requires distributed training using multiple computation workers. However, by nature, workers need to frequently communicate gradients, causing severe bottlenecks, especially on lower bandwidth connections. A few methods have been proposed to compress gradient for efficient communication, but they either suffer a low compression ratio or significantly harm the resulting model accuracy, particularly when applied to convolutional neural networks. To address these issues, we propose a method to reduce the communication overhead of distributed deep learning. Our key observation is that gradient updates can be delayed until an unambiguous (high amplitude, low variance) gradient has been calculated. We also present an efficient algorithm to compute the variance and prove that it can be obtained with negligible additional cost. We experimentally show that our method can achieve very high compression ratio while maintaining the result model accuracy. We also analyze the efficiency using computation and communication cost models and provide the evidence that this method enables distributed deep learning for many scenarios with commodity environments. Deep neural networks are attracting attention because of their outstanding prediction power in many application fields such as image recognition, natural language processing, and speech recognition. In addition, software frameworks are publicly available, making it easier to apply deep learning. However, their crucial drawback is the substantial computational cost on training. For example, it takes over a week to train ResNet-50 on the ImageNet dataset if using a single GPU. Such long training time limits the number of trials possible when creating models. Therefore, we must conduct distributed training using multiple computation workers (e.g., multiple GPUs in different nodes). However, by nature, workers need to frequently communicate gradients, which yields a severe bottleneck for scalability, especially when using lower bandwidth connections. For example, when using 1000BASE-T Ethernet, communication takes at least ten times longer than forward and backward computation for ResNet-50, making multiple nodes impractical. High performance interconnections such as InfiniBand and Omni-Path are an order of magnitude more expensive than commodity interconnections, which limits research and development of deep learning using large-scale datasets to a small number of researchers.Although several methods have been proposed to compress gradient for efficient communication, they either suffer a low compression ratio or significantly harm the resulting model accuracy, particularly when applied to convolutional neural networks. There are mainly two lines of research: quantization and sparsification. Quantization-based methods include 1-bit SGD BID9 and TernGrad (Wen et al., 2017) . Though they achieve small loss of accuracy by using at least one bit for each parameter, the compression ratio is limited. Sparsification-based methods include BID11 and QSGD (Alistarh et al., 2017) . While they can achieve high compression ratio, as we will see in our experiments, they harm the resulting model accuracy or suffer a low compression ratio, particularly when applied to convolutional neural networks.To address these issues, we propose a new gradient compression algorithm to reduce the communication overhead of distributed deep learning. The proposed method belongs to the sparsification approaches. Our key observation is that the variance of the gradient for each parameter point over iterations is a useful signal for compression. As almost all previous approaches of both sparsification and quantization only look at the magnitude of gradient, we believe that we are opening a new door for this field. In addition, we also show that our method can be combined with previous compression methods to further boost performance. We also present an efficient algorithm to compute the variance and prove that it can be obtained with negligible additional cost.We experimentally demonstrate that our method can achieve a high compression ratio while maintaining result model accuracy. We also analyze the efficiency using computation and communication cost models and provide evidence that our method enables distributed deep learning for many scenarios with commodity environments.Organization. The remainder of this paper is organized as follows: Section 2 provides the definitions and notations used in this paper. Section 3 reviews related work in this field. Section 4 presents the proposed method. Section 5 analyzes performance. Section 6 shows our experimental results, and we conclude in Section 7. We proposed a novel method for gradient compression. Our method can reduce communication cost significantly with no or only slight accuracy degradation. Contributions of our work can be summarized in the following three points. First, we proposed a novel measurement of ambiguity (high variance, low amplitude) to determine when a gradient update is required. Second, we showed the application of this measurement as a threshold for updates significantly reduces update requirements, while providing comparable accuracy. Third, we demonstrated this method can be combined with other efficient gradient compression approaches to further reduce communication cost.",Due substantial computational cost training state-of-the-art deep neural networks large-scale datasets often requires distributed training using multiple computation workers. However nature workers need frequently communicate gradients causing severe bottlenecks especially lower bandwidth connections. methods have been proposed compress gradient efficient communication either suffer low compression ratio significantly harm resulting model accuracy particularly when applied convolutional neural networks. address issues propose method reduce communication overhead distributed deep learning. key observation is that gradient updates can be delayed unambiguous high amplitude low variance gradient has been calculated. also present efficient algorithm compute variance prove can be obtained negligible additional cost. experimentally show method can achieve high compression ratio maintaining result model accuracy. also analyze efficiency using computation communication cost models provide evidence method enables distributed deep learning many scenarios commodity environments. Deep neural networks are attracting attention outstanding prediction power many application fields image recognition natural language processing speech recognition. addition software frameworks are publicly available making easier apply deep learning. However crucial drawback is the substantial computational cost training. example takes week train ResNet-50 ImageNet dataset if using single GPU. long training time limits number trials possible when creating models. Therefore must conduct distributed training using multiple computation workers e.g multiple GPUs different nodes However nature workers need frequently communicate gradients which yields severe bottleneck scalability especially when using lower bandwidth connections. example when using 1000BASE-T Ethernet communication takes least ten times longer forward backward computation ResNet-50 making multiple nodes impractical. High performance interconnections InfiniBand Omni-Path are an order magnitude expensive commodity interconnections which limits research development deep learning using large-scale datasets small number researchers.Although several methods have been proposed compress gradient efficient communication either suffer low compression ratio significantly harm resulting model accuracy particularly when applied convolutional neural networks. are mainly two lines research:quantization sparsification. Quantization-based methods include 1-bit SGD BID9 TernGrad Wenetal. 2017 Though achieve small loss accuracy using least one bit parameter compression ratio is limited. Sparsification-based methods include BID11 QSGD Alistarhetal. 2017 can achieve high compression ratio will see experiments harm resulting model accuracy suffer low compression ratio particularly when applied convolutional neural networks.To address issues propose new gradient compression algorithm reduce communication overhead distributed deep learning. proposed method belongs sparsification approaches. key observation is that the variance gradient parameter point iterations is a useful signal compression. almost previous approaches sparsification quantization look magnitude gradient believe are opening new door field. addition also show method can be combined previous compression methods boost performance. also present efficient algorithm compute variance prove can be obtained negligible additional cost.We experimentally demonstrate method can achieve high compression ratio maintaining result model accuracy. also analyze efficiency using computation communication cost models provide evidence method enables distributed deep learning many scenarios commodity environments.Organization. remainder paper is organized follows:Section 2 provides definitions notations used paper. Section 3 reviews related work field. Section 4 presents proposed method. Section 5 analyzes performance. Section 6 shows experimental results conclude Section7. proposed novel method gradient compression. method can reduce communication cost significantly slight accuracy degradation. Contributions work can be summarized following three points. First proposed novel measurement ambiguity high variance low amplitude determine when a gradient update is required. Second showed application measurement threshold updates significantly reduces update requirements providing comparable accuracy. Third demonstrated method can be combined efficient gradient compression approaches reduce communication cost.,942,659,283,0.009,1.429,2025/11/05 17:18:54,0.0,1.448,0.308411214953271,311.47
"In this work, we face the problem of unsupervised domain adaptation with a novel deep learning approach which leverages our finding that entropy minimization is induced by the optimal alignment of second order statistics between source and target domains. We formally demonstrate this hypothesis and, aiming at achieving an optimal alignment in practical cases, we adopt a more principled strategy which, differently from the current Euclidean approaches, deploys alignment along geodesics. Our pipeline can be implemented by adding to the standard classification loss (on the labeled source domain), a source-to-target regularizer that is weighted in an unsupervised and data-driven fashion. We provide extensive experiments to assess the superiority of our framework on standard domain and modality adaptation benchmarks. Learning visual representations that are invariant across different domains is an important task in computer vision. Actually, data labeling is onerous and even impossible in some cases. It is thus desirable to train a model with full supervision on a source, labeled domain and then learn how to transfer it on a target domain, as opposed to retrain it completely from scratch. Moreover, the latter stage is actually not possible if the target domain is totally unlabelled: this is the setting we consider in our work. In the literature, this problem is known as unsupervised domain adaptation which can be regarded as a special semi-supervised learning problem, where labeled and unlabeled data come from different domains. Since no labels are available in the target domain, source-to-target adaptation must be carried out in a fully unsupervised manner. Clearly, this is an arguably difficult task since transferring a model across domains is complicated by the so-called domain shift [Torralba & Efros (2011) ]. In fact, while switching from the source to the target, even if dealing with the same K visual categories in both domains, different biases may arise related to several factors. For instance, dissimilar points of view, illumination changes, background clutter, etc.In the previous years, a broad class of approaches has leveraged on entropy optimization as a proxy for (unsupervised) domain adaptation, borrowing this idea from semi-supervised learning [Grandvalet & Bengio (2004) ]. By either performing entropy regularization [Tzeng et al. (2015) ; Carlucci et al. (2017) ; Saito et al. (2017) ], explicit entropy minimization [Haeusser et al. (2017) ], or implicit entropy maximization through adversarial training [Ganin & Lempitsky (2015) ; Tzeng et al. (2017) ], this statistical tool has demonstrated to be powerful for adaptation purposes.Alternatively, there exist methods which try to align the source to the target domain by learning an explicit transformation between the two so that the target data distribution can be matched to the one of the source one [Glorot et al. (2011); Kan et al. (2015) ; Shekhar et al. (2013) ; Gopalan & Li (2011); Gong et al. (2012a) ]. Within this paradigm, correlation alignment minimizes the distance between second order statistics computed in the form of covariance representations between features from the source a [Fernando et al. (2013) ; Sun et al. (2016) ; Sun & Saenko (2016) ].Apparently , correlation alignment and entropy minimization may seem two unrelated and approaches in optimizing models for domain adaptation. However, in this paper, we will show that this is not the case and, indeed, we claim that the two classes of approaches are deeply intertwined. In addition to formally discuss the latter aspect, we also obtain a solution for the prickly problem of hyperparameter validation in unsupervised domain adaptation. Indeed, one can construct a validation set out of source data but the latter is not helpful since not representative of target data. At the same time, due to the lack of annotations on the target domain, usual (supervised) validation techniques can not be applied.In summary, this paper brings the following contributions.1. We explore the two paradigms of correlation alignment and entropy minimization, by formally demonstrating that, at its optimum, correlation alignment attains the minimum of the sum of cross-entropy on the source domain and of the entropy on the target.2. Motivated by the urgency of penalizing correlation misalignments in practical terms, we observe that an Euclidean penalty, as adopted in [Sun et al. (2016); Sun & Saenko (2016) ], is not taking into account the structure of the manifold where covariance matrices lie in. Hence, we propose a different loss function that is inspired by a geodesic distance that takes into account the manifold's curvature while computing distances.3. When aligning second order statistics, a hyper-parameter controls the balance between the reduction of the domain shift and the supervised classification on the source domain. In this respect , a manual cross-validation of the parameter is not straightforward: doing it on the source domain may not be representative, and it is not possible to do on the target due to the lack of annotations. Owing to our principled connection between correlation alignment and entropy regularization, we devise an entropy-based criterion to accomplish such validation in a data-driven fashion.4. We combine the geodesic correlation alignment with the entropy-based criterion in a unique pipeline that we call minimal-entropy correlation alignment. Through an extensive experimental analysis on publicly available benchmarks for transfer object categorization, we certify the effectiveness of the proposed approach in terms of systematic improvements over former alignment methods and state-of-the-art techniques for unsupervised domain adaptation in general.The rest of the paper is outlined as follows. In Section 2, we report the most relevant related work as background material. Section 3 presents our theoretical analysis which inspires our proposed method for domain adaptation (Section 4). We report a broad experimental validation in Section 5. Finally, Section 6 draws conclusions. In this paper we carried out a principled connection between correlation alignment and entropy minimization, formally demonstrating that the optimal solution to the former problem gives for free the optimal solution of the latter. This improved knowledge brought us to two algorithmic advances. First, we achieved a more effective alignment of covariance operators which guarantees a superior performance. Second, we derived a novel cross-validation approach for the hyper-parameter λ so that we can obtain the maximum performance on the target, even not having access to its labels. These two components, when combined in our proposed MECA pipeline, provide a solid performance against state-of-the-art methods for unsupervised domain adaptation.L.J.P van der Maaten and G.E. Hinton. Visualizing high-dimensional data using t-sne. For the problem of (unsupervised) domain adaptation, a first class of methods aims at learning transformations which align feature representations in the source and target sets. For instance, in [Glorot et al. (2011) ] auto-encoders are exploited to learn common features. In [Kan et al. (2015) ], a bi-shifting auto-encoder (BSA) is instead intended to shift source domain samples into target ones and, similarly, other methods approach the same problem by means of techniques based on dictionary learning (as in [Shekhar et al. (2013)] ). Geodesic methods (such as [Gopalan & Li (2011); Gong et al. (2012a) ] aim at projecting source and target datasets on a common manifold in such a way that the projection already solves the alignment problem. The approaches [Gong et al. (2012b) ; Gopalan et al. FORMULA0 ] learns a smooth transition between the source and data manifold by means of Principal Components Analysis and Partial Least Squares, respectively. Inspired by the idea of adapting second order statistics between the two domains, [Sun et al. (2016); Fernando et al. (2013) ] propose a transformation to minimize the distance between the covariances of source and target datasets in order to, ultimately, achieve correlation alignment. Due to the well known properties of covariance operators, in some cases [Sun et al. (2016) ], the alignment can be written down in closed-form. But, since the latter operation can be prohibitively expensive in terms of computational cost, Sun & Saenko (2016) implements correlation alignment in an end-to-end fashion by means of backpropagation.A complementary family of approaches exploit the powerful statistical tool of entropy optimization in order to carry out adaptation. Indeed, the notion of association [Haeusser et al. (2017) ] is actually implementing explicit entropy minimization [Grandvalet & Bengio (2004) ] to align the target to the source embedding by navigating the data manifold by means of closed cyclic paths that interconnect instances belonging to the same objects' classes. In parallel, there are cases [Ganin & Lempitsky (2015) ; Tzeng et al. (2017) ] where minimax optimization is responsible for doing the following adversarial training. One seeks for feature representations that are effective for the primary visual recognition task being at the same time invariant while changing from source to target. The latter stage is implemented as the attempt of devising a random chance classifier which is asked to detect whether a given feature vector has been computed from a source or target data instance. Therefore, those approaches are implicitly promoting entropy maximization 3 at the classifier level. Finally, entropy regularization is accomplished in [Tzeng et al. (2015); Carlucci et al. (2017); Saito et al. (2017) ] as a complementary step to boost adaptation. Indeed, already established techniques for adaptation such as Batch Normalization [Ioffe & Szegedy (2015) ; Li et al. (2016) ] are applied in low-level layers to align the representations. On top of that, adaptation is refined at the end of the feature hierarchy by introducing a entropy-based regularizer on the target domain based. Practically, the latter exploits network's prediction to generate pseudo-labels [Lee FORMULA0","work face problem unsupervised domain adaptation novel deep learning approach which leverages finding entropy minimization is induced optimal alignment second order statistics source target domains. formally demonstrate hypothesis aiming achieving optimal alignment practical cases adopt principled strategy which,differently current Euclidean approaches deploys alignment along geodesics. pipeline can be implemented adding standard classification loss labeled source domain source-to-target regularizer is weighted unsupervised data-driven fashion. provide extensive experiments assess superiority framework standard domain modality adaptation benchmarks. Learning visual representations are invariant across different domains is an important task computer vision. Actually data labeling is onerous even impossible cases. is thus desirable train model full supervision source where labeled domain learn how to transfer target domain opposed retrain completely scratch. Moreover latter stage is actually possible if the target domain is totally unlabelled:is the setting consider work. literature problem is known unsupervised domain adaptation which can be regarded special semi-supervised learning problem where labeled unlabeled data come different domains. Since labels are available target domain source-to-target adaptation must carried fully unsupervised manner. Clearly is an arguably difficult task since transferring model across domains is complicated so-called domain shift Torralba Efros 2011 fact switching source do on the target even if dealing K visual categories domains different biases may arise related several factors. instance dissimilar points view illumination changes background clutter etc.In previous years broad class approaches has leveraged entropy optimization proxy unsupervised domain adaptation borrowing idea semi-supervised learning Grandvalet Bengio 2004 either performing entropy regularization Tzengetal. 2015 Carluccietal. 2017 Saitoetal. 2017 explicit entropy minimization Haeusseretal. 2017 implicit entropy maximization adversarial training Ganin Lempitsky 2015 Tzengetal. 2017 statistical tool has demonstrated powerful adaptation purposes.Alternatively exist methods which try align source do on the target domain learning explicit transformation two target data distribution can be matched one source one Glorotetal. 2011 Kanetal. 2015 Shekharetal. 2013 Gopalan Li 2011 Gongetal. 2012a Within paradigm correlation alignment minimizes distance second order statistics computed form covariance representations features source Fernandoetal. 2013 Sunetal. 2016 Sun Saenko 2016.Apparently correlation alignment entropy minimization may seem two unrelated approaches optimizing models domain adaptation. However paper will show is not case indeed claim two classes approaches are deeply intertwined. addition formally discuss latter aspect also obtain solution prickly problem hyperparameter validation unsupervised domain adaptation. Indeed one can construct validation set source data latter is not helpful since representative target data. time due lack annotations target domain usual supervised validation techniques can not be applied.In summary paper brings following contributions.1 explore two paradigms correlation alignment entropy minimization formally demonstrating optimum correlation alignment attains minimum sum cross-entropy source domain entropy target.2 Motivated urgency penalizing correlation misalignments practical terms observe Euclidean penalty adopted Sunetal. 2016 Sun Saenko 2016 is taking account structure manifold where covariance matrices lie in. Hence propose different loss function is inspired geodesic distance takes account manifold's curvature computing distances.3 When aligning second order statistics hyper-parameter controls balance reduction domain shift supervised classification source domain. respect manual cross-validation parameter is not straightforward:source domain may representative is possible do on the target due lack annotations. Owing principled connection correlation alignment entropy regularization devise entropy-based criterion accomplish validation data-driven fashion.4 combine geodesic correlation alignment entropy-based criterion unique pipeline call minimal-entropy correlation alignment. extensive experimental analysis publicly available benchmarks transfer object categorization certify effectiveness proposed approach terms systematic improvements former alignment methods state-of-the-art techniques unsupervised domain adaptation general.The rest paper is outlined follows. Section2 report relevant related work background material. Section 3 presents theoretical analysis which inspires proposed method domain adaptation Section4 report broad experimental validation Section5. Finally Section 6 draws conclusions. paper carried principled connection correlation alignment entropy minimization formally demonstrating optimal solution former problem gives free optimal solution latter. improved knowledge broughtus two algorithmic advances. First achieved effective alignment covariance operators which guarantees superior performance. Second derived novel cross-validation approach hyper-parameterλ can obtain maximum performance target even access labels. two components when combined proposed MECA pipeline provide solid performance state-of-the-art methods unsupervised domain adaptation.L.J.P van der Maaten G.E Hinton. Visualizing high-dimensional data using t-sne problem unsupervised domain adaptation first class methods aims learning transformations which align feature representations source target sets. instance Glorotetal. 2011 auto-encoders are exploited learn common features. Kanetal. 2015 bi-shifting auto-encoder BSA is instead intended shift source domain samples target ones similarly methods approach problem means techniques based dictionary learning Shekharetal. 2013 Geodesic methods Gopalan Li 2011 Gongetal. 2012a aim projecting source target datasets common manifold way projection already solves alignment problem. approaches Gongetal. 2012b Gopalanetal. FORMULA0 learns smooth transition source data manifold means Principal Components Analysis Partial Least Squares respectively. Inspired idea adapting second order statistics two domains Sunetal. 2016 Fernandoetal. 2013 propose transformation minimize distance covariances source target datasets order ultimately achieve correlation alignment. Due well known properties covariance operators are cases Sunetal. 2016 alignment can be written closed-form since latter operation can be prohibitively expensive terms computational cost Sun Saenko 2016 implements correlation alignment end-to-end fashion means backpropagation.A complementary family approaches exploit powerful statistical tool entropy optimization order carry adaptation. Indeed notion association Haeusseretal. 2017 is actually implementing explicit entropy minimization Grandvalet Bengio 2004 align target source embedding navigating data manifold means closed cyclic paths interconnect instances belonging objects' classes. parallel are cases Ganin Lempitsky 2015 Tzengetal. 2017 where minimax optimization is responsible following adversarial training. One seeks feature representations are effective primary visual recognition task time invariant changing source do on the target. latter stage is implemented attempt devising random chance classifier which is asked detect whether given feature vector has been computed source target data instance. Therefore approaches are implicitly promoting entropy maximization 3 classifier level. Finally entropy regularization is accomplished Tzengetal. 2015 Carluccietal. 2017 Saitoetal. 2017 complementary step boost adaptation. Indeed already established techniques adaptation Batch Normalization Ioffe Szegedy 2015 Lietal. 2016 are applied low-level layers align representations. top adaptation is refined end feature hierarchy introducing entropy-based regularizer target domain based. Practically latter exploits network's prediction generate pseudo-labels Lee FORMULA0",2078,1382,696,0.03,1.504,2025/11/05 17:18:54,0.01,1.35,0.542056074766355,724.445
"Catastrophic interference has been a major roadblock in the research of continual learning. Here we propose a variant of the back-propagation algorithm, ""Conceptor-Aided Backprop"" (CAB), in which gradients are shielded by conceptors against degradation of previously learned tasks. Conceptors have their origin in reservoir computing, where they have been previously shown to overcome catastrophic forgetting. CAB extends these results to deep feedforward networks. On the disjoint and permuted MNIST tasks, CAB outperforms two other methods for coping with catastrophic interference that have recently been proposed. Agents with general artificial intelligence are supposed to learn and perform well on multiple tasks. Continual learning refers to the scenarios where a machine learning system can retain previously acquired skills while learning new ones. However, when trained on a sequence of tasks, neural networks usually forget about previous tasks after their weights are adjusted for a new task. This notorious problem known as catastrophic interference (CI) BID15 BID16 BID3 BID11 ) poses a serious challenge towards continual learning.Many approaches have been proposed to overcome or mitigate the problem of CI in the last three decades BID5 BID1 BID0 BID2 BID20 . Especially recently, an avalanche of new methods in the deep learning field has brought about dramatic improvements in continual learning in neural networks. BID10 introduced a regularization-based method called elastic weight consolidation (EWC), which uses the posterior distribution of parameters for the old tasks as a prior for the new task. They approximated the posterior by a Gaussian distribution with the parameters for old tasks as the mean and the inverse diagonal of the Fisher information matrix as the variance. BID13 introduced two incremental moment matching (IMM) methods called mean-IMM and mode-IMM. Mean-IMM approximates the distribution of parameters for both old and new tasks by a Gaussian distribution, which is estimated by minimizing its KL-divergence from the mixture of two Gaussian posteriors, one for the old task and the other one for the new task. Mode-IMM estimates the mode of this mixture of two Gaussians and uses it as the optimal parameters for both tasks.In the field of Reservoir Computing BID6 BID14 , an effective solution to CI using conceptors was proposed by BID7 to incrementally train a recurrent neural network to generate spatial-temporal signals. Conceptors are a general-purpose neuro-computational mechanism that can be used in a diversity of neural information processing tasks including temporal pattern classification, one-shot learning, human motion pattern generation, de-noising and signal separation BID8 . In this paper, we adopt and extend the method introduced in BID7 and propose a conceptor-aided backpropagation (CAB) algorithm to train feed-forward networks. For each layer of a network, CAB computes a conceptor to characterize the linear subspace spanned by the neural activations in that layer that have appeared in already learned tasks. When the network is trained on a new task, CAB uses the conceptor to adjust the gradients given by backpropagation so that the linear transformation restricted to the characterized subspace will be preserved after the gradient descent procedure. Experiment results of two benchmark tests showed highly competitive performance of CAB.The rest of this paper is structured as follows. Section 2 introduces conceptors and their application to incremental learning by ridge regression. Section 3 extends the method to stochastic gradient descent and describes the CAB algorithm. Section 4 compares its performance on the permuted and disjoint MNIST tasks to recent methods that address the same problem. Finally we conclude our paper in Section 5. In this work, we first reviewed the conceptor-based incremental ridge regression algorithm, introduced in section 3.11 of Jaeger (2014) for memory management in recurrent neural networks. Then we derived its stochastic gradient descent version for optimizing the same objective. Finally we designed a conceptor-aided backprop algorithm by applying a conceptor to every linear layer of a feed-forward network. This method uses conceptors to guide gradients of parameters during the backpropagation procedure. As a result, learning a new task interferes only minimally with previously learned tasks, and the amount of already used network capacity can be monitored via the singular value spectra and quota of conceptors.In Jaeger (2014), different scenarios for continual learning are investigated in a reservoir computing setting. Two extreme cases are obtained when (i) the involved learning tasks are entirely unrelated to each other, versus (ii) all tasks come from the same parametric family of learning tasks. The two cases differ conspicuously with regards to the geometry of involved conceptors, and with regards to opportunities to re-use previously acquired functionality in subsequent learning episodes. The permuted MNIST task is an example of (i) while the disjoint MNIST task rather is of type (ii).Conceptors provide an analytical tool to discuss the ""family relatedness"" and enabling/disabling conditions for continual learning in geometrical terms. Ongoing and future research is devoted to a comprehensive mathematical analysis of these phenomena which in our view lie at the heart of understanding continual learning.",Catastrophic interference has been a major roadblock research continual learning. propose variant back-propagation algorithm Conceptor-Aided Backprop CAB which gradients are shielded conceptors degradation previously learned tasks. Conceptors have their origin reservoir computing where they have previously shown overcome catastrophic forgetting. CAB extends results deep feedforward networks. disjoint permuted MNIST tasks CAB outperforms two methods coping catastrophic interference have recently proposed. Agents general artificial intelligence are supposed learn perform well multiple tasks. Continual learning refers scenarios where a machine learning system can retain previously acquired skills learning new ones. However when trained sequence tasks neural networks usually forget previous tasks weights are adjusted new task. notorious problem known catastrophic interference CI BID15 BID16 BID3 BID11 poses serious challenge towards continual learning.Many approaches have been proposed overcome mitigate problem CI last three decades BID5 BID1 BID0 BID2 BID20. Especially recently avalanche new methods deep learning field has brought dramatic improvements continual learning neural networks. BID10 introduced regularization-based method called elastic weight consolidation EWC which uses posterior distribution parameters old tasks prior new task. approximated posterior Gaussian distribution parameters old tasks mean inverse diagonal Fisher information matrix variance. BID13 introduced two incremental moment matching IMM methods called mean-IMM mode-IMM Mean-IMM approximates distribution parameters old new tasks Gaussian distribution which is estimated minimizing KL-divergence mixture two Gaussian posteriors one old task one new task. Mode-IMM estimates mode mixture two Gaussians uses optimal parameters tasks.In field Reservoir Computing BID6 BID14 effective solution CI using conceptors was proposed BID7 incrementally train recurrent neural network generate spatial-temporal signals. Conceptors are a general-purpose neuro-computational mechanism can be used diversity neural information processing tasks including temporal pattern classification one-shot learning human motion pattern generation de-noising signal separation BID8. paper adopt extend method introduced BID7 propose conceptor-aided backpropagation CAB algorithm train feed-forward networks. layer network CAB computes conceptor characterize linear subspace spanned neural activations layer have appeared already learned tasks. When the network is trained new task CAB uses conceptor adjust gradients given backpropagation linear transformation restricted characterized subspace will be preserved gradient descent procedure. Experiment results two benchmark tests showed highly competitive performance CAB.The rest paper is structured follows. Section 2 introduces conceptors application incremental learning ridge regression. Section 3 extends method stochastic gradient descent describes CAB algorithm. Section 4 compares performance permuted disjoint MNIST tasks recent methods address problem. Finally conclude paper Section5. work first reviewed conceptor-based incremental ridge regression algorithm introduced section 3.11 Jaeger 2014 memory management recurrent neural networks. derived stochastic gradient descent version optimizing objective. Finally designed conceptor-aided backprop algorithm applying conceptor every linear layer feed-forward network. method uses conceptors guide gradients parameters backpropagation procedure. result learning new task interferes minimally previously learned tasks amount already used network capacity can be monitored via singular value spectra quota conceptors.In Jaeger 2014 different scenarios continual learning are investigated reservoir computing setting. Two extreme cases are obtained when(i)involved learning tasks are entirely unrelated versus ii tasks come parametric family learning tasks. two cases differ conspicuously regards geometry involved conceptors regards opportunities re-use previously acquired functionality subsequent learning episodes. permuted MNIST task is an example disjoint MNIST task rather is of type ii.Conceptors provide analytical tool discuss family relatedness enabling/disabling conditions continual learning geometrical terms. Ongoing future research is devoted comprehensive mathematical analysis phenomena which in our view lie heart understanding continual learning.,1018,712,306,0.01,1.43,2025/11/05 17:18:54,0.0,1.625,0.3115264797507784,309.881
"Recent advances in neural Sequence-to-Sequence (Seq2Seq) models reveal a purely data-driven approach to the response generation task. Despite its diverse variants and applications, the existing Seq2Seq models are prone to producing short and generic replies, which blocks such neural network architectures from being utilized in practical open-domain response generation tasks. In this research, we analyze this critical issue from the perspective of the optimization goal of models and the specific characteristics of human-to-human conversational corpora. Our analysis is conducted by decomposing the goal of Neural Response Generation (NRG) into the optimizations of word selection and ordering. It can be derived from the decomposing that Seq2Seq based NRG models naturally tend to select common words to compose responses, and ignore the semantic of queries in word ordering. On the basis of the analysis, we propose a max-marginal ranking regularization term to avoid Seq2Seq models from producing the generic and uninformative responses. The empirical experiments on benchmarks with several metrics have validated our analysis and proposed methodology. Past years have witnessed the dramatic progress on the application of generative sequential models (also noted as seq2seq learning (Sutskever et Despite these promising results, current Sequence-to-Sequence (Seq2Seq) architectures for response generation are still far from steadily generating relevant and coherent replies. The essential issue identified by many studies is the Universal Replies: the model tends to generate short and general replies which contain limited information, such as ""That's great!"", ""I don't know"", etc. Nevertheless, most previous analysis over the issue are empirical and lack of statistical evidence. Therefore, in this paper, we conduct an in-depth investigation on the performance of seq2seq models on the NRG task. In our inspections on the existing dialog corpora, it is shown that those repeatedly appeared replies have two essential traits: 1) Most of them are composed of highly frequent words; 2) They cover a large portion of the dialog corpora that each universal reply stands for the response of various queries. Above characteristics of universal replies deviate the NRG from other successful applications of sea2seq model such as translation, and lead current generative NRG models to prefer common replies. To discuss the influences from the specific distributed corpus, we decompose the target sequence's probability into two parts and analyze the probability respectively. To break down the mentioned characteristics of dialog corpora in the model training step, we propose a ranking-oriented regularization term to prune the scores of those irrelevant replies. Experimental results reveal that the model with such regularization can produce better results and avoid generating ambiguous responses. Also, case studies show that the issue of generic response is alleviated that these common responses are ranked relatively lower than more appropriate answers.The main contributions of this paper are concluded as follows: 1) We analyze the loss function of Seq2seq models on NRG task and conclude several critical reasons that the NRG models prefer universal replies; 2) Based on the analysis, a max-marginal ranking regularization is presented to help the model converge to informative responses. On the basis of Lemma 1, the word ordering probability could be deducted as: DISPLAYFORM0 All the possible y i satisfying S(y i ) ⊆ S(y) can be divided into three categories: ground-truth reply y, universal replies y ur and other replies y o . From above, we can get the following direct proportion according to the Lemma 2 and Lemma 3, On the basis of Eq. 7 and Lemma 4, for any reply y not belonging to universal replies, the Eq. 6 can be further deducted as: DISPLAYFORM1 where = 1 + 2 > 0, which is also a sufficiently small positive value. Thus, optimizing the word ordering probability for the non-universal replies is partially equivalent to maximizing p(y|S(y)).In fact the term p(y|S(y)) is the language model probability and it is irrelevant with the query x FIG6 ). In the sequential models, it is performed as t p(y t |y 1:t−1 , S(y)), in other words the sequences are generated based only on previously outputted words. This equation indicates that optimizing the mainly seeks the grammatical competence based on the selected words. Eliminating generic responses is the essence for the widely practical utilization of the Seq2Seq based neural response generation architectures, and thus, this paper has conducted a thorough investigation on the cause of such uninformative responses and proposed the solution from the statistical perspective. The main contributions of this work can be summarized as follows: a) The theoretical analysis is performed to capture the root reason of NRG models producing generic responses through the optimization goal of models and the statistical characteristics of human-to-human conversational corpora, which has been little studied currently. In detail, we have decomposed the goal of NRG into the optimizations of word selection and word ordering, and finally derived that NRG models tend to select common words as responses and order words from the language model perspective which ignores queries. b) According to the analysis, a max-marginal ranking regularization term is proposed to cooperate with the learning target of Seq2Seq, so as to help NRG models converge to the status of producing informative responses, rather than merely manipulating the decoding procedure to constrain the generation of universal replies. Furthermore, the empirical experiments on the conversation dataset indicate that the models utilizing this strategy notably outperform the current baseline models.",Recent advances neural Sequence-to-Sequence Seq2Seq models reveal purely data-driven approach response generation task. Despite diverse variants applications existing Seq2Seq models are prone producing short generic replies which blocks neural network architectures utilized practical open-domain response generation tasks. research analyze critical issue perspective optimization goal models specific characteristics human-to-human conversational corpora. analysis is conducted decomposing goal Neural Response Generation NRG optimizations word selection ordering. can be derived decomposing Seq2Seq based NRG models naturally tend select common words compose responses ignore semantic queries word ordering. basis analysis propose max-marginal ranking regularization term avoid Seq2Seq models producing generic uninformative responses. empirical experiments benchmarks several metrics have validated analysis proposed methodology. Past years have witnessed dramatic progress application generative sequential models also noted seq2seq learning Sutskever et Despite promising results current Sequence-to-Sequence Seq2Seq architectures response generation are still far steadily generating relevant coherent replies. essential issue identified many studies is the Universal Replies:model tends generate short general replies which contain limited information That's great! know etc. Nevertheless previous analysis issue are empirical lack statistical evidence. Therefore paper conduct in-depth investigation performance seq2seq models NRG task. inspections existing dialog corpora is shown repeatedly appeared replies have two essential traits:1 are composed highly frequent words;2 cover large portion dialog corpora universal reply stands response various queries. characteristics universal replies deviate NRG successful applications sea2seq model translation lead current generative NRG models prefer common replies. discuss influences specific distributed corpus decompose target sequence's probability two parts analyze probability respectively. break mentioned characteristics dialog corpora model training step propose ranking-oriented regularization term prune scores irrelevant replies. Experimental results reveal model regularization can produce better results avoid generating ambiguous responses. Also case studies show issue generic response is alleviated common responses are ranked relatively lower appropriate answers.The main contributions paper are concluded follows:1 analyze loss function Seq2seq models NRG task conclude several critical reasons NRG models prefer universal replies;2 Based analysis max-marginal ranking regularization is presented help model converge informative responses. basis Lemma1 word ordering probability could deducted as:DISPLAYFORM0 possible satisfying ⊆ canbe divided three categories:ground-truth reply universal replies ur replies o. can get following direct proportion according Lemma2 Lemma3 basis Eq. 7 Lemma4 reply belonging universal replies Eq. 6 can be further deducted as:DISPLAYFORM1 where=1+2 0 which is also sufficiently small positive value. Thus optimizing word ordering probability non-universal replies is partially equivalent maximizingp y|S.In fact termp y|S is the language model probability is irrelevant query x FIG6 sequential models is performed p |y1:t−1 words sequences are generated based previously outputted words. equation indicates optimizing mainly seeks grammatical competence based selected words. Eliminating generic responses is the essence widely practical utilization Seq2Seq based neural response generation architectures thus paper has conducted thorough investigation cause uninformative responses proposed solution statistical perspective. main contributions work can be summarized follows:theoretical analysis is performed capture root reason NRG models producing generic responses optimization goal models statistical characteristics human-to-human conversational corpora which has been little studied currently. detail have decomposed goal NRG optimizations word selection word ordering finally derived NRG models tend select common words responses order words language model perspective which ignores queries. b According analysis max-marginal ranking regularization term is proposed cooperate learning target Seq2Seq help NRG models converge status producing informative responses rather merely manipulating decoding procedure constrain generation universal replies. Furthermore empirical experiments conversation dataset indicate models utilizing strategy notably outperform current baseline models.,1107,729,378,0.011,1.519,2025/11/05 17:18:54,0.01,1.333,0.5887850467289715,335.966
"The ability to generate natural language sequences from source code snippets has a variety of applications such as code summarization, documentation, and retrieval. Sequence-to-sequence (seq2seq) models, adopted from neural machine translation (NMT), have achieved state-of-the-art performance on these tasks by treating source code as a sequence of tokens. We present code2seq: an alternative approach that leverages the syntactic structure of programming languages to better encode source code. Our model represents a code snippet as the set of compositional paths in its abstract syntax tree (AST) and uses attention to select the relevant paths while decoding.
 We demonstrate the effectiveness of our approach for two tasks, two programming languages, and four datasets of up to 16M examples. Our model significantly outperforms previous models that were specifically designed for programming languages, as well as general state-of-the-art NMT models. An interactive online demo of our model is available at http://code2seq.org. Our code, data and trained models are available at http://github.com/tech-srl/code2seq. Modeling the relation between source code and natural language can be used for automatic code summarization BID2 , documentation BID19 , retrieval BID1 , and even generation BID7 BID28 BID40 BID14 BID24 . In this work, we consider the general problem of generating a natural language sequence from a given snippet of source code.A direct approach is to frame the problem as a machine translation problem, where the source sentence is the sequence of tokens in the code and the target sentence is a corresponding natural language sequence. This approach allows one to apply state-of-the-art neural machine translation (NMT) models from the sequence-to-sequence (seq2seq) paradigm BID23 BID39 , yielding state-ofthe-art performance on various code captioning and documentation benchmarks BID19 BID2 BID22 ) despite having extremely long source sequences.We present an alternative approach for encoding source code that leverages the syntactic structure of programming languages: CODE2SEQ. We represent a given code snippet as a set of compositional paths over its abstract syntax tree (AST), where each path is compressed to a fixed-length vector using LSTMs BID17 . During decoding, CODE2SEQ attends over a different weighted average of the path-vectors to produce each output token, much like NMT models attend over token representations in the source sentence.We show the effectiveness of our code2seq model on two tasks: (1) code summarization (Figure 1a) , where we predict a Java method's name given its body, and (2) code captioning (Figure 1b) , where we predict a natural language sentence that describes a given C# snippet. We presented a novel code-to-sequence model which considers the unique syntactic structure of source code with a sequential modeling of natural language. The core idea is to sample paths in the Abstract Syntax Tree of a code snippet, encode these paths with an LSTM, and attend to them while generating the target sequence.We demonstrate our approach by using it to predict method names across three datasets of varying sizes, predict natural language captions given partial and short code snippets, and to generate method documentation, in two programming languages. Our model performs significantly better than previous programming-language-oriented works and state-of-the-art NMT models applied in our settings.We believe that the principles presented in this paper can serve as a basis for a wide range of tasks which involve source code and natural language, and can be extended to other kinds of generated outputs. To this end, we make all our code, datasets, and trained models publicly available.",ability generate natural language sequences source code snippets has a variety applications code summarization documentation retrieval. Sequence-to-sequence seq2seq models adopted neural machine translation NMT have achieved state-of-the-art performance tasks treating source code sequence tokens. present code2seq:alternative approach leverages syntactic structure programming languages better encode source code. model represents code snippet set compositional paths abstract syntax tree AST uses attention select relevant paths decoding. demonstrate effectiveness approach two tasks two programming languages four datasets 16M examples. model significantly outperforms previous models were specifically designed programming languages well general state-of-the-art NMT models. interactive online demo model is available http://code2seq.org. code data trained models are available http://github.com/tech-srl/code2seq. Modeling relation source code natural language can be used automatic code summarization BID2 documentation BID19 retrieval BID1 even generation BID7 BID28 BID40 BID14 BID24. work consider general problem generating natural language sequence given snippet source code.A direct approach is to frame problem machine translation problem where the source sentence is the sequence tokens code target sentence is a corresponding natural language sequence. approach allows one apply state-of-the-art neural machine translation NMT models sequence-to-sequence seq2seq paradigm BID23 BID39 yielding state-ofthe-art performance various code captioning documentation benchmarks BID19 BID2 BID22 despite extremely long source sequences.We present alternative approach encoding source code leverages syntactic structure programming languages:CODE2SEQ. represent given code snippet set compositional paths abstract syntax tree AST where each path is compressed fixed-length vector using LSTMs BID17. decoding CODE2SEQ attends different weighted average path-vectors produce output token much like NMT models attend token representations source sentence.We show effectiveness code2seq model two tasks:1 code summarization Figure1a where we predict Java method's name given body 2 code captioning Figure1b where we predict natural language sentence describes given C#snippet. presented novel code-to-sequence model which considers unique syntactic structure source code sequential modeling natural language. core idea is to sample paths Abstract Syntax Tree code snippet encode paths LSTM attend generating target sequence.We demonstrate approach using predict method names across three datasets varying sizes predict natural language captions given partial short code snippets generate method documentation two programming languages. model performs significantly better previous programming-language-oriented works state-of-the-art NMT models applied settings.We believe principles presented paper can serve basis wide range tasks which involve source code natural language can be extended kinds generated outputs. end make code datasets trained models publicly available.,728,510,218,0.006,1.427,2025/11/05 17:18:54,0.0,1.556,0.3021806853582554,244.738
"We propose a novel attention mechanism to enhance Convolutional Neural Networks for fine-grained recognition. The proposed mechanism reuses CNN feature activations to find the most informative parts of the image at different depths with the help of gating mechanisms and without part annotations. Thus, it can be used to augment any layer of a CNN to extract low- and high-level local information to be more discriminative. 

 Differently, from other approaches, the mechanism we propose just needs a single pass through the input and it can be trained end-to-end through SGD. As a consequence, the proposed mechanism is modular, architecture-independent, easy to implement, and faster than iterative approaches.

 Experiments show that, when augmented with our approach, Wide Residual Networks systematically achieve superior performance on each of five different fine-grained recognition datasets: the Adience age and gender recognition benchmark, Caltech-UCSD Birds-200-2011, Stanford Dogs, Stanford Cars, and UEC Food-100, obtaining competitive and state-of-the-art scores. Humans and animals process vasts amounts of information with limited computational resources thanks to attention mechanisms which allow them to focus resources on the most informative chunks of information. These biological mechanisms have been extensively studied (see BID0 ; BID2 ), concretely those mechanisms concerning visual attention, e.g. the work done by BID25 .In this work, we inspire on the advantages of visual and biological attention mechanisms for finegrained visual recognition with Convolutional Neural Networks (CNN) (see BID11 ). This is a particularly difficult task since it involves looking for details in large amounts of data (images) while remaining robust to deformation and clutter. In this sense, different attention mechanisms for fine-grained recognition exist in the literature: (i) iterative methods that process images using ""glimpses"" with recurrent neural networks (RNN) or long short-term memory (LSTM) (e.g. the work done by BID22 ; BID35 ), (ii) feed-forward attention mechanisms that augment vanilla CNNs, such as the Spatial Transformer Networks (STN) by BID8 , or a top-down feed-forward attention mechanism (FAM) BID19 ). Although it is not applied to fine-grained recognition, the Residual Attention introduced by BID28 is another example of feed-forward attention mechanism that takes advantage of residual connections BID6 ) to enhance or dampen certain regions of the feature maps in an incremental manner.Inspired by all the previous research about attention mechanisms in computer vision, we propose a novel feed-forward attention architecture (see FIG0 ) that accumulates and enhances most of the desirable properties from previous approaches:1. Detect and process in detail the most informative parts of an image: more robust to deformation and clutter. 2. Feed-forward trainable with SGD: faster inference than iterative models, faster convergence rate than Reinforcement Learning-based (RL) methods like the ones presented by BID22 ; BID15 . The proposed mechanism. Feature maps at different levels are processed to generate spatial attention masks and use them to output a class hypothesis based on local information and a confidence score (C). The final prediction consists of the average of all the hypotheses weighted by the normalized confidence scores. We have presented a novel attention mechanism to improve CNNs for fine-grained recognition. The proposed mechanism finds the most informative parts of the CNN feature maps at different depth levels and combines them with a gating mechanism to update the output distribution.Moreover, we thoroughly tested all the components of the proposed mechanism on Cluttered Translated MNIST, and demonstrate that the augmented models generalize better on the test set than their plain counterparts. We hypothesize that attention helps to discard noisy uninformative regions, avoiding the network to memorize them.Unlike previous work, the proposed mechanism is modular, architecture independent, fast, and simple and yet WRN augmented with it show higher accuracy in each of the following tasks: Age and Gender Recognition (Adience dataset), CUB200-2011 birds, Stanford Dogs, Stanford Cars, and UEC Food-100. Moreover, state of the art performance is obtained on gender, dogs, and cars. Figure 6: Test accuracy logs for the five fine-grained datasets. As it can be seen, the augmented models (WRNA) achieve higher accuracy at similar convergence rates. For the sake of space we only show one of the five folds of the Adience dataset.",propose novel attention mechanism enhance Convolutional Neural Networks fine-grained recognition. proposed mechanism reuses CNN feature activations find informative parts image different depths help gating mechanisms without part annotations. Thus can be used augment layer CNN extract low- high-level local information discriminative. Differently approaches mechanism propose needs single pass input can be trained end-to-end SGD. consequence proposed mechanism is modular architecture-independent easy implement faster iterative approaches. Experiments show when augmented approach Wide Residual Networks systematically achieve superior performance five different fine-grained recognition datasets:Adience age gender recognition benchmark Caltech-UCSD Birds-200-2011 Stanford Dogs Stanford Cars UEC Food-100 obtaining competitive state-of-the-art scores. Humans animals process vasts amounts information limited computational resources thanks attention mechanisms which allow focus resources informative chunks information. biological mechanisms have been extensively studied see BID0;BID2 concretely mechanisms concerning visual attention e.g work done BID25.In work inspire advantages visual biological attention mechanisms finegrained visual recognition Convolutional Neural Networks CNN see BID11 is particularly difficult task since involves looking details large amounts data images remaining robust deformation clutter. sense different attention mechanisms fine-grained recognition exist literature:iterative methods process images using glimpses recurrent neural networks RNN long short-term memory LSTM e.g work done BID22;BID35 ii feed-forward attention mechanisms augment vanilla CNNs Spatial Transformer Networks STN BID8 top-down feed-forward attention mechanism FAM BID19 Although is not applied fine-grained recognition Residual Attention introduced BID28 is another example feed-forward attention mechanism takes advantage residual connections BID6 enhance dampen certain regions feature maps incremental manner.Inspired previous research attention mechanisms computer vision propose novel feed-forward attention architecture see FIG0 accumulates enhances desirable properties previous approaches:1 Detect process detail informative parts image:robust deformation clutter. 2. Feed-forward trainable SGD:faster inference iterative models faster convergence rate Reinforcement Learning-based RL methods like ones presented BID22;BID15. proposed mechanism. Feature maps different levels are processed generate spatial attention masks use output class hypothesis based local information confidence score C final prediction consists average hypotheses weighted normalized confidence scores. have presented novel attention mechanism improve CNNs fine-grained recognition. proposed mechanism finds informative parts CNN feature maps different depth levels combines gating mechanism update output distribution.Moreover thoroughly tested components proposed mechanism Cluttered Translated MNIST demonstrate when augmented models generalize better test set plain counterparts. hypothesize attention helps discard noisy uninformative regions avoiding network memorize them.Unlike previous work proposed mechanism is modular architecture independent fast simple yet WRN augmented show higher accuracy following tasks:Age Gender Recognition Adience dataset CUB200-2011 birds Stanford Dogs Stanford Cars UEC Food-100 Moreover state art performance is obtained gender dogs cars. Figure6:Test accuracy logs five fine-grained datasets. can be seen augmented models WRNA achieve higher accuracy similar convergence rates. sake space show one five folds Adience dataset.,887,590,297,0.008,1.503,2025/11/05 17:18:54,0.0,1.385,0.5389408099688469,285.671
"Most existing GANs architectures that generate images use transposed convolution or resize-convolution as their upsampling algorithm from lower to higher resolution feature maps in the generator. We argue that this kind of fixed operation is problematic for GANs to model objects that have very different visual appearances. We propose a novel adaptive convolution method that learns the upsampling algorithm based on the local context at each location to address this problem. We modify a baseline GANs architecture by replacing normal convolutions with adaptive convolutions in the generator. Experiments on CIFAR-10 dataset show that our modified models improve the baseline model by a large margin. Furthermore, our models achieve state-of-the-art performance on CIFAR-10 and STL-10 datasets in the unsupervised setting. Generative Adversarial Networks BID6 (GANs) are an unsupervised learning method that is able to generate realistic looking images from noise. GANs employs a minimax game where a generator network learns to generate synthesized data from random noise and in conjunction, a discriminator network learns to distinguish between real and generated data. Theoretically, the training processes of the two networks intertwine and iterate until both networks reach a Nash equilibrium where real and synthesized data are indistinguishable.However, in practice, GANs are notoriously hard to train. For the learning of the generator to happen effectively, hyper-parameters, as well as the architectures of the generator and discriminator, must be chosen carefully. Nevertheless, on datasets with visually similar images, such as bedroom scenes and faces , GANs have produced good results BID15 . This success, however, does not translate to datasets that have diverse visual categories. GANs models trained on ImageNet BID16 were only able to learn basic image statistics and some shapes, but they did not learn any object BID17 . Recent works address this problem by incorporating additional high-level information to guide the generator, such as training the discriminator in a semi-supervised manner BID17 , adding a second training objective to direct the generator toward similar samples from the training set BID19 or using artificial class labels by clustering in the representation space BID7 .We take a different approach to tackle this problem. We hypothesize that the rigidity of the normal convolution operator is partially responsible for the difficulty of GANs to learn on diverse visual datasets. Most GANs generators upsample low resolution feature maps toward higher resolution using fixed convolutions (note that a transposed convolution is equivalent to a convolution) or resize-convolution BID13 . Such operations are unintuitive, because, pixel locations have different local contexts and belong to diverse object categories. Consequently , different pixel locations should have different upsampling schemes. This shortcoming of normal convolution is especially problematic in the early upsampling layers where higher level information usually associates with the object shapes and the context of images.We propose the use of a novel adaptive convolution BID12 architecture, called Adaptive Convolution Block, that replaces normal convolutions to address the aforementioned shortcoming of GANs generators. Instead of learning a fixed convolution for the upsampling of all pixels from the lower to the higher resolution feature map, an AdaConvBlock learns to generate the convolution weights and biases of the upsampling operation adaptively based on the local feature map at each pixel location. AdaConvBlock helps the generator to learn to generate upsampling algorithms that take into account the local context. We believe that this kind of adaptive convolution is more intuitive and more akin to the process when a human draws something: the same thought process is used in the whole drawing but the style of each stroke should vary and depend on the local context around each pixel position.We conduct experiments to compare our adaptive convolution method to normal convolution in the unsupervised setting. We progressively replace all convolutions of a GANs generator with AdaConvBlocks from the lowest resolution to the highest resolution. Experiments on CIFAR-10 dataset show that the modified adaptive convolution models have superior qualitative and quantitative performance over the baseline architecture and just replacing convolution of the upsampling from the lowest resolution feature map with adaptive convolution can have significant impacts on the baseline model. Furthermore, our best models achieve state-of-the-art unsupervised performance on both CIFAR-10 and STL-10 datasets. Our code and models will be released. We have demonstrated that using adaptive convolutions to replace normal convolutions in a GANs generator can improve the performance of a weak baseline model significantly on visually diverse datasets. Our AdaGAN models were able to beat other state-of-the-art methods without using any augmented training objectives. The samples generated by our models show that they seem to be able to learn the global context pretty well and be able to learn the rough shapes of the objects in most cases and the sample quality is quite reasonable on CIFAR-10 dataset. Furthermore, there are not much visible convolution artifacts in the generated images. The success of our models suggests that non-trivial performance improvement can be gained from modifying architectures for GANs.The approach we take is different from other methods that try to inject high level information into the discriminator. These existing methods and AdaGAN can complement each other. More experiments need to be done, but we believe that our architectures can benefit from the augmented training objectives from existing methods.Our method is not without a downside. Even though we used depthwise separable convolution to reduce the cost, the amount of memory and computation is still extremely high. More tricks could be applied to alleviate this issue. For example, in a similar manner to BID12 work, both the local convolutions and the convolution to regress the adaptive weights for the local convolutions in our AdaConvBlock can be approximated by separate 1-D convolutions. This can reduce the cost by more than 50%. Another idea is to exploit locality. We expect the adaptive convolution weights and biases of a pixel location to be quite similar to its neighbors and can be interpolated in a certain way. We will address this issue in our future work.A SAMPLES GENERATED BY OUR MODELS ON CIFAR-10 AND STL-10",existing GANs architectures generate images use transposed convolution resize-convolution upsampling algorithm lower higher resolution feature maps generator. argue kind fixed operation is problematic GANs model objects have very different visual appearances. propose novel adaptive convolution method learns upsampling algorithm based local context location address problem. modify baseline GANs architecture replacing normal convolutions adaptive convolutions generator. Experiments CIFAR-10 dataset show modified models improve baseline model large margin. Furthermore models achieve state-of-the-art performance CIFAR-10 STL-10 datasets unsupervised setting. Generative Adversarial Networks BID6 GANs are an unsupervised learning method is able generate realistic looking images noise. GANs employs minimax game where a generator network learns generate synthesized data random noise conjunction discriminator network learns distinguish real generated data. Theoretically training processes two networks intertwine iterate networks reach Nash equilibrium where real synthesized data are indistinguishable.However practice GANs are notoriously hard train. learning generator happen effectively hyper-parameters well architectures generator discriminator must chosen carefully. Nevertheless datasets visually similar images bedroom scenes faces GANs have produced good results BID15. success however does not translate datasets have diverse visual categories. GANs models trained ImageNet BID16 were only were able learn basic image statistics shapes did learn object BID17. Recent works address problem incorporating additional high-level information guide generator training discriminator semi-supervised manner BID17 adding second training objective direct generator toward similar samples training set BID19 using artificial class labels clustering representation space BID7.We take different approach tackle problem. hypothesize rigidity normal convolution operator is partially responsible difficulty GANs learn diverse visual datasets. GANs generators upsample low resolution feature maps toward higher resolution using fixed convolutions note transposed convolution is equivalent convolution resize-convolution BID13. operations are unintuitive pixel locations have different local contexts belong diverse object categories. Consequently different pixel locations should have different upsampling schemes. shortcoming normal convolution is especially problematic early upsampling layers where higher level information usually associates object shapes context images.We propose use novel adaptive convolution BID12 architecture called Adaptive Convolution Block replaces normal convolutions address aforementioned shortcoming GANs generators. Instead learning fixed convolution upsampling pixels lower higher resolution feature map AdaConvBlock learns generate convolution weights biases upsampling operation adaptively based local feature map pixel location. AdaConvBlock helps generator learn generate upsampling algorithms take account local context. believe kind adaptive convolution is more intuitive akin process when a human draws something:thought process is used whole drawing style stroke should vary depend local context around pixel position.We conduct experiments compare adaptive convolution method normal convolution unsupervised setting. progressively replace convolutions GANs generator AdaConvBlocks lowest resolution highest resolution. Experiments CIFAR-10 dataset show modified adaptive convolution models have superior qualitative quantitative performance baseline architecture replacing convolution upsampling lowest resolution feature map adaptive convolution can have significant impacts baseline model. Furthermore best models achieve state-of-the-art unsupervised performance CIFAR-10 STL-10 datasets. code models will be released. have demonstrated using adaptive convolutions replace normal convolutions GANs generator can improve performance weak baseline model significantly visually diverse datasets. AdaGAN models were only were able beat state-of-the-art methods without using augmented training objectives. samples generated models show seem able learn global context pretty well able learn rough shapes objects cases sample quality is quite reasonable CIFAR-10 dataset. Furthermore are not much visible convolution artifacts generated images. success models suggests non-trivial performance improvement can be gained modifying architectures GANs.The approach take is different methods try inject high level information discriminator. existing methods AdaGAN can complement other. experiments need done believe architectures can benefit augmented training objectives existing methods.Our method is not without downside. Even though used depthwise separable convolution reduce cost amount memory computation is still extremely high. tricks could applied alleviate issue. example similar manner BID12 work local convolutions convolution regress adaptive weights local convolutions AdaConvBlock can be approximated separate 1-D convolutions. can reduce cost 50%. Another idea is to exploit locality. expect adaptive convolution weights biases pixel location quite similar neighbors can be interpolated certain way. will address issue future work.A SAMPLES GENERATED MODELS CIFAR-10 STL-10,1203,829,374,0.012,1.451,2025/11/05 17:18:54,0.01,1.372,0.3769470404984424,359.837
"Techniques such as ensembling and distillation promise model quality improvements when paired with almost any base model. However, due to increased test-time cost (for ensembles) and increased complexity of the training pipeline (for distillation), these techniques are challenging to use in industrial settings. In this paper we explore a variant of distillation which is relatively straightforward to use as it does not require a complicated multi-stage setup or many new hyperparameters. Our first claim is that online distillation enables us to use extra parallelism to fit very large datasets about twice as fast. Crucially, we can still speed up training even after we have already reached the point at which additional parallelism provides no benefit for synchronous or asynchronous stochastic gradient descent. Two neural networks trained on disjoint subsets of the data can share knowledge by encouraging each model to agree with the predictions the other model would have made. These predictions can come from a stale version of the other model so they can be safely computed using weights that only rarely get transmitted. Our second claim is that online distillation is a cost-effective way to make the exact predictions of a model dramatically more reproducible. We support our claims using experiments on the Criteo Display Ad Challenge dataset, ImageNet, and the largest to-date dataset used for neural language modeling, containing $6\times 10^{11}$ tokens and based on the Common Crawl repository of web data. For large-scale, commercially valuable neural net training problems, practitioners would be willing to devote many more machines to training if it sped up training time dramatically or improved the quality of the final model. Currently, distributed stochastic gradient descent (SGD), in both its synchronous and asynchronous forms , is the dominant algorithm for large-scale neural network training across multiple interconnected machines. Unfortunately, as the number of machines increases, there are diminishing improvements to the time needed to train a high quality model, to a point where adding workers does not further improve training time. A combination of infrastructure limitations and optimization barriers constrain the scalability of distributed minibatch SGD. The overhead of communicating weight updates and the long tail of the machine and network latency distributions slow down execution and produce thorny engineering challenges. For the synchronous algorithm, there are rapidly diminishing returns from increasing the effective batch size BID11 BID9 . For the asynchronous algorithm, gradient interference from inconsistent weights can cause updates to thrash and even, in some cases, result in worse final accuracy or completely stall learning progress. The precise scalability limit for distributed SGD will depend on implementation details of the algorithm, specifics of the infrastructure, and the capabilities of the hardware, but in our experience it can be very difficult to scale effectively much beyond a hundred GPU workers in realistic setups. No algorithm for training neural nets will be infinitely scalable, but even scaling a bit beyond the limits of distributed SGD would be extremely valuable.Once we have reached the limits of adding workers to distributed SGD, we could instead use extra machines to train another copy of the model and create an ensemble to improve accuracy (or trade this accuracy for training time by training the members of the ensemble for fewer steps). As an added benefit, the ensemble will make more stable and reproducible predictions, which can be useful in practical applications. However, ensembling increases the cost at test time, potentially violating latency or other cost constraints. Alternatively, to get nearly the same benefits of the ensemble without increasing test time costs, we can distill BID8 BID2 an n-way ensemble of models into a single still-servable model using a two-phase process: first we use nM machines to train an n-way ensemble with distributed SGD and then use M machines to train the servable student network to mimic the n-way ensemble. By adding another phase to the training process and using more machines, distillation in general increases training time and complexity in return for a quality improvement close to the larger teacher ensemble model.We believe that the additional training costs, in terms of both time and pipeline complexity, discourage practitioners from using ensemble distillation, even though it almost always would improve results. In this work, we describe a simpler online variant of distillation we call codistillation. Codistillation trains n copies of a model in parallel by adding a term to the loss function of the ith model to match the average prediction of the other models.Through large-scale experiments we show that, compared to distributed SGD, codistillation improves accuracy and speeds up training by allowing the productive use of more computational resources even beyond the point where adding more workers provides no additional speedup for SGD. Specifically, codistillation provides the benefits of distilling an ensemble of models without increasing training time. Codistillation is also quite simple to use in practice compared to a multi-phase distillation training procedure. Multi-phase distillation tends to encourage human intervention between the training phases to decide when to stop training the ensemble and start distilling it into a single model. We also show that codistillation does not lose the reproducibility benefits of ensembles of neural networks, reducing churn in the predictions of different retrains of the same model. Reducing prediction churn can be essential when testing and launching new versions of a model in a non-disruptive way in an existing service, although it is not as well-studied in the academic machine learning community.Given the obvious relationship to distillation, very similar algorithms to codistillation have been independently described by multiple researchers. For example, BID21 describes another simultaneous distillation algorithm but does not investigate the benefits in the distributed training case and only presents it as a potential quality improvement over regular distillation. We view the experimental validation of codistillation at scale as the primary contribution of our work. Another contribution of this work is our exploration of different design choices and implementation considerations for codistillation which we believe has produced recommendations of substantial practical utility.In general, we believe the quality gains of codistillation over well-tuned offline distillation will be minor in practice and the more interesting research direction is exploring codistillation as a distributed training algorithm that uses an additional form of communication that is far more delay tolerant. Distillation is a surprisingly flexible tool, especially when performed during model training instead of after. It can be used to accelerate training, improve quality, distribute training in new, more communication efficient ways, and reduce prediction churn. However, there are still many questions we would like to explore. For example, we mostly focused on pairs of models codistilling from each other. It stands to reason that if pairs are useful then so are other topologies. Fully connected graphs might make the models too similar, too quickly so ring structures might also be interesting. We also did not explore the limits of how accurate the predictions from the teacher models have to be. It might be possible to aggressively quantize the teacher model to make codistillation almost as cheap as normal training even for very large models.It is somewhat paradoxical that bad models codistilling from each other can learn faster than models training independently. Somehow the mistakes made by the teacher model carry enough information to help the student model do better than the teacher, and better than just seeing the actual label in the data. Characterizing the ideal properties of a teacher model is an exciting avenue for future work.In this work we only extract predictions from the checkpoints, as predictions are identifiable and, unlike the internal structure of the networks, have no spurious symmetries. That said, it might be possible to extract more information from a checkpoint than just predictions without hitting the same issues faced by workers communicating gradients, allowing the use of the teacher models as a stronger regularizer. Perhaps distillation-based methods could be used to augment federated learning BID12 in particularly bandwidth-constrained settings.",Techniques ensembling distillation promise model quality improvements when paired almost base model. However due increased test-time cost ensembles increased complexity training pipeline distillation techniques are challenging use industrial settings. paper explore variant distillation which is relatively straightforward use does not require complicated multi-stage setup many new hyperparameters. first claim is that online distillation enablesus use extra parallelism fit large datasets twice fast. Crucially can are still speed training even have already reached point which additional parallelism provides benefit synchronous asynchronous stochastic gradient descent. Two neural networks trained disjoint subsets data can share knowledge encouraging model agree predictions model would have made. predictions can come stale version model can be safely computed using weights rarely get transmitted. second claim is that online distillation is a cost-effective way make exact predictions model dramatically reproducible. support claims using experiments Criteo Display Ad Challenge dataset ImageNet largest to-date dataset used neural language modeling containing $6\times 10^ 11 tokens based Common Crawl repository web data. large-scale commercially valuable neural net training problems practitioners would willing devote many machines training if it sped training time dramatically improved quality final model. Currently distributed stochastic gradient descent SGD synchronous asynchronous forms is the dominant algorithm large-scale neural network training across multiple interconnected machines. Unfortunately number machines increases are diminishing improvements time needed train high quality model point where adding workers does not further improve training time. combination infrastructure limitations optimization barriers constrain scalability distributed minibatch SGD. overhead communicating weight updates long tail machine network latency distributions slow execution produce thorny engineering challenges. synchronous algorithm are rapidly diminishing returns increasing effective batch size BID11 BID9. asynchronous algorithm gradient interference inconsistent weights can cause updates thrash even cases result worse final accuracy completely stall learning progress. precise scalability limit distributed SGD will depend implementation details algorithm specifics infrastructure capabilities hardware experience can be very difficult scale effectively much beyond hundred GPU workers realistic setups. algorithm training neural nets will be infinitely scalable even scaling bit beyond limits distributed SGD would extremely valuable.Once have reached limits adding workers distributed SGD could instead use extra machines train another copy model create ensemble improve accuracy trade accuracy training time training members ensemble fewer steps added benefit ensemble will make stable reproducible predictions which can be useful practical applications. However ensembling increases cost test time potentially violating latency cost constraints. Alternatively get nearly benefits ensemble without increasing test time costs can distill BID8 BID2 n-way ensemble models single still-servable model using two-phase process:first use nM machines train n-way ensemble distributed SGD use machines train servable student network mimic n-way ensemble. adding another phase training process using machines distillation general increases training time complexity return quality improvement close larger teacher ensemble model.We believe additional training costs terms time pipeline complexity discourage practitioners using ensemble distillation even though almost always would improve results. work describe simpler online variant distillation call codistillation. Codistillation trains n copies model parallel adding term loss function ith model match average prediction models.Through large-scale experiments show compared distributed SGD codistillation improves accuracy speeds training allowing productive use computational resources even beyond point where adding workers provides additional speedup SGD. Specifically codistillation provides benefits distilling ensemble models without increasing training time. Codistillation is also quite simple use practice compared multi-phase distillation training procedure. Multi-phase distillation tends encourage human intervention training phases decide when to stop training ensemble start distilling single model. also show codistillation does not lose reproducibility benefits ensembles neural networks reducing churn predictions different retrains model. Reducing prediction churn can be essential when testing launching new versions model non-disruptive way existing service although is not as well-studied academic machine learning community.Given obvious relationship distillation similar algorithms codistillation have been independently described multiple researchers. example BID21 describes another simultaneous distillation algorithm does not investigate benefits distributed training case presents potential quality improvement regular distillation. view experimental validation codistillation scale primary contribution work. Another contribution work is our exploration different design choices implementation considerations codistillation which we believe has produced recommendations substantial practical utility.In general believe quality gains codistillation well-tuned offline distillation will be minor practice interesting research direction is exploring codistillation distributed training algorithm uses additional form communication is far delay tolerant. Distillation is a surprisingly flexible tool especially when performed model training instead after. can be used accelerate training improve quality distribute training new communication efficient ways reduce prediction churn. However can are still many questions would like explore. example mostly focused pairs models codistilling other. stands reason if pairs are useful are other topologies. Fully connected graphs might make models similar quickly ring structures might also interesting. also did not explore limits how accurate predictions teacher models havetobe. might possible aggressively quantize teacher model make codistillation almost cheap normal training even large models.It is somewhat paradoxical bad models codistilling can learn faster models training independently. Somehow mistakes made teacher model carry enough information help student model do better teacher better seeing actual label data. Characterizing ideal properties teacher model is an exciting avenue future work.In work extract predictions checkpoints predictions are identifiable unlike internal structure networks have no spurious symmetries. said might possible extract information checkpoint predictions without hitting issues faced workers communicating gradients allowing use teacher models stronger regularizer. Perhaps distillation-based methods could used augment federated learning BID12 particularly bandwidth-constrained settings.,1540,1044,496,0.018,1.475,2025/11/05 17:18:54,0.01,1.544,0.4517133956386294,513.089
"Support Vector Machines (SVMs) are one of the most popular algorithms for classification and regression analysis. Despite their popularity, even efficient implementations have proven to be computationally expensive to train at a large-scale, especially in streaming settings. In this paper, we propose a novel coreset construction algorithm for efficiently generating compact representations of massive data sets to speed up SVM training. A coreset is a weighted subset of the original data points such that SVMs trained on the coreset are provably competitive with those trained on the original (massive) data set. We provide both lower and upper bounds on the number of samples required to obtain accurate approximations to the SVM problem as a function of the complexity of the input data. Our analysis also establishes sufficient conditions on the existence of sufficiently compact and representative coresets for the SVM problem. We empirically evaluate the practical effectiveness of our algorithm against synthetic and real-world data sets. Popular machine learning algorithms are computationally expensive, or worse yet, intractable to train on Big Data. The notion of using coresets BID6 BID3 BID2 , small weighted subsets of the input points that provably approximate the original data set, has shown promise in accelerating machine learning algorithms such as kmeans clustering BID6 , mixture model training , and logistic regression BID12 .Coreset constructions were originally introduced in the context of computational geometry BID1 and subsequently generalized for applications to other problems BID14 BID6 . Coresets provide a compact representation of the structure of static and streaming data, with provable approximation guarantees with respect to specific algorithms. For instance , a data set consisting of K clusters would yield a coreset of size K, with each cluster represented by one coreset point. Even if the data has no structure (e.g., uniformly distributed), coresets will correctly down sample the data to within prescribed error bounds. For domains where the data has structure, the coreset representation has the potential to greatly and effectively reduce the time required to manually label data for training and the computation time for training, while at the same time providing a mechanism of supporting machine learning systems for applications with streaming data.Coresets are constructed by approximating the relative importance of each data point in the original data set to define a sampling distribution and sampling sufficiently many points in accordance with this distribution. This construction scheme suggests that beyond providing a means of conducting provably fast and accurate inference, coresets also serve as efficient representations of the full data set and may be used to automate laborious representation tasks, such as automatically generating semantic video representations or detecting outliers in data BID17 .The representative power and provable guarantees provided by coresets also motivate their use in training of one of the most popular algorithms for classification and regression analysis: Support Vector Machines (SVMs). Despite their popularity , SVMs are computationally expensive to train on massive data sets, which has proven to be computationally problematic with the rising availability of Big Data. In this paper, we present a novel coreset construction algorithm for efficient, large-scale Support Vector Machine training.1. A practical coreset construction algorithm for accelerating SVM training based on an efficient importance evaluation scheme for approximating the importance of each point.2. An analysis proving lower bounds on the number of samples required by any coreset construction algorithm to approximately represent the data.3. An analysis proving the efficiency and theoretical guarantees of our algorithm and characterizing the family of data sets for which applications of coresets are most suited.4. Evaluations against synthetic and real-world data sets that demonstrate the practical effectiveness of our algorithm for large-scale SVM training. We presented an efficient coreset construction algorithm for generating compact representations of the input data points that provide provably accurate inference. We presented both lower and upper bounds on the number of samples required to obtain accurate approximations to the SVM problem as a function of input data complexity and established sufficient conditions for the existence of compact representations. Our experimental results demonstrate the effectiveness of our approach in speeding up SVM training when compared to uniform sub-samplingThe method presented in this paper is also applicable to streaming settings, using the merge-andreduce technique from coresets literature BID3 .We conjecture that our coreset construction method can be extended to significantly speed up SVM training for nonlinear kernels as well as other popular machine learning algorithms, such as deep learning. 8 APPENDIX Figure 3 : The estimator variance of query evaluations. We note that due to the use of a judicious sampling distribution based on the points' sensitivities, the variance of our coreset estimator is lower than that of uniform sampling for all data sets.",Support Vector Machines SVMs are one popular algorithms classification regression analysis. Despite popularity even efficient implementations have proven computationally expensive train large-scale especially streaming settings. paper propose novel coreset construction algorithm efficiently generating compact representations massive data sets speed SVM training. coreset is a weighted subset original data points SVMs trained coreset are provably competitive trained original massive data set. provide lower upper bounds number samples required obtain accurate approximations SVM problem function complexity input data. analysis also establishes sufficient conditions existence sufficiently compact representative coresets SVM problem. empirically evaluate practical effectiveness algorithm synthetic real-world data sets. Popular machine learning algorithms are computationally expensive worse yet intractable train Big Data. notion using coresets BID6 BID3 BID2 small weighted subsets input points provably approximate original data set has shown promise accelerating machine learning algorithms kmeans clustering BID6 mixture model training logistic regression BID12.Coreset constructions were originally introduced context computational geometry BID1 subsequently generalized which applications problems BID14 BID6. Coresets provide compact representation structure static streaming data provable approximation guarantees respect specific algorithms. instance data set consisting K clusters would yield coreset sizeK cluster represented one coreset point. Even if the data has no has structure e.g uniformly distributed coresets will correctly sample data within prescribed error bounds. domains where the data has no has structure coreset representation has the potential greatly effectively reduce time required manually label data training computation time training time providing mechanism supporting machine learning systems which applications streaming data.Coresets are constructed approximating relative importance data point original data set define sampling distribution sampling sufficiently many points accordance distribution. construction scheme suggests beyond providing means conducting provably fast accurate inference coresets also serve efficient representations full data set may used automate laborious representation tasks automatically generating semantic video representations detecting outliers data BID17.The representative power provable guarantees provided coresets also motivate use training one popular algorithms classification regression analysis:Support Vector Machines SVMs Despite popularity SVMs are computationally expensive train massive data sets which has proven computationally problematic rising availability Big Data. paper present novel coreset construction algorithm efficient large-scale Support Vector Machine training.1 practical coreset construction algorithm accelerating SVM training based efficient importance evaluation scheme approximating importance point.2 analysis proving lower bounds number samples required coreset construction algorithm approximately represent data.3 analysis proving efficiency theoretical guarantees algorithm characterizing family data sets which applications coresets are most suited.4 suited.4 Evaluations synthetic real-world data sets demonstrate practical effectiveness algorithm large-scale SVM training. presented efficient coreset construction algorithm generating compact representations input data points provide provably accurate inference. presented lower upper bounds number samples required obtain accurate approximations SVM problem function input data complexity established sufficient conditions existence compact representations. experimental results demonstrate effectiveness approach speeding SVM training when compared uniform sub-samplingThe method presented paper is also applicable streaming settings using merge-andreduce technique coresets literature BID3.We conjecture coreset construction method can be extended significantly speed SVM training nonlinear kernels well popular machine learning algorithms deep learning. 8 APPENDIX Figure3:estimator variance query evaluations. note due use judicious sampling distribution based points' sensitivities variance coreset estimator is lower uniform sampling data sets.,934,641,293,0.009,1.457,2025/11/05 17:18:54,0.0,1.429,0.3956386292834891,300.952
"The sign stochastic gradient descent method (signSGD) utilizes only the sign of the stochastic gradient in its updates. Since signSGD carries out one-bit quantization of the gradients, it is extremely practical for distributed optimization where gradients need to be aggregated from different processors. For the first time, we establish convergence rates for signSGD on general non-convex functions under transparent conditions. We show that the rate of signSGD to reach first-order critical points matches that of SGD in terms of number of stochastic gradient calls, up to roughly a linear factor in the dimension. We carry out simple experiments to explore the behaviour of sign gradient descent (without the stochasticity) close to saddle points and show that it often helps completely avoid them without using either stochasticity or curvature information. Deep neural network training takes place in an error landscape that is high-dimensional, non-convex and stochastic. In practice, simple optimization techniques perform surprisingly well but have very limited theoretical understanding. While stochastic gradient descent (SGD) is widely used, algorithms like Adam (Kingma & Ba, 2015) , RMSprop BID19 and Rprop (Riedmiller & Braun, 1993) are also popular. These latter algorithms involve component-wise rescaling of gradients, and so bear closer relation to signSGD than SGD. Currently, convergence rates have only been derived for close variants of SGD for general non-convex functions, and indeed the Adam paper gives convex theory.Recently, another class of optimization algorithms has emerged which also pays attention to the resource requirements for training, in addition to obtaining good performance. Primarily, they focus on reducing costs for communicating gradients across different machines in a distributed training environment BID17 BID18 BID14 BID0 BID21 . Often, the techniques involve quantizing the stochastic gradients at radically low numerical precision. Empirically, it was demonstrated that one can get away with using only one-bit per dimension without losing much accuracy BID17 BID18 . The theoretical properties of these approaches are however not well-understood. In particular, it was not known until now how quickly signSGD (the simplest incarnation of one-bit SGD) converges or even whether it converges at all to the neighborhood of a meaningful solution. Our contribution: we supply the non-convex rate of convergence to first order critical points for signSGD. The algorithm updates parameter vector x k according to DISPLAYFORM0 whereḡ k is the mini-batch stochastic gradient and k is the learning rate. We show that for nonconvex problems, signSGD entertains convergence rates as good as SGD, up to a linear factor in the dimension. Our statements impose a particular learning rate and mini-batch schedule.Ours is the first work to provide non-convex convergence rates for a biased quantisation procedure as far as we know, and therefore does not require the randomisation that other gradient quantisation algorithms need to ensure unbiasedness. The technical challenge we overcome is in showing how to carry the stochasticity in the gradient through the sign non-linearity of the algorithm in a controlledfashion.Whilst our analysis is for first order critical points, we experimentally test the performance of sign gradient descent without stochasticity (signGD) around saddle points. We removed stochasticity in order to investigate whether signGD has an inherent ability to escape saddle points, which would suggest superiority over gradient descent (GD) which can take exponential time to escape saddle points if it gets too close to them BID5 .In our work we make three assumptions. Informally , we assume that the objective function is lowerbounded, smooth, and that each component of the stochastic gradient has bounded variance. These assumptions are very general and hold for a much wider class of functions than just the ones encountered in deep learning. Outline of paper: in Sections 3, 4 and 5 we give non-convex theory of signSGD. In Section 6 we experimentally test the ability of the signGD (without the S) to escape saddle points. And in Section 7 we pit signSGD against SGD and Adam on CIFAR-10. First we wish to discuss the connections between signSGD and Adam BID10 . Note that setting the Adam hyperparameters 1 = 2 = ✏ = 0, Adam and signSGD are equivalent. Indeed the authors of the Adam paper suggest that during optimisation the Adam step will commonly look like a binary vector of ±1 (multiplied by the learning rate) and thus resemble the sign gradient step. If this algorithmic correspondence is valid, then there seems to be a discrepancy between our theoretical results and the empirical good performance of Adam. Our convergence rates suggest that signSGD should be worse than SGD by roughly a factor of dimension d. In deep neural network applications d can easily be larger than 10 6 . We suggest a resolution to this proposed discrepancy-there is structure present in deep neural network error surfaces that is not captured by our simplistic theoretical assumptions. We have already discussed in Section 5 how the signSGD bound is improved by a factor d in the case of gradients distributed uniformly across dimensions. It is also reasonable to expect that neural network error surfaces might exhibit only weak coupling across dimensions. To provide intuition for how such an assumption can help improve the dimension scaling of signSGD, note that in the idealised case of total decoupling (the Hessian is everywhere diagonal) then the problem separates into d independent one dimensional problems, so the dimension dependence is lost.Next, let's talk about saddle points. Though general non-convex functions are littered with local minima, recent work rather characterises successful optimisation as the evasion of a web of saddle points BID4 . Current theoretical work focuses either on using noise Levy (2016); BID5 or curvature information (Allen-Zhu, 2017b) to establish bounds on the amount of time needed to escape saddle points. We noted that merely passing the gradient through the sign operation introduces an algorithmic instability close to saddle points, and we wanted to empirically investigate whether this could be enough to escape them. We removed stochasticity from the algorithm to focus purely on the effect of the sign function.We found that when the objective function was axis aligned, then sign gradient descent without stochasticity (signGD) made progress unhindered by the saddles. We suggest that this is because signGD has a greater ability to 'explore', meaning it typically takes larger steps in regions of small gradient than SGD, and it can take steps almost orthogonal to the true gradient direction. This exploration ability could potentially allow it to break out of subspaces convergent on saddle points without sacrificing its convergence rate-we hypothesise that this may contribute to the often more robust practical performance of algorithms like Rprop and Adam, which bear closer relation to signSGD than SGD. For non axis-aligned objectives, signGD could sometimes get stuck in perfect periodic orbits around saddle points, though we hypothesise that this behaviour may be much less likely for higher dimensional objectives (the testbed function had dimension 10) with non-constant learning rate.Finally we want to discuss the implications of our results for gradient quantisation schemes. Whilst we do not analyse the multi-machine case of distributed optimisation, we imagine that our results will extend naturally to that setting. In particular our results stand as a proof of concept that we can provide guarantees for biased gradient quantisation schemes. Existing quantisation schemes with guarantees require delicate randomisation to ensure unbiasedness. If a scheme as simple as ours can yield provable guarantees on convergence, then there is a hope that exploring further down this avenue can yield new and useful practical quantisation algorithms. BID8 of 91.25%. Note the broad similarity in general shape of the heatmap between Adam and signSGD, supporting a notion of algorithmic similarity. Also note that whilst SGD has a larger region of very high-scoring hyperparameter configurations, signSGD and Adam appear more stable for large learning rates. We have investigated the theoretical properties of the sign stochastic gradient method (signSGD) as an algorithm for non-convex optimisation. The study was motivated by links that the method has both to deep learning stalwarts like Adam and Rprop, as well as to newer quantisation algorithms that intend to cheapen the cost of gradient communication in distributed machine learning. We have proved non-convex convergence rates for signSGD to first order critical points. Insofar as the rates can directly be compared, they are of the same order as SGD in terms of number of gradient evaluations, but worse by a linear factor in dimension. SignSGD has the advantage over existing gradient quantisation schemes with provable guarantees, in that it doesn't need to employ randomisation tricks to remove bias from the quantised gradient.We wish to propose some interesting directions for future work. First our analysis only looks at convergence to first order critical points. Whilst we present preliminary experiments exhibiting success and failure modes of the algorithm around saddle points, a more detailed study attempting to pin down exactly when we can expect signSGD to escape saddle points efficiently would be welcome. This is an interesting direction seeing as existing work always relies on either stochasticity or second order curvature information to avoid saddles. Second the link that signSGD has to both Adam-like algorithms and gradient quantisation schemes is enticing. In future work we intend to investigate whether this connection can be exploited to develop large scale machine learning algorithms that get the best of both worlds in terms of optimisation speed and communication efficiency.",sign stochastic gradient descent method signSGD utilizes sign stochastic gradient updates. Since signSGD carries one-bit quantization gradients is extremely practical distributed optimization where gradients need aggregated different processors. first time establish convergence rates signSGD general non-convex functions transparent conditions. show rate signSGD reach first-order critical points matches SGD terms number stochastic gradient calls roughly linear factor dimension. carry simple experiments explore behaviour sign gradient descent without stochasticity close saddle points show often helps completely avoid without using either stochasticity curvature information. Deep neural network training takes place error landscape is high-dimensional non-convex stochastic. practice simple optimization techniques perform surprisingly well have very limited theoretical understanding. stochastic gradient descent SGD is widely used algorithms like Adam Kingma Ba 2015 RMSprop BID19 Rprop Riedmiller Braun 1993 are also popular. latter algorithms involve component-wise rescaling gradients which bear closer relation signSGD SGD. Currently convergence rates have only been derived close variants SGD general non-convex functions indeed Adam paper gives convex theory.Recently another class optimization algorithms has emerged which also pays attention resource requirements training addition obtaining good performance. Primarily focus reducing costs communicating gradients across different machines distributed training environment BID17 BID18 BID14 BID0 BID21. Often techniques involve quantizing stochastic gradients radically low numerical precision. Empirically was demonstrated one can get away using one-bit per dimension without losing much accuracy BID17 BID18. theoretical properties approaches are however well-understood particular was not known how quickly signSGD simplest incarnation one-bit SGD converges even whether converges neighborhood meaningful solution. contribution:supply non-convex rate convergence first order critical points signSGD. algorithm updates parameter vector x k according DISPLAYFORM0 whereḡk is the mini-batch stochastic gradient k is the learning rate. show nonconvex problems signSGD entertains convergence rates good SGD linear factor dimension. statements impose particular learning rate mini-batch schedule.Ours is the is for first work provide non-convex convergence rates biased quantisation procedure far know therefore does not require randomisation gradient quantisation algorithms need ensure unbiasedness. technical challenge overcome is in showing how to carry stochasticity gradient sign non-linearity algorithm controlledfashion.Whilst analysis is the is for first order critical points experimentally test performance sign gradient descent without stochasticity signGD around saddle points. removed stochasticity order investigate whether signGD has an inherent ability escape saddle points would suggest superiority gradient descent GD which can take exponential time escape saddle points if it gets close BID5.In work make three assumptions. Informally assume when the objective function is lowerbounded smooth component stochastic gradient has bounded variance. assumptions are very general hold much wider class functions ones encountered deep learning. Outline paper:Sections3 4 5 give non-convex theory signSGD. Section6 experimentally test ability signGD without escape saddle points. Section7 pit signSGD SGD Adam CIFAR-10 First wish discuss connections signSGD Adam BID10. Note setting Adam hyperparameters1 2 ✏ 0 Adam signSGD are equivalent. Indeed authors Adam paper suggest optimisation Adam step will commonly look like binary vector ±1 multiplied learning rate thus resemble sign gradient step. If this algorithmic correspondence is valid seems discrepancy theoretical results empirical good performance Adam. convergence rates suggest signSGD should be worse SGD roughly factor dimension d. deep neural network applications can easily larger 106. suggest resolution proposed discrepancy-there is structure present deep neural network error surfaces is not captured simplistic theoretical assumptions. have already discussed Section5 how the signSGD bound is improved factor case gradients distributed uniformly across dimensions. is also reasonable expect neural network error surfaces might exhibit weak coupling across dimensions. provide intuition how such an assumption can help improve dimension scaling signSGD note idealised case total decoupling Hessian is everywhere diagonal problem separates independent one dimensional problems dimension dependence is lost.Next let's talk saddle points. Though general non-convex functions are littered local minima recent work rather characterises successful optimisation evasion web saddle points BID4. Current theoretical work focuses either using noise Levy 2016 BID5 curvature information Allen-Zhu 2017b establish bounds amount time needed escape saddle points. noted merely passing gradient sign operation introduces algorithmic instability close saddle points wanted empirically investigate whether could enough escape them. removed stochasticity algorithm focus purely effect sign function.We found when the objective function was axis aligned sign gradient descent without stochasticity signGD made progress unhindered saddles. suggest is because signGD has a greater ability 'explore' meaning typically takes larger steps regions small gradient SGD can take steps almost orthogonal true gradient direction. exploration ability could potentially allow break subspaces convergent saddle points without sacrificing convergence rate-we hypothesise may contribute often robust practical performance algorithms like Rprop Adam which bear closer relation signSGD SGD. non axis-aligned objectives signGD could sometimes get stuck perfect periodic orbits around saddle points though hypothesise behaviour may much less likely higher dimensional objectives testbed function had dimension10 non-constant learning rate.Finally want discuss implications results gradient quantisation schemes. Whilst do not analyse multi-machine case distributed optimisation imagine results will extend naturally setting. particular results stand proof concept can provide guarantees biased gradient quantisation schemes. Existing quantisation schemes guarantees require delicate randomisation ensure unbiasedness. If a scheme simple can yield provable guarantees convergence is hope exploring avenue can yield new useful practical quantisation algorithms. BID8 91.25%. Note broad similarity general shape heatmap Adam signSGD supporting notion algorithmic similarity. Also note whilst SGD has a larger region high-scoring hyperparameter configurations signSGD Adam appear stable large learning rates. have investigated theoretical properties sign stochastic gradient method signSGD algorithm non-convex optimisation. study was motivated links method has both to deep learning stalwarts like Adam Rprop well newer quantisation algorithms intend cheapen cost gradient communication distributed machine learning. have proved non-convex convergence rates signSGD first order critical points. Insofar rates can directly compared areof order SGD terms number gradient evaluations worse linear factor dimension. SignSGD has the advantage existing gradient quantisation schemes provable guarantees need employ randomisation tricks remove bias quantised gradient.We wish propose interesting directions future work. First analysis looks convergence first order critical points. Whilst present preliminary experiments exhibiting success failure modes algorithm around saddle points detailed study attempting pin exactly when we can expect signSGD escape saddle points efficiently would welcome. is an interesting direction seeing existing work always relies either stochasticity second order curvature information avoid saddles. Second link signSGD has to both Adam-like algorithms gradient quantisation schemes is enticing. future work intend investigate whether connection can be exploited develop large scale machine learning algorithms get best worlds terms optimisation speed communication efficiency.,1929,1352,577,0.022,1.427,2025/11/05 17:18:54,0.01,1.521,0.3021806853582554,577.053
"Deep learning has found numerous applications thanks to its versatility and accuracy on pattern recognition problems such as visual object detection. Learning and inference in deep neural networks, however, are memory and compute intensive and so improving efficiency is one of the major challenges for frameworks such as PyTorch, Tensorflow, and Caffe. While the efficiency problem can be partially addressed with specialized hardware and its corresponding proprietary libraries, we believe that neural network acceleration should be transparent to the user and should support all hardware platforms and deep learning libraries. 

 To this end, we introduce a transparent middleware layer for neural network acceleration. The system is built around a compiler for deep learning, allowing one to combine device-specific libraries and custom optimizations while supporting numerous hardware devices. In contrast to other projects, we explicitly target the optimization of both prediction and training of neural networks. We present the current development status and some preliminary but encouraging results: on a standard x86 server, using CPUs our system achieves a 11.8x speed-up for inference and a 8.0x for batched-prediction (128); on GPUs we achieve a 1.7x and 2.3x speed-up respectively.",Deep learning has found numerous applications thanks versatility accuracy pattern recognition problems visual object detection. Learning inference deep neural networks however are memory compute intensive improving efficiency is one major challenges frameworks PyTorch Tensorflow Caffe. efficiency problem can be partially addressed specialized hardware corresponding proprietary libraries believe neural network acceleration should be transparent user should support hardware platforms deep learning libraries. end introduce transparent middleware layer neural network acceleration. system is built around compiler deep learning allowing one combine device-specific libraries custom optimizations supporting numerous hardware devices. contrast projects explicitly target optimization prediction training neural networks. present current development status preliminary encouraging results:standard x86 server using CPUs system achieves 11.8x speed-up inference 8.0x batched-prediction 128 GPUs achieve 1.7x 2.3x speed-up respectively.,236,159,77,0.003,1.484,2025/11/05 17:18:54,0.0,1.286,0.4797507788161991,90.213
"Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. In particular, to aid convolutional neural networks in learning rotation invariance, we consider a simple, efficient conic convolutional scheme that encodes rotational equivariance, along with a method for integrating the magnitude response of the 2D-discrete-Fourier transform (2D-DFT) to encode global rotational invariance. We call our new method the Conic Convolution and DFT Network (CFNet). We evaluated the efficacy of CFNet as compared to a standard CNN and group-equivariant CNN (G-CNN) for several different image classification tasks and demonstrated improved performance, including classification accuracy, computational efficiency, and its robustness to hyperparameter selection. Taken together, we believe CFNet represents a new scheme that has the potential to improve many imaging analysis applications. Though the appeal of neural networks is their versatility for arbitrary classification tasks, there is still much benefit in designing them for particular problem settings. In particular, their effectiveness can be greatly increased by encoding invariance to uniformative augmentations of the data BID17 . If such invariance is not explicitly encoded, the network must learn it from the data, perhaps with the help of data augmentation, requiring more parameters and thereby increasing its susceptibility to overfitting.A key invariance inherent to several computer vision settings, including satellite imagery and all forms of microscopy imagery, is rotation BID3 BID1 . Recently, there have been a variety of proposed approaches for encoding rotation equivariance and invariance, the most promising of which have formulated convolution over groups BID6 BID24 . Notably, G-CNNs have been applied to several biological imaging tasks, producing state-of-the-art results BID24 BID0 BID18 .Here we propose a new rotation-equivariant convolutional scheme, called conic convolution, which, in contrast to group convolution, encodes equivariance while still operating over only the spatial domain. Rather than convolving each filter across the entire image, as in standard convolution, rotated filters are convolved over corresponding conic regions of the input feature map that emanate from the origin, thereby transforming rotations in the input directly to rotations in the output. This scheme is intuitive, simple to implement, and computationally efficient. We also show that the method yields improved performance over group convolution on several relevant applications.Additionally, we propose the integration of the magnitude response of the 2D-discrete-Fourier transform (2D-DFT) into a transition layer between convolutional and fully-connected layers to encode rotational invariance. Though the insight of using the DFT to encode rotational invariance has been employed for texture classification using wavelets BID9 BID13 BID21 BID2 and for general image classification BID23 , as of yet, its application to CNNs has been overlooked. As in these prior works, rotations of the input are transformed to circular shifts, to which the magnitude response of the 2D-DFT is invariant, in the transformed space. Most other recently proposed rotationinvariance CNNs impose this invariance by applying a permutation-invariant operation, such as the average or maximum, over the rotation group, but since this operation is applied for each filter individually, possibly valuable pose information between filters is lost. In contrast, the 2D-DFT is able to integrate mutual pose information between different filter responses, yielding richer features for subsequent layers.We demonstrate the effectiveness of these two novel contributions for various applications: classifying rotated MNIST images, classifying synthetic images that model biomarker expression in microscopy images of cells, and localizing proteins in budding yeast cells BID15 . We show that CFNet improves classification accuracy generally over the standard raster convolution formulation and over the equivariant method of G-CNN across these settings. We also show that the 2D-DFT clearly improves performance across these diverse data sets, and that not only for conic convolution, but also for group convolution. Source code for the implementation of CFNet will be made available on GitHub.2 RELATED WORK BID6 introduced G-CNNs by formulating convolution over groups, including rotation, translation, and flips, for neural networks, which has inspired many subsequent improvements. By convolving over groups, equivariance to these groups is maintained throughout the convolutional layers, and invariance is enforced at the end of the network by pooling over groups. This work was improved upon by the design of steerable filters BID24 for convolution, similar to those proposed by BID25 , which allow for finer sampling of rotations of filters without inducing artifacts. Steerable filters were first proposed by BID10 and had been explored previously for image classification BID19 , but as shallow features in the context of HOG descriptors.An alternative means of encoding rotational equivariance is to transform the domain of the image to an alternative domain, such as the log-polar domain BID23 BID11 in which rotation becomes some other transformation that is easier to manage, in this case, translations. The suitability of this transformation depends upon the signal of interest, since this warping will introduce distortion, as pixels near the center of the image are sampled more densely than pixels near the perimeter. In addition, its stability to translations in the original domain is of concern. Our proposed CFNet, by convolving over conic regions, also encodes global rotation equivariance about the origin, but without introducing such distortion, which greatly helps mitigate its susceptibility to translation. The recently developed spatial transform layer BID12 and deformable convolutional layer BID7 allow the network to learn non-regular sampling patterns and can potentially help learning rotation invariance, though invariance is not explicitly enforced, which would most likely be a challenge for tasks with small training data.A simple means for achieving rotation equivariance and invariance was proposed by BID8 , in which feature maps of standard CNNs are made equivariant or invariant to rotation by combinations of cyclic slicing, stacking, rolling, and pooling. RotEqNet BID20 improved upon this idea by storing , for each feature map for a corresponding filter, only the maximal response across rotations and the value of the corresponding rotation, to preserve pose information. This approach yielded improved results and considerable storage savings over BID8 and G-CNN. These methods are most similar to our proposed conic convolution . However, in contrast, our method applies each filter only at the appropriate rotation within each conic region, which further saves on storage.To enforce rotation invariance, as noted, most of the previous methods apply some permutationinvariant, or pooling, operation over rotations. BID3 recently proposed a strategy of encouraging a network to learn a rotation invariant transform, and follow-up work improved this learning process by incorporating a Fisher discriminant penalty BID4 . However, the convolutional layers of the network do not maintain the property of rotation equivariance with the input image, which requires that the network learn this equivariance and could therefore hinder performance. Also, learning such a transform that generalizes to unseen data could prove difficult for settings with limited training data. BID23 previously proposed the 2D-DFT for rotational invariance. However , no method has yet been proposed to integrate the 2D-DFT into a rotation-equivariant CNN.","Performance neural networks can be significantly improved encoding known invariance particular tasks. Many image classification tasks related cellular imaging exhibit invariance rotation. particular aid convolutional neural networks learning rotation invariance consider simple efficient conic convolutional scheme encodes rotational equivariance along method integrating magnitude response 2D-discrete-Fourier transform 2D-DFT encode global rotational invariance. call new method Conic Convolution DFT Network CFNet evaluated efficacy CFNet compared standard CNN group-equivariant CNN G-CNN several different image classification tasks demonstrated improved performance including classification accuracy computational efficiency robustness hyperparameter selection. Taken together believe CFNet represents new scheme has the potential improve many imaging analysis applications. Though appeal neural networks is their versatility arbitrary classification tasks is still much benefit designing particular problem settings. particular effectiveness can be greatly increased encoding invariance uniformative augmentations data BID17. If such invariance is not explicitly encoded network must learn data perhaps help data augmentation requiring parameters thereby increasing susceptibility overfitting.A key invariance inherent several computer vision settings including satellite imagery forms microscopy imagery is rotation BID3 BID1. Recently have been variety proposed approaches encoding rotation equivariance invariance promising which have formulated convolution groups BID6 BID24. Notably G-CNNs have been applied several biological imaging tasks producing state-of-the-art results BID24 BID0 BID18.Here propose new rotation-equivariant convolutional scheme called conic convolution which,in contrast group convolution encodes equivariance still operating spatial domain. Rather convolving filter across entire image standard convolution rotated filters are convolved corresponding conic regions input feature map emanate origin thereby transforming rotations input directly rotations output. scheme is intuitive simple implement computationally efficient. also show method yields improved performance group convolution several relevant applications.Additionally propose integration magnitude response 2D-discrete-Fourier transform 2D-DFT transition layer convolutional fully-connected layers encode rotational invariance. Though insight using DFT encode rotational invariance has been employed texture classification using wavelets BID9 BID13 BID21 BID2 general image classification BID23 yet application CNNs has been overlooked. prior works rotations input are transformed circular shifts which the magnitude response 2D-DFT is invariant transformed space. recently proposed rotationinvariance CNNs impose invariance applying permutation-invariant operation average maximum is rotation group since operation is applied filter individually possibly valuable pose information filters is lost. contrast 2D-DFT is able integrate mutual pose information different filter responses yielding richer features subsequent layers.We demonstrate effectiveness two novel contributions various applications:classifying rotated MNIST images classifying synthetic images model biomarker expression microscopy images cells localizing proteins budding yeast cells BID15. show CFNet improves classification accuracy generally standard raster convolution formulation equivariant method G-CNN across settings. also show 2D-DFT clearly improves performance across diverse data sets conic convolution also group convolution. Source code implementation CFNet will be made available GitHub.2 RELATED WORK BID6 introduced G-CNNs formulating convolution groups including rotation translation flips neural networks which has inspired many subsequent improvements. convolving groups equivariance groups is maintained throughout convolutional layers invariance is enforced end network pooling groups. work was improved upon design steerable filters BID24 convolution similar proposed BID25 which allow finer sampling rotations filters without inducing artifacts. Steerable filters were first proposed BID10 had been explored previously image classification BID19 shallow features context HOG descriptors.An alternative means encoding rotational equivariance is to transform domain image alternative domain log-polar domain BID23 BID11 which rotation becomes transformation is easier manage case translations. suitability transformation depends upon signal interest since warping will introduce distortion pixels near center image are sampled densely pixels near perimeter. addition stability translations original domain is of concern. proposed CFNet convolving conic regions also encodes global rotation equivariance origin without introducing distortion which greatly helps mitigate susceptibility translation. recently developed spatial transform layer BID12 deformable convolutional layer BID7 allow network learn non-regular sampling patterns can potentially help learning rotation invariance though invariance is not explicitly enforced would likely challenge tasks small training data.A simple means achieving rotation equivariance invariance was proposed BID8 which feature maps standard CNNs are made equivariant invariant rotation combinations cyclic slicing stacking rolling pooling. RotEqNet BID20 improved upon idea storing which feature map corresponding filter maximal response across rotations value corresponding rotation preserve pose information. approach yielded improved results considerable storage savings BID8 G-CNN methods are most similar proposed conic convolution. However which,in contrast method applies filter appropriate rotation within conic region which further saves storage.To enforce rotation invariance noted previous methods apply permutationinvariant pooling operation rotations. BID3 recently proposed strategy encouraging network learn rotation invariant transform follow-up work improved learning process incorporating Fisher discriminant penalty BID4. However convolutional layers network do not maintain property rotation equivariance input image which requires network learn equivariance could therefore hinder performance. Also learning transform generalizes unseen data could prove difficult settings limited training data. BID23 previously proposed 2D-DFT rotational invariance. However method has yet proposed integrate 2D-DFT rotation-equivariant CNN.",1475,1020,455,0.016,1.446,2025/11/05 17:18:54,0.01,1.478,0.3613707165109031,448.952
"The problem of visual metamerism is defined as finding a family of perceptually
 indistinguishable, yet physically different images. In this paper, we propose our
 NeuroFovea metamer model, a foveated generative model that is based on a mixture
 of peripheral representations and style transfer forward-pass algorithms. Our
 gradient-descent free model is parametrized by a foveated VGG19 encoder-decoder
 which allows us to encode images in high dimensional space and interpolate
 between the content and texture information with adaptive instance normalization
 anywhere in the visual field. Our contributions include: 1) A framework for
computing metamers that resembles a noisy communication system via a foveated
feed-forward encoder-decoder network – We observe that metamerism arises as a
byproduct of noisy perturbations that partially lie in the perceptual null space; 2)
A perceptual optimization scheme as a solution to the hyperparametric nature of
our metamer model that requires tuning of the image-texture tradeoff coefficients
everywhere in the visual field which are a consequence of internal noise; 3) An
 ABX psychophysical evaluation of our metamers where we also find that the rate
 of growth of the receptive fields in our model match V1 for reference metamers
 and V2 between synthesized samples. Our model also renders metamers at roughly
 a second, presenting a ×1000 speed-up compared to the previous work, which now
 allows for tractable data-driven metamer experiments. The history of metamers originally started through color matching theory, where two light sources were used to match a test light's wavelength, until both light sources are indistinguishable from each other producing what is called a color metamer. This leads to the definition of visual metamerism: when two physically different stimuli produce the same perceptual response (See Figure 1 for an example). Motivated by BID1 's work of local texture matching in the periphery as a mechanism that explains visual crowding, BID7 were the first to create such point-of-fixation driven metamers through such local texture matching models that tile the entire visual field given log-polar pooling regions that simulate the V1 and V2 receptive field sizes, as well as having global image statistics that match the metamer with the original image. The essence of their algorithm is to use gradient descent to match the local texture BID22 ) and image statistics of the original image throughout the visual field given a point of fixation until convergence thus producing two images that are perceptually indistinguishable to each other.However, metamerism research currently faces 2 main limitations: The first is that metamer rendering faces no unique solution. Consider the potentially trivial examples of having an image I and its metamer M where all pixel values are identical except for one which is set to zero (making this difference unnoticeable), or the case where the metameric response arises from an imperceptible equal perturbation across all pixels as suggested in BID16 ; BID7 . This is a concept similar to Just Noticeable Differences BID21 BID5 ). However, like the work of BID7 ; BID17 ; BID23 ; BID1 , we are interested in creating point-of-fixation driven metamers, which create images that preserve information in the fovea, yet lose spatial information in the periphery such that this loss is unnoticeable contingent of a point of fixation (Figure 1 ). The second issue is that the current state of the art for a full field of view rendering of a 512px × 512px metamer takes 6 hours for a grayscale image and roughly a day for a color image. This computational constraint makes data- There has been a recent surge in interest with regards to developing and testing new metamer models: The SideEye model developed by BID8 , uses a fully convolutional network (FCN) as in BID20 and learns to map an input image into a Texture Tiling Model (TTM) mongrel BID23 ). Their end-to-end model is also feedforward like ours, but no use of noise is incorporated in the generation pipeline making their model fully deterministic. At first glance this seems to be an advantage rather a limitation, however it limits the biological plausilibility of metameric response as the same input image should be able to create more than one metamer. Another model which has recently been proposed is the CNN synthesis model developed by BID29 . The CNN synthesis model is gradient-descent based and is closest in flavor to the FS model, with the difference that their texture statistics are provided by a gramian matrix of filter activations of multiple layers of a VGGNet, rather than those used in BID22 .The question of whether the scaling parameter is the only parameter to be optimized for metamerism still seems to be open. This has been questioned early in BID23 , and recently proposed and studied by BID29 , who suggest that metamers are driven by image content, rather than bouma's law (scaling factor). FIG3 suggests that on average, it does seem that α must increase in proportion to retinal eccentricity, but this is conditioned by the image content of each receptive field. We believe that the hyperparametric nature of our model sheds some light into reconciling these two theories. Recall that in FIG0 , we found that certain images can be pushed stronger in the direction of it's texturized version versus others given their location in the encoded space, the local geometry of the surface, and their projection in the perceptual space. This suggests that the average maximal distortion one can do is fixed contingent on the size of the receptive field, but we are allowed to push further (increase α) for some images more than others, because the direction of the distortion lies closer to the perceptual null space (making this difference perceptually un-noticeable to the human observer). This is usually the case for regions of images that are periodic like skies, or grass. Along the same lines, we elaborate in the Supplementary Material on how our model may potentially explain why creating synthesized samples are metameric to each other at the scales of (V1;V2), but only generated samples at the scale of V1 (s = 0.25) are metameric to the reference image.Our model is also different to others (FS and recently Wallis et al. FORMULA0 ) given the role of noise in the computational pipeline. The previously mentioned models used noise as an initial seed for the texture matching pipeline via gradient-descent, while we use noise as a proxy for texture distortion that is directly associated with crowding in the visual field. One could argue that the same response is achieved via both approaches, but our approach seems to be more biologically plausible at the algorithmic level. In our model an image is fed through a non-linear hierarchical system (simulated through a deep-net), and is corrupted by noise that matches the texture properties of the input image (via AdaIN). This perceptual representation is perturbed along the direction of the texture-matched patch for each receptive field, and inverting such perturbed representation results in a metamer. FIG7 illustrates such perturbations which produce metamers when projected to a 2D subspace via the locally linear embedding (LLE) algorithm (Roweis & Saul FORMULA1 ). Indeed, the 10 encoded images do not fully overlap to each other and they are quite distant as seen in the 2D projection. However, foveated representations when perturbed with texture-like noise seem to finely tile the perceptual space, and might act as a type of biological regularizer for human observers who are consistently making eye-movements when processing visual information. This suggests that robust representations might be achieved in the human visual system given its foveated nature as non-uniform high-resolution imagery does not map to the same point in perceptual space. If this holds, perceptually invariant data-augmentation schemes driven by metamerism may be a useful enhancement for artificial systems that react oddly to adversarial perturbations that exploit coarse perceptual mappings (Goodfellow et al. FORMULA0 ; BID26 ; Berardino et al. FORMULA0 ).Understanding the underlying representations of metamerism in the human visual system still remains a challenge. In this paper we propose a model that emulates metameric responses via a foveated feed-forward style transfer network. We find that correctly calibrating such perturbations (a consequence of internal noise that match texture representation) in the perceptual space and inverting such encoded representation results in a metamer. Though our model is hyper-parametric in nature we propose a way to reduce the parametrization via a perceptual optimization scheme. Via a psychophysical experiment we empirically find that the critical scaling factor also matches the rate of growth of the receptive fields in V2 (s = 0.5) as in BID7 when performing visual discrimination between synthesized metamers, and match V1 (0.25) for reference metamers similar to BID29 . Finally, while our choice of texture statistics and transfer is relu4_1 of a VGG19 and AdaIN respectively, our ×1000-fold accelerated feed-forward metamer generation pipeline should be extendible to other models that correctly compute texture/style statistics and transfer. This opens the door to rapidly generating multiple flavors of visual metamers with applications in neuroscience and computer vision.6 Supplementary Material FIG0 : Reference Metamers at the scale of s = 0.25, at which they are indiscriminable to the human observer. The color coding scheme matches the data points of the optimization in Experiment 1 and the psychophysics of Experiment 2. All images used in the experiments were generated originally at 512 × 512 px subtending 26 × 26 d.v.a (degrees of visual angle). for each α ∈ [0 : DISPLAYFORM0 Compute metamer M NF (I) 9:end for 10:Find the α for each receptive field that minimizes: E(∆-SSIM) 2 . 11:Fit the γ s (•) function to collection of α values. 12:endfor 13: end for 14: Perform Permutation test on γ s for all s. 15: if γ s is independent of s then 16: γ s = γ 17: else 18:Perform regression of parameters of γ s as a function f of s. 19: DISPLAYFORM1 end if 21: end procedure",problem visual metamerism is defined finding family perceptually indistinguishable yet physically different images. paper propose NeuroFovea metamer model foveated generative model is based mixture peripheral representations style transfer forward-pass algorithms. gradient-descent free model is parametrized foveated VGG19 encoder-decoder which allowsus encode images high dimensional space interpolate content texture information adaptive instance normalization anywhere visual field. contributions include:1 framework computing metamers resembles noisy communication system via foveated feed-forward encoder-decoder network – observe metamerism arises byproduct noisy perturbations partially lie perceptual null space;2 perceptual optimization scheme solution hyperparametric nature metamer model requires tuning image-texture tradeoff coefficients everywhere visual field which are a consequence internal noise;3 ABX psychophysical evaluation metamers where we also find rate growth receptive fields model matchV1 reference metamers V2 synthesized samples. model also renders metamers roughly second presenting ×1000 speed-up compared previous work which now allows tractable data-driven metamer experiments. history metamers originally started color matching theory where two light sources were used match test light's wavelength light sources are indistinguishable producing what is called color metamer. leads definition visual metamerism:when two physically different stimuli produce perceptual response See Figure1 example Motivated BID1 's work local texture matching periphery mechanism explains visual crowding BID7 were the first create point-of-fixation driven metamers local texture matching models tile entire visual field given log-polar pooling regions simulate V1 V2 receptive field sizes well global image statistics match metamer original image. essence algorithm is to use gradient descent match local texture BID22 image statistics original image throughout visual field given point fixation convergence thus producing two images are perceptually indistinguishable other.However metamerism research currently faces 2 main limitations:first is that metamer rendering faces unique solution. Consider potentially trivial examples image metamer where all pixel values are identical except one which is set zero making difference unnoticeable case where the metameric response arises imperceptible equal perturbation across pixels suggested BID16;BID7. is a concept similar Noticeable Differences BID21 BID5 However like work BID7;BID17;BID23;BID1 are interested creating point-of-fixation driven metamers which create images preserve information fovea yet lose spatial information periphery loss is unnoticeable contingent point fixation Figure1 second issue is that the current state art full field view rendering 512px × 512px metamer takes 6 hours grayscale image roughly day color image. computational constraint makes data- has been a recent surge interest regards developing testing new metamer models:SideEye model developed BID8 uses fully convolutional network FCN BID20 learns map input image Texture Tiling Model TTM mongrel BID23 end-to-end model is also feedforward like use noise is incorporated generation pipeline making model fully deterministic. first glance seems advantage rather limitation however limits biological plausilibility metameric response input image should be able create one metamer. Another model which has recently proposed is the CNN synthesis model developed BID29. CNN synthesis model is gradient-descent based is closest flavor FS model difference texture statistics are provided gramian matrix filter activations multiple layers VGGNet rather used BID22.The question whether scaling parameter is the only parameter optimized metamerism still seems open. has been questioned early BID23 recently proposed studied BID29 who suggest metamers are driven image content rather bouma's law scaling factor FIG3 suggests average does seem α must increase proportion retinal eccentricity is conditioned image content receptive field. believe hyperparametric nature model sheds light reconciling two theories. Recall FIG0 found certain images can be pushed stronger direction texturized version versus others given location encoded space local geometry surface projection perceptual space. suggests average maximal distortion one can do is fixed contingent size receptive field are allowed push increaseα images others direction distortion lies closer perceptual null space making difference perceptually un-noticeable human observer is usually case regions images are periodic like skies grass. Along lines elaborate Supplementary Material how our model may potentially explain why creating synthesized samples are metameric scales V1;V2 generated samples scale V1 0.25 are metameric reference image.Our model is also different others FS recently Wallisetal. FORMULA0 given role noise computational pipeline. previously mentioned models used noise initial seed texture matching pipeline via gradient-descent use noise proxy texture distortion is directly associated crowding visual field. One could argue response is achieved via approaches approach seems biologically plausible algorithmic level. model image is fed non-linear hierarchical system simulated deep-net is corrupted noise matches texture properties input image via AdaIN perceptual representation is perturbed along direction texture-matched patch receptive field inverting perturbed representation results metamer. FIG7 illustrates perturbations which produce metamers when projected 2D subspace via locally linear embedding LLE algorithm Roweis Saul FORMULA1 Indeed 10 encoded images do not fully overlap are quite distant seen 2D projection. However foveated representations when perturbed texture-like noise seem finely tile perceptual space might act type biological regularizer human observers who are consistently making eye-movements when processing visual information. suggests robust representations might achieved human visual system given foveated nature non-uniform high-resolution imagery does not map point perceptual space. If this holds perceptually invariant data-augmentation schemes driven metamerism may useful enhancement artificial systems react oddly adversarial perturbations exploit coarse perceptual mappings Goodfellowetal. FORMULA0;BID26;Berardinoetal. FORMULA0.Understanding underlying representations metamerism human visual system still remains challenge. paper propose model emulates metameric responses via foveated feed-forward style transfer network. find correctly calibrating perturbations consequence internal noise match texture representation perceptual space inverting encoded representation results metamer. Though model is hyper-parametric nature propose way reduce parametrization via perceptual optimization scheme. Via psychophysical experiment empirically find critical scaling factor also matches rate growth receptive fields V2 0.5 BID7 when performing visual discrimination synthesized metamers matchV1 0.25 reference metamers similar BID29. Finally choice texture statistics transfer is relu4_1 VGG19 AdaIN respectively ×1000-fold accelerated feed-forward metamer generation pipeline should be extendible models correctly compute texture/style statistics transfer. opens door rapidly generating multiple flavors visual metamers applications neuroscience computer vision.6 Supplementary Material FIG0:Reference Metamers scale 0.25 which they are indiscriminable human observer. color coding scheme matches data points optimization Experiment1 psychophysics Experiment2. images used experiments were generated originally 512 × 512px subtending26×26.v.a degrees visual angle α∈ 0:DISPLAYFORM0 Compute metamer NF 9:end 10:Find α receptive field minimizes:E ∆-SSIM 2. 11:Fit γ • function collection α values. 12:endfor13:end 14:Perform Permutation test γ s. 15:ifγ is independent 16:γ γ17:else18:Perform regression parameters γ functionf s. 19:DISPLAYFORM1 end if21:end procedure,2149,1464,685,0.023,1.468,2025/11/05 17:18:54,0.01,1.438,0.4299065420560745,707.14
"Past works have shown that, somewhat surprisingly, over-parametrization can help generalization in neural networks. Towards explaining this phenomenon, we adopt a margin-based perspective. We establish: 1) for multi-layer feedforward relu networks, the global minimizer of a weakly-regularized cross-entropy loss has the maximum normalized margin among all networks, 2) as a result, increasing the over-parametrization improves the normalized margin and generalization error bounds for deep networks. In the case of two-layer networks, an infinite-width neural network enjoys the best generalization guarantees. The typical infinite feature methods are kernel methods; we compare the neural net margin with that of kernel methods and construct natural instances where kernel methods have much weaker generalization guarantees. We validate this gap between the two approaches empirically. Finally, this infinite-neuron viewpoint is also fruitful for analyzing optimization. We show that a perturbed gradient flow on infinite-size networks finds a global optimizer in polynomial time. In deep learning, over-parametrization refers to the widely-adopted technique of using more parameters than necessary (Krizhevsky et al., 2012; Livni et al., 2014) . Both computationally and statistically, over-parametrization is crucial for learning neural nets. Controlled experiments demonstrate that over-parametrization eases optimization by smoothing the non-convex loss surface (Livni et al., 2014; Sagun et al., 2017) . Statistically, increasing model size without any regularization still improves generalization even after the model interpolates the data perfectly (Neyshabur et al., 2017b) . This is surprising given the conventional wisdom on the trade-off between model capacity and generalization.In the absence of an explicit regularizer, algorithmic regularization is likely the key contributor to good generalization. Recent works have shown that gradient descent finds the minimum norm solution fitting the data for problems including logistic regression, linearized neural networks, and matrix factorization (Soudry et al., 2018; BID17 Li et al., 2018; BID16 Ji & Telgarsky, 2018) . Many of these proofs require a delicate analysis of the algorithm's dynamics, and some are not fully rigorous due to assumptions on the iterates. To the best of our knowledge, it is an open question to prove analogous results for even two-layer relu networks. (For example, the technique of Li et al. (2018) on two-layer neural nets with quadratic activations still falls within the realm of linear algebraic tools, which apparently do not suffice for other activations.)We propose a different route towards understanding generalization: making the regularization explicit. The motivations are: 1) with an explicit regularizer, we can analyze generalization without fully understanding optimization; 2) it is unknown whether gradient descent provides additional implicit regularization beyond what 2 regularization already offers; 3) on the other hand, with a sufficiently weak 2 regularizer, we can prove stronger results that apply to multi-layer relu networks. Additionally , explicit regularization is perhaps more relevant because 2 regularization is typically used in practice.Concretely, we add a norm-based regularizer to the cross entropy loss of a multi-layer feedforward neural network with relu activations. We show that the global minimizer of the regularized objective achieves the maximum normalized margin among all the models with the same architecture, if the regularizer is sufficiently weak (Theorem 2.1). Informally, for models with norm 1 that perfectly classify the data, the margin is the smallest difference across all datapoints between the classifier score for the true label and the next best score. We are interested in normalized margin because its inverse bounds the generalization error (see recent work BID5 Neyshabur et al., 2017a; BID14 or Proposition 3.1). Our work explains why optimizing the training loss can lead to parameters with a large margin and thus, better generalization error (see Corollary 3.2). We further note that the maximum possible margin is non-decreasing in the width of the architecture, and therefore the generalization bound of Corollary 3.2 can only improve as the size of the network grows (see Theorem 3.3). Thus, even if the dataset is already separable, it could still be useful to increase the width to achieve larger margin and better generalization.At a first glance, it might seem counterintuitive that decreasing the regularizer is the right approach. At a high level, we show that the regularizer only serves as a tiebreaker to steer the model towards choosing the largest normalized margin. Our proofs are simple, oblivious to the optimization procedure, and apply to any norm-based regularizer. We also show that an exact global minimum is unnecessary: if we approximate the minimum loss within a constant factor, we obtain the max-margin within a constant factor (Theorem 2.2).To better understand the neural network max-margin, in Section 4 we compare the max-margin two-layer network obtained by optimizing both layers jointly to kernel methods corresponding to fixing random weights for the hidden layer and solving a 2-norm max-margin on the top layer. We design a simple data distribution ( FIG3 ) where neural net margin is large but the kernel margin is small. This translates to an Ω( √ d) factor gap between the generalization error bounds for the two approaches and demonstrates the power of neural nets compared to kernel methods. We experimentally confirm that a gap does indeed exist.In the setting of two-layer networks, we also study how over-parametrization helps optimization. Prior works (Mei et al., 2018; BID10 Sirignano & Spiliopoulos, 2018; Rotskoff & Vanden-Eijnden, 2018) show that gradient descent on two-layer networks becomes Wasserstein gradient flow over parameter distributions in the limit of infinite neurons. For this setting, we prove that perturbed Wasserstein gradient flow finds a global optimizer in polynomial time.Finally, we empirically validate several claims made in this paper. First, we confirm that neural networks do generalize better than kernel methods. Second, we show that for two-layer networks, the test error decreases and margin increases as the hidden layer grows, as predicted by our theory. Zhang et al. (2016) and Neyshabur et al. (2017b) show that neural network generalization defies conventional explanations and requires new ones. Neyshabur et al. (2014) initiate the search for the "" inductive bias"" of neural networks towards solutions with good generalization. Recent papers (Hardt et al., 2015; BID8 BID9 ) study inductive bias through training time and sharpness of local minima. Neyshabur et al. (2015a) propose a new steepest descent algorithm in a geometry invariant to weight rescaling and show that this improves generalization. Morcos et al. (2018) relate generalization in deep nets to the number of ""directions"" in the neurons. Other papers BID15 Soudry et al., 2018; Nacson et al., 2018; BID17 Li et al., 2018; BID16 ) study implicit regularization towards a specific solution. Ma et al. (2017) show that implicit regularization can help gradient descent avoid overshooting optima. Rosset et al. (2004a; b) study logistic regression with a weak regularization and show convergence to the max margin solution. We adopt their techniques and extend their results. We have made the case that maximizing margin is one of the inductive biases of relu networks obtained from optimizing weakly-regularized cross-entropy loss. Our framework allows us to directly analyze generalization properties of the network without considering the optimization algorithm used to obtain it. Using this perspective, we provide a simple explanation for why over-parametrization can improve generalization. It is a fascinating question for future work to characterize other generalization properties of the max-margin solution. On the optimization side, we make progress towards understanding over-parametrized gradient descent by analyzing infinite-size neural networks. A natural direction for future work is to apply our theory to optimize the margin of finite-sized neural networks. Proof. We will argue in the setting of Theorem 2.1 where L λ is the multi-class cross entropy loss, because the logistic loss case is analogous. We first note that L λ is continuous in Θ because f is continuous in Θ and the term inside the logarithm is always positive. DISPLAYFORM0 However, there must be a value Θ λ which attains inf Θ ≤M L λ (Θ), because {Θ : Θ ≤ M } is a compact set and L λ is continuous. Thus, inf Θ L λ (Θ) is attained by some Θ λ .",Past works have shown somewhat surprisingly over-parametrization can help generalization neural networks. Towards explaining phenomenon adopt margin-based perspective. establish:1 multi-layer feedforward relu networks global minimizer weakly-regularized cross-entropy loss has the maximum normalized margin among networks 2 result increasing over-parametrization improves normalized margin generalization error bounds deep networks. case two-layer networks infinite-width neural network enjoys best generalization guarantees. typical infinite feature methods are kernel methods;compare neural net margin kernel methods construct natural instances where kernel methods have much weaker generalization guarantees. validate gap two approaches empirically. Finally infinite-neuron viewpoint is also fruitful analyzing optimization. show perturbed gradient flow infinite-size networks finds global optimizer polynomial time. deep learning over-parametrization refers widely-adopted technique using parameters necessary Krizhevskyetal. 2012;Livnietal. 2014 computationally statistically over-parametrization is crucial learning neural nets. Controlled experiments demonstrate over-parametrization eases optimization smoothing non-convex loss surface Livnietal. 2014;Sagunetal. 2017 Statistically increasing model size without regularization still improves generalization even model interpolates data perfectly Neyshaburetal. 2017b is surprising given conventional wisdom trade-off model capacity generalization.In absence explicit regularizer algorithmic regularization is likely key contributor good generalization. Recent works have shown gradient descent finds minimum norm solution fitting data problems including logistic regression linearized neural networks matrix factorization Soudryetal. 2018;BID17Lietal. 2018;BID16Ji Telgarsky 2018 Many proofs require delicate analysis algorithm's dynamics are fully rigorous due assumptions iterates. best knowledge is an open question prove analogous results even two-layer relu networks. example technique Lietal. 2018 two-layer neural nets quadratic activations still falls within realm linear algebraic tools which apparently do not suffice activations. propose different route towards understanding generalization:making regularization explicit. motivations are:1 explicit regularizer can analyze generalization without fully understanding optimization;2 is unknown whether gradient descent provides additional implicit regularization beyond what 2 regularization already offers;3 hand sufficiently weak 2 regularizer can prove stronger results apply multi-layer relu networks. Additionally explicit regularization is perhaps relevant 2 regularization is typically used practice.Concretely add norm-based regularizer cross entropy loss multi-layer feedforward neural network relu activations. show global minimizer regularized objective achieves maximum normalized margin among models architecture if the regularizer is sufficiently weak Theorem 2.1 Informally models norm1 perfectly classify data margin is the smallest difference across datapoints classifier score true label next best score. are interested normalized margin inverse bounds generalization error see recent work BID5 Neyshaburetal. 2017a;BID14 Proposition 3.1 work explains why optimizing training loss can lead parameters large margin thus better generalization error see Corollary 3.2 note maximum possible margin is non-decreasing width architecture therefore generalization bound Corollary 3.2 can only can improve size network grows see Theorem 3.3 Thus even if the dataset is already separable could still useful increase width achieve larger margin better generalization.At first glance might seem counterintuitive decreasing regularizer is the right approach. high level show regularizer serves tiebreaker steer model towards choosing largest normalized margin. proofs are simple oblivious optimization procedure apply norm-based regularizer. also show exact global minimum is unnecessary:if we approximate minimum loss within constant factor obtain max-margin within constant factor Theorem 2.2.To better understand neural network max-margin Section4 compare max-margin two-layer network obtained optimizing layers jointly kernel methods corresponding fixing random weights hidden layer solving 2-norm max-margin top layer. design simple data distribution FIG3 where neural net margin is large kernel margin is small. translates Ω √ factor gap generalization error bounds two approaches demonstrates power neural nets compared kernel methods. experimentally confirm gap does indeed exist.In setting two-layer networks also study how over-parametrization helps optimization. Prior works Meietal. 2018;BID10 Sirignano Spiliopoulos 2018;Rotskoff Vanden-Eijnden 2018 show gradient descent two-layer networks becomes Wasserstein gradient flow parameter distributions limit infinite neurons. setting can prove perturbed Wasserstein gradient flow finds global optimizer polynomial time.Finally empirically validate several claims made paper. First confirm neural networks do generalize better kernel methods. Second show two-layer networks test error decreases margin increases hidden layer grows predicted theory. Zhangetal. 2016 Neyshaburetal. 2017b show neural network generalization defies conventional explanations requires new ones. Neyshaburetal. 2014 initiate search inductive bias neural networks towards solutions good generalization. Recent papers Hardtetal. 2015;BID8 BID9 study inductive bias training time sharpness local minima. Neyshaburetal. 2015a propose new steepest descent algorithm geometry invariant weight rescaling show improves generalization. Morcosetal. 2018 relate generalization deep nets number directions neurons. papers BID15 Soudryet al. 2018;Nacsonetal. 2018;BID17Lietal. 2018;BID16 study implicit regularization towards specific solution. etal. 2017 show implicit regularization can help gradient descent avoid overshooting optima. Rossetetal. 2004a;b study logistic regression weak regularization show convergence max margin solution. adopt techniques extend results. have made case maximizing margin is one inductive biases relu networks obtained optimizing weakly-regularized cross-entropy loss. framework allowsus directly analyze generalization properties network without considering optimization algorithm used obtain it. Using perspective provide simple explanation why over-parametrization can only can improve generalization. is a fascinating question future work characterize generalization properties max-margin solution. optimization side make progress towards understanding over-parametrized gradient descent analyzing infinite-size neural networks. natural direction future work is to apply theory optimize margin finite-sized neural networks. Proof. will argue setting Theorem 2.1 whereLλ is the multi-class cross entropy loss logistic loss case is analogous. first note Lλ is continuous Θ f is continuous Θ term inside logarithm is always positive. DISPLAYFORM0 However must valueΘλ which attains infΘ≤M Lλ Θ Θ:Θ≤ is a compact set Lλ is continuous. Thus infΘLλ Θ is attained Θλ.,1830,1339,491,0.019,1.367,2025/11/05 17:18:54,0.01,1.236,0.1152647975077879,522.899
"We propose a distributed architecture for deep reinforcement learning at scale, that enables agents to learn effectively from orders of magnitude more data than previously possible. The algorithm decouples acting from learning: the actors interact with their own instances of the environment by selecting actions according to a shared neural network, and accumulate the resulting experience in a shared experience replay memory; the learner replays samples of experience and updates the neural network. The architecture relies on prioritized experience replay to focus only on the most significant data generated by the actors. Our architecture substantially improves the state of the art on the Arcade Learning Environment, achieving better final performance in a fraction of the wall-clock training time. A broad trend in deep learning is that combining more computation BID7 with more powerful models (Kaiser et al., 2017) and larger datasets BID8 ) yields more impressive results. It is reasonable to hope that a similar principle holds for deep reinforcement learning. There are a growing number of examples to justify this optimism: effective use of greater computational resources has been a critical factor in the success of such algorithms as Gorila (Nair et al., 2015) , A3C (Mnih et al., 2016) , GPU Advantage Actor Critic BID2 , Distributed PPO BID10 and AlphaGo (Silver et al., 2016) .Deep learning frameworks such as TensorFlow BID0 support distributed training, making large scale machine learning systems easier to implement and deploy. Despite this, much current research in deep reinforcement learning concerns itself with improving performance within the computational budget of a single machine, and the question of how to best harness more resources is comparatively underexplored.In this paper we describe an approach to scaling up deep reinforcement learning by generating more data and selecting from it in a prioritized fashion (Schaul et al., 2016) . Standard approaches to distributed training of neural networks focus on parallelizing the computation of gradients, to more rapidly optimize the parameters BID7 . In contrast , we distribute the generation and selection of experience data, and find that this alone suffices to improve results. This is complementary to distributing gradient computation, and the two approaches can be combined, but in this work we focus purely on data-generation.We use this distributed architecture to scale up variants of Deep Q-Networks (DQN) and Deep Deterministic Policy Gradient (DDPG), and we evaluate these on the Arcade Learning Environment benchmark BID4 , and on a range of continuous control tasks. Our architecture achieves a new state of the art performance on Atari games, using a fraction of the wall-clock time compared to the previous state of the art, and without per-game hyperparameter tuning.We empirically investigate the scalability of our framework, analysing how prioritization affects performance as we increase the number of data-generating workers. Our experiments include an analysis of factors such as the replay capacity, the recency of the experience, and the use of different data-generating policies for different workers. Finally, we discuss implications for deep reinforcement learning agents that may apply beyond our distributed framework. We have designed, implemented, and analyzed a distributed framework for prioritized replay in deep reinforcement learning. This architecture achieved state of the art results in a wide range of discrete and continuous tasks, both in terms of wall-clock learning speed and final performance.In this paper we focused on applying the Ape-X framework to DQN and DPG, but it could also be combined with any other off-policy reinforcement learning update. For methods that use temporally extended sequences (e.g., Mnih et al., 2016; BID10 , the Ape-X framework may be adapted to prioritize sequences of past experiences instead of individual transitions.Ape-X is designed for regimes in which it is possible to generate large quantities of data in parallel. This includes simulated environments but also a variety of real-world applications, such as robotic arm farms, self-driving cars, online recommender systems, or other multi-user systems in which data is generated by many instances of the same environment (c.f. Silver et al., 2013) . In applications where data is costly to obtain, our approach will not be directly applicable. With powerful function approximators, overfitting is an issue: generating more training data is the simplest way of addressing it, but may also provide guidance towards data-efficient solutions.Many deep reinforcement learning algorithms are fundamentally limited by their ability to explore effectively in large domains. Ape-X uses a naive yet effective mechanism to address this issue: generating a diverse set of experiences and then identifying and learning from the most useful events. The success of this approach suggests that simple and direct approaches to exploration may be feasible, even for synchronous agents.Our architecture illustrates that distributed systems are now practical both for research and, potentially, large-scale applications of deep reinforcement learning. We hope that the algorithms, architecture, and analysis we have presented will help to accelerate future efforts in this direction.Richard S Sutton and Andrew G Barto. fixed set of 6 values for . Blue: full range of values for . In both cases, the curve plotted is from a separate actor that does not add data to the replay memory, and which follows an -greedy policy with = 0.00164.",propose distributed architecture deep reinforcement learning scale enables agents learn effectively orders magnitude data previously possible. algorithm decouples acting learning:actors interact instances environment selecting actions according shared neural network accumulate resulting experience shared experience replay memory;learner replays samples experience updates neural network. architecture relies prioritized experience replay focus significant data generated actors. architecture substantially improves state art Arcade Learning Environment achieving better final performance fraction wall-clock training time. broad trend deep learning is that combining computation BID7 powerful models Kaiseretal. 2017 larger datasets BID8 yields impressive results. is reasonable hope similar principle holds deep reinforcement learning. are a growing number examples justify optimism:effective use greater computational resources has been a critical factor success algorithms Gorila Nairetal. 2015 A3C Mnihetal. 2016 GPU Advantage Actor Critic BID2 Distributed PPO BID10 AlphaGo Silveretal. 2016.Deep learning frameworks TensorFlow BID0 support distributed training making large scale machine learning systems easier implement deploy. Despite much current research deep reinforcement learning concerns improving performance within computational budget single machine question how to best harness resources is comparatively underexplored.In paper describe approach scaling deep reinforcement learning generating data selecting prioritized fashion Schauletal. 2016 Standard approaches distributed training neural networks focus parallelizing computation gradients rapidly optimize parameters BID7. contrast distribute generation selection experience data find alone suffices improve results. is complementary distributing gradient computation two approaches can be combined work focus purely data-generation.We use distributed architecture scale variants Deep Q-Networks DQN Deep Deterministic Policy Gradient DDPG evaluate Arcade Learning Environment benchmark BID4 range continuous control tasks. architecture achieves new state art performance Atari games using fraction wall-clock time compared previous state art without per-game hyperparameter tuning.We empirically investigate scalability framework analysing how prioritization affects performance increase number data-generating workers. experiments include analysis factors replay capacity recency experience use different data-generating policies different workers. Finally discuss implications deep reinforcement learning agents may apply beyond distributed framework. have designed implemented analyzed distributed framework prioritized replay deep reinforcement learning. architecture achieved state art results wide range discrete continuous tasks terms wall-clock learning speed final performance.In paper focused applying Ape-X framework DQN DPG could also combined off-policy reinforcement learning update. methods use temporally extended sequences e.g Mnihetal. 2016;BID10 Ape-X framework may adapted prioritize sequences past experiences instead individual transitions.Ape-X is designed regimes which it is possible generate large quantities data parallel. includes simulated environments also variety real-world applications robotic arm farms self-driving cars online recommender systems multi-user systems which data is generated many instances environment c.f Silveret al. 2013 applications where data is costly obtain approach will not be directly applicable. powerful function approximators overfitting is an issue:generating training data is the simplest way addressing may also provide guidance towards data-efficient solutions.Many deep reinforcement learning algorithms are fundamentally limited ability explore effectively large domains. Ape-X uses naive yet effective mechanism address issue:generating diverse set experiences identifying learning useful events. success approach suggests simple direct approaches exploration may feasible even synchronous agents.Our architecture illustrates distributed systems are now practical research potentially large-scale applications deep reinforcement learning. hope algorithms architecture analysis have presented will help accelerate future efforts direction.Richard Sutton Andrew G Barto. fixed set 6 values for. Blue:full range values for. cases curve plotted is from a separate actor does not add data replay memory which follows -greedy policy 0.00164,1042,691,351,0.011,1.508,2025/11/05 17:18:54,0.01,1.615,0.5545171339563861,321.998
"Designing neural networks for continuous-time stochastic processes is challenging, especially when observations are made irregularly. In this article, we analyze neural networks from a frame theoretic perspective to identify the sufficient conditions that enable smoothly recoverable representations of signals in L^2(R). Moreover, we show that, under certain assumptions, these properties hold even when signals are irregularly observed. As we converge to the family of (convolutional) neural networks that satisfy these conditions, we show that we can optimize our convolution filters while constraining them so that they effectively compute a Discrete Wavelet Transform. Such a neural network can efficiently divide the time-axis of a signal into orthogonal sub-spaces of different temporal scale and localization. We evaluate the resulting neural network on an assortment of synthetic and real-world tasks: parsimonious auto-encoding, video classification, and financial forecasting. The predominant assumption made in deep learning for time series analysis is that observations are made regularly, with the same duration of time separating each successive timestamps BID10 BID14 BID27 BID20 BID29 BID3 . However, this assumption is often inappropriate, as many real-world time series are observed irregularly and are, occasionally, event-driven (e.g., financial data, social networks, internet-of-things).One common approach in working with irregularly observed time series is to interpolate the observations to realign them to a regular time-grid. However , interpolation schemes may result in spurious statistical artifacts, as shown in BID17 BID4 . Fortunately , procedures for working with irregularly observed time series in their unaltered form have been devised, notably in the field of Gaussian-processes and kernel-learning BID17 BID4 and more recently in deep learning BID24 .In this article , we investigate the underlying representation of time series data as it is processed by a neural network. Our objective is to identify a class of neural networks that provably guarantee information preservation for certain irregularly observed signals. In doing so, we must analyze neural networks from a frame theoretic perspective, which has enabled a clear understanding of the impact discrete sampling has on representations of continuous-time signals BID7 BID5 BID6 BID13 BID15 BID22 .Although frame theory has historically been studied in the linear setting, recent work by BID26 has related frames with non-linear operators in Banach space, to what can be interpreted as non-linear frames. Here, we extend this generalization of frames to characterize entire families of neural networks. In doing so, we can show that the composition of certain non-linear neural layers (i.e., convolutions and fully-connected layers) form non-linear frames in L 2 (R), while others do not (i.e., recurrent layers).Moreover, frame theory can be used to analyze randomly-observed time series. In particular, when observations are made according to a family of self-exciting point processes known as Hawkes processes BID12 . We prove that such processes, under certain assumptions of stability, almost surely yield non-linear frames on a class of band-limited functions. That is to say , that despite having discrete and irregular observations, the signal of interest can still be smoothly recovered.As we obtain a family of convolutional neural networks that constitute non-linear frames, we show that under certain conditions, such networks can efficiently divide the time-axis of a time series into orthogonal sub-spaces of different temporal scale and localization. Namely, we optimize the weights of our convolution filters while constraining them so that they effectively compute a Discrete Wavelet Transform BID23 . Our numerical experiments on synthetic data highlight this unique capacity that allows neural networks to learn sparse representations of signals in L 2 (R), and how such a property is particularly powerful when training parsimoniously parameterized auto-encoders. Such auto-encoders learn optimal ways of compressing certain classes of input signals.Finally, we show that the ability of these networks to divide time series into a set sub-spaces, corresponding to different temporal scales and localization, can be composed with existing predictive frameworks to improve both accuracy and efficiency. This is demonstrated on real-world video classification and financial forecasting tasks. DISPLAYFORM0 We introduce the article with a theoretical analysis of the sufficient conditions on neural networks that enable smoothly recoverable representations of signals in L 2 (R) and prove that, under certain assumptions, this property holds true in the irregularly observed setting. In this article, we analyze neural networks from a frame theoretic perspective. In doing so, we come to the conclusion that by considering time series as an irregularly observed continuous-time stochastic processes, we are better able to devise robust and efficient convolutional neural networks. By leveraging recent contributions to frame theory, we prove properties about non-linear frames that allow us to make guarantees over an entire class of convolutional neural networks. Particularly regarding their capacity to produce discrete representations of continuous time signals that are both injective and bi-Lipschitz. Moreover, we show that, under certain conditions, these properties almost certainly hold, even when the signal is irregularly observed in an event-driven manner. Finally, we show that bounded-output recurrent neural networks do not satisfy the sufficient conditions to yield non-linear frames.This article is not limited to the theoretical statements it makes. In particular, we show that we can build a convolutional neural network that effectively computes a Discrete Wavelet Transform. The network's filters are dynamically learned while being constrained to produce outputs that preserve both orthogonality and the properties associated with non-linear frames. Our numerical experiments on real-world prediction tasks further demonstrate the benefits of such neural networks. Notably, their ability to produce compact representations that allow for efficient learning on latent continuous-time stochastic processes.","Designing neural networks continuous-time stochastic processes is challenging especially when observations are made irregularly. article analyze neural networks frame theoretic perspective identify sufficient conditions enable smoothly recoverable representations signals L^2 R Moreover show certain assumptions properties hold even when signals are irregularly observed. converge family convolutional neural networks satisfy conditions show can optimize convolution filters constraining effectively compute Discrete Wavelet Transform. neural network can efficiently divide time-axis signal orthogonal sub-spaces different temporal scale localization. evaluate resulting neural network assortment synthetic real-world tasks:parsimonious auto-encoding video classification financial forecasting. predominant assumption made deep learning time series analysis is that observations are made regularly duration time separating successive timestamps BID10 BID14 BID27 BID20 BID29 BID3. However assumption is often inappropriate many real-world time series are observed irregularly are,occasionally event-driven e.g financial data social networks internet-of-things.One common approach working irregularly observed time series is to interpolate observations realign regular time-grid However interpolation schemes may result spurious statistical artifacts shown BID17 BID4. Fortunately procedures working irregularly observed time series unaltered form have been devised notably field Gaussian-processes kernel-learning BID17 BID4 recently deep learning BID24.In article investigate underlying representation time series data is processed neural network. objective is to identify class neural networks provably guarantee information preservation certain irregularly observed signals. must analyze neural networks frame theoretic perspective which has enabled clear understanding impact discrete sampling has on representations continuous-time signals BID7 BID5 BID6 BID13 BID15 BID22.Although frame theory has historically studied linear setting recent work BID26 has related frames non-linear operators Banach space what can interpreted non-linear frames. extend generalization frames characterize entire families neural networks. can show composition certain non-linear neural layers.e convolutions fully-connected layers form non-linear frames L2 R others do not(i.e recurrent layers.Moreover frame theory can be used analyze randomly-observed time series. particular when observations are made according family self-exciting point processes known Hawkes processes BID12. prove processes certain assumptions stability almost surely yield non-linear frames class band-limited functions. is to say despite discrete irregular observations signal interest can still smoothly recovered.As obtain family convolutional neural networks constitute non-linear frames show certain conditions networks can efficiently divide time-axis time series orthogonal sub-spaces different temporal scale localization. Namely optimize weights convolution filters constraining effectively compute Discrete Wavelet Transform BID23. numerical experiments synthetic data highlight unique capacity allows neural networks learn sparse representations signals L2 R how property is particularly powerful when training training parsimoniously parameterized auto-encoders auto-encoders learn optimal ways compressing certain classes input signals.Finally show ability networks divide time series set sub-spaces corresponding different temporal scales localization can be composed existing predictive frameworks improve accuracy efficiency. is demonstrated real-world video classification financial forecasting tasks. DISPLAYFORM0 introduce article theoretical analysis sufficient conditions neural networks enable smoothly recoverable representations signals L2 R prove certain assumptions property holds true irregularly observed setting. article analyze neural networks frame theoretic perspective. come conclusion considering time series irregularly observed continuous-time stochastic processes are better able devise robust efficient convolutional neural networks. leveraging recent contributions frame theory prove properties non-linear frames allowus make guarantees entire class convolutional neural networks. Particularly regarding capacity produce discrete representations continuous time signals are both injective bi-Lipschitz Moreover show certain conditions properties almost certainly hold even when the signal is irregularly observed event-driven manner. Finally show bounded-output recurrent neural networks do not satisfy sufficient conditions yield non-linear frames.This article is not limited theoretical statements makes. particular show can build convolutional neural network effectively computes Discrete Wavelet Transform. network's filters are dynamically learned constrained produce outputs preserve orthogonality properties associated non-linear frames. numerical experiments real-world prediction tasks demonstrate benefits neural networks. Notably ability produce compact representations allow efficient learning latent continuous-time stochastic processes.",1143,779,364,0.013,1.467,2025/11/05 17:18:54,0.01,1.487,0.4267912772585671,345.364
"Most state-of-the-art neural machine translation systems, despite being different
 in architectural skeletons (e.g., recurrence, convolutional), share an indispensable
 feature: the Attention. However, most existing attention methods are token-based
 and ignore the importance of phrasal alignments, the key ingredient for the success
 of phrase-based statistical machine translation. In this paper, we propose
 novel phrase-based attention methods to model n-grams of tokens as attention
 entities. We incorporate our phrase-based attentions into the recently proposed
 Transformer network, and demonstrate that our approach yields improvements of
 1.3 BLEU for English-to-German and 0.5 BLEU for German-to-English translation
 tasks, and 1.75 and 1.35 BLEU points in English-to-Russian and Russian-to-English translation tasks 
 on WMT newstest2014 using WMT’16 training data.
 Neural Machine Translation (NMT) has established breakthroughs in many different translation tasks, and has quickly become the standard approach to machine translation. NMT offers a simple encoder-decoder architecture that is trained end-to-end. Most NMT models (except a few like BID5 and BID4 ) possess attention mechanisms to perform alignments of the target tokens to the source tokens. The attention module plays a role analogous to the word alignment model in Statistical Machine Translation or SMT BID9 . In fact, the Transformer network introduced recently by BID19 achieves state-of-the-art performance in both speed and BLEU scores BID12 by using only attention modules.On the other hand, phrasal interpretation is an important aspect for many language processing tasks, and forms the basis of Phrase-Based Machine Translation BID9 . Phrasal alignments BID10 can model one-to-one, one-to-many, many-to-one, and many-to-many relations between source and target tokens, and use local context for translation. They are also robust to non-compositional phrases. Despite the advantages, the concept of phrasal attentions has largely been neglected in NMT, as most NMT models generate translations token-by-token autoregressively, and use the token-based attention method which is order invariant. Therefore, the intuition of phrase-based translation is vague in existing NMT systems that solely depend on the underlying neural architectures (recurrent, convolutional, or self-attention) to incorporate contextual information. However, the information aggregation strategies employed by the underlying neural architectures provide context-relevant clues only to represent the current token, and do not explicitly model phrasal alignments. We argue that having an explicit inductive bias for phrases and phrasal alignments is necessary for NMT to exploit the strong correlation between source and target phrases.In this paper, we propose phrase-based attention methods for phrase-level alignments in NMT. Specifically, we propose two novel phrase-based attentions, namely CONVKV and QUERYK, designed to assign attention scores directly to phrases in the source and compute phrase-level attention vector for the target. We also introduce three new attention structures, which apply these methods to conduct phrasal alignments. Our homogeneous and heterogeneous attention structures perform token-to-token and token-to-phrase mappings, while the interleaved heterogeneous attention structure models all token-to-token, token-to-phrase, phrase-to-token, and phrase-to-phrase alignments.To show the effectiveness of our approach, we apply our phrase-based attention methods to all multi-head attention layers of the Transformer. Our experiments on WMT'14 translation tasks show improvements of up to 1.3 and 0.5 BLEU points for English-to-German and German-to-English respectively, and up to 1.75 and 1.35 BLEU points for English-to-Russian and Russian-to-English respectively, compared to the baseline Transformer network trained in identical settings.",state-of-the-art neural machine translation systems despite different architectural skeletons e.g recurrence convolutional share indispensable feature:Attention. However existing attention methods are token-based ignore importance phrasal alignments key ingredient success phrase-based statistical machine translation. paper propose novel phrase-based attention methods model n-grams tokens attention entities. incorporate phrase-based attentions recently proposed Transformer network demonstrate approach yields improvements 1.3 BLEU English-to-German 0.5 BLEU German-to-English translation tasks 1.75 1.35 BLEU points English-to-Russian Russian-to-English translation tasks WMT newstest2014 using WMT16 training data. Neural Machine Translation NMT has established breakthroughs many different translation tasks has quickly become standard approach machine translation. NMT offers simple encoder-decoder architecture is trained trained end-to-end NMT models except like BID5 BID4 possess attention mechanisms perform alignments target tokens source tokens. attention module plays role analogous word alignment model Statistical Machine Translation SMT BID9. fact Transformer network introduced recently BID19 achieves state-of-the-art performance speed BLEU scores BID12 using attention modules.On hand phrasal interpretation is an important aspect many language processing tasks forms basis Phrase-Based Machine Translation BID9. Phrasal alignments BID10 can model one-to-one one-to-many many-to-one many-to-many relations source target tokens use local context translation. are also robust non-compositional phrases. Despite advantages concept phrasal attentions has largely neglected NMT NMT models generate translations token-by-token autoregressively use token-based attention method which is order invariant. Therefore intuition phrase-based translation is vague existing NMT systems solely depend underlying neural architectures recurrent convolutional self-attention incorporate contextual information. However information aggregation strategies employed underlying neural architectures provide context-relevant clues represent current token do not explicitly model phrasal alignments. argue explicit inductive bias phrases phrasal alignments is necessary NMT exploit strong correlation source target phrases.In paper propose phrase-based attention methods phrase-level alignments NMT. Specifically propose two novel phrase-based attentions namely CONVKV QUERYK designed assign attention scores directly phrases source compute phrase-level attention vector target. also introduce three new attention structures which apply methods conduct phrasal alignments. homogeneous heterogeneous attention structures perform token-to-token token-to-phrase mappings interleaved heterogeneous attention structure models token-to-token token-to-phrase phrase-to-token phrase-to-phrase alignments.To show effectiveness approach which apply phrase-based attention methods multi-head attention layers Transformer. experiments WMT'14 translation tasks show improvements 1.3 0.5 BLEU points English-to-German German-to-English respectively 1.75 1.35 BLEU points English-to-Russian Russian-to-English respectively compared baseline Transformer network trained identical settings.,770,554,216,0.006,1.39,2025/11/05 17:18:54,0.0,1.308,0.1869158878504667,215.329
"Intuitively, unfamiliarity should lead to lack of confidence. In reality, current algorithms often make highly confident yet wrong predictions when faced with unexpected test samples from an unknown distribution different from training. Unlike domain adaptation methods, we cannot gather an ""unexpected dataset"" prior to test, and unlike novelty detection methods, a best-effort original task prediction is still expected. We compare a number of methods from related fields such as calibration and epistemic uncertainty modeling, as well as two proposed methods that reduce overconfident errors of samples from an unknown novel distribution without drastically increasing evaluation time: (1) G-distillation, training an ensemble of classifiers and then distill into a single model using both labeled and unlabeled examples, or (2) NCR, reducing prediction confidence based on its novelty detection score. Experimentally, we investigate the overconfidence problem and evaluate our solution by creating ""familiar"" and ""novel"" test splits, where ""familiar"" are identically distributed with training and ""novel"" are not. We discover that calibrating using temperature scaling on familiar data is the best single-model method for improving novel confidence, followed by our proposed methods. In addition, some methods' NLL performance are roughly equivalent to a regularly trained model with certain degree of smoothing. Calibrating can also reduce confident errors, for example, in gender recognition by 95% on demographic groups different from the training data. In machine learning and computer vision, the i.i.d. assumption, that training and test sets are sampled from the same distribution (henceforth ""familiar"" distribution), is so prevalent as to be left unwritten. In experiments, it is easy to satisfy the i.i.d. condition by randomly sampling training and test data from a single pool, such as photos of employees' faces. But in real-life applications, test samples are often sampled differently (e.g., faces of internet users) and may not be well-represented, if at all, by the training samples.Prior work BID24 has shown networks to be unreliable when tested on semantically unrelated input (e.g. feeding CIFAR into MNIST-trained networks), but users would not expect useful predictions on these data. However, we find this issue extends to semantically related input as well, such as gender classifiers applied to faces of older or younger people than those seen during training, which is a more common occurrence in practice and more problematic from a user's perspective. We demonstrate that, counter to the intuition that unfamiliarity should lead to lack of confidence, current algorithms (deep networks) are more likely to make highly confident wrong predictions when faced with such ""novel"" samples, both for real-world image datasets (Figure 1 ; see caption) and for toy datasets FIG1 ; see subcaption 2(a) and Appendix A). The reason is simple: the classification function, such as a deep network, is undefined or loosely regulated for areas of the feature space that are unobserved in training, so the learner may extrapolate wildly without penalty.Confident errors on novel samples can be catastrophic. Whether one would ride in a self-driving car with a 99.9% accurate vision system, probably depends on how well-behaved the car is on the 0.1% mistakes. When a trained model labeled a person as a gorilla BID52 , the public trust in that system was reduced. When a driving vision system confidently mistook a tractor trailer BID50 , a person died. Scholars that study the impact of AI on society consider differently distributed samples to be a major risk BID47 : ""This is one form of epistemic Novel herptile, model: 99.4% bird (ours: 76.5%) Novel fish, model: 99.0% bird (ours: 92.0%)Figure 1: Deep networks can often make highly confident mistakes when samples are drawn from outside the distribution observed during training. Shown are example images that have ages, breeds, or species that are not observed during training and are misclassified by a deep network model with high confidence. Using our methods (shown here is G-distillation, to distill an ensemble of networks on both training and unsupervised examples) makes fewer confident errors for novel examples, increasing the reliability of prediction confidence overall.uncertainty that is quite relevant to safety because training on a dataset from a different distribution can cause much harm."" Our trust in a system requires its ability to avoid confident errors.Unfortunately, these novel samples may differ from training in both expected and unexpected ways. This means gathering a set of ""unexpected"" training samples, though required by covariate shift and domain adaptation methods, becomes unviable BID47 . One may use novelty detection methods to identify novel samples at test time (to report an error or seek human guidance), but this may be insufficient. These ""outliers"" (e.g. underrepresented faces that users upload) are perfectly normal samples in the eyes of a user and they would reasonably expect a prediction. Also, human guidance may not be fast enough or affordable.In this paper, our aim is to reduce confident errors for predictions on samples from a different (often non-overlapping) but unknown distribution (henceforth ""novel"" distribution). In contrast with most recent work, we focus on the confidence of the prediction rather than only the most likely prediction (accuracy) or the confidence ordering (average precision or ROC). In addition to reviewing the effectiveness of established methods, we propose and evaluate two ideas that are straightforward extensions to ensemble and rejection methods. One is that multiple learners, with different initializations or subsamples of training data, may make different predictions on novel data (see BID24 ). Hence, ensembles of classifiers tend to be better behaved. But ensembles are slow to evaluate. If we distill BID18 an ensemble into a single model using the training data, the distilled classifier will have the original problem of being undefined for novel areas of the feature space. Fortunately, it is often possible to acquire many unlabeled examples, such as faces from a celebrity dataset. By distilling the ensemble on both the training set and on unsupervised examples, we can produce a single model that outperforms, in terms of prediction confidence, single and standard distilled models on both identically and differently distributed samples.Another idea is that if the training set does not provide enough information for the unseen data, therefore it may be desired to simply avoid confident predictions. We can lower their confidence according to the output of an off-the-shelf novelty detector. This means reducing confident errors by reducing confidence, regardless of correctness. It may improve novel sample prediction quality, but in turn degrade performance on familiar samples. Although this idea sounds like a natural extension to novelty detection, we are unaware of any implementation or analysis in the literature.Experimentally, we investigate the confidence problem and perform an extensive study by creating ""familiar"" and ""novel"" test splits, where ""familiar"" are identically distributed with training and (a) Demonstration of deep networks' generalization behavior with a 2-dimensional toy dataset ""square"". Column 1: we design a binary ground truth for classification on a 2-dimensional feature space. Column 2: for training, we only provide samples on the left and lower portions (the ""familiar"" distribution), and reserve the upper-right only for testing (the ""novel"" distribution). Column 3-7: we show negative log likelihood (NLL) predicted for each point in the feature space. A small NLL indicates correct prediction, while a very large NLL indicates a confident error. Column 3, 4: multiple runs of the network have similar performances on familiar regions but vary substantially in novel regions where the training data imposes little or no regulation, due to optimization randomness. Column 5: an ensemble of 10 such networks can smooth the predictions and reduce confident errors at the sacrifice of test efficiency. Column 6: distilling the ensemble using the training samples results in the same irregularities as single models. Column 7: one of our proposals is to distill the ensemble into a single model using both the labeled training data and unsupervised data from a ""general"" distribution. ""novel"" are not. For example, in cat vs. dog classification, the novel examples are from breeds not seen during training, or in gender classification, the novel examples are people that are older or younger than those seen during training. Our evaluation focuses on negative log likelihood (NLL) and the fraction of highly confident predictions that are misclassified (""E99""). They measure both prediction accuracy and how often confident errors occur. To summarize, our contributions are:• Draw attention to a counter-intuitive yet important problem of highly confident wrong predictions when samples are drawn from a unknown distribution that is different than training.• Evaluate and compare the effectiveness of methods in related fields, including two proposed methods to reduce such overconfident errors.• Propose an experimental methodology to study the problem by explicitly creating familiar and novel test splits and measuring performance with NLL and E99. In this paper, we draw attention to the importance of minimizing harm from confident errors in unexpected novel samples different from training. We propose an experiment methodology to explicitly study generalization issues with unseen novel data, and compare methods from several related fields. We propose two simple methods that use an ensemble and distillation to better regularize network behavior outside the training distribution, or reduce confidence on detected novel samples, and consequently reduce confident errors. For future work, it can be beneficial to investigate the ability to handle adversarial examples using this framework, and improve calibration with unexpected novel samples taken into account.",Intuitively unfamiliarity should lead lack confidence. reality current algorithms often make highly confident yet wrong predictions when faced unexpected test samples unknown distribution different training. Unlike domain adaptation methods cannot gather unexpected dataset prior test unlike novelty detection methods best-effort original task prediction is still expected. compare number methods related fields calibration epistemic uncertainty modeling well two proposed methods reduce overconfident errors samples unknown novel distribution without drastically increasing evaluation time:1 G-distillation if at all training ensemble classifiers distill single model using labeled unlabeled examples 2 NCR reducing prediction confidence based novelty detection score. Experimentally investigate overconfidence problem evaluate solution creating familiar novel test splits where familiar are identically distributed training novel are not. discover calibrating using temperature scaling familiar data is the best single-model method improving novel confidence followed proposed methods. addition methods' NLL performance are roughly equivalent regularly trained model certain degree smoothing. Calibrating can also reduce confident errors example gender recognition 95% demographic groups different training data. machine learning computer vision.i.d assumption if at all training test sets are sampled distribution henceforth familiar distribution is so prevalent left unwritten. experiments is easy satisfy.i.d condition randomly sampling training test data single pool photos employees' faces. real-life applications test samples are often sampled differently e.g faces internet users may well-represented if at all if at all training samples.Prior work BID24 has shown networks unreliable when tested semantically unrelated input e.g feeding CIFAR MNIST-trained networks users would expect useful predictions data. However find issue extends semantically related input well gender classifiers applied faces older younger people seen training whichisa common occurrence practice problematic user's perspective. demonstrate counter intuition unfamiliarity should lead lack confidence current algorithms deep networks are more likely make highly confident wrong predictions when faced novel samples real-world image datasets Figure1;see caption toy datasets FIG1;see subcaption2 Appendix reason is simple:classification function deep network is undefined loosely regulated areas feature space are unobserved training learner may extrapolate wildly without penalty.Confident errors novel samples can be catastrophic. Whether one would ride self-driving car 99.9 accurate vision system probably depends how well-behaved car is on the 0.1 0.1 mistakes. When a trained model labeled person gorilla BID52 public trust system was reduced. When a driving vision system confidently mistook tractor trailer BID50 person died. Scholars study impact AI society consider differently distributed samples major risk BID47:is one form epistemic Novel herptile model:99.4 bird ours:76.5 Novel fish model:99.0 bird ours:92.0 Figure1:Deep networks can often make highly confident mistakes when samples are drawn outside distribution observed training. Shown are example images have ages breeds species are not observed training are misclassified deep network model high confidence. Using methods shown is G-distillation distill ensemble networks training unsupervised examples makes fewer confident errors novel examples increasing reliability prediction confidence overall.uncertainty is quite relevant safety training dataset different distribution can cause much harm. trust system requires ability avoid confident errors.Unfortunately novel samples may differ training expected unexpected ways. means gathering set unexpected training samples though required covariate shift domain adaptation methods becomes unviable BID47. One may use novelty detection methods identify novel samples test time report error seek human guidance may insufficient. outliers e.g underrepresented faces users upload are perfectly normal samples eyes user would reasonably expect prediction. Also human guidance may fast enough affordable.In paper aim is to reduce confident errors predictions samples different often non-overlapping unknown distribution henceforth novel distribution contrast recent work focus confidence prediction rather likely prediction accuracy confidence ordering average precision ROC addition reviewing effectiveness established methods propose evaluate two ideas are straightforward extensions ensemble rejection methods. One is that multiple learners different initializations subsamples training data may make different predictions novel data see BID24 Hence ensembles classifiers tend better behaved. ensembles are slow evaluate. If we distill BID18 ensemble single model using training data distilled classifier will have the original problem undefined novel areas feature space. Fortunately is often possible acquire many unlabeled examples faces celebrity dataset. distilling ensemble training set unsupervised examples can produce single model outperforms terms prediction confidence single standard distilled models identically differently distributed samples.Another idea is that if the training set does not provide enough information unseen data therefore may desired simply avoid confident predictions. can lower confidence according output off-the-shelf novelty detector. means reducing confident errors reducing confidence regardless correctness. may improve novel sample prediction quality turn degrade performance familiar samples. Although idea sounds like natural extension novelty detection are unaware implementation analysis literature.Experimentally investigate confidence problem perform extensive study creating familiar novel test splits where familiar are identically distributed training Demonstration deep networks' generalization behavior 2-dimensional toy dataset square. Column1:design binary ground truth classification 2-dimensional feature space. Column2:training provide samples left lower portions familiar distribution reserve upper-right testing novel distribution Column 3-7 show negative log likelihood NLL predicted point feature space. small NLL indicates correct prediction large NLL indicates confident error. Column3 4:multiple runs network have similar performances familiar regions vary substantially novel regions where the training data imposes little regulation due optimization randomness. Column5:ensemble 10 networks can smooth predictions reduce confident errors sacrifice test efficiency. Column6:distilling ensemble using training samples results irregularities single models. Column7:one proposals is to distill ensemble single model using labeled training data unsupervised data general distribution. novel are not. example catvs. dog classification novel examples are from breeds seen training gender classification novel examples are people are older younger seen training. evaluation focuses negative log likelihood NLL fraction highly confident predictions are misclassified E99 measure prediction accuracy how often confident errors occur. summarize contributions are:• Draw attention counter-intuitive yet important problem highly confident wrong predictions when samples are drawn unknown distribution is different training.• Evaluate compare effectiveness methods related fields including two proposed methods reduce overconfident errors.• Propose experimental methodology study problem explicitly creating familiar novel test splits measuring performance NLL E99. paper draw attention importance minimizing harm confident errors unexpected novel samples different training. propose experiment methodology explicitly study generalization issues unseen novel data compare methods several related fields. propose two simple methods use ensemble distillation better regularize network behavior outside training distribution reduce confidence detected novel samples consequently reduce confident errors. future work can be beneficial investigate ability handle adversarial examples using framework improve calibration unexpected novel samples taken account.,1959,1285,674,0.025,1.525,2025/11/05 17:18:54,0.01,1.435,0.6074766355140183,689.764
"Progress in deep learning is slowed by the days or weeks it takes to train large models. The natural solution of using more hardware is limited by diminishing returns, and leads to inefficient use of additional resources. In this paper, we present a large batch, stochastic optimization algorithm that is both faster than widely used algorithms for fixed amounts of computation, and also scales up substantially better as more computational resources become available. Our algorithm implicitly computes the inverse Hessian of each mini-batch to produce descent directions; we do so without either an explicit approximation to the Hessian or Hessian-vector products. We demonstrate the effectiveness of our algorithm by successfully training large ImageNet models (InceptionV3, ResnetV1-50, ResnetV1-101 and InceptionResnetV2) with mini-batch sizes of up to 32000 with no loss in validation error relative to current baselines, and no increase in the total number of steps. At smaller mini-batch sizes, our optimizer improves the validation error in these models by 0.8-0.9\%. Alternatively, we can trade off this accuracy to reduce the number of training steps needed by roughly 10-30\%. Our work is practical and easily usable by others -- only one hyperparameter (learning rate) needs tuning, and furthermore, the algorithm is as computationally cheap as the commonly used Adam optimizer. Large deep neural networks trained on massive data sets have led to major advances in machine learning performance BID21 ). Current practice is to train networks using gradient descent (SGD) and momentum optimizers, along with natural-gradient-like methods BID16 ; Zeiler (2012); BID10 ; BID20 ). As distributed computation availability increases, total wall-time to train large models has become a substantial bottleneck, and approaches that decrease total wall-time without sacrificing model generalization are very valuable.In the simplest version of mini-batch SGD, one computes the average gradient of the loss over a small set of examples, and takes a step in the direction of the negative gradient. It is well known that the convergence of the original SGD algorithm BID28 ) has two terms, one of which depends on the variance of the gradient estimate. In practice, decreasing the variance by increasing the batch size suffers from diminishing returns, often resulting in speedups that are sublinear in batch size, and even worse, in degraded generalization performance BID19 ). Some recent work BID12 ; BID40 b) ) suggests that by carefully tuning learning rates and other hyperparameter schedules, it is possible to train architectures like ResNets and AlexNet on Imagenet with large mini-batches of up to 8192 with no loss of accuracy, shortening training time to hours instead of days or weeks.There have been many attempts to incorporate second-order Hessian information into stochastic optimizers (see related work below). Such algorithms either explicitly approximate the Hessian (or its inverse), or exploit the use of Hessian-vector products. Unfortunately, the additional computational cost and implementation complexity often outweigh the benefit of improved descent directions. Con-sequently, their adoption has been limited, and it has largely been unclear whether such algorithms would be successful on large modern machine learning tasks.In this work, we attack the problem of training with reduced wall-time via a novel stochastic optimization algorithm that uses (limited) second order information without explicit approximations of Hessian matrices or even Hessian-vector products. On each mini-batch, our algorithm computes a descent direction by solving an intermediate optimization problem, and inverting the Hessian of the mini-batch. Explicit computations with Hessian matrices are extremely expensive, so we develop an inner loop iteration that applies the Hessian inverse without explicitly representing the Hessian, or computing a Hessian vector product. The key ingredients in this iteration are the Neumann series expansion for the matrix inverse, and an observation that allows us to replace each occurrence of the Hessian with a single gradient evaluation.We conduct large-scale experiments using real models (Inception-V3, Resnet-50, Resnet-101, Inception-Resnet-V2) on the ImageNet dataset. Compared to recent work, our algorithm has favourable scaling properties; we are able to obtain linear speedup up to a batch size of 32000, while maintaining or even improving model quality compared to the baseline. Additionally, our algorithm when run using smaller mini-batches is able to improve the validation error by 0.8-0.9% across all the models we try; alternatively, we can maintain baseline model quality and obtain a 10-30% decrease in the number of steps. Our algorithm is easy to use in practice, with the learning rate as the sole hyperparameter. In this paper, we have presented a large batch optimization algorithm for training deep neural nets; roughly speaking, our algorithm implicitly inverts the Hessian of individual mini-batches. Our algorithm is practical, and the only hyperparameter that needs tuning is the learning rate. Experimentally, we have shown the optimizer is able to handle very large mini-batch sizes up to 32000 without any degradation in quality relative to current baseline models. Intriguingly, at smaller mini-batch sizes, the optimizer is able to produce models that generalize better, and improve top-1 validation error by 0.8-0.9% across a variety of architectures with no attendant drop in the classification loss.We believe the latter phenomenon is worth further investigation, especially since the Neumann optimizer does not improve the training loss. This indicates that, somehow, the optimizer has found a different local optimum. We think that this confirms the general idea that optimization and generalization can not be decoupled in deep neural nets.Matthew D Zeiler. Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701, 2012.",Progress deep learning is slowed days weeks takes train large models. natural solution using hardware is limited diminishing returns leads inefficient use additional resources. paper present large batch stochastic optimization algorithm is both faster widely used algorithms fixed amounts computation also scales substantially better computational resources become available. algorithm implicitly computes inverse Hessian mini-batch produce descent directions;do so without either explicit approximation Hessian Hessian-vector products. demonstrate effectiveness algorithm successfully training large ImageNet models InceptionV3 ResnetV1-50 ResnetV1-101 InceptionResnetV2 mini-batch sizes 32000 loss validation error relative current baselines increase total number steps. smaller mini-batch sizes optimizer improves validation error models 0.8-0.9\ %. Alternatively can trade accuracy reduce number training steps needed roughly 10-30\%. work is practical easily usable others one hyperparameter learning rate needs tuning furthermore algorithm is as computationally cheap commonly used Adam optimizer. Large deep neural networks trained massive data sets have led major advances machine learning performance BID21 Current practice is to train networks using gradient descent SGD momentum optimizers along natural-gradient-like methods BID16;Zeiler 2012 BID10;BID20 distributed computation availability increases total wall-time train large models has become substantial bottleneck approaches decrease total wall-time without sacrificing model generalization are very valuable.In simplest version mini-batch SGD one computes average gradient loss small set examples takes step direction negative gradient. is well known convergence original SGD algorithm BID28 has two terms one which depends variance gradient estimate. practice decreasing variance increasing batch size suffers diminishing returns often resulting speedups are sublinear batch size even worse degraded generalization performance BID19 recent work BID12;BID40b suggests carefully tuning learning rates hyperparameter schedules is possible train architectures like ResNets AlexNet Imagenet large mini-batches 8192 loss accuracy shortening training time hours instead days weeks.There have been many attempts incorporate second-order Hessian information stochastic optimizers see related work algorithms either explicitly approximate Hessian inverse exploit use Hessian-vector products. Unfortunately additional computational cost implementation complexity often outweigh benefit improved descent directions. Con-sequently adoption has been limited has largely unclear whether algorithms would successful large modern machine learning tasks.In work attack problem training reduced wall-time via novel stochastic optimization algorithm uses limited second order information without explicit approximations Hessian matrices even Hessian-vector products. mini-batch algorithm computes descent direction solving intermediate optimization problem inverting Hessian mini-batch Explicit computations Hessian matrices are extremely expensive develop inner loop iteration applies Hessian inverse without explicitly representing Hessian computing Hessian vector product. key ingredients iteration are the Neumann series expansion matrix inverse observation allowsus replace occurrence Hessian single gradient evaluation.We conduct large-scale experiments using real models Inception-V3 Resnet-50 Resnet-101 Inception-Resnet-V2 ImageNet dataset. Compared recent work algorithm has favourable scaling properties;are able obtain linear speedup batch size 32000 maintaining even improving model quality compared baseline. Additionally algorithm when run using smaller mini-batches is able improve validation error 0.8-0.9 across models try;alternatively can maintain baseline model quality obtain 10-30 decrease number steps. algorithm is easy use practice learning rate sole hyperparameter. paper have presented large batch optimization algorithm training deep neural nets;roughly speaking algorithm implicitly inverts Hessian individual mini-batches algorithm is practical hyperparameter needs tuning is the learning rate. Experimentally have shown optimizer is able handle large mini-batch sizes 32000 without degradation quality relative current baseline models. Intriguingly smaller mini-batch sizes optimizer is able produce models generalize better improve top-1 validation error 0.8-0.9 across variety architectures attendant drop classification loss.We believe latter phenomenon is worth investigation especially since Neumann optimizer does not improve training loss. indicates somehow optimizer has found different local optimum. think confirms general idea optimization generalization can not be decoupled deep neural nets.Matthew Zeiler. Adadelta:adaptive learning rate method. arXiv preprint arXiv:1212.5701 2012.,1183,822,361,0.011,1.439,2025/11/05 17:18:54,0.01,1.353,0.3395638629283489,342.731
"Recent work has shown that performing inference with fast, very-low-bitwidth
 (e.g., 1 to 2 bits) representations of values in models can yield surprisingly accurate
 results. However, although 2-bit approximated networks have been shown to
 be quite accurate, 1 bit approximations, which are twice as fast, have restrictively
 low accuracy. We propose a method to train models whose weights are a mixture
 of bitwidths, that allows us to more finely tune the accuracy/speed trade-off. We
 present the “middle-out” criterion for determining the bitwidth for each value, and
 show how to integrate it into training models with a desired mixture of bitwidths.
 We evaluate several architectures and binarization techniques on the ImageNet
 dataset. We show that our heterogeneous bitwidth approximation achieves superlinear
 scaling of accuracy with bitwidth. Using an average of only 1.4 bits, we are
 able to outperform state-of-the-art 2-bit architectures. With Convolutional Neural Nets (CNNs) now outperforming humans in vision classification tasks BID11 , it is clear that CNNs will be a mainstay of AI applications. However, CNNs are known to be computationally demanding, and are most comfortably run on GPUs. For execution in mobile and embedded settings, or when a given CNN is evaluated many times, using a GPU may be too costly. The search for inexpensive variants of CNNs has yielded techniques such as hashing BID0 , vector quantization BID4 , and pruning BID5 . One particularly promising track is binarization BID1 , which replaces 32-bit floating point values with single bits, either +1 or -1, and (optionally) replaces floating point multiplies with packed bitwise popcount-xnors . Binarization can reduce the size of models by up to 32×, and reduce the number of operations executed by up to 64×.Binarized CNNs are faster and smaller, but also less accurate. Much research has therefore focused on reducing the accuracy gap between binary models and their floating point counterparts. The typical approach is to add bits to the activations and weights of a network, giving a better approximation of the true values. However, the cost of extra bits is quite high. Using n bits to approximate just the weights increases the computation and memory required by a factor of n compared to 1-bit binarization. Further using n bits to approximate activations as well requires n 2 times the resources as one bit. There is thus a strong motivation to use as few bits as possible while still achieving acceptable accuracy. However, today's binary approximations are locked to use the same number of bits for all approximated values, and the gap in accuracy between bits can be substantial. For example, recent work concludes 1-bit accuracy is unsatisfactory while 2-bit accuracy is quite high BID12 (also see TAB0 ).In order to bridge the gap between integer bits, we introduce Heterogeneous Bitwidth Neural Networks (HBNNs), which use a mix of integer bitwidths to allow values to have effectively (i.e., on average) fractional bitwidths. The freedom to select from multiple bitwidths allows HBNNs to approximate each value better than fixed-bitwidth schemes, giving them disproportionate accuracy gains for the number of effective bits used. For instance, Alexnet trained with an average of 1.4 bits has comparable (actually, slightly higher) accuracy to training with a fixed two bits TAB0 .Our main contributions are:(1) We propose HBNNs as a way to break the integer-bitwidth barrier in binarized networks.(2) We study several techniques for distributing the bitwidths in a HBNN, and introduce the middle-out bitwidth selection algorithm, which uses the full representational power of heterogeneous bitwidths to learn good bitwidth distributions. (3) We perform a comprehensive study of heterogeneous binarization on the ImageNet dataset using an AlexNet architecture. We evaluate many fractional bitwidths and compare to state of the art results. HBNNs typically yield the smallest and fastest networks at each accuracy. Further, we show that it is usually possible to equal, or improve upon, 2-bitbinarized networks with an average of 1.4 bits. (4) We show that heterogeneous binarization is applicable to MobileNet BID6 , demonstrating that its benefits apply even to modern, optimized architectures. In this paper, we present Heterogeneous Bitwidth Neural Networks (HBNNs), a new type of binary network that is not restricted to integer bitwidths. Allowing effectively fractional bitwidths in networks gives a vastly improved ability to tune the trade-offs between accuracy, compression, and speed that come with binarization. We show a simple method of distributing bits across a tensor lead to a linear relationship between accuracy and number of bits, but using a more informed method allows higher accuracy with fewer bits. We introduce middle-out bit selection as the top performing technique for determining where to place bits in a heterogeneous bitwidth tensor and find that Middle-Out enables a heterogeneous representation to be more powerful than a homogeneous one. On the ImageNet dataset with AlexNet and MobileNet models, we perform extensive experiments to validate the effectiveness of HBNNs compared to the state of the art and full precision accuracy. The results of these experiments are highly compelling, with HBNNs matching or outperforming competing binarization techniques while using fewer average bits. The use of HBNNs enables applications which require higher compression and speeds offered by a low bitwidth but also need the accuracy of a high bitwidth. As future work, we will investigate modifying the bit selection method to make heterogeneous bit tensors more amenable for CPU computation as well as develop a HBNN FPGA implementation which can showcase both the speed and accuracy benefits of heterogeneous binarization.",Recent work has shown performing inference fast very-low-bitwidth e.g 1 2 bits representations values models can yield surprisingly accurate results. However although 2-bit approximated networks have been shown quite accurate 1 bit approximations which are twice fast have restrictively low accuracy. propose method train models whose weights are a mixture bitwidths allowsus finely tune accuracy/speed trade-off present middle-out criterion determining bitwidth value show how to integrate training models desired mixture bitwidths. evaluate several architectures binarization techniques ImageNet dataset. show heterogeneous bitwidth approximation achieves superlinear scaling accuracy bitwidth. Using average 1.4 bits are able outperform state-of-the-art 2-bit architectures. Convolutional Neural Nets CNNs outperforming humans vision classification tasks BID11 is clear CNNs will be a mainstay AI applications. However CNNs are known computationally demanding are most comfortably run GPUs. execution mobile embedded settings when a given CNN is evaluated many times using GPU may costly. search inexpensive variants CNNs has yielded techniques hashing BID0 vector quantization BID4 pruning BID5. One particularly promising track is binarization BID1 which replaces 32-bit floating point values single bits either+1 -1 optionally replaces floating point multiplies packed bitwise popcount-xnors Binarization can reduce size models 32× reduce number operations executed 64×.Binarized CNNs are faster smaller also less accurate. Much research has therefore focused reducing accuracy gap binary models floating point counterparts. typical approach is to add bits activations weights network giving better approximation true values. However cost extra bits is quite high. Using n bits approximate weights increases computation memory required factor n compared 1-bit binarization. using n bits approximate activations well requiresn2 times resources one bit. is thus strong motivation use bits possible still achieving acceptable accuracy. However today's binary approximations are locked use number bits approximated values gap accuracy bits can be substantial. example recent work concludes 1-bit accuracy is unsatisfactory 2-bit accuracy is quite high BID12 also see TAB0.In order bridge gap integer bits introduce Heterogeneous Bitwidth Neural Networks HBNNs which use mix integer bitwidths allow values have effectively.e average fractional bitwidths. freedom select multiple bitwidths allows HBNNs approximate value better fixed-bitwidth schemes giving disproportionate accuracy gains number effective bits used. instance Alexnet trained average 1.4 bits has comparable actually slightly higher accuracy training fixed two bits TAB0.Our main contributions are:1 propose HBNNs way break integer-bitwidth barrier binarized networks. 2 study several techniques distributing bitwidths HBNN introduce middle-out bitwidth selection algorithm which uses full representational power heterogeneous bitwidths learn good bitwidth distributions. 3 perform comprehensive study heterogeneous binarization ImageNet dataset using AlexNet architecture. evaluate many fractional bitwidths compare state art results. HBNNs typically yield smallest fastest networks accuracy. show is usually possible equal improve upon 2-bitbinarized networks average 1.4 bits. 4 show heterogeneous binarization is applicable MobileNet BID6 demonstrating benefits apply even modern optimized architectures. paper present Heterogeneous Bitwidth Neural Networks HBNNs new type binary network is not restricted integer bitwidths. Allowing effectively fractional bitwidths networks gives vastly improved ability tune trade-offs accuracy compression speed come binarization. show simple method distributing bits across tensor lead linear relationship accuracy number bits using informed method allows higher accuracy fewer bits. introduce middle-out bit selection top performing technique determining where to place bits heterogeneous bitwidth tensor find Middle-Out enables heterogeneous representation powerful homogeneous one. ImageNet dataset AlexNet MobileNet models perform extensive experiments validate effectiveness HBNNs compared state art full precision accuracy. results experiments are highly compelling HBNNs matching outperforming competing binarization techniques using fewer average bits. use HBNNs enables applications which require higher compression speeds offered low bitwidth also need accuracy high bitwidth. future work will investigate modifying bit selection method make heterogeneous bit tensors amenable CPU computation well develop HBNN FPGA implementation which can showcase speed accuracy benefits heterogeneous binarization.,1198,830,368,0.012,1.443,2025/11/05 17:18:54,0.01,1.342,0.35202492211838,347.767
"Pruning units in a deep network can help speed up inference and training as well as reduce the size of the model. We show that bias propagation is a pruning technique which consistently outperforms the common approach of merely removing units,  regardless of the architecture and the dataset.   We also show how a simple adaptation to an existing scoring function allows us to select the best units to prune.   Finally,  we show that the units selected by the best performing scoring functions are somewhat consistent over the course of training, implying the dead parts of the network appear during the stages of training. Pruning is a successful method for reducing the size of a trained neural network and accelerating inference. Pruning consists of deleting the parts of the network whose removal least affects the network performance. Many pruning methods proposed in the literature differ in computational cost and in effectiveness in ways that are hard to assess.In an interesting recent work, BID3 argue for the so called ""winning ticket"" hypothesis. More precisely, they train a large network after saving the random initial value of each parameter. After training, they prune the large network to produce a smaller network with one fifth of the weights. Setting its weights to their saved initial values and retraining achieves a performance close to that of the large trained network with a much reduced computational cost. This result opens up a new frontier for pruning methods, where they are used to detect useless units early in the training and therefore accelerating the inference.This contribution studies the effect of pruning methods throughout the training process. We also present mean replacement, a unit pruning method that extends the idea of bias propagation introduced in (Ye et al., 2018) to the non-constrained training setting. The main observations of our work can then be summarized as follows:• Regardless of the scoring function used, bias propagation reduces the pruning penalty for networks without batch normalization.• Fine-tuning the pruned network with additional training iterations reduces the bias propagation advantage but not very quickly.• Absolute valued approximation of the pruning penalty provides superior performance over the normal first order approximation. This finding confirms the observations made by BID11 .• Units that are selected by the best performing scoring function seem to come from a small subset of units. This finding confirms BID3 's comments on the lottery ticket and BID2 's claims about dead units.The rest of the paper is organized as follows. After reviewing the related work in Section 2. we define our pruning methods and scoring functions in Section 3. Section 4 provides an empirical evaluation comparing various combinations of scoring functions and methods under varying pruning fractions, datasets, and models. We briefly provide some concluding remarks and discuss future work in Section 5. This work presents an experimental comparison of unit pruning strategies throughout the training process. We introduce the mean replacement approach and show that it substantially reduces the impact of the unit removal on the loss function. We also show that fine-tuning the pruned networks does not reduce the mean replacement advantage very quickly. We argue that direct first order approximation of the pruning penalty are poor predictors of the pruning penalty incurred by the simultaneous removal of multiple units because the neglected high order terms can become significant. In contrast the absolute value versions of these approximations achieve the best performance. Finally we provide some evidence showing that our best pruning methods identify a stable set of prunable units relatively early in the training process.This last observation begs for future work. Can we combine pruning and training in a manner that reduces the computational training cost to a quantity comparable to training the ""winning ticket"" network? If we decided that we will be using Mean Replacement as our pruning method, we can define a new scoring function, i.e. the first order Taylor approximation of the pruning penalty after mean replacement. We name this new saliency function as Mean Replacement Saliency (MRS) Let us parameterize the loss as a function with activations and write down the first order approximation of the absolute change in the loss. DISPLAYFORM0 where DISPLAYFORM1 If we were interested in the average change in the loss we can write down the Equation 5 without the absolute values. In other words approximations on absolute change penalizes both directions, emphasizing the change in the neural network itself rather then the loss function.",Pruning units deep network can help speed inference training well reduce size model. show bias propagation is a pruning technique which consistently outperforms common approach merely removing units regardless architecture dataset. also show how a simple adaptation existing scoring function allows us select best units prune. Finally show units selected best performing scoring functions are somewhat consistent course training implying dead parts network appear stages training. Pruning is a successful method reducing size trained neural network accelerating inference. Pruning consists deleting parts network whose removal least affects network performance. Many pruning methods proposed literature differ computational cost effectiveness ways are hard assess.In interesting recent work BID3 argue called winning ticket hypothesis. precisely train large network saving random initial value parameter. training prune large network produce smaller network one fifth weights. Setting weights saved initial values retraining achieves performance close large trained network much reduced computational cost. result opens new frontier pruning methods where they are used detect useless units early training therefore accelerating inference.This contribution studies effect pruning methods throughout training process. also present mean replacement unit pruning method extends idea bias propagation introduced Yeetal. 2018 non-constrained training setting. main observations work can then be summarized follows:• Regardless scoring function used bias propagation reduces pruning penalty networks without batch normalization.• Fine-tuning pruned network additional training iterations reduces bias propagation advantage quickly.• Absolute valued approximation pruning penalty provides superior performance normal first order approximation. finding confirms observations made BID11.• Units are selected best performing scoring function seem come small subset units. finding confirms BID3's comments lottery ticket BID2 's claims dead units.The rest paper is organized follows. reviewing related work Section2. define pruning methods scoring functions Section3. Section 4 provides empirical evaluation comparing various combinations scoring functions methods varying pruning fractions datasets models. briefly provide concluding remarks discuss future work Section5. work presents experimental comparison unit pruning strategies throughout training process. introduce mean replacement approach show substantially reduces impact unit removal loss function. also show fine-tuning pruned networks does not reduce mean replacement advantage quickly. argue direct first order approximation pruning penalty are poor predictors pruning penalty incurred simultaneous removal multiple units neglected high order terms can become significant. contrast absolute value versions approximations achieve best performance. Finally provide evidence showing best pruning methods identify stable set prunable units relatively early training process.This last observation begs future work. Can we combine pruning training manner reduces computational training cost quantity comparable training winning ticket network? If we decided will be using Mean Replacement pruning method can define new scoring function.e first order Taylor approximation pruning penalty mean replacement. name new saliency function Mean Replacement Saliency MRS Let us parameterize loss function activations write first order approximation absolute change loss. DISPLAYFORM0 where DISPLAYFORM1 If we were interested average change loss can write Equation 5 without absolute values. words approximations absolute change penalizes directions emphasizing change neural network rather loss function.,845,559,286,0.008,1.512,2025/11/05 17:18:54,0.0,1.619,0.5669781931464173,280.24
"Due to the phenomenon of “posterior collapse,” current latent variable generative models pose a challenging design choice that either weakens the capacity of the decoder or requires altering the training objective. We develop an alternative that utilizes the most powerful generative models as decoders, optimize the variational lower bound, and ensures that the latent variables preserve and encode useful information. Our proposed δ-VAEs achieve this by constraining the variational family for the posterior to have a minimum distance to the prior. For sequential latent variable models, our approach resembles the classic representation learning approach of slow feature analysis. We demonstrate our method’s efficacy at modeling text on LM1B and modeling images: learning representations, improving sample quality, and achieving state of the art log-likelihood on CIFAR-10 and ImageNet 32 × 32. Deep latent variable models trained with amortized variational inference have led to advances in representation learning on high-dimensional datasets BID25 BID33 . These latent variable models typically have simple decoders, where the mapping from the latent variable to the input space is unimodal, for example using a conditional Gaussian decoder. This typically results in representations that are good at capturing the global structure in the input, but fail at capturing more complex local structure (e.g. texture BID28 ). In parallel, advances in autoregressive models have led to drastic improvements in density modeling and sample quality without explicit latent variables BID39 . While these models are good at capturing local statistics, they often fail to produce globally coherent structures BID30 .Combining the power of tractable densities from autoregressive models with the representation learning capabilities of latent variable models could result in higher-quality generative models with useful latent representations. While much prior work has attempted to join these two models, a common problem remains. If the autoregressive decoder is expressive enough to model the data density, then the model can learn to ignore the latent variables, resulting in a trivial posterior that collapses to the prior. This phenomenon has been frequently observed in prior work and has been referred to as optimization challenges of VAEs by BID5 , the information preference property by , and the posterior collapse problems by several others (e.g. van den BID40 BID14 . Ideally, an approach that mitigates posterior collapse would not alter the evidence lower bound (ELBO) training objective, and would allow the practitioner to leverage the most recent advances in powerful autoregressive decoders to improve performance. To the best of our knowledge , no prior work has succeeded at this goal. Most common approaches either change the objective BID20 BID1 Zhao et al., 2017; BID29 Goyal et al., 2017) , or weaken the decoder BID5 BID18 . Additionally, these approaches are often challenging to tune and highly sensitive to hyperparameters BID1 .In this paper, we propose δ-VAEs , a simple framework for selecting variational families that prevent posterior collapse without altering the ELBO training objective or weakening the decoder. By restricting the parameters or family of the posterior, we ensure that there is a minimum KL divergence, δ, between the posterior and the prior.We demonstrate the effectiveness of this approach at learning latent-variable models with powerful decoders on images (CIFAR-10, and ImageNet 32 × 32), and text (LM1B). We achieve state of the art log-likelihood results with image models by additionally introducing a sequential latent-variable model with an anti-causal encoder structure. Our experiments demonstrate the utility of δ-VAEs at learning useful representations for downstream tasks without sacrificing performance on density modeling. In this work, we have demonstrated that δ-VAEs provide a simple, intuitive, and effective solution to posterior collapse in latent variable models, enabling them to be paired with powerful decoders. Unlike prior work, we do not require changes to the objective or weakening of the decoder, and we can learn useful representations as well as achieving state-of-the-art likelihoods. While our work presents two simple posterior-prior pairs, there are a number of other possibilities that could be explored in future work. Our work also points to at least two interesting challenges for latentvariable models: (1) can they exceed the performance of a strong autoregressive baseline, and (2) can they learn representations that improve downstream applications such as classification? DISPLAYFORM0 B DERIVATION OF THE KL-DIVERGENCE BETWEEN AR(1) AND DIAGONAL GAUSSIAN, AND ITS LOWER-BOUND DISPLAYFORM1 Noting the analytic form for the KL-divergence for two uni-variate Gaussian distributions: DISPLAYFORM2 we now derive the lower-bound for KL-divergence. To avoid clutter we assume a single dimension per timestep but extend the results to the general multivariate case at the end of this section. DISPLAYFORM3 C DERIVATION OF THE LOWER-BOUND Removing non-negative quadratic terms involving µ i in equation 3 and expanding back f inside the summation yields DISPLAYFORM4 Consider f a (x) = ax − ln(x) − 1 and its first and second order derivatives, f a (x) = a − 1 x and f a (x) ≥ 0. Thus, f a is convex and obtains its minimum value of ln(a) at x = a −1 . Substituting σ DISPLAYFORM5 When using multi-dimensional z i at each timestep, the committed rate is the sum of the KL for each individual dimension: DISPLAYFORM6 The most common choice for variational families is to assume that the components of the posterior are independent, for example using a multivariate Gaussian with a diagonal covariance: q φ (z|x) = N (z; µ q (x), σ q (x)). When paired with a standard Gaussian prior, p(z) = N (z; 0, 1), we can guarantee a committed information rate δ by constraining the mean and variance of the variational family (see Appendix C) DISPLAYFORM7 We can, thus, numerically solve DISPLAYFORM8 where the above equation has a solution for µ q , and the committed rate δ. Posterior parameters can thus be parameterised as: DISPLAYFORM9 Where φ parameterises the data-dependent part of µ q ad σ q , which allow the rate to go above the designated lower-bound δ.We compare this model with the temporal version of δ-VAE discussed in the paper and report the results in Table 3 . While independent δ-VAE also prevents the posterior from collapsing to prior, its performance in density modeling lags behind temporal δ-VAE.","Due phenomenon posterior collapse current latent variable generative models pose challenging design choice either weakens capacity decoder requires altering training objective. develop alternative utilizes powerful generative models decoders optimize variational lower bound ensures latent variables preserve encode useful information. proposed δ-VAEs achieve constraining variational family posterior have a minimum distance prior. sequential latent variable models approach resembles classic representation learning approach slow feature analysis. demonstrate methods efficacy modeling text LM1B modeling images:learning representations improving sample quality achieving state art log-likelihood CIFAR-10 ImageNet32×32. Deep latent variable models trained amortized variational inference have led advances representation learning high-dimensional datasets BID25 BID33. latent variable models typically have simple decoders where the mapping latent variable input space is unimodal example using conditional Gaussian decoder. typically results representations are good capturing global structure input fail capturing complex local structure e.g texture BID28 parallel advances autoregressive models have led drastic improvements density modeling sample quality without explicit latent variables BID39. models are good capturing local statistics often fail produce globally coherent structures BID30.Combining power tractable densities autoregressive models representation learning capabilities latent variable models could result higher-quality generative models useful latent representations. much prior work has attempted join two models common problem remains. If the autoregressive decoder is expressive enough model data density model can learn ignore latent variables resulting trivial posterior collapses prior. phenomenon has been frequently observed prior work has been referred optimization challenges VAEs BID5 information preference property posterior collapse problems several others e.g van den BID40 BID14. Ideally approach mitigates posterior collapse would alter evidence lower bound ELBO training objective would allow practitioner leverage recent advances powerful autoregressive decoders improve performance. best knowledge prior work has succeeded goal. common approaches either change objective BID20 BID1 Zhao etal. 2017;BID29 Goyaletal. 2017 weaken decoder BID5 BID18. Additionally approaches are often challenging tune highly sensitive hyperparameters BID1.In paper propose δ-VAEs simple framework selecting variational families prevent posterior collapse without altering ELBO training objective weakening decoder. restricting parameters family posterior ensure is a minimum KL divergence δ posterior prior.We demonstrate effectiveness approach learning latent-variable models powerful decoders images CIFAR-10 ImageNet32×32 text LM1B achieve state art log-likelihood results image models additionally introducing sequential latent-variable model anti-causal encoder structure. experiments demonstrate utility δ-VAEs learning useful representations downstream tasks without sacrificing performance density modeling. work have demonstrated δ-VAEs provide simple intuitive effective solution posterior collapse latent variable models enabling paired powerful decoders. Unlike prior work do not require changes objective weakening decoder can learn useful representations well achieving state-of-the-art likelihoods. work presents two simple posterior-prior pairs are a number possibilities could explored future work. work also points least two interesting challenges latentvariable models:1 can they exceed performance strong autoregressive baseline 2 can they learn representations improve downstream applications classification? DISPLAYFORM0 B DERIVATION KL-DIVERGENCE AR 1 DIAGONAL GAUSSIAN LOWER-BOUND DISPLAYFORM1 Noting analytic form KL-divergence two uni-variate Gaussian distributions:DISPLAYFORM2 derive lower-bound KL-divergence avoid clutter assume single dimension per timestep extend results general multivariate case end section. DISPLAYFORM3 C DERIVATION LOWER-BOUND Removing non-negative quadratic terms involvingµ equation3 expanding back f inside summation yields DISPLAYFORM4 Consider f x ax−ln x −1 first second order derivatives f x −1x f x ≥0. Thus f is convex obtains minimum value ln x −1 Substituting σ DISPLAYFORM5 When using multi-dimensionalz timestep committed rate is the sum KL individual dimension:DISPLAYFORM6 common choice variational families is to assume components posterior are independent example using multivariate Gaussian diagonal covariance:qφ z|x N z;µq x σq x When paired standard Gaussian prior p z N z;0 1 can guarantee committed information rateδ constraining mean variance variational family see AppendixC DISPLAYFORM7 can,thus numerically solve DISPLAYFORM8 where the above equation has a solution µq committed rateδ. Posterior parameters can thus parameterised as:DISPLAYFORM9 Where φ parameterises data-dependent part µqadσ q which allow rate go designated lower-bound δ.We compare model temporal version δ-VAE discussed paper report results Table3. independent δ-VAE also prevents posterior collapsing prior performance density modeling lags behind temporal δ-VAE",1320,895,425,0.013,1.475,2025/11/05 17:18:54,0.01,1.457,0.4517133956386294,399.66
"Mini-batch gradient descent and its variants are commonly used in deep learning. The principle of mini-batch gradient descent is to use noisy gradient calculated on a batch to estimate the real gradient, thus balancing the computation cost per iteration and the uncertainty of noisy gradient. However, its batch size is a fixed hyper-parameter requiring manual setting before training the neural network. Yin et al. (2017) proposed a batch adaptive stochastic gradient descent (BA-SGD) that can dynamically choose a proper batch size as learning proceeds. We extend the BA-SGD to momentum algorithm and evaluate both the BA-SGD and the batch adaptive momentum (BA-Momentum) on two deep learning tasks from natural language processing to image classification. Experiments confirm that batch adaptive methods can achieve a lower loss compared with mini-batch methods after scanning the same epochs of data. Furthermore, our BA-Momentum is more robust against larger step sizes, in that it can dynamically enlarge the batch size to reduce the larger uncertainty brought by larger step sizes. We also identified an interesting phenomenon, batch size boom. The code implementing batch adaptive framework is now open source, applicable to any gradient-based optimization problems. Efficiency of training large neural networks becomes increasingly important as deep neural networks tend to have more parameters and require more training data to achieve the state-of-the-art performance on a wide variety of tasks BID4 . For training deep neural networks, stochastic gradient descent (SGD) (Robbins & Monro, 1951) and its variants, including momentum, which utilizes past updates with an exponential decay BID11 , and other methods that can adapt different learning rates for each dimension, such as ADAGRAD BID1 , ADADELTA BID19 and ADAM BID6 , are commonly used. SGD approximates the gradient by only using a single data instance in each iteration, which may lead to uncertainty of approximation. This uncertainty can be reduced by adopting a batch of instances to do the approximation. In mini-batch SGD, the batch size is a fixed hyper parameter requiring manual setting before training the neural network. Setting the batch size typically involves a tuning procedure in which the best batch size is chosen by a series of attempts. BID18 has developed a batch adaptive stochastic gradient descent (BA-SGD) that can dynamically choose a proper batch size as learning proceeds. BA-SGD models the decrease of objective value as a Gaussian random walk game with rebound on the basis of Taylor extension and central limit theorem. Its core idea is to only update the parameters when the ratio between the expected decrease of objective value and the current batch size is large enough, otherwise enlarge the batch size to better approximate the gradient. It claimed that by smartly choosing the batch size, the BA-SGD not only conserves the fast convergence of SGD algorithm but also avoids too frequent model updates, and compared with mini-batch SGD, its objective value decreases more, after scanning the same amount of data.However, the experiment in BID18 was only conducted on some simple classification tasks using fully connected neural network with one input layer, one output layer and two hidden layers. What about the evaluation on some complex neural networks, such as convolutional neural network (CNN) and recurrent neural network (RNN)? How well would the batch adaptive algorithm perform on other complicated tasks related to natural language processing and computer vision? Furthermore, empirical studies reveal that SGD usually performs not so well in some deep and complex neural networks BID15 . Can this batch adaptive framework be extended to other gradient based optimization algorithms except SGD? Therefore, in this paper we extend the batch adaptive framework to momentum algorithm, and evaluate both the batch adaptive SGD (BA-SGD) and the batch adaptive momentum (BA-Momentum) on two deep learning tasks from natural language processing to image classification. These two tasks use RNN and CNN respectively, which cover most of the deep learning models.In our experiments, we have the following observations. First, for batch adaptive methods, their loss functions converge to lower values after scanning same epoches of data, compared with fixedbatch-size methods. Second, BA-Momentum is more robust against large step sizes by dynamically enlarging the batch size to counteract with the larger noise brought by larger step sizes. Third, we observed a batch size boom, a concentrated period where the batch size frequently increases to larger values, in the training of BA-Momentum. The batch size boom is of significance in that it always appears at the point where mini-batch method starts to reach its lowest possible loss and it helps BA-Momentum keep dropping to even lower loss. More details on these observations and their analysis can be found in Section 4. The code implementing the batch adaptive framework using Theano (AlR) is now open source 1 , which is applicable to any gradient-based optimization problems.This paper is organized as follows. In Section 2, we briefly introduce the batch adaptive framework proposed by BID18 . In Section 3, we extend the batch adaptive framework to momentum algorithm. In Section 4, we demonstrate the performance of BA-M and BA-SGD on Fashion-MNIST BID17 and relation extraction task, and then reveal the robustness of BA-Momentum against large step sizes. In Section 5, we discuss some efficiency issue concerned with implementing this batch adaptive framework, and also propose several promising applications based on this framework. In this work we developed BA-Momentum algorithm, an extension of the BA-SGD proposed by BID18 . We also evaluate the two algorithms on natural language processing and image classification tasks using RNN and CNN respectively. The experiments show that in most cases both batch adaptive methods can achieve lower loss than mini-batch methods after scanning same epochs of data. Furthermore, we also confirm that within a certain range of step sizes, BA-Momentum is more robust against large step size compared with mini-batch methods.In the experiments, we did not evaluate the decrease of training loss with respect to training time. This is because, in the BA-SGD and BA-Momentum algorithm, we have to calculate the derivatives of the loss of each instance from a batch with respect to parameters, and then derive a covariance matrix through Equation 4 from the derivatives. Computing derivatives by backpropagation is time consuming, and now we have to compute all the derivatives of every instance in a batch. However, in mini-batch gradient descent, it is a common practice to calculate an average loss from a batch and then the derivative of this average loss, which requires less time. A feasible approach to reduce the computation cost might be to modify the way Theano do the derivation for a batch of instances and return the square sum of the derivatives, which we plan to study in future work.The batch adaptive framework can have many important applications. It can be adapted to accelerate distributed deep learning. For distributed deep learning, communication cost for synchronizing gradients and parameters among workers and parameter server is its well-known bottleneck BID7 b; BID16 . A larger batch may help make more accurate updates, thus reducing the total number of iterations needed to converge, lowering the communication cost. However, a larger batch also causes a higher computation cost per iteration. In this update-costly environment, the batch adaptive framework may be modified to take both the computation and communication cost into consideration when deciding a proper batch size, which is worth further exploring.Another application is that the batch adaptive framework may help remedy the generalization degradation of using large batch studied by BID5 . They provided solid numeric evidence suggesting that using a larger batch will degrade the quality of the model, as measured by its ability to generalize. They also studied the cause for this generalization drop and presented evidence supporting the view that large-batch methods tend to converge to sharp minimizers of the training and testing functions, which causes this generalization drop. Several strategies to help large-batch methods eliminate this generalization drop was proposed in their work. The most promising one is to warm-start with certain epochs of small-batch regime, and then use large batch for the rest of the training. However, the number of epochs needed to warm start with small batch varies for different data sets, thus a batch adaptive method that can dynamically change the batch size against the characteristics of data is the key to solving this problem. The batch adaptive framework sheds light on this issue. Difficulty lies in how to identify a sharp minima accurately and efficiently in the process of learning and limit the batch size when encountering a sharp minima, which we plan to study in future work.","Mini-batch gradient descent variants are commonly used deep learning. principle mini-batch gradient descent is to use noisy gradient calculated batch estimate real gradient thus balancing computation cost per iteration uncertainty noisy gradient. However batch size is a fixed hyper-parameter requiring manual setting training neural network. Yinetal. 2017 proposed batch adaptive stochastic gradient descent BA-SGD can dynamically choose proper batch size learning proceeds. extend BA-SGD momentum algorithm evaluate BA-SGD batch adaptive momentum BA-Momentum two deep learning tasks natural language processing image classification. Experiments confirm batch adaptive methods can achieve lower loss compared mini-batch methods scanning epochs data. Furthermore BA-Momentum is more robust larger step sizes can dynamically enlarge batch size reduce larger uncertainty brought larger step sizes. also identified interesting phenomenon batch size boom. code implementing batch adaptive framework is now open source which is applicable gradient-based optimization problems. Efficiency training large neural networks becomes increasingly important deep neural networks tend have more parameters require training data achieve state-of-the-art performance wide variety tasks BID4. training deep neural networks stochastic gradient descent SGD Robbins Monro 1951 variants including momentum which utilizes past updates exponential decay BID11 methods can adapt different learning rates dimension ADAGRAD BID1 ADADELTA BID19 ADAM BID6 are commonly used. SGD approximates gradient using single data instance iteration may lead uncertainty approximation. uncertainty can be reduced adopting batch instances do the approximation. mini-batch SGD batch size is a fixed hyper parameter requiring manual setting training neural network. Setting batch size typically involves tuning procedure which the best batch size is chosen series attempts. BID18 has developed batch adaptive stochastic gradient descent BA-SGD can dynamically choose proper batch size learning proceeds. BA-SGD models decrease objective value Gaussian random walk game rebound basis Taylor extension central limit theorem. core idea is to only update parameters when the ratio expected decrease objective value current batch size is large enough otherwise enlarge batch size better approximate gradient. claimed smartly choosing batch size BA-SGD conserves fast convergence SGD algorithm also avoids frequent model updates compared mini-batch SGD objective value decreases scanning amount data.However experiment BID18 was only conducted simple classification tasks using fully connected neural network one input layer one output layer two hidden layers. What about the evaluation complex neural networks convolutional neural network CNN recurrent neural network RNN How well would batch adaptive algorithm perform complicated tasks related natural language processing computer vision? Furthermore empirical studies reveal SGD usually performs well deep complex neural networks BID15. Can this batch adaptive framework extended gradient based optimization algorithms except SGD? Therefore paper extend batch adaptive framework momentum algorithm did not evaluate batch adaptive SGD BA-SGD batch adaptive momentum BA-Momentum two deep learning tasks natural language processing image classification. two tasks use RNN CNN respectively which cover deep learning models.In experiments have the following observations. First batch adaptive methods loss functions converge lower values scanning epoches data compared fixedbatch-size methods. Second BA-Momentum is more robust large step sizes dynamically enlarging batch size counteract larger noise brought larger step sizes. Third observed batch size boom concentrated period where the batch size frequently increases larger values training BA-Momentum batch size boom is of significance always appears point where mini-batch method starts reach lowest possible loss helps BA-Momentum keep dropping even lower loss. details observations analysis can be found Section4. code implementing batch adaptive framework using Theano AlR is now open source1 which is applicable gradient-based optimization problems.This paper is organized follows. Section2 briefly introduce batch adaptive framework proposed BID18. Section3 extend batch adaptive framework momentum algorithm. Section4 demonstrate performance BA-M BA-SGD Fashion-MNIST BID17 relation extraction task reveal robustness BA-Momentum large step sizes. Section5 discuss efficiency issue concerned implementing batch adaptive framework also propose several promising applications based framework. work developed BA-Momentum algorithm extension BA-SGD proposed BID18. also evaluate two algorithms natural language processing image classification tasks using RNN CNN respectively. experiments show cases batch adaptive methods can achieve lower loss mini-batch methods scanning epochs data. Furthermore also confirm within certain range step sizes BA-Momentum is more robust large step size compared mini-batch methods.In experiments did not evaluate decrease training loss respect training time. is because,BA-SGD BA-Momentum algorithm have to calculate derivatives loss instance batch respect have more parameters derive covariance matrix Equation4 derivatives. Computing derivatives backpropagation is time consuming haveto compute derivatives every instance batch. However mini-batch gradient descent is a common practice calculate average loss batch derivative average loss which requires less time. feasible approach reduce computation cost might modify way Theano do the derivation batch instances return square sum derivatives which we plan study future work.The batch adaptive framework can have many important applications. can be adapted accelerate distributed deep learning. distributed deep learning communication cost synchronizing gradients parameters among workers parameter server is its well-known bottleneck BID7b;BID16. larger batch may help make accurate updates thus reducing total number iterations needed converge lowering communication cost. However larger batch also causes higher computation cost per iteration. update-costly environment batch adaptive framework may modified take computation communication cost consideration when deciding proper batch size which is worth exploring.Another application is that the batch adaptive framework may help remedy generalization degradation using large batch studied BID5. provided solid numeric evidence suggesting using larger batch will degrade quality model measured ability generalize. also studied cause generalization drop presented evidence supporting view large-batch methods tend converge sharp minimizers training testing functions which causes generalization drop. Several strategies help large-batch methods eliminate generalization drop was proposed work. promising one is to warm-start certain epochs small-batch regime use large batch rest training. However number epochs needed warm start small batch varies different data sets thus batch adaptive method can dynamically change batch size characteristics data is the key solving problem. batch adaptive framework sheds light issue. Difficulty lies how to identify sharp minima accurately efficiently process learning limit batch size when encountering sharp minima which we plan study future work.",1703,1175,528,0.022,1.449,2025/11/05 17:18:54,0.01,1.679,0.3707165109034268,529.592
"Deep learning models for graphs have advanced the state of the art on many tasks. Despite their recent success, little is known about their robustness. We investigate training time attacks on graph neural networks for node classification that perturb the discrete graph structure.   Our core principle is to use meta-gradients to solve the bilevel problem underlying training-time attacks, essentially treating the graph as a hyperparameter to optimize. Our experiments show that small graph perturbations consistently lead to a strong decrease in performance for graph convolutional networks, and even transfer to unsupervised embeddings. Remarkably, the perturbations created by our algorithm can misguide the graph neural networks such that they perform worse than a simple baseline that ignores all relational information. Our attacks do not assume any knowledge about or access to the target classifiers. Graphs are a powerful representation that can model diverse data from virtually any domain, such as biology (protein interaction networks), chemistry (molecules), or social networks (Facebook). Not surprisingly, machine learning on graph data has a longstanding history, with tasks ranging from node classification, over community detection, to generative modeling.In this paper, we study node classification, which is an instance of semi-supervised classification: given a single (attributed) network and a subset of nodes whose class labels are known (e.g., the topic of a paper in a citation graph), the goal is to infer the classes of the unlabeled nodes. While there exist many classical approaches to node classification (London & Getoor, 2014; Chapelle et al., 2006) , recently deep learning on graphs has gained much attention BID7 Bojchevski & Günnemann, 2018a; BID2 BID11 Bojchevski et al., 2018; Klicpera et al., 2019) . Specifically, graph convolutional approaches (Kipf & Welling, 2017; BID12 have improved the state of the art in node classification.However, recent works have also shown that such approaches are vulnerable to adversarial attacks both at test time (evasion) as well as training time (poisoning attacks) BID18 Dai et al., 2018) . A core strength of models using graph convolution -exploiting the information in a node's neighborhood to improve classification -is also a major vulnerability: because of these propagation effects, an attacker can change a single node's prediction without even changing any of its attributes or edges. This is because the foundational assumption that all samples are independent of each other does not hold for node classification. Network effects such as homophily (London & Getoor, 2014) support the classification, while on the other hand they enable indirect adversarial attacks.So far, all existing attacks on node classification models are targeted, that is, aim to provoke misclassification of a specific single node, e.g. a person in a social network. In this work, we propose the first algorithm for poisoning attacks that is able to compromise the global node classification performance of a model. We show that even under restrictive attack settings and without access to the target classifier, our attacks can render it near-useless for use in production (i.e., on test data).Our approach is based on the principle of meta learning, which has traditionally been used for hyperparameter optimization BID4 , or, more recently, few-shot learning (Finn et al., 2017) . In essence, we turn the gradient-based optimization procedure of deep learning models upside down and treat the input data -the graph at hand -as a hyperparameter to learn. We propose an algorithm for training-time adversarial attacks on (attributed) graphs, focusing on the task of node classification. We use meta-gradients to solve the bilevel optimization problem underlying the challenging class of poisoning adversarial attacks. Our experiments show that attacks created using our meta-gradient approach consistently lead to a strong decrease in classification performance of graph convolutional models and even transfer to unsupervised models. Remarkably, even small perturbations to a graph based on our approach can lead to graph neural networks performing worse than a baseline ignoring all relational information. We further propose approximations of the metagradients that are less expensive to compute and, in many cases, have a similarly destructive impact on the training of node classification models. While we are able to show small statistical differences of adversarial and 'normal' edges, it is still an open question what makes the edges inserted/removed by our algorithm so destructive, which could then be used to detect or defend against attacks.",Deep learning models graphs have advanced state art many tasks. Despite recent success little is known robustness. investigate training time attacks graph neural networks node classification perturb discrete graph structure. core principle is to use meta-gradients solve bilevel problem underlying training-time attacks essentially treating graph hyperparameter optimize. experiments show small graph perturbations consistently lead strong decrease performance graph convolutional networks even transfer unsupervised embeddings. Remarkably perturbations created algorithm can misguide graph neural networks perform worse simple baseline ignores relational information. attacks do not assume knowledge access target classifiers. Graphs are a powerful representation can model diverse data virtually domain biology protein interaction networks chemistry molecules social networks Facebook surprisingly machine learning graph data has a longstanding history tasks ranging node classification community detection generative modeling.In paper study node classification which is an instance semi-supervised classification:given single attributed network subset nodes whose class labels are known e.g topic paper citation graph goal is to infer classes unlabeled nodes. exist many classical approaches node classification London Getoor 2014;Chapelleetal. 2006 recently deep learning graphs has gained much attention BID7 Bojchevski Günnemann 2018a;BID2 BID11 Bojchevskiet al. 2018;Klicperaetal. 2019 Specifically graph convolutional approaches Kipf Welling 2017;BID12 have improved state art node classification.However recent works have also shown approaches are vulnerable adversarial attacks test time evasion well training time poisoning attacks BID18 Daietal. 2018 core strength models using graph convolution -exploiting information node's neighborhood improve classification -is also major vulnerability:propagation effects attacker can change single node's prediction without even changing attributes edges. is because the foundational assumption samples are independent does hold node classification. Network effects homophily London Getoor 2014 support classification hand enable indirect adversarial attacks.So far existing attacks node classification models are targeted aim provoke misclassification specific single node e.g person social network. work propose first algorithm poisoning attacks is able compromise global node classification performance model. show even restrictive attack settings without access target classifier attacks can render near-useless use production.e test data.Our approach is based principle meta learning which has traditionally used hyperparameter optimization BID4 recently few-shot learning Finnetal. 2017 essence turn gradient-based optimization procedure deep learning models upside treat input data -the graph hand -as hyperparameter learn. propose algorithm training-time adversarial attacks attributed graphs focusing task node classification. use meta-gradients solve bilevel optimization problem underlying challenging class poisoning adversarial attacks. experiments show attacks created using meta-gradient approach consistently lead strong decrease classification performance graph convolutional models even transfer unsupervised models. Remarkably even small perturbations graph based approach can lead graph neural networks performing worse baseline ignoring relational information. propose approximations metagradients are less expensive compute many cases have a similarly destructive impact training node classification models. are able show small statistical differences adversarial 'normal' edges is still open question what makes edges inserted/removed algorithm destructive could used detect defend attacks.,919,611,308,0.009,1.504,2025/11/05 17:18:54,0.0,1.367,0.542056074766355,294.152
"Numerous models for grounded language understanding have been recently proposed, including (i) generic models that can be easily adapted to any given task and (ii) intuitively appealing modular models that require background knowledge to be instantiated. We compare both types of models in how much they lend themselves to a particular form of systematic generalization. Using a synthetic VQA test, we evaluate which models are capable of reasoning about all possible object pairs after training on only a small subset of them. Our findings show that the generalization of modular models is much more systematic and that it is highly sensitive to the module layout, i.e. to how exactly the modules are connected. We furthermore investigate if modular models that generalize well could be made more end-to-end by learning their layout and parametrization. We find that end-to-end methods from prior work often learn inappropriate layouts or parametrizations that do not facilitate systematic generalization. Our results suggest that, in addition to modularity, systematic generalization in language understanding may require explicit regularizers or priors.
 In recent years, neural network based models have become the workhorse of natural language understanding and generation. They empower industrial machine translation BID34 ) and text generation BID20 systems and show state-of-the-art performance on numerous benchmarks including Recognizing Textual Entailment BID8 , Visual Question Answering BID17 , and Reading Comprehension BID33 . Despite these successes, a growing body of literature suggests that these approaches do not generalize outside of the specific distributions on which they are trained, something that is necessary for a language understanding system to be widely deployed in the real world. Investigations on the three aforementioned tasks have shown that neural models easily latch onto statistical regularities which are omnipresent in existing datasets BID0 BID10 BID16 and extremely hard to avoid in large scale data collection. Having learned such dataset-specific solutions, neural networks fail to make correct predictions for examples that are even slightly out of domain, yet are trivial for humans. These findings have been corroborated by a recent investigation on a synthetic instruction-following task , in which seq2seq models BID32 BID2 have shown little systematicity BID6 in how they generalize, that is they do not learn general rules on how to compose words and fail spectacularly when for example asked to interpret ""jump twice"" after training on ""jump"", ""run twice"" and ""walk twice"".An appealing direction to improve the generalization capabilities of neural models is to add modularity and structure to their design to make them structurally resemble the kind of rules they are supposed to learn BID1 BID7 . For example, in the Neural Module Network paradigm (NMN, BID1 ), a neural network is assembled from several neural modules, where each module is meant to perform a particular subtask of the input processing, much like a computer program composed of functions. The NMN approach is intuitively appealing but its widespread adoption has been hindered by the large amount of domain knowledge that is required to decide BID1 or predict BID19 BID12 how the modules should be created (parametrization) and how they should be connected (layout) based on a natural language utterance. Besides , their performance has often been matched by more traditional neural models, such as FiLM BID28 , Relations Networks BID29 , and MAC networks BID14 . Lastly , generalization properties of NMNs, to the best of our knowledge, have not been rigorously studied prior to this work.Here, we investigate the impact of explicit modularity and structure on systematic generalization of NMNs and contrast their generalization abilities to those of generic models. For this case study, we focus on the task of visual question answering (VQA), in particular its simplest binary form, when the answer is either ""yes"" or ""no"". Such a binary VQA task can be seen as a fundamental task of language understanding, as it requires one to evaluate the truth value of the utterance with respect to the state of the world. Among many systematic generalization requirements that are desirable for a VQA model, we choose the following basic one: a good model should be able to reason about all possible object combinations despite being trained on a very small subset of them. We believe that this is a key prerequisite to using VQA models in the real world, because they should be robust at handling unlikely combinations of objects. We implement our generalization demands in the form of a new synthetic dataset, called Spatial Queries On Object Pairs (SQOOP), in which a model has to perform spatial relational reasoning about pairs of randomly scattered letters and digits in the image (e.g. answering the question ""Is there a letter A left of a letter B?""). The main challenge in SQOOP is that models are evaluated on all possible object pairs, but trained on only a subset of them.Our first finding is that NMNs do generalize better than other neural models when layout and parametrization are chosen appropriately. We then investigate which factors contribute to improved generalization performance and find that using a layout that matches the task (i.e. a tree layout, as opposed to a chain layout), is crucial for solving the hardest version of our dataset. Lastly, and perhaps most importantly , we experiment with existing methods for making NMNs more end-to-end by inducing the module layout BID19 or learning module parametrization through soft-attention over the question BID12 . Our experiments show that such end-to-end approaches often fail by not converging to tree layouts or by learning a blurred parameterization for modules, which results in poor generalization on the hardest version of our dataset. We believe that our findings challenge the intuition of researchers in the field and provide a foundation for improving systematic generalization of neural approaches to language understanding. We have conducted a rigorous investigation of an important form of systematic generalization required for grounded language understanding: the ability to reason about all possible pairs of objects despite being trained on a small subset of such pairs. Our results allow one to draw two important conclusions. For one, the intuitive appeal of modularity and structure in designing neural architectures for language understanding is now supported by our results, which show how a modular model consisting of general purpose residual blocks generalizes much better than a number of baselines, including architectures such as MAC, FiLM and RelNet that were designed specifically for visual reasoning. While this may seem unsurprising, to the best of our knowledge, the literature has lacked such a clear empirical evidence in favor of modular and structured networks before this work. Importantly, we have also shown how sensitive the high performance of the modular models is to the layout of modules, and how a tree-like structure generalizes much stronger than a typical chain of layers.Our second key conclusion is that coming up with an end-to-end and/or soft version of modular models may be not sufficient for strong generalization. In the very setting where strong generalization is required, end-to-end methods often converge to a different, less compositional solution (e.g. a chain layout or blurred attention). This can be observed especially clearly in our NMN layout and parametrization induction experiments on the #rhs/lhs=1 version of SQOOP, but notably, strong initialization sensitivity of layout induction remains an issue even on the #rhs/lhs=18 split. This conclusion is relevant in the view of recent work in the direction of making NMNs more end-toend BID31 BID13 BID14 BID9 . Our findings suggest that merely replacing hard-coded components with learnable counterparts can be insufficient, and that research on regularizers or priors that steer the learning towards more systematic solutions can be required. That said, our parametrization induction results on the #rhs/lhs=2 split are encouraging, as they show that compared to generic models, a weaker nudge (in the form of a richer training signal or a prior) towards systematicity may suffice for end-to-end NMNs.While our investigation has been performed on a synthetic dataset, we believe that it is the realworld language understanding where our findings may be most relevant. It is possible to construct a synthetic dataset that is bias-free and that can only be solved if the model has understood the entirety of the dataset's language. It is, on the contrary, much harder to collect real-world datasets that do not permit highly dataset-specific solutions, as numerous dataset analysis papers of recent years have shown (see Section 5 for a review). We believe that approaches that can generalize strongly from imperfect and biased data will likely be required, and our experiments can be seen as a simulation of such a scenario. We hope, therefore, that our findings will inform researchers working on language understanding and provide them with a useful intuition about what facilitates strong generalization and what is likely to inhibit it. We can observe a clear correlation between κ and error rate for 1, 2 and 4 rhs/lhs. Also note that perfect generalization is always associated with κ close to 1.Next, we experiment with a hard-coded variation of MAC. In this model, we use hard-coded control scores such that given a SQOOP question X R Y, the first half of all modules focuses on X while the second half focuses on Y. The relationship between MAC and hardcoded MAC is similar to that between NMN-Tree and end-to-end NMN with parameterization induction. However, this model has not performed as well as the successful runs of MAC. We hypothesize that this could be due to the interactions between the control scores and the visual attention part of the model.","Numerous models grounded language understanding have been recently proposed including generic models can be easily adapted given task ii intuitively appealing modular models require background knowledge instantiated. compare types models how much lend particular form systematic generalization. Using synthetic VQA test evaluate which models are capable reasoning possible object pairs training small subset them. findings show generalization modular models is much systematic is highly sensitive module layout.e how exactly modules are connected. furthermore investigate if modular models can generalize well could made end-to-end learning layout parametrization. find end-to-end methods prior work often learn inappropriate layouts parametrizations do not facilitate systematic generalization. results suggest addition modularity systematic generalization language understanding may require explicit regularizers priors. recent years neural network based models have become workhorse natural language understanding generation. empower industrial machine translation BID34 text generation BID20 systems show state-of-the-art performance numerous benchmarks including Recognizing Textual Entailment BID8 Visual Question Answering BID17 Reading Comprehension BID33. Despite successes growing body literature suggests approaches do not do generalize outside specific distributions which they are trained something is necessary language understanding system widely deployed real world. Investigations three aforementioned tasks have shown neural models easily latch onto statistical regularities which are omnipresent existing datasets BID0 BID10 BID16 extremely hard avoid large scale data collection. learned dataset-specific solutions neural networks fail make correct predictions examples are even slightly domain yet are trivial humans. findings have been corroborated recent investigation synthetic instruction-following task which seq2seq models BID32 BID2 have shown little systematicity BID6 how they generalize is they do not learn general rules how to compose words fail spectacularly when for example asked interpret jump twice training jump run twice walk twice.An appealing direction improve generalization capabilities neural models is to add modularity structure design make structurally resemble kind rules are supposed learn BID1 BID7. example Neural Module Network paradigm NMN BID1 neural network is assembled several neural modules where each module is meant perform particular subtask input processing much like computer program composed functions. NMN approach is intuitively appealing widespread adoption has been hindered large amount domain knowledge is required decide BID1 predict BID19 BID12 how the modules should be created parametrization how they shouldbe connected layout based natural language utterance. Besides performance has often matched traditional neural models FiLM BID28 Relations Networks BID29 MAC networks BID14. Lastly generalization properties NMNs best knowledge have not been rigorously studied prior work.Here investigate impact explicit modularity structure systematic generalization NMNs contrast generalization abilities generic models. case study focus task visual question answering VQA particular simplest binary form when the answer is either yes no. binary VQA task can be seen fundamental task language understanding requires one evaluate truth value utterance respect state world. Among many systematic generalization requirements are desirable VQA model choose following basic one:good model should be able reason possible object combinations despite trained small subset them. believe is a key prerequisite using VQA models real world should robust handling unlikely combinations objects. implement generalization demands form new synthetic dataset called Spatial Queries Object Pairs SQOOP which model has to perform spatial relational reasoning pairs randomly scattered letters digits image e.g answering question Is there a letter left letterB? main challenge SQOOP is that models are evaluated possible object pairs trained subset them.Our first finding is that NMNs do not do generalize better neural models when layout parametrization are chosen appropriately. investigate which factors contribute improved generalization performance find using layout matches task.e tree layout opposed chain layout is crucial solving hardest version dataset. Lastly perhaps importantly experiment existing methods making NMNs end-to-end inducing module layout BID19 learning module parametrization soft-attention question BID12. experiments show end-to-end approaches often fail converging tree layouts learning blurred parameterization modules which results poor generalization hardest version dataset. believe findings challenge intuition researchers field provide foundation improving systematic generalization neural approaches language understanding. have conducted rigorous investigation important form systematic generalization required grounded language understanding:ability reason possible pairs objects despite trained small subset pairs. results allow one draw two important conclusions. one intuitive appeal modularity structure designing neural architectures language understanding is now supported results which show how a modular model consisting general purpose residual blocks generalizes much better number baselines including architectures MAC FiLM RelNet were designed specifically visual reasoning. may seem unsurprising best knowledge literature has lacked clear empirical evidence favor modular structured networks work. Importantly have also shown how sensitive high performance modular models is to the layout modules how a tree-like structure generalizes much stronger typical chain layers.Our second key conclusion is that coming end-to-end/soft version modular models may sufficient strong generalization. setting where strong generalization is required end-to-end methods often converge different less compositional solution e.g chain layout blurred attention can observed especially clearly NMN layout parametrization induction experiments#rhs/lhs=1 version SQOOP notably strong initialization sensitivity layout induction remains issue even#rhs/lhs=18 split. conclusion is relevant view recent work direction making NMNs end-toend BID31 BID13 BID14 BID9. findings suggest merely replacing hard-coded components learnable counterparts can be insufficient research regularizers priors steer learning towards systematic solutions can be required. said parametrization induction results#rhs/lhs=2 split are encouraging which show compared generic models weaker nudge form richer training signal prior towards systematicity may suffice end-to-end NMNs.While investigation has been has not performed synthetic dataset believe is the realworld language understanding where our findings may relevant. is possible construct synthetic dataset is bias-free can only solved if the model has understood entirety dataset's language. is,on contrary much harder collect real-world datasets do not permit highly dataset-specific solutions numerous dataset analysis papers recent years have shown see Section5 review believe approaches can generalize strongly imperfect biased data will likely required experiments can be seen simulation scenario. hope therefore findings will inform researchers working language understanding provide useful intuition what facilitates strong generalization what is likely inhibit it. can observe clear correlation κ error rate 1 2 4 rhs/lhs. Also note perfect generalization is always associated κ close 1.Next experiment hard-coded variation MAC. model use hard-coded control scores given SQOOP questionXR first half modules focuses X second half focuses Y. relationship MAC hardcoded MAC is similar NMN-Tree end-to-end NMN parameterization induction. However model has been has not performed well successful runs MAC. hypothesize could due interactions control scores visual attention part model.",1920,1290,630,0.025,1.488,2025/11/05 17:18:54,0.01,1.51,0.4922118380062303,706.692
"The behavioral dynamics of multi-agent systems have a rich and orderly structure, which can be leveraged to understand these systems, and to improve how artificial agents learn to operate in them. Here we introduce Relational Forward Models (RFM) for multi-agent learning, networks that can learn to make accurate predictions of agents' future behavior in multi-agent environments. Because these models operate on the discrete entities and relations present in the environment, they produce interpretable intermediate representations which offer insights into what drives agents' behavior, and what events mediate the intensity and valence of social interactions. Furthermore, we show that embedding RFM modules inside agents results in faster learning systems compared to non-augmented baselines. 
 As more and more of the autonomous systems we develop and interact with become multi-agent in nature, developing richer analysis tools for characterizing how and why agents make decisions is increasingly necessary. Moreover, developing artificial agents that quickly and safely learn to coordinate with one another, and with humans in shared environments, is crucial. The study of multi-agent systems has received considerable attention in recent years and some of the most advanced autonomous systems in the world today are multi-agent in nature (e.g. assembly lines and warehouse management systems). In particular, research in multi-agent reinforcement learning (MARL), where multiple learning agents perceive and act in a shared environment, has produced impressive results BID15 BID23 BID14 BID26 BID19 BID0 .One of the outstanding challenges in this domain is how to foster coordinated behavior among learning agents. In hand-engineered multi-agent systems (e.g. assembly lines), it is possible to obtain coordination by design, where expert engineers carefully orchestrate each agent's behavior and role in the system. This , however, rules out situations where either humans or artificial learning agents are present in the environment. In learning-based systems, there have been some successes by introducing a centralized controller BID4 BID6 BID12 BID20 . However , these cannot scale to large number of agents or to mixed human-robot ensembles. There is thus an increasing focus on multi-agent systems that learn how to coordinate on their own BID15 BID23 .Alongside the challenges of learning coordinated behaviors, there are also the challenges of measuring them. In learning-based systems, the analysis tools currently available to researchers focus on the functioning of each single agent, and are ill-equipped to characterize systems of diverse agents as a whole. Moreover, there has been little development of tools for measuring the contextual interdependence of agents' behaviors in complex environment, which will be valuable for identifying the conditions under which agents are successfully coordinating.Here we address these two challenges by developing Relational Forward Models (RFM) for multiagent systems. We build on recent advances in neural networks that effectively perform relational reasoning with graph networks (GN) BID2 to construct models that learn to predict the forward dynamics of multi-agent systems. First, we show that our models can surpass previous top methods on this task BID16 Hoshen, 2017) . Perhaps more importantly , they produce intermediate representations that support the social analysis of multi-agent systems: we use our models to propose a new way to characterize what drives each agent's behavior, track when agents influence each other, and identify which factors in the environment mediate the presence and valence of social interactions. Finally, we embed our models inside agents and use them to augment the host agent's observations with predictions of others' behavior. Our results show that this leads to agents that learn to coordinate with one another faster than non-augmented baselines. Here we showed that our Relational Forward Model can capture the rich social dynamics of multiagent environments, that its intermediate representations contained valuable interpretable information, and that providing this information to learning agents results in faster learning system. The analysis tools we introduced allow researchers to answer new questions, which are specifically tailored to multi-agent systems, such as what entities, relations and social interactions drive agents' behaviors, and what environment events or behavior patterns mediate these social and non-social influence signals. Importantly our methods require no access to agents internals, only to behavioral trajectories, making them amenable to analyzing human behavior, sports and ecological systems.Providing agents with access the output of RFM modules results in agents that learn to coordinate with one another faster than non-augmented baselines. We posit that explicit modeling of teammates and opponents is an important research direction in multi-agent RL, and one that might alleviate the need for communication, parameter sharing or centralized controllers to achieve coordination. Future work will see our methods applied to more complex and varied domains where artificial and non-artificial agents interact and learn in shared environments. We will focus on identifying entire patterns of behavior for in-agent modeling, so as to adapt the host agent policy more efficiently.",behavioral dynamics multi-agent systems have a rich orderly structure which can be leveraged understand systems improve how artificial agents learn operate them. introduce Relational Forward Models RFM multi-agent learning networks can learn make accurate predictions agents' future behavior multi-agent environments. models operate discrete entities relations present environment produce interpretable intermediate representations which offer insights what drives agents' behavior what events mediate intensity valence social interactions. Furthermore show embedding RFM modules inside agents results faster learning systems compared non-augmented baselines. autonomous systems develop interact become multi-agent nature developing richer analysis tools characterizing how and why agents make decisions is increasingly necessary. Moreover developing artificial agents quickly safely learn coordinate one another humans shared environments is crucial. study multi-agent systems has received considerable attention recent years advanced autonomous systems world today are multi-agent nature e.g assembly lines warehouse management systems particular research multi-agent reinforcement learning MARL where multiple learning agents perceive act shared environment has produced impressive results BID15 BID23 BID14 BID26 BID19 BID0.One outstanding challenges domain is how to foster coordinated behavior among learning agents. hand-engineered multi-agent systems e.g assembly lines is possible obtain coordination design where expert engineers carefully orchestrate agent's behavior role system. however rules situations where either humans artificial learning agents are present environment. learning-based systems have been successes introducing centralized controller BID4 BID6 BID12 BID20. However cannot scale large number agents mixed human-robot ensembles. is thus increasing focus multi-agent systems can learn how to coordinate BID15 BID23.Alongside challenges learning coordinated behaviors are also challenges measuring them. learning-based systems analysis tools currently available researchers focus functioning single agent are ill-equipped characterize systems diverse agents whole. Moreover has been little development tools measuring contextual interdependence agents' behaviors complex environment which will be valuable identifying conditions which agents are successfully coordinating.Here address two challenges developing Relational Forward Models RFM multiagent systems. build recent advances neural networks effectively perform relational reasoning graph networks GN BID2 construct models can learn predict forward dynamics multi-agent systems. First show models can surpass previous top methods task BID16 Hoshen 2017 Perhaps importantly produce intermediate representations support social analysis multi-agent systems:use models propose new way characterize what drives agent's behavior track when agents influence identify which factors environment mediate presence valence social interactions. Finally embed models inside agents use augment host agent's observations predictions others' behavior. results show leads agents can learn coordinate one another faster non-augmented baselines. showed Relational Forward Model can capture rich social dynamics multiagent environments intermediate representations contained valuable interpretable information providing information learning agents results faster learning system. analysis tools introduced allow researchers answer new questions which are specifically tailored multi-agent systems what entities relations social interactions drive agents' behaviors what environment events behavior patterns mediate social non-social influence signals. Importantly methods require access agents internals behavioral trajectories making amenable analyzing human behavior sports ecological systems.Providing agents access output RFM modules results agents can learn coordinate one another faster non-augmented baselines. posit explicit modeling teammates opponents is an important research direction multi-agentRL one might alleviate need communication parameter sharing centralized controllers achieve coordination. Future work will see methods applied complex varied domains where artificial non-artificial agents interact learn shared environments. will focus identifying entire patterns behavior in-agent modeling adapt host agent policy efficiently.,957,655,302,0.01,1.461,2025/11/05 17:18:54,0.0,1.35,0.4080996884735203,315.396
"We show that gradient descent on an unregularized logistic regression
 problem, for almost all separable datasets, converges to the same direction as the max-margin solution. The result generalizes also to other monotone decreasing loss functions with an infimum at infinity, and we also discuss a multi-class generalizations to the cross entropy loss. Furthermore,
 we show this convergence is very slow, and only logarithmic in the
 convergence of the loss itself. This can help explain the benefit
 of continuing to optimize the logistic or cross-entropy loss even
 after the training error is zero and the training loss is extremely
 small, and, as we show, even if the validation loss increases. Our
 methodology can also aid in understanding implicit regularization
 in more complex models and with other optimization methods. It is becoming increasingly clear that implicit biases introduced by the optimization algorithm play a crucial role in deep learning and in the generalization ability of the learned models BID7 BID1 BID15 BID5 Wilson et al., 2017) . In particular, minimizing the training error, without any explicit regularization, over models with more parameters and more capacity then the number of training examples, often yields good generalization, despite the empirical optimization problem being highly underdetermined. That is, there are many global minima of the training objective, most of which will not generalize well, but the optimization algorithm (e.g. gradient descent) biases us toward a particular minimum that does generalize well. Unfortunately, we still do not have a good understanding of the biases introduced by different optimization algorithms in different situations.We do have a decent understanding of the implicit regularization introduced by early stopping of stochastic methods or, at an extreme, of one-pass (no repetition) stochastic optimization. However, as discussed above, in deep learning we often benefit from implicit bias even when optimizing the (unregularized) training error to convergence, using stochastic or batch methods. For loss functions with attainable, finite, minimizers, such as the squared loss, we have some understanding of this: In particular, when minimizing an underdetermined least squares problem using gradient descent starting from the origin, we know we will converge to the minimum Euclidean norm solution. But the logistic loss, and its generalization the cross-entropy loss which is often used in deep learning, do not admit a finite minimizer on separable problems. Instead, to drive the loss toward zero and thus minimize it, the predictor must diverge toward infinity. Do we still benefit from implicit regularization when minimizing the logistic loss on separable data? Clearly the norm of the predictor itself is not minimized, since it grows to infinity. However, for prediction, only the direction of the predictor, i.e. the normalized w(t)/ w(t) , is important. How does w(t)/ w(t) behave as t → ∞ when we minimize the logistic (or similar) loss using gradient descent on separable data, i.e., when it is possible to get zero misclassification error and thus drive the loss to zero?In this paper, we show that even without any explicit regularization, for all most all datasets (except a zero measure set), when minimizing linearly separable logistic regression problems using gradient descent, we have that w(t)/ w(t) converges to the L 2 maximum margin separator, i.e. to the solution of the hard margin SVM. This happens even though the norm w , nor the margin constraint, are in no way part of the objective nor explicitly introduced into optimization. More generally, we show the same behavior for generalized linear problems with any smooth, monotone strictly decreasing, lower bounded loss with an exponential tail. Furthermore , we characterize the rate of this convergence, and show that it is rather slow, with the distance to the max-margin predictor decreasing only as O(1/ log(t)). This explains why the predictor continues to improve even when the training loss is already extremely small. We emphasize and demonstrate that this bias is specific to gradient descent, and changing the optimization algorithm, e.g. using adaptive learning rate methods such as ADAM BID6 , changes this implicit bias.","show gradient descent unregularized logistic regression problem almost separable datasets converges direction max-margin solution. result generalizes also monotone decreasing loss functions infimum infinity also discuss multi-class generalizations cross entropy loss. Furthermore show convergence is very slow logarithmic convergence loss itself. can help explain benefit continuing optimize logistic cross-entropy loss even training error is zero training loss is extremely small show even if the validation loss increases. methodology can also aid understanding implicit regularization complex models optimization methods. is becoming increasingly clear implicit biases introduced optimization algorithm play crucial role deep learning generalization ability learned models BID7 BID1 BID15 BID5 Wilsonet al. 2017 particular when minimizing training error without explicit regularization models parameters capacity number training examples often yields good generalization despite empirical optimization problem highly underdetermined. is,there are many global minima training objective which will not generalize well optimization algorithm e.g gradient descent biases us toward particular minimum does generalize well. Unfortunately still do not have a good understanding biases introduced different optimization algorithms different situations.We do have a decent understanding implicit regularization introduced early stopping stochastic methods extreme one-pass repetition stochastic optimization. However discussed deep learning often benefit implicit bias even when optimizing unregularized training error convergence using stochastic batch methods. loss functions attainable finite minimizers squared loss have some understanding this:particular when minimizing underdetermined least squares problem using gradient descent starting origin know will converge minimum Euclidean norm solution. logistic loss generalization cross-entropy loss which is often used deep learning do not admit finite minimizer separable problems. Instead drive loss toward zero thus minimize predictor must diverge toward infinity. Do we still benefit implicit regularization when minimizing logistic loss separable data? Clearly norm predictor is not minimized since grows infinity. However prediction direction predictor.e normalizedw/w is important. How doesw/w behave →∞ when we minimize logistic similar loss using gradient descent separable data.e when it is possible get zero misclassification error thus drive loss zero? paper show even without explicit regularization datasets except zero measure set when minimizing linearly separable logistic regression problems using gradient descent have thatw/w converges L 2 maximum margin separator.e solution hard margin SVM. happens even though normw margin constraint are in no way part objective explicitly introduced optimization. generally show behavior generalized linear problems smooth monotone strictly decreasing lower bounded loss exponential tail. Furthermore characterize rate convergence show is rather slow distance max-margin predictor decreasing 1/log explains why the predictor continues improve even when the training loss is already extremely small. emphasize demonstrate bias is specific gradient descent changing optimization algorithm e.g using adaptive learning rate methods ADAM BID6 changes implicit bias.",837,527,310,0.009,1.588,2025/11/05 17:18:54,0.0,1.686,0.8037383177570094,282.087
"Despite impressive performance as evaluated on i.i.d. holdout data, deep neural networks depend heavily on superficial statistics of the training data and are liable to break under distribution shift. For example, subtle changes to the background or texture of an image can break a seemingly powerful classifier. Building on previous work on domain generalization, we hope to produce a classifier that will generalize to previously unseen domains, even when domain identifiers are not available during training. This setting is challenging because the model may extract many distribution-specific (superficial) signals together with distribution-agnostic (semantic) signals. To overcome this challenge, we incorporate the gray-level co-occurrence matrix (GLCM) to extract patterns that our prior knowledge suggests are superficial: they are sensitive to the texture but unable to capture the gestalt of an image. Then we introduce two techniques for improving our networks' out-of-sample performance. The first method is built on the reverse gradient method that pushes our model to learn representations from which the GLCM representation is not predictable. The second method is built on the independence introduced by projecting the model's representation onto the subspace orthogonal to GLCM representation's.
 We test our method on the battery of standard domain generalization data sets and, interestingly, achieve comparable or better performance as compared to other domain generalization methods that explicitly require samples from the target distribution for training. Imagine training an image classifier to recognize facial expressions. In the training data, while all images labeled ""smile"" may actually depict smiling people, the ""smile"" label might also be correlated with other aspects of the image. For example, people might tend to smile more often while outdoors, and to frown more in airports. In the future, we might encounter photographs with previously unseen backgrounds, and thus we prefer models that rely as little as possible on the superficial signal.The problem of learning classifiers robust to distribution shift, commonly called Domain Adaptation (DA), has a rich history. Under restrictive assumptions, such as covariate shift BID43 BID16 , and label shift (also known as target shift or prior probability shift) BID44 BID41 BID48 BID30 , principled methods exist for estimating the shifts and retraining under the importance-weighted ERM framework. Other papers bound worst-case performance under bounded shifts as measured by divergence measures on the train v.s. test distributions BID3 BID33 BID20 .While many impossibility results for DA have been proven BID4 , humans nevertheless exhibit a remarkable ability to function out-of-sample, even when confronting dramatic Example illustration of train/validation/test data. The first row is ""happiness"" sentiment and the second row is ""sadness"" sentiment. The background and sentiment labels are correlated in training and validation set, but independent in testing set.distribution shift. Few would doubt that given photographs of smiling and frowning astronauts on the Martian plains, we could (mostly) agree upon the correct labels.While we lack a mathematical description of how precisely humans are able to generalize so easily out-of-sample, we can often point to certain classes of perturbations that should not effect the semantics of an image. For example for many tasks, we know that the background should not influence the predictions made about an image. Similarly, other superficial statistics of the data, such as textures or subtle coloring changes should not matter. The essential assumption of this paper is that by making our model depend less on known superficial aspects, we can push the model to rely more on the difference that makes a difference. This paper focuses on visual applications, and we focus on high-frequency textural information as the relevant notion of superficial statistics that we do not want our model to depend upon.The contribution of this paper can be summarized as follows.• We propose a new differentiable neural network building block (neural gray-level cooccurrence matrix) that captures textural information only from images without modeling the lower-frequency semantic information that we care about (Section 3.1).• We propose an architecture-agnostic , parameter-free method that is designed to discard this superficial information, (Section 3.2).• We introduce two synthetic datasets for DA/DG studies that are more challenging than regular DA/DG scenario in the sense that the domain-specific information is correlated with semantic information. FIG0 is a toy example (Section 4). We introduced two novel components: NGLCM that only extracts textural information from an image, and HEX that projects the textural information out and forces the model to focus on semantic information. Limitations still exist. For example, NGLCM cannot be completely free of semantic information of an image. As a result, if we apply our method on standard MNIST data set, we will 3 ) learns garbage information and HEX degenerates to the baseline model. To overcome these limitations, we invented several training heuristics, such as optimizing F P and F G sequentially and then fix some weights. However, we did not report results with training heuristics (expect for PACS experiment) because we hope to simplify the methods. Another limitation we observe is that sometimes the training performance of HEX fluctuates dramatically during training, but fortunately, the model picked up by highest validation accuracy generally performs better than competing methods. Despite these limitations, we still achieved impressive performance on both synthetic and popular DG data sets.",Despite impressive performance evaluated.i.d holdout data deep neural networks depend heavily superficial statistics training data are liable break distribution shift. example subtle changes background texture image can break seemingly powerful classifier. Building previous work domain generalization hope produce classifier will generalize previously unseen domains even when domain identifiers are not available training. setting is challenging model may extract many distribution-specific superficial signals together distribution-agnostic semantic signals. overcome challenge incorporate gray-level co-occurrence matrix GLCM extract patterns prior knowledge suggests are superficial:are sensitive texture unable capture gestalt image. introduce two techniques improving networks' out-of-sample performance. first method is built reverse gradient method pushes model learn representations which the GLCM representation is not predictable. second method is built independence introduced projecting model's representation onto subspace orthogonal GLCM representation's test method battery standard domain generalization data sets interestingly achieve comparable better performance compared domain generalization methods explicitly require samples target distribution training. Imagine training image classifier recognize facial expressions. training data images labeled smile may actually depict smiling people smile label might also correlated aspects image. example people might tend smile often outdoors frown airports. future might encounter photographs previously unseen backgrounds thus prefer models rely little possible superficial signal.The problem learning classifiers robust distribution shift commonly called Domain Adaptation DA has a rich history. restrictive assumptions covariate shift BID43 BID16 label shift also known target shift prior probability shift BID44 BID41 BID48 BID30 principled methods exist estimating shifts retraining importance-weighted ERM framework. papers bound worst-case performance bounded shifts measured divergence measures train v.s test distributions BID3 BID33 BID20.While many impossibility results DA have been proven BID4 humans nevertheless exhibit remarkable ability function out-of-sample even when confronting dramatic Example illustration train/validation/test data. first row is happiness sentiment second row is sadness sentiment. background sentiment labels are correlated training validation set independent testing set.distribution shift. would doubt given photographs smiling frowning astronauts Martian plains could mostly agree upon correct labels.While lack mathematical description how precisely humans are able generalize easily out-of-sample can often point certain classes perturbations should not effect semantics image. example many tasks know background should not influence predictions made image. Similarly superficial statistics data textures subtle coloring changes should not matter. essential assumption paper is that by making model depend less known superficial aspects can push model rely difference makes difference. paper focuses visual applications focus high-frequency textural information relevant notion superficial statistics do not want model depend upon.The contribution paper can be summarized follows.• propose new differentiable neural network building block neural gray-level cooccurrence matrix captures textural information images without modeling lower-frequency semantic information care Section 3.1.• propose architecture-agnostic parameter-free method is designed discard superficial information Section 3.2.• introduce two synthetic datasets DA/DG studies are more challenging regularDA/DG scenario sense domain-specific information is correlated semantic information. FIG0 is a toy example Section4 introduced two novel components:NGLCM extracts textural information image HEX projects textural information forces model focus semantic information. Limitations still exist. example NGLCM cannot completely free semantic information image. result if we apply method standard MNIST data set will3 learns garbage information HEX degenerates baseline model. overcome limitations invented several training heuristics optimizingFP F G sequentially fix weights. However did not report results training heuristics expect PACS experiment hope simplify methods. Another limitation observe is that sometimes training performance HEX fluctuates dramatically training fortunately model picked highest validation accuracy generally performs better competing methods. Despite limitations still achieved impressive performance synthetic popular DG data sets.,1076,714,362,0.011,1.507,2025/11/05 17:18:54,0.01,1.486,0.551401869158878,330.694
"In this paper, we conduct an intriguing experimental study about the physical adversarial attack on object detectors in the wild. In particular, we learn a camouflage pattern to hide vehicles from being detected by state-of-the-art convolutional neural network based detectors. Our approach alternates between two threads. In the first, we train a neural approximation function to imitate how a simulator applies a camouflage to vehicles and how a vehicle detector performs given images of the camouflaged vehicles. In the second, we minimize the approximated detection score by searching for the optimal camouflage. Experiments show that the learned camouflage can not only hide a vehicle from the image-based detectors under many test cases but also generalizes to different environments, vehicles, and object detectors. Is it possible to paint a unique pattern on a vehicle's body and hence hide it from being detected by surveillance cameras? We conjecture the answer is affirmative mainly for two reasons. First, deep neural networks will be widely used in modern surveillance and autonomous driving systems for automatic vehicle detection. Second, unfortunately, these neural networks are intriguingly vulnerable to adversarial examples BID1 . BID39 found that adding imperceptible perturbations to clean images can result in the failure of neural networks trained for image classification. This motivates a rich line of work on developing defense techniques for the neural networks BID1 and powerful attack methods to defeat those defenses BID3 . Moreover, the adversarial attack has been extended to other tasks, such as semantic segmentation BID2 , object detection BID44 , image captioning BID9 , etc.Figure 1: A Toyota Camry XLE in the center of the image fools the Mask R-CNN object detector after we apply the learned camouflage to it (on the right), whereas neither plain colors (on the left) nor a random camouflage (in the middle) is able to escape the Camry from being detected.It is worth noting that the adversarial examples in the works mentioned above are not physical, i.e., the adversary directly manipulates image pixels. Although it is arguably more challenging to create physical adversarial objects than to produce adversarial images, some existing works have shown promising results with adversarial patches BID7 , stop signs BID14 BID11 , and small objects like baseballs and 3D turtle models BID4 .To this end, we are reasonably optimistic about designing a special pattern to camouflage a 3D car, in order to make it difficult to detect by the deep learning based vehicle detectors.It is undoubtedly challenging to run experiments in the real world considering financial and time constraints. In this paper, we instead demonstrate results using a simulation engine (Unreal) with a high-fidelity 3D sedan model and a 3D SUV. Fig. 1 shows that the vehicle in the simulation is photo-realistic such that, even covered with random camouflage, it can still be detected by the Mask R-CNN detector BID18 ) trained on COCO BID21 .The simulation engine enables us to test the physically adversarial cars under a considerable spectrum of environmental conditions: lighting, backgrounds, camera-to-object distances, viewing angles, occlusions, etc. In contrast, existing experiments on physical adversarial attacks are all executed in simplified scenarios. BID14 , BID13 , and BID11 attack neural classifiers and detectors of stop signs. While projective transformations could be used to render the planar stop signs to various images, it is more involved to image the nonplanar 3D vehicles considered in this paper; we learn a neural approximation function instead. BID4 synthesize objects (e.g., baseball , turtle, etc.) which are adversarial within a small range of camera-to-object distances and viewing angles.Given a 3D vehicle model in the simulation engine, we learn a camouflage for it by following the expectation over transformation (EoT) principle first formalized by BID4 . The main idea is to consider a variety of transformations under which the camouflage can consistently hide the vehicle from a neural detector. A transformation imitates the imaging procedure and produces an image of the 3D vehicle model in the simulated environment. If a camouflage works under many transformations seen in the training phase, it is expected to also generalize to unseen transformations in the test phase.One of the major challenges is that the simulator's image generation procedure is non-differentiable. A seemingly plausible solution is to train a neural network to approximate this procedure. The network takes as input the environment, a camouflage pattern, and the 3D vehicle model and outputs an image as close as possible to the one rendered by the simulator. Although this approach is viable, it is extremely difficult to generate high-resolution images. State-of-the-art methods (e.g., RenderNet (Nguyen-Phuoc et al., 2018) ) can only generate simple 3D objects without any backgrounds.We tackle the above challenge by drawing the following observation. In EoT BID4 BID11 , the gradients propagate back to the physical object from the detector/classifier's decision values. If we jointly consider the object detector and the imaging procedure of the simulator as a whole black box, it is easier to learn a function to approximate this black box's behavior than to train the image generation neural network. Hence, we learn a substitute neural network which takes as input a camouflage , the vehicle model, and the environment and outputs the vehicle detector's decision value. Equipped with this substitute network, we can readily run the EoT algorithm BID4 over our simulator in order to infer an adversarial camouflage for the vehicles.Finally, we make some remarks about the significance and potential impact of this work. In the real world, multiclass visual object detection neural networks BID18 BID32 have become the cornerstone of multiple industrial applications, such as surveillance systems BID27 , autonomous driving BID19 , and military systems BID30 . Among these applications, cars are one of the most crucial objects. Attacking vehicle detectors in the physical world will be enormously valuable and impactful from the perspective of the malicious adversaries. Compared with the stop sign, it is legal in the United States to paint a car while defacing a stop sign is criminal. This poses a more significant threat to autonomous driving systems since anyone has access to perturb public machine learning based systems legally. This observation motivates us to focus our approach on cars. We limit our camouflage within the legally paintable car body parts, which means that we will leave discriminative visual cues, such as the tires, windows, grille, lights, etc. unaltered for the detectors. In this paper, we investigate whether it is possible to physically camouflage 3D objects of complex shapes, i.e., vehicles, in order to hide them from state-of-the-art object detectors. We conduct extensive experimental studies with a photo-realistic simulation engine. We propose to use a clone network to mimic the simulator and the detector's joint response to the 3D vehicles. Then, we infer a camouflage for a 3D vehicle by minimizing the output of the clone network. Our learned camouflage significantly reduces the detectability of a Toyota Camry and a SUV. Moreover, we find that the camouflage is transferable across different environments. For future work, We plan to look into possible ways to white-box the entire process so as to propose a more effective camouflage.",paper conduct intriguing experimental study physical adversarial attack object detectors wild. particular learn camouflage pattern hide vehicles detected state-of-the-art convolutional neural network based detectors. approach alternates two threads. first train neural approximation function imitate how a simulator applies camouflage vehicles how a vehicle detector performs given images camouflaged vehicles. second minimize approximated detection score searching optimal camouflage. Experiments show learned camouflage can not only hide vehicle image-based detectors many test cases also generalizes different environments vehicles object detectors. Is it possible paint unique pattern vehicle's body hence hide detected surveillance cameras? conjecture answer is affirmative mainly two reasons. First deep neural networks will be widely used modern surveillance autonomous driving systems automatic vehicle detection. Second unfortunately neural networks are intriguingly vulnerable adversarial examples BID1. BID39 found adding imperceptible perturbations clean images can result failure neural networks trained image classification. motivates rich line work developing defense techniques neural networks BID1 powerful attack methods defeat defenses BID3. Moreover adversarial attack has been extended tasks semantic segmentation BID2 object detection BID44 image captioning BID9 etc.Figure1:Toyota Camry XLE center image fools Mask R-CNN object detector apply learned camouflage right whereas neither plain colors left random camouflage middle is able escape Camry detected.It is worth noting adversarial examples works mentioned are not physical.e adversary directly manipulates image pixels. Although is arguably challenging create physical adversarial objects produce adversarial images existing works have shown promising results adversarial patches BID7 stop signs BID14 BID11 small objects like baseballs 3D turtle models BID4.To end are reasonably optimistic designing special pattern camouflage 3D car order make difficult detect deep learning based vehicle detectors.It is undoubtedly challenging run experiments real world considering financial time constraints. paper instead demonstrate results using simulation engine Unreal high-fidelity 3D sedan model 3D SUV. Fig. 1 shows vehicle simulation is photo-realistic even covered random camouflage can still detected Mask R-CNN detector BID18 trained COCO BID21.The simulation engine enablesus test physically adversarial cars considerable spectrum environmental conditions:lighting backgrounds camera-to-object distances viewing angles occlusions etc. contrast existing experiments physical adversarial attacks are all executed simplified scenarios. BID14 BID13 BID11 attack neural classifiers detectors stop signs. projective transformations could used render planar stop signs various images is more involved image nonplanar 3D vehicles considered paper;learn neural approximation function instead. BID4 synthesize objects e.g baseball turtle etc. which are adversarial within small range camera-to-object distances viewing angles.Given 3D vehicle model simulation engine learn camouflage following expectation transformation EoT principle first formalized BID4. main idea is to consider variety transformations which the camouflage can consistently hide vehicle neural detector. transformation imitates imaging procedure produces image 3D vehicle model simulated environment. If a camouflage works many transformations seen training phase is expected also generalize unseen transformations test phase.One major challenges is that the simulator's image generation procedure is non-differentiable non-differentiable seemingly plausible solution is to train neural network approximate procedure. network takes input environment camouflage pattern 3D vehicle model outputs image close possible one rendered simulator. Although approach is viable is extremely difficult generate high-resolution images. State-of-the-art methods e.g RenderNet Nguyen-Phuocetal. 2018 can only generate simple 3D objects without backgrounds.We tackle challenge drawing following observation. EoT BID4 BID11 gradients propagate back physical object detector/classifier's decision values. If we jointly consider object detector imaging procedure simulator whole black box is easier learn function approximate black box's behavior train image generation neural network. Hence learn substitute neural network which takes input camouflage vehicle model environment outputs vehicle detector's decision value. Equipped substitute network can readily run EoT algorithm BID4 simulator order infer adversarial camouflage vehicles.Finally make remarks significance potential impact work. real world multiclass visual object detection neural networks BID18 BID32 have become cornerstone multiple industrial applications surveillance systems BID27 autonomous driving BID19 military systems BID30. Among applications cars are one crucial objects. Attacking vehicle detectors physical world will be enormously valuable impactful perspective malicious adversaries. Compared stop sign is legal United States paint car defacing stop sign is criminal. poses significant threat autonomous driving systems since anyone has access perturb public machine learning based systems legally. observation motivatesus focus approach cars. limit camouflage within legally paintable car body parts which means will leave discriminative visual cues tires windows grille lights etc. unaltered detectors. paper investigate whether is possible physically camouflage 3D objects complex shapes.e vehicles order hide state-of-the-art object detectors. conduct extensive experimental studies photo-realistic simulation engine. propose use clone network mimic simulator detector's joint response 3D vehicles. infer camouflage 3D vehicle minimizing output clone network. learned camouflage significantly reduces detectability Toyota Camry SUV. Moreover find camouflage is transferable across different environments. future work plan look possible ways white-box entire process propose effective camouflage.,1467,991,476,0.016,1.48,2025/11/05 17:18:54,0.01,1.457,0.467289719626168,457.896
"As deep learning-based classifiers are increasingly adopted in real-world applications, the importance of understanding how a particular label is chosen grows. Single decision trees are an example of a simple, interpretable classifier, but are unsuitable for use with complex, high-dimensional data. On the other hand, the variational autoencoder (VAE) is designed to learn a factored, low-dimensional representation of data, but typically encodes high-likelihood data in an intrinsically non-separable way.   We introduce the differentiable decision tree (DDT) as a modular component of deep networks and a simple, differentiable loss function that allows for end-to-end optimization of a deep network to compress high-dimensional data for classification by a single decision tree.   We also explore the power of labeled data in a  supervised VAE (SVAE) with a Gaussian mixture prior, which leverages label information to produce a high-quality generative model with improved bounds on log-likelihood.   We combine the SVAE with the DDT to get our classifier+VAE (C+VAE), which is competitive in both classification error and log-likelihood, despite optimizing both simultaneously and using a very simple encoder/decoder architecture. While deep learning approaches are very effective in many classification problems, interpretability of the classifier (why a particular classification was made) can be very difficult, yet critical for many applications. Decision trees are highly interpretable classifiers, so long as the data is encoded such that the classes can be easily separated. We present a differentiable decision tree (DDT) that we connect to a variational autoencoder (VAE) to learn an embedding of the data that the tree can classify with low expected loss. The expected loss of the DDT is differentiable, so standard gradient-based methods may be applied in training.Since we work in a supervised learning setting, it is natural to exploit the label information when training the VAE. Thus, we employ a supervised VAE (SVAE) that uses a class-specific Gaussian mixture distribution as its prior distribution. We found that the SVAE was very effective in exploiting label information, resulting in improved log-likelihood due to separation of classes in latent space. Further, when we combined SVAE with DDT (yielding our Classifier+VAE, or C+VAE), we got a model that is competitive in both classification error and log-likelihood, despite optimizing both simultaneously and using a very simple encoder/decoder architecture. Further, the resultant decision tree revealed clear semantic meanings in its internal nodes.",deep learning-based classifiers are increasingly adopted real-world applications importance understanding how a particular label is chosen grows. Single decision trees are an example simple interpretable classifier are unsuitable use complex high-dimensional data. hand variational autoencoder VAE is designed learn factored low-dimensional representation data typically encodes high-likelihood data intrinsically non-separable way. introduce differentiable decision tree DDT modular component deep networks simple differentiable loss function allows end-to-end optimization deep network compress high-dimensional data classification single decision tree. also explore power labeled data supervised VAE SVAE Gaussian mixture prior which leverages label information produce high-quality generative model improved bounds log-likelihood combine SVAE DDT get classifier+VAE C+VAE which is competitive classification error log-likelihood despite optimizing simultaneously using simple encoder/decoder architecture. deep learning approaches are very effective many classification problems interpretability classifier why a particular classification was made can be very difficult yet critical many applications. Decision trees are highly interpretable classifiers long data is encoded classes can be easily separated. present differentiable decision tree DDT connect variational autoencoder VAE learn embedding data tree can classify low expected loss. expected loss DDT is differentiable standard gradient-based methods may applied training.Since work supervised learning setting is natural exploit label information when training VAE. Thus employ supervised VAE SVAE uses class-specific Gaussian mixture distribution prior distribution. found SVAE was very effective exploiting label information resulting improved log-likelihood due separation classes latent space. when we combined SVAE DDT yielding Classifier+VAE C+VAE got model is competitive classification error log-likelihood despite optimizing simultaneously using simple encoder/decoder architecture. resultant decision tree revealed clear semantic meanings internal nodes.,513,341,172,0.005,1.504,2025/11/05 17:18:54,0.0,1.455,0.542056074766355,173.962
"We propose Regularized Learning under Label shifts (RLLS), a principled and a practical domain-adaptation algorithm to correct for shifts in the label distribution between a source and a target domain. We first estimate importance weights using labeled source data and unlabeled target data, and then train a classifier on the weighted source samples. We derive a generalization bound for the classifier on the target domain which is independent of the (ambient) data dimensions, and instead only depends on the complexity of the function class. To the best of our knowledge, this is the first generalization bound for the label-shift problem where the labels in the target domain are not available. Based on this bound, we propose a regularized estimator for the small-sample regime which accounts for the uncertainty in the estimated weights. Experiments on the CIFAR-10 and MNIST datasets show that RLLS improves classification accuracy, especially in the low sample and large-shift regimes, compared to previous methods. When machine learning models are employed ""in the wild"", the distribution of the data of interest(target distribution) can be significantly shifted compared to the distribution of the data on which the model was trained (source distribution). In many cases, the publicly available large-scale datasets with which the models are trained do not represent and reflect the statistics of a particular dataset of interest. This is for example relevant in managed services on cloud providers used by clients in different domains and regions, or medical diagnostic tools trained on data collected in a small number of hospitals and deployed on previously unobserved populations and time frames. In this work, we establish the first generalization guarantee for the label shift setting and propose an importance weighting procedure for which no prior knowledge of q(y)/p(y ) is required. Although RLLS is inspired by BBSL, it leads to a more robust importance weight estimator as well as generalization guarantees in particular for the small sample regime, which BBSL does not allow for. RLLS is also equipped with a sample-size-dependent regularization technique and further improves the classifier in both regimes.We consider this work a necessary step in the direction of solving shifts of this type, although the label shift assumption itself might be too simplified in the real world. In future work, we plan to also study the setting when it is slightly violated. For instance , x in practice cannot be solely explained by the wanted label y, but may also depend on attributes z which might not be observable. In the disease prediction task for example, the symptoms might not only depend on the disease but also on the city and living conditions of its population. In such a case , the label shift assumption only holds in a slightly modified sense, i.e. P(X|Y = y, Z = z) = Q(X|Y = y, Z = z). If the attributes Z are observed, then our framework can readily be used to perform importance weighting.Furthermore, it is not clear whether the final predictor is in fact ""better"" or more robust to shifts just because it achieves a better target accuracy than a vanilla unweighted estimator. In fact, there is a reason to believe that under certain shift scenarios, the predictor might learn to use spurious correlations to boost accuracy. Finding a procedure which can both learn a robust model and achieve high accuracies on new target sets remains to be an ongoing challenge. Moreover, the current choice of regularization depends on the number of samples rather than data-driven regularization which is more desirable.An important direction towards active learning for the same disease-symptoms scenario is when we also have an expert for diagnosing a limited number of patients in the target location. Now the question is which patients would be most ""useful"" to diagnose to obtain a high accuracy on the entire target set? Furthermore, in the case of high risk , we might be able to choose some of the patients for further medical diagnosis or treatment, up to some varying cost. We plan to extend the current framework to the active learning setting where we actively query the label of certain x's BID5 as well as the cost-sensitive setting where we also consider the cost of querying labels (Krishnamurthy et al., 2017) .Consider a realizable and over-parameterized setting, where there exists a deterministic mapping from x to y, and also suppose a perfect interpolation of the source data with a minimum proper norm is desired. In this case, weighting the samples in the empirical loss might not alter the trained classifier BID3 . Therefore, our results might not directly help the design of better classifiers in this particular regime. However, for the general overparameterized settings, it remains an open problem of how the importance weighting can improve the generalization. We leave this study for future work.",propose Regularized Learning Label shifts RLLS principled practical domain-adaptation algorithm correct shifts label distribution source target domain. first estimate importance weights using labeled source data unlabeled target data train classifier weighted source samples. derive generalization bound classifier target domain which is independent ambient data dimensions instead depends complexity function class. best knowledge is the first generalization bound label-shift problem where the labels target domain are not available. Based bound propose regularized estimator small-sample regime which accounts uncertainty estimated weights. Experiments CIFAR-10 MNIST datasets show RLLS improves classification accuracy especially low sample large-shift regimes compared previous methods. When machine learning models are employed wild distribution data interest target distribution can be significantly shifted compared distribution data which the model was trained source distribution many cases publicly available large-scale datasets which the models are trained do not represent reflect statistics particular dataset interest. is for example relevant managed services cloud providers used clients different domains regions medical diagnostic tools trained data collected small number hospitals deployed previously unobserved populations time frames. work establish first generalization guarantee label shift setting propose importance weighting procedure which no prior knowledge q/p is required. Although RLLS is inspired BBSL leads robust importance weight estimator well generalization guarantees particular small sample regime which BBSL does not allow for. RLLS is is when we also equipped sample-size-dependent regularization technique improves classifier regimes.We consider work necessary step direction solving shifts type although label shift assumption might simplified real world. future work plan also study setting when it is slightly violated. instance x practice cannot solely explained wanted label may also depend attributesz might observable. disease prediction task example symptoms might depend disease also city living conditions population. case label shift assumption holds slightly modified sense.eP X|Y Z z Q X|Y Z z If the attributesZ are observed framework can readily used perform importance weighting.Furthermore is not clear whether final predictor is in fact better robust shifts achieves better target accuracy vanilla unweighted estimator. fact is a reason believe certain shift scenarios predictor might learn use spurious correlations boost accuracy. Finding procedure which can both learn robust model achieve high accuracies new target sets remains ongoing challenge. Moreover current choice regularization depends number samples rather data-driven regularization which is more desirable.An important direction towards active learning disease-symptoms scenario is is when we also have an expert diagnosing limited number patients target location. question is which patients would useful diagnose obtain high accuracy entire target set? Furthermore case high risk might able choose patients medical diagnosis treatment varying cost. plan extend current framework active learning setting where we actively query label certain x's BID5 well cost-sensitive setting where we also consider cost querying labels Krishnamurthyetal. 2017.Consider realizable over-parameterized setting where there exists deterministic mapping x also suppose perfect interpolation source data minimum proper norm is desired. case weighting samples empirical loss might alter trained classifier BID3. Therefore results might directly help design better classifiers particular regime. However general overparameterized settings remains open problem how the importance weighting can improve generalization. leave study future work.,957,613,344,0.01,1.561,2025/11/05 17:18:54,0.01,1.763,0.7196261682242987,311.522
"The statistics of the real visual world presents a long-tailed distribution: a few classes have significantly more training instances than the remaining classes in a dataset. This is because the real visual world has a few classes that are common while others are rare. Unfortunately, the performance of a convolutional neural network is typically unsatisfactory when trained using a long-tailed dataset. To alleviate this issue, we propose a method that discriminatively learns an embedding in which a simple Bayesian classifier can balance the class-priors to generalize well for rare classes. To this end, the proposed approach uses a Gaussian mixture model to factor out class-likelihoods and class-priors in a long-tailed dataset. The proposed method is simple and easy-to-implement in existing deep learning frameworks. Experiments on publicly available datasets show that the proposed approach improves the performance on classes with few training instances, while maintaining a comparable performance to the state-of-the-art on classes with abundant training examples. Deep convolutional neural networks (CNN) have achieved impressive results in large-scale visual recognition tasks BID13 BID25 BID29 BID18 BID8 BID10 . However, despite the significant impact in visual perception, the vast majority of these advancements learn from artificially balanced largescale datasets that are not representative of the real visual world BID19 BID5 BID3 BID21 BID15 BID23 . The statistics of the real visual world follow a long-tailed distribution BID36 BID32 BID24 BID33 BID34 . This means that a few classes are predominant in the world while others are rare. Consequently, representative real-world datasets have a few classes with significantly more training instances than the remaining classes in the set; see Fig. 1 (a) for an illustration of a long-tailed dataset. We refer to classes with abundant training instances as classes in the head, and unrepresented classes as classes in the tail.As BID32 note, the main motivation for visual recognition is to understand and learn from the real visual world. Thus, while the state-of-the-art can challenge humans in visual recognition tasks, it misses a mechanism that effectively learns from long-tailed datasets. As BID32 found, training models using long-tailed datasets often leads to unsatisfying performance. This is because classifiers tend to generalize well for classes in the head, but lack generalization for classes in the tail.To alleviate this issue, learned classifiers need to generalize for classes in the tail while maintaining a good performance for all the classes. Recent efforts that aim to learn from long-tailed datasets consider penalities in the optimization-learning problem BID9 , sampling-based methods BID7 , and transfer-learning algorithms BID33 BID34 . In contrast with these solutions, the proposed method aims to learn an embedding in which the distribution of the real visual world allows a simple Bayesian classifier to predict robustly given a long-tailed dataset.Long-tailed datasets have class-prior statistics that heavily skew towards classes in the head. This skew can bias classifiers towards classes in the head, and consequently can reduce generalization for classes in the tail. To remove this skew, we appeal to Bayesian classifiers that can explicitly Figure 1: (a) The real visual world yields long-tailed datasets. Classes in the head are common (e.g., cats) while classes in the tail are rare (e.g., white reindeers). (b) The proposed approach builds a generative (Bayesian) classifier over a learned embedding to compute class-posterior probabilities. In an empirical Bayesian framework, posteriors are computed through class likelihoods and priors fit to the data (e.g., sample means, variances, and counts assuming Gaussian Mixture Models). We introduce an end-to-end pipeline for jointly learning embeddings and Bayesian models built upon them. (c) Bayesian models are particularly well-suited for long-tailed datasets because class priors and likelihoods can be fixed to be uniform and isotropic, ensuring that the learned representation is balanced across the head and tail.factor out the likelihood and prior when computing posteriors over class labels. Thus, the main goal of this work is to learn a feature embedding in which class prior statistics do not affect/skew class likelihoods. The proposed approach uses a simple Gaussian mixture model (GMM) to describe the statistics of a long-tailed dataset. This is because it enables a clean factorization of the class-likelihoods and class-priors. Moreover, it easily fits within an empirical Bayesian classification framework, because a GMM enables the computation of closed-form maximum likelihood estimation (MLE) of class-specific means, covariance matrices, and priors. We show that such closed-form estimates can be integrated into existing deep learning optimizers without much effort. By fixing the covariance matrices of all the classes to be the identity and the priors over each class to be uniform, we can explicitly enforce that both rare classes in the tail and dominant classes in the head have equal weight for Bayesian classification. In simple terms: we learn a discriminative embedding of training data such that Bayesian classifiers with balanced priors produce accurate class posteriors. As a point of clarity, the proposed approach does not learn an embedding in the traditional Bayesian sense, which might define a prior distribution over embeddings that is then combined with training data to produce a posterior embedding. Rather, it learns a single embedding that is discriminatively trained to produce accurate features for Bayesian classifiers. See Fig. 1 for an illustration about the proposed approach.A GMM not only is useful for learning an embedding using a long-tailed dataset, but also provides flexibility at the evaluation stage. This is because it enables the measurement of generalization for classes in the tail by simply setting equal class-prior probabilities. In addition, it enables the possibility of giving more importance to the most frequent classes by adjusting their respective class-prior probabilities.In sum, the proposed approach aims to learn an embedding in which a GMM enables a Bayesian classifier to generalize well for classes in the tail by balancing out class-priors. The proposed method is simple, easy-to-train using deep learning frameworks, and increases classification performance for classes in the tail. The experiments on publicly available datasets show that this approach tends to perform better on classes in the tail than the competing methods, while performing comparable to the state-of-the-art on classes with abundant training instances. Other probabilistic models: Our analysis and experiments focus on Gaussian Mixture Models, but the general learning problem from Eq. (4) holds for other probabilistic models. For example, deep embeddings can be learned for rectified (nonnegative) or binary features BID0 BID4 . For such embeddings, likelihood models based on rectified Gaussians or multivariate Bernoulli distributions may be more appropriate BID27 BID30 . Such models do not appear to have closed form maximum likelihood estimates, and so may be challenging to formulate precisely as a constrained optimization problem.Relationship to softmax: The GMM-based formulation has a direct relationship with softmax classifiers. This relationship can be obtained by expanding the squared distance terms in the classposterior probability, yielding the following: DISPLAYFORM0 where v j = µ j and DISPLAYFORM1 2 is a common term between the numerator and denominator. This relationship thus indicates that the proposed approach fits linear classifiers with restricted biases. This relationship is useful for an easy implementation in many deep learning frameworks. This is because this approach can be implemented using a dense layer without the bias terms. In addition, this relationship shows that the proposed approach requires fewer parametersto-learn in comparison with classical CNN-softmax models. An more intuitive comparison between GMMs and softmax classifiers can be made with respect to to their parameter updates. Intuitively, during softmax training, an ""easy"" example of a class will not generate a model update. In some sense, this might be considered paradoxical. When children learn a new concept (for say, a neverbefore-seen animal), they tend to be presented with an easy or ""protypical"" example. On the other hand, an easy example of a class will change its centroid, generating a signal for learning -see FIG1 . This work introduced a method that improves the classification performance for classes in the tail. The proposed approach is based on a Gaussian mixture model that allows a Bayesian classifier to represent the distribution of a long-tailed dataset and to compute the class-prediction probabilities. The experiments on publicly available dataset show that the proposed approach tends to increase the classification accuracy for classes in the tail while maintaining a comparable accuracy to that of a softmax classifier for classes in the head. In addition, this work introduced an evaluation method for methods that tackle the learning of concepts from a long-tailed dataset. Finally, this work demon-strated that class-centroid approaches overall tend to generalize well for classes in the tail while maintaining a comparable performance to that of a softmax classifiers for classes in the head.",statistics real visual world presents long-tailed distribution:classes have significantly training instances remaining classes dataset. is because the real visual world has a few classes are common others are rare. Unfortunately performance convolutional neural network is typically unsatisfactory when trained using long-tailed dataset. alleviate issue propose method is discriminatively learns embedding which a simple Bayesian classifier can balance class-priors generalize well rare classes. end proposed approach uses Gaussian mixture model factor class-likelihoods class-priors long-tailed dataset. proposed method is simple easy-to-implement existing deep learning frameworks. Experiments publicly available datasets show proposed approach improves performance classes training instances maintaining comparable performance state-of-the-art classes abundant training examples. Deep convolutional neural networks CNN have achieved impressive results large-scale visual recognition tasks BID13 BID25 BID29 BID18 BID8 BID10. However despite significant impact visual perception vast majority advancements learn artificially balanced largescale datasets are not representative real visual world BID19 BID5 BID3 BID21 BID15 BID23. statistics real visual world follow long-tailed distribution BID36 BID32 BID24 BID33 BID34. means classes are predominant world others are rare. Consequently representative real-world datasets have a few classes significantly training instances remaining classes set;see Fig. 1 illustration long-tailed dataset. refer classes abundant training instances classes head unrepresented classes classes tail.As BID32 note main motivation visual recognition is to understand learn real visual world. Thus state-of-the-art can challenge humans visual recognition tasks misses mechanism effectively learns long-tailed datasets. BID32 found training models using long-tailed datasets often leads unsatisfying performance. is because classifiers tend generalize well classes head lack generalization classes tail.To alleviate issue learned classifiers need generalize classes tail maintaining good performance classes. Recent efforts aim learn long-tailed datasets consider penalities optimization-learning problem BID9 sampling-based methods BID7 transfer-learning algorithms BID33 BID34. contrast solutions proposed method aims learn embedding which the distribution real visual world allows simple Bayesian classifier predict robustly given long-tailed dataset.Long-tailed datasets have class-prior statistics heavily skew towards classes head. skew can bias classifiers towards classes head consequently can reduce generalization classes tail. remove skew appeal Bayesian classifiers can explicitly Figure1:real visual world yields long-tailed datasets. Classes head are common e.g cats classes tail are rare e.g white reindeers b proposed approach builds generative Bayesian classifier learned embedding compute class-posterior probabilities. empirical Bayesian framework posteriors are computed class likelihoods priors fit data e.g sample means variances counts assuming Gaussian Mixture Models introduce end-to-end pipeline jointly learning embeddings Bayesian models built upon them. c Bayesian models are particularly well-suited long-tailed datasets class priors likelihoods can be fixed uniform isotropic ensuring learned representation is balanced across head tail.factor likelihood prior when computing posteriors class labels. Thus main goal work is to learn feature embedding which class prior statistics do not affect/skew class likelihoods. proposed approach uses simple Gaussian mixture model GMM describe statistics long-tailed dataset. is because it enables clean factorization class-likelihoods class-priors Moreover easily fits within empirical Bayesian classification framework GMM enables computation closed-form maximum likelihood estimation MLE class-specific means covariance matrices priors. show closed-form estimates can be integrated existing deep learning optimizers without much effort. fixing covariance matrices classes identity priors class uniform can explicitly enforce rare classes tail dominant classes head have equal weight Bayesian classification. simple terms:learn discriminative embedding training data Bayesian classifiers balanced priors produce accurate class posteriors. point clarity proposed approach does not learn embedding traditional Bayesian sense might define prior distribution embeddings is then combined training data produce posterior embedding. Rather learns single embedding is discriminatively trained produce accurate features Bayesian classifiers. See Fig. 1 illustration proposed approach.A GMM is useful learning embedding using long-tailed dataset also provides flexibility evaluation stage. is because it enables measurement generalization classes tail simply setting equal class-prior probabilities. addition enables possibility giving importance frequent classes adjusting respective class-prior probabilities.In sum proposed approach aims learn embedding which a GMM enables Bayesian classifier generalize well classes tail balancing class-priors proposed method is simple easy-to-train using deep learning frameworks increases classification performance classes tail. experiments publicly available datasets show approach tends perform better classes tail competing methods performing comparable state-of-the-art classes abundant training instances. probabilistic models:analysis experiments focus Gaussian Mixture Models general learning problem Eq. 4 holds probabilistic models. example deep embeddings can be learned rectified nonnegative binary features BID0 BID4. embeddings likelihood models based rectified Gaussians multivariate Bernoulli distributions may appropriate BID27 BID30. models do not appear have closed form maximum likelihood estimates may challenging formulate precisely constrained optimization problem.Relationship softmax:GMM-based formulation has a direct relationship softmax classifiers. relationship can be obtained expanding squared distance terms classposterior probability yielding following:DISPLAYFORM0 wherevj µj DISPLAYFORM12 is a common term numerator denominator. relationship thus indicates proposed approach fits linear classifiers restricted biases. relationship is useful easy implementation many deep learning frameworks. is because this approach can be implemented using dense layer without bias terms. addition relationship shows proposed approach requires fewer parametersto-learn comparison classical CNN-softmax models. intuitive comparison GMMs softmax classifiers can be made respect parameter updates. Intuitively softmax training easy example class will not generate model update. sense might considered paradoxical. When children learn new concept say neverbefore-seen animal tend presented easy protypical example. hand easy example class will change centroid generating signal learning -see FIG1. work introduced method improves classification performance classes tail. proposed approach is based Gaussian mixture model allows Bayesian classifier represent distribution long-tailed dataset compute class-prediction probabilities. experiments publicly available dataset show proposed approach tends increase classification accuracy classes tail maintaining comparable accuracy softmax classifier classes head. addition work introduced evaluation method methods tackle learning concepts long-tailed dataset. Finally work demon-strated class-centroid approaches overall tend generalize well classes tail maintaining comparable performance softmax classifiers classes head.,1792,1212,580,0.024,1.479,2025/11/05 17:18:54,0.01,1.545,0.4641744548286605,543.273
"As deep reinforcement learning is being applied to more and more tasks, there is a growing need to better understand and probe the learned agents. Visualizing and understanding the decision making process can be very valuable to comprehend and identify problems in the learned behavior. However, this topic has been relatively under-explored in the reinforcement learning community. In this work we present a method for synthesizing states of interest for a trained agent. Such states could be situations (e.g. crashing or damaging a car) in which specific actions are necessary. Further, critical states in which a very high or a very low reward can be achieved (e.g. risky states) are often interesting to understand the situational awareness of the system. To this end, we learn a generative model over the state space of the environment and use its latent space to optimize a target function for the state of interest. In our experiments we show that this method can generate insightful visualizations for a variety of environments and reinforcement learning methods. We explore these issues in the standard Atari benchmark games as well as in an autonomous driving simulator. Based on the efficiency with which we have been able to identify significant decision scenarios with this technique, we believe this general approach could serve as an important tool for AI safety applications. Humans can naturally learn and perform well at a wide variety of tasks, driven by instinct and practice; more importantly, they are able to justify why they would take a certain action. Artificial agents should be equipped with the same capability, so that their decision making process is interpretable by researchers. Following the enormous success of deep learning in various domains, such as the application of convolutional neural networks (CNNs) to computer vision BID19 BID18 BID20 BID33 , a need for understanding and analyzing the trained models has arisen. Several such methods have been proposed and work well in this domain, for example for image classification BID35 BID44 BID8 , sequential models BID12 or through attention BID41 .Deep reinforcement learning (RL) agents also use CNNs to gain perception and learn policies directly from image sequences. However , little work has been so far done in analyzing RL networks. We found that directly applying common visualization techniques to RL agents often leads to poor results. In this paper, we present a novel technique to generate insightful visualizations for pre-trained agents.Currently, the generalization capability of an agent is-in the best case-evaluated on a validation set of scenarios. However , this means that this validation set has to be carefully crafted to encompass as many potential failure cases as possible. As an example, consider the case of a self-driving agent, where it is near impossible to exhaustively model all interactions of the agent with other drivers, pedestrians, cyclists, weather conditions, even in simulation. Our goal is to extrapolate from the training scenes to novel states that induce a specified behavior in the agent.In our work, we learn a generative model of the environment as an input to the agent. This allows us to probe the agent's behavior in novel states created by an optimization scheme to induce specific actions in the agent. For example we could optimize for states in which the agent sees the only option as being to slam on the brakes; or states in which the agent expects to score exceptionally low. Visualizing such states allows to observe the agent's interaction with the environment in critical scenarios to understand its shortcomings. Furthermore , it is possible to generate states based on an objective function specified by the user. Lastly, our method does not affect and does not depend on the training of the agent and thus is applicable to a wide variety of reinforcement learning algorithms. We have presented a method to synthesize inputs to deep reinforcement learning agents based on generative modeling of the environment and user-defined objective functions. Training the generator to produce states that the agent perceives as those from the real environment enables optimizing its latent space to sample states of interest. We believe that understanding and visualizing agent behavior in safety critical situations is a crucial step towards creating safer and more robust agents using reinforcement learning. We have found that the methods explored here can indeed help accelerate the detection of problematic situations for a given learned agent. As such we intend to build upon this work.",deep reinforcement learning is being applied tasks is a growing need better understand probe learned agents. Visualizing understanding decision making process can be very valuable comprehend identify problems learned behavior. However topic has been relatively under-explored reinforcement learning community. work present method synthesizing states interest trained agent. states could situations e.g crashing damaging car which specific actions are necessary. critical states which a very high low reward can be achieved e.g risky states are often interesting understand situational awareness system. end learn generative model state space environment use latent space optimize target function state interest. experiments show method can generate insightful visualizations variety environments reinforcement learning methods. explore issues standard Atari benchmark games well autonomous driving simulator. Based efficiency which we have able identify significant decision scenarios technique believe general approach could serve important tool AI safety applications. Humans can naturally learn perform well wide variety tasks driven instinct practice;importantly are able justify would take certain action. Artificial agents should be equipped capability decision making process is interpretable researchers. Following enormous success deep learning various domains application convolutional neural networks CNNs computer vision BID19 BID18 BID20 BID33 need understanding analyzing trained models has arisen. Several methods have been proposed work well domain example image classification BID35 BID44 BID8 sequential models BID12 attention BID41.Deep reinforcement learning RL agents also use CNNs gain perception learn policies directly image sequences. However little work has been so far done analyzing RL networks. have found directly applying common visualization techniques RL agents often leads poor results. paper present novel technique generate insightful visualizations pre-trained agents.Currently generalization capability agent is-in best case-evaluated validation set scenarios. However means validation set has to be carefully crafted encompass many potential failure cases possible. example consider case self-driving agent where it is near impossible exhaustively model interactions agent drivers pedestrians cyclists weather conditions even simulation. goal is to extrapolate training scenes novel states induce specified behavior agent.In work learn generative model environment input agent. allowsus probe agent's behavior novel states created optimization scheme induce specific actions which the agent. example could optimize states which the agent sees option slam brakes;states which the agent expects score exceptionally low. Visualizing states allows observe agent's interaction environment critical scenarios understand shortcomings. Furthermore is possible generate states based objective function specified user. Lastly method does not affect does not depend training agent thus is applicable wide variety reinforcement learning algorithms. have presented method synthesize inputs deep reinforcement learning agents based generative modeling environment user-defined objective functions. Training generator produce states agent perceives real environment enables optimizing latent space sample states interest. believe understanding visualizing agent behavior safety critical situations is a crucial step towards creating safer robust agents using reinforcement learning. have found methods explored can indeed help accelerate detection problematic situations given learned agent. intend build upon work.,843,547,296,0.009,1.541,2025/11/05 17:18:54,0.0,1.767,0.6573208722741429,297.066
"We introduce the deep abstaining classifier -- a deep neural network trained with a novel loss function that provides an abstention option during training. This allows the  DNN to abstain on confusing or difficult-to-learn examples while improving performance on the non-abstained samples. We show that such deep abstaining classifiers can: (i) learn representations for structured noise -- where noisy training labels or confusing examples are correlated with underlying features -- and then learn to abstain based on such features; (ii) enable robust learning in the presence of arbitrary or unstructured noise by identifying noisy samples; and (iii) be used as an effective out-of-category detector that learns to reliably abstain when presented with samples from  unknown classes. We provide analytical results on loss function behavior that enable automatic tuning of accuracy and coverage, and demonstrate the utility of the deep abstaining classifier using multiple image benchmarks, Results indicate significant improvement in learning in the presence of label noise. Machine learning algorithms are expected to increasingly replace humans in decision-making pipelines. With the deployment of AI-based systems in high risk fields such as medical diagnosis BID23 , autonomous vehicle control BID19 and the legal sector BID3 , an erroneous prediction that should have otherwise been flagged for human interventionbecause the system has not robustly learned when it is likely to get the wrong answer -can have severe consequences.In these situations, the quality of ""knowing when it doesn't know"" and abstaining from predicting is an essential trait for a classifier to possess. This allows the decision-making to be routed to a human or another more accurate, but possibly more expensive, classifier, with the assumption being that the additional cost incurred is greatly surpassed by the consequences of a wrong prediction.Since learning systems have been around for multiple decades, there has been extensive theoretical and empirical investigation into rejection (or abstention) classification with the bulk of this being in the area of shallow learners BID5 BID7 BID10 and multilayer perceptrons BID8 . A framework for ""self-aware learning"" was analyzed in the context of Markov decision processes in BID20 . In the context of deep networks, this has been an under-explored area with BID11 recently proposing an effective technique of selective classification for optimizing risk-vs-coverage profiles based on the output of a trained model.The abstention formulations in all the previous works have been in a post-processing setting i.e., a classifier is first trained as usual, and an abstention threshold is determined based on post-training performance on a calibration set. In this paper, we introduce a method to train DNNs that utilizes an abstention option while training. Using a novel loss function -a modified version of the multi-class categorical cross-entropy loss that includes an abstention output -the representational capacity of a DNN is exploited for learning when abstention is a better option, while at the same improving performance on the non-abstained samples. We illustrate the utility of a DNN trained in this way in multiple situations: first, when labeling errors are correlated with some underlying feature of the data (systematic or structured label noise), abstention training allows the DNN to learn features that are indicative of unreliable training signals and which are thus likely to lead to uncertain predictions. This kind of representation learning for abstention is useful both for effectively eliminating structured noise and also for interpreting the reasons for abstention. Second, we show how an abstention-based approach can be used as a very effective data cleaner when training data contains arbitrary (or unstructured) label noise: a DNN trained with an abstention option can be used to identify and filter out noisy training data leading to significant performance benefits for downstream training using a cleaner set. Finally, we also consider the problem of open-set detection since real-world systems are often deployed in open-domain situations; when presented with samples from unknown classes, abstention is often the safest choice. We describe a method for utilizing abstention training for effective open-set detection by training the DNN to pickup only features associated with known classes, and abstain when such features are absent. To summarize, the contributions of this paper are:• The introduction of the deep abstaining classifier (DAC) -a DNN trained with a novel loss function that uses an abstention class while training -enabling robust learning in the presence of label noise.• The demonstration of the ability of the DAC to learn features associated with systematic label noise. Through numerous experiments, we show how the DAC is able to pick up (and then abstain on) such features with remarkable precision.• Demonstration of the utility of the DAC as a highly effective data cleaner in the presence of arbitrary label noise. We provide results on learning with noisy labels on multiple image benchmarks (CIFAR-10, CIFAR-100 and Fashion-MNIST) that are competitive and in many cases, significantly improve performance compared to existing methods.• Illustration of the DAC as an effective open-set detector that learns to reliably abstain when presented with samples from unknown classes.We note that, while ideally such an abstaining classifier should also learn to reliably abstain when presented with adversarially perturbed samples BID26 BID35 MoosaviDezfooli et al., 2017) , in this work we do not consider adversarial settings and leave that for future exploration. The rest of the paper is organized as follows: Section 2 describes the loss function formulation and an algorithm for automatically tuning abstention behavior. Section 3 discusses learning in the presence of structured noise, including experimental results and visual interpretations of abstention. Section 4 presents the utility of the DAC for data cleaning in the presence of unstructured (arbitrary) noise. Section 5 has further discussions on abstention behavior in the context of memorization. Section 6 discusses open set detection with the DAC. We conclude in Section 7. We introduced and the illustrated the utility of a deep abstaining classifier -a DNN trained on a novel loss function that learns to abstain as opposed to abstention calibration after training. We illustrated the utility of the DAC in multiple situations: as a representation learner in the presence of structured noise, as an effective data cleaner in the presence of arbitrary noise, and as an effective out-of-category detector. While adversarial settings were not considered in this work, the DAC, and abstention in general, might be considered as part of the defense arsenal against adversarial attacks; we leave this for future work. In summary, our results here indicate that the representational power of DNNs can be used very effectively as a means of self-calibration -""knowing when it doesn't know"". Figure 6 : Results on blurred-image experiment with noisy labels (a)20% of the images are blurred in the train set, and their labels randomized (b) Validation accuracy for baseline vs DAC (non-abstained) (c)Abstention behavior for the DAC during training (d) Distribution of predictions on the blurred validation images for the DAC. We also observed (not shown) that for the baseline DNN, the accuracy on the blurred images in the validation set is no better than random.Results The DAC abstains remarkably well on the blurred images in the test set (Figure 6d ), while maintaining classification accuracy over the remaining samples in the validation set (≈ 79%). The baseline DNN accuracy drops to 63% (Figure 6b ), while the basline accuracy over the smudged images alone is no better than random (≈ 9.8%) . The abstention behavior of the DAC on the blurred images in the test set can be explained by how abstention evolves during training (Figure 6c ). Once abstention is introduced at epoch 20, the DAC initially opts to abstain on a high percentage of the traning data, while continuing to learn (since the gradients w.r.t the true-class pre-activations are always negative.). In the later epochs, sufficient learning has taken place on the non-randomized samples but the DAC continues to abstain on about 20% of the training data, which corresponds to the blurred images indicating that a strong association has been made between blurring and abstention.",introduce deep abstaining classifier deep neural network trained novel loss function provides abstention option training. allows DNN abstain confusing difficult-to-learn examples improving performance non-abstained samples. show deep abstaining classifiers can:learn representations structured noise where noisy training labels confusing examples are correlated underlying features learn abstain based features;ii enable robust learning presence arbitrary unstructured noise identifying noisy samples;iii used effective out-of-category detector learns reliably abstain when presented samples unknown classes. provide analytical results loss function behavior enable automatic tuning accuracy coverage demonstrate utility deep abstaining classifier using multiple image benchmarks Results indicate significant improvement learning presence label noise. Machine learning algorithms are expected increasingly replace humans decision-making pipelines. deployment AI-based systems high risk fields medical diagnosis BID23 autonomous vehicle control BID19 legal sector BID3 erroneous prediction should have otherwise flagged human interventionbecause system has not robustly learned when it is likely get wrong answer -can have severe consequences.In situations quality knowing when it doesn't know abstaining predicting is an essential trait classifier possess. allows decision-making routed human another accurate possibly expensive classifier assumption additional cost incurred is greatly surpassed consequences wrong prediction.Since learning systems have been around multiple decades has been extensive theoretical empirical investigation rejection abstention classification bulk area shallow learners BID5 BID7 BID10 multilayer perceptrons BID8. framework self-aware learning was analyzed context Markov decision processes BID20. context deep networks has been under-explored area BID11 recently proposing effective technique selective classification optimizing risk-vs-coverage profiles based output trained model.The abstention formulations previous works have been in a post-processing setting.e classifier is first trained usual abstention threshold is determined based post-training performance calibration set. paper introduce method train DNNs utilizes abstention option training. Using novel loss function-a modified version multi-class categorical cross-entropy loss includes abstention output -the representational capacity DNN is exploited learning when abstention is a is no better option improving performance non-abstained samples. illustrate utility DNN trained way multiple situations:first when labeling errors are correlated underlying feature data systematic structured label noise abstention training allows DNN learn features are indicative unreliable training signals which are thus likely lead uncertain predictions. kind representation learning abstention is useful effectively eliminating structured noise also interpreting reasons abstention. Second show how an abstention-based approach can be used effective data cleaner when training data contains arbitrary unstructured label noise:DNN trained abstention option can be used identify filter noisy training data leading significant performance benefits downstream training using cleaner set. Finally also consider problem open-set detection since real-world systems are often deployed open-domain situations;when presented samples unknown classes abstention is often safest choice. describe method utilizing abstention training effective open-set detection training DNN pickup features associated known classes abstain when such features are absent. summarize contributions paper are:• introduction deep abstaining classifier DAC -a DNN trained novel loss function uses abstention class training -enabling robust learning presence label noise.• demonstration ability DAC learn features associated systematic label noise. numerous experiments show how the DAC is able pick abstain features remarkable precision.• Demonstration utility DAC highly effective data cleaner presence arbitrary label noise. provide results learning noisy labels multiple image benchmarks CIFAR-10 CIFAR-100 Fashion-MNIST are competitive many cases significantly improve performance compared existing methods.• Illustration DAC effective open-set detector learns reliably abstain when presented samples unknown classes.We note ideally abstaining classifier should also learn reliably abstain when presented adversarially perturbed samples BID26 BID35 MoosaviDezfoolietal. 2017 work do not consider adversarial settings leave future exploration. rest paper is organized follows:Section 2 describes loss function formulation algorithm automatically tuning abstention behavior. Section 3 discusses learning presence structured noise including experimental results visual interpretations abstention. Section 4 presents utility DAC data cleaning presence unstructured arbitrary noise. Section5 has further discussions abstention behavior context memorization. Section 6 discusses open set detection DAC. conclude Section7. introduced illustrated utility deep abstaining classifier-a DNN trained novel loss function learns abstain opposed abstention calibration training. illustrated utility DAC multiple situations:representation learner presence structured noise effective data cleaner presence arbitrary noise effective out-of-category detector. adversarial settings were not considered work DAC abstention general might considered part defense arsenal adversarial attacks;leave future work. summary results indicate representational power DNNs can be used effectively means self-calibration -knowing when it doesn't know. Figure6:Results blurred-image experiment noisy labels 20% images are blurred train set labels randomized b Validation accuracy baseline vs DAC non-abstained c Abstention behavior DAC training Distribution predictions blurred validation images DAC. also observed shown baseline DNN accuracy blurred images validation set is a is no better random.Results DAC abstains remarkably well blurred images test set Figure6d maintaining classification accuracy remaining samples validation set ≈79% baseline DNN accuracy drops 63% Figure6b basline accuracy smudged images alone is a is no better random ≈ 9.8 abstention behavior DAC blurred images test set can be explained how abstention evolves training Figure6c abstention is introduced epoch20 DAC initially opts abstain high percentage traning data continuing learn since gradientsw.r.t true-class pre-activations are always negative. later epochs sufficient learning has taken place non-randomized samples DAC continues abstain 20% training data which corresponds blurred images indicating strong association has been made blurring abstention.,1648,1090,558,0.02,1.512,2025/11/05 17:18:54,0.01,1.51,0.5669781931464173,513.036
"Temporal Difference learning with function approximation has been widely used recently and has led to several successful results.   However, compared with the original tabular-based methods, one major drawback of temporal difference learning with neural networks and other function approximators is that they tend to over-generalize across temporally successive states, resulting in slow convergence and even instability. In this work, we propose a novel TD learning method, Hadamard product Regularized TD (HR-TD), that reduces over-generalization and thus leads to faster convergence. This approach can be easily applied to both linear and nonlinear function approximators. 
 HR-TD is evaluated on several linear and nonlinear benchmark domains, where we show improvement in learning behavior and performance. Temporal Difference (TD) learning is one of the most important paradigms in Reinforcement Learning BID15 . Techniques based on combining TD learning with nonlinear function approximators and stochastic gradient descent, such as deep networks, have led to significant breakthroughs in large-scale problems to which these methods can be applied BID8 BID12 .At its heart, the TD learning update is straightforward. v(s ) estimates the value of being in a state s. After an action a that transitions the agent from s to next state s , v(s) is altered to be closer to the (discounted) estimated value of s , v(s ) (plus any received reward, r). The difference between these estimated values is called the temporal difference error (TD error) and is typically denoted as δ. Formally, δ = r + γv(s ) − v(s), where γ is the discount factor, and r + γv(s ) is known as the TD target.When states are represented individually (the tabular case), v(s) can be altered independently from v(s ) using the update rule v(s) ← v(s) + αδ, where α is the learning rate. In fully deterministic environments , α can be set to 1, thus causing v(s) to change all the way to the TD target. Otherwise, in a stochastic environment , α is set less than 1 so that v(s) only moves part of the way towards the TD target, thus avoiding over-generalization from a single example. When, on the other hand, states are represented with a function approximator, as is necessary in large or continuous environments, v(s) can no longer be updated independently from v(s ). That is because s and s are likely to be similar (assuming actions have local effects), any change to v(s) is likely to also alter v(s ). While such generalization is desirable in principle, it also has the unintended consequence of changing the TD target, which in turn can cause the TD update to lead to an increase in the TD error between s and s . This unintended consequence can be seen as a second form of over-generalization: one that can be much more difficult to avoid.Past work has identified this form of over-generalization in RL, has observed that it is particularly relevant in methods that use neural network function approximators such as DQN BID8 , and has proposed initial solutions BID4 BID10 . In this paper, we present a deeper analysis of the reasons for this form of over-generalization and introduce a novel learning algorithm termed HR-TD, based on the recursive proximal mapping formulation of TD learning BID1 , which offers a mathematical framework for parameter regularization that allows one to control for this form of over-generalization. Empirical results across multiple domains demonstrate that our novel algorithm learns more efficiently (from fewer samples) than prior approaches.The rest of the paper is organized as follows. Section 2 offers a brief background on TD learning, the over-generalization problem, and optimization techniques used in the derivation of our algorithm. In Section 3, we discuss the state-of-the-art research in this direction. The motivation and the design of our algorithm are presented in Section 4. Finally , the experimental results of Section 5 validate the effectiveness of the proposed algorithm. In this paper, we analyze the problem of over-generalization in TD learning with function approximation. This analysis points to the potential pitfalls of over-generalization in TD-learning. Based on the analysis, we propose a novel regularization scheme based on the Hadamard product. We also show that with the right weight on the regularization, the solution of this method is the same as that of TD. Finally, we experimentally validate the effectiveness of our algorithm on benchmarks of varying complexity.","Temporal Difference learning function approximation has been widely used recently has led several successful results. However compared original tabular-based methods one major drawback temporal difference learning neural networks function approximators is that they tend over-generalize across temporally successive states resulting slow convergence even instability. work propose novel TD learning method Hadamard product RegularizedTD HR-TD reduces over-generalization thus leads faster convergence. approach can be easily applied linear nonlinear function approximators. HR-TD is evaluated several linear nonlinear benchmark domains where we show improvement learning behavior performance. Temporal Difference TD learning is one important paradigms Reinforcement Learning BID15. Techniques based combining TD learning nonlinear function approximators stochastic gradient descent deep networks have led significant breakthroughs large-scale problems which these methods can be applied BID8 BID12.At heart TD learning update is straightforward. v estimates value state s. action transitions agent next state v is can altered closer discounted estimated value v plus received reward r difference estimated values is called temporal difference error TD error is typically denoted δ. Formally δ r+γv −v where γ is the discount factor r+γv is known TD target.When states are represented individually tabular case v is can altered independently v using update rulev ←v+αδ whereα is the learning rate. fully deterministic environments whereα can be set 1 thus causingv change way TD target. Otherwise stochastic environment whereα is set less 1 v moves part way towards TD target thus avoiding over-generalization single example. When,on the hand states are represented function approximator is necessary large continuous environments v can longer updated independently v is is becauses are likely similar assuming actions have local effects change v is likely also alterv generalization is desirable principle also has the unintended consequence changing TD target which in turn can cause TD update lead increase TD error s. unintended consequence can be seen second form over-generalization one can be much difficult avoid.Past work has identified form over-generalization RL has observed is particularly relevant methods use neural network function approximators DQN BID8 has proposed initial solutions BID4 BID10. paper present deeper analysis reasons form over-generalization introduce novel learning algorithm termed HR-TD based recursive proximal mapping formulation TD learning BID1 which offers mathematical framework parameter regularization allows one control form over-generalization Empirical results across multiple domains demonstrate novel algorithm learns efficiently fewer samples prior approaches.The rest paper is organized follows. Section 2 offers brief background TD learning over-generalization problem optimization techniques used derivation algorithm. Section3 discuss state-of-the-art research direction. motivation design algorithm are presented Section4. Finally experimental results Section 5 validate effectiveness proposed algorithm. paper analyze problem over-generalization TD learning function approximation. analysis points potential pitfalls over-generalization TD-learning Based analysis propose novel regularization scheme based Hadamard product. also show right weight regularization solution method is the sameas TD. Finally experimentally validate effectiveness algorithm benchmarks varying complexity.",901,580,321,0.01,1.553,2025/11/05 17:18:54,0.0,1.5,0.6947040498442364,303.979
"We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. 
 To this end, we replace conventional convolution kernels with linear combinations of differential operators that are weighted by learnable parameters. Differential operators can be efficiently estimated on unstructured grids using one-ring neighbors, and learnable parameters can be optimized through standard back-propagation. As a result, we obtain extremely efficient neural networks that match or outperform state-of-the-art network architectures in terms of performance but with a significantly lower number of network parameters. We evaluate our algorithm in an extensive series of experiments on a variety of computer vision and climate science tasks, including shape classification, climate pattern segmentation, and omnidirectional image semantic segmentation. Overall, we present (1) a novel CNN approach on unstructured grids using parameterized differential operators for spherical signals, and (2) we show that our unique kernel parameterization allows our model to achieve the same or higher accuracy with significantly fewer network parameters. A wide range of machine learning problems in computer vision and related areas require processing signals in the spherical domain; for instance, omnidirectional RGBD images from commercially available panorama cameras, such as Matterport , panaramic videos coupled with LIDAR scans from self-driving cars BID17 , or planetary signals in scientific domains such as climate science BID31 . Unfortunately, naively mapping spherical signals to planar domains results in undesirable distortions. Specifically, projection artifacts near polar regions and handling of boundaries makes learning with 2D convolutional neural networks (CNNs) particularly challenging and inefficient. Very recent work, such as BID10 and BID16 , propose network architectures that operate natively in the spherical domain, and are invariant to rotations in the SO(3) group. Such invariances are desirable in a set of problems -e.g., machine learning problems of molecules -where gravitational effects are negligible and orientation is arbitrary. However, for other different classes of problems at large, assumed orientation information is crucial to the predictive capability of the network. A good example of such problems is the MNIST digit recognition problem, where orientation plays an important role in distinguishing digits ""6"" and ""9"". Other examples include omnidirectional images, where images are naturally oriented by gravity; and planetary signals, where planets are naturally oriented by their axis of rotation.In this work, we present a new convolution kernel for CNNs on arbitrary manifolds and topologies, discretized by an unstructured grid (i.e., mesh), and focus on its applications in the spherical domain approximated by an icosahedral spherical mesh. We propose and evaluate the use of a new parameterization scheme for CNN convolution kernels, which we call Parameterized Differential Operators (PDOs), which is easy to implement on unstructured grids. We call the resulting convolution operator that operates on the mesh using such kernels the MeshConv operator. This parameterization scheme utilizes only 4 parameters for each kernel, and achieves significantly better performance Illustration for the MeshConv operator using parameterized differential operators to replace conventional learnable convolutional kernels. Similar to classic convolution kernels that establish patterns between neighboring values, differential operators computes ""differences"", and a linear combination of differential operators establishes similar patterns.than competing methods, with much fewer parameters. In particular, we illustrate its use in various machine learning problems in computer vision and climate science.In summary, our contributions are as follows:• We present a general approach for orientable CNNs on unstructured grids using parameterized differential operators.• We show that our spherical model achieves significantly higher parameter efficiency compared to state-of-the-art network architectures for 3D classification tasks and spherical image semantic segmentation.• We release and open-source the codes developed and used in this study for other potential extended applications 1 .We organize the structure of the paper as follows. We first provide an overview of related studies in the literature in Sec. 2; we then introduce details of our methodology in Sec. 3, followed by an empirical assessment of the effectiveness of our model in Sec. 4. Finally , we evaluate the design choices of our kernel parameterization scheme in Sec. 5. We have presented a novel method for performing convolution on unstructured grids using parameterized differential operators as convolution kernels. Our results demonstrate its applicability to machine learning problems with spherical signals and show significant improvements in terms of overall performance and parameter efficiency. We believe that these advances are particularly valuable with the increasing relevance of omnidirectional signals, for instance, as captured by real-world 3D or LIDAR panorama sensors.",present efficient convolution kernel Convolutional Neural Networks CNNs unstructured grids using parameterized differential operators focusing spherical signals panorama images planetary signals. end replace conventional convolution kernels linear combinations differential operators are weighted learnable parameters. Differential operators can be efficiently estimated unstructured grids using one-ring neighbors learnable parameters can be optimized standard back-propagation result obtain extremely efficient neural networks match outperform state-of-the-art network architectures terms performance significantly lower number network parameters. evaluate algorithm extensive series experiments variety computer vision climate science tasks including shape classification climate pattern segmentation omnidirectional image semantic segmentation. Overall present 1 novel CNN approach unstructured grids using parameterized differential operators spherical signals 2 show unique kernel parameterization allows model achieve higher accuracy significantly fewer network parameters. wide range machine learning problems computer vision related areas require processing signals spherical domain;instance omnidirectional RGBD images commercially available panorama cameras Matterport panaramic videos coupled LIDAR scans self-driving cars BID17 planetary signals scientific domains climate science BID31. Unfortunately naively mapping spherical signals planar domains results undesirable distortions. Specifically projection artifacts near polar regions handling boundaries makes learning 2D convolutional neural networks CNNs particularly challenging inefficient. recent work BID10 BID16 propose network architectures operate natively spherical domain are invariant rotations 3 group. invariances are desirable set problems-e.g machine learning problems molecules -where gravitational effects are negligible orientation is arbitrary. However different classes problems large assumed orientation information is crucial predictive capability network. good example problems is the MNIST digit recognition problem where orientation plays important role distinguishing digits6 9. examples include omnidirectional images where images are naturally oriented gravity;planetary signals where planets are naturally oriented axis rotation.In work present new convolution kernel CNNs arbitrary manifolds topologies discretized unstructured grid.e mesh focus applications spherical domain approximated icosahedral spherical mesh. propose evaluate use new parameterization scheme CNN convolution kernels which we call Parameterized Differential Operators PDOs which is easy implement unstructured grids. call resulting convolution operator operates mesh using kernels MeshConv operator. parameterization scheme utilizes 4 parameters kernel achieves significantly better performance Illustration MeshConv operator using parameterized differential operators replace conventional learnable convolutional kernels. Similar classic convolution kernels establish patterns neighboring values differential operators computes differences linear combination differential operators establishes similar patterns.than competing methods much fewer parameters. particular illustrate use various machine learning problems computer vision climate science.In summary contributions are as follows:• present general approach orientable CNNs unstructured grids using parameterized differential operators.• show spherical model achieves significantly higher parameter efficiency compared state-of-the-art network architectures 3D classification tasks spherical image semantic segmentation.• release open-source codes developed used study potential extended applications1.We organize structure paper follows. first provide overview related studies literature Sec. 2;introduce details methodology Sec. 3 followed empirical assessment effectiveness model Sec. 4. Finally evaluate design choices kernel parameterization scheme Sec. 5. have presented novel method performing convolution unstructured grids using parameterized differential operators convolution kernels. results demonstrate applicability machine learning problems spherical signals show significant improvements terms overall performance parameter efficiency. believe advances are particularly valuable increasing relevance omnidirectional signals instance captured real-world3D LIDAR panorama sensors.,929,638,291,0.009,1.456,2025/11/05 17:18:54,0.0,1.333,0.392523364485981,296.533
"Prediction is arguably one of the most basic functions of an intelligent system. In general, the problem of predicting events in the future or between two waypoints is exceedingly difficult. However, most phenomena naturally pass through relatively predictable bottlenecks---while we cannot predict the precise trajectory of a robot arm between being at rest and holding an object up, we can be certain that it must have picked the object up. To exploit this, we decouple visual prediction from a rigid notion of time. While conventional approaches predict frames at regularly spaced temporal intervals, our time-agnostic predictors (TAP) are not tied to specific times so that they may instead discover predictable ""bottleneck"" frames no matter when they occur. We evaluate our approach for future and intermediate frame prediction across three robotic manipulation tasks. Our predictions are not only of higher visual quality, but also correspond to coherent semantic subgoals in temporally extended tasks. Imagine taking a bottle of water and laying it on its side. Consider what happens to the surface of the water as you do this: which times can you confidently make predictions about? The surface is initially flat, then becomes turbulent, until it is flat again, as shown in Fig 1. Predicting the exact shape of the turbulent liquid is extremely hard, but its easy to say that it will eventually settle down.Prediction is thought to be fundamental to intelligence BID2 BID3 BID10 . If an agent can learn to predict the future, it can take anticipatory actions, plan through its predictions, and use prediction as a proxy for representation learning. The key difficulty in prediction is uncertainty. Visual prediction approaches attempt to mitigate uncertainty by predicting iteratively in heuristically chosen small timesteps, such as, say, 0.1s. In the bottle-tilting case, such approaches generate blurry images of the chaotic states at t = 0.1s, 0.2s, . . ., and this blurriness compounds to make predictions unusable within a few steps. Sophisticated probabilistic approaches have been proposed to better handle this uncertainty BID0 BID19 BID4 BID39 .What if we instead change the goal of our prediction models? Fixed time intervals in prediction are in many ways an artifact of the fact that cameras and monitors record and display video at fixed frequencies. Rather than requiring predictions at regularly spaced future frames, we ask: if a frame prediction is treated as a bet on that frame occurring at some future point, what should we predict? Such time-agnostic prediction (TAP) has two immediate effects: (i) the predictor may skip more uncertain states in favor of less uncertain ones, and (ii) while in the standard approach, a prediction is wrong if it occurs at t ± rather than at t, our formulation considers such predictions equally correct.Recall the bottle-tilting uncertainty profile. Fig 1 depicts uncertainty profiles for several other prediction settings, including both forward/future prediction (given a start frame) and intermediate prediction (given start and end frames). Our time-agnostic reframing of the prediction problem targets the minima of these profiles, where prediction is intuitively easiest. We refer to these minima states as ""bottlenecks.""At this point, one might ask: are these ""easy"" bottlenecks actually useful to predict? Intuitively, bottlenecks naturally correspond to reliable subgoals-an agent hoping to solve the maze in Fig 1 (e) would do well to target its bottlenecks as subgoals. In our experiments, we evaluate the usefulness of our predictions as subgoals in simulated robotic manipulation tasks.Figure 1: (a) Over time as the bottle is tilted, the uncertainty first rises and then falls as the bottle is held steady after tilting. (b)-(e) Similar uncertainty profiles corresponding to various scenarios-a ball rolling down the side of a bowl, a car driving on a highway with an exit 100m away, an iron pellet tossed in the direction of a magnet, and intermediate frame prediction in a maze traversal given start and end states. The red asterisks along the x-axis correspond to the asterisks in the maze-these ""bottleneck"" states must occur in any successful traversal.Our main contributions are: (i) we reframe the video prediction problem to be time-agnostic, (ii) we propose a novel technical approach to solve this problem, (iii) we show that our approach effectively identifies ""bottleneck states"" across several tasks, and (iv) we show that these bottlenecks correspond to subgoals that aid in planning towards complex end goals. The standard paradigm for prediction tasks demands that a predictor not only make good predictions, but that it make them on a set schedule. We have argued for redefining the prediction task so that the predictor need only care that its prediction occur at some time, rather than that it occur at a specific scheduled time. We define this time-agnostic prediction task and propose novel technical approaches to solve it, that require relatively small changes to standard prediction methods. Our results show that reframing prediction objectives in this way yields higher quality predictions that are also semantically coherent-unattached to a rigid schedule of regularly specified timestamps, model predictions instead naturally attach to specific semantic ""bottleneck"" events, like a grasp. In our preliminary experiments with a hierarchical visual planner, our results suggest that such predictions could serve as useful subgoals for complex tasks.In future work, we would like to address some limitations of our TAP formulation, of which we will mention two here. First, TAP currently benefits not only from selecting which times to predict, but also from not having to provide timestamps attached to its predictions. We would like to study: could we retain the benefits of time-agnostic prediction while also providing timestamps for when each predicted state will occur? Second, our current TAP formulation may not generalize to prediction problems in all settings of interest. As an example, for videos of juggling or waving, which involve repeated frames, TAP might collapse to predicting the input state repeatedly. We would like to investigate more general TAP formulations: for example, rather than choosing E t in Eq 5 to encourage predicting farther away times, we could conceivably penalize predictions that look too similar to the input context frames. More broadly, we believe that our results thus far hold great promise for many applications of prediction including hierarchical planning and model-based reinforcement learning, and we hope to build further on these results. In these appendices, we provide details omitted in the main text for space. Note that more supplementary material, such as video examples, is hosted at: https://sites.google.com/view/ ta-pred",Prediction is arguably one basic functions intelligent system. general problem predicting events future two waypoints is exceedingly difficult. However phenomena naturally pass relatively predictable bottlenecks -while cannot predict precise trajectory robot arm rest holding object can certain must have picked object up. exploit decouple visual prediction rigid notion time. conventional approaches predict frames regularly spaced temporal intervals time-agnostic predictors TAP are not tied specific times may instead discover predictable bottleneck frames matter when they occur. evaluate approach future intermediate frame prediction across three robotic manipulation tasks. predictions are not only of higher visual quality also correspond coherent semantic subgoals temporally extended tasks. Imagine taking bottle water laying side. Consider what happens surface water do this:which times can you confidently make predictions about? surface is initially flat becomes turbulent is flat shown Fig1. Predicting exact shape turbulent liquid is extremely hard easy say will eventually settle down.Prediction is thought fundamental intelligence BID2 BID3 BID10. If an agent can learn predict future can take anticipatory actions plan predictions use prediction proxy representation learning. key difficulty prediction is uncertainty. Visual prediction approaches attempt mitigate uncertainty predicting iteratively heuristically chosen small timesteps say 0.1s bottle-tilting case approaches generate blurry images chaotic states 0.1s 0.2s blurriness compounds make predictions unusable within steps. Sophisticated probabilistic approaches have been proposed better handle uncertainty BID0 BID19 BID4 BID39.What if we instead change goal prediction models? Fixed time intervals prediction are in many ways artifact fact cameras monitors record display video fixed frequencies. Rather requiring predictions regularly spaced future frames ask:if a frame prediction is treated bet frame occurring future point what should we predict? time-agnostic prediction TAP has two immediate effects:predictor may skip uncertain states favor less uncertain ones ii standard approach where prediction is wrong if it occurs ± rather formulation considers predictions equally correct.Recall bottle-tilting uncertainty profile. Fig 1 depicts uncertainty profiles several prediction settings including forward/future prediction given start frame intermediate prediction given start end frames time-agnostic reframing prediction problem targets minima profiles where prediction is intuitively easiest. refer minima states bottlenecks.At point one might ask:are these easy bottlenecks actually useful predict? Intuitively bottlenecks naturally correspond reliable subgoals-an agent hoping solve maze Fig1 e would do well target bottlenecks subgoals. experiments evaluate usefulness predictions subgoals simulated robotic manipulation tasks.Figure 1:time bottle is tilted uncertainty first rises falls bottle is held steady tilting. b - e Similar uncertainty profiles corresponding various scenarios-a ball rolling side bowl car driving highway exit 100m away iron pellet tossed direction magnet intermediate frame prediction maze traversal given start end states. red asterisks along x-axis correspond asterisks maze-these bottleneck states must occur successful traversal.Our main contributions are:reframe video prediction problem time-agnostic ii propose novel technical approach solve problem iii show approach effectively identifies bottleneck states across several tasks iv show bottlenecks correspond subgoals aid planning towards complex end goals. standard paradigm prediction tasks demands predictor make good predictions make set schedule. have argued redefining prediction task predictor need care prediction occur time rather occur specific scheduled time. define time-agnostic prediction task propose novel technical approaches solve require relatively small changes standard prediction methods. results show reframing prediction objectives way yields higher quality predictions are also semantically coherent-unattached rigid schedule regularly specified timestamps model predictions instead naturally attach specific semantic bottleneck events like grasp. preliminary experiments hierarchical visual planner results suggest predictions could serve useful subgoals complex tasks.In future work would like address limitations TAP formulation whichwe will mention two here. First TAP currently benefits selecting which times predict also provide timestamps attached predictions. would like study:could retain benefits time-agnostic prediction also providing timestamps when each predicted state will occur? Second current TAP formulation may generalize prediction problems settings interest. example videos juggling waving which involve repeated frames TAP might collapse predicting input state repeatedly. would like investigate general TAP formulations:example rather choosingE Eq5 encourage predicting farther away times could conceivably penalize predictions look similar input context frames. broadly believe results thus far hold great promise many applications prediction including hierarchical planning model-based reinforcement learning hope build results. appendices provide details omitted main text space. Note supplementary material video examples is hosted at:https://sites.google.com/view/ta-pred,1355,879,476,0.013,1.542,2025/11/05 17:18:54,0.01,1.395,0.660436137071651,398.645
"In cities with tall buildings, emergency responders need an accurate floor level location to find 911 callers quickly. We introduce a system to estimate a victim's floor level via their mobile device's sensor data in a two-step process. First, we train a neural network to determine when a smartphone enters or exits a building via GPS signal changes. Second, we use a barometer equipped smartphone to measure the change in barometric pressure from the entrance of the building to the victim's indoor location. Unlike impractical previous approaches, our system is the first that does not require the use of beacons, prior knowledge of the building infrastructure, or knowledge of user behavior. We demonstrate real-world feasibility through 63 experiments across five different tall buildings throughout New York City where our system predicted the correct floor level with 100% accuracy.
 Indoor caller floor level location plays a critical role during 911 emergency calls. In one use case, it can help pinpoint heart attack victims or a child calling on behalf of an incapacitated adult. In another use case, it can help locate firefighters and other emergency personnel within a tall or burning building. In cities with tall buildings, traditional methods that rely on GPS or Wi-Fi fail to provide reliable accuracy for these situations. In these emergency situations knowing the floor level of a victim can speed up the victim search by a factor proportional to the number of floors in that building. In recent years methods that rely on smartphone sensors and Wi-Fi positioning BID28 have been used to formulate solutions to this problem.In this paper we introduce a system that delivers an estimated floor level by combining deep learning with barometric pressure data obtained from a Bosch bmp280 sensor designed for ""floor level accuracy"" BID3 and available in most smartphones today 1 . We make two contributions: the first is an LSTM BID13 trained to classify a smartphone as either indoors or outdoors (IO) using GPS, RSSI, and magnetometer sensor readings. Our model improves on a previous classifier developed by BID1 . We compare the LSTM against feedforward neural networks, logistic regression, SVM, HMM and Random Forests as baselines. The second is an algorithm that uses the classifier output to measure the change in barometric pressure of the smartphone from the building entrance to the smartphone's current location within the building. The algorithm estimates the floor level by clustering height measurements through repeated building visits or a heuristic value detailed in section 4.5.We designed our method to provide the most accurate floor level estimate without relying on external sensors placed inside the building, prior knowledge of the building, or user movement behavior. It merely relies on a smartphone equipped with GPS and barometer sensors and assumes an arbitrary user could use our system at a random time and place. We offer an extensive discussion of potential real-world problems and provide solutions in (appendix B).We conducted 63 test experiments across six different buildings in New York City to show that the system can estimate the floor level inside a building with 65.0% accuracy when the floor-ceiling distance in the building is unknown. However , when repeated visit data can be collected, our simple clustering method can learn the floor-ceiling distances and improve the accuracy to 100%. All code , data and data collection app are available open-source on github.2 . In this paper we presented a system that predicted a device's floor level with 100% accuracy in 63 trials across New York City. Unlike previous systems explored by BID1 , BID26 , BID20 , BID17 BID27 , our system is completely selfcontained and can generalize to various types of tall buildings which can exceed 19 or more stories. This makes our system realistic for real-world deployment with no infrastructure support required.We also introduced an LSTM, that solves the indoor-outdoor classification problem with 90.3% accuracy. The LSTM matched our baseline feedforward network, and outperformed SVMs, random forests, logistic regression and previous systems designed by BID22 and BID30 . The LSTM model also serves as a first step for future work modeling the overall system end-to-end within the LSTM.Finally, we showed that we could learn the distribution of floor heights within a building by aggregating m ∆ measurements across different visits to the building. This method allows us to generate precise floor level estimates via unsupervised methods. Our overall system marries these various elements to make it a feasible approach to speed up real-world emergency rescues in cities with tall buildings.",cities tall buildings emergency responders need accurate floor level location find 911 callers quickly. introduce system estimate victim's floor level via mobile device's sensor data two-step process. First train neural network determine when a smartphone enters exits building via GPS signal changes. Second use barometer equipped smartphone measure change barometric pressure entrance building victim's indoor location. Unlike impractical previous approaches system is the first does not require use beacons prior knowledge building infrastructure knowledge user behavior. demonstrate real-world feasibility 63 experiments across five different tall buildings throughout New York City where our system predicted correct floor level 100% accuracy. Indoor caller floor level location plays critical role 911 emergency calls. one use case can help pinpoint heart attack victims child calling behalf incapacitated adult. another use case can help locate firefighters emergency personnel within tall burning building. cities tall buildings traditional methods rely GPS Wi-Fi fail provide reliable accuracy situations. emergency situations knowing floor level victim can speed victim search factor proportional number floors building. recent years methods rely smartphone sensors Wi-Fi positioning BID28 have been used formulate solutions problem.In paper introduce system delivers estimated floor level combining deep learning barometric pressure data obtained Bosch bmp280 sensor designed floor level accuracy BID3 available smartphones today1. make two contributions:first is an LSTM BID13 trained classify smartphone either indoors outdoors IO using GPS RSSI magnetometer sensor readings. model improves previous classifier developed BID1. compare LSTM feedforward neural networks logistic regression SVM HMM Random Forests baselines. second is an algorithm uses classifier output measure change barometric pressure smartphone building entrance smartphone's current location within building. algorithm estimates floor level clustering height measurements repeated building visits heuristic value detailed section4. 5.We designed method provide accurate floor level estimate without relying external sensors placed inside building prior knowledge building user movement behavior. merely relies smartphone equipped GPS barometer sensors assumes arbitrary user could use system random time place. offer extensive discussion potential real-world problems provide solutions appendixB.We conducted 63 test experiments across six different buildings New York City show system can estimate floor level inside building 65.0 accuracy when the floor-ceiling distance building is unknown. However when repeated visit data can be collected simple clustering method can learn floor-ceiling distances improve accuracy 100%. code data data collection app are available open-source github.2 paper presented system predicted device's floor level 100% accuracy 63 trials across New York City. Unlike previous systems explored BID1 BID26 BID20 BID17 BID27 system is completely selfcontained can generalize various types tall buildings which can exceed19 stories. makes system realistic real-world deployment infrastructure support required.We also introduced LSTM solves indoor-outdoor classification problem 90.3 accuracy. LSTM matched baseline feedforward network outperformed SVMs random forests logistic regression previous systems designed BID22 BID30. LSTM model also serves first step future work modeling overall system end-to-end within LSTM.Finally showed could learn distribution floor heights within building aggregating ∆ measurements across different visits building. method allowsus generate precise floor level estimates via unsupervised methods. overall system marries various elements make feasible approach speed real-world emergency rescues cities tall buildings.,899,627,272,0.008,1.434,2025/11/05 17:18:54,0.0,1.526,0.3239875389408096,295.794
"Sparse reward is one of the most challenging problems in reinforcement learning (RL). Hindsight Experience Replay (HER) attempts to address this issue by converting a failure experience to a successful one by relabeling the goals. Despite its effectiveness, HER has limited applicability because it lacks a compact and universal goal representation. We present Augmenting experienCe via TeacheR's adviCE (ACTRCE), an efficient reinforcement learning technique that extends the HER framework using natural language as the goal representation. We first analyze the differences among goal representation, and show that ACTRCE can efficiently solve difficult reinforcement learning problems in challenging 3D navigation tasks, whereas HER with non-language goal representation failed to learn. We also show that with language goal representations, the agent can generalize to unseen instructions, and even generalize to instructions with unseen lexicons. We further demonstrate it is crucial to use hindsight advice to solve challenging tasks, but we also found that little amount of hindsight advice is sufficient for the learning to take off, showing the practical aspect of the method. Many impressive deep reinforcement learning (deep RL) applications rely on carefully-crafted reward functions to encourage the desired behavior. However, designing a good reward function is nontrivial (Ng et al., 1999) , and requires a significant engineering effort. For example, even for the seemingly simple task of stacking Lego blocks, Popov et al. (2017) needed 5 complicated reward terms with different importance weights. Moreover, handcrafted reward shaping BID9 can lead to biased learning, which may cause the agent to learn unexpected and undesired behaviors BID6 .One approach to avoid defining a complicated reward function is to use a sparse and binary reward function, i.e., give only a positive or negative reward at the terminal state, depending on the success of the task. However , the sparse reward makes learning difficult.Hindsight Experience Replay (HER) BID1 attempts to address this issue. The main idea of HER is to utilize failed experiences by substituting with a fake goal in order to convert them to successful experiences. For their algorithm to work, Andrychowicz et al. made the non-trivial assumption that for every state in the environment, there exists a goal which is achieved in that state. As the authors pointed out, this assumption can be trivially satisfied by choosing the goal space to be the state space. However, representing the goal using the enormous state space is very inefficient and contains much redundant information. For example, if we want to ask an agent to avoid collisions while driving where the state is the raw pixel value from the camera, then there can be many states (i.e. frames) that achieve this goal. It is redundant to represent the goal using each state.Therefore, we need a goal representation that is (1) expressive and flexible enough to satisfy the assumption in HER, while also being (2) compact and informative where similar goals are represented using similar features. Natural language representation of goals satisfies both requirements. First, language can flexibly describe goals across tasks and environments. Second, language representation is abstract , hence able to compress any redundant information in the states. Recall the previous driving example, for which we can simply describe ""avoid collisions"" to represent all states that satisfy this goal. Moreover, the compositional nature of language provides transferable features for generalizing across goals.In this paper, we combine the HER framework with natural language goal representation, and propose an efficient technique called Augmenting experienCe via TeacheR's adviCE (ACTRCE; pronounced ""actress"") to a broad range of reinforcement learning problems. Our method works as follows. Whenever an agent finishes an episode, a teacher gives advice in natural language to the agent based on the episode. The agent takes the advice to form a new experience with a corresponding reward, alleviating the sparse reward problem. For example, a teacher can describe what the agent has achieved in the episode, and the agent can replace the original goal with the advice and a reward of 1. We show many benefits brought by language goal representation when combining with hindsight advice. The agent can efficiently solve reinforcement learning problems in challenging 2D and 3D environments; it can generalize to unseen instructions, and even generalize to instruction with unseen lexicons. We further demonstrate it is crucial to use hindsight advice to solve challenging tasks, but we also found that little amount of hindsight advice is sufficient for the learning to take off, showing the practical aspect of the method.We note that our work is also interesting from a language learning perspective. Learning to achieve goals described in natural language is part of a class of problem called language grounding BID10 , which has recently received increasing interest, as grounding is believed to be necessary for more general understanding of natural language. Early attempts to ground language in a simulated physical world (Winograd, 1972; Siskind, 1994) consisted of hard coded rules which could not scale beyond their original domain. Recent work has been using reinforcement learning techniques to address this problem BID12 BID4 . Our work combines reinforcement learning and rich language advice , providing an efficient technique for language grounding. In this work, we propose the ACTRCE method that uses natural language as a goal representation for hindsight advice. The main point of the paper is to show that using language as goal representations can bring many benefits, when combined with hindsight advice. We analyzed the differences among goal representation, and show that ACTRCE can efficiently solve difficult reinforcement learning problems in challenging 3D navigation tasks, whereas HER with non-language goal representation failed to learn. We also show that with language goal representations, the agent can generalize to unseen instructions. With pre-trained language component, the agent can even generalize to instructions with unseen lexicons, demonstrating its potential to deal with noisy natural language advice from humans. Although ACTRCE algorithm crucially relies on hindsight advice, we showed that little amount of advice is sufficient for the learning to take off, showing its great practicality.",Sparse reward is one challenging problems reinforcement learning RL Hindsight Experience Replay attempts address issue converting failure experience successful one relabeling goals. Despite effectiveness has limited applicability lacks compact universal goal representation. present Augmenting experienCe via TeacheR's adviCE ACTRCE efficient reinforcement learning technique extends framework using natural language goal representation. first analyze differences among goal representation show ACTRCE can efficiently solve difficult reinforcement learning problems challenging 3D navigation tasks whereas non-language goal representation failed learn. also show language goal representations agent can generalize unseen instructions even generalize instructions unseen lexicons. demonstrate is crucial use hindsight advice solve challenging tasks also found little amount hindsight advice is sufficient learning take showing practical aspect method. Many impressive deep reinforcement learning deepRL applications rely carefully-crafted reward functions encourage desired behavior. However designing good reward function is nontrivial Ngetal. 1999 requires significant engineering effort. example even seemingly simple task stacking Lego blocks Popovetal. 2017 needed 5 complicated reward terms different importance weights. Moreover handcrafted reward shaping BID9 can lead biased learning may cause agent learn unexpected undesired behaviors BID6.One approach avoid defining complicated reward function is to use sparse binary reward function.e give positive negative reward terminal state depending success task. However sparse reward makes learning difficult.Hindsight Experience Replay BID1 attempts address issue. main idea is to utilize failed experiences substituting fake goal order convert successful experiences. algorithm work Andrychowiczetal. made non-trivial assumption every state environment exists goal which is achieved state. authors pointed assumption can be trivially satisfied choosing goal space state space. However representing goal using enormous state space is very inefficient contains much redundant information. example if we want ask agent avoid collisions driving where the state is the raw pixel value camera can many states.e frames achieve goal. is redundant represent goal using state.Therefore need goal representation is(1 expressive flexible enough satisfy assumption also 2 compact informative where similar goals are represented using similar features. Natural language representation goals satisfies requirements. First language can flexibly describe goals across tasks environments. Second language representation is abstract hence able compress redundant information states. Recall previous driving example whichwe can simply describe avoid collisions represent states satisfy goal. Moreover compositional nature language provides transferable features generalizing across goals.In paper combine framework natural language goal representation propose efficient technique called Augmenting experienCe via TeacheR's adviCE ACTRCE;pronounced actress broad range reinforcement learning problems. method works follows. Whenever agent finishes episode teacher gives advice natural language agent based episode. agent takes advice form new experience corresponding reward alleviating sparse reward problem. example teacher can describe what the agent has achieved episode agent can replace original goal advice reward 1. show many benefits brought language goal representation when combining hindsight advice. agent can efficiently solve reinforcement learning problems challenging2D 3D environments;can generalize unseen instructions even generalize instruction unseen lexicons. demonstrate is crucial use hindsight advice solve challenging tasks also found little amount hindsight advice is sufficient learning take showing practical aspect method.We note work is also interesting language learning perspective. Learning achieve goals described natural language is part class problem called language grounding BID10 which has recently received increasing interest grounding is believed necessary general understanding natural language. Early attempts ground language simulated physical world Winograd 1972;Siskind 1994 consisted hard coded rules could scale beyond original domain. Recent work has been using reinforcement learning techniques address problem BID12 BID4. work combines reinforcement learning rich language advice providing efficient technique language grounding. work propose ACTRCE method uses natural language goal representation hindsight advice. main point paper is to show using language goal representations can bring many benefits when combined hindsight advice. analyzed differences among goal representation show ACTRCE can efficiently solve difficult reinforcement learning problems challenging 3D navigation tasks whereas non-language goal representation failed learn. also show language goal representations agent can generalize unseen instructions. pre-trained language component agent can even generalize instructions unseen lexicons demonstrating potential deal noisy natural language advice humans. Although ACTRCE algorithm crucially relies hindsight advice showed little amount advice is sufficient learning take showing great practicality.,1207,818,389,0.012,1.476,2025/11/05 17:18:54,0.01,1.35,0.4548286604361368,402.013
"Learning rich and compact representations is an open topic in many fields such as word embedding, visual question-answering, object recognition or image retrieval. Although deep neural networks (convolutional or not) have made a major breakthrough during the last few years by providing hierarchical, semantic and abstract representations for all of these tasks, these representations are not necessary as rich as needed nor as compact as expected. Models using higher order statistics, such as bilinear pooling, provide richer representations at the cost of higher dimensional features. Factorization schemes have been proposed but without being able to reach the original compactness of first order models, or at a heavy loss in performances. This paper addresses these two points by extending factorization schemes to codebook strategies, allowing compact representations with the same dimensionality as first order representations, but with second order performances. Moreover, we extend this framework with a joint codebook and factorization scheme, granting a reduction both in terms of parameters and computation cost. This formulation leads to state-of-the-art results and compact second-order models with few additional parameters and intermediate representations with a dimension similar to that of first-order statistics. Learning rich and compact representations is an open topic in many fields such as word embedding BID16 ), visual question-answering ), object recognition BID23 ) or image retrieval BID19 ). The standard approach extracts features from the input data (text, image, etc.) and builds a representation that will be next processed for a given task (classification, retrieval, etc.) . These features are usually extracted with deep neural networks and the representation is trained in an end-to-end manner. Recently, representations that compute first order statistics over input data have been outperformed by improved models that compute higher order statistics such as bilinear models. This embedding strategy generates richer representations and has been applied in a wide range of tasks : word embedding BID2 ), VQA BID9 ), fine grained classification BID28 ), etc. and gets state-of-the-art results. For instance, Bilinear models perform the best for fine grained visual classification tasks by producing efficient representations that model more details within an image than classical first order statistics BID14 ).However , even if the increase in performances is unquestionable, second order models suffer from a collection of drawbacks: Their intermediate dimension increases quadratically with respect to input features dimension, they require a projection to lower dimension that is costly both in number of parameters and in computation, they are harder to train than first order models due to the increased dimension, they lack a proper adapted pooling scheme which leads to sub-optimal representations.The two main downsides, namely the high dimensional output representations and the sub-efficient pooling scheme, have been widely studied over the last decade. On one hand, the dimensionality issue has been studied through factorization scheme, either representation oriented such as Compact Bilinear Pooling ) and Hadamard Product for Low Rank Bilinear Pooling BID9 ), or task oriented as Low-rank Bilinear Pooling BID10 ). While these factorization schemes are efficient in term of computation cost and number of parameters, the intermediate representation is still too large (typically 10k dimension) to ease the training process and using lower dimension greatly deteriorate performances.On the other hand, it is well-known that global average pooling schemes aggregate unrelated features. This problem has been tackled by the use of codebooks such as VLAD BID0 ) or, in the case of second-order information, Fisher Vectors BID20 ). These strategies have been enhanced to be trainable in an end-to-end manner BID1 ; BID24 ). However , using a codebook on end-to-end trainable second order features leads to an unreasonably large model, since the already large second order model has to be duplicated for each entry of the codebook. This is for example the case in MFAFVNet BID13 ) for which the second order layer alone (i.e., without the CNN part) already costs over 25M parameters and 40 GFLOP, or about as much as an entire ResNet50.In this paper, we tackle both of these shortcomings (intermediate representation cost and lack of proper pooling) by exploring joint factorization and codebook strategies. Our main results are the following:-We first show that state-of-the-art factorization schemes can already be improved by the use of a codebook pooling, albeit at a prohibitive cost. -We then propose our main contribution, a joint codebook and factorization scheme that achieves similar results at a much reduced cost.Since our approach focuses on representation learning and is task agnostic, we validate it in a retrieval context on several image datasets to show the relevance of the learned representations. We show our model achieves competitive results on these datasets at a very reasonable cost.The remaining of this paper is organized as follows: in the next section, we present the related work on second order pooling, factorization schemes and codebook strategies. In section 3, we present our factorization with the codebook strategy and how we improve its integration. In section 4, we show an ablation study on the Stanford Online Products dataset BID18 ). Finally, we compare our approach to the state-of-the-art methods on three image retrieval datasets (Stanford Online Products, CUB-200-2001, Cars-196) . In this paper, we propose a new pooling scheme based which is both efficient in performances (rich representation) and in representation dimension (compact representation). This is thanks to the second-order information that allows richer representation than first-order statistics and thanks to a codebook strategy which pools only related features. To control the computational cost, we extend this pooling scheme with a factorization that shares sets of projections between each entry of the codebook, trading fewer parameters and fewer computation for a small loss in performance. We achieve state-of-the-art results on Stanford Online Products and Cars-196, two image retrieval datasets. Even if our tests are performed on image retrieval datasets, we believe our method can readily be used in place of global average pooling for any task.",Learning rich compact representations is an open topic many fields word embedding visual question-answering object recognition image retrieval. Although deep neural networks convolutional have made major breakthrough last years providing hierarchical semantic abstract representations tasks representations are not necessary rich needed compact expected. Models using higher order statistics bilinear pooling provide richer representations cost higher dimensional features. Factorization schemes have been proposed without able reach original compactness first order models heavy loss performances. paper addresses two points extending factorization schemes codebook strategies allowing compact representations dimensionality first order representations second order performances. Moreover extend framework joint codebook factorization scheme granting reduction terms parameters computation cost. formulation leads state-of-the-art results compact second-order models additional parameters intermediate representations dimension similar first-order statistics. Learning rich compact representations is an open topic many fields word embedding BID16 visual question-answering object recognition BID23 image retrieval BID19 standard approach extracts features input data text image etc. builds representation will be next processed given task classification retrieval etc. features are usually extracted deep neural networks representation is trained end-to-end manner. Recently representations compute first order statistics input data have been outperformed improved models compute higher order statistics bilinear models. embedding strategy generates richer representations has been applied wide range tasks:word embedding BID2 VQA BID9 fine grained classification BID28 etc. gets state-of-the-art results. instance Bilinear models perform best fine grained visual classification tasks producing efficient representations model details within image classical first order statistics BID14.However even if the increase performances is unquestionable second order models suffer collection drawbacks:intermediate dimension increases quadratically respect input features dimension require projection lower dimension is costly number parameters computation are harder train first order models due increased dimension lack proper adapted pooling scheme which leads sub-optimal representations.The two main downsides namely high dimensional output representations sub-efficient pooling scheme have been widely studied last decade. one hand dimensionality issue has been studied factorization scheme either representation oriented Compact Bilinear Pooling Hadamard Product Low Rank Bilinear Pooling BID9 task oriented Low-rank Bilinear Pooling BID10 factorization schemes are efficient term computation cost number parameters intermediate representation is still large typically 10k dimension ease training process using lower dimension greatly deteriorate performances.On hand is well-known global average pooling schemes aggregate unrelated features. problem has been tackled use codebooks VLAD BID0 case second-order information Fisher Vectors BID20 strategies have been enhanced trainable end-to-end manner BID1;BID24 However using codebook end-to-end trainable second order features leads unreasonably large model since already large second order model has to be duplicated entry codebook. is for example case MFAFVNet BID13 which the second order layer alone.e without CNN part already costs 25M parameters 40 GFLOP much entire ResNet50.In paper tackle shortcomings intermediate representation cost lack proper pooling exploring joint factorization codebook strategies. main results are the following:-We first show state-of-the-art factorization schemes can already improved use codebook pooling albeit prohibitive cost. -We propose main contribution joint codebook factorization scheme achieves similar results much reduced cost.Since approach focuses representation learning is task agnostic validate retrieval context several image datasets show relevance learned representations. show model achieves competitive results datasets reasonable cost.The remaining paper is organized follows:next section present related work second order pooling factorization schemes codebook strategies. section3 present factorization codebook strategy how we improve integration. section4 show ablation study Stanford Online Products dataset BID18 Finally compare approach state-of-the-art methods three image retrieval datasets Stanford Online Products CUB-200-2001 Cars-196 paper propose new pooling scheme based which is both efficient performances rich representation representation dimension compact representation is thanks second-order information allows richer representation first-order statistics thanks codebook strategy which pools related features. control computational cost extend pooling scheme factorization shares sets projections entry codebook trading fewer parameters fewer computation small loss performance. achieve state-of-the-art results Stanford Online Products Cars-196 two image retrieval datasets. Even if our tests are performed image retrieval datasets believe method can readily used place global average pooling task.,1210,814,396,0.012,1.486,2025/11/05 17:18:55,0.01,1.571,0.4859813084112147,361.348
"Natural language understanding research has recently shifted towards complex Machine Learning and Deep Learning algorithms. Such models often outperform their simpler counterparts significantly. However, their performance relies on the availability of large amounts of labeled data, which are rarely available. To tackle this problem, we propose a methodology for extending training datasets to arbitrarily big sizes and training complex, data-hungry models using weak supervision. We apply this methodology on biomedical relation extraction, a task where training datasets are excessively time-consuming and expensive to create, yet has a major impact on downstream applications such as drug discovery. We demonstrate in two small-scale controlled experiments that our method consistently enhances the performance of an LSTM network, with performance improvements comparable to hand-labeled training data. Finally, we discuss the optimal setting for applying weak supervision using this methodology. The amount of scientific papers in the biomedical field is ever increasing. Published papers contain important information, however, encoded in unstructured text, making it difficult for researchers to locate it. Extracting this information in a structured format and storing it within a knowledge base can have a remarkable impact on a variety of important tasks, ranging from drug design to detecting adverse drug effects. During the past decade, there have been efforts towards automation of Information Extraction BID15 , due to the fact that manual annotation of documents from domain experts is labor-intensive to perform on a large scale BID16 .The broader focus of this work is to help automation of semantic triple extraction from biomedical abstracts. We apply our methodology on two different relations: (a ) Regulations, indicating that a Chemical increases (up-regulates) or decreases (down-regulates) the production of a Protein (CPR) and ( b) Chemically Induced Diseases (CID). Both relations are particularly important for areas such as drug design, safety, and discovery, as it will enable researchers to filter out or select chemical substances with specific properties, faster BID16 . We have shown that weak supervision is a tool which can be used for enhancing the performance of complex models, such as deep neural networks, while utilizing both unlabeled data and multiple base learners. Additionally, we have shown that the proposed methodology is practically feasible for the task at hand, as we have succeeded on defining a combination of base learners, which model the problem space sufficiently and allow us to take advantage of additional, unlabeled data. This comes under the requirement that the unlabeled data are drawn from the same domain/distribution as our labeled data, so that our base learners can generalize and perform adequately on D U . In practice, our methodology shifts the human effort from hand-labeling examples to feature engineering and construction of diverse learners. More importantly, once a satisfactory set of diverse learners is available, we can use this method to scale the training datasets in arbitrarily high levels while consistently improving the performance over the supervised learning paradigm. Moreover, the same pipeline can be re-used on similar tasks with the only requirement of providing the appropriate datasets. On the contrary, in the typical supervised learning paradigm, we would have to repeatedly hand-label large datasets.Despite demonstrating the usability of our method using a controlled, small-scale dataset, it is crucial to further explore the requirements of constructing a large enough unlabelled dataset and perform the same experiments there. That would likely improve the metalearner performance further (which is currently upper-bounded by the small dataset size) and allow us to draw stronger conclusions on the research questions of Subsection 6.2. Additionally it would allow us to inspect how performance improves with the increase of D U in a different scale of magnitude and if there seems to be a certain performance threshold, which we cannot surpass using weak supervision. Our preliminary experiments demonstrate that collecting an appropriate unlabeled dataset given a labeled one is a challenging task itself, along with the definition of ""appropriate"", and semi-supervised algorithms should not take the existence of an appropriate unlabeled dataset for granted.Further, it would be very important to conclude on a more appropriate metric than the F1 score for the evaluation of marginal weak labels. Currently, the absence of an appropriate metric prevents us from drawing conclusions directly from the weak labels, without having to introduce an additional step (train the meta-learner). This would also allow us to select the optimal hyperparameters of the Generative Model and could have a significant impact upon the final performance.Other areas for further investigation include experimenting with the meta-learner (eg. using pre-trained word embeddings or other model architectures) and defining a more appropriate selection method for the Base Learners. Last, it would be interesting to examine how this system would behave if the Base Learners abstained from voting on the examples they are less certain about. One could simply delete a percentage of the votes which are closer to the classification boundary, or perform a probability calibration on the output of the Base Learners and set a minimum confidence threshold below which they would abstain voting. This could also provide the Generative Model with a modeling advantage, compared to unweighted methods (such as Majority Voting), as described in an analysis related to the trade-offs of weak supervision BID29 .",Natural language understanding research has recently shifted towards complex Machine Learning Deep Learning algorithms. models often outperform simpler counterparts significantly. However performance relies availability large amounts labeled data which are rarely available. tackle problem propose methodology extending training datasets arbitrarily big sizes training complex data-hungry models using weak supervision. apply methodology biomedical relation extraction task where training datasets are excessively time-consuming expensive create yet has a major impact downstream applications drug discovery. demonstrate two small-scale controlled experiments method consistently enhances performance LSTM network performance improvements comparable hand-labeled training data. Finally discuss optimal setting applying weak supervision using methodology. amount scientific papers biomedical field is ever increasing. Published papers contain important information however encoded unstructured text making difficult researchers locate it. Extracting information structured format storing within knowledge base can have a remarkable impact variety important tasks ranging drug design detecting adverse drug effects. past decade have been efforts towards automation Information Extraction BID15 due fact manual annotation documents domain experts is labor-intensive perform large scale BID16.The broader focus work is to help automation semantic triple extraction biomedical abstracts. apply methodology two different relations:Regulations indicating Chemical increases up-regulates decreases down-regulates production Protein CPR b Chemically Induced Diseases CID relations are particularly important areas drug design safety discovery will enable researchers filter select chemical substances specific properties faster BID16. have shown weak supervision is a tool which can be used enhancing performance complex models deep neural networks utilizing unlabeled data multiple base learners. Additionally have shown proposed methodology is practically feasible task hand have succeeded defining combination base learners which model problem space sufficiently allowus take advantage additional unlabeled data. comes requirement unlabeled data are drawn domain/distribution labeled data base learners can generalize perform adequately U. practice methodology shifts human effort hand-labeling examples feature engineering construction diverse learners. importantly satisfactory set diverse learners is available can use method scale training datasets arbitrarily high levels consistently improving performance supervised learning paradigm. Moreover pipeline can be re-used similar tasks requirement providing appropriate datasets. contrary typical supervised learning paradigm would have to repeatedly hand-label large datasets.Despite demonstrating usability method using controlled small-scale dataset is crucial explore requirements constructing large enough unlabelled dataset perform experiments there. would likely improve metalearner performance which is currently upper-bounded small dataset size allowus draw stronger conclusions research questions Subsection 6.2 Additionally would allowus inspect how performance improves increase U different scale magnitude if there seems certain performance threshold which we cannot surpass using weak supervision. preliminary experiments demonstrate collecting appropriate unlabeled dataset given labeled one is a challenging task along definition appropriate semi-supervised algorithms should not take existence appropriate unlabeled dataset granted.Further would important conclude appropriate metric F1 score evaluation marginal weak labels. Currently absence appropriate metric preventsus drawing conclusions directly weak labels without introduce additional step train meta-learner would also allowus select optimal hyperparameters Generative Model could have a significant impact upon final performance.Other areas investigation include experimenting meta-learner eg. using pre-trained word embeddings model architectures defining appropriate selection method Base Learners. Last would interesting examine how this system would behave if the Base Learners abstained voting examples are less certain about. One could simply delete percentage votes which are closer classification boundary perform probability calibration output Base Learners set minimum confidence threshold would abstain voting. could also provide Generative Model modeling advantage compared unweighted methods Majority Voting described analysis related trade-offs weak supervision BID29.,1021,662,359,0.01,1.542,2025/11/05 17:18:55,0.01,1.541,0.660436137071651,321.565
"We introduce contextual explanation networks (CENs)---a class of models that learn to predict by generating and leveraging intermediate explanations. CENs are deep networks that generate parameters for context-specific probabilistic graphical models which are further used for prediction and play the role of explanations. Contrary to the existing post-hoc model-explanation tools, CENs learn to predict and to explain jointly. Our approach offers two major advantages: (i) for each prediction, valid instance-specific explanations are generated with no computational overhead and (ii) prediction via explanation acts as a regularization and boosts performance in low-resource settings. We prove that local approximations to the decision boundary of our networks are consistent with the generated explanations. Our results on image and text classification and survival analysis tasks demonstrate that CENs are competitive with the state-of-the-art while offering additional insights behind each prediction, valuable for decision support. Model interpretability is a long-standing problem in machine learning that has become quite acute with the accelerating pace of widespread adoption of complex predictive algorithms. While high performance often supports our belief in predictive capabilities of a system, perturbation analysis reveals that black-box models can be easily broken in an unintuitive and unexpected manner BID0 BID1 . Therefore, for a machine learning system to be used in a social context (e.g., in healthcare) it is imperative to provide a sound reasoning for each decision.Restricting the class of models to only human-intelligible BID2 ) is a potential remedy, but often is limiting in modern practical settings. Alternatively, we may fit a complex model and explain its predictions post-hoc, e.g., by searching for linear local approximations of the decision boundary BID22 . While such approaches achieve their goal, the explanations are generated a posteriori, require additional computation per data instance, and most importantly are never the basis for the predictions made in the first place which may lead to erroneous interpretations.Explanation is a fundamental part of the human learning and decision process (Lombrozo, 2006) . Inspired by this fact, we introduce contextual explanation networks (CENs)-a class of deep neural networks that generate parameters for probabilistic graphical models. The generated models not only play the role of explanations but are used for prediction and can encode arbitrary prior knowledge. The data often consists of two representations: (1) low-level or unstructured features (e.g., text, image pixels, sensory inputs), and (2) high-level or human-interpretable features (e.g., categorical variables). To ensure interpretability, CENs use deep networks to process the low-level representation (called the context) and construct explanations as context-specific probabilistic models on the high-level features (cf. Koller & Friedman, 2009, Ch. 5.3) . Importantly, the explanation mechanism is an integral part of CEN, and our models are trained to predict and to explain jointly.A motivating example. Consider a CEN for diagnosing the risk of developing heart arrhythmia ( FIG0 ). The causes of the condition are quite diverse, ranging from smoking and diabetes to an injury from previous heart attacks, and may carry different effects on the risk of arrhythmia in different contexts. Assume that the data for each patient consists of medical notes in the form of raw text (which is used as the context) and a number of specific attributes (such as high blood pressure, diabetes, smoking, etc.). Further, assume that we have access to a parametric class of expert-designed models that relate the attributes to the condition. The CEN maps the medical notes to the parameters of the model class to produce a context-specific hypothesis, which is further used to make a prediction. In the sequel, we formalize these intuitions and refer to this toy example in our discussion to illustrate different aspects of the framework. The main contributions of the paper are as follows:(i ) We formally define CENs as a class of probabilistic models, consider special cases (e.g., Jacobs et al., 1991) , and derive learning and inference algorithms for simple and structured outputs. ( ii) We prove that post-hoc approximations of CEN's decision boundary are consistent with the generated explanations and show that, in practice, while both methods tend to produce virtually identical explanations, CENs construct them orders of magnitude faster. (iii) It turns out that noisy features can render post-hoc methods inconsistent and misleading, and we show how CENs can help to detect and avoid such situations. (iv) We implement CENs by extending a number of established domain-specific deep architectures for image and text data and design new architectures for survival analysis. Experimentally, we demonstrate the value of learning with explanations for prediction and model diagnostics. Moreover, we find that explanations can act as a regularizer and improve sample efficiency. In this paper, we have introduced contextual explanation networks (CENs)-a class of models that learn to predict by generating and leveraging intermediate context-specific explanations. We have formally defined CENs as a class of probabilistic models, considered a number of special cases (e.g., the mixture of experts), and derived learning and inference procedures within the encoder-decoder framework for simple and sequentially-structured outputs. We have shown that, while explanations generated by CENs are provably equivalent to those generated post-hoc under certain conditions, there are cases when post-hoc explanations are misleading. Such cases are hard to detect unless explanation is a part of the prediction process itself. Besides, learning to predict and to explain jointly turned out to have a number of benefits, including strong regularization, consistency, and ability to generate explanations with no computational overhead.We would like to point out a few limitations of our approach and potential ways of addressing those in the future work. Firstly, while each prediction made by CEN comes with an explanation, the process of conditioning on the context is still uninterpretable. Ideas similar to context selection (Liu et al., 2017) or rationale generation (Lei et al., 2016) may help improve interpretability of the conditioning. Secondly, the space of explanations considered in this work assumes the same graphical structure and parameterization for all explanations and uses a simple sparse dictionary constraint. This might be limiting, and one could imagine using a more hierarchically structured space of explanations instead, bringing to bear amortized inference techniques (Rudolph et al., 2017) . Nonetheless, we believe that the proposed class of models is useful not only for improving prediction capabilities, but also for model diagnostics, pattern discovery, and general data analysis, especially when machine learning is used for decision support in high-stakes applications.",introduce contextual explanation networks CENs -a class models learn predict generating leveraging intermediate explanations. CENs are deep networks generate parameters context-specific probabilistic graphical models which are further used prediction play role explanations. Contrary existing post-hoc model-explanation tools CENs learn predict explain jointly. approach offers two major advantages:prediction valid instance-specific explanations are generated computational overhead ii prediction via explanation acts regularization boosts performance low-resource settings. prove local approximations decision boundary networks are consistent generated explanations. results image text classification survival analysis tasks demonstrate CENs are competitive state-of-the-art offering additional insights behind prediction valuable decision support. Model interpretability is a long-standing problem machine learning has become quite acute accelerating pace widespread adoption complex predictive algorithms. high performance often supports belief predictive capabilities system perturbation analysis reveals black-box models can be easily broken unintuitive unexpected manner BID0 BID1. Therefore machine learning system used social context e.g healthcare is imperative provide sound reasoning decision.Restricting class models human-intelligible BID2 is a potential remedy often is limiting modern practical settings. Alternatively may fit complex model explain predictions post-hoc e.g searching linear local approximations decision boundary BID22. approaches achieve goal explanations are generated posteriori require additional computation per data instance importantly are never basis predictions made first place may lead erroneous interpretations.Explanation is a fundamental part human learning decision process Lombrozo 2006 Inspired fact introduce contextual explanation networks CENs -a class deep neural networks generate parameters probabilistic graphical models. generated models play role explanations are used prediction can encode arbitrary prior knowledge. data often consists two representations:1 low-level unstructured features e.g text image pixels sensory inputs 2 high-level human-interpretable features e.g categorical variables ensure interpretability CENs use deep networks process low-level representation called context construct explanations context-specific probabilistic models high-level features cf. Koller Friedman 2009 Ch. 5.3 Importantly explanation mechanism is an integral part CEN models are trained predict explain jointly.A motivating example. Consider CEN diagnosing risk developing heart arrhythmia FIG0 causes condition are quite diverse ranging smoking diabetes injury previous heart attacks may carry different effects risk arrhythmia different contexts. Assume data patient consists medical notes form raw text which is used context number specific attributes high blood pressure diabetes smoking etc. assume have access parametric class expert-designed models relate attributes condition. CEN maps medical notes parameters model class produce context-specific hypothesis which is further used make prediction. sequel formalize intuitions refer toy example discussion illustrate different aspects framework. main contributions paper are as follows:formally define CENs class probabilistic models consider special cases e.g Jacobsetal. 1991 derive learning inference algorithms simple structured outputs. ii prove post-hoc approximations CEN's decision boundary are consistent generated explanations show practice methods tend produce virtually identical explanations CENs construct orders magnitude faster. iii turns noisy features can render post-hoc methods inconsistent misleading show how CENs can help detect avoid situations. iv implement CENs extending number established domain-specific deep architectures image text data design new architectures survival analysis. Experimentally demonstrate value learning explanations prediction model diagnostics. Moreover find explanations can act regularizer improve sample efficiency. paper have introduced contextual explanation networks CENs -a class models learn predict generating leveraging intermediate context-specific explanations. have formally defined CENs class probabilistic models considered number special cases e.g mixture experts derived learning inference procedures within encoder-decoder framework simple sequentially-structured outputs. have shown explanations generated CENs are provably equivalent generated post-hoc certain conditions are cases when post-hoc explanations are misleading. cases are hard detect unless explanation is a part prediction process itself. Besides learning predict explain jointly turned have a number benefits including strong regularization consistency ability generate explanations computational overhead.We would like point limitations approach potential ways addressing future work. Firstly prediction made CEN comes explanation process conditioning context is still uninterpretable. Ideas similar context selection Liuetal. 2017 rationale generation Leietal. 2016 may help improve interpretability conditioning. Secondly space explanations considered work assumes graphical structure parameterization explanations uses simple sparse dictionary constraint. might limiting one could imagine using hierarchically structured space explanations instead bringing bear amortized inference techniques Rudolphetal. 2017 Nonetheless believe proposed class models is useful improving prediction capabilities also model diagnostics pattern discovery general data analysis especially when machine learning is used decision support high-stakes applications.,1351,888,463,0.016,1.521,2025/11/05 17:18:55,0.01,1.325,0.595015576323987,447.709
"The goal of imitation learning (IL) is to enable a learner to imitate an expert’s behavior given the expert’s demonstrations. Recently, generative adversarial imitation learning (GAIL) has successfully achieved it even on complex continuous control tasks. However, GAIL requires a huge number of interactions with environment during training. We believe that IL algorithm could be more applicable to the real-world environments if the number of interactions could be reduced. To this end, we propose a model free, off-policy IL algorithm for continuous control. The keys of our algorithm are two folds: 1) adopting deterministic policy that allows us to derive a novel type of policy gradient which we call deterministic policy imitation gradient (DPIG), 2) introducing a function which we call state screening function (SSF) to avoid noisy policy updates with states that are not typical of those appeared on the expert’s demonstrations. Experimental results show that our algorithm can achieve the goal of IL with at least tens of times less interactions than GAIL on a variety of continuous control tasks. Recent advances in reinforcement learning (RL) have achieved super-human performance on several domains BID16 BID17 BID13 . However, on most of domains with the success of RL, the design of reward, that explains what agent's behavior is favorable, is clear enough for humans. Conversely, on domains where it is unclear how to design the reward, agents trained by RL algorithms often obtain poor policies and their behavior is far from what we want them to do. Imitation learning (IL) comes in such cases. The goal of IL is to enable the learner to imitate the expert's behavior given the expert's demonstrations but the reward signals. We are interested in IL because we desire an algorithm that can be applied in real-world environments where it is often hard to design the reward. Besides, since it is generally hard to model a variety of the real-world environments with an algorithm, and the state-action pairs in a vast majority of the real-world applications such as robotics control can be naturally represented in continuous spaces, we focus on model free IL for continuous control.A widely used approach of existing model free IL methods is the combination of Inverse Reinforcement Learning (IRL) BID22 BID18 BID1 BID32 and RL. Recently, BID10 has proposed generative adversarial imitation learning (GAIL) on the line of those works. GAIL has achieved state-of-the art performance on a variety of continuous control tasks. However, as pointed out by BID10 , a crucial drawback of GAIL is requirement of a huge number of interactions between the learner and the environments during training 1 . Since the interactions with environment can be too much time-consuming especially in the real-world environments, we believe that model free IL could be more applicable to the real-world environments if the number could be reduced while keeping the imitation capability satisfied as well as GAIL.To reduce the number of interactions, we propose a model free, off-policy IL algorithm for continuous control. As opposed to GAIL and its variants BID2 BID30 BID8 BID12 those of which adopt a stochastic policy as the learner's policy, we adopt a deterministic policy while following adversarial training fashion as GAIL. We show that combining the deterministic policy into the adversarial off-policy IL objective derives a novel type of policy gradient which we call deterministic policy imitation gradient (DPIG). Because DPIG only integrates over the state space as deterministic policy gradient (DPG) algorithms BID25 , the number of the interactions is expected to be less than that for stochastic policy gradient (PG) which integrates over the state-action space. Besides, we introduce a function which we call state screening function (SSF) to avoid noisy policy update with states that are not typical of those appeared on the experts demonstrations.In order to evaluate our algorithm, we used 6 physics-based control tasks that were simulated with MuJoCo physics simulator BID29 . The experimental results show that our algorithm enables the learner to achieve the same performance as the expert does with at least tens of times less interactions than GAIL. It indicates that our algorithm is more applicable to the real-world environments than GAIL. A wide variety of IL methods have been proposed in these last few decades. The simplest IL method among those is BC (Pomerleau, 1991) which learns a mapping from states to actions in the expert's demonstrations using supervised learning. Since the learner with the mapping learned by BC does not interacts with the environments, inaccuracies of the mapping are never corrected once the training has done, whereas our algorithm corrects the learner's behavior through the interactions. A noticeable point in common between BC and our algorithm is that the both just consider the relationship between single time-step state-action pairs but information over entire trajectories of the behavior in the optimizations. In other words, the both assume that the reward structure is dense and the reasonable rewards for the states s ∈ S \ S E can not be defined. A drawback of BC due to ignorance of the information over the trajectories is referred to as the problem of compounding error BID21 ) -the inaccuracies compounds over time and can lead the learner to encounter unseen states in th expert's demonstrations. For the state s ∈ S β * E , it is assumed in our algorithm that the immediate reward is greater if the learner's behavior is more likely to the expert's behavior, and the expert's behavior yields the greatest cumulative reward. That is, maximizing the immediate reward for the state s ∈ S β * E ⊂ S E implies maximizing the cumulative reward for trajectories stating from the state in our algorithm, and thus the information over the trajectories is implicitly incorporated in log R ω of the objective (11). Therefore, our algorithm is less affected by the compounding error than BC.Another widely used approach for IL the combination of IRL and RL that we considered in this paper. The concept of IRL was originally proposed by BID22 , and a variety of IRL algorithms have been proposed so far. Early works on IRL BID18 BID1 BID32 represented the parameterized reward function as a linear combination of hand-designed features. Thus, its capabilities to represent the reward were limited in comparison with that of nonlinear functional representation. Indeed, applications of the early works were often limited in small discrete domains. The early works were extended to algorithms that enable to learn nonlinear functions for representing the reward BID11 BID6 . A variety of complex tasks including continuous control in the real-world environment have succeeded with the nonlinear functional representation BID6 . As well as those methods, our algorithm can utilize the nonlinear functions if it is differentiable with respect to the action.In recent years, the connection between GANs and the IL approach has been pointed out BID10 BID5 . BID10 showed that IRL is a dual problem of RL which can be deemed as a problem to match the learner's occupancy measure BID28 to that of the expert, and found a choice of regularizer for the cost function yields an objective which is analogous to that of GANs. After that, their algorithm, namely GAIL, has become a popular choice for IL and some extensions of GAIL have been proposed BID2 BID30 BID8 BID12 . However, those extensions have never addressed reducing the number of interactions during training whereas we address it, and our algorithm significantly reduce the number while keeping the imitation capability as well as GAIL.The way of deriving policy gradients using gradients of the parameterized reward function with respect to actions executed by the current learner's policy is similar to DPG BID25 and deep DPG BID13 . However, they require parameterized Q-function approximator with known reward function whereas our algorithm does not use Q-function besides the parameterized reward function learned by IRL. In IL literature, MGAIL BID2 uses the gradients derived from parameterized discriminator to update the learner's policy. However, MGAIL is modelbased method and requires to train parameterized forward-model to derive the gradients whereas our algorithm is model free. Although model based methods have been thought to need less environment interactions than model free methods in general, the experimental results showed that MGAIL needs more interactions than our model free algorithm. We think that the reasons are the need for training the forward model besides that for the policy, and lack of care for the noisy policy updates issue that MGAIL essentially has. In this paper, we proposed a model free, off-policy IL algorithm for continuous control. The experimental results showed that our algorithm enables the learner to achieve the same performance as the expert does with several tens of times less interactions than GAIL.Although we implemented shallow neural networks to represent the parameterized functions in the experiment, deep neural networks can also be applied to represent the functions in our algorithm. We expect that the that advanced techniques used in deep GANs enable us to apply our algorithm to more complex tasks.A DETAILED DESCRIPTION OF EXPERIMENT TAB2 summarizes the description of each task, an agents performance with random policy, and the performance of the experts.","goal imitation learning IL is to enable learner imitate experts behavior given experts demonstrations. Recently generative adversarial imitation learning GAIL has successfully achieved even complex continuous control tasks. However GAIL requires huge number interactions environment training. believe IL algorithm could applicable real-world environments if the number interactions could reduced. end propose model free off-policy IL algorithm continuous control. keys algorithm are two folds:1 adopting deterministic policy allowsus derive novel type policy gradient which we call deterministic policy imitation gradient DPIG 2 introducing function which we call state screening function SSF avoid noisy policy updates states are not typical appeared experts demonstrations. Experimental results show algorithm can achieve goal IL least tens times less interactions GAIL variety continuous control tasks. Recent advances reinforcement learning RL have achieved super-human performance several domains BID16 BID17 BID13. However domains success RL design reward explains what agent's behavior is favorable is clear enough humans. Conversely domains where it is unclear how to design reward agents trained RL algorithms often obtain poor policies behavior is far what we want do. Imitation learning IL comes cases. goal IL is to enable learner imitate expert's behavior given expert's demonstrations reward signals. are interested IL desire algorithm can be applied real-world environments where it is often hard design reward. Besides since is generally hard model variety real-world environments algorithm state-action pairs vast majority real-world applications robotics control can be naturally represented continuous spaces focus model freeIL continuous control.A widely used approach existing model freeIL methods is the combination Inverse Reinforcement Learning IRL BID22 BID18 BID1 BID32 RL. Recently BID10 has proposed generative adversarial imitation learning GAIL line works. GAIL has achieved state-of-the art performance variety continuous control tasks. However pointed BID10 crucial drawback GAIL is requirement huge number interactions learner environments training1. Since interactions environment can be too much time-consuming especially real-world environments believe model free IL could applicable real-world environments if the number could reduced keeping imitation capability satisfied well GAIL.To reduce number interactions propose model free off-policy IL algorithm continuous control. opposed GAIL variants BID2 BID30 BID8 BID12 which adopt stochastic policy learner's policy adopt deterministic policy following adversarial training fashion GAIL. show combining deterministic policy adversarial off-policy IL objective derives novel type policy gradient which we call deterministic policy imitation gradient DPIG DPIG integrates state space deterministic policy gradient DPG algorithms BID25 number interactions is expected less stochastic policy gradient PG which integrates state-action space. Besides introduce function which we call state screening function SSF avoid noisy policy update states are not typical appeared experts demonstrations.In order evaluate algorithm used 6 physics-based control tasks were simulated MuJoCo physics simulator BID29. experimental results show algorithm enables learner achieve performance expert does with at least tens times less interactions GAIL. indicates algorithm is more applicable real-world environments GAIL. wide variety IL methods have been proposed last decades. simplest IL method among isBC Pomerleau 1991 which learns mapping states actions expert's demonstrations using supervised learning. Since learner mapping learned BC does not interacts environments inaccuracies mapping are never corrected training has done whereas algorithm corrects learner's behavior interactions. noticeable point common BC algorithm is that the both consider relationship single time-step state-action pairs information entire trajectories behavior optimizations. words assume reward structure is dense reasonable rewards states ∈ E can not be defined. drawback BC due ignorance information trajectories is referred problem compounding error BID21 -the inaccuracies compounds time can lead learner encounter unseen states th expert's demonstrations. state ∈ β*E is assumed algorithm immediate reward is greater if the learner's behavior is more likely expert's behavior expert's behavior yields greatest cumulative reward. is,maximizing immediate reward state ∈ β*E⊂ E implies maximizing cumulative reward trajectories stating state algorithm thus information trajectories is implicitly incorporated logRω objective 11 Therefore algorithm is less affected compounding error BC.Another widely used approach IL combination IRL RL considered paper. concept IRL was originally proposed BID22 variety IRL algorithms have been proposed far. Early works IRL BID18 BID1 BID32 represented parameterized reward function linear combination hand-designed features. Thus capabilities represent reward were limited comparison nonlinear functional representation. Indeed applications early works were often limited small discrete domains. early works were extended algorithms enable learn nonlinear functions representing reward BID11 BID6. variety complex tasks including continuous control real-world environment have succeeded nonlinear functional representation BID6. well methods algorithm can utilize nonlinear functions if it is differentiable respect action.In recent years connection GANs IL approach has been pointed BID10 BID5. BID10 showed IRL is a dual problem RL which can be deemed problem match learner's occupancy measure BID28 expert found choice regularizer cost function yields objective which is analogous GANs. algorithm namely GAIL has become popular choice IL extensions GAIL have been proposed BID2 BID30 BID8 BID12. However extensions have never addressed reducing number interactions training whereas address algorithm significantly reduce number keeping imitation capability well GAIL.The way deriving policy gradients using gradients parameterized reward function respect actions executed current learner's policy is similar DPG BID25 deep DPG BID13. However require parameterized Q-function approximator known reward function whereas algorithm does not use Q-function besides parameterized reward function learned IRL. IL literature MGAIL BID2 uses gradients derived parameterized discriminator update learner's policy. However MGAIL is modelbased method requires train parameterized forward-model derive gradients whereas algorithm is model free. Although model based methods have been thought need less environment interactions model free methods general experimental results showed MGAIL needs interactions model free algorithm. think reasons are the need training forward model besides policy lack care noisy policy updates issue MGAIL essentially has. paper proposed model free off-policy IL algorithm continuous control. experimental results showed algorithm enables learner achieve performance expert does with several tens times less interactions GAIL.Although implemented shallow neural networks represent parameterized functions experiment deep neural networks can also applied represent functions algorithm. expect advanced techniques used deep GANs enableus apply algorithm complex tasks.A DETAILED DESCRIPTION EXPERIMENT TAB2 summarizes description task agents performance random policy performance experts.",1807,1211,596,0.024,1.492,2025/11/05 17:18:55,0.01,1.563,0.5046728971962615,674.908
"Convolution acts as a local feature extractor in convolutional neural networks (CNNs). However, the convolution operation is not applicable when the input data is supported on an irregular graph such as with social networks, citation networks, or knowledge graphs. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network that generalizes CNN architectures to graph-structured data and provides a systematic way to design a set of fixed-size learnable filters to perform convolutions on graphs. The topologies of these filters are adaptive to the topology of the graph when they scan the graph to perform convolution, replacing the square filter for the grid-structured data in traditional CNNs. The outputs are the weighted sum of these filters’ outputs, extraction of both vertex features and strength of correlation between vertices. It
 can be used with both directed and undirected graphs. The proposed TAGCN not only inherits the properties of convolutions in CNN for grid-structured data, but it is also consistent with convolution as defined in graph signal processing. Further, as no approximation to the convolution is needed, TAGCN exhibits better performance than existing graph-convolution-approximation methods on a number
 of data sets. As only the polynomials of degree two of the adjacency matrix are used, TAGCN is also computationally simpler than other recent methods. Convolutional neural network (CNN) architectures exhibit state-of-the-art performance on a variety of learning tasks dealing with 1D, 2D, and 3D grid-structured data such as acoustic signals, images, and videos, in which convolution serves as a feature extractor BID12 . However, the (usual) convolution operation is not applicable when applying CNN to data that is supported on an arbitrary graph rather than on a regular grid structure, since the number of neighbors of each vertex on the graph varies, and it is difficult to design a fixed-size filter scanning over the graph-structured data for feature extraction.Recently, there has been an increasing interest in graph CNNs (Bruna et al., 2014; BID3 BID10 BID13 , attempting to generalize deep learning methods to graph-structured data, specifically focusing on the design of graph CNN . In this paper, we propose the topology adaptive graph convolutional network (TAGCN), a unified convolutional neural network to learn nonlinear representations for the graph-structured data. It slides a set of fixed-size learnable filters on the graph simultaneously, and the output is the weighted sum of these filters' outputs, which extract both vertex features and strength of correlation between vertices. Each filter is adaptive to the topology of the local region on the graph where it is applied. TAGCN unifies filtering in both the spectrum and vertex domains; and applies to both directed and undirected graphs.In general, the existing graph CNNs can be grouped into two types: spectral domain techniques and vertex domain techniques. In Bruna et al. (2014) , CNNs have been generalized to graph-structured data, where convolution is achieved by a pointwise product in the spectrum domain according to the convolution theorem. Later, BID3 and BID13 proposed spectrum filtering based methods that utilize Chebyshev polynomials and Cayley polynomials, respectively. The assumption of symmetric adjacency matrix in these spectrum based methods restrict the application to undirected graphs. BID10 simplified this spectrum method and obtained a filter in the vertex domain, which achieves state-of-the-art performance. Other researchers BID0 worked on designing feature propagation models in the vertex domain for graph CNNs. BID22 ; BID2 ; Grover & Leskovec (2016) ; BID5 study transforming graph-structured data to embedding vectors for learning problems. Nevertheless, it still remains open how to extend CNNs from grid-structured data to arbitrary graph-structured data with local feature extraction capability. This paper proposes a modification to the graph convolution step in CNNs that is particularly relevant for graph structured data. Our proposed TAGCN is graph-based convolution and draws on techniques from graph signal processing. We define rigorously the graph convolution operation on the vertex domain as multiplication by polynomials of the graph adjacency matrix, which is consistent with the notion of convolution in graph signal processing. In graph signal processing, polynomials of the adjacency matrix are graph filters, extending to graph based data from the usual concept of filters in traditional time or image based signal processing. Thus, comparing ours with existing work on graph CNNs, our paper provides a solid theoretical foundation for our proposed convolution step instead of an ad-hoc approach to convolution in CNNs for graph structured data.Further, our method avoids computing the spectrum of the graph Laplacian as in Bruna et al. (2014) , or approximating the spectrum using high degree Chebyshev polynomials of the graph Laplacian matrix (in BID3 , it is suggested that one needs a 25 th degree Chebyshev polynomial to provide a good approximation to the graph Laplacian spectrum) or using high degree Cayley polynomials of the graph Laplacian matrix (in BID13 , 12 th degree Cayley polynomials are needed). We also clarify that the GCN method in BID10 is a first order approximation of the Chebyshev polynomials approximation in BID3 , which is very different from our method. Our method has a much lower computational complexity than the complexity of the methods proposed in Bruna et al. (2014) ; BID3 ; BID13 , since our method only uses polynomials of the adjacency matrix with maximum degree 2 as shown in our experiments. Finally, the method that we propose exhibits better performance than existing methods. Our contributions are summarized follows:• We propose a general K-localized filter for graph convolution in the vertex domain to extract local features on a set of size-1 up to size-K receptive fields. The topologies of these filters are adaptive to the topology of the graph as they scan the graph to perform convolution. It replaces the fixed square filters in traditional CNNs for the input gridstructured data volumes in traditional CNNs. Thus, our convolution definition that we use in the convolution step for the vertex domain is consistent with convolution in traditional CNNs.• TAGCN is based on the graph signal processing and it is consistent with the convolution in graph signal processing. It applies to both directed and undirected graphs. Moreover , it has a much lower computational complexity compared with recent methods since it only needs polynomials of the adjacency matrix with maximum degree 2 compared with the 25 th and 12 th degree Laplacian matrix polynomials in BID3 and BID13 .• As no approximation to the convolution is needed in TAGCN, it achieves better performance compared with existing methods. We contrast TAGCN with recently proposed graph CNN including both spectrum filtering methods (Bruna et al., 2014; BID3 and vertex domain propagation methods BID10 BID0 , evaluating their performances on three commonly used data sets for graph vertices classification. Our experimental tests show that TAGCN outperforms consistently all other approaches for each of these data sets. We have defined a novel graph convolutional network that rearchitects the CNN architecture for graph-structured data. The proposed method, known as TAGCN, is adaptive to the graph topology as the filter scans the graph. Further, TAGCN inherits properties of the convolutional layer in classical CNN, i.e., local feature extraction and weight sharing. It can further extract the strength of correlation between vertices in the filtering region. On the other hand, by the convolution theorem, TAGCN that implements in the vertex domain offers implement in the spectrum domain unifying graph CNN in both the spectrum domain and the vertex domain. TAGCN is consistent with convolution in graph signal processing. These nice properties lead to a noticeable performance advantage in classification accuracy on different graph-structured datasets for semi-supervised graph vertex classification problems with low computational complexity.",Convolution acts local feature extractor convolutional neural networks CNNs However which where convolution operation is not applicable when the input data is supported irregular graph social networks citation networks knowledge graphs. paper proposes topology adaptive graph convolutional network TAGCN novel graph convolutional network generalizes CNN architectures graph-structured data provides systematic way design set fixed-size learnable filters perform convolutions graphs. topologies filters are adaptive topology graph when they scan graph perform convolution replacing square filter grid-structured data traditional CNNs. outputs are the weighted sum filters outputs extraction vertex features strength correlation vertices. can be used directed undirected graphs. proposed TAGCN inherits properties convolutions CNN grid-structured data is also consistent convolution defined graph signal processing. approximation convolution is needed TAGCN exhibits better performance existing graph-convolution-approximation methods number data sets. polynomials degree two adjacency matrix are used TAGCN is also computationally simpler recent methods. Convolutional neural network CNN architectures exhibit state-of-the-art performance variety learning tasks dealing 1D 2D 3D grid-structured data acoustic signals images videos which where convolution serves feature extractor BID12. However usual convolution operation is not applicable when applying CNN data is supported arbitrary graph rather regular grid structure since number neighbors vertex graph varies is difficult design fixed-size filter scanning graph-structured data feature extraction.Recently has been increasing interest graph CNNs Brunaetal. 2014;BID3 BID10 BID13 attempting generalize deep learning methods graph-structured data specifically focusing design graph CNN. paper propose topology adaptive graph convolutional network TAGCN unified convolutional neural network learn nonlinear representations graph-structured data. slides set fixed-size learnable filters graph simultaneously output is the weighted sum filters' outputs which extract vertex features strength correlation vertices. filter is adaptive topology local region graph where it is applied. TAGCN unifies filtering spectrum vertex domains;applies directed undirected graphs.In general existing graph CNNs can be grouped two types:spectral domain techniques vertex domain techniques. Brunaetal. 2014 CNNs have been generalized graph-structured data which where convolution is achieved pointwise product spectrum domain according convolution theorem. Later BID3 BID13 proposed spectrum filtering based methods utilize Chebyshev polynomials Cayley polynomials respectively. assumption symmetric adjacency matrix spectrum based methods restrict application undirected graphs. BID10 simplified spectrum method obtained filter vertex domain which achieves state-of-the-art performance. researchers BID0 worked designing feature propagation models vertex domain graph CNNs. BID22;BID2;Grover Leskovec 2016 BID5 study transforming graph-structured data embedding vectors learning problems. Nevertheless still remains open how to extend CNNs grid-structured data arbitrary graph-structured data local feature extraction capability. paper proposes modification graph convolution step CNNs is particularly relevant graph structured data. proposed TAGCN is graph-based convolution draws techniques graph signal processing. define rigorously graph convolution operation vertex domain multiplication polynomials graph adjacency matrix which is consistent notion convolution graph signal processing. graph signal processing polynomials adjacency matrix are graph filters extending graph based data usual concept filters traditional time image based signal processing. Thus comparing existing work graph CNNs paper provides solid theoretical foundation proposed convolution step instead ad-hoc approach convolution CNNs graph structured data.Further method avoids computing spectrum graph Laplacian Brunaetal. 2014 approximating spectrum using high degree Chebyshev polynomials graph Laplacian matrix BID3 is suggested one needs 25 th degree Chebyshev polynomial provide good approximation graph Laplacian spectrum using high degree Cayley polynomials graph Laplacian matrix BID13 12 th degree Cayley polynomials are needed also clarify GCN method BID10 is a first order approximation Chebyshev polynomials approximation BID3 which is very different method. method has a much lower computational complexity complexity methods proposed Brunaetal. 2014 BID3;BID13 since method uses polynomials adjacency matrix maximum degree2 shown experiments. Finally method propose exhibits better performance existing methods. contributions are summarized follows:• propose general K-localized filter graph convolution vertex domain extract local features set size-1 size-K receptive fields. topologies filters are adaptive topology graph scan graph perform convolution. replaces fixed square filters traditional CNNs input gridstructured data volumes traditional CNNs. Thus which where convolution definition use convolution step vertex domain is consistent convolution traditional CNNs.• TAGCN is based graph signal processing is consistent convolution graph signal processing. applies directed undirected graphs. Moreover has a much lower computational complexity compared recent methods since needs polynomials adjacency matrix maximum degree 2 compared 25th 12 th degree Laplacian matrix polynomials BID3 BID13.• approximation convolution is needed TAGCN which achieves better performance compared existing methods. contrast TAGCN recently proposed graph CNN including spectrum filtering methods Brunaetal. 2014;BID3 vertex domain propagation methods BID10 BID0 evaluating performances three commonly used data sets graph vertices classification. experimental tests show TAGCN outperforms consistently approaches data sets. have defined novel graph convolutional network rearchitects CNN architecture graph-structured data. proposed method known TAGCN is adaptive graph topology filter scans graph. TAGCN inherits properties convolutional layer classical CNN.e local feature extraction weight sharing. can further extract strength correlation vertices filtering region. hand which where convolution theorem TAGCN implements vertex domain offers implement spectrum domain unifying graph CNN spectrum domain vertex domain. TAGCN is consistent convolution graph signal processing. nice properties lead noticeable performance advantage classification accuracy different graph-structured datasets semi-supervised graph vertex classification problems low computational complexity.,1588,1104,484,0.017,1.438,2025/11/05 17:18:55,0.01,1.442,0.3364485981308407,480.845
"Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a ``forgetting event'' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance. Many machine learning models, in particular neural networks, cannot perform continual learning. They have a tendency to forget previously learnt information when trained on new tasks, a phenomenon usually called catastrophic forgetting BID17 BID29 . One of the hypothesized causes of catastrophic forgetting in neural networks is the shift in the input distribution across different tasks-e.g., a lack of common factors or structure in the inputs of different tasks might lead standard optimization techniques to converge to radically different solutions each time a new task is presented. In this paper, we draw inspiration from this phenomenon and investigate the extent to which a related forgetting process occurs as a model learns examples traditionally considered to belong to the same task.Similarly to the continual learning setting, in stochastic gradient descent (SGD) optimization, each mini-batch can be considered as a mini-""task"" presented to the network sequentially. In this context, we are interested in characterizing the learning dynamics of neural networks by analyzing (catastrophic) example forgetting events. These occur when examples that have been ""learnt"" (i.e., correctly classified) at some time t in the optimization process are subsequently misclassifiedor in other terms forgotten -at a time t > t. We thus switch the focus from studying interactions between sequentially presented tasks to studying interactions between sequentially presented dataset examples during SGD optimization. Our starting point is to understand whether there exist examples that are consistently forgotten across subsequent training presentations and, conversely, examples that are never forgotten. We will call the latter unforgettable examples. We hypothesize that specific examples consistently forgotten between subsequent presentations, if they exist, must not share commonalities with other examples from the same task. We therefore analyze the proportion of forgettable/unforgettable examples for a given task and what effects these examples have on a model's decision boundary and generalization error.The goal of our investigation is two-fold. First, we attempt to gain insight into the optimization process by analyzing interactions among examples during learning and their influence on the final decision boundary. We are particularly interested in whether we can glean insight on the compressibility of a dataset, and thereby increase data efficiency without compromising generalization accuracy. It is a timely problem that has been the recent focus of few-shot learning approaches via meta-learning BID8 BID28 . Second, we aim to characterize whether forgetting statistics can be used to identify ""important"" samples and detect outliers and examples with noisy labels BID12 BID3 BID32 BID11 .Identifying important, or most informative examples is an important line of work and was extensively studied in the literature. Techniques of note -among others -are predefined curricula of examples BID1 , self-paced learning BID21 , and more recently meta-learning BID7 . These research directions usually define ""hardness"" or ""commonality"" of an example as a function of the loss on that particular example at some point during training (or possibly at convergence). They do not consider whether some examples are consistently forgotten throughout learning. Very recently, BID4 consider re-weighting examples by accounting for the variance of their predictive distribution. This is related to our definition of forgetting events, but the authors provide little analysis of the extent to which the phenomenon occurs in their proposed tasks. Our purpose is to study this phenomenon from an empirical standpoint and characterize its prevalence in different datasets and across different model architectures.Our experimental findings suggest that: a) there exist a large number of unforgettable examples, i.e., examples that are never forgotten once learnt, those examples are stable across seeds and strongly correlated from one neural architecture to another; b) examples with noisy labels are among the most forgotten examples, along with images with ""uncommon"" features, visually complicated to classify; c) training a neural network on a dataset where a very large fraction of the least forgotten examples have been removed still results in extremely competitive performance on the test set. In this paper, inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks when training on single classification tasks. We show that catastrophic forgetting can occur in the context of what is usually considered to be a single task. Inspired by this result, we find that some examples within a task are more prone to being forgotten, while others are consistently unforgettable. We also find that forgetting statistics seem to be fairly stable with respect to the various characteristics of training, suggesting that they actually uncover intrinsic properties of the data rather than idiosyncrasies of the training schemes. Furthermore, the unforgettable examples seem to play little part in the final performance of the classifier as they can be removed from the training set without hurting generalization. This supports recent research interpreting deep neural networks as max margin classifiers in the linear case. Future work involves understanding forgetting events better from a theoretical perspective, exploring potential applications to other areas of supervised learning, such as speech or text and to reinforcement learning where forgetting is prevalent due to the continual shift of the underlying distribution. permutedMNIST The permutedMNIST data set is obtained by applying a fixed random permutation of the pixels to all the images of the standard MNIST data set. This typically makes the data set harder to learn for convolutional neural networks as local patterns, e.g. the horizontal bar of the 7, get shuffled. This statement is supported by the two following facts:",Inspired phenomenon catastrophic forgetting investigate learning dynamics neural networks train single classification tasks. goal is to understand whether related phenomenon occurs when data does not undergo clear distributional shift. define forgetting event have occurred when an individual training example transitions classified correctly incorrectly course learning. Across several benchmark data sets find that:certain examples are forgotten high frequency all;ii data set's un forgettable examples generalize across neural architectures;iii based forgetting dynamics significant fraction examples can be omitted training data set still maintaining state-of-the-art generalization performance. Many machine learning models particular neural networks cannot perform continual learning. have a tendency forget previously learnt information when trained new tasks phenomenon usually called catastrophic forgetting BID17 BID29. One hypothesized causes catastrophic forgetting neural networks is the shift input distribution across different tasks-e.g lack common factors structure inputs different tasks might lead standard optimization techniques converge radically different solutions time new task is presented. paper draw inspiration phenomenon investigate extent which a related forgetting process occurs model learns examples traditionally considered belong task.Similarly continual learning setting stochastic gradient descent SGD optimization mini-batch can be considered mini-task presented network sequentially. context are interested characterizing learning dynamics neural networks analyzing catastrophic example forgetting events. occur when examples have been learnt.e correctly classified time optimization process are subsequently misclassifiedor terms forgotten -at time t. thus switch focus studying interactions sequentially presented tasks studying interactions sequentially presented dataset examples SGD optimization. starting point is to understand whether exist examples are consistently forgotten across subsequent training presentations conversely examples are never forgotten. will call latter unforgettable examples. hypothesize specific examples consistently forgotten subsequent presentations if they exist must share commonalities examples task. therefore analyze proportion forgettable/unforgettable examples given task what effects examples have on a model's decision boundary generalization error.The goal investigation is two-fold two-fold First attempt gain insight optimization process analyzing interactions among examples learning influence final decision boundary. are particularly interested whether can glean insight compressibility dataset thereby increase data efficiency without compromising generalization accuracy. is a timely problem has been the recent focus few-shot learning approaches via meta-learning BID8 BID28. Second aim characterize whether forgetting statistics can be used identify important samples detect outliers examples noisy labels BID12 BID3 BID32 BID11.Identifying important informative examples is an important line work was extensively studied literature. Techniques note -among others -are predefined curricula examples BID1 self-paced learning BID21 recently meta-learning BID7. research directions usually define hardness commonality example function loss particular example point training possibly convergence do consider whether examples are consistently forgotten throughout learning. recently BID4 consider re-weighting examples accounting variance predictive distribution. is related definition forgetting events authors provide little analysis extent which the phenomenon occurs proposed tasks. purpose is to study phenomenon empirical standpoint characterize prevalence different datasets across different model architectures.Our experimental findings suggest that:exist large number unforgettable examples.e examples are never forgotten learnt examples are stable across seeds strongly correlated one neural architecture another;b examples noisy labels are among forgotten examples along images uncommon features visually complicated classify;c training neural network dataset where a very large fraction least forgotten examples have been removed still results extremely competitive performance test set. paper inspired phenomenon catastrophic forgetting investigate learning dynamics neural networks when training single classification tasks. show catastrophic forgetting can occur context what is usually considered single task. Inspired result find examples within task are more prone forgotten others are consistently unforgettable. also find forgetting statistics seem fairly stable respect various characteristics training suggesting actually uncover intrinsic properties data rather idiosyncrasies training schemes. Furthermore unforgettable examples seem play little part final performance classifier can be removed training set without hurting generalization. supports recent research interpreting deep neural networks max margin classifiers linear case. Future work involves understanding forgetting events better theoretical perspective exploring potential applications areas supervised learning speech text reinforcement learning where forgetting is prevalent due continual shift underlying distribution. permutedMNIST permutedMNIST data set is obtained applying fixed random permutation pixels images standard MNIST data set. typically makes data set harder learn convolutional neural networks local patterns e.g horizontal bar 7 get shuffled. statement is supported two following facts:,1207,799,408,0.013,1.511,2025/11/05 17:18:55,0.01,1.531,0.5638629283489092,366.524
"Discovering objects and their attributes is of great importance for autonomous agents to effectively operate in human environments. This task is particularly challenging due to the ubiquitousness of objects and all their nuances in perceptual and semantic detail. In this paper we present an unsupervised approach for learning disentangled representations of objects entirely from unlabeled monocular videos. These continuous representations are not biased by or limited by a discrete set of labels determined by human labelers. The proposed representation is trained with a metric learning loss, where objects with homogeneous features are pushed together, while those with heterogeneous features are pulled apart. We show these unsupervised embeddings allow to discover object attributes and can enable robots to self-supervise in previously unseen environments. We quantitatively evaluate performance on a large-scale synthetic dataset with 12k object models, as well as on a real dataset collected by a robot and show that our unsupervised object understanding generalizes to previously unseen objects. Specifically, we demonstrate the effectiveness of our approach on robotic manipulation tasks, such as pointing at and grasping of objects. An interesting and perhaps surprising finding in this approach is that given a limited set of objects, object correspondences will naturally emerge when using metric learning without requiring explicit positive pairs. The ability to autonomously train to recognize and differentiate previously unseen objects as well as infer general properties and attributes is an important skill for robotic agents. Increased autonomy leads to robustness, one of the main challenges real-world robotics faces. It also renders scaling up data collection practical. Additionally, removing human supervision from the loop has the potential to enable learning richer and less biased continuous representations than ones supervised by a limited set of discrete labels. Unbiased representations can prove useful in unknown future environments different from the ones seen during supervision, a typical challenge for robotics.In this work we present an unsupervised method that learns representations that disentangle perceptual and semantic object attributes such as class, function, and color. We automatically acquire training data by capturing videos with a real robot; a robot base moves around a table to capture objects in various arrangements. Assuming a pre-existing objectness detector, we extract objects from random frames within a same scene containing the same objects, and let the metric learning system decide how to assign positive and negative pairs of embeddings. Representations that generalize across objects naturally emerge despite not being given groundtruth matches. Unlike previous methods, we abstain from employing additional self-supervisory training signals such as tracking or depth. The only inputs to the system are monocular videos. This simplifies data collection and allows our embedding to integrate into existing end-to-end learning pipelines. We demonstrate that a trained Object-Contrastive Network (OCN) embedding allows us to reliably identify object instances based on their visual features such as color and shape. Moreover, we show that objects are also organized along their semantic or functional properties. For example, a cup might not only be associated with other cups, but also with other containers like bowls or vases.The key contributions of this work are: (1) an unsupervised algorithm for learning representations of objects (naturally encoding attributes like class, color, texture and function) which generalize to previously unseen objects; (2) showing monocular videos are sufficient to contrast similar and dissimilar objects pairs naturally without requiring explicit correspondences; (3) demonstrating the autonomy of the system, using a robot from data collection to tasks such as pointing and grasping similar objects to ones presented to it. We introduced a novel unsupervised representation learning algorithm that allows us to differentiate object attributes, such as color, shape, and function. An OCN embedding is learned by contrasting the features of objects captured from two frames of single view camera trajectories of table-top indoor environments. We specifically attend to individual objects by detecting object bounding boxes and leverage a metric learning loss to disentangle subtle variations of object attributes. The resulting embedding space allows to organize objects along multiple dimensions and serves as representation for robotic learning. We show that an OCN embedding can be used on real robotic tasks such as Figure 7 : Robot experiment of grasping the object that is closest to the query object (held by hand). Images on the left are captured by the robot camera, and the images on the right are the video frames from a third person view camera. The leftmost object (black border) is the query object and its nearest neighbors are listed in descending order. The top row and the bottom row show the robot successfully identifies and grasps the object with similar color and shape attribute respectively.grasping and pointing, where it is important to differentiate visual and semantic attributes of individual object instances. Finally, we show that an OCN can be trained efficiently from RGB videos that are automatically obtained from a real robotic agent.",Discovering objects attributes is of great importance autonomous agents effectively operate human environments. task is particularly challenging due ubiquitousness objects nuances perceptual semantic detail. paper present unsupervised approach learning disentangled representations objects entirely unlabeled monocular videos. continuous representations are not biased limited discrete set labels determined human labelers. proposed representation is trained metric learning loss where objects homogeneous features are pushed together heterogeneous features are pulled apart. show unsupervised embeddings allow discover object attributes can enable robots self-supervise previously unseen environments. quantitatively evaluate performance large-scale synthetic dataset 12k object models well real dataset collected robot show unsupervised object understanding generalizes previously unseen objects. Specifically demonstrate effectiveness approach robotic manipulation tasks pointing grasping objects. interesting perhaps surprising finding approach is that given limited set objects object correspondences will naturally emerge when using metric learning without requiring explicit positive pairs. ability autonomously train recognize differentiate previously unseen objects well infer general properties attributes is an important skill robotic agents. Increased autonomy leads robustness one main challenges real-world robotics faces. also renders scaling data collection practical. Additionally removing human supervision loop has the potential enable learning richer less biased continuous representations ones supervised limited set discrete labels. Unbiased representations can prove useful unknown future environments different ones seen supervision typical challenge robotics.In work present unsupervised method learns representations disentangle perceptual semantic object attributes class function color. automatically acquire training data capturing videos real robot;robot base moves around table capture objects various arrangements. Assuming pre-existing objectness detector extract objects random frames within scene containing objects let metric learning system decide how to assign positive negative pairs embeddings. Representations generalize across objects naturally emerge despite given groundtruth matches. Unlike previous methods abstain employing additional self-supervisory training signals tracking depth. inputs system are monocular videos. simplifies data collection allows embedding integrate existing end-to-end learning pipelines. demonstrate trained Object-Contrastive Network OCN embedding allowsus reliably identify object instances based visual features color shape. Moreover show objects are also organized along semantic functional properties. example cup might associated cups also containers like bowls vases.The key contributions work are:1 unsupervised algorithm learning representations objects naturally encoding attributes like class color texture function which generalize previously unseen objects;2 showing monocular videos are sufficient contrast similar dissimilar objects pairs naturally without requiring explicit correspondences;3 demonstrating autonomy system using robot data collection tasks pointing grasping similar objects ones presented it. introduced novel unsupervised representation learning algorithm allowsus differentiate object attributes color shape function. OCN embedding is learned contrasting features objects captured two frames single view camera trajectories table-top indoor environments. specifically attend individual objects detecting object bounding boxes leverage metric learning loss disentangle subtle variations object attributes. resulting embedding space allows organize objects along multiple dimensions serves representation robotic learning. show OCN embedding can be used real robotic tasks Figure7:Robot experiment grasping object is closest query object held hand Images left are captured robot camera images right are the video frames third person view camera. leftmost object black border is the query object nearest neighbors are listed descending order. top row bottom row show robot successfully identifies grasps object similar color shape attribute respectively.grasping pointing where it is important differentiate visual semantic attributes individual object instances. Finally show OCN can be trained efficiently RGB videos are automatically obtained real robotic agent.,950,650,300,0.009,1.462,2025/11/05 17:18:55,0.0,1.414,0.4112149532710277,308.624
"Learning from a scalar reward in continuous action space environments is difficult and often requires millions if not billions of interactions.   We introduce state aligned vector rewards, which are easily defined in metric state spaces and allow our deep reinforcement learning agent to tackle the curse of dimensionality.   Our agent learns to map from action distributions to state change distributions implicitly defined in a quantile function neural network.    We further introduce a new reinforcement learning technique inspired by quantile regression which does not limit agents to explicitly parameterized action distributions.   Our results in high dimensional state spaces show that training with vector rewards allows our agent to learn multiple times faster than an agent training with scalar rewards. Reinforcement learning BID32 ) is a powerful paradigm in which an agent learns about an environment through interaction. The common formulation consists of a Markov Decision Process (MDP) modeled as a 5-tuple (S, A, P, r, γ) where S is the (possibly infinite) set of states, A is the (possibly infinite) set of actions available to the agent, P : (S × A × S) → [0, 1] : P (s |s, a) is the transition probability of reaching state s ∈ S given state s ∈ S and action a ∈ A, r : (S × A) → R : r(s, a) is the reward received for taking action a in state s and γ is the reward discount factor. The goal of the agent is to maximize the cumulative discounted reward R = ∞ t=0 γ t r(s t , a t ) by choosing actions a t according to some (possibly stochastic) policy π : (S × A) → [0, 1] : π(a t |s t ). Sometimes it is further useful to make a distinction between the actual state space S and the correlated observation space O of the agent. In this case π : (O × A) → [0, 1] : π(a t |o t ) with o t ∈ O. The use of deep neural networks allowed this formulation to scale to high dimensional visual inputs approaching continuity in state space BID20 while others extended deep reinforcement learning to continuous action spaces BID15 BID21 . While neural networks are powerful function approximators, they require large amounts of training data to converge. In the case of reinforcement learning this means interactions with the environment, a requirement easy to fulfill in simulation, yet impractical when the agent should interact with the real world. This problem is aggravated by the weak training signal of classical reinforcement learning -a simple scalar reward.While originally the dopamine activity in mammal brains was linked to general ""rewarding"" events, BID28 point out that the diversity of dopamine circuits in the mid brain is better modeled by viral vector strategies. BID8 also show that human reinforcement learning incorporates effector specific value estimations to cope with the high dimensional action space. Inspired by these biological insights, we improve the sample efficiency of a deep reinforcement learning algorithm in this work by modeling a d-dimensional vector reward. A vector reward can in some domains easily be defined in alignment with the state space. We say that two vector spaces are aligned if their dimensions correlate and show that if state and action space are not aligned, a mapping from action distribution to state change distribution can be learned.As a motivating example, consider the agent in Figure 1 (a) trying to reach the goal (marked by the blue dot). If we take p as the position vector of the agent relative to the goal, a sensible reward to guide the agent to the goal in this environment would be r = ||p|| − ||p + a|| where || · || can be any norm in the vector space of the environment. For illustration purposes we'll focus on the L 1 norm in this example and throughout this paper. During training the agent might try action a which moves Figure 1: (a) An agent freely moving in a 2D world might try to reach a goal at position (0, 0) by taking action a. A sensible reward in this environment is the change in absolute distance to the goal. With a scalar reward this would be summarized as r = r x − r y , whereas a vector reward would keep the two reward dimensions distinguishable. (b) In most cases action and state space are however not aligned, therefore a mapping from action to state change must be learned.it closer to the goal in x direction, but a bit further away from the goal in y direction. The scalar reward would then just convey the information, that the action was rather positive (since the agent got closer to the goal) but miss out on the distinction that the action was good in x-direction but bad in y-direction. To provide this distinction, a more informative reward would keep the dimensions separate and therefore be a vector itself: r = |p| − |p + a| where | · | denotes the element-wise absolute value here. Note that this reward is dimension wise aligned with the position p, the state, of the agent. Since we focus on reaching problems in this work, we'll use the terms ""position"" and ""state"" interchangeably.The problem with such a state aligned vector reward is however that the action space is in most cases not state aligned. To see this, consider the schematic robot arm in Figure 1 (b): The action dimensions a 1 and a 2 correspond to the torques of the robot arm and do not directly translate to a shift in x and y dimension, respectively. To address this issue we use the method proposed by BID5 a) to train a deep neural network to approximate the quantile function, in our case of the position change, given the current observation and quantile target. Additionally we give a parameterization of the action probability distribution as input to this position change prediction network (short PCPN). We then train the agent, parameterized by another neural network which maps from observations to action probability distributions, through a new reinforcement learning method we call quantile regression reinforcement learning (short QRRL). A schematic overview of our setup can be seen in FIG1 .To summarize, the contributions of this paper are the following:• We extend the reinforcement learning paradigm to allow for faster training based on more informative state aligned vector rewards.• We present an architecture that learns a probability distribution over possible state changes based on a probability distribution over possible actions.• We introduce a new reinforcement learning algorithm to train stochastic continuous action policies with arbitrary action probability distributions. In this work we present the idea of state aligned vector rewards for faster reinforcement learning. While the idea is straight forward and simple, we are unaware of any work that addresses it so far. Additionally, we also present a new reinforcement learning technique based on quantile regression in this work which we term QRRL. QRRL allows for complex stochastic policies in continuous action spaces, not limiting agents to Gaussian actions. Combining both, we show that the agent network in our SAVER agent can be trained through a quantile network pretrained in the environment. We show that SAVER is capable of training orders of magnitudes faster in high dimensional metric spaces. While d-dimensional metric spaces are mainly mathematical constructs for d > 3, we see a lot of potential in SAVER to be applied to problems in mathematics and related fields, including the field of deep (reinforcement) learning itself.",Learning scalar reward continuous action space environments is difficult often requires millions if not billions interactions. introduce state aligned vector rewards which are easily defined metric state spaces allow deep reinforcement learning agent tackle curse dimensionality. agent learns map action distributions state change distributions implicitly defined quantile function neural network. introduce new reinforcement learning technique inspired quantile regression which does not limit agents explicitly parameterized action distributions. results high dimensional state spaces show training vector rewards allows agent learn multiple times faster agent training scalar rewards. Reinforcement learning BID32 is a powerful paradigm which an agent learns environment interaction. common formulation consists Markov Decision Process MDP modeled 5-tuple P r γ whereSis possibly infinite set states is the possibly infinite set actions available agent P:× × → 0 1 P |s is transition probability reaching state ∈ given state ∈ action ∈ r:× →R:r is the reward received taking action state γ is the reward discount factor. goal agent is to maximize cumulative discounted rewardR ∞ t=0γ r choosing actions according possibly stochastic policyπ:× → 0 1 π |s Sometimes is further useful make distinction actual state space correlated observation space agent. caseπ:× → 0 1 π |o ∈ O. use deep neural networks allowed formulation scale high dimensional visual inputs approaching continuity state space BID20 others extended deep reinforcement learning continuous action spaces BID15 BID21. neural networks are powerful function approximators require large amounts training data converge. case reinforcement learning means interactions environment requirement easy fulfill simulation yet impractical when the agent should interact real world. problem is aggravated weak training signal classical reinforcement learning-a simple scalar reward.While originally dopamine activity mammal brains was linked general rewarding events BID28 point diversity dopamine circuits mid brain is better modeled viral vector strategies. BID8 also show human reinforcement learning incorporates effector specific value estimations cope high dimensional action space. Inspired biological insights improve sample efficiency deep reinforcement learning algorithm work modeling d-dimensional vector reward. vector reward can in some domains easily defined alignment state space. say two vector spaces are are not aligned if their dimensions correlate show if state action space are are not aligned mapping action distribution state change distribution can be learned.As motivating example consider agent Figure1 trying reach goal marked blue dot If we takep position vector agent relative goal sensible reward guide agent goal environment would r ||p|| − ||p+a|| where||·|| can be any norm vector space environment. illustration purposes focus L 1 norm example throughout paper. training agent might try action which moves Figure1:agent freely moving 2D world might try reach goal position 0 0 taking action a. sensible reward environment is the change absolute distance goal. scalar reward would summarized r rx−r whereas vector reward would keep two reward dimensions distinguishable. b cases action state space are however aligned therefore mapping action state change must learned.it closer goal x direction bit away goal direction. scalar reward would convey information action was rather positive since agent got closer goal miss distinction action was good x-direction bad y-direction provide distinction informative reward would keep dimensions separate therefore vector itself:r |p|−|p+a| where|· denotes element-wise absolute value here. Note reward is dimension wise aligned positionp state agent. Since focus reaching problems work use terms position state interchangeably.The problem state aligned vector reward is however action space is in most cases state aligned. see consider schematic robot arm Figure1 b action dimensions 1 2 correspond torques robot arm do not directly translate shift x dimension respectively. address issue use method proposed BID5 train deep neural network approximate quantile function case position change given current observation quantile target. Additionally give parameterization action probability distribution input position change prediction network short PCPN train agent parameterized another neural network which maps observations action probability distributions new reinforcement learning method call quantile regression reinforcement learning short QRRL schematic overview setup can be seen FIG1.To summarize contributions paper are the following:• extend reinforcement learning paradigm allow faster training based informative state aligned vector rewards.• present architecture learns probability distribution possible state changes based probability distribution possible actions.• introduce new reinforcement learning algorithm train stochastic continuous action policies arbitrary action probability distributions. work present idea state aligned vector rewards faster reinforcement learning. idea is straight forward simple are unaware work addresses far. Additionally also present new reinforcement learning technique based quantile regression work which we term QRRL. QRRL allows complex stochastic policies continuous action spaces limiting agents Gaussian actions. Combining show agent network SAVER agent can be trained quantile network pretrained environment. show SAVER is capable training orders magnitudes faster high dimensional metric spaces. d-dimensional metric spaces are mainly mathematical constructs 3 see lot potential SAVER applied problems mathematics related fields including field deep reinforcement learning itself.,1490,940,550,0.017,1.585,2025/11/05 17:18:55,0.01,1.66,0.7943925233644857,493.532
"We propose Episodic Backward Update - a new algorithm to boost the performance of a deep reinforcement learning agent by fast reward propagation. In contrast to the conventional use of the replay memory with uniform random sampling, our agent samples a whole episode and successively propagates the value of a state into its previous states. Our computationally efficient recursive algorithm allows sparse and delayed rewards to propagate effectively throughout the sampled episode. We evaluate our algorithm on 2D MNIST Maze Environment and 49 games of the Atari 2600 Environment and show that our agent improves sample efficiency with a competitive computational cost. Recently, deep reinforcement learning (RL) has been very successful in many complex environments such as the Arcade Learning Environment (Bellemare et al., 2013) and Go . Deep Q-Network (DQN) algorithm BID11 with the help of experience replay BID8 BID9 enjoys more stable and sample-efficient learning process, so is able to achieve super-human performance on many tasks. Unlike simple online reinforcement learning, the use of experience replay with random sampling breaks down the strong ties between correlated transitions and also allows the transitions to be reused multiple times throughout the training process.Although DQN has shown impressive performances, it is still impractical in terms of data efficiency. To achieve a human-level performance in the Arcade Learning Environment, DQN requires 200 million frames of experience for training, which is approximately 39 days of game play in real time. Remind that it usually takes no more than a couple of hours for a skilled human player to get used to such games. So we notice that there is still a tremendous amount of gap between the learning process of humans and that of a deep reinforcement learning agent. This problem is even more crucial in environments such as autonomous driving, where we cannot risk many trials and errors due to the high cost of samples.One of the reasons why the DQN agent suffers from such low sample efficiency could be the sampling method over the replay memory. In many practical problems, the agent observes sparse and delayed reward signals. There are two problems when we sample one-step transitions uniformly at random from the replay memory. First, we have a very low chance of sampling the transitions with rewards for its sparsity. The transitions with rewards should always be updated, otherwise the agent cannot figure out which action maximizes its expected return in such situations. Second, there is no point in updating a one-step transition if the future transitions have not been updated yet. Without the future reward signals propagated, the sampled transition will always be trained to return a zero value.In this work, we propose Episodic Backward Update (EBU) to come up with solutions for such problems. Our idea originates from a naive human strategy to solve such RL problems. When we observe an event, we scan through our memory and seek for another event that has led to the former one. Such episodic control method is how humans normally recognize the cause and effect relationship BID7 . We can take a similar approach to train an RL agent. We can solve the first problem above by sampling transitions in an episodic manner. Then, we can be assured that at least one transition with non-zero reward is being updated. We can solve the second problem by updating transitions in a backward way in which the transitions were made. By then, we can perform an efficient reward propagation without any meaningless updates. This method faithfully follows the principle of dynamic programing.We evaluate our update algorithm on 2D MNIST Maze Environment and the Arcade Learning Environment. We observe that our algorithm outperforms other baselines in many of the environments with a notable amount of performance boosts.",propose Episodic Backward Update - new algorithm boost performance deep reinforcement learning agent fast reward propagation. contrast conventional use replay memory uniform random sampling agent samples whole episode successively propagates value state previous states. computationally efficient recursive algorithm allows sparse delayed rewards propagate effectively throughout sampled episode. evaluate algorithm 2D MNIST Maze Environment 49 games Atari 2600 Environment show agent improves sample efficiency competitive computational cost. Recently deep reinforcement learning RL has been very successful many complex environments Arcade Learning Environment Bellemareetal. 2013 Go. Deep Q-Network DQN algorithm BID11 help experience replay BID8 BID9 enjoys stable sample-efficient learning process is able achieve super-human performance many tasks. Unlike simple online reinforcement learning use experience replay random sampling breaks strong ties correlated transitions also allows transitions reused multiple times throughout training process.Although DQN has shown impressive performances is still impractical terms data efficiency. achieve human-level performance Arcade Learning Environment DQN requires 200 million frames experience training which is approximately 39 days game play real time. Remind usually takes couple hours skilled human player get used games. notice is still tremendous amount gap learning process humans deep reinforcement learning agent. problem is even crucial environments autonomous driving where we cannot risk many trials errors due high cost samples.One reasons why the DQN agent suffers low sample efficiency could sampling method replay memory. many practical problems agent observes sparse delayed reward signals. are two problems when we sample one-step transitions uniformly random replay memory. First havea low chance sampling transitions rewards sparsity. transitions rewards should always updated otherwise agent cannot figure which action maximizes expected return situations. Second is no point updating one-step transition if the future transitions have not been updated yet. Without future reward signals propagated sampled transition will always trained return zero value.In work propose Episodic Backward Update EBU come solutions problems. idea originates naive human strategy solve RL problems. When we observe event scan memory seek another event has led former one. episodic control method is how humans normally recognize cause effect relationship BID7. can take similar approach train RL agent. can solve first problem sampling transitions episodic manner. can assured least one transition non-zero reward is being updated. can solve second problem updating transitions backward way which the transitions were made. can perform efficient reward propagation without meaningless updates. method faithfully follows principle dynamic programing.We evaluate update algorithm 2D MNIST Maze Environment Arcade Learning Environment. observe algorithm outperforms baselines many environments notable amount performance boosts.,728,492,236,0.007,1.48,2025/11/05 17:18:55,0.0,1.536,0.467289719626168,259.716
"Survival Analysis (time-to-event analysis) in the presence of multiple possible adverse events, i.e., competing risks, is a challenging, yet very important problem in medicine, finance, manufacturing, etc. Extending classical survival analysis to competing risks is not trivial since only one event (e.g. one cause of death) is observed and hence, the incidence of an event of interest is often obscured by other related competing events. This leads to the nonidentifiability of the event times’ distribution parameters, which makes the problem significantly more challenging. In this work we introduce Siamese Survival Prognosis Network, a novel Siamese Deep Neural Network architecture that is able to effectively learn from data in the presence of multiple adverse events. The Siamese Survival Network is especially crafted to issue pairwise concordant time-dependent risks, in which longer event times are assigned lower risks. Furthermore, our architecture is able to directly optimize an approximation to the C-discrimination index, rather than relying on well-known metrics of cross-entropy etc., and which are not able to capture the unique requirements of survival analysis with competing risks. Our results show consistent performance improvements on a number of publicly available medical datasets over both statistical and deep learning state-of-the-art methods. Competing risks settings are ubiquitous in medicine. They can be encountered in cardiovascular diseases, in cancer, and in the geriatric population suffering from multiple diseases. To solve the challenging problem of learning the model parameters from time-to-event data while handling right censoring, we have developed a novel deep learning architecture for estimating personalized risk scores in the presence of competing risks which is based on the well-known Siamese network architecture. Our method is able to capture complex non-linear representations missed out by classical machine learning and statistical models. Experimental results show that our method is able to outperform existing competing risk methods by successfully learning representations which can flexibly describe non-proportional hazard rates with complex interactions between covariates and survival times that are common in many diseases with heterogeneous phenotypes.",Survival Analysis time-to-event analysis presence multiple possible adverse events.e competing risks is a challenging yet important problem medicine finance manufacturing etc. Extending classical survival analysis competing risks is not trivial since one event e.g one cause death is observed hence incidence event interest is often obscured related competing events. leads nonidentifiability event times distribution parameters which makes problem significantly challenging. work introduce Siamese Survival Prognosis Network novel Siamese Deep Neural Network architecture is able effectively learn data presence multiple adverse events. Siamese Survival Network is especially crafted issue pairwise concordant time-dependent risks which longer event times are assigned lower risks. Furthermore architecture is able directly optimize approximation C-discrimination index rather relying well-known metrics cross-entropy etc. which are able capture unique requirements survival analysis competing risks. results show consistent performance improvements number publicly available medical datasets statistical deep learning state-of-the-art methods. Competing risks settings are ubiquitous medicine. can be encountered cardiovascular diseases cancer geriatric population suffering multiple diseases. solve challenging problem learning model parameters time-to-event data handling right censoring have developed novel deep learning architecture estimating personalized risk scores presence competing risks which is based well-known Siamese network architecture. method is able capture complex non-linear representations missed classical machine learning statistical models. Experimental results show method is able outperform existing competing risk methods successfully learning representations which can flexibly describe non-proportional hazard rates complex interactions covariates survival times are common many diseases heterogeneous phenotypes.,403,287,116,0.004,1.404,2025/11/05 17:18:55,0.0,1.353,0.2305295950155758,124.33
"The digitization of data has resulted in making datasets available to millions of users in the form of relational databases and spreadsheet tables. However, a majority of these users come from diverse backgrounds and lack the programming expertise to query and analyze such tables. We present a system that allows for querying data tables using natural language questions, where the system translates the question into an executable SQL query. We use a deep sequence to sequence model in wich the decoder uses a simple type system of SQL expressions to structure the output prediction. Based on the type, the decoder either copies an output token from the input question using an attention-based copying mechanism or generates it from a fixed vocabulary. We also introduce a value-based loss function that transforms a distribution over locations to copy from into a distribution over the set of input tokens to improve training of our model. We evaluate our model on the recently released WikiSQL dataset and show that our model trained using only supervised learning significantly outperforms the current state-of-the-art Seq2SQL model that uses reinforcement learning. The IT revolution of the past few decades has resulted in a large-scale digitization of data, making it accessible to millions of users in the form of databases and spreadsheet tables. Despite advances in designing new high-level programming languages and user interfaces, querying and analyzing such tables usually still requires users to write small programs in languages such as SQL or Excel, which is unfortunately beyond the programming expertise of a majority of end-users BID8 . Thus, building effective semantic parsers that can translate natural language questions into executable programs has been a long-standing goal to improve end-user data accessibility BID22 BID30 BID20 BID15 BID9 .Recent work has shown that recurrent neural networks with attention and copying mechanisms BID4 BID18 BID13 can be used effectively to build successful semantic parsers. Notably , BID32 recently introduced the state-ofthe-art Seq2SQL model for question to SQL translation in the supervised setting, where programs are explicitly provided with their corresponding questions. The Seq2SQL model shows that using separate decoders for different parts of a query (i.e., aggregation operation, target column, and where predicates) increases prediction accuracy, and reinforcement learning further improves the model by allowing it to learn semantically equivalent queries beyond supervision.In this paper, we present a new encoder-decoder model as an extension of the attentional seq2seq model for natural language to SQL program translation and a training approach that is capable of learning the model in an effective and stable manner. FIG0 shows an example table-question pair and how our system generates the answer by executing the synthesized SQL program.First, we present a simple type system to control the decoding mode at each decoding step (cf. Sect. 2). Based on the SQL grammar, a decoder cell is specialized to either select a token from the SQL built-in vocabulary, generate a pointer over the table header and the input question to copy a table column, or generate a pointer to copy a constant from the user's question. The type system allows us to have a fine-grain control over the decoding process while retaining the simplicity of the sequence structure, as opposed to designing multiple decoders for different language components or adding extra controllers for expansion of production rules . FIG0 . The model encodes table columns as well as the user question with a bidirectional LSTM and then decodes the hidden state with a typed LSTM, where the decoding action for each cell is statically determined.Second, we constructed an objective function that allows us to effectively train our model to copy correct values (cf. Sect. 3). Training copying decoders can be challenging when the value to be copied appears in multiple places in the input (i.e. both in the question and the table headers). Our solution to the problem is to use a new value-based loss function that transfers the distribution over the pointer locations in the input into a distribution over the set of tokens observed in the input, by summing up the probabilities of the same vocabulary value appearing at different input indices. Our results show that our training strategy performs better than alternatives (e.g., direct supervision on pointers). Our approach is very robust and consistently converges to high-accuracy models starting from random initializations.We have evaluated our approach on the recently released WikiSQL dataset BID32 , a corpus consisting of over 80,000 natural language question and pairs. Our results in Sect. 4 show that our model can significantly outperform the current state-of-the-art Seq2SQL model BID32 , without requiring a reinforcement learning refinement phase (59.5% vs 48.3% for exact syntactic match and 65.1% vs 59.4% for execution accuracy). Also, with a series of ablation experiments, we analyze the influence of different components of our model on the overall results. We presented a new sequence to sequence based neural architecture to translate natural language questions over tables into executable SQL queries. Our approach uses a simple type system to guide the decoder to either copy a token from the input using a pointer-based copying mechanism or generate a token from a finite vocabulary. We presented a sum-transfer value based loss function that transforms a distribution over pointer locations into a distribution over token values in the input to efficiently train the architecture. Our evaluation on the WikiSQL dataset showed that our model significantly outperforms the current state-of-the-art Seq2SQL model.","digitization data has resulted making datasets available millions users form relational databases spreadsheet tables. However majority users come diverse backgrounds lack programming expertise query analyze tables. present system allows querying data tables using natural language questions where the system translates question executable SQL query. use deep sequence sequence model wich decoder uses simple type system SQL expressions structure output prediction. Based type decoder either copies output token input question using attention-based copying mechanism generates fixed vocabulary. also introduce value-based loss function transforms distribution locations copy distribution set input tokens improve training model. evaluate model recently released WikiSQL dataset show model trained using supervised learning significantly outperforms current state-of-the-art Seq2SQL model uses reinforcement learning. revolution past decades has resulted large-scale digitization data making accessible millions users form databases spreadsheet tables. Despite advances designing new high-level programming languages user interfaces querying analyzing tables usually still requires users write small programs languages SQL Excel which is unfortunately beyond programming expertise majority end-users BID8. Thus building effective semantic parsers can translate natural language questions executable programs has been a long-standing goal improve end-user data accessibility BID22 BID30 BID20 BID15 BID9.Recent work has shown recurrent neural networks attention copying mechanisms BID4 BID18 BID13 can be used effectively build successful semantic parsers. Notably BID32 recently introduced state-ofthe-art Seq2SQL model question SQL translation supervised setting where programs are explicitly provided corresponding questions. Seq2SQL model shows using separate decoders different parts query.e aggregation operation target column where predicates increases prediction accuracy reinforcement learning improves model allowing learn semantically equivalent queries beyond supervision.In paper present new encoder-decoder model extension attentional seq2seq model natural language SQL program translation training approach is capable learning model effective stable manner. FIG0 shows example table-question pair how our system generates answer executing synthesized SQL program.First present simple type system control decoding mode decoding step cf. Sect. 2 Based SQL grammar decoder cell is specialized either select token SQL built-in vocabulary generate pointer table header input question copy table column generate pointer copy constant user's question. type system allowsus have a fine-grain control decoding process retaining simplicity sequence structure opposed designing multiple decoders different language components adding extra controllers expansion production rules. FIG0. model encodes table columns well user question bidirectional LSTM decodes hidden state typed LSTM where the decoding action cell is statically determined.Second constructed objective function allowsus effectively train model copy correct values cf. Sect. 3 Training copying decoders can be challenging when the value copied appears multiple places input.e question table headers solution problem is to use new value-based loss function transfers distribution pointer locations input distribution set tokens observed input summing probabilities vocabulary value appearing different input indices. results show training strategy performs better alternatives e.g direct supervision pointers approach is very robust consistently converges high-accuracy models starting random initializations.We have evaluated approach recently released WikiSQL dataset BID32 corpus consisting 80,000 natural language question pairs. results Sect. 4 show model can significantly outperform current state-of-the-art Seq2SQL model BID32 without requiring reinforcement learning refinement phase 59.5 vs 48.3 exact syntactic match 65.1 vs 59.4 execution accuracy Also series ablation experiments analyze influence different components model overall results. presented new sequence sequence based neural architecture translate natural language questions tables executable SQL queries. approach uses simple type system guide decoder either copy token input using pointer-based copying mechanism generate token finite vocabulary. presented sum-transfer value based loss function transforms distribution pointer locations distribution token values input efficiently train architecture. evaluation WikiSQL dataset showed model significantly outperforms current state-of-the-art Seq2SQL model.",1074,718,356,0.011,1.496,2025/11/05 17:18:55,0.01,1.545,0.5171339563862927,335.573
"To backpropagate the gradients through stochastic binary layers, we propose the augment-REINFORCE-merge (ARM) estimator that is unbiased, exhibits low variance, and has low computational complexity. Exploiting variable augmentation, REINFORCE, and reparameterization, the ARM estimator achieves adaptive variance reduction for Monte Carlo integration by merging two expectations via common random numbers. The variance-reduction mechanism of the ARM estimator can also be attributed to either antithetic sampling in an augmented space, or the use of an optimal anti-symmetric ""self-control"" baseline function together with the REINFORCE estimator in that augmented space. Experimental results show the ARM estimator provides state-of-the-art performance in auto-encoding variational inference and maximum likelihood estimation, for discrete latent variable models with one or multiple stochastic binary layers. Python code for reproducible research is publicly available. Given a function f (z) of a random variable z = (z 1 , . . . , z V )T , which follows a distribution q φ (z) parameterized by φ, there has been significant recent interest in estimating φ to maximize (or minimize) the expectation of f (z) with respect to z ∼ q φ (z), expressed as DISPLAYFORM0 In particular, this expectation objective appears in both maximizing the evidence lower bound (ELBO) for variational inference BID12 and approximately maximizing the log marginal likelihood of a hierarchal Bayesian model BID1 , two fundamental problems in statistical inference. To maximize (1), if ∇ z f (z) is tractable to compute and z ∼ q φ (z) can be generated via reparameterization as z = T φ ( ), ∼ p( ), where are random noises and T φ (·) denotes a deterministic transform parameterized by φ, then one may apply the reparameterization trick BID14 BID27 to compute the gradient as DISPLAYFORM1 This trick, however, is often inapplicable to discrete random variables, as widely used to construct discrete latent variable models such as sigmoid belief networks BID22 BID31 .To maximize (1) for discrete z, using the score function ∇ φ log q φ (z) = ∇ φ q φ (z)/q φ (z), one may compute ∇ φ E(φ) via REINFORCE BID38 as its high Monte-Carlo-integration variance often limits its use in practice. Note that if f (z) depends on φ, then we assume it is true that E z∼q φ (z) [∇ φ f (z)] = 0. For example, in variational inference, we need to maximize the ELBO as E z∼q φ (z) [f (z)], where f (z) = log[p(x | z)p(z)/q φ (z)]. In this case, although f (z) depends on φ, as E z∼q φ (z) [∇ φ log q φ (z)] = ∇ φ q φ (z)dz = ∇ φ q φ (z)dz = 0, we have E z∼q φ (z) [∇ φ f (z)] = 0.To address the high-variance issue, one may introduce an appropriate baseline (a.k.a. control variate) to reduce the variance of REINFORCE BID24 BID26 BID19 BID9 BID20 BID29 BID21 . Alternatively , one may first relax the discrete random variables with continuous ones and then apply the reparameterization trick to estimate the gradients, which reduces the variance of Monte Carlo integration at the expense of introducing bias BID11 . Combining both REINFORCE and the continuous relaxation of discrete random variables, REBAR of BID35 and RELAX of BID7 both aim to produce a low-variance and unbiased gradient estimator by introducing a continuous relaxation based baseline function, whose parameters, however, need to be estimated at each mini-batch by minimizing the sample variance of the estimator with stochastic gradient descent (SGD). Estimating the baseline parameters often clearly increases the computation. Moreover, the potential conflict, between minimizing the sample variance of the gradient estimate and maximizing the expectation objective, could slow down or even prevent convergence and increase the risk of overfitting. Another interesting variance-control idea applicable to discrete latent variables is using local expectation gradients, which estimates the gradients based on REINFORCE, by performing Monte Carlo integration using a single global sample together with exact integration of the local variable for each latent dimension BID34 .Distinct from the usual idea of introducing baseline functions and optimizing their parameters to reduce the estimation variance of REINFORCE, we propose the augment-REINFORCE-merge (ARM) estimator, a novel unbiased and low-variance gradient estimator for binary latent variables that is also simple to implement and has low computational complexity. We show by rewriting the expectation with respect to Bernoulli random variables as one with respect to augmented exponential random variables, and then expressing the gradient as an expectation via REINFORCE, one can derive the ARM estimator in the augmented space with the assistance of appropriate reparameterization. In particular, in the augmented space, one can derive the ARM estimator by using either the strategy of sharing common random numbers between two expectations, or the strategy of applying antithetic sampling. Both strategies, as detailedly discussed in BID23 , can be used to explain why the ARM estimator is unbiased and could lead to significant variance reduction. Moreover, we show that the ARM estimator can be considered as improving the REINFORCE estimator in an augmented space by introducing an optimal baseline function subject to an anti-symmetric constraint; this baseline function can be considered as a ""self-control"" one, as it exploits the function f itself and correlated random noises for variance reduction, and adds no extra parameters to learn. This ""self-control"" feature makes the ARM estimator distinct from both REBAR and RELAX, which rely on minimizing the sample variance of the gradient estimate to optimize the baseline function.We perform experiments on a representative toy optimization problem and both auto-encoding variational inference and maximum likelihood estimation for discrete latent variable models, with one or multiple binary stochastic layers. Our extensive experiments show that the ARM estimator is unbiased, exhibits low variance, converges fast, has low computation, and provides state-of-the-art out-of-sample prediction performance for discrete latent variable models, suggesting the effectiveness of using the ARM estimator for gradient backpropagation through stochastic binary layers. Python code for reproducible research is available at https://github.com/mingzhang-yin/ARM-gradient. To train a discrete latent variable model with one or multiple stochastic binary layers, we propose the augment-REINFORCE-merge (ARM) estimator to provide unbiased and low-variance gradient estimates of the parameters of Bernoulli distributions. With a single Monte Carlo sample, the estimated gradient is the product of uniform random noises and the difference of a function of two vectors of correlated binary latent variables. Without relying on estimating a baseline function with extra learnable parameters for variance reduction, it maintains efficient computation and avoids increasing the risk of overfitting. Applying the ARM gradient leads to not only fast convergence, but also low test negative log-likelihoods (and low test negative evidence lower bounds for variational inference), on both auto-encoding variational inference and maximum likelihood estimation for stochastic binary feedforward neural networks. Some natural extensions of the proposed ARM estimator include generalizing it to multivariate categorical latent variables, combining it with a baseline or local-expectation based variance reduction method, and applying it to reinforcement learning whose action space is discrete.Initialize w1:T , ψ randomly; while not converged do Sample a mini-batch of x from data; DISPLAYFORM0 ) T ∇w t Tw t (bt−1) ; end wt = wt + ρtgw t with step-size ρt end ψ = ψ + ηt∇ ψ f (b1:T ; ψ) with step-size ηt end",backpropagate gradients stochastic binary layers propose augment-REINFORCE-merge ARM estimator is unbiased exhibits low variance has has low computational complexity. Exploiting variable augmentation REINFORCE reparameterization ARM estimator achieves adaptive variance reduction Monte Carlo integration merging two expectations via common random numbers. variance-reduction mechanism ARM estimator can also attributed either antithetic sampling augmented space use optimal anti-symmetric self-control baseline function together REINFORCE estimator augmented space. Experimental results show ARM estimator provides state-of-the-art performance auto-encoding variational inference maximum likelihood estimation discrete latent variable models one multiple stochastic binary layers. Python code reproducible research is publicly available. Given functionf z random variablez z1 zV which follows distributionqφ z parameterized φ has been significant recent interest estimatingφ maximize minimize expectation f z respect z∼qφ z expressed DISPLAYFORM0 particular expectation objective appears maximizing evidence lower bound ELBO variational inference BID12 approximately maximizing log marginal likelihood hierarchal Bayesian model BID1 two fundamental problems statistical inference. maximize 1 if∇zf z is tractable compute z∼qφ z can be generated via reparameterization z φ ∼p where are random noises φ · denotes deterministic transform parameterized φ one may apply reparameterization trick BID14 BID27 compute gradient DISPLAYFORM1 trick however is often inapplicable discrete random variables widely used construct discrete latent variable models sigmoid belief networks BID22 BID31.To maximize 1 discretez using score function∇φ logqφ z if∇φqφ z/qφ z one may compute∇ φE φ via REINFORCE BID38 high Monte-Carlo-integration variance often limits use practice. Note iff z depends φ assume is true E z∼qφ z if∇φf z 0. example variational inference need maximize ELBO E z∼qφ z wheref z wheref z log p x z p z/qφ z case althoughf z depends φ have E z∼qφ z if ∇ φ logq φ z if∇φqφ z dz ∇φqφ z dz 0 have E z∼qφ z if∇φf z 0.To address high-variance issue one may introduce appropriate baseline.k.a control variate reduce variance REINFORCE BID24 BID26 BID19 BID9 BID20 BID29 BID21. Alternatively one may first relax discrete random variables continuous ones apply reparameterization trick estimate gradients which reduces variance Monte Carlo integration expense introducing bias BID11. Combining REINFORCE continuous relaxation discrete random variables REBAR BID35 RELAX BID7 aim produce low-variance unbiased gradient estimator introducing continuous relaxation based baseline function whose parameters however need estimated mini-batch minimizing sample variance estimator stochastic gradient descent SGD Estimating baseline parameters often clearly increases computation. Moreover potential conflict minimizing sample variance gradient estimate maximizing expectation objective could slow even prevent convergence increase risk overfitting. Another interesting variance-control idea applicable discrete latent variables is using local expectation gradients which estimates gradients based REINFORCE performing Monte Carlo integration using single global sample together exact integration local variable latent dimension BID34.Distinct usual idea introducing baseline functions optimizing parameters reduce estimation variance REINFORCE propose augment-REINFORCE-merge ARM estimator novel unbiased low-variance gradient estimator binary latent variables is also simple implement has low computational complexity. show rewriting expectation respect Bernoulli random variables one respect augmented exponential random variables expressing gradient expectation via REINFORCE one can derive ARM estimator augmented space assistance appropriate reparameterization. particular augmented space one can derive ARM estimator using either strategy sharing common random numbers two expectations strategy applying antithetic sampling. strategies detailedly discussed BID23 can be used explain why the ARM estimator is unbiased could lead significant variance reduction. Moreover show ARM estimator can be considered improving REINFORCE estimator augmented space introducing optimal baseline function subject anti-symmetric constraint;baseline function can be considered self-control one exploits functionf correlated random noises variance reduction adds extra parameters learn. self-control feature makes ARM estimator distinct REBAR RELAX which rely minimizing sample variance gradient estimate optimize baseline function.We perform experiments representative toy optimization problem auto-encoding variational inference maximum likelihood estimation discrete latent variable models one multiple binary stochastic layers. extensive experiments show ARM estimator is unbiased exhibits low variance converges fast has has low computation provides state-of-the-art out-of-sample prediction performance discrete latent variable models suggesting effectiveness using ARM estimator gradient backpropagation stochastic binary layers. Python code reproducible research is available https://github.com/mingzhang-yin/ARM-gradient. train discrete latent variable model one multiple stochastic binary layers propose augment-REINFORCE-merge ARM estimator provide unbiased low-variance gradient estimates parameters Bernoulli distributions. single Monte Carlo sample estimated gradient is the product uniform random noises difference function two vectors correlated binary latent variables. Without relying estimating baseline function extra learnable parameters variance reduction maintains efficient computation avoids increasing risk overfitting. Applying ARM gradient leads fast convergence also low test negative log-likelihoods low test negative evidence lower bounds variational inference auto-encoding variational inference maximum likelihood estimation stochastic binary feedforward neural networks. natural extensions proposed ARM estimator include generalizing multivariate categorical latent variables combining baseline local-expectation based variance reduction method applying reinforcement learning whose action space is discrete.Initializew1:ψ randomly;converged do Sample mini-batch x data;DISPLAYFORM0 ∇w Tw bt−1 endwt wt+ρtgw step-size ρt endψ ψ+ηt∇ψ f b1:T;ψ step-size ηt end,1630,1130,500,0.025,1.442,2025/11/05 17:18:55,0.01,1.188,0.3489096573208719,493.497
"Mini-batch stochastic gradient descent (SGD) is state of the art in large scale distributed training. The scheme can reach a linear speed-up with respect to the number of workers, but this is rarely seen in practice as the scheme often suffers from large network delays and bandwidth limits. To overcome this communication bottleneck recent works propose to reduce the communication frequency. An algorithm of this type is local SGD that runs SGD independently in parallel on different workers and averages the sequences only once in a while. This scheme shows promising results in practice, but eluded thorough theoretical analysis.
    
 We prove concise convergence rates for local SGD on convex problems and show that it converges at the same rate as mini-batch SGD in terms of number of evaluated gradients, that is, the scheme achieves linear speed-up in the number of workers and mini-batch size. The number of  communication rounds can be reduced up to a factor of T^{1/2}---where T denotes the number of total steps---compared to mini-batch SGD. This also holds for asynchronous implementations.

 Local SGD can also be used for large scale training of deep learning models. The results shown here aim serving as a guideline to further explore the theoretical and practical aspects of local SGD in these applications. Stochastic Gradient Descent (SGD) BID29 consists of iterations of the form DISPLAYFORM0 for iterates (weights) x t , x t+1 ∈ R d , stepsize (learning rate) η t > 0, and stochastic gradient g t ∈ R d with the property E g t = ∇f (x t ), for a loss function f : R d → R. This scheme can easily be parallelized by replacing g t in (1) by an average of stochastic gradients that are independently computed in parallel on separate workers (parallel SGD). This simple scheme has a major drawback: in each iteration the results of the computations on the workers have to be shared with the other workers to compute the next iterate x t+1 . Communication has been reported to be a major bottleneck for many large scale deep learning applications, see e.g. BID32 BID17 . Mini-batch parallel SGD addresses this issue by increasing the compute to communication ratio. Each worker computes a mini-batch of size b ≥ 1 before communication. This scheme is implemented in state-of-the-art distributed deep learning frameworks BID0 BID26 BID31 . Recent work in BID43 BID10 explores various limitations of this approach, as in general it is reported that performance degrades for too large mini-batch sizes BID13 BID18 BID42 .In this work we follow an orthogonal approach, still with the goal to increase the compute to communication ratio: Instead of increasing the mini-batch size, we reduce the communication frequency. Rather than keeping the sequences on different machines in sync, we allow them to evolve locally on each machine, independent from each other, and only average the sequences once in a while (local SGD). Such strategies have been explored widely in the literature, under various names.An extreme instance of this concept is one-shot SGD (McDonald et al., 2009; BID53 where the local sequences are only exchanged once, after the local runs have converged. Zhang et al. (2013 ) show statistical convergence (see also BID33 BID9 BID12 ), but the analysis restricts the algorithm to at most one pass over the data, which is in general not enough for the training error to converge. More practical are schemes that perform more frequent averaging of the parallel sequences, as e.g. BID22 for perceptron training (iterative parameter mixing), see also BID6 , BID48 BID4 BID46 for the training of deep neural networks (model averaging) or in federated learning BID23 .The question of how often communication rounds need to be initiated has eluded a concise theoretical answer so far. Whilst there is practical evidence, the theory does not even resolve the question whether averaging helps when optimizing convex functions. Concretely, whether running local SGD on K workers is K times faster than running just a single instance of SGD on one worker. Theorem 2.2. Let f be L-smooth and µ-strongly convex, DISPLAYFORM0 are generated according to (4) with gap(I T ) ≤ H and for stepsizes η t = 4 µ(a+t) with shift parameter a > max{16κ, H}, for DISPLAYFORM1 DISPLAYFORM2 We were not especially careful to optimize the constants (and the lower order terms) in (5), so we now state the asymptotic result. Corollary 2.3. Letx T be as defined as in Theorem 2.2, for parameter a = max{16κ, H}. Then DISPLAYFORM3 For the last estimate we used E µ x 0 − x ≤ 2G for µ-strongly convex f , as derived in (Rakhlin et al., 2012, Lemma 2) . Remark 2.4 (Mini-batch local SGD). So far, we assumed that each worker only computes a single stochastic gradient. In mini-batch local SGD, each worker computes a mini-batch of size b in each iteration. This reduces the variance by a factor of b, and thus Theorem (2.2) gives the convergence rate of mini-batch local SGD when σ 2 is replaced by DISPLAYFORM4 We now state some consequences of equation FORMULA17 . For the ease of the exposition we omit the dependency on L, µ, σ 2 and G 2 below, but depict the dependency on the local mini-batch size b.Convergence rate. For T large enough and assuming σ > 0, the very first term is dominating in (6) and local SGD converges at rate O(1/(KT b)). That is, local SGD achieves a linear speedup in both, the number of workers K and the mini-batch size b. Global synchronization steps. It needs to hold H = O( T /(Kb)) to get the linear speedup. This yields a reduction of the number of communication rounds by a factor O( T /(Kb)) compared to parallel mini-batch SGD without hurting the convergence rate. Extreme Cases. We have not optimized the result for extreme settings of H, K, L or σ. For instance, we do not recover convergence for the one-shot averaging, i.e. the setting H = T (though convergence for H = o(T ), but at a lower rate). Unknown Time Horizon/Adaptive Communication Frequency BID46 empirically observe that more frequent communication at the beginning of the optimization can help to get faster time-to-accuracy (see also BID16 ). Indeed, when the number of total iterations T is not known beforehand (as it e.g. depends on the target accuracy, cf. (6) and also Section 4 below), then increasing the communication frequency seems to be a good strategy to keep the communication low, why still respecting the constraint H = O( T /(Kb)) for all T . DISPLAYFORM5 . It will be useful to define DISPLAYFORM6 Observex t+1 =x t − η t g t and E g t =ḡ t .Now the proof proceeds as follows: we show (i) that the virtual sequence {x t } t≥0 almost behaves like mini-batch SGD with batch size K (Lemma 3.1 and 3.2), and (ii ) the true iterates {x k t } t≥0,k∈[K] do not deviate much from the virtual sequence FIG6 . These are the main ingredients in the proof. To obtain the rate we exploit a technical lemma from BID35 . Lemma 3.1 . Let {x t } t≥0 and {x t } t≥0 for k ∈ [K] be defined as in (4) and (7) and let f be L-smooth and µ-strongly convex and η t ≤ 1 4L . Then DISPLAYFORM7 Bounding the variance. From equation FORMULA21 it becomes clear that we should derive an upper bound on E g t −ḡ t 2 . We will relate this to the variance σ 2 . DISPLAYFORM8 Bounding the deviation. Further, we need to bound DISPLAYFORM9 For this we impose a condition on I T and an additional condition on the stepsize η t . Lemma 3.3. If gap(I T ) ≤ H and sequence of decreasing positive stepsizes {η t } t≥0 satisfying η t ≤ 2η t+H for all t ≥ 0, then DISPLAYFORM10 where G 2 is a constant such that DISPLAYFORM11 Optimal Averaging. Similar as in BID14 BID34 BID28 we define a suitable averaging scheme for the iterates {x t } t≥0 to get the optimal convergence rate. In contrast to BID14 ) that use linearly increasing weights, we use quadratically increasing weights, as for instance BID34 BID35 . Lemma 3.4 ((Stich et al., 2018) ). Let {a t } t≥0 , a t ≥ 0, {e t } t≥0 , e t ≥ 0 be sequences satisfying DISPLAYFORM12 DISPLAYFORM13 for w t = (a + t) 2 and S T := T −1 DISPLAYFORM14 Proof. This is a reformulation of Lemma 3.3 in BID35 . We prove convergence of synchronous and asynchronous local SGD and are the first to show that local SGD (for nontrivial values of H) attains theoretically linear speedup on strongly convex functions when parallelized among K workers. We show that local SGD saves up to a factor of O(T 1/2 ) in global communication rounds compared to mini-batch SGD, while still converging at the same rate in terms of total stochastic gradient computations.Deriving more concise convergence rates for local SGD could be an interesting future direction that could deepen our understanding of the scheme. For instance one could aim for a more fine grained analysis in terms of bias and variance terms (similar as e.g. in BID7 BID12 ), relaxing the assumptions (here we relied on the bounded gradient assumption), or investigating the data dependence (e.g. by considering data-depentent measures like e.g. gradient diversity BID42 ). There are also no apparent reasons that would limit the extension of the theory to non-convex objective functions; Lemma 3.3 does neither use the smoothness nor the strong convexity assumption, so this can be applied in the non-convex setting as well. We feel that the positive results shown here can motivate and spark further research on non-convex problems. Indeed, very recent work (Zhou & Cong, 2018; BID44 analyzes local SGD for non-convex optimization problems and shows convergence of SGD to a stationary point, though the restrictions on H are stronger than here.","Mini-batch stochastic gradient descent SGD is state art large scale distributed training. scheme can reach linear speed-up respect number workers is rarely seen practice scheme often suffers large network delays bandwidth limits. overcome communication bottleneck recent works propose reduce communication frequency. algorithm type is is,local SGD runs SGD independently parallel different workers averages sequences while. scheme shows promising results practice eluded thorough theoretical analysis. prove concise convergence rates local SGD convex problems show converges rate mini-batch SGD terms number evaluated gradients is,scheme achieves linear speed-up number workers mini-batch size. number communication rounds can be reduced factor T^ 1/2 -where denotes number total steps -compared mini-batch SGD. also holds asynchronous implementations. Local SGD can also used large scale training deep learning models. results shown aim serving guideline explore theoretical practical aspects local SGD applications. Stochastic Gradient Descent SGD BID29 consists iterations form DISPLAYFORM0 iterates weights x x+1∈R stepsize learning rate η 0 stochastic gradientg ∈R propertyEg ∇f x loss functionf:R →R. scheme can easily parallelized replacingg 1 average stochastic gradients are independently computed parallel separate workers parallel SGD simple scheme has a major drawback:iteration results computations workers have to be shared workers compute next iteratex+1. Communication has been reported major bottleneck many large scale deep learning applications see e.g BID32 BID17. Mini-batch parallel SGD addresses issue increasing compute communication ratio. worker computes mini-batch sizeb≥1 communication. scheme is implemented state-of-the-art distributed deep learning frameworks BID0 BID26 BID31. Recent work BID43 BID10 explores various limitations approach which is in general is reported performance degrades large mini-batch sizes BID13 BID18 BID42.In work follow orthogonal approach why still goal increase compute communication ratio:Instead increasing mini-batch size reduce communication frequency. Rather keeping sequences different machines sync allow evolve locally machine independent average sequences local SGD strategies have been explored widely literature various names.An extreme instance concept is one-shot SGD McDonaldetal. 2009;BID53 where the local sequences are only exchanged local runs have converged. Zhangetal. 2013 show statistical convergence see also BID33 BID9 BID12 analysis restricts algorithm one pass data which is in general enough training error converge. practical are schemes perform frequent averaging parallel sequences e.g BID22 perceptron training iterative parameter mixing see also BID6 BID48 BID4 BID46 training deep neural networks model averaging federated learning BID23.The question how often communication rounds need initiated has eluded concise theoretical answer far. Whilst is practical evidence theory does not even resolve question whether averaging helps when optimizing convex functions. Concretely whether running local SGD K workers is K times faster running single instance SGD one worker. Theorem 2.2 Letf L-smooth µ-strongly convex DISPLAYFORM0 are generated according 4 gap ≤H stepsizesη 4µ+shift parameter max 16κ H DISPLAYFORM1 DISPLAYFORM2 were not especially careful optimize constants lower order terms 5 is state asymptotic result. Corollary 2.3 Letx defined Theorem 2.2 parameter max 16κ H DISPLAYFORM3 last estimate usedEµx 0−x≤ 2G µ-strongly convexf derived Rakhlinetal. 2012 Lemma2 Remark 2.4 Mini-batch local SGD far assumed worker computes single stochastic gradient. mini-batch local SGD worker computes mini-batch sizeb iteration. reduces variance factor b thus Theorem 2.2 gives convergence rate mini-batch local SGD whenσ2 is replaced DISPLAYFORM4 state consequences equation FORMULA17. ease exposition omit dependency L µ σ2 G2 depict dependency local mini-batch size b.Convergence rate. large enough assumingσ 0 first term is dominating 6 local SGD converges rate 1/KTb isis,local SGD achieves linear speedup number workersK mini-batch sizeb. Global synchronization steps. needs holdH/Kb get linear speedup. yields reduction number communication rounds factor/Kb compared parallel mini-batch SGD without hurting convergence rate. Extreme Cases. have not optimized result extreme settings H K L σ. instance do not recover convergence one-shot averaging.e settingH though convergence H lower rate Unknown Time Horizon/Adaptive Communication Frequency BID46 empirically observe frequent communication beginning optimization can help get faster time-to-accuracy see also BID16 Indeed when the number total iterations is not known beforehand e.g depends target accuracy cf. 6 are also Section4 increasing communication frequency seems good strategy keep communication low why still respecting constraintH/Kb T. DISPLAYFORM5. will be useful define DISPLAYFORM6 Observex+1=x −η g Eg =ḡ.Now proof proceeds follows:show virtual sequence x t≥0 almost behaves like mini-batch SGD batch sizeK Lemma 3.1 3.2 ii true iterates xk t≥0 k∈ K do not deviate much virtual sequence FIG6. are the main ingredients proof. obtain rate exploit technical lemma BID35. Lemma 3.1 Let x t≥0 x t≥0 k∈ K defined 4 7 letf L-smooth µ-strongly convex η ≤14L. DISPLAYFORM7 Bounding variance. equation FORMULA21 becomes clear should derive upper bound Eg −ḡ 2. will relate varianceσ2. DISPLAYFORM8 Bounding deviation. need bound DISPLAYFORM9 impose condition additional condition stepsizeη t. Lemma 3.3 If gap ≤H sequence decreasing positive stepsizes η t≥0 satisfyingη ≤2η+H ≥0 DISPLAYFORM10 whereG2 is a constant DISPLAYFORM11 Optimal Averaging. Similar BID14 BID34 BID28 define suitable averaging scheme iterates x t≥0 get optimal convergence rate. contrast BID14 use linearly increasing weights use quadratically increasing weights instance BID34 BID35. Lemma 3.4 Stichetal. 2018 Let t≥0 ≥0 e t≥0 e ≥0 sequences satisfying DISPLAYFORM12 DISPLAYFORM13 w+2 T:−1 DISPLAYFORM14 Proof. is a reformulation Lemma 3.3 BID35. prove convergence synchronous asynchronous local SGD are the first show local SGD nontrivial values H attains theoretically linear speedup strongly convex functions when parallelized among K workers. show local SGD saves factor 1/2 global communication rounds compared mini-batch SGD why still converging rate terms total stochastic gradient computations.Deriving concise convergence rates local SGD could interesting future direction could deepen understanding scheme. instance one could aim fine grained analysis terms bias variance terms similar e.g BID7 BID12 relaxing assumptions relied bounded gradient assumption investigating data dependence e.g considering data-depentent measures like e.g gradient diversity BID42 are also apparent reasons would limit extension theory non-convex objective functions;Lemma 3.3 does neither use smoothness strong convexity assumption can applied non-convex setting well. feel positive results shown can motivate spark research non-convex problems. Indeed recent work Zhou Cong 2018;BID44 analyzes local SGD non-convex optimization problems shows convergence SGD stationary point though restrictions H are stronger here.",2243,1470,773,0.03,1.526,2025/11/05 17:18:55,0.01,1.436,0.6105919003115264,737.785
"Extracting relevant information, causally inferring and predicting the future states with high accuracy is a crucial task for modeling complex systems. The endeavor to address these tasks is made even more challenging when we have to deal with high-dimensional heterogeneous data streams. Such data streams often have higher-order inter-dependencies across spatial and temporal dimensions. We propose to perform a soft-clustering of the data and learn its dynamics to produce a compact dynamical model while still ensuring the original objectives of causal inference and accurate predictions. To efficiently and rigorously process the dynamics of soft-clustering, we advocate for an information theory inspired approach that incorporates stochastic calculus and seeks to determine a trade-off between the predictive accuracy and compactness of the mathematical representation. We cast the model construction as a maximization of the compression of the state variables such that the predictive ability and causal interdependence (relatedness) constraints between the original data streams and the compact model are closely bounded. We provide theoretical guarantees concerning the convergence of the proposed learning algorithm. To further test the proposed framework, we consider a high-dimensional Gaussian case study and describe an iterative scheme for updating the new model parameters. Using numerical experiments, we demonstrate the benefits on compression and prediction accuracy for a class of dynamical systems. Finally, we apply the proposed algorithm to the real-world dataset of multimodal sentiment intensity and show improvements in prediction with reduced dimensions. The use of machine learning for making inference and prediction from the real-world data has shown unprecedented growth. There exist a plethora of approaches for complex system (CS) modeling (e.g., multi-input multi-output state space identification (Stoica & Jansson, 2000) , expectation maximization (EM) BID17 , regularization BID6 , graphical models (Meinshausen & Buhlmann, 2006) , combined regularization and Bayesian learning BID11 BID10 BID3 , kernel-based regularization (Pillonetto & Chiuso, 2015) ). With the increase in the size of data, the complexity of the accurate models also increases, making inference and predictions slower. The major challenges of the upcoming era, hence, are likely to deal with the massive and diverse data sources, and still making quick decisions. Therefore, the compact modeling of time-varying complex systems 1 is a challenging task and appealing for more investigation. The real-world data has complex inter-dependencies across spatial and temporal dimensions. We aim to identify such dependencies and carefully construct a compact representation of the given CS model while still ensuring accurate predictions. We do so by performing a soft-clustering of such inter-dependencies to preserve only the relevant information. For the CS model in the form of a dynamical system, we additionally argue that similar to the data, the most relevant information also gets transformed at each hop in an alternate dynamical system. From a bird's-eye view, we track how the most relevant information propagates across the given dynamical system. We represent this propagation via an alternate dynamical system (compact model) and develop an unsupervised learning technique of such process.The most relevant work in this regard is information bottleneck (IB) principle (Tishby et al., 2000) . For fixed two random variables, it performs a soft-clustering to compress one variable while predicting another, given the joint probability distribution. The IB has been successfully applied to speech recognition (Hecht & Tishby, 2005) , document classification (Slonim & Tishby, 2000) , gene expression BID12 ) and deep learning (Tishby & Zaslavsky, 2015) , etc., and it has shown good performance. In contrast, we aim to learn a dynamics of the soft-clustering across the given dynamical system, and propose a general optimization framework to study the trade-offs between compactness and the resulting accuracies.The problem statement addressed in this work is: Given a dynamical system, we aim to develop a compact model by learning the dynamics of the soft-clustering in an unsupervised manner, or alternate dynamical process, through Information Bottleneck hierarchy (IBH). The main contributions of the present work are as follows: (i) By learning the dynamics of the soft-clustering, we propose an alternate compact dynamical system of the given process, with emphasis on the prediction accuracies. (ii) We formulate a novel optimization setup, compact perception problem, and characterize general solution to the information theoretic problem. (iii) We quantify how most relevant information about future gets transformed at each hop in the alternatively designed dynamical system.A brief mention of the mathematical notations is provided in the next part. In this paper, we have introduced a novel information-theoretic inspired approach to learn the compact dynamics of a time-varying complex system. The trade-off between the predictive accuracy and the compactness of the mathematical representation is formulated as a multi-hop compact perception optimization problem. A key ingredient to solve the aforementioned problem is to exploit variational calculus in order to derive the general solution expressions. Additionally, we have investigated the guaranteed convergence of the proposed iterative algorithm. Moreover, considering a specific class of distributions (Gaussian), we have provided closed-form expressions for the model parameters' update in our algorithm. Interestingly, the proposed compact perception shows improvements in prediction with reduced dimension on challenging real-world problems.The quantification of information flow across a dynamical system can have an enormous impact on understanding and improving the current state-of-the-art in neural networks as realized in (Tishby & Zaslavsky, 2015) . Moreover, modeling with dynamical systems is a standard approach, and by using the proposed framework, we can make a better compact representation of the system. The driving force of a dynamical system can enforce different behaviors of information flow, as realized in defining dynamical entropy by (Sinai, 1959) . Therefore, measuring the information flow can help in estimating/differentiating the actual driving component behind the observed activities. Such concepts are useful in predicting brain imagined tasks from observed electroencephalogram activities.The appendix is arranged as follows: In the Section A, we provide the proof of Theorem 1. In the Section B, we provide the iterative procedure (mentioned as Corollary 1) to minimize the functional in (4). Next, in Section C, we present the detailed proof of the Lemma 1, and finally, in Section D, a detailed proof of Theorem 2 is presented.A PROOF OF THEOREM 1Proof. For the sake of simplicity, a sketch of the proof is given for discrete variables. The Lagrangian associated with the minimization problem is the following DISPLAYFORM0 where α 1 (X k−1 ) and α 2 (B k ) are Lagrange multipliers for the normalization of the distributions p(B k |X k−1 ) and p(B k+1 |B k ), respectively. Taking the derivative of each term of the Lagrangian L with respect to p(B k |X k−1 ), we have DISPLAYFORM1 Setting the derivative of the Lagrangian equal to zero and arranging the terms we obtain the self consistent equation FORMULA7 . Note that all the constant terms in the derivative independent of B k will be captured by the Lagrange multiplier α 1 (X k−1 ). The derivative of the Lagrangian L with respect to p(B k+1 |B k ) involves only the two last terms from the functional F and the term that ensures the normalization condition. Then, we have DISPLAYFORM2 DISPLAYFORM3 Thus, the variational condition is written as follows DISPLAYFORM4 where α 2 (B k ) is the summation of the Lagrange multiplier α 2 (B k ) and the terms independent of B k+1 , and hence the equation FORMULA8 follows.",Extracting relevant information causally inferring predicting future states high accuracy is a crucial task modeling complex systems. endeavor address tasks is made even challenging when we have to deal high-dimensional heterogeneous data streams. data streams often have higher-order inter-dependencies across spatial temporal dimensions. propose perform soft-clustering data learn dynamics produce compact dynamical model still ensuring original objectives causal inference accurate predictions. efficiently rigorously process dynamics soft-clustering advocate information theory inspired approach incorporates stochastic calculus seeks determine trade-off predictive accuracy compactness mathematical representation. cast model construction maximization compression state variables predictive ability causal interdependence relatedness constraints original data streams compact model are closely bounded. provide theoretical guarantees concerning convergence proposed learning algorithm. test proposed framework consider high-dimensional Gaussian case study describe iterative scheme updating new model parameters. Using numerical experiments demonstrate benefits compression prediction accuracy class dynamical systems. Finally apply proposed algorithm real-world dataset multimodal sentiment intensity show improvements prediction reduced dimensions. use machine learning making inference prediction real-world data has shown unprecedented growth. exist plethora approaches complex system CS modeling e.g multi-input multi-output state space identification Stoica Jansson 2000 expectation maximization EM BID17 regularization BID6 graphical models Meinshausen Buhlmann 2006 combined regularization Bayesian learning BID11 BID10 BID3 kernel-based regularization Pillonetto Chiuso 2015 increase size data complexity accurate models also increases making inference predictions slower. major challenges upcoming era hence are likely deal massive diverse data sources still making quick decisions. Therefore compact modeling time-varying complex systems1 is a challenging task appealing investigation. real-world data has complex inter-dependencies across spatial temporal dimensions. aim identify dependencies carefully construct compact representation given CS model still ensuring accurate predictions. do so by performing soft-clustering inter-dependencies preserve relevant information. CS model form dynamical system additionally argue similar data relevant information also gets transformed hop alternate dynamical system. bird's-eye view track how the most how most relevant information propagates across given dynamical system. represent propagation via alternate dynamical system compact model develop unsupervised learning technique process.The relevant work regard is information bottleneck IB principle Tishbyetal. 2000 fixed two random variables performs soft-clustering compress one variable predicting another given joint probability distribution. IB has been successfully applied speech recognition Hecht Tishby 2005 document classification Slonim Tishby 2000 gene expression BID12 deep learning Tishby Zaslavsky 2015 etc. has shown good performance. contrast aim learn dynamics soft-clustering across given dynamical system propose general optimization framework study trade-offs compactness resulting accuracies.The problem statement addressed work is:Given dynamical system aim develop compact model learning dynamics soft-clustering unsupervised manner alternate dynamical process Information Bottleneck hierarchy IBH main contributions present work are as follows:learning dynamics soft-clustering propose alternate compact dynamical system given process emphasis prediction accuracies. ii formulate novel optimization setup compact perception problem characterize general solution information theoretic problem. iii quantify how the most how most relevant information future gets transformed hop alternatively designed dynamical system.A brief mention mathematical notations is provided next part. paper have introduced novel information-theoretic inspired approach learn compact dynamics time-varying complex system. trade-off predictive accuracy compactness mathematical representation is formulated multi-hop compact perception optimization problem. key ingredient solve aforementioned problem is to exploit variational calculus order derive general solution expressions. Additionally have investigated guaranteed convergence proposed iterative algorithm. Moreover considering specific class distributions Gaussian have provided closed-form expressions model parameters' update algorithm. Interestingly proposed compact perception shows improvements prediction reduced dimension challenging real-world problems.The quantification information flow across dynamical system can have an enormous impact understanding improving current state-of-the-art neural networks realized Tishby Zaslavsky 2015 Moreover modeling dynamical systems is a standard approach using proposed framework can make better compact representation system. driving force dynamical system can enforce different behaviors information flow realized defining dynamical entropy Sinai 1959 Therefore measuring information flow can help estimating/differentiating actual driving component behind observed activities. concepts are useful predicting brain imagined tasks observed electroencephalogram activities.The appendix is arranged follows:Section provide proof Theorem1. SectionB provide iterative procedure mentioned Corollary1 minimize functional 4 Next SectionC present detailed proof Lemma1 finally Section detailed proof Theorem2 is presented.A PROOF THEOREM 1Proof. sake simplicity sketch proof is given discrete variables. Lagrangian associated minimization problem is the following DISPLAYFORM0 whereα1 X k−1 α2 Bk are Lagrange multipliers normalization distributionsp B k |X k−1 p Bk+1 |Bk respectively. Taking derivative term LagrangianL respect p B k |X k−1 have DISPLAYFORM1 Setting derivative Lagrangian equal zero arranging terms obtain self consistent equation FORMULA7. Note constant terms derivative independent Bk will be captured Lagrange multiplierα1 X k−1 derivative LagrangianL respect p Bk+1 |Bk involves two last terms functionalF term ensures normalization condition. have DISPLAYFORM2 DISPLAYFORM3 Thus variational condition is written follows DISPLAYFORM4 whereα2 Bk is the summation Lagrange multiplierα2 Bk terms independent Bk+1 hence equation FORMULA8 follows.,1594,1064,530,0.019,1.498,2025/11/05 17:18:55,0.01,1.487,0.5233644859813082,492.222
"We propose the dense RNN, which has the fully connections from each hidden state to multiple preceding hidden states of all layers directly. As the density of the connection increases, the number of paths through which the gradient flows can be increased. It increases the magnitude of gradients, which help to prevent the vanishing gradient problem in time. Larger gradients, however, can also cause exploding gradient problem. To complement the trade-off between two problems, we propose an attention gate, which controls the amounts of gradient flows. We describe the relation between the attention gate and the gradient flows by approximation. The experiment on the language modeling using Penn Treebank corpus shows dense connections with the attention gate improve the model’s performance. In order to analyze sequential data, it is important to choose an appropriate model to represent the data. Recurrent neural network (RNN), as one of the model capturing sequential data, has been applied to many problems such as natural language , machine translation BID0 , speech recognition BID6 . There are two main research issues to improve the RNNs performance: 1) vanishing and exploding gradient problems and 2) regularization.The vanishing and exploding gradient problems occur as the sequential data has long-term dependency BID10 BID18 . One of the solutions is to add gate functions such as the long short-term memory (LSTM) and gated recurrent unit (GRU). The LSTM has additional gate functions and memory cells BID11 . The gate function can prevent the gradient from being vanished during back propagation through time. Gated recurrent unit (GRU) has similar performance with less gate functions BID1 .The part of sequential data whose boundary to distinguish the consecutive other parts, has the hierarchical structures. To handle the hierarchy, the model should capture the multiple timescales. In hierarchical multiple recurrent neural network (HM-RNN, Chung et al. (2016) ), the boundary information is also learned by implementing three operations such as update, copy and flush operator. In clockwork RNN BID14 , the hidden states are divided into multiple sub-modules, which act with different periods to capture multiple timescales. As all previous states within the recurrent depth do not always affect the next state, memory-augmented neural network (MANN, BID7 ) uses the memory to remember previous states and retrieve some of previous states if necessary.The basic way to handle multiple timescales along with preventing the vanishing gradient problem is to increases both of feedforward depth and recurrent depth to capture multiple timescales. Feedforward depth is the longest path from the input layer to the output layer. Recurrent depth is the longest path from arbitrary hidden state at time t to same hidden sate at time t + t . Increasing feedforward depth means stacking multiple recurrent layers deeply. It can capture fast and slow changing components in the sequential data BID19 BID3 BID9 . The low level layer in the stacked RNN captures short-term dependency. As the layer is higher , the aggregated information from lower layer is abstracted. Thus, as the layer is higher, the capacity to model long-term dependency increases. The number of nonlinearities in the stacked RNN, however, is proportional to the number of unfolded time steps regardless of the feedforward depth. Thus, the simple RNN and stacked RNN act identically in terms of long run.Increasing recurrent depth also increases the capability to capture long-term dependency in the data. The hidden state in vanilla RNN has only connection to previous time step's hidden state in the same layer. Adding the connections to multiple previous time steps hidden states can make the shortcut paths, which alleviates the vanishing problem. Nonlinear autoregressive exogenous model (NARX) handles the vanishing gradient problem by adding direct connections from the distant past in the same layer BID15 . Similarly, higher-order RNN (HO-RNN ) has the direct connections to multiple previous states with gating to each time step BID20 . Unlike other recurrent models that use one connection between two consecutive time steps, the recurrent highway network (RHN) adds multiple connections with sharing parameters between transitions in the same layer BID23 .The vanilla RNN has only one path connected with previous hidden states. Thus, it is hard to apply standard dropout technique for regularization as the information is being diluted during training of long-term sequences. By selecting the same dropout mask for feedforward , recurrent connections, respectively, the dropout can apply to the RNN, which is called a variational dropout BID4 . This paper proposes a dense RNN that has both of feedforward and recurrent depths. The stacked RNN increases the complexity by increasing feedforward depth. NARX-RNN and HO-RNN increase the complexity by increasing recurrent depth. The model with the feedforward depth can be combined with the model with the recurrent depth, as the feedforward depth and recurrent depth have an orthogonal relationship. Gated feedback RNN has the fully connection between two consecutive timesteps. As the connection of gated feedback is not overlapped with the model with orthogonal depths, all three features, adding feedforward depth, recurrent depth, and gated feedback, can be modeled jointly . With the three features, we propose the attention gate, which controls the flows from each state so that it enhances the overall performance.The contributions of this paper are summarized: 1) dense RNN that is aggregated model with feedforward depth, recurrent depth and gated feedback function, 2) extension of the variational dropout to the dense RNN. This paper proposed dense RNN, which has fully connections from each hidden state to multiple preceding hidden states of all layers directly. Each previous hidden state has its attention gate that controls the amount of information flows. To evaluate the effect of dense connections, we used Penn Treebank corpus (PTB). The result of dense connection was confirmed by varying the recurrent depth with the attention gate. The dense connections with the attention gate made the model's perplexity less than conventional RNN.",propose dense RNN which has the which has fully connections hidden state multiple preceding hidden states layers directly. density connection increases number paths which the gradient flows can be increased. increases magnitude gradients which help prevent vanishing gradient problem time. Larger gradients however can also cause exploding gradient problem. complement trade-off two problems propose attention gate which controls amounts gradient flows. describe relation attention gate gradient flows approximation. experiment language modeling using Penn Treebank corpus shows dense connections attention gate improve models performance. order analyze sequential data is important choose appropriate model represent data. Recurrent neural network RNN one model capturing sequential data has been applied many problems natural language machine translation BID0 speech recognition BID6. are two main research issues improve RNNs performance:1 vanishing exploding gradient problems 2 regularization.The vanishing exploding gradient problems occur sequential data has long-term dependency BID10 BID18. One solutions is to add gate functions long short-term memory LSTM gated recurrent unit GRU LSTM has additional gate functions memory cells BID11. gate function can prevent gradient vanished back propagation time. Gated recurrent unit GRU has similar performance less gate functions BID1.The part sequential data whose boundary distinguish consecutive parts has the hierarchical structures. handle hierarchy model should capture multiple timescales. hierarchical multiple recurrent neural network HM-RNN Chungetal. 2016 boundary information is also learned implementing three operations update copy flush operator. clockwork RNN BID14 hidden states are divided multiple sub-modules which act different periods capture multiple timescales. previous states within recurrent depth do not always affect next state memory-augmented neural network MANN BID7 uses memory remember previous states retrieve previous states if necessary.The basic way handle multiple timescales along preventing vanishing gradient problem is to increases feedforward depth recurrent depth capture multiple timescales. Feedforward depth is the longest path input layer output layer. Recurrent depth is the longest path arbitrary hidden state time hidden sate time+t. Increasing feedforward depth means stacking multiple recurrent layers deeply. can capture fast slow changing components sequential data BID19 BID3 BID9. low level layer stacked RNN captures short-term dependency. layer is higher aggregated information lower layer is abstracted. Thus layer is higher capacity model long-term dependency increases. number nonlinearities stacked RNN however is proportional number unfolded time steps regardless feedforward depth. Thus simple RNN stacked RNN act identically terms long run.Increasing recurrent depth also increases capability capture long-term dependency data. hidden state vanilla RNN has only connection previous time step's hidden state layer. Adding connections multiple previous time steps hidden states can make shortcut paths which alleviates vanishing problem. Nonlinear autoregressive exogenous model NARX handles vanishing gradient problem adding direct connections distant past layer BID15. Similarly higher-order RNN HO-RNN has the direct connections multiple previous states gating time step BID20. Unlike recurrent models use one connection two consecutive time steps recurrent highway network RHN adds multiple connections sharing parameters transitions layer BID23.The vanilla RNN has only one path connected previous hidden states. Thus is hard apply standard dropout technique regularization information is being diluted training long-term sequences. selecting dropout mask feedforward recurrent connections respectively dropout can apply RNN which is called variational dropout BID4. paper proposes dense RNN has both of feedforward recurrent depths. stacked RNN increases complexity increasing feedforward depth. NARX-RNN HO-RNN increase complexity increasing recurrent depth. model feedforward depth can be combined model recurrent depth feedforward depth recurrent depth have an orthogonal relationship. Gated feedback RNN has the fully connection two consecutive timesteps. connection gated feedback is not overlapped model orthogonal depths three features adding feedforward depth recurrent depth gated feedback can be modeled jointly. three features propose attention gate which controls flows state enhances overall performance.The contributions paper are summarized:1 dense RNN is aggregated model feedforward depth recurrent depth gated feedback function 2 extension variational dropout dense RNN. paper proposed dense RNN which has the which has fully connections hidden state multiple preceding hidden states layers directly. previous hidden state has its attention gate controls amount information flows. evaluate effect dense connections used Penn Treebank corpus PTB result dense connection was confirmed varying recurrent depth attention gate. dense connections attention gate made model's perplexity less conventional RNN.,1204,860,344,0.012,1.4,2025/11/05 17:18:55,0.01,1.511,0.2180685358255447,357.569
"We propose a new algorithm for training generative adversarial networks to jointly learn latent codes for both identities (e.g. individual humans) and observations (e.g. specific photographs). In practice, this means that by fixing the identity portion of latent codes, we can generate diverse images of the same subject, and by fixing the observation portion we can traverse the manifold of subjects while maintaining contingent aspects such as lighting and pose. Our algorithm features a pairwise training scheme in which each sample from the generator consists of two images with a common identity code. Corresponding samples from the real dataset consist of two distinct photographs of the same subject. In order to fool the discriminator, the generator must produce images that are both photorealistic, distinct, and appear to depict the same person. We augment both the DCGAN and BEGAN approaches with Siamese discriminators to accommodate pairwise training. Experiments with human judges and an off-the-shelf face verification system demonstrate our algorithm’s ability to generate convincing, identity-matched photographs. In many domains, a suitable generative process might consist of several stages. To generate a photograph of a product, we might wish to first sample from the space of products, and then from the space of photographs of that product. Given such disentangled representations in a multistage generative process, an online retailer might diversify its catalog, depicting products in a wider variety of settings. A retailer could also flip the process, imagining new products in a fixed setting. Datasets for such domains often contain many labeled identities with fewer observations of each (e.g. a collection of face portraits with thousands of people and ten photos of each). While we may know the identity of the subject in each photograph, we may not know the contingent aspects of the observation (such as lighting, pose and background). This kind of data is ubiquitous; given a set of commonalities, we might want to incorporate this structure into our latent representations.Generative adversarial networks (GANs) learn mappings from latent codes z in some low-dimensional space Z to points in the space of natural data X BID9 . They achieve this power through an adversarial training scheme pitting a generative model G : Z → X against a discriminative model D : X → [0, 1] in a minimax game. While GANs are popular, owing to their ability to generate high-fidelity images, they do not, in their original form, explicitly disentangle the latent factors according to known commonalities.In this paper, we propose Semantically Decomposed GANs (SD-GANs), which encourage a specified portion of the latent space to correspond to a known source of variation.1,2 The technique Figure 1 : Generated samples from SD-BEGAN. Each of the four rows has the same identity code z I and each of the fourteen columns has the same observation code z O .decomposes the latent code Z into one portion Z I corresponding to identity, and the remaining portion Z O corresponding to the other contingent aspects of observations. SD-GANs learn through a pairwise training scheme in which each sample from the real dataset consists of two distinct images with a common identity. Each sample from the generator consists of a pair of images with common z I ∈ Z I but differing z O ∈ Z O . In order to fool the discriminator, the generator must not only produce diverse and photorealistic images, but also images that depict the same identity when z I is fixed. For SD-GANs, we modify the discriminator so that it can determine whether a pair of samples constitutes a match.As a case study, we experiment with a dataset of face photographs, demonstrating that SD-GANs can generate contrasting images of the same subject ( Figure 1 ; interactive web demo in footnote on previous page). The generator learns that certain properties are free to vary across observations but not identity. For example, SD-GANs learn that pose, facial expression, hirsuteness, grayscale vs. color, and lighting can all vary across different photographs of the same individual. On the other hand, the aspects that are more salient for facial verification remain consistent as we vary the observation code z O . We also train SD-GANs on a dataset of product images, containing multiple photographs of each product from various perspectives FIG2 ).We demonstrate that SD-GANs trained on faces generate stylistically-contrasting, identity-matched image pairs that human annotators and a state-of-the-art face verification algorithm recognize as depicting the same subject. On measures of identity coherence and image diversity, SD-GANs perform comparably to a recent conditional GAN method (Odena et al., 2017) ; SD-GANs can also imagine new identities, while conditional GANs are limited to generating existing identities from the training data. Our evaluation demonstrates that SD-GANs can disentangle those factors of variation corresponding to identity from the rest. Moreover, with SD-GANs we can sample never-before-seen identities, a benefit not shared by conditional GANs. In FIG1 , we demonstrate that by varying the observation vector z O , SD-GANs can change the color of clothing, add or remove sunnies, or change facial pose. They can also perturb the lighting, color saturation, and contrast of an image, all while keeping the apparent identity fixed. We note, subjectively, that samples from SD-DCGAN tend to appear less photorealistic than those from SD-BEGAN. Given a generator trained with SD-GAN, we can independently interpolate along the identity and observation manifolds ( FIG4 ).On the shoe dataset, we find that the SD-DCGAN model produces convincing results. As desired, manipulating z I while keeping z O fixed yields distinct shoes in consistent poses FIG2 . The identity code z I appears to capture the broad categories of shoes (sneakers, flip-flops, boots, etc.) . Surprisingly , neither original BEGAN nor SD-BEGAN can produce diverse shoe images (Appendix G).In this paper , we presented SD-GANs, a new algorithm capable of disentangling factors of variation according to known commonalities. We see several promising directions for future work. One logical extension is to disentangle latent factors corresponding to more than one known commonality. We also plan to apply our approach in other domains such as identity-conditioned speech synthesis. We estimate latent vectors for unseen images and demonstrate that the disentangled representations of SD-GANs can be used to depict the estimated identity with different contingent factors. In order to find a latent vectorẑ such that G(ẑ) (pretrained G) is similar to an unseen image x, we can minimize the distance between x and G(ẑ): minẑ ||G(ẑ) − x|| In FIG5 , we depict estimation and linear interpolation across both subspaces for two pairs of images using SD-BEGAN. We also display the corresponding source images being estimated. For both pairs,ẑ I (identity) is consistent in each row andẑ O (observation) is consistent in each column.","propose new algorithm training generative adversarial networks jointly learn latent codes identities e.g individual humans observations e.g specific photographs practice means fixing identity portion latent codes can generate diverse images subject fixing observation portion can traverse manifold subjects maintaining contingent aspects lighting pose. algorithm features pairwise training scheme which each sample generator consists two images common identity code. Corresponding samples real dataset consist two distinct photographs subject. order fool discriminator generator must produce images are both photorealistic distinct appear depict person. augment DCGAN BEGAN approaches Siamese discriminators accommodate pairwise training. Experiments human judges off-the-shelf face verification system demonstrate algorithms ability generate convincing identity-matched photographs. many domains suitable generative process might consist several stages. generate photograph product might wish first sample space products space photographs product. Given disentangled representations multistage generative process online retailer might diversify catalog depicting products wider variety settings. retailer could also flip process imagining new products fixed setting. Datasets domains often contain many labeled identities fewer observations e.g collection face portraits thousands people ten photos may know identity subject photograph may know contingent aspects observation lighting pose background kind data is ubiquitous;given set commonalities might want incorporate structure latent representations.Generative adversarial networks GANs learn mappings latent codesz low-dimensional spaceZ points space natural data X BID9. achieve power adversarial training scheme pitting generative modelG:Z→X discriminative model D:X→ 0 1 minimax game. GANs are popular owing ability generate high-fidelity images do not do not original form explicitly disentangle latent factors according known commonalities.In paper propose Semantically Decomposed GANs SD-GANs which encourage specified portion latent space correspond known source variation.1,2 technique Figure1:Generated samples SD-BEGAN four rows has the same identity codez fourteen columns has the same observation codez.decomposes latent codeZ one portionZ corresponding identity remaining portionZ corresponding contingent aspects observations. SD-GANs learn pairwise training scheme which each sample real dataset consists two distinct images common identity. sample generator consists pair images commonz ∈Z differingz ∈Z O. order fool discriminator generator must produce diverse photorealistic images also images depict identity whenz is fixed. SD-GANs modify discriminator can determine whether pair samples constitutes match.As case study experiment dataset face photographs demonstrating SD-GANs can generate contrasting images subject Figure1;interactive web demo footnote previous page generator learns certain properties are free vary across observations identity. example SD-GANs learn pose facial expression hirsuteness grayscalevs. color lighting can all vary across different photographs individual. hand aspects are more salient facial verification remain consistent vary observation codez O. also train SD-GANs dataset product images containing multiple photographs product various perspectives FIG2.We demonstrate SD-GANs trained faces generate stylistically-contrasting identity-matched image pairs human annotators state-of-the-art face verification algorithm recognize depicting subject. measures identity coherence image diversity SD-GANs perform comparably recent conditional GAN method Odenaetal. 2017 SD-GANs can also imagine new identities conditional GANs are limited generating existing identities training data. evaluation demonstrates SD-GANs can disentangle factors variation corresponding identity rest. Moreover SD-GANs can sample never-before-seen identities benefit shared conditional GANs. FIG1 demonstrate varying observation vectorz SD-GANs can change color clothing add remove sunnies change facial pose. can also perturb lighting color saturation contrast image keeping apparent identity fixed. note subjectively samples SD-DCGAN tend appear less photorealistic SD-BEGAN Given generator trained SD-GAN can independently interpolate along identity observation manifolds FIG4.On shoe dataset find SD-DCGAN model produces convincing results. desired manipulatingz keepingz fixed yields distinct shoes consistent poses FIG2. identity codez appears capture broad categories shoes sneakers flip-flops boots etc. Surprisingly neither original BEGAN SD-BEGAN can produce diverse shoe images AppendixG.In paper presented SD-GANs new algorithm capable disentangling factors variation according known commonalities. see several promising directions future work. One logical extension is to disentangle latent factors corresponding one known commonality. also plan apply approach domains identity-conditioned speech synthesis. estimate latent vectors unseen images demonstrate disentangled representations SD-GANs can be used depict estimated identity different contingent factors. order find latent vectorẑ G ẑ pretrainedG is similar unseen imagex can minimize distance x G ẑ minẑ ||G ẑ − x|| FIG5 depict estimation linear interpolation across subspaces two pairs images using SD-BEGAN also display corresponding source images estimated. pairs ẑ identity is consistent row andẑ observation is consistent column.",1447,948,499,0.014,1.526,2025/11/05 17:18:55,0.01,1.367,0.6105919003115264,448.009
"The goal of unpaired cross-domain translation is to learn useful mappings between two domains, given unpaired sets of datapoints from these domains. While this formulation is highly underconstrained, recent work has shown that it is possible to learn mappings useful for downstream tasks by encouraging approximate cycle consistency in the mappings between the two domains [Zhu et al., 2017]. In this work, we propose AlignFlow, a framework for unpaired cross-domain translation that ensures exact cycle consistency in the learned mappings. Our framework uses a normalizing flow model to specify a single invertible mapping between the two domains. In contrast to prior works in cycle-consistent translations, we can learn AlignFlow via adversarial training, maximum likelihood estimation, or a hybrid of the two methods. Theoretically, we derive consistency results for AlignFlow which guarantee recovery of desirable mappings under suitable assumptions. Empirically, AlignFlow demonstrates significant improvements over relevant baselines on image-to-image translation and unsupervised domain adaptation tasks on benchmark datasets. Given data from two domains, cross-domain translation refers to the task of learning a mapping from one domain to another, such as translating text across two languages or image colorization. This ability to learn a meaningful alignment between two domains has a broad range of applications across machine learning, including relational learning BID1 , domain adaptation BID2 BID4 , image and video translation for computer vision BID6 , and machine translation for natural language processing BID7 .Broadly , there are two learning paradigms for cross-domain translation: paired and unpaired. In paired cross-domain translation, we assume access to pairs of datapoints across the two domains, e.g., black and white images and their respective colorizations. However, paired data can be expensive to obtain or may not even exist, as in neural style transfer BID8 where the goal is to translate across the works of two artists that typically do not exhibit a direct correspondence.Unpaired cross-domain translation tackles this regime where paired data is not available and learns an alignment between two domains given only unpaired sets of datapoints from the domains. Formally , we seek to learn a joint distribution over two domains, say A and B, given samples only from the marginal distributions over A and B. CycleGAN BID0 , a highly successful approach to this problem, learns a pair of conditional generative models, say G A→B and G B→A , to match the marginal distributions over A and B via an adversarial objective BID9 . The marginal matching constraints alone are insufficient to learn the desired joint distribution, both in theory and practice. To further constrain the problem, an additional desideratum is imposed in the form of cycle-consistency. That is, given any datapoint A = a, the cycle-consistency term in the learning objective prefers mappings G A→B and G B→A such that G B→A (G A→B (a)) ≈ a. Symmetrically, cycle-consistency in the reverse direction implies G A→B (G B→A (b)) ≈ b for all datapoints B = b. Intuitively , this encourages the learning of approximately bijective mappings.While empirically effective, the CycleGAN objective only imposes a soft cycle-consistency penalty and provides no guarantee that G A→B and G B→A are true inverses of each other. A natural question, then, is whether the cycle-consistency objective can be replaced with a single, invertible model G A→B . Drawing inspiration from the literature on invertible generative models (Rezende and BID10 BID11 BID13 , we propose AlignFlow, a learning framework for cross-domain translations which uses normalizing flow models to represent the mappings. In AlignFlow, we compose a pair of invertible flow models G Z→A and G Z→B , to represent the mapping G A→B = G Z→B • G −1 Z→A . Here, Z is a shared latent space between the two domains. Since composition of invertible mappings preserves invertibility , the mapping G A→B is invertible and the reverse mapping from B → A is simply given as G B→A = G −1 A→B . Hence, AlignFlow guarantees exact cycle-consistency by design and simplifies the standard CycleGAN learning objective by learning a single, invertible mapping.Furthermore, AlignFlow provides flexibility in specifying the training objective. In addition to adversarial training, we can also specify a prior distribution over the latent variables Z and train the two component models G Z→B and G Z→A via maximum likelihood estimation (MLE). MLE is statistically efficient, exhibits stable training dynamics , and can have a regularizing effect when used in conjunction with adversarial training of invertible generative models BID14 . In this work, we presented AlignFlow, a learning framework for cross-domain translations based on normalizing flow models. The use of normalizing flow models is an attractive choice for several reasons we highlight: it guarantees exact cycle-consistency via a single cross-domain mapping, learns a shared latent space across two domains, and permits a flexible training objective which is a hybrid of terms corresponding to adversarial training and exact maximum likelihood estimation. Theoretically, we derived conditions under which the AlignFlow model learns marginals that are consistent with the underlying data distributions. Finally, our empirical evaluation demonstrated significant gains on the tasks of image-to-image translation and unsupervised domain adaptation, along with an increase in inference capabilities due to the use of invertible models, e.g., paired interpolations in the latent space for two domains.In the future, we would like to consider extensions of AlignFlow to learning stochastic, multimodal mappings BID37 and translations across more than two domains BID38 . In spite of strong empirical results in domain alignments in the last few years, a well-established theory explaining such results is lacking. With a handle on model likelihoods and exact invertibility for inference, we are optimistic that AlignFlow can potentially aid the development of such a theory and characterize structure that leads to provably identifiable recovery of cross-domain mappings. Exploring the latent space of AlignFlow from a manifold learning perspective to domain alignment BID44 is also an interesting direction for future research.","goal unpaired cross-domain translation is to learn useful mappings two domains given unpaired sets datapoints domains. formulation is highly underconstrained recent work has shown is possible learn mappings useful downstream tasks encouraging approximate cycle consistency mappings two domains Zhuetal. 2017 work propose AlignFlow framework unpaired cross-domain translation ensures exact cycle consistency learned mappings. framework uses normalizing flow model specify single invertible mapping two domains. contrast prior works cycle-consistent translations can learn AlignFlow via adversarial training maximum likelihood estimation hybrid two methods. Theoretically derive consistency results AlignFlow which guarantee recovery desirable mappings suitable assumptions. Empirically AlignFlow demonstrates significant improvements relevant baselines image-to-image translation unsupervised domain adaptation tasks benchmark datasets. Given data two domains cross-domain translation refers task learning mapping one domain another translating text across two languages image colorization. ability learn meaningful alignment two domains has a broad range applications across machine learning including relational learning BID1 domain adaptation BID2 BID4 image video translation computer vision BID6 machine translation natural language processing BID7.Broadly are two learning paradigms cross-domain translation:paired unpaired. paired cross-domain translation assume access pairs datapoints across two domains e.g black white images respective colorizations. However paired data can be expensive obtain may even exist neural style transfer BID8 where the goal is to translate across works two artists typically do not exhibit direct correspondence.Unpaired cross-domain translation tackles regime where paired data is not available learns alignment two domains given unpaired sets datapoints domains. Formally seek learn joint distribution two domains say B given samples marginal distributions B. CycleGAN BID0 highly successful approach problem learns pair conditional generative models say G A→B G B→A match marginal distributions B via adversarial objective BID9. marginal matching constraints alone are insufficient learn desired joint distribution theory practice. constrain problem additional desideratum is imposed form cycle-consistency is,given datapoint cycle-consistency term learning objective prefers mappings G A→B G B→A G B→A G A→B ≈ a. Symmetrically cycle-consistency reverse direction impliesG A→B G B→A b ≈b datapointsB b. Intuitively encourages learning approximately bijective mappings.While empirically effective CycleGAN objective imposes soft cycle-consistency penalty provides guarantee G A→B G B→A are true inverses other. natural question is whether cycle-consistency objective can be replaced single invertible model G A→B Drawing inspiration literature invertible generative models Rezende BID10 BID11 BID13 propose AlignFlow learning framework cross-domain translations which uses normalizing flow models represent mappings. AlignFlow compose pair invertible flow modelsG Z→A G Z→B represent mapping G A→B G Z→B•G −1 Z→A Z is a shared latent space two domains. Since composition invertible mappings preserves invertibility mapping G A→B is invertible reverse mapping B→ is simply given G B→A G −1 A→B Hence AlignFlow guarantees exact cycle-consistency design simplifies standard CycleGAN learning objective learning single invertible mapping.Furthermore AlignFlow provides flexibility specifying training objective. addition adversarial training can also specify prior distribution latent variablesZ train two component modelsG Z→B G Z→A via maximum likelihood estimation MLE MLE is statistically efficient exhibits stable training dynamics can have regularizing effect when used conjunction adversarial training invertible generative models BID14. work presented AlignFlow learning framework cross-domain translations based normalizing flow models. use normalizing flow models is an attractive choice several reasons highlight:guarantees exact cycle-consistency via single cross-domain mapping learns shared latent space across two domains permits flexible training objective which is a hybrid terms corresponding adversarial training exact maximum likelihood estimation. Theoretically derived conditions which the AlignFlow model learns marginals are consistent underlying data distributions. Finally empirical evaluation demonstrated significant gains tasks image-to-image translation unsupervised domain adaptation along increase inference capabilities due use invertible models e.g paired interpolations latent space two domains.In future would like consider extensions AlignFlow learning stochastic multimodal mappings BID37 translations across two domains BID38. spite strong empirical results domain alignments last years well-established theory explaining results is lacking. handle model likelihoods exact invertibility inference are optimistic AlignFlow can potentially aid development theory characterize structure leads provably identifiable recovery cross-domain mappings. Exploring latent space AlignFlow manifold learning perspective domain alignment BID44 is also interesting direction future research.",1257,892,365,0.013,1.409,2025/11/05 17:18:55,0.01,1.417,0.2461059190031151,353.79
"Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, that maps the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, it is commonly formulated as a constraint satisfaction problem, where input-output examples are expressed constraints, and solved with a constraint solver. A key challenge of this formulation is that of scalability: While constraint solvers work well with few well-chosen examples, constraining the entire set of example constitutes a significant overhead in both time and memory. In this paper we address this challenge by constructing a representative subset of examples that is both small and is able to constrain the solver sufficiently. We build the subset one example at a time, using a trained discriminator to predict the probability of unchosen input-output examples conditioned on the chosen input-output examples, adding the least probable example to the subset. Experiment on a diagram drawing domain shows our approach produces subset of examples that are small and representative for the constraint solver. Program synthesis (or synthesis for short) is a special class of regression problems where rather than minimizing the error on an example dataset, one seeks an exact fit of the examples in the form of a program. Applications include synthesizing database relations BID19 ), inferring excelformulas BID11 ), and compilation BID16 ). In these domains, the synthesizer was able to come up with complex programs consisting of branches, loops, and other programming constructs. Recent efforts BID5 ; BID19 ) show an interest in applying the synthesis technique to large sets of examples, but scalability remains an open problem. In this paper we present a technique to select from a large dataset of examples a representative subset that is sufficient to synthesize a correct program, yet small enough to solve efficiently.There are two key ingredients to a synthesis problem: a domain specific language (DSL for short) and a specification. The DSL defines a space of candidate programs which serve as the model class. The specification is commonly expressed as a set of example input-output pairs which the candidate program needs to fit exactly. The DSL restricts the structure of the programs in such a way that it is difficult to fit the input-output examples in an ad-hoc fashion: This structure aids generalization to an unseen input despite ""over"" fitting the input-output examples during training.Given the precise and combinatorial nature of a synthesis problem, gradient-descent based approaches perform poorly and an explicit search over the solution space is required ). For this reason, synthesis is commonly casted as a constraint satisfaction problem (CSP) (Solar-Lezama (2013) ; BID12 ). In such a setting, the DSL and its execution can be thought of as a parametrized function F , which is encoded as a logical formula. Its free variables s ∈ S correspond to different parametrization within the DSL, and the input-output examples D are expressed as constraints which the instantiated program needs to satisfy, namely, producing the correct output on a given input.",Program synthesis is a class regression problems where one seeks solution form source-code program maps inputs corresponding outputs exactly. Due precise combinatorial nature is commonly formulated constraint satisfaction problem where input-output examples are expressed constraints solved constraint solver. key challenge formulation is that of scalability:constraint solvers work well well-chosen examples constraining entire set example constitutes significant overhead time memory. paper address challenge constructing representative subset examples is both are small is able constrain solver sufficiently. build subset one example time using trained discriminator predict probability unchosen input-output examples conditioned chosen input-output examples adding least probable example subset. Experiment diagram drawing domain shows approach produces subset examples is both are small representative constraint solver. Program synthesis synthesis short is a special class regression problems where rather minimizing error example dataset one seeks exact fit examples form program. Applications include synthesizing database relations BID19 inferring excelformulas BID11 compilation BID16 domains synthesizer was able come complex programs consisting branches loops programming constructs. Recent efforts BID5;BID19 show interest applying synthesis technique large sets examples scalability remains open problem. paper present technique select large dataset examples representative subset is sufficient synthesize correct program yet small enough solve efficiently.There are two key ingredients synthesis problem:domain specific language DSL short specification. DSL defines space candidate programs which serve model class. specification is commonly expressed set example input-output pairs which the candidate program needs fit exactly. DSL restricts structure programs way is difficult fit input-output examples ad-hoc fashion:structure aids generalization unseen input despite fitting input-output examples training.Given precise combinatorial nature synthesis problem gradient-descent based approaches perform poorly explicit search solution space is required reason synthesis is commonly casted constraint satisfaction problem CSP Solar-Lezama 2013 BID12 setting DSL execution can be thought parametrized functionF which is encoded logical formula. free variables ∈ correspond different parametrization within DSL where input-output examples are expressed constraints which the instantiated program needs satisfy namely producing correct output given input.,598,386,212,0.006,1.549,2025/11/05 17:18:55,0.0,1.391,0.6822429906542052,233.226
"Humans possess an ability to abstractly reason about objects and their interactions, an ability not shared with state-of-the-art deep learning models. Relational networks, introduced by Santoro et al. (2017), add the capacity for relational reasoning to deep neural networks, but are limited in the complexity of the reasoning tasks they can address. We introduce recurrent relational networks which increase the suite of solvable tasks to those that require an order of magnitude more steps of relational reasoning. We use recurrent relational networks to solve Sudoku puzzles and achieve state-of-the-art results by solving 96.6% of the hardest Sudoku puzzles, where relational networks fail to solve any. We also apply our model to the BaBi textual QA dataset solving 19/20 tasks which is competitive with state-of-the-art sparse differentiable neural computers. The recurrent relational network is a general purpose module that can augment any neural network model with the capacity to do many-step relational reasoning.",Humans possess ability abstractly reason objects interactions ability shared state-of-the-art deep learning models. Relational networks introduced Santoroetal. 2017 add capacity relational reasoning deep neural networks are limited complexity reasoning tasks can address. introduce recurrent relational networks which increase suite solvable tasks require order magnitude steps relational reasoning. use recurrent relational networks solve Sudoku puzzles achieve state-of-the-art results solving 96.6 hardest Sudoku puzzles where relational networks fail solve any. also apply model BaBi textual QA dataset solving19/20 tasks which is competitive state-of-the-art sparse differentiable neural computers. recurrent relational network is a general purpose module can augment neural network model capacity do many-step relational reasoning.,190,136,54,0.002,1.397,2025/11/05 17:18:55,0.0,1.25,0.2087227414330216,75.714
"Empirical risk minimization (ERM), with proper loss function and regularization, is the common practice of supervised classification. In this paper, we study training arbitrary (from linear to deep) binary classifier from only unlabeled (U) data by ERM. We prove that it is impossible to estimate the risk of an arbitrary binary classifier in an unbiased manner given a single set of U data, but it becomes possible given two sets of U data with different class priors. These two facts answer a fundamental question---what the minimal supervision is for training any binary classifier from only U data. Following these findings, we propose an ERM-based learning method from two sets of U data, and then prove it is consistent. Experiments demonstrate the proposed method could train deep models and outperform state-of-the-art methods for learning from two sets of U data. With some properly chosen loss function (e.g., BID2 BID50 BID39 and regularization (e.g., BID51 BID46 , empirical risk minimization (ERM) is the common practice of supervised classification BID54 . Actually, ERM is used in not only supervised learning but also weakly-supervised learning. For example, in semi-supervised learning (Chapelle et al., 2006) , we have very limited labeled (L) data and a lot of unlabeled (U) data, where L data share the same form with supervised learning. Thus, it is easy to estimate the risk from only L data in order to carry out ERM, and U data are needed exclusively in regularization (including but not limited to BID16 BID3 BID25 BID29 BID20 BID49 BID24 Kamnitsas et al., 2018) .Nevertheless , L data may differ from supervised learning in not only the amount but also the form. For instance , in positive-unlabeled learning BID12 BID55 ), all L data are from the positive class, and due to the lack of L data from the negative class it becomes impossible to estimate the risk from only L data. To this end , a two-step approach to ERM has been considered (du BID9 BID34 BID18 . Firstly, the risk is rewritten into an equivalent expression, such that it just involves the same distributions from which L and U data are sampled-this step leads to certain risk estimators. Secondly, the risk is estimated from both L and U data, and the resulted empirical training risk is minimized (e.g. by BID41 Kingma & Ba, 2015) . In this two-step approach, U data are needed absolutely in ERM itself. This indicates that risk rewrite (i.e., the technique of making the risk estimable from observable data via an equivalent expression) enables ERM in positive-unlabeled learning and is the key of success.One step further from positive-unlabeled learning is learning from only U data without any L data. This is significantly harder than previous learning problems (cf. FIG1 ). However, we would still like to train arbitrary binary classifier, in particular, deep networks BID15 . Note that for this purpose clustering is suboptimal for two major reasons. First, successful translation of clusters into meaningful classes completely relies on the critical assumption that one cluster exactly In the left panel, (a) and (b) show positive (P) and negative (N) components of the Gaussian mixture; (c) and (d) show two distributions (with class priors 0.9 and 0.4) where U training data are drawn (marked as black points). The right panel shows the test distribution (with class prior 0.3) and data (marked as blue for P and red for N), as well as four learned classifiers. In the legend, ""CCN"" refers to BID31 , ""UU-biased "" means supervised learning taking larger-/smaller-class-prior U data as P/N data, ""UU"" is the proposed method, and ""Oracle"" means supervised learning from the same amount of L data. See Appendix B for more information. We can see that UU is almost identical to Oracle and much better than the other two methods. corresponds to one class, and hence even perfect clustering might still result in poor classification. Second, clustering must introduce additional geometric or information-theoretic assumptions upon which the learning objectives of clustering are built (e.g., BID57 BID14 . As a consequence, we prefer ERM to clustering and then no more assumption is required.The difficulty is how to estimate the risk from only U data, and our solution is again ERM-enabling risk rewrite in the aforementioned two-step approach. The first step should lead to an unbiased risk estimator that will be used in the second step. Subsequently, we can evaluate the empirical training and/or validation risk by plugging only U training/validation data into the risk estimator. Thus, this two-step ERM needs no L validation data for hyperparameter tuning, which is a huge advantage in training deep models nowadays. Note that given only U data, by no means could we learn the class priors BID27 , so that we assume all necessary class priors are also given. This is the unique type of supervision we will leverage throughout this paper, and hence this learning problem still belongs to weakly-supervised learning rather than unsupervised learning.In this paper, we raise a fundamental question in weakly-supervised learning-how many sets of U data with different class priors are necessary for rewriting the risk? Our answer has two aspects:• Risk rewrite is impossible given a single set of U data (see Theorem 2 in Sec. 3);• Risk rewrite becomes possible given two sets of U data (see Theorem 4 in Sec. 4).This suggests that three class priors 1 are all you need to train deep models from only U data, while any two 2 should not be enough. The impossibility is a proof by contradiction, and the possibility is a proof by construction, following which we explicitly design an unbiased risk estimator. Therefore, with the help of this risk estimator, we propose an ERM-based learning method from two sets of U data. Thanks to the unbiasedness of our risk estimator, we derive an estimation error bound which certainly guarantees the consistency of learning BID30 BID44 .3 Experiments demonstrate that the proposed method could train multilayer perceptron, AllConvNet BID45 and ResNet (He et al., 2016) from two sets of U data; it could outperform state-of-the-art methods for learning from two sets of U data. See FIG1 for how the proposed method works on a Gaussian mixture of two components .As mentioned earlier, learning from two sets of U data is already studied in du BID8 and BID27 . Both of them adopt (4) as the performance measure. In the former paper, g is learned by estimating sign(p tr (x) − p tr (x)). In the latter paper, g is learned by taking noisy L data from p tr (x) and p tr (x) as clean L data from p p (x) and p n (x), and then its threshold is moved to the correct value by post-processing. In summary, instead of ERM, they evidence the possibility of empirical balanced risk minimization , and no impossibility is proven.Our findings are compatible with learning from label proportions BID36 BID58 . BID36 proves that the minimal number of U sets is equal to the number of classes. However, their finding only holds for the linear model, the logistic loss, and their proposed method based on mean operators. On the other hand, BID58 is not ERM-based; it is based on discriminative clustering together with expectation regularization BID25 .At first glance, our data generation process, using the names from BID27 , looks quite similar to class-conditional noise (CCN, BID0 in learning with noisy labels (cf. BID31 . 4 In fact, BID27 makes use of mutually contaminated distributions (MCD, BID43 that is more general than CCN . Denote byỹ andp(·) the corrupted label and distributions. Then, CCN and MCD are defined by DISPLAYFORM0 where both of T CCN and T MCD are 2-by-2 matrices but T CCN is column normalized and T MCD is row normalized. It has been proven in BID27 that CCN is a strict special case of MCD. To DISPLAYFORM1 Due to this covariate shift, CCN methods do not fit MCD problem setting, though MCD methods fit CCN problem setting. To the best of our knowledge, the proposed method is the first MCD method based on ERM.3 LEARNING FROM ONE SET OF U DATA From now on, we prove that knowing π p and θ is insufficient for rewriting R(g). We focused on training arbitrary binary classifier, ranging from linear to deep models, from only U data by ERM. We proved that risk rewrite as the core of ERM is impossible given a single set of U data, but it becomes possible given two sets of U data with different class priors, after we assumed that all necessary class priors are also given. This possibility led to an unbiased risk estimator, and with the help of this risk estimator we proposed UU learning, the first ERM-based learning method from two sets of U data. Experiments demonstrated that UU learning could successfully train fully connected, all convolutional and residual networks, and it compared favorably with state-of-the-art methods for learning from two sets of U data.",Empirical risk minimization ERM proper loss function regularization is the common practice supervised classification. paper study training arbitrary linear deep binary classifier unlabeled U data ERM. prove is impossible estimate risk arbitrary binary classifier unbiased manner given single set U data becomes possible given two sets U data different class priors. two facts answer fundamental question -what minimal supervision is for training binary classifier U data. Following findings propose ERM-based learning method two sets U data prove is consistent. Experiments demonstrate proposed method could train deep models outperform state-of-the-art methods learning two sets U data. properly chosen loss function e.g BID2 BID50 BID39 regularization e.g BID51 BID46 empirical risk minimization ERM is the common practice supervised classification BID54. Actually ERM is used supervised learning also weakly-supervised learning. example semi-supervised learning Chapelleetal. 2006 have limited labeled L data lot unlabeled U data where L data share form supervised learning. Thus is easy estimate risk which L data order carry ERM U data are needed exclusively regularization including limited BID16 BID3 BID25 BID29 BID20 BID49 BID24 Kamnitsas etal. 2018.Nevertheless where L data may differ supervised learning amount also form. instance positive-unlabeled learning BID12 BID55 L data are from the positive class due lack L data negative class becomes impossible estimate risk which L data. end two-step approach ERM has been considered du BID9 BID34 BID18. Firstly risk is rewritten equivalent expression involves distributions whichL U data are sampled-this step leads certain risk estimators. Secondly risk is estimated whichL U data resulted empirical training risk is minimized e.g BID41 Kingma Ba 2015 two-step approach U data are needed absolutely ERM itself. indicates risk rewrite.e technique making risk estimable observable data via equivalent expression enables ERM positive-unlabeled learning is the key success.One step positive-unlabeled learning is learning U data without L data. is significantly harder previous learning problems cf. FIG1 However would still like train arbitrary binary classifier particular deep networks BID15. Note purpose clustering is suboptimal two major reasons. First successful translation clusters meaningful classes completely relies critical assumption one cluster exactly left panel b show positive P negative N components Gaussian mixture;c show two distributions class priors 0.9 0.4 where U training data are drawn marked black points right panel shows test distribution class prior 0.3 data marked blue P red N well four learned classifiers. legend CCN refers BID31 UU-biased means supervised learning taking larger-/smaller-class-prior U data P/N data UU is the proposed method Oracle means supervised learning amount L data. See AppendixB information. can see UU is almost identical Oracle much better two methods. corresponds one class hence even perfect clustering might still result poor classification. Second clustering must introduce additional geometric information-theoretic assumptions upon which the learning objectives clustering are built e.g BID57 BID14. consequence prefer ERM clustering assumption is required.The difficulty is how to estimate risk U data solution is again ERM-enabling risk rewrite aforementioned two-step approach. first step should lead unbiased risk estimator will be used second step. Subsequently can evaluate empirical training/validation risk plugging U training/validation data risk estimator. Thus two-step ERM needs L validation data hyperparameter tuning which is a huge advantage training deep models nowadays. Note given U data means could learn class priors BID27 assume necessary class priors are also given. is the unique type supervision will leverage throughout paper hence learning problem still belongs weakly-supervised learning rather unsupervised learning.In paper raise fundamental question weakly-supervised learning-how many sets U data different class priors are necessary rewriting risk? answer has two aspects:• Risk rewrite is impossible given single set U data see Theorem2 Sec. 3 • Risk rewrite becomes possible given two sets U data see Theorem4 Sec. 4.This suggests three class priors1 are all you need train deep models U data two2 should not be enough. impossibility is a proof contradiction possibility is a proof construction following which we explicitly design unbiased risk estimator. Therefore help risk estimator propose ERM-based learning method two sets U data. Thanks unbiasedness risk estimator derive estimation error bound which certainly guarantees consistency learning BID30 BID44.3 Experiments demonstrate proposed method could train multilayer perceptron AllConvNet BID45 ResNet etal. 2016 two sets U data;could outperform state-of-the-art methods learning two sets U data. See FIG1 how the proposed method works Gaussian mixture two components.As mentioned earlier learning two sets U data is already studied du BID8 BID27. adopt 4 performance measure. former paper g is learned estimating sign ptr x −ptr x latter paper g is learned taking noisy L data ptr x ptr x clean L data pp x pn x threshold is moved correct value post-processing summary instead ERM evidence possibility empirical balanced risk minimization impossibility is proven.Our findings are compatible learning label proportions BID36 BID58. BID36 proves minimal number U sets is equal number classes. However finding holds linear model logistic loss proposed method based mean operators. hand BID58 is not ERM-based ERM-based is based discriminative clustering together expectation regularization BID25.At first glance data generation process using names BID27 looks quite similar class-conditional noise CCN BID0 learning noisy labels cf. BID31. 4 fact BID27 makes use mutually contaminated distributions MCD BID43 is more general CCN. Denote byỹ andp · corrupted label distributions. CCN MCD are defined DISPLAYFORM0 where both of T CCN MCD are 2-by-2 matrices CCN is column normalized MCD is row normalized. has been proven BID27 CCN is a strict special case MCD. DISPLAYFORM1 Due covariate shift CCN methods do not fit MCD problem setting though MCD methods fit CCN problem setting. best knowledge proposed method is the first MCD method based ERM.3 LEARNING ONE SET U DATA prove knowingπp θ is insufficient rewritingR g focused training arbitrary binary classifier ranging linear deep models U data ERM. proved risk rewrite core ERM is impossible given single set U data becomes possible given two sets U data different class priors assumed necessary class priors are also given. possibility led unbiased risk estimator help risk estimator proposed UU learning first ERM-based learning method two sets U data. Experiments demonstrated UU learning could successfully train fully connected convolutional residual networks compared favorably state-of-the-art methods learning two sets U data.,1942,1325,617,0.027,1.466,2025/11/05 17:18:55,0.01,1.5,0.4236760124610589,686.475
"Deep Neural Networks (DNNs) excel on many complex perceptual tasks but it has proven notoriously difficult to understand how they reach their decisions. We here introduce a high-performance DNN architecture on ImageNet whose decisions are considerably easier to explain. Our model, a simple variant of the ResNet-50 architecture called BagNet, classifies an image based on the occurrences of small local image features without taking into account their spatial ordering. This strategy is closely related to the bag-of-feature (BoF) models popular before the onset of deep learning and reaches a surprisingly high accuracy on ImageNet (87.6% top-5 for 32 x 32 px features and Alexnet performance for 16 x16 px features). The constraint on local features makes it straight-forward to analyse how exactly each part of the image influences the classification. Furthermore, the BagNets behave similar to state-of-the art deep neural networks such as VGG-16, ResNet-152 or DenseNet-169 in terms of feature sensitivity, error distribution and interactions between image parts. This suggests that the improvements of DNNs over previous bag-of-feature classifiers in the last few years is mostly achieved by better fine-tuning rather than by qualitatively different decision strategies. A big obstacle in understanding the decision-making of DNNs is due to the complex dependencies between input and hidden activations: for one, the effect of any part of the input on a hidden activation depends on the state of many other parts of the input. Likewise, the role of a hidden unit on downstream representations depends on the activity of many other units. This dependency makes it extremely difficult to understand how DNNs reach their decisions.To circumvent this problem we here formulate a new DNN architecture that is easier to interpret by design. Our architecture is inspired by bag-of-feature (BoF) models which -alongside extensions such as VLAD encoding or Fisher Vectors -have been the most successful approaches to large-scale object recognition before the advent of deep learning (up to 75% top-5 on ImageNet) and classify images based on the counts, but not the spatial relationships, of a set of local image features. This structure makes the decisions of BoF models particularly easy to explain.To be concise, throughout this manuscript the concept of interpretability refers to the way in which evidence from small image patches is integrated to reach an image-level decision. While basic BoF models perform just a simple and transparent spatial aggregate of the patch-wise evidences, DNNs non-linearly integrate information across the whole image.In this paper we show that it is possible to combine the performance and flexibility of DNNs with the interpretability of BoF models, and that the resulting model family (called BagNets) is able to reach high accuracy on ImageNet even if limited to fairly small image patches. Given the simplicity of BoF models we imagine many use cases for which it can be desirable to trade a bit of accuracy for better interpretability, just as this is common e.g. for linear function approximation. This includes diagnosing failure cases (e.g. adversarial examples) or non-iid. settings (e.g. domain transfer), benchmarking diagnostic tools (e.g. attribution methods) or serving as interpretable parts of a computer vision pipeline (e.g. with a relational network on top of the local features).In addition, we demonstrate similarities between the decision-making behaviour of BagNets and popular DNNs in computer vision. These similarities suggest that current network architectures base their decisions on a large number of relatively weak and local statistical regularities and are not sufficiently encouraged -either through their architecture, training procedure or task specification -to learn more holistic features that can better appreciate causal relationships between different parts of the image. In this paper we introduced and analysed a novel interpretable DNN architecture -coined BagNets -that classifies images based on linear bag-of-local-features representations. The results demonstrate that even complex perceptual tasks like ImageNet can be solved just based on small image features and without any notion of spatial relationships. In addition we showed that the key properties of BagNets, in particlar invariance to spatial relationships as well as weak interactions between image features, are also present to varying degrees in many common computer vision models like ResNet-50 Table 1 : Average probability of leading class after masking the 100 patches (8 × 8 pixels) with the highest attribution according to different heatmaps (columns).or VGG-16, suggesting that the decision-making of many DNNs trained on ImageNet follows at least in part a similar bag-of-feature strategy. In contrast to the perceived ""leap"" in performance from bag-of-feature models to deep neural networks, the representations learnt by DNNs may in the end still be similar to the pre-deep learning era.VGG-16 is particularly close to bag-of-feature models, as demonstrated by the weak interactions (Figure 6 ) and the sensitivity to the same small image patches as BagNets (Figure 8 ). Deeper networks, on the other hand, exhibit stronger nonlinear interactions between image parts and are less sensitive to local maskings. This might explain why texturisation (Figure 5 ) works well in VGG-16 but fails for ResNet-and DenseNet-architectures.Clearly, ImageNet alone is not sufficient to force DNNs to learn more physical and causal representation of the world -simply because such a representation is not necessary to solve the task (local image features are enough). This might explain why DNNs generalise poorly to distribution shifts: a DNN trained on natural images has learnt to recognize the textures and local image features associated with different objects (like the fur and eyes of a cat or the keys of a typewriter) and will inevitably fail if presented with cartoon-like images as they lack the key local image features upon which it bases its decisions.One way forward is to define novel tasks that cannot be solved using local statistical regularities. Here the BagNets can serve as a way to evaluate a lower-bound on the task performance as a function of the observable length-scales. Furthermore, BagNets can be an interesting tool in any application in which it is desirable to trade some accuracy for better interpretability. For example, BagNets can make it much easier to spot the relevant spatial locations and image features that are predictive of certain diseases in medical imaging. Likewise, they can serve as diagnostic tools to benchmark feature attribution techniques since ground-truth attributions are directly available. BagNets can also serve as interpretable parts of a larger computer vision pipeline (e.g. in autonomous cars) as they make it easier to understand edge and failure cases. We released the pretrained BagNets (BagNet-9, BagNet-17 and BagNet-33) for PyTorch and Keras at https://github.com/wielandbrendel/ bag-of-local-features-models.Taken together, DNNs might be more powerful than previous hand-tuned bag-of-feature algorithms in discovering weak statistical regularities, but that does not necessarily mean that they learn substantially different representations. We hope that this work will encourage and inspire future work to adapt tasks, architectures and training algorithms to encourage models to learn more causal models of the world.A APPENDIXThe architecture of the BagNets is detailed in Figure A. 1. Training of the models was performed in PyTorch using the default ImageNet training script of Torchvision (https://github.com/ pytorch/vision, commit 8a4786a) with default parameters. In brief, we used SGD with momentum (0.9), a batchsize of 256 and an initial learning rate of 0.01 which we decreased by a factor of 10 every 30 epochs. Images were resized to 256 pixels (shortest side) after which we extracted a random crop of size 224 × 224 pixels.",Deep Neural Networks DNNs excel many complex perceptual tasks has proven notoriously difficult understand how they reach decisions. introduce high-performance DNN architecture ImageNet whose decisions are considerably easier explain. model simple variant ResNet-50 architecture called BagNet classifies image based occurrences small local image features without taking account spatial ordering. strategy is closely related bag-of-feature BoF models popular onset deep learning reaches surprisingly high accuracy ImageNet 87.6 top-5 32x32px features Alexnet performance 16 x16 px features constraint local features makes straight-forward analyse how exactly part image influences classification. Furthermore BagNets behave similar state-of-the art deep neural networks VGG-16 ResNet-152 DenseNet-169 terms feature sensitivity error distribution interactions image parts. suggests improvements DNNs previous bag-of-feature classifiers last years is mostly achieved better fine-tuning rather qualitatively different decision strategies. big obstacle understanding decision-making DNNs is due complex dependencies input hidden activations:one effect part input hidden activation depends state many parts input. Likewise role hidden unit downstream representations depends activity many units. dependency makes extremely difficult understand how DNNs reach decisions.To circumvent problem formulate new DNN architecture is easier interpret design. architecture is inspired bag-of-feature BoF models which -alongside extensions VLAD encoding Fisher Vectors -have successful approaches large-scale object recognition advent deep learning 75% top-5 ImageNet classify images based counts spatial relationships set local image features. structure makes decisions BoF models particularly easy explain.To concise throughout manuscript concept interpretability refers way which evidence small image patches is integrated reach image-level decision. basic BoF models perform simple transparent spatial aggregate patch-wise evidences DNNs non-linearly integrate information across whole image.In paper show is possible combine performance flexibility DNNs interpretability BoF models resulting model family called BagNets is able reach high accuracy ImageNet even if limited fairly small image patches. Given simplicity BoF models imagine many use cases which it can desirable trade bit accuracy better interpretability is common commone.g linear function approximation. includes diagnosing failure cases e.g adversarial examples non-iid settings e.g domain transfer benchmarking diagnostic tools e.g attribution methods serving interpretable parts computer vision pipeline e.g relational network top local features.In addition demonstrate similarities decision-making behaviour BagNets popular DNNs computer vision. similarities suggest current network architectures base decisions large number relatively weak local statistical regularities are not sufficiently encouraged -either architecture training procedure task specification -to learn holistic features can better appreciate causal relationships different parts image. paper introduced analysed novel interpretable DNN architecture -coined BagNets -that classifies images based linear bag-of-local-features representations. results demonstrate even complex perceptual tasks like ImageNet can be solved based small image features without notion spatial relationships. addition showed key properties BagNets particlar invariance spatial relationships well weak interactions image features are also present varying degrees many common computer vision models like ResNet-50 Table 1:Average probability leading class masking 100 patches 8 × 8 pixels highest attribution according different heatmaps columns.or VGG-16 suggesting decision-making many DNNs trained ImageNet follows least part similar bag-of-feature strategy. contrast perceived leap performance bag-of-feature models deep neural networks representations learnt DNNs may end still similar pre-deep learning era.VGG-16 is particularly close bag-of-feature models demonstrated weak interactions Figure6 sensitivity small image patches BagNets Figure8 Deeper networks hand exhibit stronger nonlinear interactions image parts are less sensitive local maskings. might explain why texturisation Figure5 works well VGG-16 fails ResNet-and DenseNet-architectures.Clearly ImageNet alone is not sufficient force DNNs learn physical causal representation world -simply representation is not necessary solve task local image features are enough might explain why DNNs generalise poorly distribution shifts:DNN trained natural images has learnt recognize textures local image features associated different objects like fur eyes cat keys typewriter will inevitably fail if presented cartoon-like images lack key local image features upon which it bases decisions.One way forward is to define novel tasks cannot solved using local statistical regularities. BagNets can serve way evaluate lower-bound task performance function observable length-scales Furthermore BagNets can be an interesting tool application which it is desirable trade accuracy better interpretability. example BagNets can make much easier spot relevant spatial locations image features are predictive certain diseases medical imaging. Likewise can serve diagnostic tools benchmark feature attribution techniques since ground-truth attributions are directly available. BagNets can also serve interpretable parts larger computer vision pipeline e.g autonomous cars make easier understand edge failure cases. released pretrained BagNets BagNet-9 BagNet-17 BagNet-33 PyTorch Keras https://github.com/wielandbrendel/bag-of-local-features-models.Taken together DNNs might powerful previous hand-tuned bag-of-feature algorithms discovering weak statistical regularities does necessarily mean learn substantially different representations. hope work will encourage inspire future work adapt tasks architectures training algorithms encourage models learn causal models world.A APPENDIXThe architecture BagNets is detailed Figure A. 1. Training models was performed PyTorch using default ImageNet training script Torchvision https://github.com/pytorch/vision commit 8a4786a default parameters. brief used SGD momentum 0.9 batchsize 256 initial learning rate 0.01 which we decreased factor 10 every 30 epochs. Images were resized 256 pixels shortest side which we extracted random crop size 224 × 224 pixels.,1609,1115,494,0.016,1.443,2025/11/05 17:18:55,0.01,1.327,0.35202492211838,500.228
"Somatic cancer mutation detection at ultra-low variant allele frequencies (VAFs) is an unmet challenge that is intractable with current state-of-the-art mutation calling methods. Specifically, the limit of VAF detection is closely related to the depth of coverage, due to the requirement of multiple supporting reads in extant methods, precluding the detection of mutations at VAFs that are orders of magnitude lower than the depth of coverage. Nevertheless, the ability to detect cancer-associated mutations in ultra low VAFs is a fundamental requirement for low-tumor burden cancer diagnostics applications such as early detection, monitoring, and therapy nomination using liquid biopsy methods (cell-free DNA). Here we defined a spatial representation of sequencing information adapted for convolutional architecture that enables variant detection at VAFs, in a manner independent of the depth of sequencing. This method enables the detection of cancer mutations even in VAFs as low as 10x-4^, >2 orders of magnitude below the current state-of-the-art. We validated our method on both simulated plasma and on clinical cfDNA plasma samples from cancer patients and non-cancer controls. This method introduces a new domain within bioinformatics and personalized medicine – somatic whole genome mutation calling for liquid biopsy. The cancer genome acquires somatic mutations which drive its proliferative capacity BID8 . Mutations in the cancer genome also provide critical information regarding the evolutionary history and mutational processes active in each cancer (Martincorena et al., 2017; BID0 . Cancer mutation calling in patient tumor biopsies has become a pivotal step in determining patient outcomes and nomination of personalized therapeutics.Identifying cancer mutations in liquid biopsy techniques, such as cell-free circulating DNA (cfDNA), has been suggested as a transformative platform for early-stage cancer screening and residual disease monitoring. cfDNA released from dying tumor cells enables surveys the somatic genome dynamically over time for clinical purposes, empowered by the ability to obtain cancer-related genetic material non-invasively through a simple blood draw. Circulating tumor DNA (ctDNA) can be found and measured in the plasma cfDNA of cancer patients. ctDNA was shown to correlate with tumor burden and change in response to treatment or surgery BID4 . For example, ctDNA can be detected even in early stage non-small cell lung cancer (NSCLC) and therefore has the potential to transform NSCLC diagnosis and treatment BID15 BID17 BID1 BID20 . Nevertheless, the fraction of ctDNA of the total cfDNA is typically exceedingly low, especially in low disease-burden contexts such as early detection or detection of residual disease after therapeutic interventions. While detection of cancer through cfDNA in the low disease-burden setting may be of significant clinical benefit, it challenges our current methods for identifying somatic mutations due to the ultra-low VAFs compared with the available depth of sequencing.The most common type of somatic mutations is single-nucleotide variants (SNVs) , which occur at a frequency of 1-100 per million bases. These variants are typically identified in sequencing data through a careful comparison of the DNA sequencing reads which map to a particular genomic locus in both the cancer DNA and the matched germline DNA. This process has been enabled through tools of ever-increasing sophistication that refine the statistical comparison between the number of reads supporting a candidate mutated variant in the cancer vs. the germline sample BID39 BID42 .These statistical methods fundamentally require multiple independent observations (supporting reads) of the somatic variant at any given genomic location to distinguish true mutations from sequencing artifacts. Mutect , a state-of-the-art low-allele frequency somatic mutation caller, subjects each SNV to Bayesian classifiers that assume that the SNV either results from sequencing noise or that the site contains a true cancer variant. A true cancer-related SNV call is made when the log-likelihood ratio from the two models strongly favors the true cancer Bayesian classifier. This "" locus-centric"" type of cancer mutation detection can be readily achieved through increased depth of sequencing -so long as the tumor sample contains a high proportion of tumor DNA. However , these methods are significantly challenged in the ctDNA setting where the VAF is expected to be well below 1%. For example , a decrease of VAF to 5% and sequencing depth to 10X resulted in a decreased in the sensitivity of Mutect to below 0.1 BID39 BID42 . Thus, locus-centric mutation callers are unable to perform effective mutation calling in the ultra-low VAFs observed in low disease-burden cfDNA settings.We reasoned that to tackle this challenge, we would need a novel mutation detection framework. Specifically, we would need methodology to accurately distinguish true somatic cancer mutations from sequencing artifacts, even in ultra low tumor fractions that preclude the presence of multiple supporting independent observations (reads) in any given genomic location. We propose a ""readcentric "" alternative approach, and developed a convolutional neural network classifier -Kittyhawk -trained to discriminate between individual sequencing reads containing sequencing artifacts and sequencing reads harboring somatic cancer mutations. We take advantage of the fact that both cancer mutations and sequencing errors are systemic and governed by distinct signatures that can be learned and used for efficient signal to noise discrimination (e.g., mutagenesis processes such as exposure to tobacco or UV light are enriched in specific sequence contexts; BID0 ) 0.01%-1%, as well as with cfDNA samples from patients with early stage lung cancer and an individual with non-malignant lung nodules as controls. Ultra-low tumor fraction such as observed in cfDNA fundamentally challenge the prevailing mutation calling paradigm. State-of-the-art mutation callers share a common unifying principle: mutation calling at a particular genomic location based on the observation of the cancer variant in multiple FIG6 : PPV, enrichment, and sensitivity of CA0044 synthetic cfDNA.overlapping reads. However, in the ultra-low tumor fraction context, at best, only a single mutated read is observed, limiting the ability of traditional mutation calling.The need for extending the mutation-calling framework to ultra-low tumor fraction contexts motivated us to rethink the mutation calling process from a locus-centric approach to a read-centric approach. This approach uses every individual read as input for a classifier and lends itself to the application of convolutional neuronal network learning. To realize this novel methodology, we embodied the information captured in the sequencing read (nucleotide sequence, context, quality metrics) in a spatial representation typically applied for image analysis. While we anticipate that our ongoing efforts to include larger training datasets, will result in further performance improvement, even at this proof-of-principle stage the algorithm is providing a 30-fold enrichment in a manner that is completely independent from variant allele fraction or depth of coverage, a unique performance feature that addresses a major emerging unmet need. Indeed, stable enrichment performance extends to tumor fractions as low as 10 4 .While Kittyhawk captures position in the read by using a fully connected sigmoid layer, there are other architectures, which may be suited for capturing relative position on the read. Additionally , we have excluded an extra source of information contained in the read-pair that comes from the DNA fragment. The read pair can be used to determine both the strand of origin (Watson or Crick) and to estimate the DNA fragment size. It has been observed that ctDNA have a distinct fragment size distribution compared to other cfDNA from normal cells BID19 . It has been shown that recurrent neural networks (RNN) are a powerful tool for using length as a feature in bioinformatics at distances even up to 1kb, far beyond the size of a ctDNA fragment BID6 . These results suggest that integrating an RNN instead of a logistic regression layer could increase performance even further. In addition, while Kittyhawk was developed for the context of low tumor fraction mutation calling in cfDNA, we note that this framework can be adapted to other contexts. For example, it may be used in mutation (or germline SNP) detection in low pass genome sequencing (0.01-1X) across a wide range of applications. Furthermore, a read-centric approach may be also integrated with a more traditional locus-centric mutation calling approach, by adding Kittyhawk predictions as an additional input metric for extant statistical or machine learning mutation calling algorithms.In summary, Kittyhawk is the first somatic mutation caller designed specifically to function in the ultra-low allele frequency setting where at best a single supporting read is available for candidate mutation identification, such as liquid biopsy for early stage cancer detection. We apply a novel representation of a read together with a hand-engineered architecture to capture the entirety of informative features associated with a read and its alignment. This work sets the stage for a new family of somatic mutation callers to aid detection in liquid biopsy, paving the way for pivotal non-invasive screening and prognosis.",Somatic cancer mutation detection ultra-low variant allele frequencies VAFs is an unmet challenge is intractable current state-of-the-art mutation calling methods. Specifically limit VAF detection is closely related depth coverage due requirement multiple supporting reads extant methods precluding detection mutations VAFs are orders magnitude lower depth coverage. Nevertheless ability detect cancer-associated mutations ultra low VAFs is a fundamental requirement low-tumor burden cancer diagnostics applications early detection monitoring therapy nomination using liquid biopsy methods cell-free DNA defined spatial representation sequencing information adapted convolutional architecture enables variant detection VAFs manner independent depth sequencing. method enables detection cancer mutations even VAFs low 10x-4^ 2 orders magnitude current state-of-the-art validated method simulated plasma clinical cfDNA plasma samples cancer patients non-cancer controls. method introduces new domain within bioinformatics personalized medicine – somatic whole genome mutation calling liquid biopsy. cancer genome acquires somatic mutations which drive proliferative capacity BID8. Mutations cancer genome also provide critical information regarding evolutionary history mutational processes active cancer Martincorenaetal. 2017;BID0. Cancer mutation calling patient tumor biopsies has become pivotal step determining patient outcomes nomination personalized therapeutics.Identifying cancer mutations liquid biopsy techniques cell-free circulating DNA cfDNA has been suggested transformative platform early-stage cancer screening residual disease monitoring. cfDNA released dying tumor cells enables surveys somatic genome dynamically time clinical purposes empowered ability obtain cancer-related genetic material non-invasively simple blood draw. Circulating tumor DNA ctDNA can be found measured plasma cfDNA cancer patients. ctDNA was shown correlate tumor burden change response treatment surgery BID4. example ctDNA can be detected even early stage non-small cell lung cancer NSCLC therefore has the potential transform NSCLC diagnosis treatment BID15 BID17 BID1 BID20. Nevertheless fraction ctDNA total cfDNA is typically exceedingly low especially low disease-burden contexts early detection detection residual disease therapeutic interventions. detection cancer cfDNA low disease-burden setting may significant clinical benefit challenges current methods identifying somatic mutations due ultra-low VAFs compared available depth sequencing.The common type somatic mutations is single-nucleotide variants SNVs which occur frequency 1-100 per million bases. variants are typically identified sequencing data careful comparison DNA sequencing reads which map particular genomic locus cancer DNA matched germline DNA. process has been enabled tools ever-increasing sophistication refine statistical comparison number reads supporting candidate mutated variant cancervs. germline sample BID39 BID42.These statistical methods fundamentally require multiple independent observations supporting reads somatic variant given genomic location distinguish true mutations sequencing artifacts. Mutect state-of-the-art low-allele frequency somatic mutation caller subjects SNV Bayesian classifiers assume SNV either results sequencing noise site contains true cancer variant. true cancer-related SNV call is made when the log-likelihood ratio two models strongly favors true cancer Bayesian classifier. locus-centric type cancer mutation detection can be readily achieved increased depth sequencing -so long tumor sample contains high proportion tumor DNA. However methods are significantly challenged ctDNA setting where the VAF is expected well 1%. example decrease VAF 5% sequencing depth 10X resulted decreased sensitivity Mutect 0.1 BID39 BID42. Thus locus-centric mutation callers are unable perform effective mutation calling ultra-low VAFs observed low disease-burden cfDNA settings.We reasoned tackle challenge would need novel mutation detection framework. Specifically would need methodology accurately distinguish true somatic cancer mutations sequencing artifacts even ultra low tumor fractions preclude presence multiple supporting independent observations reads given genomic location. propose readcentric alternative approach developed convolutional neural network classifier -Kittyhawk -trained discriminate individual sequencing reads containing sequencing artifacts sequencing reads harboring somatic cancer mutations. take advantage fact cancer mutations sequencing errors are systemic governed distinct signatures can be learned used efficient signal noise discrimination e.g mutagenesis processes exposure tobacco UV light are enriched specific sequence contexts;BID0 0.01%-1 well cfDNA samples patients early stage lung cancer individual non-malignant lung nodules controls. Ultra-low tumor fraction observed cfDNA fundamentally challenge prevailing mutation calling paradigm. State-of-the-art mutation callers share common unifying principle:mutation calling particular genomic location based observation cancer variant multiple FIG6:PPV enrichment sensitivity CA0044 synthetic cfDNA.overlapping reads. However ultra-low tumor fraction context best single mutated read is observed limiting ability traditional mutation calling.The need extending mutation-calling framework ultra-low tumor fraction contexts motivatedus rethink mutation calling process locus-centric approach read-centric approach. approach uses every individual read input classifier lends application convolutional neuronal network learning. realize novel methodology embodied information captured sequencing read nucleotide sequence context quality metrics spatial representation typically applied image analysis. anticipate ongoing efforts include larger training datasets will result performance improvement even proof-of-principle stage algorithm is providing 30-fold enrichment manner is completely independent variant allele fraction depth coverage unique performance feature addresses major emerging unmet need. Indeed stable enrichment performance extends tumor fractions low 10 4.While Kittyhawk captures position read using fully connected sigmoid layer are other architectures may suited capturing relative position read. Additionally have excluded extra source information contained read-pair comes DNA fragment. read pair can be used determine strand origin Watson Crick estimate DNA fragment size. has been observed ctDNA have a distinct fragment size distribution compared cfDNA normal cells BID19. has been shown recurrent neural networks RNN are a powerful tool using length feature bioinformatics distances even 1kb far beyond size ctDNA fragment BID6. results suggest integrating RNN instead logistic regression layer could increase performance even further. addition Kittyhawk was developed context low tumor fraction mutation calling cfDNA note framework can be adapted contexts. example may used mutation germline SNP detection low pass genome sequencing 0.01-1X across wide range applications. Furthermore read-centric approach may also integrated traditional locus-centric mutation calling approach adding Kittyhawk predictions additional input metric extant statistical machine learning mutation calling algorithms.In summary Kittyhawk is the first somatic mutation caller designed specifically function ultra-low allele frequency setting where at best single supporting read is available candidate mutation identification liquid biopsy early stage cancer detection. apply novel representation read together hand-engineered architecture capture entirety informative features associated read alignment. work sets stage new family somatic mutation callers aid detection liquid biopsy paving way pivotal non-invasive screening prognosis.,1778,1254,524,0.018,1.418,2025/11/05 17:18:55,0.01,1.455,0.2741433021806849,530.661
"This paper presents the formal release of {\em MedMentions}, a new manually annotated resource for the recognition of biomedical concepts. What distinguishes MedMentions from other annotated biomedical corpora is its size (over 4,000 abstracts and over 350,000 linked mentions), as well as the size of the concept ontology (over 3 million concepts from UMLS 2017) and its broad coverage of biomedical disciplines. In addition to the full corpus, a sub-corpus of MedMentions is also presented, comprising annotations for a subset of UMLS 2017 targeted towards document retrieval. To encourage research in Biomedical Named Entity Recognition and Linking, data splits for training and testing are included in the release, and a baseline model and its metrics for entity linking are also described. One recognized challenge in developing automated biomedical entity extraction systems is the lack of richly annotated training datasets. While there are a few such datasets available, the annotated corpus often contains no more than a few thousand annotated entity mentions. Additionally, the annotated entities are limited to a few types of biomedical concepts such as diseases BID4 , gene ontology terms BID18 , or chemicals and diseases BID9 . Researchers targeting the recognition of multiple biomedical entity types have had to resort to specialized machine learning techniques for combining datasets labelled with subsets of the full target set, e.g. using multi-task learning BID3 , or a modified Conditional Random Field cost which allows un-labeled tokens to take any labels not in the current dataset's target set BID5 . To promote the development of state-of-the-art entity linkers targeting a more comprehensive coverage of biomedical concepts, we decided to create a large concept-mention annotated gold standard dataset named 'MedMentions' BID11 .With the release of MedMentions, we hope to address two key needs for developing better biomedical concept recognition systems: (i) a much broader coverage of the fields of biology and medicine through the use of the Unified Medical Language System (UMLS) as the target ontology, and (ii ) a significantly larger annotated corpus than available today, to meet the data demands of today's more complex machine learning models for concept recognition.The paper begins with an introduction to the MedMentions annotated corpus, including a subcorpus aimed at information retrieval systems. This is followed by a comparison with a few other large datasets annotated with biomedical entities. Finally , to promote further research on large ontology named entity recognition and linking, we present metrics for a baseline end-to-end concept recognition (entity type recognition and entity linking) model trained on the MedMentions corpus. We presented the formal release of a new resource, named MedMentions, for biomedical concept recognition, with a large manually annotated annotated corpus of over 4,000 abstracts targeting a very large fine-grained concept ontology consisting of over 3 million concepts. We also included in this release a targeted sub-corpus (MedMentions ST21pv), with standard training, development and test splits of the data, and the metrics of a baseline concept recognition model trained on this subset, to allow researchers to compare the metrics of their concept recognition models.","paper presents formal release \em MedMentions new manually annotated resource recognition biomedical concepts. What distinguishes MedMentions annotated biomedical corpora is its size 4,000 abstracts 350,000 linked mentions well size concept ontology 3 million concepts UMLS 2017 broad coverage biomedical disciplines. addition full corpus sub-corpus MedMentions is also presented comprising annotations subset UMLS 2017 targeted towards document retrieval. encourage research Biomedical Named Entity Recognition Linking data splits training testing are included release baseline model metrics entity linking are also described. One recognized challenge developing automated biomedical entity extraction systems is the lack richly annotated training datasets. area datasets available annotated corpus often contains thousand annotated entity mentions. Additionally annotated entities are limited types biomedical concepts diseases BID4 gene ontology terms BID18 chemicals diseases BID9. Researchers targeting recognition multiple biomedical entity types have had to resort specialized machine learning techniques combining datasets labelled subsets full target set e.g using multi-task learning BID3 modified Conditional Random Field cost which allows un-labeled tokens take labels current dataset's target set BID5. promote development state-of-the-art entity linkers targeting comprehensive coverage biomedical concepts decided create large concept-mention annotated gold standard dataset named 'MedMentions' BID11.With release MedMentions hope address two key needs developing better biomedical concept recognition systems:much broader coverage fields biology medicine use Unified Medical Language System UMLS target ontology ii significantly larger annotated corpus available today meet data demands today's complex machine learning models concept recognition.The paper begins introduction MedMentions annotated corpus including subcorpus aimed information retrieval systems. is followed comparison large datasets annotated biomedical entities. Finally promote research large ontology named entity recognition linking present metrics baseline end-to-end concept recognition entity type recognition entity linking model trained MedMentions corpus. presented formal release new resource named MedMentions biomedical concept recognition large manually annotated annotated corpus 4,000 abstracts targeting large fine-grained concept ontology consisting 3 million concepts. also included release targeted sub-corpus MedMentions ST21pv standard training development test splits data metrics baseline concept recognition model trained subset allow researchers compare metrics concept recognition models.",621,413,208,0.006,1.504,2025/11/05 17:18:55,0.0,1.455,0.542056074766355,186.442
"In this paper we propose a Deep Autoencoder Mixture Clustering (DAMIC) algorithm. It is based on a mixture of deep autoencoders where each cluster is represented by an autoencoder. A clustering network transforms the data into another space and then selects one of the clusters. Next, the autoencoder associated with this cluster is used to reconstruct the data-point. The clustering algorithm jointly learns the nonlinear data representation and the set of autoencoders. The optimal clustering is found by minimizing the reconstruction loss of the mixture of autoencoder network. Unlike other deep clustering algorithms, no regularization term is needed to avoid data collapsing to a single point. Our experimental evaluations on image and text corpora show significant improvement over state-of-the-art methods. Effective automatic grouping of objects into clusters is one of the fundamental problems in machine learning and data analysis. In many approaches, the first step toward clustering a dataset is extracting a feature vector from each object. This reduces the problem to the aggregation of groups of vectors in a feature space. A commonly used clustering algorithm in this case is the k-means. Clustering high-dimensional datasets is, however, hard because inter-point distances become less informative in high-dimensional spaces. As a result, representation learning has been used to map the input data into a low-dimensional feature space. In recent years, motivated by the success of deep neural network in supervised learning, there are many attempts to apply unsupervised deep learning approaches for clustering. Most methods are focused on clustering over a low-dimensional feature space of an autoencoder or a variational autoencoder. Recent good overviews of deep clustering methods can be found in BID1 and BID14 .Using deep neural networks, it is possible to learn nonlinear mappings allowing to transform the data into more clustering-friendly representations. A deep version of k-means is based on learning a data representation and applying k-means in the embedded space. A straightforward implementation of the deep k-means algorithm would lead, however, to a trivial solution where the features are collapsed to a single point in the embedded space and the centroids are collapsed into a single entity. The objective function of most deep clustering algorithms is, therefore, composed of a clustering term computed in the embedded space and a regularization term in the form of reconstruction error to avoid data collapsing. Deep Embedded Clustering (DEC) BID16 ) is first pre-trained using an autoencoder reconstruction loss and then optimizes cluster centroids in the embedded space through a Kullback-Leibeler divergence loss. Deep Clustering network (DCN) BID17 ) is another autoencoder-based method that uses k-means for clustering. Similar to DEC, in the first phase, the network is pre-trained using the autoencoder reconstruction loss. In the second phase, in contrast to DEC, the network is jointly trained using a mathematical combination of the autoencoder reconstruction loss and the k-means clustering loss function. Thus, due to the fact that strict cluster assignments were used during the training (instead of probabilities such as in DEC) the method requires an alternation process between the network training and the cluster updates.In this paper we propose an algorithm to perform unsupervised clustering within the mixture-ofexperts framework BID8 ). Each cluster is represented by an autoencoder neuralnetwork and the clustering itself is performed in a low-dimensional embedded space by a softmax classification layer that directs the input data to the most suitable autoencoder. Unlike most deep clustering algorithms the proposed algorithm is deep in nature and not a deep variant of a classical clustering algorithm. The proposed algorithm does not suffer from the clustering collapsing problem and therefore there is no need for regularization terms that have to be tuned separately for each dataset. Note that parameter tuning in clustering is problematic since it is based, either explicitly or implicitly, on the data labels which are not supposed to be available in the clustering process. Another major difference of the proposed method from previous approaches is the learning method of the embedding latent space where the actual clustering operation is taking place. In most previous methods, the embedded space is controlled by an autoencoder. Thus, in order to gain a good reconstruction, it requires to encode into the embedded space information that can be entirely irrelevant to the clustering process. In contrast, in our algorithm no decoding is applied to the clustering embedded space and the only goal of the embedded space is to find a good organization of the data into separated clusters.We validate the method on standard real datasets including various document and image corpora. Evidently, visible improvement from the respective state-of-art is observed for all the tested datasets. The contribution of this paper is twofold: (i) a novel deep learning clustering method that unlike deep variants of k-means, does not require a tuned regularization term to avoid clustering collapsing to a single point; and (ii) state-of-the-art performance on standard datasets. In this study we presented a clustering technique which leverages the strength of deep neural network. Our technique has two major properties: first, unlike most previous methods, the clusters are represented by an autoencoder network instead of a single centroid vector in the embedded space. This enables a much richer representation of each cluster. Second, The algorithm does not cause a data collapsing problem. Hence, there is no need for regularization terms that have to be tuned for each dataset separately. Experiments on a variety of real datasets showed the improved performance of the proposed algorithm.","paper propose Deep Autoencoder Mixture Clustering DAMIC algorithm. is based mixture deep autoencoders where each cluster is represented autoencoder. clustering network transforms data another space selects one clusters. Next autoencoder associated cluster is used reconstruct data-point clustering algorithm jointly learns nonlinear data representation set autoencoders. optimal clustering is found minimizing reconstruction loss mixture autoencoder network. Unlike deep clustering algorithms regularization term is needed avoid data collapsing single point. experimental evaluations image text corpora show significant improvement state-of-the-art methods. Effective automatic grouping objects clusters is one fundamental problems machine learning data analysis. many approaches first step toward clustering dataset is extracting feature vector object. reduces problem aggregation groups vectors feature space. commonly used clustering algorithm case is the k-means k-means Clustering high-dimensional datasets is,however hard inter-point distances become less informative high-dimensional spaces. result representation learning has been used map input data low-dimensional feature space. recent years motivated success deep neural network supervised learning are many attempts apply unsupervised deep learning approaches clustering. methods are focused clustering low-dimensional feature space autoencoder variational autoencoder. Recent good overviews deep clustering methods can be found BID1 BID14.Using deep neural networks is possible learn nonlinear mappings allowing transform data clustering-friendly representations. deep version k-means is based learning data representation applying k-means embedded space. straightforward implementation deep k-means algorithm would lead however trivial solution where the features are collapsed single point embedded space centroids are collapsed single entity. objective function deep clustering algorithms is,therefore composed clustering term computed embedded space regularization term form reconstruction error avoid data collapsing. Deep Embedded Clustering DEC BID16 is first pre-trained using autoencoder reconstruction loss optimizes cluster centroids embedded space Kullback-Leibeler divergence loss. Deep Clustering network DCN BID17 is another autoencoder-based method uses k-means clustering. Similar DEC first phase network is pre-trained using autoencoder reconstruction loss. second phase contrast DEC network is jointly trained using mathematical combination autoencoder reconstruction loss k-means clustering loss function. Thus due fact strict cluster assignments were used training instead probabilities DEC method requires alternation process network training cluster updates.In paper propose algorithm perform unsupervised clustering within mixture-ofexperts framework BID8 cluster is represented autoencoder neuralnetwork clustering is performed low-dimensional embedded space softmax classification layer directs input data suitable autoencoder. Unlike deep clustering algorithms proposed algorithm is deep nature deep variant classical clustering algorithm. proposed algorithm does not suffer clustering collapsing problem therefore is no need regularization terms have to be tuned separately dataset. Note parameter tuning clustering is problematic since is based either explicitly implicitly data labels which are not supposed available clustering process. Another major difference proposed method previous approaches is the learning method embedding latent space where the actual clustering operation is taking place. previous methods embedded space is controlled autoencoder. Thus order gain good reconstruction requires encode embedded space information can be entirely irrelevant clustering process. contrast algorithm decoding is applied clustering embedded space goal embedded space is to find good organization data separated clusters.We validate method standard real datasets including various document image corpora. Evidently visible improvement respective state-of-art is observed tested datasets. contribution paper is twofold:novel deep learning clustering method unlike deep variants k-means does not require tuned regularization term avoid clustering collapsing single point;ii state-of-the-art performance standard datasets. study presented clustering technique which leverages strength deep neural network. technique has two major properties:first unlike previous methods clusters are represented autoencoder network instead single centroid vector embedded space. enables much richer representation cluster. Second algorithm does not cause data collapsing problem. Hence is no need regularization terms have to be tuned dataset separately. Experiments variety real datasets showed improved performance proposed algorithm.",1084,738,346,0.011,1.469,2025/11/05 17:18:55,0.01,1.447,0.4330218068535826,342.592
"We propose a new Integral Probability Metric (IPM) between distributions: the Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions for functions (critic) restricted to a Sobolev ball defined with respect to a dominant measure mu. We show that the Sobolev IPM compares two distributions in high dimensions based on weighted conditional Cumulative Distribution Functions (CDF) of each coordinate on a leave one out basis. The Dominant measure mu plays a crucial role as it defines the support on which conditional CDFs are compared. Sobolev IPM can be seen as an extension of the one dimensional Von-Mises Cramer statistics to high dimensional distributions. We show how Sobolev IPM can be used to train Generative Adversarial Networks (GANs). We then exploit the intrinsic conditioning implied by Sobolev IPM in text generation. Finally we show that a variant of Sobolev GAN achieves competitive results in semi-supervised learning on CIFAR-10, thanks to the smoothness enforced on the critic by Sobolev GAN which relates to Laplacian regularization. In order to learn Generative Adversarial Networks BID14 , it is now well established that the generator should mimic the distribution of real data, in the sense of a certain discrepancy measure. Discrepancies between distributions that measure the goodness of the fit of the neural generator to the real data distribution has been the subject of many recent studies BID1 BID36 BID20 BID30 BID17 , most of which focus on training stability.In terms of data modalities, most success was booked in plausible natural image generation after the introduction of Deep Convolutional Generative Adversarial Networks (DCGAN) BID39 . This success is not only due to advances in training generative adversarial networks in terms of loss functions and stable algorithms, but also to the representation power of convolutional neural networks in modeling images and in finding sufficient statistics that capture the continuous density function of natural images. When moving to neural generators of discrete sequences generative adversarial networks theory and practice are still not very well understood. Maximum likelihood pre-training or augmentation, in conjunction with the use of reinforcement learning techniques were proposed in many recent works for training GAN for discrete sequences generation BID50 BID40 . Other methods included using the Gumbel Softmax trick BID23 ) and the use of auto-encoders to generate adversarially discrete sequences from a continuous space BID51 . End to end training of GANs for discrete sequence generation is still an open problem BID38 . Empirical successes of end to end training have been reported within the framework of WGAN-GP BID17 , using a proxy for the Wasserstein distance via a pointwise gradient penalty on the critic. Inspired by this success, we propose in this paper a new Integral Probability Metric (IPM) between distributions that we coin Sobolev IPM. Intuitively an IPM BID35 between two probability distributions looks for a witness function f , called critic, that maximally discriminates between samples coming from the two distributions: DISPLAYFORM0 Traditionally, the function f is defined over a function class F that is independent to the distributions at hand BID48 . The Wasserstein-1 distance corresponds for instance to an IPM where the witness functions are defined over the space of Lipschitz functions; The MMD distance corresponds to witness functions defined over a ball in a Reproducing Kernel Hilbert Space (RKHS).We will revisit in this paper Fisher IPM defined in , which extends the IPM definition to function classes defined with norms that depend on the distributions. Fisher IPM can be seen as restricting the critic to a Lebsegue ball defined with respect to a dominant measure µ. The Lebsegue norm is defined as follows: DISPLAYFORM1 where µ is a dominant measure of P and Q.In this paper we extend the IPM framework to critics bounded in the Sobolev norm: DISPLAYFORM2 In contrast to Fisher IPM, which compares joint probability density functions of all coordinates between two distributions, we will show that Sobolev IPM compares weighted (coordinate-wise) conditional Cumulative Distribution Functions for all coordinates on a leave on out basis. Matching conditional dependencies between coordinates is crucial for sequence modeling.Our analysis and empirical verification show that the modeling of the conditional dependencies can be built in to the metric used to learn GANs as in Sobolev IPM. For instance, this gives an advantage to Sobolev IPM in comparing sequences over Fisher IPM. Nevertheless, in sequence modeling when we parametrize the critic and the generator with a neural network, we find an interesting tradeoff between the metric used and the architectures used to parametrize the critic and the generator as well as the conditioning used in the generator. The burden of modeling the conditional long term dependencies can be handled by the IPM loss function as in Sobolev IPM (more accurately the choice of the data dependent function class of the critic) or by a simpler metric such as Fisher IPM together with a powerful architecture for the critic that models conditional long term dependencies such as LSTM or GRUs in conjunction with a curriculum conditioning of the generator as done in BID38 . Highlighting those interesting tradeoffs between metrics, data dependent functions classes for the critic (Fisher or Sobolev) and architectures is crucial to advance sequence modeling and more broadly structured data generation using GANs.3. The intrinsic conditioning and the CDF matching make Sobolev IPM suitable for discrete sequence matching and explain the success of the gradient pernalty in WGAN-GP and Sobolev GAN in discrete sequence generation. 4. We give in Section 5 an ALM (Augmented Lagrangian Multiplier) algorithm for training Sobolev GAN. Similar to Fisher GAN, this algorithm is stable and does not compromise the capacity of the critic. 5. We show in Appendix A that the critic of Sobolev IPM satisfies an elliptic Partial Differential Equation (PDE). We relate this diffusion to the Fokker-Planck equation and show the behavior of the gradient of the optimal Sobolev critic as a transportation plan between distributions. 6. We empirically study Sobolev GAN in character level text generation (Section 6.1). We validate that the conditioning implied by Sobolev GAN is crucial for the success and stability of GAN in text generation. As a take home message from this study, we see that text generation succeeds either by implicit conditioning i.e using Sobolev GAN (or WGAN-GP) together with convolutional critics and generators, or by explicit conditioning i.e using Fisher IPM together with recurrent critic and generator and curriculum learning. 7. We finally show in Section 6.2 that a variant of Sobolev GAN achieves competitive semisupervised learning results on CIFAR-10, thanks to the smoothness implied by the Sobolev regularizer. We introduced the Sobolev IPM and showed that it amounts to a comparison between weighted (coordinate-wise) CDFs. We presented an ALM algorithm for training Sobolev GAN. The intrinsic conditioning implied by the Sobolev IPM explains the success of gradient regularization in Sobolev GAN and WGAN-GP on discrete sequence data, and particularly in text generation. We highlighted the important tradeoffs between the implicit conditioning introduced by the gradient regularizer in Sobolev IPM, and the explicit conditioning of Fisher IPM via recurrent critics and generators in conjunction with the curriculum conditioning. Both approaches succeed in text generation. We showed that Sobolev GAN achieves competitive semi-supervised learning results without the need of any normalization, thanks to the smoothness induced by the gradient regularizer. We think the Sobolev IPM point of view will open the door for designing new regularizers that induce different types of conditioning for general structured/discrete/graph data beyond sequences.",propose new Integral Probability Metric IPM distributions:Sobolev IPM. Sobolev IPM compares mean discrepancy two distributions functions critic restricted Sobolev ball defined respect dominant measuremu. show Sobolev IPM compares two distributions high dimensions based weighted conditional Cumulative Distribution Functions CDF coordinate leave one basis. Dominant measure mu plays crucial role defines support which conditional CDFs are compared. Sobolev IPM can be seen extension one dimensional Von-Mises Cramer statistics high dimensional distributions. show how Sobolev IPM can be used train Generative Adversarial Networks GANs exploit intrinsic conditioning implied Sobolev IPM text generation. Finally show variant Sobolev GAN achieves competitive results semi-supervised learning CIFAR-10 thanks smoothness enforced critic Sobolev GAN which relates Laplacian regularization. order learn Generative Adversarial Networks BID14 is now well established generator should mimic distribution real data sense certain discrepancy measure. Discrepancies distributions measure goodness fit neural generator real data distribution has been the subject many recent studies BID1 BID36 BID20 BID30 BID17 which focus training stability.In terms data modalities success was booked plausible natural image generation introduction Deep Convolutional Generative Adversarial Networks DCGAN BID39. success is not only due advances training generative adversarial networks terms loss functions stable algorithms also representation power convolutional neural networks modeling images finding sufficient statistics capture continuous density function natural images. When moving neural generators discrete sequences generative adversarial networks theory practice are still well understood. Maximum likelihood pre-training augmentation conjunction use reinforcement learning techniques were proposed many recent works training GAN discrete sequences generation BID50 BID40. methods included using Gumbel Softmax trick BID23 use auto-encoders generate adversarially discrete sequences continuous space BID51. End end training GANs discrete sequence generation is still open problem BID38. Empirical successes end end training have been reported within framework WGAN-GP BID17 using proxy Wasserstein distance via pointwise gradient penalty critic. Inspired success propose paper new Integral Probability Metric IPM distributions coin Sobolev IPM. Intuitively IPM BID35 two probability distributions looks witness functionf called critic maximally discriminates samples coming two distributions:DISPLAYFORM0 Traditionally functionf is defined function classF is independent distributions hand BID48. Wasserstein-1 distance corresponds instance IPM where the witness functions are defined space Lipschitz functions;MMD distance corresponds witness functions defined ball Reproducing Kernel Hilbert Space RKHS.We will revisit paper Fisher IPM defined which extends IPM definition function classes defined norms depend distributions. Fisher IPM can be seen restricting critic Lebsegue ball defined respect dominant measureµ. Lebsegue norm is defined follows:DISPLAYFORM1 whereµ is a dominant measure P Q.In paper extend IPM framework critics bounded Sobolev norm:DISPLAYFORM2 contrast Fisher IPM which compares joint probability density functions coordinates two distributions will show Sobolev IPM compares weighted coordinate-wise conditional Cumulative Distribution Functions coordinates leave basis. Matching conditional dependencies coordinates is crucial sequence modeling.Our analysis empirical verification show modeling conditional dependencies can be built metric used learn GANs Sobolev IPM. instance gives advantage Sobolev IPM comparing sequences Fisher IPM. Nevertheless sequence modeling when we parametrize critic generator neural network find interesting tradeoff metric used architectures used parametrize critic generator well conditioning used generator. burden modeling conditional long term dependencies can be handled IPM loss function Sobolev IPM accurately choice data dependent function class critic simpler metric Fisher IPM together powerful architecture critic models conditional long term dependencies LSTM GRUs conjunction curriculum conditioning generator done BID38. Highlighting interesting tradeoffs metrics data dependent functions classes critic Fisher Sobolev architectures is crucial advance sequence modeling broadly structured data generation using GANs.3 intrinsic conditioning CDF matching make Sobolev IPM suitable discrete sequence matching explain success gradient pernalty WGAN-GP Sobolev GAN discrete sequence generation. 4. give Section5 ALM Augmented Lagrangian Multiplier algorithm training Sobolev GAN. Similar Fisher GAN algorithm is stable does not compromise capacity critic. 5. show Appendix critic Sobolev IPM satisfies elliptic Partial Differential Equation PDE relate diffusion Fokker-Planck equation show behavior gradient optimal Sobolev critic transportation plan distributions. 6. empirically study Sobolev GAN character level text generation Section 6.1 validate conditioning implied Sobolev GAN is crucial success stability GAN text generation. take home message study see text generation succeeds either implicit conditioning.e using Sobolev GAN WGAN-GP together convolutional critics generators explicit conditioning.e using Fisher IPM together recurrent critic generator curriculum learning. 7. finally show Section 6.2 variant Sobolev GAN achieves competitive semisupervised learning results CIFAR-10 thanks smoothness implied Sobolev regularizer. introduced Sobolev IPM showed amounts comparison weighted coordinate-wise CDFs. presented ALM algorithm training Sobolev GAN. intrinsic conditioning implied Sobolev IPM explains success gradient regularization Sobolev GAN WGAN-GP discrete sequence data particularly text generation. highlighted important tradeoffs implicit conditioning introduced gradient regularizer Sobolev IPM explicit conditioning Fisher IPM via recurrent critics generators conjunction curriculum conditioning. approaches succeed text generation. showed Sobolev GAN achieves competitive semi-supervised learning results without need normalization thanks smoothness induced gradient regularizer. think Sobolev IPM point view will open door designing new regularizers induce different types conditioning general structured/discrete/graph data beyond sequences.,1600,1116,484,0.015,1.434,2025/11/05 17:18:55,0.01,1.412,0.3239875389408096,471.934
"We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. Generative Adversarial Nets (GANs) BID10 are a recent novel class of deep generative models that are successfully applied to a large variety of applications such as image, video generation, image inpainting, semantic segmentation, image-to-image translation, and text-to-image synthesis, to name a few BID9 . From the game theory metaphor, the model consists of a discriminator and a generator playing a two-player minimax game, wherein the generator aims to generate samples that resemble those in the training data whilst the discriminator tries to distinguish between the two as narrated in BID10 . Training GAN, however, is challenging as it can be easily trapped into the mode collapsing problem where the generator only concentrates on producing samples lying on a few modes instead of the whole data space BID9 .Many GAN variants have been recently proposed to address this problem. They can be grouped into two main categories: training either a single generator or many generators. Methods in the former include modifying the discriminator's objective (Salimans et al., 2016; BID22 , modifying the generator's objective (Warde-Farley & Bengio, 2016) , or employing additional discriminators to yield more useful gradient signals for the generators (Nguyen et al., 2017; BID7 . The common theme in these variants is that generators are shown, at equilibrium, to be able to recover the data distribution, but convergence remains elusive in practice. Most experiments are conducted on toy datasets or on narrow-domain datasets such as LSUN (Yu et al., 2015) or CelebA BID20 . To our knowledge , only Warde-Farley & Bengio (2016) and Nguyen et al. (2017) perform quantitative evaluation of models trained on much more diverse datasets such as STL-10 (Coates et al., 2011) and ImageNet (Russakovsky et al., 2015) .Given current limitations in the training of single-generator GANs, some very recent attempts have been made following the multi-generator approach. Tolstikhin et al. (2017) apply boosting techniques to train a mixture of generators by sequentially training and adding new generators to the mixture. However, sequentially training many generators is computational expensive. Moreover, this approach is built on the implicit assumption that a single-generator GAN can generate very good images of some modes, so reweighing the training data and incrementally training new generators will result in a mixture that covers the whole data space. This assumption is not true in practice since current single-generator GANs trained on diverse datasets such as ImageNet tend to generate images of unrecognizable objects. BID2 train a mixture of generators and discriminators, and optimize the minimax game with the reward function being the weighted average reward function between any pair of generator and discriminator. This model is computationally expensive and lacks a mechanism to enforce the divergence among generators. BID8 train many generators by using a multi-class discriminator that, in addition to detecting whether a data sample is fake, predicts which generator produces the sample. The objective function in this model punishes generators for generating samples that are detected as fake but does not directly encourage generators to specialize in generating different types of data.We propose in this paper a novel approach to train a mixture of generators. Unlike aforementioned multi-generator GANs, our proposed model simultaneously trains a set of generators with the objective that the mixture of their induced distributions would approximate the data distribution, whilst encouraging them to specialize in different data modes. The result is a novel adversarial architecture formulated as a minimax game among three parties: a classifier, a discriminator, and a set of generators. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. We term our proposed model as Mixture Generative Adversarial Nets (MGAN). We provide analysis that our model is optimized towards minimizing the Jensen-Shannon Divergence (JSD) between the mixture of distributions induced by the generators and the data distribution while maximizing the JSD among generators.Empirically, our proposed model can be trained efficiently by utilizing parameter sharing among generators, and between the classifier and the discriminator. In addition, simultaneously training many generators while enforcing JSD among generators helps each of them focus on some modes of the data space and learn better. Trained on CIFAR-10, each generator learned to specialize in generating samples from a different class such as horse, car, ship, dog, bird or airplane. Overall, the models trained on the CIFAR-10, STL-10 and ImageNet datasets successfully generated diverse, recognizable objects and achieved state-of-the-art Inception scores (Salimans et al., 2016) . The model trained on the CIFAR-10 even outperformed GANs trained in a semi-supervised fashion (Salimans et al., 2016; Odena et al., 2016) .In short, our main contributions are: (i) a novel adversarial model to efficiently train a mixture of generators while enforcing the JSD among the generators; (ii) a theoretical analysis that our objective function is optimized towards minimizing the JSD between the mixture of all generators' distributions and the real data distribution, while maximizing the JSD among generators; and (iii) a comprehensive evaluation on the performance of our method on both synthetic and real-world large-scale datasets of diverse natural scenes. We have presented a novel adversarial model to address the mode collapse in GANs. Our idea is to approximate data distribution using a mixture of multiple distributions wherein each distribution captures a subset of data modes separately from those of others. To achieve this goal, we propose a minimax game of one discriminator, one classifier and many generators to formulate an optimization problem that minimizes the JSD between P data and P model , i.e., a mixture of distributions induced by the generators, whilst maximizes JSD among such generator distributions. This helps our model generate diverse images to better cover data modes, thus effectively avoids mode collapse. We term our proposed model Mixture Generative Adversarial Network (MGAN).The MGAN can be efficiently trained by sharing parameters between its discriminator and classifier, and among its generators, thus our model is scalable to be evaluated on real-world largescale datasets. Comprehensive experiments on synthetic 2D data, CIFAR-10, STL-10 and ImageNet databases demonstrate the following capabilities of our model: (i) achieving state-of-the-art Inception scores; (ii) generating diverse and appealing recognizable objects at different resolutions; and (iv) specializing in capturing different types of objects by the generators. In our proposed method, generators G 1 , G 2 , ... G K are deep convolutional neural networks parameterized by θ G . These networks share parameters in all layers except for the input layers. The input layer for generator G k is parameterized by the mapping f θ G ,k (z) that maps the sampled noise z to the first hidden layer activation h. The shared layers are parameterized by the mapping g θ G (h) that maps the first hidden layer to the generated data. The pseudo-code of sampling from the mixture is described in Alg. 1. Classifier C and classifier D are also deep convolutional neural networks that are both parameterized by θ CD . They share parameters in all layers except for the last layer . The pseudo-code of alternatively learning θ G and θ CD using stochastic gradient descend is described in Alg. 2.Algorithm 1 Sampling from MGAN's mixture of generators. 1: Sample noise z from the prior P z . 2: Sample a generator index u from Mult (π 1 , π 2 , ..., π K ) with predefined mixing probability π = (π 1 , π 2 , ..., π K ). DISPLAYFORM0 Return generated data x and the index u.Algorithm 2 Alternative training of MGAN using stochastic gradient descent.1: for number of training iterations do 2:Sample a minibatch of M data points DISPLAYFORM1 Sample a minibatch of N generated data points ) and N indices (u 1 , u 2 , ..., u N ) from the current mixture. DISPLAYFORM2 4: DISPLAYFORM3 5: DISPLAYFORM4 Update classifier C and discriminator D by descending along their gradient: DISPLAYFORM5 Sample a minibatch of N generated data points ) and N indices (u 1 , u 2 , ..., u N ) from the current mixture. DISPLAYFORM6 8: DISPLAYFORM7 Update the mixture of generators G by ascending along its gradient: ∇ θ G L G . 10: end for B APPENDIX: PROOFS FOR SECTION 3.1 Proposition 1 FIG0 . For fixed generators G 1 , G 2 , ..., G K and mixture weights π 1 , π 2 , ..., π K , the optimal classifier C * = C * 1:K and discriminator D * for J (G, C, D) are: DISPLAYFORM8 Proof. The optimal D * was proved in Prop. 1 in BID9 . This section shows a similar proof for the optimal C * . Assuming that C * can be optimized in the functional space, we can calculate the functional derivatives of J (G, C, D)with respect to each C k (x) for k ∈ {2, ..., K} and set them equal to zero: DISPLAYFORM9 Setting DISPLAYFORM10 to 0 for k ∈ {2, ..., K}, we get: DISPLAYFORM11 DISPLAYFORM12 results from Eq. (6) due to the fact that DISPLAYFORM13 Reformulation of L (G 1:K ). Replacing the optimal C * and D * into Eq. (2), we can reformulate the objective function for the generator as follows: DISPLAYFORM14 The sum of the first two terms in Eq. FORMULA29 was shown in BID10 to be 2 · JSD (P data P model ) − log 4. The last term β{ * } of Eq. FORMULA29 is related to the JSD for the K distributions: DISPLAYFORM15 where H (P ) is the Shannon entropy for distribution P . Thus, L (G 1:K ) can be rewritten as: DISPLAYFORM16 Theorem 3 (Thm. 3 restated). If the data distribution has the form: DISPLAYFORM17 where the mixture components q k (x)(s) are well-separated, the minimax problem in Eq. (2) or the optimization problem in Eq. (3) has the following solution: DISPLAYFORM18 , and the corresponding objective value of the optimization problem in Eq. (3) DISPLAYFORM19 Proof. We first recap the optimization problem for finding the optimal G * : DISPLAYFORM20 The JSD in Eq. FORMULA30 is given by: DISPLAYFORM21 The i-th expectation in Eq. (9) can be derived as follows: DISPLAYFORM22 and the equality occurs if DISPLAYFORM23 = 1 almost everywhere or equivalently for almost every x except for those in a zero measure set, we have: DISPLAYFORM24 Therefore, we obtain the following inequality: DISPLAYFORM25 and the equality occurs if for almost every x except for those in a zero measure set, we have: DISPLAYFORM26 and we peak the minimum if p G k = q k , ∀k since this solution satisfies both DISPLAYFORM27 and the conditions depicted in Eq. (10). That concludes our proof.C APPENDIX: ADDITIONAL EXPERIMENTS DISPLAYFORM28 The true data is sampled from a 2D mixture of 8 Gaussian distributions with a covariance matrix 0.02I and means arranged in a circle of zero centroid and radius 2.0. We use a simple architecture of 8 generators with two fully connected hidden layers and a classifier and a discriminator with one shared hidden layer. All hidden layers contain the same number of 128 ReLU units. The input layer of generators contains 256 noise units sampled from isotropic multivariate Gaussian distribution N (0, I). We do not use batch normalization in any layer. We refer to Tab. 3 for more specifications of the network and hyperparameters. ""Shared"" is short for parameter sharing among generators or between the classifier and the discriminator . Feature maps of 8/1 in the last layer for C and D means that two separate fully connected layers are applied to the penultimate layer, one for C that outputs 8 logits and another for D that outputs 1 logit. Optimizer Adam(β 1 = 0.5, β 2 = 0.999) Weight, bias initialization N (µ = 0, σ = 0.02I), 0The effect of the number of generators on generated samples. Fig. 6 shows samples produced by MGANs with different numbers of generators trained on synthetic data for 25,000 epochs . The model with 1 generator behaves similarly to the standard GAN as expected. The models with 2, 3 and 4 generators all successfully cover 8 modes, but the ones with more generators draw fewer points scattered between adjacent modes. Finally, the model with 10 generators also covers 8 modes wherein 2 generators share one mode and one generator hovering around another mode. Figure 6: Samples generated by MGAN models trained on synthetic data with 2, 3, 4 and 10 generators. Data samples from the 8 Gaussians are in red, and generated data by each generator are in a different color.The effect of β on generated samples. To examine the behavior of the diversity coefficient β, Fig. 7 compares samples produced by our MGAN with 4 generators after 25,000 epochs of training with different values of β. Without the JSD force (β = 0), generated samples cluster around one mode. When β = 0.25, generated data clusters near 4 different modes. When β = 0.75 or 1.0, the JSD force is too strong and causes the generators to collapse, generating 4 increasingly tight clusters. When β = 0.5, generators successfully cover all of the 8 modes. DISPLAYFORM29 Figure 7: Samples generated by MGAN models trained on synthetic data with different values of diversity coefficient β. Generated data are in blue and data samples from the 8 Gaussians are in red.","propose paper new approach train Generative Adversarial Nets GANs mixture generators overcome mode collapsing problem. main intuition is to employ multiple generators instead using single one original GAN. idea is simple yet proven extremely effective covering diverse data modes easily overcoming mode collapsing problem delivering state-of-the-art results. minimax formulation was able establish among classifier discriminator set generators similar spirit GAN. Generators create samples are intended come distribution training data whilst discriminator determines whether samples are true data generated generators classifier specifies which generator sample comes from. distinguishing feature is that internal samples are created multiple generators one will be randomly selected final output similar mechanism probabilistic mixture model. term method Mixture Generative Adversarial Nets MGAN develop theoretical analysis prove equilibrium Jensen-Shannon divergence JSD mixture generators distributions empirical data distribution is minimal whilst JSD among generators distributions is maximal hence effectively avoiding mode collapsing problem. utilizing parameter sharing proposed model adds minimal computational cost standard GAN thus can also efficiently scale large-scale datasets. conduct extensive experiments synthetic 2D data natural image databases CIFAR-10 STL-10 ImageNet demonstrate superior performance MGAN achieving state-of-the-art Inception scores latest baselines generating diverse appealing recognizable objects different resolutions specializing capturing different types objects generators. Generative Adversarial Nets GANs BID10 are a recent novel class deep generative models are successfully applied large variety applications image video generation image inpainting semantic segmentation image-to-image translation text-to-image synthesis name BID9. game theory metaphor model consists discriminator generator playing two-player minimax game wherein generator aims generate samples resemble training data whilst discriminator tries distinguish two narrated BID10. Training GAN however is challenging can be easily trapped mode collapsing problem where the generator concentrates producing samples lying modes instead whole data space BID9.Many GAN variants have been recently proposed address problem. can be grouped two main categories:training either single generator many generators. Methods former include modifying discriminator's objective Salimansetal. 2016;BID22 modifying generator's objective Warde-Farley Bengio 2016 employing additional discriminators yield useful gradient signals generators Nguyenetal. 2017;BID7. common theme variants is that generators are shown equilibrium able recover data distribution convergence remains elusive practice. experiments are conducted toy datasets narrow-domain datasets LSUN Yuetal. 2015 CelebA BID20. knowledge Warde-Farley Bengio 2016 Nguyenetal. 2017 perform quantitative evaluation models trained much diverse datasets STL-10 Coatesetal. 2011 ImageNet Russakovskyetal. 2015.Given current limitations training single-generator GANs recent attempts have been made following multi-generator approach. Tolstikhinetal. 2017 apply boosting techniques train mixture generators sequentially training adding new generators mixture. However sequentially training many generators is computational expensive. Moreover approach is built implicit assumption single-generator GAN can generate good images modes reweighing training data incrementally training new generators will result mixture covers whole data space. assumption is not true practice since current single-generator GANs trained diverse datasets ImageNet tend generate images unrecognizable objects. BID2 train mixture generators discriminators optimize minimax game reward function weighted average reward function pair generator discriminator. model is computationally expensive lacks mechanism enforce divergence among generators. BID8 train many generators using multi-class discriminator addition detecting whether data sample is fake predicts which generator produces sample. objective function model punishes generators generating samples are detected fake does not directly encourage generators specialize generating different types data.We propose paper novel approach train mixture generators. Unlike aforementioned multi-generator GANs proposed model simultaneously trains set generators objective mixture induced distributions would approximate data distribution whilst encouraging specialize different data modes. result is a novel adversarial architecture formulated minimax game among three parties:classifier discriminator set generators. Generators create samples are intended come distribution training data whilst discriminator determines whether samples are true data generated generators classifier specifies which generator sample comes from. term proposed model Mixture Generative Adversarial Nets MGAN provide analysis model is optimized towards minimizing Jensen-Shannon Divergence JSD mixture distributions induced generators data distribution maximizing JSD among generators.Empirically proposed model can be trained efficiently utilizing parameter sharing among generators classifier discriminator. addition simultaneously training many generators enforcing JSD among generators helps focus modes data space learn better. Trained CIFAR-10 generator learned specialize generating samples different class horse car ship dog bird airplane. Overall models trained CIFAR-10 STL-10 ImageNet datasets successfully generated diverse recognizable objects achieved state-of-the-art Inception scores Salimansetal. 2016 model trained CIFAR-10 even outperformed GANs trained semi-supervised fashion Salimansetal. 2016;Odenaetal. 2016.In short main contributions are:novel adversarial model efficiently train mixture generators enforcing JSD among generators;ii theoretical analysis objective function is optimized towards minimizing JSD mixture generators' distributions real data distribution maximizing JSD among generators;iii comprehensive evaluation performance method synthetic real-world large-scale datasets diverse natural scenes. have presented novel adversarial model address mode collapse GANs. idea is to approximate data distribution using mixture multiple distributions wherein distribution captures subset data modes separately others. achieve goal propose minimax game one discriminator one classifier many generators formulate optimization problem minimizes JSD P data P model.e mixture distributions induced generators whilst maximizes JSD among generator distributions. helps model generate diverse images better cover data modes thus effectively avoids mode collapse. term proposed model Mixture Generative Adversarial Network MGAN.The MGAN can be efficiently trained sharing parameters discriminator classifier among generators thus model is scalable evaluated real-world largescale datasets. Comprehensive experiments synthetic 2D data CIFAR-10 STL-10 ImageNet databases demonstrate following capabilities model:achieving state-of-the-art Inception scores;ii generating diverse appealing recognizable objects different resolutions;iv specializing capturing different types objects generators. proposed method generatorsG1 G2...GK are deep convolutional neural networks parameterized θG. networks share parameters layers except input layers. input layer generatorGk is parameterized mappingfθG k z maps sampled noisez first hidden layer activation h. shared layers are parameterized mappinggθG h maps first hidden layer generated data. pseudo-code sampling mixture is described Alg. 1. ClassifierC classifier are also deep convolutional neural networks are both parameterized θCD. share parameters layers except last layer. pseudo-code alternatively learningθG θ CD using stochastic gradient descend is described Alg. 2.Algorithm 1 Sampling MGAN's mixture generators. 1:Sample noisez priorPz. 2:Sample generator indexu Mult π1 π2... πK predefined mixing probabilityπ π1 π2... πK DISPLAYFORM0 Return generated data x index u.Algorithm 2 Alternative training MGAN using stochastic gradient descent.1 number training iterations do2:Sample minibatch data points DISPLAYFORM1 Sample minibatch N generated data points N indices u1 u2... uN current mixture. DISPLAYFORM24:DISPLAYFORM35:DISPLAYFORM4 Update classifierC discriminator descending along gradient:DISPLAYFORM5 Sample minibatch N generated data points N indices u1 u2... uN current mixture. DISPLAYFORM68:DISPLAYFORM7 Update mixture generatorsG ascending along gradient:∇θGL G. 10:end B APPENDIX:PROOFS SECTION 3.1 Proposition1 FIG0. fixed generatorsG1 G2... GK mixture weightsπ1 π2... πK optimal classifierC* C*1:K discriminator * J G C are:DISPLAYFORM8 Proof. optimal * was proved Prop. 1 BID9. section shows similar proof optimal C * Assuming C* can be optimized functional space can calculate functional derivatives J G C respect Ck x k∈ 2... K set equal zero:DISPLAYFORM9 Setting DISPLAYFORM10 0 k∈ 2... K get:DISPLAYFORM11 DISPLAYFORM12 results Eq. 6 due fact DISPLAYFORM13 Reformulation L G1:K Replacing optimalC* * Eq. 2 can reformulate objective function generator follows:DISPLAYFORM14 sum first two terms Eq. FORMULA29 was shown BID10 2 · JSD P data P model − log4. last termβ * Eq. FORMULA29 is related JSD K distributions:DISPLAYFORM15 whereH P is the Shannon entropy distributionP. Thus L G1:K can be rewritten as:DISPLAYFORM16 Theorem3 Thm. 3 restated If the data distribution has the form:DISPLAYFORM17 where the mixture componentsqk x are well-separated minimax problem Eq. 2 optimization problem Eq. 3 has the following solution:DISPLAYFORM18 corresponding objective value optimization problem Eq. 3 DISPLAYFORM19 Proof. first recap optimization problem finding optimal G * DISPLAYFORM20 JSD Eq. FORMULA30 is given by:DISPLAYFORM21 i-th expectation Eq. 9 can be derived follows:DISPLAYFORM22 equality occurs if DISPLAYFORM23 1 almost everywhere equivalently almost every x except zero measure set have:DISPLAYFORM24 Therefore obtain following inequality:DISPLAYFORM25 equality occurs if for almost every x except zero measure set have:DISPLAYFORM26 peak minimum ifpGk qk ∀k since solution satisfies DISPLAYFORM27 conditions depicted Eq. 10 concludes proof.C APPENDIX:ADDITIONAL EXPERIMENTS DISPLAYFORM28 true data is sampled 2D mixture 8 Gaussian distributions covariance matrix 0.02I means arranged circle zero centroid radius 2.0 do not use simple architecture 8 generators two fully connected hidden layers classifier discriminator one shared hidden layer. hidden layers contain number 128 ReLU units. input layer generators contains 256 noise units sampled isotropic multivariate Gaussian distribution N 0 do not use batch normalization layer. refer Tab. 3 specifications network hyperparameters. Shared is short parameter sharing among generators classifier discriminator. Feature maps 8/1 last layer C means two separate fully connected layers are applied penultimate layer one C outputs 8 logits another outputs 1 logit. Optimizer Adam β1 0.5 β2 0.999 Weight bias initializationN µ 0 σ 0.02I 0The effect number generators generated samples. Fig. 6 shows samples produced MGANs different numbers generators trained synthetic data 25,000 epochs. model 1 generator behaves similarly standard GAN expected. models 2 3 4 generators successfully cover 8 modes ones generators draw fewer points scattered adjacent modes. Finally model 10 generators also covers 8 modes wherein2 generators share one mode one generator hovering around another mode. Figure6:Samples generated MGAN models trained synthetic data 2 3 4 10 generators. Data samples 8 Gaussians are in red generated data generator are in a different color.The effect β generated samples. examine behavior diversity coefficientβ Fig. 7 compares samples produced MGAN 4 generators 25,000 epochs training different values β. Without JSD force β 0 generated samples cluster around one mode. Whenβ 0.25 generated data clusters near 4 different modes. Whenβ 0.75 1.0 JSD force is too strong causes generators collapse generating 4 increasingly tight clusters. Whenβ 0.5 generators successfully cover 8 modes. DISPLAYFORM29 Figure7:Samples generated MGAN models trained synthetic data different values diversity coefficientβ. Generated data are in blue data samples 8 Gaussians are in red.",3329,2311,1018,0.055,1.441,2025/11/05 17:18:55,0.02,1.432,0.3457943925233644,1062.378
"Allowing humans to interactively train artificial agents to understand language instructions is desirable for both practical and scientific reasons.   Though, given  the lack of sample efficiency in current learning methods, reaching this goal may require substantial research efforts. We introduce the BabyAI research platform, with the goal of supporting investigations towards including humans in the loop for grounded language learning. The BabyAI platform comprises an extensible suite of 19 levels of increasing difficulty. Each level gradually leads the agent towards acquiring a combinatorially rich synthetic language, which is a proper subset of English. The platform also provides a hand-crafted bot agent, which simulates a human teacher.   We report estimated amount of supervision required for training neural reinforcement and behavioral-cloning agents on some BabyAI levels. We put forward strong evidence that current deep learning methods are not yet sufficiently sample-efficient in the context of learning a language with compositional properties. How can a human train an intelligent agent to understand natural language instructions? We believe that this research question is important from both technological and scientific perspectives. No matter how advanced AI technology becomes, human users will likely want to customize their intelligent helpers to better understand their desires and needs. On the other hand, developmental psychology, cognitive science and linguistics study similar questions but applied to human children, and a synergy is possible between research in grounded language learning by computers and research in human language acquisition.In this work, we present the BabyAI research platform, whose purpose is to facilitate research on grounded language learning. In our platform we substitute a simulated human expert for a real human; yet our aspiration is that BabyAI-based studies enable substantial progress towards putting an actual human in the loop. The current domain of BabyAI is a 2D gridworld in which synthetic natural-looking instructions (e.g. ""put the red ball next to the box on your left"") require the agent to navigate the world (including unlocking doors) and move objects to specified locations. BabyAI improves upon similar prior setups BID16 BID7 BID41 by supporting simulation of certain essential aspects of the future human in the loop agent training: curriculum learning and interactive teaching. The usefulness of curriculum learning for training machine learning models has been demonstrated numerous times in the literature BID6 BID23 BID42 BID15 , and we believe that gradually increasing the difficulty of the task will likely be essential for achieving efficient humanmachine teaching, as in the case of human-human teaching. To facilitate curriculum learning studies, BabyAI currently features 19 levels in which the difficulty of the environment configuration and the complexity of the instruction language are gradually increased. Interactive teaching, i.e. teaching differently based on what the learner can currently achieve, is another key capability of human teachers. Many advanced agent training methods, including DAGGER BID28 , TAMER BID35 and learning from human preferences BID38 BID11 , assume that interaction between the learner and the teacher is possible. To support interactive experiments, BabyAI provides a bot agent that can be used to generate new demonstrations on the fly and advise the learner on how to continue acting.Arguably, the main obstacle to language learning with a human in the loop is the amount of data (and thus human-machine interactions) that would be required. Deep learning methods that are used in the context of imitation learning or reinforcement learning paradigms have been shown to be very effective in both simulated language learning settings BID25 BID16 and applications BID32 BID3 BID39 . These methods, however, require enormous amounts of data, either in terms of millions of reward function queries or hundreds of thousands of demonstrations. To show how our BabyAI platform can be used for sample efficiency research, we perform several case studies. In particular, we estimate the number of demonstrations/episodes required to solve several levels with imitation and reinforcement learning baselines. As a first step towards improving sample efficiency, we additionally investigate to which extent pretraining and interactive imitation learning can improve sample efficiency.The concrete contributions of this paper are two-fold. First, we contribute the BabyAI research platform for learning to perform language instructions with a simulated human in the loop. The platform already contains 19 levels and can easily be extended. Second, we establish baseline results for all levels and report sample efficiency results for a number of learning approaches. The platform and pretrained models are available online. We hope that BabyAI will spur further research towards improving sample efficiency of grounded language learning, ultimately allowing human-in-the-loop training. We present the BabyAI research platform to study language learning with a human in the loop. The platform includes 19 levels of increasing difficulty, based on a decomposition of tasks into a set of basic competencies. Solving the levels requires understanding the Baby Language, a subset of English with a formally defined grammar which exhibits compositional properties. The language is minimalistic and the levels seem simple, but empirically we have found them quite challenging to solve. The platform is open source and extensible, meaning new levels and language concepts can be integrated easily.The results in Section 4 suggest that current imitation learning and reinforcement learning methods scale and generalize poorly when it comes to learning tasks with a compositional structure. Hundreds of thousands of demonstrations are needed to learn tasks which seem trivial by human standards. Methods such as curriculum learning and interactive learning can provide measurable improvements in terms of sample efficiency, but, in order for learning with an actual human in the loop to become realistic, an improvement of at least three orders of magnitude is required.An obvious direction of future research to find strategies to improve sample efficiency of language learning. Tackling this challenge will likely require new models and new teaching methods. Approaches that involve an explicit notion of modularity and subroutines, such as Neural Module Networks BID1 or Neural Programmer-Interpreters BID27 , seem like a promising direction. It is our hope that the BabyAI platform can serve as a challenge and a benchmark for the sample efficiency of language learning for years to come.",Allowing humans interactively train artificial agents understand language instructions is desirable practical scientific reasons. Though given lack sample efficiency current learning methods reaching goal may require substantial research efforts. introduce BabyAI research platform goal supporting investigations towards including humans loop grounded language learning. BabyAI platform comprises extensible suite 19 levels increasing difficulty. level gradually leads agent towards acquiring combinatorially rich synthetic language which is a proper subset English. platform also provides hand-crafted bot agent which simulates human teacher. report estimated amount supervision required training neural reinforcement behavioral-cloning agents BabyAI levels. put forward strong evidence current deep learning methods are not yet sufficiently sample-efficient context learning language compositional properties. How can a human train intelligent agent understand natural language instructions? believe research question is important technological scientific perspectives. matter how advanced AI technology becomes human users will likely want customize intelligent helpers better understand desires needs. hand developmental psychology cognitive science linguistics study similar questions applied human children synergy is possible research grounded language learning computers research human language acquisition.In work present BabyAI research platform whose purpose is to facilitate research grounded language learning. platform substitute simulated human expert real human;yet aspiration is that BabyAI-based studies enable substantial progress towards putting actual human loop. current domain BabyAI is a 2D gridworld which synthetic natural-looking instructions e.g put red ball next box left require agent navigate world including unlocking doors move objects specified locations. BabyAI improves upon similar prior setups BID16 BID7 BID41 supporting simulation certain essential aspects future human loop agent training:curriculum learning interactive teaching. usefulness curriculum learning training machine learning models has been demonstrated numerous times literature BID6 BID23 BID42 BID15 believe gradually increasing difficulty task will likely essential achieving efficient humanmachine teaching case human-human teaching. facilitate curriculum learning studies BabyAI currently features19 levels which the difficulty environment configuration complexity instruction language are gradually increased. Interactive teaching.e teaching differently based what the learner can currently achieve is another key capability human teachers. Many advanced agent training methods including DAGGER BID28 TAMER BID35 learning human preferences BID38 BID11 assume interaction learner teacher is possible. support interactive experiments BabyAI provides bot agent can be are used generate new demonstrations fly advise learner how to continue acting.Arguably main obstacle language learning human loop is the amount data thus human-machine interactions would required. Deep learning methods can be are used context imitation learning reinforcement learning paradigms have been shown effective simulated language learning settings BID25 BID16 applications BID32 BID3 BID39. methods however require enormous amounts data either terms millions reward function queries hundreds thousands demonstrations. show how our BabyAI platform can be used sample efficiency research perform several case studies. particular estimate number demonstrations/episodes required solve several levels imitation reinforcement learning baselines. first step towards improving sample efficiency additionally investigate which extent pretraining interactive imitation learning can improve sample efficiency.The concrete contributions paper are two-fold two-fold First contribute BabyAI research platform learning perform language instructions simulated human loop. platform already contains19 levels can easily extended. Second establish baseline results levels report sample efficiency results number learning approaches. platform pretrained models are available online. hope BabyAI will spur research towards improving sample efficiency grounded language learning ultimately allowing human-in-the-loop training. present BabyAI research platform study language learning human loop. platform includes 19 levels increasing difficulty based decomposition tasks set basic competencies. Solving levels requires understanding Baby Language subset English formally defined grammar which exhibits compositional properties. language is minimalistic levels seem simple empirically have found quite challenging solve. platform is open source extensible meaning new levels language concepts can be integrated easily.The results Section 4 suggest current imitation learning reinforcement learning methods scale generalize poorly when it comes learning tasks compositional structure. Hundreds thousands demonstrations are needed learn tasks which seem trivial human standards. Methods curriculum learning interactive learning can provide measurable improvements terms sample efficiency order learning actual human loop become realistic improvement least three orders magnitude is required.An obvious direction future research find strategies improve sample efficiency language learning. Tackling challenge will likely require new models new teaching methods. Approaches involve explicit notion modularity subroutines Neural Module Networks BID1 Neural Programmer-Interpreters BID27 seem like promising direction. is our hope BabyAI platform can serve challenge benchmark sample efficiency language learning years come.,1185,836,349,0.013,1.417,2025/11/05 17:18:55,0.01,1.477,0.2710280373831775,363.649
"Recently, there has been growing interest in methods that perform neural network compression, namely techniques that attempt to substantially reduce the size of a neural network without significant reduction in performance. However, most existing methods are post-processing approaches in that they take a learned neural network as input and output a compressed network by either forcing several parameters to take the same value (parameter tying via quantization) or pruning irrelevant edges (pruning) or both. In this paper, we propose a novel algorithm that jointly learns and compresses a neural network. The key idea in our approach is to change the optimization criteria by adding $k$ independent Gaussian priors over the parameters and a sparsity penalty. We show that our approach is easy to implement using existing neural network libraries, generalizes L1 and L2 regularization and elegantly enforces parameter tying as well as pruning constraints. Experimentally, we demonstrate that our new algorithm yields state-of-the-art compression on several standard benchmarks with minimal loss in accuracy while requiring little to no hyperparameter tuning as compared with related, competing approaches. Neural networks represent a family of highly flexible and scalable models that have rapidly achieved state-of-the-art performance in diverse domains including computer vision BID18 BID8 BID14 , speech BID5 , and sentiment analysis BID10 . Despite their successes, the storage requirements of large, modern neural networks make them impractical for certain applications with storage limitations (e.g., mobile devices). Moreover, as they are often trained on small datasets compared to their number of parameters (typically in the millions for state-of-the-art models), they can potentially overfit. In recent work, BID6 showed that a large proportion of neural network parameters are in fact not required for their generalization performance, and interest in model compression has surged.A variety of methods have been proposed to perform compression including pruning BID20 BID12 , quantization BID13 , lowrank approximation BID6 BID7 BID16 , group lasso BID27 , variational dropout BID23 , teacher-student training BID25 , etc. Here, we focus on the quantization/parameter tying approach to compression combined with pruning. Parameter tying assumptions occur naturally in the construction of convolutional neural networks (CNNs), but in these applications, the parameters to be tied are usually selected in advance of training. Recent work has focused on automatic parameter tying, i.e., automatically discovering which parameters of the model should be tied together. BID24 proposed a soft parameter tying scheme based on a mixtures of Gaussians prior and suggested a gradient descent method to jointly optimize both the weights in the network and the parameters of the mixture model. proposed a random parameter tying scheme based on hashing functions. BID13 proposed a compression pipeline that involved thresholding to prune low-magnitude parameters, k-means clustering to tie parameters layer-wise, and a final retraining stage to fine-tune tied parameters. This work demonstrated that high compression rates are achievable without much loss in accuracy. Building on the work of BID24 , K. Ullrich (2017) imposed a Gaussian mixture prior on the parameters to encourage clustering. At convergence, they proposed clustering the weights by assigning them to the mixture component that generates each weight with highest probability. BID22 proposed a full Bayesian approach to compression using scale mixture priors. This approach has the advantage that posterior distributions can be used to estimate the significance of individual bits in the learned weights. BID22 demonstrated that this approach can yield state-of-the-art compression results for some problems. BID1 recently proposed a soft-to-hard quantization approach in which scalar quantization is gradually learned through annealing a softened version of quantization distortion; compression is achieved with low-entropy parameter distribution instead of pruning.While much of the previous work has demonstrated that significant compression can be achieved while preserving the accuracy of the final network (in many cases ≈ 1% loss in accuracy), many of these approaches have potential drawbacks that can limit their applications. The Gaussian mixture approach of BID24 and K. Ullrich (2017) can be computationally expensive, as the time and memory requirements for backpropagation is increased K-fold under a K-component GMM prior, in addition to its large number of sensitive hyperparameters that can require extensive tuning. Moreover, the GMM objective itself suffers from well known local (and often pathological) minima issues. These local minimas are in addition to the ones encountered while training a neural network which in turn incurs high computational cost. The approach of BID13 uses separate pruning and parameter tying stages, which potentially limits its compression efficiency; additionally, the required layer-wise codebook storage can become expensive especially for deep networks. The parameter tying approach of is also only applied layerwise, and it typically requires more clusters, i.e., larger K, before the random weight sharing is effective (our experiments confirm that random parameter tying yields poor results when the number of distinct parameters is too small). The soft-to-hard quantization approach of BID1 resembles our method, but is essentially probabilistic like the GMM prior as it uses soft assignment for quantization which can be expensive. Finally, the full Bayesian approach, similar to the GMM approach, has a number of additional parameters to tune (e.g., constraints on variances, careful initialization of each of the variational parameters, etc.). The Bayesian approach also requires sampling for prediction (which can be done deterministically but with some additional loss). We hope to argue that such sophisticated methods may not be necessary to achieve good compression in practice.The approach to compression in this work uses quantization and sparsity inducing priors. For quantization, we consider an independent Gaussian prior, that is, each parameter is non-probabilistically assigned to one of K independent Gaussian distributions, and the prior penalizes each weight by its 2 distance to the mean of its respective Gaussian. This prior places no restriction on which weights can be tied together (e.g., weights from the input could be tied to weights into the output), reduces the number of hyperparameters that need to be tuned compared to probabilistic methods like Gaussian mixtures, and requires only a small change to the typical gradient descent updates with only linear time and memory overhead. We observe that quantization alone is not enough to achieve the desired level of compression, and introduce pruning by adding a standard 1 penalty on top of the quantization prior; we demonstrate experimentally that the combined prior yields state-of-the-art compression results on standard benchmark data sets.","Recently has been growing interest methods perform neural network compression namely techniques attempt substantially reduce size neural network without significant reduction performance. However existing methods are post-processing approaches take learned neural network input output compressed network either forcing several parameters take value parameter tying via quantization pruning irrelevant edges pruning both. paper propose novel algorithm jointly learns compresses neural network. key idea approach is to change optimization criteria adding $k independent Gaussian priors parameters sparsity penalty. show approach is easy implement using existing neural network libraries generalizesL1 L2 regularization elegantly enforces parameter tying well pruning constraints. Experimentally demonstrate new algorithm yields state-of-the-art compression several standard benchmarks minimal loss accuracy requiring little hyperparameter tuning compared related competing approaches. Neural networks represent family highly flexible scalable models have rapidly achieved state-of-the-art performance diverse domains including computer vision BID18 BID8 BID14 speech BID5 sentiment analysis BID10. Despite successes storage requirements large modern neural networks make impractical certain applications storage limitations e.g mobile devices Moreover are often trained small datasets compared number parameters typically millions state-of-the-art models can potentially overfit. recent work BID6 showed large proportion neural network parameters are in fact required generalization performance interest model compression has surged.A variety methods have been proposed perform compression including pruning BID20 BID12 quantization BID13 lowrank approximation BID6 BID7 BID16 group lasso BID27 variational dropout BID23 teacher-student training BID25 etc. focus quantization/parameter tying approach compression combined pruning. Parameter tying assumptions occur naturally construction convolutional neural networks CNNs applications parameters tied are usually selected advance training. Recent work has focused automatic parameter tying.e automatically discovering which parameters model should be tied together. BID24 proposed soft parameter tying scheme based mixtures Gaussians prior suggested gradient descent method jointly optimize weights network parameters mixture model. proposed random parameter tying scheme based hashing functions. BID13 proposed compression pipeline involved thresholding prune low-magnitude parameters k-means clustering tie parameters layer-wise final retraining stage fine-tune tied parameters. work demonstrated high compression rates are achievable without much loss accuracy. Building work BID24 K. Ullrich 2017 imposed Gaussian mixture prior parameters encourage clustering. convergence proposed clustering weights assigning mixture component generates weight highest probability. BID22 proposed full Bayesian approach compression using scale mixture priors. approach has the advantage posterior distributions can be used estimate significance individual bits learned weights. BID22 demonstrated approach can yield state-of-the-art compression results problems. BID1 recently proposed soft-to-hard quantization approach which scalar quantization is gradually learned annealing softened version quantization distortion;compression is achieved low-entropy parameter distribution instead pruning.While much previous work has demonstrated significant compression can be achieved preserving accuracy final network many cases≈1% loss accuracy many approaches have potential drawbacks can limit applications. Gaussian mixture approach BID24 K. Ullrich 2017 can be computationally expensive time memory requirements backpropagation is increased K-fold K-component GMM prior addition large number sensitive hyperparameters can require extensive tuning. Moreover GMM objective suffers well known local often pathological minima issues. local minimas are in addition ones encountered training neural network which in turn incurs high computational cost. approach BID13 uses separate pruning parameter tying stages which potentially limits compression efficiency;additionally required layer-wise codebook storage can become expensive especially deep networks. parameter tying approach is also applied layerwise typically requires clusters.e largerK random weight sharing is effective experiments confirm random parameter tying yields poor results when the number distinct parameters is too small soft-to-hard quantization approach BID1 resembles method is essentially probabilistic like GMM prior uses soft assignment quantization which can be expensive. Finally full Bayesian approach similar GMM approach has a number additional parameters tune e.g constraints variances careful initialization variational parameters etc. Bayesian approach also requires sampling prediction which can be done deterministically additional loss hope argue sophisticated methods may necessary achieve good compression practice.The approach compression work uses quantization sparsity inducing priors. quantization consider independent Gaussian prior is,parameter is non-probabilistically assigned one K independent Gaussian distributions prior penalizes weight 2 distance mean respective Gaussian. prior places restriction which weights can be tied together e.g weights input could tied weights output reduces number hyperparameters need tuned compared probabilistic methods like Gaussian mixtures requires small change typical gradient descent updates linear time memory overhead. observe quantization alone is not enough achieve desired level compression introduce pruning adding standard 1 penalty top quantization prior;demonstrate experimentally combined prior yields state-of-the-art compression results standard benchmark data sets.",1290,896,394,0.013,1.44,2025/11/05 17:18:55,0.01,1.467,0.3426791277258563,407.867
"The application of stochastic variance reduction to optimization has shown remarkable recent theoretical and practical success. The applicability of these techniques to the hard non-convex optimization problems encountered during training of modern deep neural networks is an open problem. We show that naive application of the SVRG technique and related approaches fail, and explore why. Stochastic variance reduction (SVR) consists of a collection of techniques for the minimization of finite-sum problems: DISPLAYFORM0 such as those encountered in empirical risk minimization, where each f i is the loss on a single training data point. Principle techniques include SVRG BID15 , SAGA BID7 , and their variants. SVR methods use control variates to reduce the variance of the traditional stochastic gradient descent (SGD) estimate f i (w) of the full gradient f (w). Control variates are a classical technique for reducing the variance of a stochastic quantity without introducing bias. Say we have some random variable X. Although we could use X as an estimate of E[X] =X, we can often do better through the use of a control variate Y . If Y is a random variable correlated with X (i.e. Cov[X, Y ] > 0), then we can estimateX with the quantity Remarkably, these methods are able to achieve linear convergence rates for smooth strongly-convex optimization problems, a significant improvement on the sub-linear rate of SGD. SVR methods are part of a larger class of methods that explicitly exploit finite-sum structures, either by dual (SDCA, BID25 MISO, Mairal, 2014; Finito, Defazio et al., 2014b) or primal (SAG, Schmidt et al., 2017) approaches. DISPLAYFORM1 Recent work has seen the fusion of acceleration with variance reduction BID26 ; BID21 ; BID6 ; BID1 ), and the extension of SVR approaches to general non-convex BID2 BID23 as well as saddle point problems BID3 .In this work we study the behavior of variance reduction methods on a prototypical non-convex problem in machine learning: A deep convolutional neural network designed for image classification. We discuss in Section 2 how standard training and modeling techniques significantly complicate the application of variance reduction methods in practice, and how to overcome some of these issues. In Sections 3 & 5 we study empirically the amount of variance reduction seen in practice on modern CNN architectures, and we quantify the properties of the network that affect the amount of variance reduction. In Sections 6 & 7 we show that streaming variants of SVRG do not improve over regular SVRG despite their theoretical ability to handle data augmentation. In Section 8 we study properties of DNN problems that actually give stochastic gradient descent an advantage over variance reduction techniques. The negative results presented here are disheartening, however we don't believe that they rule out the use of stochastic variance reduction on deep learning problems. Rather, they suggest avenues for further research. For instance, SVR can be applied adaptively; or on a meta level to learning rates; or scaling matrices; and can potentially be combined with methods like Adagrad BID9 and ADAM BID17 to yield hybrid methods.",application stochastic variance reduction optimization has shown remarkable recent theoretical practical success. applicability techniques hard non-convex optimization problems encountered training modern deep neural networks is an open problem. show naive application SVRG technique related approaches fail explore why. Stochastic variance reduction SVR consists collection techniques minimization finite-sum problems:DISPLAYFORM0 encountered empirical risk minimization where eachf is the loss single training data point. Principle techniques include SVRG BID15 SAGA BID7 variants. SVR methods use control variates reduce variance traditional stochastic gradient descent SGD estimatef w full gradientf w Control variates are a classical technique reducing variance stochastic quantity without introducing bias. Say have some random variableX. Although could useX estimate E X =X can often do better use control variate Y. If Y is a random variable correlated X.e Cov X 0 can estimateX quantity Remarkably methods are able achieve linear convergence rates smooth strongly-convex optimization problems significant improvement sub-linear rate SGD. SVR methods are part larger class methods explicitly exploit finite-sum structures either dual SDCA BID25 MISO Mairal 2014;Finito Defazioetal. 2014b primal SAG Schmidtetal. 2017 approaches. DISPLAYFORM1 Recent work has seen fusion acceleration variance reduction BID26;BID21;BID6;BID1 extension SVR approaches general non-convex BID2 BID23 well saddle point problems BID3.In work study behavior variance reduction methods prototypical non-convex problem machine learning:deep convolutional neural network designed image classification. discuss Section2 how standard training modeling techniques significantly complicate application variance reduction methods practice how to overcome issues. Sections3 5 study empirically amount variance reduction seen practice modern CNN architectures quantify properties network affect amount variance reduction. Sections6 7 show streaming variants SVRG do not improve regular SVRG despite theoretical ability handle data augmentation. Section8 study properties DNN problems actually give stochastic gradient descent advantage variance reduction techniques. negative results presented are disheartening however believe rule use stochastic variance reduction deep learning problems. Rather suggest avenues research. instance SVR can be applied adaptively;meta level learning rates;scaling matrices;can potentially combined methods like Adagrad BID9 ADAM BID17 yield hybrid methods.,653,456,197,0.006,1.432,2025/11/05 17:18:55,0.0,1.579,0.317757009345794,218.049
"The ground-breaking performance obtained by deep convolutional neural networks (CNNs) for image processing tasks is inspiring research efforts attempting to extend it for 3D geometric tasks. One of the main challenge in applying CNNs to 3D shape analysis is how to define a natural convolution operator on non-euclidean surfaces. In this paper, we present a method for applying deep learning to 3D surfaces using their spherical descriptors and alt-az anisotropic convolution on 2-sphere. A cascade set of geodesic disk filters rotate on the 2-sphere and collect spherical patterns and so to extract geometric features for various 3D shape analysis tasks. We demonstrate theoretically and experimentally that our proposed method has the possibility to bridge the gap between 2D images and 3D shapes with the desired rotation equivariance/invariance, and its effectiveness is evaluated in applications of non-rigid/ rigid shape classification and shape retrieval. A recent research effort in computer vision and geometric processing communities is towards replicating the incredible success of deep convolutional neural networks (CNNs) from the image analysis to 3D shape analysis. A straightforward extension is to treat a 3D shape as a voxel grid BID38 ; BID16 ; BID30 ; BID36 ; BID22 . ) Alternative methods include encoding a 3D shape as a collection of 2D renderings from multiple cameras BID20 ; BID31 ; ,) or projecting a 3D object onto geometric entities which can be flattened as 2D images BID27 ; BID4 ; BID25 . ) All these methods convert a 3D shape into an Euclidean grid structure which supports shift (translational) equivariance/invariance, such that conventional CNNs can work out-of-the box.Although embedded in R 3 , 3D shapes are typically represented as manifold surfaces. Recent research has particularly focused on convolutional networks for non-Euclidean domains such as manifolds or graphs. One of the main difficulties of adopting CNNs and similar methods in these nonEuclidean domains is the lack of shift-invariance on surfaces or graphs BID15 . ) Our motivation comes from the representation of 3D shapes as functions on spheres. We transfer the problem of manifold surface convolution into spherical convolution with the primary benefit of rotation invariance. Although shift-invariance is hard to achieve on general surfaces, by replacing filter translations with filter rotations, rotation equivariance/invariance can be obtained on the 2-sphere. Furthermore, spherical descriptors of 3D shapes are compact and require a network of lower capacity, compared to voxel or multi-view representations. In this work, we are primarily interested in analyzing 3D geometric data using a specific type of spherical convolution either for classification or retrieval tasks. In this paper, we presented and analyzed a convolutional neural network based on alt-az anisotropic spherical convolution operator which is different from the existing types of networks. Numerically, we implemented an efficient algorithm for computing spherical convolution with locally-supported geodesic filters using icosahedron-sphere grid. We demonstrated the efficacy of our approach for non-rigid/ rigid shape classification and retrieval and showed that it compares favorably to competing methods. Furthermore, we have shown that the proposed method can effectively generalize across rotations, and achieve state-of-the-art results on competitive 3D shape recognition tasks, without excessive data augmentation, feature engineering and task-tuning.",ground-breaking performance obtained deep convolutional neural networks CNNs image processing tasks is inspiring research efforts attempting extend 3D geometric tasks. One main challenge applying CNNs 3D shape analysis is how to define natural convolution operator non-euclidean surfaces. paper present method applying deep learning 3D surfaces using spherical descriptors alt-az anisotropic convolution 2-sphere cascade set geodesic disk filters rotate 2-sphere collect spherical patterns extract geometric features various 3D shape analysis tasks. demonstrate theoretically experimentally proposed method has the possibility bridge gap 2D images 3D shapes desired rotation equivariance/invariance effectiveness is evaluated applications non-rigid/rigid shape classification shape retrieval. recent research effort computer vision geometric processing communities is towards replicating incredible success deep convolutional neural networks CNNs image analysis 3D shape analysis. straightforward extension is to treat 3D shape voxel grid BID38;BID16;BID30;BID36;BID22. Alternative methods include encoding 3D shape collection 2D renderings multiple cameras BID20;BID31;projecting 3D object onto geometric entities which can be flattened 2D images BID27;BID4;BID25. methods convert 3D shape Euclidean grid structure which supports shift translational equivariance/invariance conventional CNNs can work out-of-the box.Although embedded R3 3D shapes are typically represented manifold surfaces. Recent research has particularly focused convolutional networks non-Euclidean domains manifolds graphs. One main difficulties adopting CNNs similar methods nonEuclidean domains is the lack shift-invariance surfaces graphs BID15. motivation comes representation 3D shapes functions spheres. transfer problem manifold surface convolution spherical convolution primary benefit rotation invariance. Although shift-invariance is hard achieve general surfaces replacing filter translations filter rotations rotation equivariance/invariance can be obtained 2-sphere Furthermore spherical descriptors 3D shapes are compact require network lower capacity compared voxel multi-view representations. work are primarily interested analyzing 3D geometric data using specific type spherical convolution either classification retrieval tasks. paper presented analyzed convolutional neural network based alt-az anisotropic spherical convolution operator which is different existing types networks. Numerically implemented efficient algorithm computing spherical convolution locally-supported geodesic filters using icosahedron-sphere grid. demonstrated efficacy approach non-rigid/rigid shape classification retrieval showed compares favorably competing methods. Furthermore have shown proposed method can effectively generalize across rotations achieve state-of-the-art results competitive 3D shape recognition tasks without excessive data augmentation feature engineering task-tuning,688,517,171,0.005,1.331,2025/11/05 17:18:55,0.0,1.474,0.0031152647975074,208.851
"Recent breakthroughs in computer vision make use of large deep neural networks, utilizing the substantial speedup offered by GPUs. For applications running on limited hardware, however, high precision real-time processing can still be a challenge.   One approach to solving this problem is training networks with binary or ternary weights, thus removing the need to calculate multiplications and significantly reducing memory size. In this work, we introduce LR-nets (Local reparameterization networks), a new method for training neural networks with discrete weights using stochastic parameters. We show how a simple modification to the local reparameterization trick, previously used to train Gaussian distributed weights, enables the training of discrete weights. Using the proposed training we test both binary and ternary models on MNIST, CIFAR-10 and ImageNet benchmarks and reach state-of-the-art results on most experiments. Deep Neural Networks have been the main driving force behind recent advancement in machine learning, notably in computer vision applications. While deep learning has become the standard approach for many tasks, performing inference on low power and constrained memory hardware is still challenging. This is especially challenging in autonomous driving in electric vehicles where high precision and high throughput constraints are added on top of the low power requirements.One approach for tackling this challenge is by training networks with binary {±1} or ternary {−1, 0, 1} weights BID0 BID15 that require an order of magnitude less memory and no multiplications, leading to significantly faster inference on dedicated hardware. The problem arises when trying to backpropagate errors as the weights are discrete. One heuristic suggested in BID0 is to use stochastic weights w, sample binary weights w b according to w for the forward pass and gradient computation and then update the stochastic weights w instead. Another idea, used by BID5 and BID15 , is to apply a ""straight-through"" estimator ∂sign ∂r = r1[|r| ≤ 1]. While these ideas were able to produce good results, even on reasonably large networks such as ResNet-18 BID4 , there is still a large gap in prediction accuracy between the full-precision network and the discrete networks.In this paper, we attempt to train neural networks with discrete weights using a more principled approach. Instead of trying to find a good ""derivative"" to a non-continuous function, we show how we can find a good smooth approximation and use its derivative to train the network. This is based on the simple observation that if at layer l we have stochastic (independent) weights w (CLT) . This allows us to model the pre-activation using a smooth distribution and use the reparameterization trick BID9 to compute derivatives. The idea of mod-eling the distribution of pre-activation, instead of the distribution of weights, was used in for Gaussian weight distributions where it was called the local reparameterization trick. We show here that with small modifications it can be used to train discrete weights and not just continuous Gaussian distributions. DISPLAYFORM0 Figure 1: The top histogram in each subfigure shows the pre-activation of a random neuron, z l i , which is calculated in a regular feed-forward setting when explicitly sampling the weights. The bottom shows samples from the approximated pre-activation using Lyapunov CLT. (a) refers to the first hidden layer whereas (b) refers to the last. We can see the approximation is very close to the actual pre-activation when sampling weights and performing standard feed-forward. In addition, we see it even holds for the first hidden layer, where the number of elements is not large (in this example, 27 elements for a 3 × 3 × 3 convolution).We experimented with both binary and ternary weights, and while the results on some datasets are quite similar, ternary weights were considerably easier to train. From a modeling perspective restricting weights to binary values {±1} forces each neuron to affect all neurons in the subsequent layer making it hard to learn representations that need to capture several independent features.In this work, we present a novel and simple method for training neural networks with discrete weights. We show experimentally that we can train binary and ternary networks to achieve stateof-the-art results on several datasets, including ResNet-18 on ImageNet, compared to previously proposed binary or ternary training algorithms. On MNIST and CIFAR-10 we can also almost match the performance of the original full-precision network using discrete weights. In this work we presented a simple, novel and effective algorithm to train neural networks with discrete weights. We showed results on various image classification datasets and reached state-ofthe-art results in both the binary and ternary settings on most datasets, paving the way for easier and more efficient training and inference of efficient low-power consuming neural networks.Moreover, comparing binary and ternary networks we advocate further research into ternary weights as a much more reasonable model than binary weights, with a modest computation and memory overhead. Further work into sparse ternary networks might help reduce, or even eliminate, this overhead compared to binary networks.",Recent breakthroughs computer vision make use large deep neural networks utilizing substantial speedup offered GPUs. applications running limited hardware however high precision real-time processing can still challenge. One approach solving problem is is by training networks binary ternary weights thus removing need calculate multiplications significantly reducing memory size. work introduce LR-nets Local reparameterization networks new method training neural networks discrete weights using stochastic parameters. show how a simple modification local reparameterization trick previously used train Gaussian distributed weights enables training discrete weights. Using proposed training test binary ternary models MNIST CIFAR-10 ImageNet benchmarks reach state-of-the-art results experiments. Deep Neural Networks have been the main driving force behind recent advancement machine learning notably computer vision applications. deep learning has become standard approach many tasks performing inference low power constrained memory hardware is still challenging. is especially challenging autonomous driving electric vehicles where high precision high throughput constraints are added top low power requirements.One approach tackling challenge is is by training networks binary ±1 ternary −1 0 1 weights BID0 BID15 require order magnitude less memory multiplications leading significantly faster inference dedicated hardware. problem arises when trying backpropagate errors weights are discrete. One heuristic suggested BID0 is to use stochastic weightsw sample binary weightsw b according w forward pass gradient computation update stochastic weights w instead. Another idea was used BID5 BID15 is to apply straight-through estimator ∂sign∂r r1 |r|≤1 ideas were able produce good results even reasonably large networks ResNet-18 BID4 is still large gap prediction accuracy full-precision network discrete networks.In paper attempt train neural networks discrete weights using principled approach. Instead trying find good derivative non-continuous function show how we can find good smooth approximation use derivative train network. is based simple observation if at layerl have stochastic independent weightsw CLT allowsus model pre-activation using smooth distribution use reparameterization trick BID9 compute derivatives. idea mod-eling distribution pre-activation instead distribution weights was used Gaussian weight distributions where it was called local reparameterization trick. show small modifications can be used train discrete weights continuous Gaussian distributions. DISPLAYFORM0 Figure1:top histogram subfigure shows pre-activation random neuron zl which is calculated regular feed-forward setting when explicitly sampling weights. bottom shows samples approximated pre-activation using Lyapunov CLT. refers first hidden layer whereas b refers last. can see approximation is very close actual pre-activation when sampling weights performing standard feed-forward addition see even holds first hidden layer where the number elements is not large example 27 elements 3×3× 3 convolution.We experimented binary ternary weights results datasets are quite similar ternary weights were considerably easier train. modeling perspective restricting weights binary values ±1 forces neuron affect neurons subsequent layer making hard learn representations need capture several independent features.In work present novel simple method training neural networks discrete weights. show experimentally can train binary ternary networks achieve stateof-the-art results several datasets including ResNet-18 ImageNet compared previously proposed binary ternary training algorithms. MNIST CIFAR-10 can also almost match performance original full-precision network using discrete weights. work presented simple novel effective algorithm train neural networks discrete weights. showed results various image classification datasets reached state-ofthe-art results binary ternary settings datasets paving way easier efficient training inference efficient low-power consuming neural networks.Moreover comparing binary ternary networks advocate research ternary weights much reasonable model binary weights modest computation memory overhead. work sparse ternary networks might help reduce even eliminate overhead compared binary networks.,1021,703,318,0.01,1.452,2025/11/05 17:18:55,0.0,1.471,0.3800623052959498,320.221
"We present Optimal Completion Distillation (OCD), a training procedure for optimizing sequence to sequence models based on edit distance. OCD is efficient, has no hyper-parameters of its own, and does not require pre-training or joint optimization with conditional log-likelihood. Given a partial sequence generated by the model, we first identify the set of optimal suffixes that minimize the total edit distance, using an efficient dynamic programming algorithm.   Then, for each position of the generated sequence, we use a target distribution which puts equal probability on the first token of all the optimal suffixes. OCD achieves the state-of-the-art performance on end-to-end speech recognition, on both Wall Street Journal and Librispeech datasets, achieving $9.3\%$ WER and $4.5\%$ WER, respectively. Recent advances in natural language processing and speech recognition hinge on the development of expressive neural network architectures for sequence to sequence (seq2seq) learning BID54 BID1 . Such encoder-decoder architectures are adopted in both machine translation BID1 BID24 and speech recognition systems BID7 BID2 BID11 achieving impressive performance above traditional multi-stage pipelines BID29 BID41 . Improving the building blocks of seq2seq models can fundamentally advance machine translation and speech recognition, and positively impact other domains such as image captioning BID62 , parsing , summarization BID47 , and program synthesis BID65 .To improve the key components of seq2seq models, one can either design better architectures, or develop better learning algorithms. Recent architectures using convolution BID20 and self attention BID57 have proved to be useful, especially to facilitate efficient training. On the other hand, despite many attempts to mitigate the limitations of Maximum Likelihood Estimation (MLE) BID43 BID60 BID4 BID30 , MLE is still considered the dominant approach for training seq2seq models. Current alternative approaches require pre-training or joint optimization with conditional log-likelihood. They are difficult to implement and require careful tuning of new hyper-parameters (e.g. mixing ratios). In addition , alternative approaches typically do not offer a substantial performance improvement over a well tuned MLE baseline, especially when label smoothing BID40 BID18 and scheduled sampling are used.In this paper, we borrow ideas from search-based structured prediction BID15 BID46 and policy distillation BID48 and develop an efficient algorithm for optimizing seq2seq models based on edit distance 1 . Our key observation is that given an arbitrary prefix (e.g. a partial sequence generated by sampling from the model), we can exactly and efficiently identify all of the suffixes that result in a minimum total edit distance (v.s. the ground truth target). Our training procedure , called Optimal Completion Distillation (OCD), is summarized as follows:The proposed OCD algorithm is efficient, straightforward to implement, and has no tunable hyperparameters of its own. Our key contributions include:• We propose OCD, a stand-alone algorithm for optimizing seq2seq models based on edit distance. OCD is scalable to real-world datasets with long sequences and large vocabularies, and consistently outperforms Maximum Likelihood Estimation (MLE) by a large margin.• Given a target sequence of length m and a generated sequence of length n, we present an O(nm) algorithm that identifies all of the optimal extensions for each prefix of the generated sequence.• We demonstrate the effectiveness of OCD on end-to-end speech recognition using attentionbased seq2seq models. On the Wall Street Journal dataset, OCD achieves a Character Error Rate (CER) of 3.1% and a Word Error Rate (WER) of 9.3% without language model rescoring, outperforming all prior work TAB1 . On Librispeech, OCD achieves state-of-the-art WER of 4.5% on ""test-clean"" and 13.3% on ""test-other"" sets TAB2 ).",present Optimal Completion Distillation OCD training procedure optimizing sequence sequence models based edit distance. OCD is efficient has no hyper-parameters does not require pre-training joint optimization conditional log-likelihood Given partial sequence generated model first identify set optimal suffixes minimize total edit distance using efficient dynamic programming algorithm. position generated sequence use target distribution which puts equal probability first token optimal suffixes. OCD achieves state-of-the-art performance end-to-end speech recognition Wall Street Journal Librispeech datasets achieving $9.3\ WER $4.5\ WER respectively. Recent advances natural language processing speech recognition hinge development expressive neural network architectures sequence sequence seq2seq learning BID54 BID1. encoder-decoder architectures are adopted machine translation BID1 BID24 speech recognition systems BID7 BID2 BID11 achieving impressive performance traditional multi-stage pipelines BID29 BID41. Improving building blocks seq2seq models can fundamentally advance machine translation speech recognition positively impact domains image captioning BID62 parsing summarization BID47 program synthesis BID65.To improve key components seq2seq models one can either design better architectures develop better learning algorithms. Recent architectures using convolution BID20 self attention BID57 have proved useful especially facilitate efficient training. hand despite many attempts mitigate limitations Maximum Likelihood Estimation MLE BID43 BID60 BID4 BID30 MLE is still considered dominant approach training seq2seq models. Current alternative approaches require pre-training joint optimization conditional log-likelihood are difficult implement does not require careful tuning new hyper-parameters e.g mixing ratios addition alternative approaches typically do not offer substantial performance improvement well tuned MLE baseline especially when label smoothing BID40 BID18 scheduled sampling are used.In paper borrow ideas search-based structured prediction BID15 BID46 policy distillation BID48 develop efficient algorithm optimizing seq2seq models based edit distance1. key observation is that given arbitrary prefix e.g partial sequence generated sampling model can exactly efficiently identify suffixes result minimum total edit distance v.s ground truth target training procedure called Optimal Completion Distillation OCD is summarized follows:proposed OCD algorithm is efficient straightforward implement has no tunable hyperparameters own. key contributions include:• propose OCD stand-alone algorithm optimizing seq2seq models based edit distance. OCD is scalable real-world datasets long sequences large vocabularies consistently outperforms Maximum Likelihood Estimation MLE large margin.• Given target sequence length generated sequence lengthn present nm algorithm identifies optimal extensions prefix generated sequence.• demonstrate effectiveness OCD end-to-end speech recognition using attentionbased seq2seq models. Wall Street Journal dataset OCD achieves Character Error Rate CER 3.1 Word Error Rate WER 9.3 without language model rescoring outperforming prior work TAB1. Librispeech OCD achieves state-of-the-art WER 4.5 test-clean 13.3 test-other sets TAB2,777,550,227,0.007,1.413,2025/11/05 17:18:55,0.0,1.278,0.2585669781931463,249.175
"As an emerging field, federated learning has recently attracted considerable attention.
 Compared to distributed learning in the datacenter setting, federated learning
 has more strict constraints on computate efficiency of the learned model and communication
 cost during the training process. In this work, we propose an efficient
 federated learning framework based on variational dropout. Our approach is able
 to jointly learn a sparse model while reducing the amount of gradients exchanged
 during the iterative training process. We demonstrate the superior performance
 of our approach on achieving significant model compression and communication
 reduction ratios with no accuracy loss. Federated Learning is an emerging machine learning approach that has recently attracted considerable attention due to its wide range of applications in mobile scenarios BID18 BID12 BID24 . It enables geographically distributed devices such as mobile phones to collaboratively learn a shared model while keeping the training data on each phone. This is different from standard machine learning approach which requires all the training data to be centralized in a server or in a datacenter. As such, federated learning enables distributing the knowledge across phones without sharing users' private data.Federated Learning uses some form of distributed stochastic gradient descent (SGD) and requires a parameter server to coordinate the training process. The server initializes the model and distributes it to all the participating devices. In each distributed SGD iteration, each device computes the gradients of the model parameters using its local data. The server aggregates the gradients from each device, averages them, and sends the averaged gradients back. Each device then updates the model parameters using the averaged gradients. In such manner, each device benefits from obtaining a better model than the one trained only on the locally stored private data.While federated learning shares some common features with distributed learning in the datacenter setting BID3 BID16 since they both use distributed SGD as the core training technique, federated learning has two more strict constraints which datacenter setting does not have:Model Constraint: Compared to datacenters, mobile devices have much less compute resources. This requires the final model learned in the federated learning setting to be computationally efficient so that it can efficiently run on mobile devices.Communication Constraint: In datacenters, communication between the server and working nodes during SGD is conducted via Gbps Ethernet or InfiniBand network with even higher bandwidth BID26 . In contrast, communication in the federated learning setting relies on wireless networks such as 4G and Wi-Fi. Both uplink and downlink bandwidths of those wireless networks are at Mbps scale, which is much lower than the Gbps scale in the datacenter setting. The limited bandwidth in the federated learning setting illustrates the necessity of reducing the communication cost to accelerate the training process.In this work, we propose an efficient federated learning framework that meets both model and communication constraints. Our approach is inspired by variational dropout BID10 . Our key idea is to jointly and iteratively sparsify the parameters of the shared model to be learned as well as the gradients exchanged between the server and the participating devices during the distributed SGD training process. By sparsifying parameters, only important parameters are kept, and the final model learned thus becomes computationally efficient run on mobile devices. By sparsifying gradients, only important gradients are transmitted, and the communication cost is thus significantly reduced. We examine the performance of our framework on three deep neural networks and five datasets that fit the federated learning setting and are appropriate to be deployed on resource-limited mobile devices. Our experiment results show that our framework is able to achieve significant model compression and communication reduction ratios with no accuracy loss.",emerging field federated learning has recently attracted considerable attention. Compared distributed learning datacenter setting federated learning has more strict constraints computate efficiency learned model communication cost training process. work propose efficient federated learning framework based variational dropout. approach is able jointly learn sparse model reducing amount gradients exchanged iterative training process. demonstrate superior performance approach achieving significant model compression communication reduction ratios accuracy loss. Federated Learning is an emerging machine learning approach has recently attracted considerable attention due wide range applications mobile scenarios BID18 BID12 BID24. enables geographically distributed devices mobile phones collaboratively learn shared model keeping training data phone. is different standard machine learning approach which requires training data centralized server datacenter. federated learning enables distributing knowledge across phones without sharing users' private data.Federated Learning uses form distributed stochastic gradient descent SGD requires parameter server coordinate training process. server initializes model distributes participating devices. distributed SGD iteration device computes gradients model parameters using local data. server aggregates gradients device averages sends averaged gradients back. device updates model parameters using averaged gradients. manner device benefits obtaining better model one trained locally stored private data.While federated learning shares common features distributed learning datacenter setting BID3 BID16 since use distributed SGD core training technique federated learning has two strict constraints which datacenter setting have:Model Constraint:Compared datacenters mobile devices have much less compute resources. requires final model learned federated learning setting computationally efficient can efficiently run mobile devices.Communication Constraint:datacenters communication server working nodes SGD is conducted via Gbps Ethernet InfiniBand network even higher bandwidth BID26. contrast communication federated learning setting relies wireless networks 4G Wi-Fi uplink downlink bandwidths wireless networks are at Mbps scale which is much lower Gbps scale datacenter setting. limited bandwidth federated learning setting illustrates necessity reducing communication cost accelerate training process.In work propose efficient federated learning framework meets model communication constraints. approach is inspired variational dropout BID10. key idea is to jointly iteratively sparsify parameters shared model learned well gradients exchanged server participating devices distributed SGD training process. sparsifying parameters important parameters are kept final model learned thus becomes computationally efficient run mobile devices. sparsifying gradients important gradients are transmitted communication cost is thus significantly reduced. examine performance framework three deep neural networks five datasets fit federated learning setting are appropriate deployed resource-limited mobile devices. experiment results show framework is able achieve significant model compression communication reduction ratios accuracy loss.,713,480,233,0.006,1.485,2025/11/05 17:18:55,0.0,1.25,0.4828660436137073,245.314
"We prove a multiclass boosting theory for the ResNet architectures which simultaneously creates a new technique for multiclass boosting and provides a new algorithm for ResNet-style architectures.   Our proposed training algorithm, BoostResNet, is particularly suitable in non-differentiable architectures.   Our method only requires the relatively inexpensive sequential training of T ""shallow ResNets"". We prove that the training error decays exponentially with the depth T if the weak module classifiers that we train perform slightly better than some weak baseline.   In other words, we propose a weak learning condition and prove a boosting theory for ResNet under the weak learning condition.   A generalization error bound based on margin theory is proved and suggests that ResNet could be resistant to overfitting using a network with l_1 norm bounded weights. Why do residual neural networks (ResNets) BID14 and the related highway networks BID35 work? And if we study closely why they work, can we come up with new understandings of how to train them and how to define working algorithms?Deep neural networks have elicited breakthrough successes in machine learning, especially in image classification and object recognition BID19 BID32 BID34 Zeiler & Fergus, 2014) in recent years. As the number of layers increases, the nonlinear network becomes more powerful, deriving richer features from input data. Empirical studies suggest that challenging tasks in image classification BID15 BID34 and object recognition BID7 BID8 BID12 BID23 often require ""deep"" networks, consisting of tens or hundreds of layers. Theoretical analyses have further justified the power of deep networks BID24 compared to shallow networks.However, deep neural networks are difficult to train despite their intrinsic representational power. Stochastic gradient descent with back-propagation (BP) BID20 and its variants are commonly used to solve the non-convex optimization problems. A major challenge that exists for training both shallow and deep networks is vanishing or exploding gradients BID1 BID9 . Recent works have proposed normalization techniques BID9 BID22 BID15 BID31 to effectively ease the problem and achieve convergence. In training deep networks, however, a surprising training performance degradation is observed BID35 BID14 : the training performance degrades rapidly with increased network depth after some saturation point. This training performance degradation is representationally surprising as one can easily construct a deep network identical to a shallow network by forcing any part of the deep network to be the same as the shallow network with the remaining layers functioning as identity maps. He et al. BID14 presented a residual network (ResNet) learning framework to ease the training of networks that are substantially deeper than those used previously. And they explicitly reformulate the layers as learning residual functions with reference to the layer inputs by adding identity loops to the layers. It is shown in BID10 that identity loops ease the problem of spurious local optima in shallow networks. BID35 introduce a novel architecture that enables the optimization of networks with virtually arbitrary depth through the use of a learned gating mechanism for regulating information flow.Empirical evidence overwhelmingly shows that these deep residual networks are easier to optimize than non-residual ones. Can we develop a theoretical justification for this observation? And does that justification point us towards new algorithms with better characteristics? Our proposed BoostResNet algorithm achieves exponentially decaying (with the depth T ) training error under the weak learning condition. BoostResNet is much more computationally efficient compared to end-to-end back-propagation in deep ResNet. More importantly, the memory required by BoostResNet is trivial compared to end-to-end back-propagation. It is particularly beneficial given the limited GPU memory and large network depth. Our learning framework is natural for nondifferentiable data. For instance, our learning framework is amenable to take weak learning oracles using tensor decomposition techniques. Tensor decomposition, a spectral learning framework with theoretical guarantees, is applied to learning one layer MLP in BID16 . We plan to extend our learning framework to non-differentiable data using general weak learning oracles. In neural network optimization, there are many commonly-used loss functions and criteria, e.g., mean squared error, negative log likelihood, margin criterion, etc. There are extensive works BID7 BID30 BID37 on selecting or modifying loss functions to prevent empirical difficulties such as exploding/vanishing gradients or slow learning BID0 . However, there are no rigorous principles for selecting a loss function in general. Other works consider variations of the multilayer perceptron (MLP) or convolutional neural network (CNN) by adding identity skip connections BID14 , allowing information to bypass particular layers. However, no theoretical guarantees on the training error are provided despite breakthrough empirical successes. Hardt et al. BID10 have shown the advantage of identity loops in linear neural networks with theoretical justifications; however the linear setting is unrealistic in practice.",prove multiclass boosting theory ResNet architectures which simultaneously creates new technique multiclass boosting provides new algorithm ResNet-style architectures. proposed training algorithm BoostResNet is particularly suitable non-differentiable architectures. method requires relatively inexpensive sequential training shallow ResNets. prove training error decays exponentially depth if the weak module classifiers train perform slightly better weak baseline. words propose weak learning condition prove boosting theory ResNet weak learning condition. generalization error bound based margin theory is proved suggests ResNet could resistant overfitting using network l_1 norm bounded weights. Why do residual neural networks ResNets BID14 related highway networks BID35 work? if we study closely why they work can we come new understandings how to train how to define working algorithms? Deep neural networks have elicited breakthrough successes machine learning especially image classification object recognition BID19 BID32 BID34 Zeiler Fergus 2014 recent years. number layers increases nonlinear network becomes powerful deriving richer features input data. Empirical studies suggest challenging tasks image classification BID15 BID34 object recognition BID7 BID8 BID12 BID23 often require deep networks consisting tens hundreds layers. Theoretical analyses have further justified power deep networks BID24 compared shallow networks.However deep neural networks are difficult train despite intrinsic representational power. Stochastic gradient descent back-propagation BP BID20 variants are commonly used solve non-convex optimization problems. major challenge exists training shallow deep networks is vanishing exploding gradients BID1 BID9. Recent works have proposed normalization techniques BID9 BID22 BID15 BID31 effectively ease problem achieve convergence. training deep networks however surprising training performance degradation is observed BID35 BID14:training performance degrades rapidly increased network depth saturation point. training performance degradation is representationally surprising one can easily construct deep network identical shallow network forcing part deep network shallow network remaining layers functioning identity maps. etal. BID14 presented residual network ResNet learning framework ease training networks are substantially deeper used previously. explicitly reformulate layers learning residual functions reference layer inputs adding identity loops layers. is shown BID10 identity loops ease problem spurious local optima shallow networks. BID35 introduce novel architecture enables optimization networks virtually arbitrary depth use learned gating mechanism regulating information flow.Empirical evidence overwhelmingly shows deep residual networks are easier optimize non-residual ones. Can we develop theoretical justification observation? does that justification point us towards new algorithms better characteristics? proposed BoostResNet algorithm achieves exponentially decaying depth training error weak learning condition. BoostResNet is much computationally efficient compared end-to-end back-propagation deep ResNet. importantly memory required BoostResNet is trivial compared end-to-end back-propagation is particularly beneficial given limited GPU memory large network depth. learning framework is natural nondifferentiable data. instance learning framework is amenable take weak learning oracles using tensor decomposition techniques. Tensor decomposition spectral learning framework theoretical guarantees is applied learning one layer MLP BID16. plan extend learning framework non-differentiable data using general weak learning oracles. neural network optimization are many commonly-used loss functions criteria e.g mean squared error negative log likelihood margin criterion etc. are extensive works BID7 BID30 BID37 selecting modifying loss functions prevent empirical difficulties exploding/vanishing gradients slow learning BID0. However are no rigorous principles selecting loss function general. works consider variations multilayer perceptron MLP convolutional neural network CNN adding identity skip connections BID14 allowing information bypass particular layers. However theoretical guarantees training error are provided despite breakthrough empirical successes. Hardtetal. BID10 have shown advantage identity loops linear neural networks theoretical justifications;however linear setting is unrealistic practice.,975,715,260,0.008,1.364,2025/11/05 17:18:55,0.0,1.306,0.1059190031152649,297.199
"We consider the problem of learning a one-hidden-layer neural network: we assume the input x is from Gaussian distribution and the label $y = a \sigma(Bx) + \xi$, where a is a nonnegative vector and  $B$ is a full-rank weight matrix, and $\xi$ is a noise vector. We first give an analytic formula for the population risk of the standard squared loss and demonstrate that it implicitly attempts to decompose a sequence of low-rank tensors simultaneously. 
	
 Inspired by the formula, we design a non-convex objective function $G$ whose landscape is guaranteed to have the following properties:	

1. All local minima of $G$ are also global minima.
 2. All global minima of $G$ correspond to the ground truth parameters.
 3. The value and gradient of $G$ can be estimated using samples.
	
 With these properties, stochastic gradient descent on $G$ provably converges to the global minimum and learn the ground-truth parameters. We also prove finite sample complexity results and validate the results by simulations. Scalable optimization has played an important role in the success of deep learning, which has immense applications in artificial intelligence. Remarkably, optimization issues are often addressed through designing new models that make the resulting training objective functions easier to be optimized. For example, over-parameterization BID19 , batch-normalization BID14 , and residual networks BID12 b) are often considered as ways to improve the optimization landscape of the resulting objective functions.How do we design models and objective functions that allow efficient optimization with guarantees? Towards understanding this question in a principled way, this paper studies learning neural networks with one hidden layer. Roughly speaking, we will show that when the input is from Gaussian distribution and under certain simplifying assumptions on the weights, we can design an objective function G(·), such that[a] all local minima of G(·) are global minima [b] all the global minima are the desired solutions, namely, the ground-truth parameters (up to permutation and some fixed transformation).We note that designing such objective functions is challenging because 1) the natural 2 loss objective does have bad local minimum, and 2) due to the permutation invariance 1 , the objective function inherently has to contain an exponential number of isolated local minima. In this paper we first give an analytic formula for the population risk of the standard 2 loss, which empirically may converge to a spurious local minimum. We then design a novel population loss that is guaranteed to have no spurious local minimum.Designing objective functions with well-behaved landscape is an intriguing and potentially fruitful direction. We hope that our techniques can be useful for characterizing and designing the optimization landscape for other settings.We conjecture that the objective αf 2 + βf 4 12 has no spurious local minimum when α, β are reasonable constants and the ground-truth parameters are in general position. We provided empirical evidence to support the conjecture.Our results assume that the input distribution is Gaussian. Extending them to other input distributions is a very interesting open problem. 2 /2 ) in the following sense 13 . For two functions f, g that map R to R, define the inner product f, g with respect to the Gaussian measure as DISPLAYFORM0 The polynomials h 0 , . . . , h m , . . . are orthogonal to each other under this inner product: DISPLAYFORM1 2 /2 ) , let the k-th Hermite coefficient of σ be defined asσ DISPLAYFORM2 Since h 0 , . . . , h m , . . . , forms a complete orthonormal basis, we have the expansion that DISPLAYFORM3 We will leverage several other nice properties of the Hermite polynomials in our proofs. The following claim connects the Hermite polynomial to the coefficients of Taylor expansion of a certain exponential function. It can also serve as a definition of Hermite polynomials. 13 We denote by Donnell, 2014, Equation 11 .8)). We have that for t, z ∈ R, DISPLAYFORM4 DISPLAYFORM5 The following Claims shows that the expectation E [h n (x)h m (y)] can be computed easily when x, y are (correlated) Gaussian random variables. Claim A.2 ((O'Donnell, 2014, Section 11.2)). Let (x, y) be ρ-correlated standard normal variables (that is, both x,y have marginal distribution N (0, 1) and E[xy] = ρ). Then, DISPLAYFORM6 As a direct corollary, we can compute Ex∼N (0,Id d×d ) σ(u x)γ(v x) by expanding in the Hermite basis and applying the Claim above. Claim A.3. Let σ, γ be two functions from R to R such that DISPLAYFORM7 2 /2 ). Then, for any unit vectors u, v ∈ R d , we have that DISPLAYFORM8 Proof of Claim A.3. Let s = u x and t = v x. Then s, t are two spherical standard normal random variables that are u, v -correlated, and we have that DISPLAYFORM9 We expand σ(s ) and γ(t ) in the Fourier basis and obtain that DISPLAYFORM10 In this section we prove Theorem 2.1 and Theorem 2.2, which both follow from the following more general Theorem. DISPLAYFORM11 2 /2 ), andŷ = a γ(Bx) with parameter a ∈ R and B ∈ R ×d . Define the population risk f γ as DISPLAYFORM12 DISPLAYFORM13 whereσ k ,γ k are the k-th Hermite coefficients of the function σ and γ respectively.We can see that Theorem 2.1 follows from choosing γ = σ and Theorem 2.2 follows from choosing γ =σ 2 h 2 +σ 4 h 4 . The key intuition here is that we can decompose σ into a weighted combination of Hermite polynomials, and each Hermite polynomial influence the population risk more or less independently (because they are orthogonal polynomials with respect to the Gaussian measure).Proof of Theorem A.4. We have DISPLAYFORM14","consider problem learning one-hidden-layer neural network:assume inputx is from is Gaussian distribution label$y \sigma Bx+\xi whereais nonnegative vector $B is a full-rank weight matrix $\xi is a noise vector. first give analytic formula population risk standard squared loss demonstrate implicitly attempts decompose sequence low-rank tensors simultaneously. Inspired formula can design non-convex objective function$G whose landscape is guaranteed have the following properties:1. local minima $G are also global minima. 2. global minima $G correspond ground truth parameters. 3. value gradient $G can be estimated using samples. properties stochastic gradient descent $G provably converges global minimum learn ground-truth parameters. also prove finite sample complexity results validate results simulations. Scalable optimization has played important role success deep learning which has immense applications artificial intelligence. Remarkably optimization issues are often addressed designing new models make resulting training objective functions easier optimized. example over-parameterization BID19 batch-normalization BID14 residual networks BID12b are often considered ways improve optimization landscape resulting objective functions.How do we design models objective functions allow efficient optimization guarantees? Towards understanding question principled way paper studies learning neural networks one hidden layer. Roughly speaking will show when the input is from is Gaussian distribution certain simplifying assumptions weights can design objective functionG · local minima G · are global minima b global minima are the desired solutions namely ground-truth parameters permutation fixed transformation.We note designing objective functions is challenging 1 natural 2 loss objective does have bad local minimum 2 due permutation invariance1 objective function inherently has to contain exponential number isolated local minima. paper first give analytic formula population risk standard 2 loss which empirically may converge have no spurious local minimum. design novel population loss is guaranteed have no spurious local minimum.Designing objective functions well-behaved landscape is an intriguing potentially fruitful direction. hope techniques can be useful characterizing designing optimization landscape settings.We conjecture objectiveαf2+βf412 has no spurious local minimum whenα β are reasonable constants ground-truth parameters are in general position. provided empirical evidence support conjecture.Our results assume when the input distribution is from is Gaussian. Extending input distributions is a very interesting open problem. 2/2 following sense13. two functionsf g mapR R define inner productf g respect Gaussian measure DISPLAYFORM0 polynomialsh0 h are orthogonal inner product:DISPLAYFORM12/2 let k-th Hermite coefficient σ defined asσ DISPLAYFORM2 Since h0 h forms complete orthonormal basis have the expansion DISPLAYFORM3 will leverage several nice properties Hermite polynomials proofs. following claim connects Hermite polynomial coefficients Taylor expansion certain exponential function. can also serve definition Hermite polynomials. 13 denote Donnell 2014 Equation11.8 have that fort z∈R DISPLAYFORM4 DISPLAYFORM5 following Claims shows expectationE hn is,x h canbe computed easily whenx are(correlated Gaussian random variables. Claim A.2 Donnell 2014 Section 11.2 Let is,x ρ-correlated standard normal variables is,x have marginal distributionN 0 1 E xy ρ DISPLAYFORM6 direct corollary can compute Ex∼N 0 Id d×d σ ux γ vx expanding Hermite basis applying Claim above. Claim A.3 Letσ γ two functions R R DISPLAYFORM72/2 unit vectorsu v∈R have DISPLAYFORM8 Proof Claim A.3 Let ux vx. are two spherical standard normal random variables areu v -correlated have DISPLAYFORM9 expandσ γ Fourier basis obtain DISPLAYFORM10 section prove Theorem 2.1 Theorem 2.2 which both follow following general Theorem. DISPLAYFORM112/2 andŷ γ Bx parameter ∈R B∈R×d Define population riskfγ DISPLAYFORM12 DISPLAYFORM13 whereσk γk are the k-th Hermite coefficients functionσ γ respectively.We can see Theorem 2.1 follows choosingγ σ Theorem 2.2 follows choosingγ=σ2 h2+σ 4h4. key intuition is thatwe can decomposeσ weighted combination Hermite polynomials Hermite polynomial influence population risk less independently are orthogonal polynomials respect Gaussian measure.Proof Theorem A.4 have DISPLAYFORM14",1291,876,415,0.012,1.474,2025/11/05 17:18:55,0.01,1.574,0.4485981308411212,360.39
"Open information extraction (OIE) systems extract relations and their
  arguments from natural language text in an unsupervised manner. The resulting
  extractions are a valuable resource for downstream tasks such as knowledge
  base construction, open question answering, or event schema induction. In this
  paper, we release, describe, and analyze an OIE corpus called OPIEC, which was
  extracted from the text of English Wikipedia. OPIEC complements the available
  OIE resources: It is the largest OIE corpus publicly available to date (over
  340M triples) and contains valuable metadata such as provenance information,
  confidence scores, linguistic annotations, and semantic annotations including
  spatial and temporal information. We analyze the OPIEC corpus by comparing its
  content with knowledge bases such as DBpedia or YAGO, which are also based on
  Wikipedia. We found that most of the facts between entities present in OPIEC
  cannot be found in DBpedia and/or YAGO, that OIE facts 
  often differ in the level of specificity compared to knowledge base facts, and
  that OIE open relations are generally highly polysemous. We believe that the
  OPIEC corpus is a valuable resource for future research on automated knowledge
  base construction. Open information extraction (OIE) is the task of extracting relations and their arguments from natural language text in an unsupervised manner BID3 . The output of such systems is usually structured in the form of (subject, relation, object)-triples. For example, from the sentence ""Bell is a telecommunication company, which is based in L. A.,"" an OIE system may yield the extractions (""Bell""; ""is""; ""telecommunication company"") and (""Bell""; ""is based in""; ""L. A.""). The extractions of OIE systems from large corpora are a valuable resource for downstream tasks BID11 BID21 such as automated knowledge base construction BID28 BID34 BID33 BID30 , open question answering BID13 , event schema induction BID2 , generating inference rules BID18 , or for improving OIE systems themselves BID35 . A number of derived resources have been produced from OIE extractions, including as entailment rules BID18 , question paraphrases BID13 , Relgrams BID1 , and OIE-based embeddings BID32 .In this paper, we release a new OIE corpus called OPIEC. 1 The OPIEC corpus has been extracted from the full text of the English Wikipedia using the Stanford CoreNLP pipeline and the state-of-the-art OIE system MinIE BID15 . OPIEC complements available OIE resources BID12 BID19 BID26 BID24 BID9 : It is the largest OIE corpus publicly available to date (with over 340M triples) and contains valuable metadata information for each of its extractions not available in existing resources (see Tab. 1 for an overview). In particular , OPIEC provides for each triple detailed provenance information, syntactic annotations (such as POS tags, lemmas, dependency parses), semantic annotations (such as polarity, modality, attribution, space, time), entity annotations (NER types and, when available, Wikipedia links), as well as confidence scores.We performed a detailed data profiling study of the OPIEC corpus to analyze its contents and potential usefulness for downstream applications. We observed that a substantial fraction of the OIE extractions was not self-contained (e.g., because no anaphora resolution was performed) or overly specific (e.g., because arguments were complex phrases). Since these extractions are more difficult to work with, we created the OPIEC-Clean subcorpus (104M triples), in which we only retained triples that express relations between concepts. In particular , OPIEC-Clean contains triples in which arguments are either named entities (as recognized by an NER system), match a Wikipedia page title (e.g., concepts such as political party or movie), or link directly to a Wikipedia page. Although OPIEC-Clean is substantially smaller than the full OPIEC corpus, it is nevertheless four times larger than the largest prior OIE corpus.To gain insight into the information present in the OPIEC corpus, we compared its content with the DBpedia BID4 and YAGO BID17 knowledge bases, which are also constructed from Wikipedia (e.g., from infoboxes). Since such an analysis is difficult to perform due to the openness and ambiguity of OIE extractions, we followed standard practice and used a simple form of distant supervision. In particular, we analyze the OPIEC-Linked subcorpus (5.8M triples), which contains only those triples in which both arguments are linked to Wikipedia articles, i.e., where we have golden labels for disambiguation. We found that most of the facts between entities present in OPIECLinked cannot be found in DBpedia and/or YAGO, that OIE facts often differ in the level of specificity compared to knowledge base facts, and that frequent OIE open relations are generally highly polysemous.Along with the OPIEC corpus as well as the OPIEC-Clean and OPIEC-Linked subcorpora, we release the codebase used to construct the corpus as well as a number of derived resources, most notably a corpus of open relations between arguments of various entity types along with their frequencies. We believe that the OPIEC corpus is a valuable resource for future research on automated knowledge base construction. We created OPIEC, a large open information extraction corpus extracted from Wikipedia. OPIEC consists of hundreds of millions of triples, along with rich metadata such as provenance information, syntactic annotations, semantic annotations, and confidence scores. We reported on a data profiling study of the OPIEC corpus as well as subcorpora. In particular, we analyzed to what extent OPIEC overlaps with the DBpedia and YAGO knowledge bases. Our study indicates that most open facts do not have counterparts in the KB such that OIE corpora contain complementary information. For the information that overlaps, open relation are often more specific, more generic, or simply correlated to KB relations (instead of semantically equivalent). We hope that the OPIEC corpus, its subcorpora, derived statistics, as well as the codebase used to create the corpus are a valuable resource for automated KB construction and downstream applications (for example, an independent study showed the utility of OPIEC in entity-aspect linking BID27 ).",Open information extraction OIE systems extract relations arguments natural language text unsupervised manner. resulting extractions are a valuable resource downstream tasks knowledge base construction open question answering event schema induction. paper release describe analyze OIE corpus called OPIEC which was extracted text English Wikipedia. OPIEC complements available OIE resources:is the largest OIE corpus publicly available date 340M triples which contains valuable metadata provenance information confidence scores linguistic annotations semantic annotations including spatial temporal information. analyze OPIEC corpus comparing content knowledge bases DBpedia YAGO which are also based Wikipedia. found facts entities present OPIEC cannot found DBpedia/YAGO OIE facts often differ level specificity compared knowledge base facts OIE open relations are generally highly polysemous. believe OPIEC corpus is a valuable resource future research automated knowledge base construction. Open information extraction OIE is the task extracting relations arguments natural language text unsupervised manner BID3. output systems is usually structured form subject relation object -triples example sentence Bell is a telecommunication company which is based L. A. OIE system may yield extractions Bell;is;telecommunication company Bell;is based in;L. A. extractions OIE systems large corpora are a valuable resource downstream tasks BID11 BID21 automated knowledge base construction BID28 BID34 BID33 BID30 open question answering BID13 event schema induction BID2 generating inference rules BID18 improving OIE systems BID35. number derived resources have been produced OIE extractions including entailment rules BID18 question paraphrases BID13 Relgrams BID1 OIE-based embeddings BID32.In paper release new OIE corpus called OPIEC. 1 OPIEC corpus has been extracted full text English Wikipedia using Stanford CoreNLP pipeline state-of-the-art OIE system MinIE BID15. OPIEC complements available OIE resources BID12 BID19 BID26 BID24 BID9:is the largest OIE corpus publicly available date 340M triples which contains valuable metadata information extractions available existing resources see Tab. 1 overview particular OPIEC provides triple detailed provenance information syntactic annotations POS tags lemmas dependency parses semantic annotations polarity modality attribution space time entity annotations NER types when available Wikipedia links well confidence scores.We performed detailed data profiling study OPIEC corpus analyze contents potential usefulness downstream applications. observed substantial fraction OIE extractions was not self-contained e.g anaphora resolution was performed overly specific e.g arguments were complex phrases Since extractions are more difficult work created OPIEC-Clean subcorpus 104M triples which retained triples express relations concepts. particular OPIEC-Clean contains triples which which both arguments are either named entities recognized NER system match Wikipedia page title e.g concepts political party movie link directly Wikipedia page. Although OPIEC-Clean is substantially smaller full OPIEC corpus is nevertheless four times larger largest prior OIE corpus.To gain insight information present OPIEC corpus compared content DBpedia BID4 YAGO BID17 knowledge bases which are also constructed Wikipedia e.g infoboxes Since analysis is difficult perform due openness ambiguity OIE extractions followed standard practice used simple form distant supervision. particular analyze OPIEC-Linked subcorpus 5.8M triples which contains triples which which both arguments are linked Wikipedia articles.e where we have golden labels disambiguation. found facts entities present OPIECLinked cannot found DBpedia/YAGO OIE facts often differ level specificity compared knowledge base facts frequent OIE open relations are generally highly polysemous.Along OPIEC corpus well OPIEC-Clean OPIEC-Linked subcorpora release codebase used construct corpus well number derived resources notably corpus open relations arguments various entity types along frequencies. believe OPIEC corpus is a valuable resource future research automated knowledge base construction. created OPIEC large open information extraction corpus extracted Wikipedia. OPIEC consists hundreds millions triples along rich metadata provenance information syntactic annotations semantic annotations confidence scores. reported data profiling study OPIEC corpus well subcorpora. particular analyzed what extent OPIEC overlaps DBpedia YAGO knowledge bases. study indicates open facts do not have counterparts KB OIE corpora contain complementary information. information overlaps open relation are often specific generic simply correlated KB relations instead semantically equivalent hope OPIEC corpus subcorpora derived statistics well codebase used create corpus are a valuable resource automated KB construction downstream applications example independent study showed utility OPIEC entity-aspect linking BID27,1323,888,435,0.013,1.49,2025/11/05 17:18:55,0.01,1.548,0.4984423676012459,367.663
"The process of designing neural architectures requires expert knowledge and extensive trial and error.
 While automated architecture search may simplify these requirements, the recurrent neural network (RNN) architectures generated by existing methods are limited in both flexibility and components.
 We propose a domain-specific language (DSL) for use in automated architecture search which can produce novel RNNs of arbitrary depth and width.
 The DSL is flexible enough to define standard architectures such as the Gated Recurrent Unit and Long Short Term Memory and allows the introduction of non-standard RNN components such as trigonometric curves and layer normalization.   Using two different candidate generation techniques, random search with a ranking function and reinforcement learning, 
we explore the novel architectures produced by the RNN DSL for language modeling and machine translation domains.
 The resulting architectures do not follow human intuition yet perform well on their targeted tasks, suggesting the space of usable RNN architectures is far larger than previously assumed. Developing novel neural network architectures is at the core of many recent AI advances BID28 BID14 BID35 . The process of architecture search and engineering is slow, costly, and laborious. Human experts, guided by intuition, explore an extensive space of potential architectures where even minor modifications can produce unexpected results. Ideally, an automated architecture search algorithm would find the optimal model architecture for a given task.Many explorations into the automation of machine learning have been made, including the optimization of hyperparameters BID3 BID24 and various methods of producing novel model architectures BID27 BID1 Zoph and Le, 2017) . For architecture search, ensuring these automated methods are able to produce results similar to humans usually requires traversing an impractically large search space, assuming high quality architectures exist in the search space at all. The choice of underlying operators composing an architecture is further typically constrained to a standard set across architectures even though recent work has found promising results in the use of non-standard operators BID31 .We propose a meta-learning strategy for flexible automated architecture search of recurrent neural networks (RNNs) which explicitly includes novel operators in the search. It consists of three stages, outlined in Figure 1 , for which we instantiate two versions.1. A candidate architecture generation function produces potential RNN architectures using a highly flexible DSL. The DSL enforces no constraints on the size or complexity of the generated tree and can be incrementally constructed using either a random policy or with an RL agent. 2. A ranking function processes each candidate architecture's DSL via a recursive neural network, predicting the architecture's performance. By unrolling the RNN representation, the ranking function can also model the interactions of a candidate architecture's hidden state over time. Figure 1: A generator produces candidate architectures by iteratively sampling the next node (either randomly or using an RL agent trained with REINFORCE). Full architectures are processed by a ranking function and the most promising candidates are evaluated. The results from running the model against a baseline experiment are then used to improve the generator and the ranking function.3. An evaluator, which takes the most promising candidate architectures, compiles their DSLs to executable code and trains each model on a specified task. The results of these evaluations form architecture-performance pairs that are then used to train the ranking function and RL generator. We introduced a flexible domain specific language for defining recurrent neural network architectures that can represent most human designed architectures. It is this flexibility that allowed our generators to come up with novel combinations in two tasks. These architectures used both core operators that are already used in current architectures as well as operators that are largely unstudied such as division or sine curves. The resulting architectures do not follow human intuition yet perform well on their targeted tasks, suggesting the space of usable RNN architectures is far larger than previously assumed. We also introduce a component-based concept for architecture search from which we instantiated two approaches: a ranking function driven search which allows for richer representations of complex RNN architectures that involve long term memory (c t ) nodes, and a Reinforcement Learning agent that internalizes knowledge about the search space to propose increasingly better architectures. As computing resources continue to grow, we see automated architecture generation as a promising avenue for future research.APPENDIX A: DOMAIN SPECIFIC LANGUAGE DISPLAYFORM0",process designing neural architectures requires expert knowledge extensive trial error. automated architecture search may simplify requirements recurrent neural network RNN architectures generated existing methods are limited flexibility components. propose domain-specific language DSL use automated architecture search which can produce novel RNNs arbitrary depth width. DSL is flexible enough define standard architectures Gated Recurrent Unit Long Short Term Memory allows introduction non-standard RNN components trigonometric curves layer normalization. Using two different candidate generation techniques random search ranking function reinforcement learning explore novel architectures produced RNN DSL language modeling machine translation domains. resulting architectures do not follow human intuition yet perform well targeted tasks suggesting space usable RNN architectures is far larger previously assumed. Developing novel neural network architectures is at the core many recent AI advances BID28 BID14 BID35. process architecture search engineering is slow costly laborious. Human experts guided intuition explore extensive space potential architectures where even minor modifications can produce unexpected results. Ideally automated architecture search algorithm would find optimal model architecture given task.Many explorations automation machine learning have been made including optimization hyperparameters BID3 BID24 various methods producing novel model architectures BID27 BID1 Zoph Le 2017 architecture search ensuring automated methods are able produce results similar humans usually requires traversing impractically large search space assuming high quality architectures exist search space all. choice underlying operators composing architecture is further typically constrained standard set across architectures even though recent work has found promising results use non-standard operators BID31.We propose meta-learning strategy flexible automated architecture search recurrent neural networks RNNs which explicitly includes novel operators search. consists three stages outlined Figure1 whichwe instantiate two versions.1 candidate architecture generation function produces potential RNN architectures using highly flexible DSL. DSL enforces constraints size complexity generated tree can be incrementally constructed using either random policy RL agent. 2. ranking function processes candidate architecture's DSL via recursive neural network predicting architecture's performance. unrolling RNN representation ranking function can also model interactions candidate architecture's hidden state time. Figure1:generator produces candidate architectures iteratively sampling next node either randomly using RL agent trained REINFORCE Full architectures are processed ranking function promising candidates are evaluated. results running model baseline experiment are then used improve generator ranking function.3 evaluator which takes promising candidate architectures compiles DSLs executable code trains model specified task. results evaluations form architecture-performance pairs are then used train ranking function RL generator. introduced flexible domain specific language defining recurrent neural network architectures can represent human designed architectures. is this flexibility allowed generators come novel combinations two tasks. architectures used core operators are already used current architectures well operators are largely unstudied division sine curves. resulting architectures do not follow human intuition yet perform well targeted tasks suggesting space usable RNN architectures is far larger previously assumed. also introduce component-based concept architecture search which we instantiated two approaches:ranking function driven search which allows richer representations complex RNN architectures involve long term memory c nodes Reinforcement Learning agent internalizes knowledge search space propose increasingly better architectures. computing resources continue grow see automated architecture generation promising avenue future research.APPENDIX A:DOMAIN SPECIFIC LANGUAGE DISPLAYFORM0,845,605,240,0.008,1.397,2025/11/05 17:18:55,0.0,1.429,0.2087227414330216,278.871
"Researches on deep neural networks with discrete parameters and their deployment in embedded systems have been active and promising topics. Although previous works have successfully reduced precision in inference, transferring both training and inference processes to low-bitwidth integers has not been demonstrated simultaneously. In this work, we develop a new method termed as ``""WAGE"" to discretize both training and inference, where weights (W), activations (A), gradients (G) and errors (E) among layers are shifted and linearly constrained to low-bitwidth integers. To perform pure discrete dataflow for fixed-point devices, we further replace batch normalization by a constant scaling layer and simplify other components that are arduous for integer implementation. Improved accuracies can be obtained on multiple datasets, which indicates that WAGE somehow acts as a type of regularization. Empirically, we demonstrate the potential to deploy training in hardware systems such as integer-based deep learning accelerators and neuromorphic chips with comparable accuracy and higher energy efficiency, which is crucial to future AI applications in variable scenarios with transfer and continual learning demands. Recently deep neural networks (DNNs) are being widely used for numerous AI applications BID11 BID21 . Depending on the massive tunable parameters, DNNs are considered to have powerful multi-level feature extraction and representation abilities. However, training DNNs needs energy-intensive devices such as GPU and CPU with high precision (float32) processing units and abundant memory, which has greatly challenged their extensive applications for portable devices. In addition, a state-of-art network often has far more weights and effective capacity to shatter all training samples , leading to overfitting easily.As a result, there is much interest in reducing the size of network during inference BID8 BID17 BID14 , as well as dedicated hardware for commercial solutions BID10 BID20 . Due to the accumulation in stochastic gradient descent (SGD) optimization, the precision demand for training is usually higher than inference BID8 . Therefore, most of the existing techniques only focus on the deployment of a well-trained compressed network, while still keeping high precision and computational complexity during training. In this work, we address this problem as how to process both training and inference with low-bitwidth integers, which is essential for implementing DNNs in dedicated hardware. To this end, two fundamental issues are addressed for discretely training DNNs: i) how to quantize all the operands and operations, and ii) how many bits or states are needed for SGD computation and accumulation.With respect to the issues, we propose a framework termed as ""WAGE"" that constrains weights (W), activations (A), gradients (G) and errors (E) among all layers to low-bitwidth integers in both training and inference. Firstly, for operands, linear mapping and orientation-preserved shifting are applied to achieve ternary weights, 8-bit integers for activations and gradients accumulation. Secondly, for operations, batch normalization BID9 is replaced by a constant scaling factor. Other techniques for fine-tuning such as SGD optimizer with momentum and L2 regularization are simplified or abandoned with little performance degradation. Considering the overall bidirectional propagation, we completely streamline inference into accumulate-compare cycles and training into low-bitwidth multiply-accumulate (MAC) cycles with alignment operations, respectively.We heuristically explore the bitwidth requirements of integers for error computation and gradient accumulation, which have rarely been discussed in previous works. Experiments indicate that it is the relative values (orientations) rather than absolute values (orders of magnitude) in error that guides previous layers to converge. Moreover, small values have negligible effects on previous orientations though propagated layer by layer, which can be partially discarded in quantization. We leverage these phenomena and use an orientation-preserved shifting operation to constrain errors. As for the gradient accumulation, though weights are quantized to ternary values in inference, a relatively higher bitwidth is indispensable to store and accumulate gradient updates.The proposed framework is evaluated on MNIST, CIFAR10, SVHN, ImageNet datasets. Comparing to those who only discretize weights and activations at inference time, it has comparable accuracy and can further alleviate overfitting, indicating some type of regularization. WAGE produces pure bidirectional low-precision integer dataflow for DNNs, which can be applied for training and inference in dedicated hardware neatly. We publish the code on GitHub 1 .",Researches deep neural networks discrete parameters deployment embedded systems have been active promising topics. Although previous works have successfully reduced precision inference transferring training inference processes low-bitwidth integers has not been demonstrated simultaneously. work develop new method termed WAGE who only discretize training inference where weights W activations gradients G errors E among layers are shifted linearly constrained low-bitwidth integers. perform pure discrete dataflow fixed-point devices replace batch normalization constant scaling layer simplify components are arduous integer implementation. Improved accuracies can be obtained multiple datasets which indicates WAGE somehow acts type regularization. Empirically demonstrate potential deploy training hardware systems integer-based deep learning accelerators neuromorphic chips comparable accuracy higher energy efficiency which is crucial future AI applications variable scenarios transfer continual learning demands. Recently deep neural networks DNNs are being widely used numerous AI applications BID11 BID21. Depending massive tunable parameters DNNs are considered have powerful multi-level feature extraction representation abilities. However training DNNs needs energy-intensive devices GPU CPU high precision float32 processing units abundant memory which has greatly challenged extensive applications portable devices. addition state-of-art network often has far weights effective capacity shatter training samples leading overfitting easily.As result is much interest reducing size network inference BID8 BID17 BID14 well dedicated hardware commercial solutions BID10 BID20. Due accumulation stochastic gradient descent SGD optimization precision demand training is usually higher inference BID8. Therefore existing techniques focus deployment well-trained compressed network still keeping high precision computational complexity training. work address problem how to process training inference low-bitwidth integers which is essential implementing DNNs dedicated hardware. end two fundamental issues are addressed discretely training DNNs:how to quantize operands operations ii how many bits states are needed SGD computation accumulation.With respect issues propose framework termed WAGE constrains weights W activations gradients G errors E among layers low-bitwidth integers training inference. Firstly operands linear mapping orientation-preserved shifting are applied achieve ternary weights 8-bit integers activations gradients accumulation. Secondly operations batch normalization BID9 is replaced constant scaling factor. techniques fine-tuning SGD optimizer momentum L2 regularization are simplified abandoned little performance degradation. Considering overall bidirectional propagation completely streamline inference accumulate-compare cycles training low-bitwidth multiply-accumulate MAC cycles alignment operations respectively.We heuristically explore bitwidth requirements integers error computation gradient accumulation which have rarely discussed previous works. Experiments indicate is the relative values orientations rather absolute values orders magnitude error guides previous layers converge. Moreover small values have negligible effects previous orientations though propagated layer layer which can be partially discarded quantization. leverage phenomena use orientation-preserved shifting operation constrain errors. gradient accumulation though weights are quantized ternary values inference relatively higher bitwidth is indispensable store accumulate gradient updates.The proposed framework is evaluated MNIST CIFAR10 SVHN ImageNet datasets. Comparing who only discretize weights activations inference time has comparable accuracy can further alleviate overfitting indicating type regularization. WAGE produces pure bidirectional low-precision integer dataflow DNNs which can be applied training inference dedicated hardware neatly. publish code GitHub1.,882,610,272,0.009,1.446,2025/11/05 17:18:55,0.0,1.5,0.3613707165109031,293.007
"Modern Convolutional Neural Networks (CNNs) are complex, encompassing millions of parameters. Their deployment exerts computational, storage and energy demands, particularly on embedded platforms. Existing approaches to prune or sparsify CNNs require retraining to maintain inference accuracy. Such retraining is not feasible in some contexts. In this paper, we explore the sparsification of CNNs by proposing three model-independent methods. Our methods are applied on-the-fly and require no retraining. We show that the state-of-the-art models' weights can be reduced by up to 73% (compression factor of 3.7x) without incurring more than 5% loss in Top-5 accuracy. Additional fine-tuning gains only 8% in sparsity, which indicates that our fast on-the-fly methods are effective. There has been a significant growth in the number of parameters (i.e., layer weights), and the corresponding number of multiply-accumulate operations (MACs), in state-of-the-art CNNs BID14 BID13 BID19 BID23 BID8 BID11 BID24 BID22 . Thus, it is to no surprise that several techniques exist for ""pruning"" or ""sparsifying"" CNNs (i.e., forcing some model weights to 0) to both compress the model and to save computations during inference. Examples of these techniques include: iterative pruning and retraining BID2 BID7 BID3 BID20 BID17 , Huffman coding BID5 , exploiting granularity BID15 BID4 , structural pruning of network connections BID25 BID16 BID0 BID18 , and Knowledge Distillation (KD) BID9 .A common theme to the aforementioned techniques is that they require a retraining of the model to fine-tune the remaining non-zero weights and maintain inference accuracy. Such retraining, while feasible in some contexts, is not feasible in others, particularly industrial ones. For example, for mobile platforms, a machine learning model is typically embedded within an app for the platform that the user directly downloads. The app utilizes the vendor's platform runtime support (often in the form of a library) to load and use the model. Thus , the platform vendor must sparsify the model at runtime, i.e., on-the-fly, within the library with no opportunity to retrain the model. Further , the vendor rarely has access to the labelled data used to train the model. While techniques such as Knowledge Distillation BID9 can address this lack of access, it is not possible to apply it on-the-fly.In this paper, we develop fast retraining-free sparsification methods that can be deployed for on-thefly sparsification of CNNs in the contexts described above. There is an inherent trade-off between sparsity and inference accuracy. Our goal is to develop model-independent methods that result in large sparsity with little loss to inference accuracy. We develop three model-independent sparsification methods: flat, triangular, and relative. We implement these methods in TensorFlow and use the framework to evaluate the sparsification of several pretrained models: Inception-v3, MobileNet-v1, ResNet, VGG, and AlexNet. Our evaluation shows that up to 81% of layer weights in some models may be forced to 0, incurring only a 5% loss in inference accuracy. While the relative method appears to be more effective for some models, the triangular method is more effective for others. Thus, a predictive modeling autotuning BID6 BID1 is needed to identify, at run-time, the optimal choice of method and it hyper-parameters.",Modern Convolutional Neural Networks CNNs are complex encompassing millions parameters. deployment exerts computational storage energy demands particularly embedded platforms. Existing approaches prune sparsify CNNs require retraining maintain inference accuracy. retraining is not feasible contexts. paper explore sparsification CNNs proposing three model-independent methods. methods are applied on-the-fly require retraining. show state-of-the-art models' weights can be reduced 73% compression factor 3.7x without incurring 5% loss Top-5 accuracy. Additional fine-tuning gains 8% sparsity which indicates fast on-the-fly methods are effective. has been a significant growth number parameters.e layer weights corresponding number multiply-accumulate operations MACs state-of-the-art CNNs BID14 BID13 BID19 BID23 BID8 BID11 BID24 BID22. Thus isto surprise several techniques exist pruning sparsifying CNNs.e forcing model weights 0 compress model save computations inference. Examples techniques include:iterative pruning retraining BID2 BID7 BID3 BID20 BID17 Huffman coding BID5 exploiting granularity BID15 BID4 structural pruning network connections BID25 BID16 BID0 BID18 Knowledge Distillation KD BID9.A common theme aforementioned techniques is that they require retraining model fine-tune remaining non-zero weights maintain inference accuracy. retraining is not feasible contexts is not feasible others particularly industrial ones. example mobile platforms machine learning model is typically embedded within app platform user directly downloads. app utilizes vendor's platform runtime support often form library load use model. Thus platform vendor must sparsify model runtime.e on-the-fly within library opportunity retrain model. vendor rarely has access labelled data used train model. techniques Knowledge Distillation BID9 can address lack access is not possible apply on-the-fly.In paper develop fast retraining-free sparsification methods can be deployed on-thefly sparsification CNNs contexts described above. is an inherent trade-off sparsity inference accuracy. goal is to develop model-independent methods result large sparsity little loss inference accuracy. develop three model-independent sparsification methods:flat triangular relative. implement methods TensorFlow use framework evaluate sparsification several pretrained models:Inception-v3 MobileNet-v1 ResNet VGG AlexNet. evaluation shows 81% layer weights models may forced 0 incurring 5% loss inference accuracy. relative method appears effective models triangular method is more effective others. Thus predictive modeling autotuning BID6 BID1 is needed identify run-time optimal choice method hyper-parameters,718,495,223,0.006,1.451,2025/11/05 17:18:55,0.0,1.684,0.3769470404984424,243.87
"Curriculum learning and Self paced learning are popular topics in the machine learning that suggest to put the training samples in order by considering their difficulty levels. Studies in these topics show that starting with a small training set and adding new samples according to difficulty levels improves the learning performance. In this paper we experimented that we can also obtain good results by adding the samples randomly without a meaningful order. We compared our method with classical training, Curriculum learning, Self paced learning and their reverse ordered versions. Results of the statistical tests show that the proposed method is better than classical method and similar with the others. These results point a new training regime that removes the process of difficulty level determination in Curriculum and Self paced learning and as successful as these methods.  BID1 named Curriculum learning the idea of following an order related with difficulty of the samples during training which provides an optimization for non convex objectives. After this many researchers tried to find the most efficient curriculum to get the best yield with this approach. In BID15 's study conventional curriculum learning did not work so well and they developed a new version. BID14 proposed three different curriculum strategies for language model adaptation of recurrent neural networks. In the field of computer vision BID13 looked for the best order of tasks to learn. Although these models have better generalization performance with the proposed curriculum methods it is not known whether the tried methods ensures the best curriculum.A curriculum is work-specific so could not be applicable for another work. In order to use the curriculum logic in different applications BID10 suggested a method that the learner decides itself which samples are easy or difficult at every stage. This method called Self paced learning was combined with Curriculum learning which provides prior information by BID9 . In another work BID7 introduced a method to automatically select the syllabus to follow for the neural networks. BID12 also proposed a way to learn simple subtasks before the complex tasks and achieved better results than using manually designed curriculum.In some cases higher learning performance could be obtainable by adding some noises to easy-tohard ordering of the samples. BID8 gave preference to both easy and diverse samples and outperform the conventional Self paced learning BID10 ) algorithm. Emphasizing the uncertain samples suggested by BID3 lead to more accurate and robust SGD training. BID0 explored the inversed versions of the Self paced learning and Self paced learning with diversity BID8 ) and demonstrated that these methods performed slightly better than their standard variants. Consistent with the literature we have showed in our previous work () that using both curriculum and anti-curriculum strategies improving generalization performance in a wide application area. These researches brings a question to minds: While it is natural and logical to obtain better results by sorting the samples from easy-to-hard why it is also better to sort the samples from hard-to-easy?In this study we point that to start with a small training set and add new samples in both curriculum and anti-curriculum learning makes these methods better. So we claim that it is possible to have better results only by adding new samples stage-by-stage without a meaningful order. We experimented two ordering types related with difficulty (easy-to-hard and hard-to-easy) and our method without a meaningful order. Training was carried out by adding a new group to the training set at every stage. We compared the proposed method with two strategies. First one is Curriculum learning which we give the difficulty levels of the samples as pre-information. Second one is Self paced learning which the trained network determines the difficulty levels of the samples at each stage. All methods including usual baseline training have been compared by using paired T-test and the results are examined. We drew our attention that both versions of training with easy-to-hard ordered and hard-to easy ordered samples have better performance. That led us to investigate what common issues they have. We considered that their common point is growing the training sets during training. Therefore, instead of ordering the samples according to difficulty we only added some samples randomly at each stage. In these experiments we obtained similar results with Curriculum, Anti-curriculum, Self Paced and Self Paced-Inversed methods which are related to difficulty levels. According to these results, we can claim that the success of Curriculum learning and Self paced learning approaches not comes from the fact that they follow a meaningful order but trained by growing training sets.In FIG0 we showed some examples for the individual instances. We started the optimization from θ A , instances under this point are considered as easy and above are difficult. If we take an easy instance it is possible or not to guide the optimization to a better minimum. It will be stop at the local minimum θ B in the worst case. Similarly if we take a difficult instance it is possible or not to obtain a better result. Implementation results also showed that both easy-to-hard and hard-to-easy ordered methods can be successful. Therefore ordering of the samples are not so important to guide the optimization.It is a better situation to shorten the distance between θ B and θ C in FIG2 to bypass the local minimum. When the points are same for a saddle point, training with growing sets will probably overcome this point and find a better minimum. This is a good condition when considering saddle points are so much than local minimums in high dimensional functions as mentioned in BID4 .On many data sets with different distributions we used ensemble method to automatically determine the difficulty of the samples for curriculum learning. Pre-processing for difficulty level determination can be thought to caused slowdown. However it has provided a faster neural network training than SPL. Also it could be said that ensemble method set a better ordering than SPL by considering their number of wins against Baseline.ACL and SPLI, which are the inverse versions of the CL and SPL methods, has performed poorly in some high error rated data sets. The effect of giving the samples at different points during the training has been studied in BID5 . In these methods , noisy examples may be effecting the output more because of giving at the beginning. Nevertheless, the inverse versions of the approaches have better performance than their standard versions. However, CL and SPL methods did not lose in any data set so this shows they have a robust aspect. It is thought that these methods must have a theoretical explanation about ensuring resistance to noises. BID6 studied on why these methods are effectiveness especially on big and noisy data.SPLI method has the most winning against Baseline. In this method strategy of selecting the samples to learn at each stage reminds pool-based active learning BID11 ) in which the learner wants to learn the uncertain samples of the unlabeled data pool. Also non-loss of CL and SPL, and more wins of ACL and SPLI shows the necessity of determining the valuable-example-based curriculum instead of easiness-based-curriculum for the future work.",Curriculum learning Self paced learning are popular topics machine learning suggest put training samples order considering difficulty levels. Studies topics show starting small training set adding new samples according difficulty levels improves learning performance. paper experimented can also obtain good results adding samples randomly without meaningful order. compared method classical training Curriculum learning Self paced learning reverse ordered versions. Results statistical tests show proposed method is is a better classical method similar others. results point new training regime removes process difficulty level determination Curriculum Self paced learning successful methods. BID1 named Curriculum learning idea following order related difficulty samples training which provides optimization non convex objectives. many researchers tried find efficient curriculum get best yield approach. BID15 's study conventional curriculum learning did not work well developed new version. BID14 proposed three different curriculum strategies language model adaptation recurrent neural networks. field computer vision BID13 looked best order tasks learn. Although models have better generalization performance proposed curriculum methods is not known whether tried methods ensures best curriculum.A curriculum is work-specific could applicable another work. order use curriculum logic different applications BID10 suggested method learner decides which samples are easy difficult every stage. method called Self paced learning was combined Curriculum learning which provides prior information BID9. another work BID7 introduced method automatically select syllabus follow neural networks. BID12 also proposed way learn simple subtasks complex tasks achieved better results using manually designed curriculum.In cases higher learning performance could obtainable adding noises easy-tohard ordering samples. BID8 gave preference easy diverse samples outperform conventional Self paced learning BID10 algorithm. Emphasizing uncertain samples suggested BID3 lead accurate robust SGD training. BID0 explored inversed versions Self paced learning Self paced learning diversity BID8 demonstrated methods performed slightly better standard variants. Consistent literature have showed previous work using curriculum anti-curriculum strategies improving generalization performance wide application area. researches brings question minds:is natural logical obtain better results sorting samples easy-to-hard why it is also better sort samples hard-to-easy study point start small training set add new samples curriculum anti-curriculum learning makes methods better. claim is possible have better results adding new samples stage-by-stage without meaningful order. experimented two ordering types related difficulty easy-to-hard hard-to-easy method without meaningful order. Training was carried adding new group training set every stage. compared proposed method two strategies. First one is Curriculum learning which we give difficulty levels samples pre-information Second one is Self paced learning which the trained network determines difficulty levels samples stage. methods including usual baseline training have been compared using paired T-test results are examined. drew attention versions training easy-to-hard ordered hard-to easy ordered samples have better performance. ledus investigate what common issues have. considered common point is growing training sets training. Therefore instead ordering samples according difficulty added samples randomly stage. experiments obtained similar results Curriculum Anti-curriculum Self Paced Self Paced-Inversed methods which are related difficulty levels. According results can claim success Curriculum learning Self paced learning approaches comes fact follow meaningful order trained growing training sets.In FIG0 have showed examples individual instances. started optimization θ instances point are considered easy are difficult. If we take easy instance is possible guide optimization have better minimum. will be stop local minimumθB worst case. Similarly if we take difficult instance is possible obtain better result. Implementation results also showed easy-to-hard hard-to-easy ordered methods can be successful. Therefore ordering samples are not so important guide optimization.It is is a better situation shorten distance θB θC FIG2 bypass local minimum. When the points are same for a saddle point training growing sets will probably overcome point find better minimum. is a good condition when considering saddle points are so much local minimums high dimensional functions mentioned BID4.On many data sets different distributions used ensemble method automatically determine difficulty samples curriculum learning. Pre-processing difficulty level determination can be thought caused slowdown. However has provided faster neural network training SPL. Also could said ensemble method set better ordering SPL considering number wins Baseline.ACL SPLI which are the inverse versions CL SPL methods has performed poorly high error rated data sets. effect giving samples different points training has been studied BID5. methods noisy examples may effecting output giving beginning. Nevertheless which are the inverse versions approaches have better performance standard versions. However CL SPL methods did not lose data set shows have a robust aspect. is thought methods must have a theoretical explanation ensuring resistance noises. BID6 studied why these methods are effectiveness especially big noisy data.SPLI method has the most winning Baseline. method strategy selecting samples learn stage reminds pool-based active learning BID11 which the learner wants learn uncertain samples unlabeled data pool. Also non-loss CL SPL wins ACL SPLI shows necessity determining valuable-example-based curriculum instead easiness-based-curriculum future work.,1346,928,418,0.015,1.45,2025/11/05 17:18:55,0.01,1.582,0.3738317757009343,464.955
"We study the problem of learning to map, in an unsupervised way, between domains $A$ and $B$, such that the samples $\vb \in B$ contain all the information that exists in samples $\va\in A$ and some additional information. For example, ignoring occlusions, $B$ can be people with glasses, $A$ people without, and the glasses, would be the added information. When mapping a sample $\va$ from the first domain to the other domain, the missing information is replicated from an independent reference sample $\vb\in B$. Thus, in the above example, we can create, for every person without glasses a version with the glasses observed in any face image. 

 Our solution employs a single two-pathway encoder and a single decoder for both domains. The common part of the two domains and the separate part are encoded as two vectors, and the separate part is fixed at zero for domain $A$. The loss terms are minimal and involve reconstruction losses for the two domains and a domain confusion term. Our analysis shows that under mild assumptions, this architecture, which is much simpler than the literature guided-translation methods, is enough to ensure disentanglement between the two domains. We present convincing results in a few visual domains, such as no-glasses to glasses, adding facial hair based on a reference image, etc. In the problem of unsupervised domain translation, the algorithm receives two sets of samples, one from each domain, and learns a function that maps between a sample in one domain to the analogous sample in the other domain BID37 BID5 BID28 BID29 BID10 BID11 BID38 b; BID26 . The term unsupervised means, in this context, that the two sets are unpaired.In this paper, we consider the problem of domain B, which contains a type of content that is not present at A. As a running example, we consider the problem of mapping between a face without eyewear (domain A) to a face with glasses (domain B). While most methods would map to a person with any glasses, our solution is guided and we attach to an image a ∈ A, the glasses that are present in a reference image b ∈ B.In comparison to other guided image to image translation methods, our method is considerably simpler. It relies on having a latent space with two parts: (i) a shared part that is common to both A and B, and (ii) a specific part that encodes the added content in B. By setting the second part to be the zero vector for all samples in A, a disentanglement emerges. Our analysis shows that this Table 1 : A comparison to other unsupervised guided image to image translation methods.† k = 5 is the number of pre-segmented face parts.‡ Used for domain confusion, not on the output.MUNIT EG-UNIT BID30 DRIT BID27 PairedCycleGAN (Chang' domains. The networks are of four types: encoders, which map images to a latent space, generators (also known as decoders), which generate images from a latent representation, discriminators that are used as part of an adversarial loss, and other, less-standard, networks.It is apparent that our method is considerably simpler than the literature methods. The main reason is that our method is based on the emergence of disentanglement, as detailed in Sec. 4. This allows us to to train with many less parameters and without the need to apply excessive tuning, in order to balance or calibrate the various components of the compound loss.The MUNIT architecture by , like our architecture, employs a shared latent space, in addition to a domain specific latent space. Their architecture is not limited to two domains 1 and unlike ours, employs separate encoders and decoders for the various domains. The type of guiding that is obtained from the target domain in MUNIT is referred to as style, while in our case, the guidance provides content. Therefore , MUNIT, as can be seen in our experiments, cannot add specific glasses, when shifting from the no-glasses domain to the faces with eyewear domain.The EG-UNIT architecture by BID30 presents a few novelties, including an adaptive method of masking-out a varying set of the features in the shared latent space. In our latent representation of domain A, some of the features are constantly zero, which is much simpler. This method also focuses on guiding for style and not for content, as is apparent form their experiments.The very recent DRIT work by BID27 learns to map between two domains using a disentangled representation. Unlike our work, this work seems to focus on style rather than content. The proposed solution differs from us in many ways: (1) it relies on two-way mapping, while we only map from A to B. (2) it relies on shared weights in order to ensure that the common representation is shared. (3) it adds a VAE-like BID24 statistical characterization of the latent space, which results in the ability to sample random attributes. As can be seen in Tab. 1, the solution of BID27 is considerably more involved than our solution.DRIT (and also MUNIT) employ two different types of encoders that enforce a separation of the latent space representations to either style or content vectors. For example, the style encoder , unlike the content encoder, employs spatial pooling and it also results in a smaller representation than the content one. This is important, in the context of these methods, in order to ensure that the two representations encode different aspects of the image. If DRIT or MUNIT were to use the same type of encoder twice, then one encoder could capture all the information, and the image-based guiding (mixing representations from two images) would become mute. In contrast, our method (i) does not separate style and content, and (ii) has a representation that is geared toward capturing the additional content.The work most similar to us in its goal, but not in method, is the PairedCycleGAN work by BID7 . This work explores the single application of applying the makeup of a reference face to a source face image. Unfortunately, the method was only demonstrated on a proprietary unshared dataset and the code is also not publicly available, making a direct comparison impossible at this time. The method itself is completely different from ours and does not employ disentanglement. Instead, a generator with two image inputs is used to produce an output image, where the makeup is transfered between the input images, and a second generator is trained to remove makeup. The generation is done separately to k = 5 pre-segmented facial regions, and the generators do not employ an encoder-decoder architecture.Lastly, there are guided methods, which are trained in the supervised domain, i.e., when there are matches between domain A and B. Unlike the earlier one-to-one work, such as pix2pix BID22 , these methods produce multiple outputs based on a reference image in the target domain. Examples include the Bicycle GAN by , who also applied, as baseline in their experiments, the methods of BID2 BID15 .Other Disentanglement Work InfoGAN BID9 learns a representation in which, due to the statistical properties of the representations, specific classes are encoded as a one-hot encoding of part of the latent vector. In the work of ; BID16 , the representation is disentangled by reducing the class based information within it. The separate class based information is different in nature from our multi-dimensional added content. BID6 , which builds upon BID16 , performs guided image to image translation, but assumes the availability of class based information, which we do not. When converting between two domains, there is an inherent ambiguity that arises from the domainspecific information in the target domain. In guided translation, the reference image in the target domain provides the missing information. Previous work has focused on the missing information that is highly tied to the texture of the image. For example, when translating between paintings and photos, DRIT adds considerable content from the reference photo. However, this is unstructured content, which is not well localized and is highly related to subsets of the image patches that exist in the target domain. In addition, the content from the reference photo that is out of the domain of paintings is not guaranteed to be fully present in the output.Our work focuses on transformations in which the domain specific content is well structured, and guarantees to replicate all of the domain specific information from the reference image. This is done using a small number of networks and a surprisingly simple set of loss terms, which, due to the emergence of a disentangled representation, solves the problem convincingly. In this section we provide notations and terminology that are were not introduced in Sec. 4 but are necessary for the proofs of the claims in this section.We say that three random variables (discrete or continuous) X 1 , X 2 , X 3 form a Markov chain, indicated with DISPLAYFORM0 The Data Processing Inequality (DPI) for a Markov chain X 1 → X 2 → X 3 ensures that I(X 1 ; X 3 ) ≤ min (I(X 1 ; X 2 ), I(X 2 ; X 3 )). In particular, it holds for X 2 = f (X 1 ) and X 3 = g(X 2 ), where f, g are deterministic processes.We denote by x ∼ log N (µ, σ 2 ) a random variable that is distributed by a log-normal distribution, i.e., log x ∼ N (µ, σ 2 ). We consider that the mean and variance of a log-normal distribution log N (µ, σ 2 ) are exp(µ + σ 2 /2) and (exp(σ 2 ) − 1) exp(2µ + σ 2 ) respectively. We denote by W U := (W k,j · U k,j ) k≤m,j≤m the Hadamard product of two matrices W , U ∈ R m×n . For a given vector x ∈ R m , we denote dim(x) := m and for a matrix W ∈ R m×n , we denote dim(W ) := mn. In addition, we denote x 2 = x x = (x 2 1 , . . . , x 2 m ) and DISPLAYFORM1","study problem learning map unsupervised way domains$A $B samples $\vb \inB$ contain information exists samples $\va\in A$ additional information. example ignoring occlusions $B can be people glasses $A people without glasses would added information. When mapping sample $\va first domain domain missing information is replicated independent reference sample $\vb\in B $. Thus example can create every person without glasses version glasses observed face image. solution employs single two-pathway encoder single decoder domains. common part two domains separate part are encoded two vectors separate part is fixed zero domain$A$. loss terms are minimal involve reconstruction losses two domains domain confusion term. analysis shows mild assumptions architecture which is much simpler literature guided-translation methods is enough ensure disentanglement two domains. present convincing results visual domains no-glasses glasses adding facial hair based reference image etc. problem unsupervised domain translation algorithm receives two sets samples one domain learns function maps sample one domain analogous sample which the domain BID37 BID5 BID28 BID29 BID10 BID11 BID38 b;BID26. term unsupervised means context two sets are unpaired.In paper consider problem domainB which contains type content is not are present A. running example consider problem mapping face without eyewear domain face glasses domainB methods would map person glasses solution is guided attach image ∈ glasses is not are present reference imageb∈ B.In comparison guided image image translation methods method is considerably simpler. relies latent space two parts:shared part is common B ii specific part encodes added content B. setting second part zero vector samples disentanglement emerges. analysis shows Table1:comparison unsupervised guided image image translation methods.† k 5 is the number pre-segmented face parts.‡ Used domain confusion output.MUNIT EG-UNIT BID30 DRIT BID27 PairedCycleGAN Chang' domains. networks are of four types:encoders which map images latent space generators also known decoders which generate images latent representation discriminators are used part adversarial loss less-standard networks.It is apparent method is considerably simpler literature methods. main reason is that our method is based emergence disentanglement detailed Sec. 4. allowsus train many less parameters without need apply excessive tuning order balance calibrate various components compound loss.The MUNIT architecture like architecture employs shared latent space addition domain specific latent space. architecture is not limited two domains1 unlike employs separate encoders decoders various domains. type guiding is obtained target domain MUNIT is referred style case guidance provides content. Therefore MUNIT can be seen experiments cannot add specific glasses when shifting no-glasses domain faces eyewear domain.The EG-UNIT architecture BID30 presents novelties including adaptive method masking-out varying set features shared latent space. latent representation domain features are constantly zero which is much simpler. method also focuses guiding style content is apparent form experiments.The recent DRIT work BID27 learns map two domains using disentangled representation. Unlike work work seems focus style rather content. proposed solution differs us many ways:1 relies two-way mapping which map B. 2 relies shared weights order ensure is common representation is shared. 3 adds VAE-like BID24 statistical characterization latent space which results ability sample random attributes. can be seen Tab. 1 solution BID27 is considerably involved solution.DRIT also MUNIT employ two different types encoders enforce separation latent space representations either style content vectors. example style encoder unlike content encoder employs spatial pooling also results smaller representation content one. is important context methods order ensure two representations encode different aspects image. If DRIT MUNIT were to use type encoder twice one encoder could capture information image-based guiding mixing representations two images would become mute. contrast method does separate style content ii has a representation is geared toward capturing additional content.The work similar us goal method is the PairedCycleGAN work BID7. work explores single application applying makeup reference face source face image. Unfortunately method was only demonstrated proprietary unshared dataset code is also publicly available making direct comparison impossible time. method is completely different does employ disentanglement. Instead generator two image inputs is used produce output image where the makeup is transfered input images second generator is trained remove makeup. generation is done separately k 5 pre-segmented facial regions generators do not employ encoder-decoder architecture.Lastly are guided methods which are trained supervised domain.e when there are matches domain B. Unlike earlier one-to-one work pix2pix BID22 methods produce multiple outputs based reference image target domain. Examples include Bicycle GAN who also applied baseline experiments methods BID2 BID15.Other Disentanglement Work InfoGAN BID9 learns representation which,due statistical properties representations specific classes are encoded one-hot encoding part latent vector. work of;BID16 representation is disentangled reducing class based information within it. separate class based information is different nature multi-dimensional added content. BID6 which builds upon BID16 performs guided image image translation assumes availability class based information which we do not. When converting two domains is an inherent ambiguity arises domainspecific information target domain. guided translation reference image target domain provides missing information. Previous work has focused missing information is highly tied texture image. example when translating paintings photos DRIT adds considerable content reference photo. However is unstructured content which is not well localized is highly related subsets image patches exist target domain. addition content reference photo is outof domain paintings is not guaranteed fully present output.Our work focuses transformations which the domain specific content is well structured guarantees replicate domain specific information reference image. is done using small number networks surprisingly simple set loss terms which,due emergence disentangled representation solves problem convincingly. section provide notations terminology are were not introduced Sec. 4 are necessary proofs claims section.We say three random variables discrete continuous X1 X2 X 3 form Markov chain indicated DISPLAYFORM0 Data Processing Inequality DPI Markov chainX1 →X2→ X 3 ensures X1;X3 ≤ min X1;X2 X2;X3 particular holds X2 f X1 X3 g X2 wheref g are deterministic processes.We denote x ∼ logN µ σ2 random variable is distributed log-normal distribution.e logx∼N µ σ2 consider mean variance log-normal distribution logN µ σ2 are exp µ+σ2/2 are exp σ2 −1 are exp 2µ+σ2 respectively. denote WU:Wk j·Uk j k≤m j≤m Hadamard product two matricesW U ∈ R m×n given vectorx∈ R denote dim x matrixW∈R m×n denote dim W mn. addition denotex2 xx x21 x2 DISPLAYFORM1",2121,1335,786,0.026,1.589,2025/11/05 17:18:55,0.01,1.4,0.8068535825545169,739.553
"Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test spits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.
 Deep learning, powered by convolutional and recurrent networks, has had remarkable success in areas involving pattern matching (such as in images BID12 , machine translation BID2 BID25 , and reinforcement learning BID17 BID22 ). However, deep models are far from achieving the robustness and flexibility exhibited by humans. They are limited in their ability to generalize beyond the environments they have experienced and are extremely brittle in the presence of adversarially constructed inputs BID23 .One area where human intelligence still differs and excels compared to neural models is discrete compositional reasoning about objects and entities, that ""algebraically generalize"" BID15 . Our ability to generalise within this domain is complex, multi-faceted, and patently different from the sorts of generalisations that permit us to, for example, translate new sentence of French into English. For example, consider the following question from mathematics, with answer ""−70x − 165"".What is g(h(f (x))), where f (x) = 2x + 3, g(x) = 7x − 4, and h(x) = −5x − 8?To solve this problem, humans use a variety of cognitive skills:• Parsing the characters into entities such as numbers, arithmetic operators, variables (which together form functions) and words (determining the question).• Planning (for example, identifying the functions in the correct order to compose).• Using sub-algorithms for function composition (addition, multiplication).• Exploiting working memory to store intermediate values (such as the composition h(f (x))).• Generally applying acquired knowledge of rules, transformations, processes, and axioms.In this paper, we introduce a dataset consisting of many different types of mathematics problems, with the motivation that it should be harder for a model to do well across a range of problem types (including generalization, which we detail below) without possessing at least some part of these abilities that allow for algebraic generalization.This domain is an important one for the analysis of neural architectures in general. In addition to providing a wide range of questions, there are several other advantages: Mathematics offers a self-consistent universe; notation is the same across different problem types, which allows for an easily extendable dataset; and rules and methods learnt on one problem type often apply elsewhere. Addition of numbers (for example ) obeys the same rules everywhere, and occurs as a ""subroutine"" in other problems (such as concretely in multiplication, and both concretely and more abstractly in addition of polynomials); models that possess the ability to transfer knowledge will do well on the dataset (and knowledge transfer may be a necessity for solving harder problems).Mathematics is also an interesting domain in its own right; although models solving the mostly school-level problems in this dataset would not themselves have applications, they may lead on to more powerful models that can solve interesting and substantial new mathematical problems. But more generally, it is no coincidence that experiments seeking to validate new architectures which aim capture algorithmic/systematic reasoning have often been drawn from this domain BID10 , and thus in providing a large scale training and evaluation framework for such models, we hope to provide a solid foundation upon which to continue such research into machine reasoning beyond mathematics.Question: Solve -42 * r + 27 * c = -1167 and 130 * r + 4 * c = 372 for r. Answer: 4 Question: Calculate -841880142.544 + 411127. Answer: -841469015.544 Question: Let x(g) = 9 * g + 1. Let q(c) = 2 * c + 1. Let f(i) = 3 * i -39. Let w(j) = q(x(j)). Calculate f(w(a )). Answer: 54 * a -30 Question: Let e(l ) = l -6. Is 2 a factor of both e(9) and 2? Answer: False Question: Let u(n) = -n ** 3 -n ** 2. Let e(c) = -2 * c ** 3 + c. Let l(j) = -118 * e(j) + 54 * u(j ). What is the derivative of l(a)? Answer: 546 * a ** 2 -108 * a -118 Question: Three letters picked without replacement from qqqkkklkqkkk. Give prob of sequence qql. Answer: 1/110Figure 1: Examples from the dataset. We have created a dataset on which current state-of-the-art neural models obtain moderate performance. Some modules are largely unsolved (for example those requiring several intermediate calculations), for which a human would find easy, and extrapolation performance is low. We hope this dataset will become a robust analyzable benchmark for developing models with more algebraic/symbolic reasoning abilities.The dataset is easily extendable, since it is modular, with all modules using a common input/output format and the common language of mathematics. The main restriction is that the answers must be well-determined (i.e. unique), but this still allows for covering a lot of mathematics up to university level. At some point it becomes harder to cover more of mathematics (for example, proofs) while maintaining the sequence-to-sequence format, but hopefully by this point the dataset in its current format will have served its purpose in developing models that can reason mathematically. Alternatively, we could consider methods for assessing answers where there is not a single unique answer; for now the full scope of possibilities is too large to include in this paper, but a few possibilities include metrics such as BLEU BID18 , by extending the data generation process to provide several reference answers, or by obtaining human paraphrases following the data augmentation process proposed by BID27 .We have not addressed linguistic variation or complexity in this dataset. Although to some extent linguistic complexity is orthogonal to the difficulty of the maths problems involved, the two cannot be entirely separated. The most obvious example of this for school-level mathematics is in algebraic word problems, where much of the difficulty lies in translating the description of the problem into an algebraic problem. Thus it would be useful to extend the dataset with ""linguistic complexity"", where the same underlying mathematical problem is phrased in quite distinct, and not-at-first-obvious, translations. One option may be to do joint training on this dataset, and that of BID14 another would be to obtain more question templates via mechanical turking, as proposed by BID27 .Finally one completely distinct direction the dataset could be extended is to include visual (e.g. geometry) problems as well. For humans, visual reasoning is an important part of mathematical reasoning, even concerning problems that are not specified in a visual format. Therefore we want to develop questions along these lines, including those that require ""intermediate visual representations"" (in a similar way to how the textual module composition requires intermediate digital representations) and visual working memory. Note that reasoning with intermediate visual representations or ideas is richer than simply analyzing a visual domain (such as is typical in visual question-answering datasets).",Mathematical reasoning -a core ability within human intelligence -presents unique challenges domain:do not come understand solve mathematical problems primarily back experience evidence basis inferring learning exploiting laws axioms symbol manipulation rules. paper present new challenge evaluation eventually design neural architectures similar system developing task suite mathematics problems involving sequential questions answers free-form textual input/output format. structured nature mathematics domain covering arithmetic algebra probability calculus enables construction training test spits designed clearly illuminate capabilities failure-modes different architectures well evaluate ability compose relate knowledge learned processes. described data generation process potential future expansions conduct comprehensive analysis models two broad classes powerful sequence-to-sequence architectures find notable differences ability resolve mathematical problems generalize knowledge. Deep learning powered convolutional recurrent networks has had remarkable success areas involving pattern matching images BID12 machine translation BID2 BID25 reinforcement learning BID17 BID22 However deep models are far achieving robustness flexibility exhibited humans. are limited ability generalize beyond environments have experienced are extremely brittle presence adversarially constructed inputs BID23.One area where human intelligence still differs excels compared neural models is discrete compositional reasoning objects entities algebraically generalize BID15. ability generalise within domain is complex multi-faceted patently different sorts generalisations permitus example translate new sentence French English. example consider following question mathematics answer −70x − 165.What isg h f x where f x 2x+3 g x 7x−4 h x −5x−8? solve problem humans use variety cognitive skills:• Parsing characters entities numbers arithmetic operators variables which together form functions words determining question.• Planning example identifying functions correct order compose.• Using sub-algorithms function composition addition multiplication.• Exploiting working memory store intermediate values compositionh f x.• Generally applying acquired knowledge rules transformations processes axioms.In paper introduce dataset consisting many different types mathematics problems motivation should be harder model do well across range problem types including generalization which we detail without possessing least part abilities allow algebraic generalization.This domain is an important one analysis neural architectures general. addition providing wide range questions are several advantages:Mathematics offers self-consistent universe;notation is the same across different problem types which allows easily extendable dataset;rules methods learnt one problem type often apply elsewhere. Addition numbers example obeys rules everywhere occurs subroutine problems concretely multiplication concretely abstractly addition polynomials models possess ability transfer knowledge will do well dataset knowledge transfer may necessity solving harder problems.Mathematics is also interesting domain right;although models solving mostly school-level problems dataset would have applications may lead powerful models can solve interesting substantial new mathematical problems. generally is no coincidence experiments seeking validate new architectures which aim capture algorithmic/systematic reasoning have often drawn domain BID10 thus providing large scale training evaluation framework models hope provide solid foundation upon which to continue research machine reasoning beyond mathematics.Question:Solve -42*r+27*c -1167 130*r+4*c 372 r. Answer:4 Question:Calculate -841880142.544+411127. Answer:-841469015.544 Question:Letx g 9*g+1. Letq c 2*c+1. Letf 3* -39 Letw j q x j Calculatef w Answer:54* -30 Question:Lete l l-6 Is2 factor e 9 2? Answer:False Question:Letu n -n**3 -n**2. Lete c -2*c* *3+c. Letl j -118*e j+54*u j Whatis derivative l Answer:546* * * 2 -108 * -118 Question:Three letters picked without replacement qqqkkklkqkkk. Give prob sequence qql. Answer:1/110Figure1:Examples dataset. have created dataset which current state-of-the-art neural models obtain moderate performance. modules are largely unsolved example requiring several intermediate calculations which human would find easy extrapolation performance is low. hope dataset will become robust analyzable benchmark developing models algebraic/symbolic reasoning abilities.The dataset is easily extendable since is modular modules using common input/output format common language mathematics. main restriction is that the answers must well-determined.e unique still allows covering lot mathematics university level. point becomes harder cover mathematics example proofs maintaining sequence-to-sequence format hopefully point dataset current format will have served purpose developing models can reason mathematically. Alternatively could consider methods assessing answers where there is not single unique answer;full scope possibilities is too large include paper possibilities include metrics BLEU BID18 extending data generation process provide several reference answers obtaining human paraphrases following data augmentation process proposed BID27.We have not addressed linguistic variation complexity dataset. Although extent linguistic complexity is orthogonal difficulty maths problems involved two cannot entirely separated. obvious example school-level mathematics is in algebraic word problems where much difficulty lies translating description problem algebraic problem. Thus would useful extend dataset linguistic complexity where the same underlying mathematical problem is phrased quite distinct not-at-first-obvious translations. One option may do joint training dataset BID14 another would obtain question templates via mechanical turking proposed BID27.Finally one completely distinct direction dataset could extended is to include visual e.g geometry problems well. humans visual reasoning is an important part mathematical reasoning even concerning problems are not specified visual format. Therefore want develop questions along lines including require intermediate visual representations similar way how the textual module composition requires intermediate digital representations visual working memory. Note reasoning intermediate visual representations ideas is richer simply analyzing visual domain is typical visual question-answering datasets,1655,1090,565,0.02,1.518,2025/11/05 17:18:55,0.01,1.463,0.585669781931464,528.221
"Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compactly supported stencils and point-wise nonlinearities.
 Commonly, the convolution operators couple features from all channels.
 For wide networks, this leads to immense computational cost in the training of and prediction with CNNs.
 In this paper, we present novel ways to parameterize the convolution more efficiently, aiming to decrease the number of parameters in CNNs and their computational complexity.
 We propose new architectures that use a sparser coupling between the channels and thereby reduce both the number of trainable weights and the computational cost of the CNN.
 Our architectures arise as new types of residual neural network (ResNet) that can be seen as discretizations of a Partial Differential Equations (PDEs) and thus have predictable theoretical properties. Our first architecture involves a convolution operator with a special sparsity structure, and is applicable to a large class of CNNs. Next, we present an architecture that can be seen as a discretization of a diffusion reaction PDE, and use it with three different convolution operators. We outline in our experiments that the proposed architectures,  although considerably reducing the number of trainable weights, yield comparable accuracy to existing CNNs that are fully coupled in the channel dimension.
 Convolutional Neural Networks (CNNs) BID18 are among the most effective machine learning approaches for processing structured high-dimensional input data and are indispensable in, e.g., in recognition tasks involving speech BID22 and image data BID16 . The essential idea behind CNNs is to replace some or all of the affine linear transformations in a neural network by convolution operators that are typically parameterized using small-dimensional stencils. This has a number of benefits including the increase of computational efficiency of the network due to the sparse connections between features, and a considerable reduction in the number of weights since stencils are shared across the whole feature map BID6 .In practical applications of CNNs, the features can be grouped into channels whose number is associated with the width of the network. This gives one several opportunities to define interactions between the different channels. Perhaps , the most common approach in CNNs is to fully couple features across channels BID7 BID6 BID16 . Following this approach, the number of convolution operators at a layer is proportional to the product of the number of input and output channels. Given that performing convolutions is often the computationally most expensive part in training of and prediction with CNNs and the number of channels is large in many applications, this scaling can be problematic for wide architectures or high-dimensional data. Another disadvantage of this type of architecture is the number of weights. Indeed, for deep neural networks, the number of weights that are associated with a wide network can easily reach millions and beyond. This makes the deployment of such networks challenging, especially on devices with limited memory.In this paper, we propose four novel ways to parameterize CNNs more efficiently, based on ideas from Partial Differential Equations (PDEs). Our goal is to dramatically reduce the number of weights in the networks and the computational costs of training and evaluating the CNNs. One ides, similar to BID13 , is to use spatial convolutions for each channel individually and add Table 1 : Cost comparison of different convolution layers for an image with n pixels, stencil of size m × m, and c input and output channels. RD denotes a reaction-diffusion architecture.no. of weights computational costs fully-coupled DISPLAYFORM0 1 × 1 convolutions to impose coupling between them. Our architectures are motivated by the interpretation of residual neural networks (ResNets) BID11 BID18 as time-dependent nonlinear PDEs BID24 . More specifically, we consider a simple Reaction-Diffusion (RD) model, that can model highly nonlinear processes. We derive new architectures by discretizing this continuous model, using 1×1 convolutions as a reaction term, together with cheap forms of a spatial convolution, that are similar to a depth-wise convolution in the number of parameters and cost. This spatial convolution acts similarly to a linear diffusion term that smooths the feature channels. Since the networks we propose originate in continuous models they have distinct theoretical properties that can be predicted using the standard theory of ODEs and PDEs BID0 .Our first approach is designed to be employed in any existing CNN layer with equal number of input and output channels. We simply replace the traditional fully coupled convolution with a linear sum of depth-wise and 1 × 1 convolution, like a mask that can be placed on a traditional convolution in any existing CNN. Our second ""explicit"" RD architecture applies the operators separately with a non-linear activation function operating only following the 1 × 1 convolution, as the non-linear reaction part of the diffusion reaction equation. The third architecture is more unique . To improve the stability of the forward propagation and increase the spatial coupling of the features, we propose a semi-implicit scheme for the forward propagation through the network. Unlike traditional CNN operators, the semi-implicit scheme applies an inverse of the depth-wise (block diagonal) convolution preceded by a non-linear step involving the 1 × 1 convolution. This way, the scheme couples all the pixels in the image in one layer, even though we are using a depth-wise 3 × 3 convolution. The inverse of the convolution operator can be efficiently computed using Fast Fourier Transforms (FFT) and over the channels and kernels.The last idea is to replace the depth-wise convolution structure with a circulant connectivity between the channels. This is motivated by the interpretation of the features as tensors and follows the definition of an efficient tensor product in BID14 whose associated tensor singular value decomposition has been successfully used for image classification in BID20 . The circulant structure renders the number of trainable convolution stencils proportional to the width of the layer. Using periodic boundary conditions in the other feature dimensions, this convolution can be computed efficiently by extending the FFT-based convolutions in BID19 BID26 along the channel dimension, which reduces the cost from O(c 2 ) to O(c log c) where c is the number of channels. Table 1 compares the number of weights and the computational complexity associated with the forward propagation through a layer for the standard and reduced architectures. In the table we assume that the explicit RD architecture is directly computed without using FFT, but the FFT-based implementation, which is necessary for the implicit scheme, can also be used for the explicit one.Our architectures pursue a similar goal than the recently proposed MobileNet architectures that are also based on a mix of 1 × 1 and ""depth-wise"" convolutions BID13 BID25 . The MobileNet architecture involves with significantly less parameters, and in particular avoids the fully coupled convolutions, except for 1 × 1 convolutions which are cheaper in both computational cost and number of parameters. What sets our work apart from these architectures is that our architectures can be seen as discretization of PDEs, which allows to control their stability and offers new ways for their analysis.The remainder of the paper is organized as follows. We first describe the mathematical formulation of the supervised classification problem with deep residual neural networks used in this paper. Subsequently, we propose the novel parameterizations of CNNs, describe their efficient implementation, and their computational costs. We perform experiments using the CIFAR10, CIFAR 100, and STL10 datasets and demonstrate that the performance of the new architectures, despite a considerable reduction in the number of trainable weights, is comparable to residual neural networks using fully-coupled convolutions. Finally, we summarize and conclude the paper. We present four new convolution models with the common goal of reducing the number of parameters and computational costs of CNNs. To this end, we propose alternative ways to the traditional full coupling of channels, and thereby obtain architectures that involve fewer expensive convolutions, avoid redundancies in the network parametrization, and thereby can be deployed more widely. Our work is similar to that of BID13 BID25 . However, our unique angle is the close relation of our architectures to continuous models given in terms of PDEs that are well understood. This highlights stability of our CNNs and paves the way toward more extensive theory.Our numerical experiments for image classification show that the new architectures can be almost as effective as more expensive fully coupled CNN architectures. We expect that our architectures will be able to replace the traditional convolutions in classification of audio and video, and also in other tasks that are treated with CNNs. It is important to realize that our new architectures become even more advantageous for 3D or 4D problems, e.g., when analyzing time series of medical or geophysical images. In these cases, the cost of each convolution is much more expensive and the computational complexity makes using 3D CNNs difficult. Here, also the number of weights imposes challenges when using computational hardware with moderate memory.",Convolutional Neural Networks CNNs filter input data using series spatial convolution operators compactly supported stencils point-wise nonlinearities. Commonly convolution operators couple features channels. wide networks leads immense computational cost training prediction CNNs. paper present novel ways parameterize convolution efficiently aiming decrease number parameters CNNs computational complexity. propose new architectures use sparser coupling channels thereby reduce number trainable weights computational cost CNN. architectures arise new types residual neural network ResNet can be seen discretizations Partial Differential Equations PDEs thus have predictable theoretical properties. first architecture involves convolution operator special sparsity structure is applicable large class CNNs. Next present architecture can be seen discretization diffusion reaction PDE is to use three different convolution operators. outline experiments proposed architectures although considerably reducing number trainable weights yield comparable accuracy existing CNNs are fully coupled channel dimension. Convolutional Neural Networks CNNs BID18 are among effective machine learning approaches processing structured high-dimensional input data are indispensable e.g recognition tasks involving speech BID22 image data BID16. essential idea behind CNNs is to replace affine linear transformations neural network convolution operators are typically parameterized using small-dimensional stencils. has a number benefits including increase computational efficiency network due sparse connections features considerable reduction number weights since stencils are shared across whole feature map BID6.In practical applications CNNs features can be grouped channels whose number is associated width network. gives one several opportunities define interactions different channels. Perhaps common approach CNNs is to fully couple features across channels BID7 BID6 BID16. Following approach number convolution operators layer is proportional product number input output channels. Given performing convolutions is often computationally expensive part training prediction CNNs number channels is large many applications scaling can be problematic wide architectures high-dimensional data. Another disadvantage type architecture is the number weights. Indeed deep neural networks number weights are associated wide network can easily reach millions beyond. makes deployment networks challenging especially devices limited memory.In paper propose four novel ways parameterize CNNs efficiently based ideas Partial Differential Equations PDEs goal is to dramatically reduce number weights networks computational costs training evaluating CNNs. One ides are similar BID13 is to use spatial convolutions channel individually add Table1:Cost comparison different convolution layers image n pixels stencil size × c input output channels. RD denotes reaction-diffusion architecture.no. weights computational costs fully-coupled DISPLAYFORM01×1 convolutions impose coupling them. architectures are motivated interpretation residual neural networks ResNets BID11 BID18 time-dependent nonlinear PDEs BID24. specifically consider simple Reaction-Diffusion RD model can model highly nonlinear processes. derive new architectures discretizing continuous model using 1×1 convolutions reaction term together cheap forms spatial convolution are similar depth-wise convolution number parameters cost. spatial convolution acts similarly linear diffusion term smooths feature channels. Since networks propose originate continuous models have distinct theoretical properties can be predicted using standard theory ODEs PDEs BID0.Our first approach is designed employed existing CNN layer equal number input output channels. simply replace traditional fully coupled convolution linear sum depth-wise 1 × 1 convolution like mask can be placed traditional convolution existing CNN. second explicit RD architecture applies operators separately non-linear activation function operating following 1 × 1 convolution non-linear reaction part diffusion reaction equation. third architecture is more unique. improve stability forward propagation increase spatial coupling features propose semi-implicit scheme forward propagation network. Unlike traditional CNN operators semi-implicit scheme applies inverse depth-wise block diagonal convolution preceded non-linear step involving 1 × 1 convolution. way scheme couples pixels image one layer even though are using depth-wise3×3 convolution. inverse convolution operator can be efficiently computed using Fast Fourier Transforms FFT channels kernels.The last idea is to replace depth-wise convolution structure circulant connectivity channels. is motivated interpretation features tensors follows definition efficient tensor product BID14 whose associated tensor singular value decomposition has been successfully used image classification BID20. circulant structure renders number trainable convolution stencils proportional width layer. Using periodic boundary conditions feature dimensions convolution can be computed efficiently extending FFT-based convolutions BID19 BID26 along channel dimension which reduces cost c2 where c logc wherec is the number channels. Table 1 compares number weights computational complexity associated forward propagation layer standard reduced architectures. table assume explicit RD architecture is directly computed without using FFT FFT-based implementation which is necessary implicit scheme can also used explicit one.Our architectures pursue similar goal recently proposed MobileNet architectures are also based mix 1×1 depth-wise convolutions BID13 BID25. MobileNet architecture involves significantly less parameters particular avoids fully coupled convolutions except 1 × 1 convolutions which are cheaper computational cost number parameters. What sets work apart architectures is that our architectures can be seen discretization PDEs which allows control stability offers new ways analysis.The remainder paper is organized follows. first describe mathematical formulation supervised classification problem deep residual neural networks used paper. Subsequently propose novel parameterizations CNNs describe efficient implementation computational costs. perform experiments using CIFAR10 CIFAR 100 STL10 datasets demonstrate performance new architectures despite considerable reduction number trainable weights is comparable residual neural networks using fully-coupled convolutions. Finally summarize conclude paper. present four new convolution models common goal reducing number parameters computational costs CNNs. end propose alternative ways traditional full coupling channels thereby obtain architectures involve fewer expensive convolutions avoid redundancies network parametrization thereby can be deployed widely. work is similar BID13 BID25. However unique angle is the close relation architectures continuous models given terms PDEs are well understood. highlights stability CNNs paves way toward extensive theory.Our numerical experiments image classification show new architectures can be almost effective expensive fully coupled CNN architectures. expect architectures will be able replace traditional convolutions classification audio video can also tasks are treated CNNs. is important realize new architectures become even advantageous 3D 4D problems e.g when analyzing time series medical geophysical images. cases cost convolution is much expensive computational complexity makes using 3D CNNs difficult. also number weights imposes challenges when using computational hardware moderate memory.,1783,1187,596,0.021,1.502,2025/11/05 17:18:56,0.01,1.417,0.5358255451713394,547.359
"In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One way to address this question is to find an upper bound on the probability (equivalently a lower bound on the negative log likelihood) that the model can assign to some data as one varies the prior and/or the likelihood function in a latent variable model. The core of our contribution is to formally show that the problem of optimizing priors in latent variable models is exactly an instance of the variational optimization problem that information theorists solve when computing rate-distortion functions, and then to use this to derive a lower bound on negative log likelihood. Moreover, we will show that if changing the prior can improve the log likelihood, then there is a way to change the likelihood function instead and attain the same log likelihood, and thus rate-distortion theory is of relevance to both optimizing priors as well as optimizing likelihood functions. We will experimentally argue for the usefulness of quantities derived from rate-distortion theory in latent variable modeling by applying them to a problem in image modeling. A statistician plans to use a latent variable model DISPLAYFORM0 where p(z) is known as the prior over the latent variables, and (x|z) is the likelihood of the data conditional on the latent variables; we will often use (p(z), (x|z)) as a shorthand for the model. Frequently, both the prior and the likelihood are parametrized and the statistician's job is to find reasonable parametric families for both -an optimization algorithm then chooses the parameter within those families. The task of designing these parametric families can sometimes be time consuming -this is one of the key modeling tasks when one adopts the representation learning viewpoint in machine learning.In this article we ask the question of how much p(z) can be improved if one fixes (x|z) and viceversa, with the goal of equipping the statistician with tools to make decisions on where to invest her time. One way to answer whether p(z) can be improved for fixed (x|z) is to drop the assumption that p(z) must belong to a particular family and ask how a model could improve in an unrestricted setting. Mathematically, given data {x 1 , · · · , x N } the first problem we study is the following optimization problem: for a fixed (x|z), DISPLAYFORM1 which as we will show, is also indirectly connected to the problem of determining if (x|z) can be improved for a given fixed p(z). The quantity being optimized in (2) is called the average negative log likelihood of the data, and is used whenever one assumes that the data {x 1 , · · · , x N } have been drawn statistically independently at random. Note that in this paper we are overloading the meaning of p(z): in (1) it refers to prior in the ""current"" latent variable model in the statistician's hands, and in (2) and other similar equations, it refers to a prior that can be optimized. We believe that the meaning will be clear depending on the context.Obviously, for any given (x|z), p(z), from the definition (1) we have the trivial upper bound DISPLAYFORM2 Can we give a good lower bound? A lower bound could tell us how far we can improve the model by changing the prior. The answer turns out to be in the affirmative. In an important paper, BID14 proved several facts about the problem of optimizing priors in latent variable models. In particular, he showed that DISPLAYFORM3 This result is very general -it holds for both discrete and continuous latent variable spaces, scalar or vector. It is also sharp -if you plug in the right prior, the upper and lower bounds match. It also has the advantage that the lower bound is written as a function of the trivial upper bound (3) -if someone proposes a latent variable model p(x) which uses a likelihood function (x|z), the optimal negative log likelihood value when we optimize the prior is thus known to be within a gap of DISPLAYFORM4 bits. The individual quantities under the sup c(z) DISPLAYFORM5 have a specific functional meaning: they can be regarded as multiplicative factors that tell you how to modify the prior to improve the log likelihood (see the Blahut-Arimoto algorithm BID3 ): DISPLAYFORM6 Lindsay (1983) derived his results with no apparent reference to earlier published work on ratedistortion theory, which is how information theorists study the problem of lossy compression BID19 . There is no reason for why this connection could be reasonably made, as it is not immediately obvious that the problems are connected; However, the quantity c(z) and the lower bound (4) in fact can be derived from ideas in Berger's book on rate-distortion theory BID2 ; in fact Lindsey's classical result that the optimal prior in a latent variable model has finite support with size equal to the size of the training data can be, drawing the appropriate connection, seen as a result of a similar result in rate-distortion theory also contained in BID2 .With time, the fundamental connection between the log likelihood optimization in latent variable modeling and the computation of rate-distortion functions became more clear. Although not explicitly mentioned in these terms, BID18 BID16 restate the optimal log likelihood as a problem of minimizing the variational free energy of a certain statistical system; this expression is identical to the one that is optimized in rate-distortion theory. The Information Bottleneck method of BID22 is a highly successful idea that exists in this boundary, having created a subfield of research that remains relevant nowadays BID23 ) BID20 . BID21 showed a fundamental connection between maximum likelihood and the information bottleneck method: ""every fixed point of the IB-functional defines a fixed point of the (log) likelihood and vice versa"". BID1 defined a rate-distortion problem where the output alphabet Z is finite and is jointly optimized with the test channel. By specializing to the case of where the distortion measure is a Bregman divergence, they showed the mathematical equivalence between this problem and that of maximum likelihood estimation where the likelihood function is an exponential family distribution derived from the Bregman divergence. BID27 study a variation of the maximum likelihood estimation for latent variable models where the maximum likelihood criterion is instead replaced with the entropic risk measure. The autoencoder concept extensively used in the neural network community is arguably directly motivated by the encoder/decoder concepts in lossy/lossless compression. BID7 proposed using a matrix based expression motivated by rate-distortion ideas in order to train autoencoders while avoiding estimating mutual information directly. Recently, BID0 exploited the β-VAE loss function of BID8 to explicitly introduce a trade-off between rate and distortion in the latent variable modeling problem, where the notions of rate and distortion have similarities to those used in our article.Latent Variable Modeling is undergoing an exciting moment as it is a form of representation learning, the latter having shown to be an important tool in reaching remarkable performance in difficult machine learning problems while simultaneously avoiding feature engineering. This prompted us to look deeper into rate-distortion theory as a tool for developing a theory of representation learning. What excites us is the possibility of using a large repertoire of tools, algorithms and theoretical results in lossy compression in meaningful ways in latent variable modeling; notably, we believe that beyond what we will state in this article, Shannon's famous lossy source coding theorem, the information theory of multiple senders and receivers, and the rich Shannon-style equalities and inequalities involving entropy and mutual information are all of fundamental relevance to the classical problem (1) and more complex variations of it.The goal of this article is laying down a firm foundation that we can use to build towards the program above. We start by proving the fundamental equivalence between these two fields by using simple convexity arguments, avoiding the variational calculus arguments that had been used before. We then take an alternate path to proving (2) also involving simple convexity arguments inspired by earlier results in rate-distortion theory.We then focus on what is a common problem -instead of improving a prior for a fixed likelihood function, improve the likelihood function for a fixed prior but for a fixed prior. Interestingly, ratedistortion theory still is relevant to this problem, although the question that we are able to answer with it is smaller in scope. Through a simple change of variable argument , we will argue that if the negative log likelihood can be improved by modifying the prior, exactly the same negative log likelihood can be attained by modifying the likelihood function instead. Thus if rate-distortion theory predicts that there is scope for improvement for a prior, the same holds for the likelihood function but conversely, while rate-distortion theory can precisely determine when it is that a prior can no longer be improved, the same cannot be said for the likelihood function.Finally, we test whether the lower bound derived and the corresponding fundamental quantity c(z) are useful in practice when making modeling decisions by applying these ideas to a problem in image modeling for which there have been several recent results involving Variational Autoencoders. The main goal for this article was to argue strongly for the inclusion of rate-distortion theory as key for developing a theory of representation learning. In the article we showed how some classical results in latent variable modeling can be seen as relatively simple consequences of results in ratedistortion function computation, and further argued that these results help in understanding whether prior or likelihood functions can be improved further (the latter with some limitations), demonstrating this with some experimental results in an image modeling problem. There is a large repertoire of tools, algorithms and theoretical results in lossy compression that we believe can be applied in meaningful ways to latent variable modeling. For example, while rate-distortion function computation is an important subject in information theory, the true crown jewel is Shannon's famous source coding theorem; to-date we are not aware of this important result being connected directly to the problem of latent variable modeling. Similarly, rate-distortion theory has evolved since Shannon's original publication to treat multiple sources and sinks; we believe that these are of relevance in more complex modeling tasks. This research will be the subject of future work.","article use rate-distortion theory branch information theory devoted problem lossy compression shed light important problem latent variable modeling data:is there room improve model? One way address question is to find upper bound probability equivalently lower bound negative log likelihood model can assign data one varies prior/likelihood function latent variable model. core contribution is to formally show problem optimizing priors latent variable models is exactly instance variational optimization problem information theorists solve when computing rate-distortion functions use derive lower bound negative log likelihood. Moreover will show if changing prior can improve log likelihood is way change likelihood function instead attain log likelihood thus rate-distortion theory is of relevance optimizing priors well optimizing likelihood functions. will experimentally argue usefulness quantities derived rate-distortion theory latent variable modeling applying problem image modeling. statistician plans use latent variable model DISPLAYFORM0 wherep z is known prior latent variables x|z is the likelihood data conditional latent variables;will often use p z x|z shorthand model. Frequently prior likelihood are parametrized statistician's job is to find reasonable parametric families -an optimization algorithm chooses parameter within families. task designing parametric families can sometimes time consuming -this is one key modeling tasks when one adopts representation learning viewpoint machine learning.In article ask question how muchp z can be improved if one fixes x|z viceversa goal equipping statistician tools make decisions where to invest time. One way answer whetherp z can be improved fixed x|z is to drop assumption p z must belong particular family ask how a model could improve unrestricted setting. Mathematically given data x1 ··· xN first problem study is the following optimization problem:fixed x|z DISPLAYFORM1 which as we will show is also indirectly connected problem determining if(x|z can be improved given fixedp z quantity optimized 2 is called average negative log likelihood data is used whenever one assumes data x1 ··· xN have been drawn statistically independently random. Note paper are overloading meaning p z 1 refers prior current latent variable model statistician's hands 2 similar equations refers prior can be is optimized. believe meaning will be clear depending context.Obviously given x|z p z definition 1 have the trivial upper bound DISPLAYFORM2 Can we give good lower bound? lower bound could tell us how far can improve model changing prior. answer turns affirmative. important paper BID14 proved several facts problem optimizing priors latent variable models. particular showed DISPLAYFORM3 result is very general -it holds discrete continuous latent variable spaces scalar vector. is also sharp -if plug right prior upper lower bounds match. is also has the advantage lower bound is written function trivial upper bound 3 -if someone proposes latent variable modelp x which uses likelihood function x|z optimal negative log likelihood value when we optimize prior is thus known within gap DISPLAYFORM4 bits. individual quantities supc z DISPLAYFORM5 have a specific functional meaning:can be regarded multiplicative factors tell how to modify prior improve log likelihood see Blahut-Arimoto algorithm BID3 DISPLAYFORM6 Lindsay 1983 derived results apparent reference earlier published work ratedistortion theory which is how information theorists study problem lossy compression BID19. is no reason why this connection could reasonably made is immediately obvious problems are connected;However quantityc z lower bound 4 fact can be derived ideas Berger's book rate-distortion theory BID2;fact Lindsey's classical result optimal prior latent variable model has finite support size equal size training data can be,drawing appropriate connection seen result similar result rate-distortion theory also contained BID2.With time fundamental connection log likelihood optimization latent variable modeling computation rate-distortion functions became clear. Although explicitly mentioned terms BID18 BID16 restate optimal log likelihood problem minimizing variational free energy certain statistical system;expression is identical one can be is optimized rate-distortion theory. Information Bottleneck method BID22 is a highly successful idea exists boundary created subfield research remains relevant nowadays BID23 BID20. BID21 showed fundamental connection maximum likelihood information bottleneck method:every fixed point IB-functional defines fixed point log is the likelihood vice versa. BID1 defined rate-distortion problem where the output alphabetZ is finite is jointly optimized test channel. specializing case where the distortion measure is a Bregman divergence showed mathematical equivalence problem maximum likelihood estimation where the likelihood function is an exponential family distribution derived Bregman divergence. BID27 study variation maximum likelihood estimation latent variable models where the maximum likelihood criterion is instead replaced entropic risk measure. autoencoder concept extensively used neural network community is arguably directly motivated encoder/decoder concepts lossy/lossless compression. BID7 proposed using matrix based expression motivated rate-distortion ideas order train autoencoders avoiding estimating mutual information directly. Recently BID0 exploited β-VAE loss function BID8 explicitly introduce trade-off rate distortion latent variable modeling problem where the notions rate distortion have similarities used article.Latent Variable Modeling is undergoing exciting moment is a form representation learning latter shown important tool reaching remarkable performance difficult machine learning problems simultaneously avoiding feature engineering. promptedus look deeper rate-distortion theory tool developing theory representation learning. What excitesus is the possibility using large repertoire tools algorithms theoretical results lossy compression meaningful ways latent variable modeling;notably believe beyond what we will state article Shannon's famous lossy source coding theorem which is how information theory multiple senders receivers rich Shannon-style equalities inequalities involving entropy mutual information are all of fundamental relevance classical problem 1 complex variations it.The goal article is laying firm foundation can use build towards program above. start proving fundamental equivalence two fields using simple convexity arguments avoiding variational calculus arguments had been used before. take alternate path proving 2 also involving simple convexity arguments inspired earlier results rate-distortion theory.We focus what is a common problem -instead improving prior fixed likelihood function improve likelihood function fixed prior fixed prior. Interestingly ratedistortion theory still is relevant problem although question are able answer is smaller scope. simple change variable argument will argue if the negative log likelihood can be improved modifying prior exactly negative log likelihood can be attained modifying likelihood function instead. Thus if rate-distortion theory predicts is scope improvement prior holds likelihood function conversely rate-distortion theory can precisely determine when it is that prior can no longer improved cannot said likelihood function.Finally test whether lower bound derived corresponding fundamental quantityc z are useful practice when making modeling decisions applying ideas problem image modeling which there have several recent results involving Variational Autoencoders. main goal article was to argue strongly inclusion rate-distortion theory key developing theory representation learning. article showed how some classical results latent variable modeling can be seen relatively simple consequences results ratedistortion function computation argued results help understanding whether prior likelihood functions can be improved latter limitations demonstrating experimental results image modeling problem. is a large repertoire tools algorithms theoretical results lossy compression believe can be applied meaningful ways latent variable modeling. example rate-distortion function computation is an important subject information theory true crown jewel is Shannon's famous source coding theorem;to-date are not aware important result connected directly problem latent variable modeling. Similarly rate-distortion theory has evolved since Shannon's original publication treat multiple sources sinks;believe are of relevance complex modeling tasks. research will be the subject future work.",2092,1428,664,0.033,1.465,2025/11/05 17:18:56,0.01,1.624,0.4205607476635514,763.687
"Backprop is the primary learning algorithm used in many machine learning algorithms. In practice, however, Backprop in deep neural networks is a highly sensitive learning algorithm and successful learning depends on numerous conditions and constraints. One set of constraints is to avoid weights that lead to saturated units. The motivation for avoiding unit saturation is that gradients vanish and as a result learning comes to a halt. Careful weight initialization and re-scaling schemes such as batch normalization ensure that input activity to the neuron is within the linear regime where gradients are not vanished and can flow. Here we investigate backpropagating error terms only linearly. That is, we ignore the saturation that arise by ensuring gradients always flow. We refer to this learning rule as Linear Backprop since in the backward pass the network appears to be linear. In addition to ensuring persistent gradient flow, Linear Backprop is also favorable when computation is expensive since gradients are never computed. Our early results suggest that learning with Linear Backprop is competitive with Backprop and saves expensive gradient computations.","Backprop is the primary learning algorithm used many machine learning algorithms. practice however Backprop deep neural networks is a highly sensitive learning algorithm successful learning depends numerous conditions constraints. One set constraints is to avoid weights lead saturated units. motivation avoiding unit saturation is that gradients vanish result learning comes halt. Careful weight initialization re-scaling schemes batch normalization ensure input activity neuron is within linear regime where gradients are not vanished can flow. investigate backpropagating error terms linearly. is,we ignore saturation arise ensuring gradients always flow. refer learning rule Linear Backprop since backward pass network appears linear. addition ensuring persistent gradient flow Linear Backprop is also favorable when computation is expensive since gradients are never computed. early results suggest learning Linear Backprop is competitive Backprop saves expensive gradient computations.",204,153,51,0.002,1.333,2025/11/05 17:18:56,0.0,1.5,0.009345794392523,82.761
"Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning  abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models,  however, despite several recent improvements, the training of discrete latent variable models has remained  challenging and their performance has mostly failed to match their continuous counterparts. Recent work on vector quantized autoencoders (VQ-VAE) has made substantial progress in this direction, with its perplexity almost matching that of a VAE on datasets such as CIFAR-10. In this work, we investigate an alternate training technique for VQ-VAE, inspired by its connection to the Expectation Maximization (EM) algorithm. Training the discrete autoencoder with EM and combining it with sequence  level knowledge distillation alows us to develop a non-autoregressive machine translation model whose accuracy almost matches a strong greedy autoregressive baseline Transformer, while being 3.3 times faster at inference.
 Unsupervised learning of meaningful representations is a fundamental problem in machine learning since obtaining labeled data can often be very expensive. Continuous representations have largely been the workhorse of unsupervised deep learning models of images BID4 BID16 BID28 BID25 , audio BID27 , and video . However, it is often the case that datasets are more naturally modeled as a sequence of discrete symbols rather than continuous ones. For example, language and speech are inherently discrete in nature and images are often concisely described by language, see e.g., . Improved discrete latent variable models could also prove useful for learning novel data compression algorithms BID32 , while having far more interpretable representations of the data.We build on Vector Quantized Variational Autoencoder (VQ-VAE) , a recently proposed training technique for learning discrete latent variables. The method uses a learned code-book combined with nearest neighbor search to train the discrete latent variable model. The nearest neighbor search is performed between the encoder output and the embedding of the latent code using the 2 distance metric. VQ-VAE adopts the standard latent variable model generative process, first sampling latent codes from a prior, P (z), which are then consumed by the decoder to generate data from P (x | z). In van den , the authors use both uniform and autoregressive priors for P (z). The resulting discrete autoencoder obtains impressive results on unconditional image, speech, and video generation. In particular, on image generation, VQ-VAE was shown to perform almost on par with continuous VAEs on datasets such as CIFAR-10 (van den ). An extension of this method to conditional supervised generation, out-performs continuous autoencoders on WMT English-German translation task .The work of introduced the Latent Transformer, which set a new stateof-the-art in non-autoregressive Neural Machine Translation. However , additional training heuristics, namely, exponential moving averages (EMA) of cluster assignment counts, and product quantization BID24 were essential to achieve competitive results with VQ-VAE. In this work, we show that tuning for the code-book size can significantly outperform the results presented in . We also exploit VQ-VAE's connection with the expectation maximization (EM) algorithm BID3 , yielding additional improvements. With both improvements, we achieve a BLEU score of 22.4 on English to German translation, outperforming by 2.6 BLEU. Knowledge distillation BID7 BID12 ) provides significant gains with our best models and EM, achieving 26.7 BLEU, which almost matches the autoregressive transformer model with no beam search at 27.0 BLEU, while being 3.3× faster.Our contributions can be summarized as follows:1. We show that VQ-VAE from van den can outperform previous state-of-the-art without product quantization. 2. Inspired by the EM algorithm, we introduce a new training algorithm for training discrete variational autoencoders, that outperforms the previous best result with discrete latent autoencoders for neural machine translation. 3. Using EM training, and combining it sequence level knowledge distillation BID7 BID12 , allows us to develop a non-autoregressive machine translation model whose accuracy almost matches a strong greedy autoregressive baseline Transformer, while being 3.3 times faster at inference. 4. On the larger English-French dataset, we show that denoising discrete autoencoders gives us a significant improvement (1.0 BLEU) on top of our non-autoregressive baseline (see Section D). We investigate an alternate training technique for VQ-VAE inspired by its connection to the EM algorithm. Training the discrete autoencoder with EM and combining it with sequence level knowledge distillation, allows us to develop a non-autoregressive machine translation model whose accuracy almost matches a greedy autoregressive baseline, while being 3.3 times faster at inference. While sequence distillation is very important for training our best model, we find that the improvements from EM on harder tasks is quite significant. We hope that our results will inspire further research on using vector quantization for fast decoding of autoregressive sequence models.",Deep neural networks discrete latent variables offer promise better symbolic reasoning learning abstractions are more useful new tasks. has been a surge interest discrete latent variable models however despite several recent improvements training discrete latent variable models has remained challenging performance has mostly failed match continuous counterparts. Recent work vector quantized autoencoders VQ-VAE has made substantial progress direction perplexity almost matching VAE datasets CIFAR-10 work investigate alternate training technique VQ-VAE inspired connection Expectation Maximization EM algorithm. Training discrete autoencoder EM combining sequence level knowledge distillation alowsus develop non-autoregressive machine translation model whose accuracy almost matches strong greedy autoregressive baseline Transformer 3.3 times faster inference. Unsupervised learning meaningful representations is a fundamental problem machine learning since obtaining labeled data can often expensive. Continuous representations have largely workhorse unsupervised deep learning models images BID4 BID16 BID28 BID25 audio BID27 video. However is often case datasets are more naturally modeled sequence discrete symbols rather continuous ones. example language speech are inherently discrete nature images are often concisely described language seee.g Improved discrete latent variable models could also prove useful learning novel data compression algorithms BID32 far interpretable representations data.We build Vector Quantized Variational Autoencoder VQ-VAE recently proposed training technique learning discrete latent variables. method uses learned code-book combined nearest neighbor search train discrete latent variable model. nearest neighbor search is performed encoder output embedding latent code using 2 distance metric. VQ-VAE adopts standard latent variable model generative process first sampling latent codes prior P z which are consumed decoder generate data P x z van den authors use uniform autoregressive priors P z resulting discrete autoencoder obtains impressive results unconditional image speech video generation. particular image generation VQ-VAE was shown perform almost par continuous VAEs datasets CIFAR-10 van den extension method conditional supervised generation out-performs continuous autoencoders WMT English-German translation task.The work introduced Latent Transformer which set new stateof-the-art non-autoregressive Neural Machine Translation. However additional training heuristics namely exponential moving averages EMA cluster assignment counts product quantization BID24 were essential achieve competitive results VQ-VAE work show tuning code-book size can significantly outperform results presented in. also exploit VQ-VAE's connection expectation maximization EM algorithm BID3 yielding additional improvements. improvements achieve BLEU score 22.4 English German translation outperforming 2.6 BLEU. Knowledge distillation BID7 BID12 provides significant gains best models EM achieving 26.7 BLEU which almost matches autoregressive transformer model beam search 27.0 BLEU 3.3× faster.Our contributions can be summarized follows:1 show VQ-VAE van den can outperform previous state-of-the-art without product quantization. 2. Inspired EM algorithm introduce new training algorithm training discrete variational autoencoders outperforms previous best result discrete latent autoencoders neural machine translation. 3. Using EM training combining sequence level knowledge distillation BID7 BID12 allowsus develop non-autoregressive machine translation model whose accuracy almost matches strong greedy autoregressive baseline Transformer 3.3 times faster inference. 4. larger English-French dataset show denoising discrete autoencoders gives us significant improvement 1.0 BLEU top non-autoregressive baseline see Section investigate alternate training technique VQ-VAE inspired connection EM algorithm. Training discrete autoencoder EM combining sequence level knowledge distillation allowsus develop non-autoregressive machine translation model whose accuracy almost matches greedy autoregressive baseline 3.3 times faster inference. sequence distillation is very important training best model find improvements EM harder tasks is quite significant. hope results will inspire research using vector quantization fast decoding autoregressive sequence models.,1039,746,293,0.009,1.393,2025/11/05 17:18:56,0.0,1.333,0.1962616822429905,295.73
"Recent research about margin theory has proved that maximizing the minimum margin like support vector machines does not necessarily lead to better performance, and instead, it is crucial to optimize the margin distribution. In the meantime, margin theory has been used to explain the empirical success of deep network in recent studies. In this paper, we present ODN (the Optimal margin Distribution Network), a network which embeds a loss function in regard to the optimal margin distribution. We give a theoretical analysis for our method using the PAC-Bayesian framework, which confirms the significance of the margin distribution for classification within the framework of deep networks. In addition, empirical results show that the ODN model always outperforms the baseline cross-entropy loss model consistently across different regularization situations. And our ODN
 model also outperforms the cross-entropy loss (Xent), hinge loss and soft hinge loss model in generalization task through limited training data. In the history of machine learning research, the large margin principle has played an important role in theoretical analysis of generalization ability, meanwhile, it also achieves remarkable practical results for classification BID3 and regression problems BID4 . More than that, this powerful principle has been used to explain the empirical success of deep neural network. BID1 and present a margin-based multi-class generalization bound for neural networks that scales with their margin-normalized spectral complexity using two different proving tools. Moreover, BID0 proposes a stronger generalization bounds for deep networks via a compression approach, which are orders of magnitude better in practice.As for margin theory, BID17 first introduces it to explain the phenomenon that AdaBoost seems resistant to overfitting problem. Two years later, BID2 indicates that the minimum margin is important to achieve a good performance. However, BID16 conjectures that the margin distribution, rather than the minimum margin, plays a key role in being empirically resistant to overfitting problem; this has been finally proved by BID6 . In order to restrict the complexity of hypothesis space suitably, a possible way is to design a classifier to obtain optimal margin distribution. BID6 proves that, to attain the optimal margin distribution, it is crucial to consider not only the margin mean but also the margin variance. Inspired by this idea, Zhang & Zhou (2016) proposes the optimal margin distribution machine (ODM) for binary classification, which optimizes the margin distribution through the first-and second-order statistics, i.e., maximizing the margin mean and minimizing the margin variance simultaneously. To expand this method to the multi-class classification problem, Zhang & Zhou (2017) presents a multi-class version of ODM.Based on these recent works, we consider the expansion of the optimal margin distribution principle on deep neural networks. In this paper, we propose an optimal margin distribution loss for convolution neural networks, which is not only maximizing the margin mean but also minimizing the margin variance as ODM does. Moreover, we use the PAC-Bayesian framework to derive a novel generalization bound based on margin distribution. Comparing to the spectrally-normalized margin bounds of BID1 and , our generalization bound shows that we can restrict the capacity of the model by setting an appropriate ratio between the first-order statistic and the second-order statistic rather than trying to control the whole product of the spectral norms of each layer. And we empirically evaluate our loss function on deep network across different datasets and model structures. Specifically, we consider the performance of these models in generalization task through limited training data.Recently, many researchers try to explain the experimental success of deep neural network. One of the research direction is to explain why the deep learning does not have serious overfitting problem. Although several common techniques, such as dropout (Srivastava et al., 2014) , batch normalization BID7 , and weight decay BID10 , do improve the generalization performance of the over-parameterized deep models, these techniques do not have a solid theoretical foundation to explain the corresponding effects. As for our optimal margin distribution loss, it has a generalization bound to prove that we can restrict the complexity of hypothesis space reasonably through searching appropriate statistics dependent on data distribution. In experimental section, we compare our optimal margin distribution loss with the baseline cross-entropy loss under different regularization methods. Recent studies disclose that maximizing the minimum margin for decision boundary does not necessarily lead to better generalization performance, and instead, it is crucial to optimize the margin distribution. However, the influence of margin distribution for deep networks still remains undiscussed. We propose ODN model trying to design a loss function which aims to control the ratio between the margin mean and the margin variance. Moreover, we present a theoretical analysis for our method, which confirms the significance of margin distribution in generalization performance. As for experiments, the results validate the superiority of our method in limited data problem. And our optimal margin distribution loss function can cooperate with batch normalization and dropout, achieving a better generalization performance.",Recent research margin theory has proved maximizing minimum margin like support vector machines does not necessarily lead better performance instead is crucial optimize margin distribution. meantime margin theory has been used explain empirical success deep network recent studies. paper present ODN Optimal margin Distribution Network network which embeds loss function regard optimal margin distribution. give theoretical analysis method using PAC-Bayesian framework which confirms significance margin distribution classification within framework deep networks. addition empirical results show ODN model always outperforms baseline cross-entropy loss model consistently across different regularization situations. ODN model also outperforms cross-entropy loss Xent hinge loss soft hinge loss model generalization task limited training data. history machine learning research large margin principle has played important role theoretical analysis generalization ability meanwhile also achieves remarkable practical results classification BID3 regression problems BID4. powerful principle has been used explain empirical success deep neural network. BID1 present margin-based multi-class generalization bound neural networks scales margin-normalized spectral complexity using two different proving tools. Moreover BID0 proposes stronger generalization bounds deep networks via compression approach which are orders magnitude better practice.As margin theory BID17 first introduces explain phenomenon AdaBoost seems resistant overfitting problem. Two years later BID2 indicates minimum margin is important achieve good performance. However BID16 conjectures margin distribution rather minimum margin plays key role empirically resistant overfitting problem;has been finally proved BID6. order restrict complexity hypothesis space suitably possible way is to design classifier obtain optimal margin distribution. BID6 proves attain optimal margin distribution is crucial consider margin mean also margin variance. Inspired idea Zhang Zhou 2016 proposes optimal margin distribution machine ODM binary classification which optimizes margin distribution first-and second-order statistics.e which is not maximizing margin mean minimizing margin variance simultaneously. expand method multi-class classification problem Zhang Zhou 2017 presents multi-class version ODM.Based recent works consider expansion optimal margin distribution principle deep neural networks. paper propose optimal margin distribution loss convolution neural networks which is not maximizing margin mean also minimizing margin variance ODM does. Moreover use PAC-Bayesian framework derive novel generalization bound based margin distribution. Comparing spectrally-normalized margin bounds BID1 generalization bound shows can restrict capacity model setting appropriate ratio first-order statistic second-order statistic rather trying control whole product spectral norms layer. empirically evaluate loss function deep network across different datasets model structures. Specifically consider performance models generalization task limited training data.Recently many researchers try explain experimental success deep neural network. One research direction is to explain why the deep learning does not have serious overfitting problem. Although several common techniques dropout Srivastavaetal. 2014 batch normalization BID7 weight decay BID10 do improve generalization performance over-parameterized deep models techniques do not have a solid theoretical foundation explain corresponding effects. optimal margin distribution loss has a generalization bound prove can restrict complexity hypothesis space reasonably searching appropriate statistics dependent data distribution. experimental section compare optimal margin distribution loss baseline cross-entropy loss different regularization methods. Recent studies disclose maximizing minimum margin decision boundary does not necessarily lead better generalization performance instead is crucial optimize margin distribution. However influence margin distribution deep networks still remains undiscussed. propose ODN model trying design loss function which aims control ratio margin mean margin variance. Moreover present theoretical analysis method which confirms significance margin distribution generalization performance. experiments results validate superiority method limited data problem. optimal margin distribution loss function can cooperate batch normalization dropout achieving better generalization performance.,988,679,309,0.01,1.455,2025/11/05 17:18:56,0.0,1.682,0.3894080996884735,318.316
"Deep network compression seeks to reduce the number of parameters in the network while maintaining a certain level of performance.   Deep network distillation seeks to train a smaller network that matches soft-max performance of a larger network.   While both regimes have led to impressive performance for their respective goals, neither provide insight into the importance of a given layer in the original model, which is useful if we are to improve our understanding of these highly parameterized models.   In this paper, we present the concept of deep net triage, which individually assesses small blocks of convolution layers to understand their collective contribution to the overall performance, which we call \emph{criticality}.  We call it triage because we assess this criticality by answering the question: what is the impact to the health of the overall network if we compress a block of layers into a single layer.
 We propose a suite of triage methods and compare them on problem spaces of varying complexity.   We ultimately show that, across these problem spaces, deep net triage is able to indicate the of relative importance of different layers.   Surprisingly, our local structural compression technique also leads to an improvement in overall accuracy when the final model is fine-tuned globally. As computational devices and methods become more powerful, deep learning models are able to grow ever deeper BID16 . To grow so deep, the most modern of networks have relied on clever intermediary layers-such as shortcut connection layers in BID5 -to overcome overfitting. While these methods allow for learning representations afforded only by very deep architectures, it is known that there are still more extraneous features and connections learned by these networks BID13 . The question of how to best remove these redundancies has been the focus of deep compression methods BID13 BID2 BID4 BID9 . Still others have investigated the ability of smaller-difficult to trainnetworks to learn from parent models via a method known as Knowledge Distillation BID6 BID14 .Both of these classes of approaches have demonstrated impressive performance for their respective goals; essentially, both lead to smaller networks that can match the performance of their larger, parent network. This performance is achieved in a variety of ways. For example, BID4 reduces the number of network parameters via low-threshold pruning, followed by retraining, weight quantization and sharing, in tandem with low-rank approximations to ensure removal of redundant and unimportant weights. These methods can be thought of as finding a sparser, compressed model which best approximates the original.Similarly, knowledge distillation methods leverage the soft-max outputs of previously trained ""teacher"" networks and network ensembles as guidance to train a smaller network, which would have otherwise been too difficult to train BID6 BID14 BID15 . These knowledge distillation networks globally train the smaller network to best approximate the soft-max output of the original network, sometimes with per-layer, intermediary targets incorporated BID0 BID11 BID17 .While impressive, these two methods do not shed any light on the criticality, or the relative importance of a given layer or block of layers to the overall output. Such layer-based analysis is important to understanding these increasingly deep networks, even if only in an empirical sense.To that end, we propose an idea called deep net triage that independently assesses small blocks of layers with respect to their importance to the overall network health. We drive the triage by using the initial parent network as an initialization, like BID1 , rather than as a means of globally retraining. Triage works by removing a connected block of network layers and replacing them with a single layer; we focus on convolution layers in this paper. We iterate over all connected blocks of layers separately thereby assessing the role each set plays in the original parent network.Our means for this triage is local structural compression, which approximates a section of a disassembled network and assesses the ability to approximate and relearn the original model. With structural compression we compress segments of a deep network-VGG16-and attempt to recover the compressed layer of the network via various initialization and training methodologies BID16 . We structure this as a compression problem as we are approximating multiple convolutional layers' representational abilities with a single, selectively initialized and trained layer. Distinctly, though , our primary goal is not to seek maximal compressive performance. Rather we seek to investigate the robustness of a network when faced with structural alterations, and how various learning techniques affect this behavior across data sets of assorted complexity. We seek overarching trends between these methods, layers, and data sets in hopes of developing a greater understanding for the representational ability, and robustness of neural networks.We perform our analysis using five approaches to structural compression for deep net triage, and four different data sets. We find that of the five approaches, methods which fine-tune over the entirety of the network achieve best performance across all data sets. Furthermore, these fine-tuned models are able to match or even exceed the performance of the baseline model. This suggests that for superior performance, a network cannot be altered without again retraining over the entire network. We additionally demonstrate that the criticality of any single layer in the network is not sufficient to inhibit relearning of the representations of the parent network. Finally, we show that knowledge distillation is an effective means of transferring the learned representations from a teacher to a student at any given intermediate point, even when the layer is altered or compressed, and improves a model's convergence. We present a novel method of analyzing deep learning methods which we refer to as deep net triage. By drawing from the field of deep network compression and knowledge distillation we design experiments which question the criticality of layers within a network structure, and assess the representations learned therein. We structurally compress a layer at a time, while conducting a series of experiments across these layers on various data sets to infer about the layer's ability to learn representations, recover from compression, and integrate itself into the global network.We show through experimentation that structurally compressed and fine-tuned models can perform equivalent to, or better than parent, uncompressed models in a layer invariant manner. Additionally, we show that parent-inspired initialization regimes applied only at the layer are unable to compete with fine-tuning over the entire global model. Lastly, we show that Student-Teacher models evaluated at intermediate layers in the form of hints from uncompressed parent models promote faster convergence to maximal accuracies, despite being unable to outperform full model training methods.Through this work, we hope to spur others to devise and rigorously test targeted assessments of deep networks, as we do in our deep net triage. While, as a community, we may continue to develop ever better performing methods for given problem spaces, we will never truly advance as a field until further intuition for and understanding of deep networks is developed. As optimization and statistical theory progresses on one side, so too must experimentalists approach from the other.",Deep network compression seeks reduce number parameters network maintaining certain level performance. Deep network distillation seeks train smaller network matches soft-max performance larger network. regimes have led impressive performance respective goals neither provide insight importance given layer original model which is useful if we are to improve understanding highly parameterized models. paper present concept deep net triage which individually assesses small blocks convolution layers understand collective contribution overall performance which we call \emph criticality call triage assess criticality answering question:what is the impact health overall network if we compress block layers single layer. propose suite triage methods compare problem spaces varying complexity. ultimately show across problem spaces do deep net triage is able indicate relative importance different layers. Surprisingly local structural compression technique also leads improvement overall accuracy when the final model is fine-tuned globally. computational devices methods become powerful do deep learning models are able grow ever deeper BID16. grow deep modern networks have relied clever intermediary layers-such shortcut connection layers BID5 -to overcome overfitting. methods allow learning representations afforded deep architectures is known are still extraneous features connections learned networks BID13. question how to best remove redundancies has been the focus deep compression methods BID13 BID2 BID4 BID9. Still others have investigated ability smaller-difficult trainnetworks learn parent models via method known Knowledge Distillation BID6 BID14.Both classes approaches have demonstrated impressive performance respective goals;essentially lead smaller networks can match performance larger parent network. performance is achieved variety ways. example BID4 reduces number network parameters via low-threshold pruning followed retraining weight quantization sharing tandem low-rank approximations ensure removal redundant unimportant weights. methods can be thought finding sparser compressed model which best approximates original.Similarly knowledge distillation methods leverage soft-max outputs previously trained teacher networks network ensembles guidance train smaller network would have otherwise difficult train BID6 BID14 BID15. knowledge distillation networks globally train smaller network best approximate soft-max output original network sometimes per-layer intermediary targets incorporated BID0 BID11 BID17.While impressive two methods do not shed light criticality relative importance given layer block layers overall output. layer-based analysis is important understanding increasingly deep networks even if only in an empirical sense.To end propose idea called deep net triage independently assesses small blocks layers respect importance overall network health. drive triage using initial parent network initialization like BID1 rather means globally retraining. Triage works removing connected block network layers replacing single layer;focus convolution layers paper. iterate connected blocks layers separately thereby assessing role set plays original parent network.Our means triage is local structural compression which approximates section disassembled network assesses ability approximate relearn original model. structural compression compress segments deep network-VGG16-and attempt recover compressed layer network via various initialization training methodologies BID16. structure compression problem are approximating multiple convolutional layers' representational abilities single selectively initialized trained layer. Distinctly though primary goal is not to seek maximal compressive performance. Rather seek investigate robustness network when faced structural alterations how various learning techniques affect behavior across data sets assorted complexity. seek overarching trends methods layers data sets hopes developing greater understanding representational ability robustness neural networks.We perform analysis using five approaches structural compression deep net triage four different data sets. find five approaches methods which fine-tune entirety network achieve best performance across data sets. Furthermore fine-tuned models are able match even exceed performance baseline model. suggests superior performance network cannot altered without retraining entire network. additionally demonstrate criticality single layer network is not sufficient inhibit relearning representations parent network. Finally show knowledge distillation is an effective means transferring learned representations teacher student given intermediate point even when the layer is altered compressed improves model's convergence. present novel method analyzing deep learning methods which we refer deep net triage. drawing field deep network compression knowledge distillation design experiments which question criticality layers within network structure assess representations learned therein. structurally compress layer time conducting series experiments across layers various data sets infer layer's ability learn representations recover compression integrate global network.We show experimentation structurally compressed fine-tuned models can perform equivalent better parent uncompressed models layer invariant manner. Additionally show parent-inspired initialization regimes applied layer are unable compete fine-tuning entire global model. Lastly show Student-Teacher models evaluated intermediate layers form hints uncompressed parent models promote faster convergence maximal accuracies despite unable outperform full model training methods.Through work hope spur others devise rigorously test targeted assessments deep networks do deep net triage. community may continue develop ever better performing methods given problem spaces will never truly advance field intuition understanding deep networks is developed. optimization statistical theory progresses one side must experimentalists approach other.,1377,912,465,0.015,1.51,2025/11/05 17:18:56,0.01,1.523,0.5607476635514017,456.4
"In this paper, we show a phenomenon, which we named ``super-convergence'', where residual networks can be trained using an order of magnitude fewer iterations than is used with standard training methods.    The existence of super-convergence is relevant to understanding why deep networks generalize well.   One of the key elements of super-convergence is training with cyclical learning rates and a large maximum learning rate.   Furthermore, we present evidence that training with large learning rates improves performance by regularizing the network. In addition, we show that super-convergence provides a  greater boost in performance relative to standard training when the amount of labeled training data is limited.   We also derive a simplification of the Hessian Free optimization method to compute an estimate of the optimal learning rate.   The architectures to replicate this work will be made available upon publication.
 While deep neural networks have achieved amazing successes in a range of applications, understanding why stochastic gradient descent (SGD) works so well remains an open and active area of research. This paper provides unique empirical evidence that supports the theories in some papers but not others. Specifically, we show that, for certain datasets, residual network architectures BID15 , and hyper-parameter values, using very large learning rates with the cyclical learning rate (CLR) method BID29 BID30 can speed up training by an order of magnitude. Analogous to the phenomenon of super-conductivity that only happens in limited circumstances and provides theoretical insights of materials, we named this phenomenon ""super-convergence."" While super-convergence might be of some practical value, the primary purpose of this paper is to provide empirical support and theoretical insights to the active discussions in the literature on SGD and understanding generalization. FIG0 provides a comparison of test accuracies from a super-convergence example and the result of a typical (piecewise constant) training regime for Cifar-10, both using a 56 layer residual network architecture. Piecewise constant training reaches a peak accuracy of 91.2% after approximately 80,000 iterations, while the super-convergence method reaches a higher accuracy (92.4%) after only 10,000 iterations. FIG1 shows the results for a range of CLR stepsize values, where training lasted only one cycle. This modified learning rate schedule achieves a higher final test accuracy (92.1%) than typical training (91.2%) after only 6,000 iterations. In addition, as the total number of iterations increases from 2,000 to 20,000, the final accuracy improves from 89.7% to 92.7%.The contributions of this paper are:1. We demonstrate a new training phenomenon and systematically investigate it. 2. We show evidence that large learning rates regularize the trained network and hypothesize that this allows SGD to find a flat local minima that generalizes well. 3. We derive a simplification of the second order, Hessian-free optimization method to estimate optimal learning rates which demonstrates that large learning rates find wide, flat minima. 4. We demonstrate that the effects of super-convergence are increasingly dramatic when less labeled training data is available. There is substantial discussion in the literature on stochastic gradient descent (SGD) and understanding why solutions generalize so well (i.e, Chaudhari et al. FORMULA1 BID20 ). Super-convergence provides empirical evidence that supports some theories, contradicts some others, and points to the need for further theoretical understanding. We hope the response to super-convergence is similar to the reaction to the initial report of network memorization , which sparked an active discussion within the deep learning research community on better understanding of the factors in SGD leading to solutions that generalize well (i.e., ).Our work impacts the line of research on SGD and the importance of noise for generalization. In this paper we focused on the use of CLR with very large learning rates, which adds noise in the middle part of training. Recently , stated that higher levels of noise lead SGD to solutions with better generalization. Specifically , they showed that the ratio of the learning rate to the batch size, along with the variance of the gradients, controlled the width of the local minima found by SGD. Independently , BID6 show that SGD performs regularization by causing SGD to be out of equilibrium, which is crucial to obtain good generalization performance, and derive that the ratio of the learning rate to batch size alone controls the entropic regularization term. They also state that data augmentation increases the diversity of SGD's gradients, leading to better generalization. These two papers provide theoretical support for the super-convergence phenomenon. In addition there are several other papers in the literature which state that wide, flat local minima produce solutions that generalize better than sharp minima BID16 BID21 BID36 . Our super-convergence results align with these results.In addition, there are several recent papers on the generalization gap between small and large minibatches and the relationship between gradient noise, learning rate, and batch size. Our results here supplements this other work by illustrating the possibility of time varying high noise levels during training. As mentioned above, showed that SGD noise is proportional to the learning rate, the variance of the loss gradients, divided by the batch size. Similarly Smith and Le derived the noise scale as g ≈ N/B(1 − m), where g is the gradient noise, the learning rate, N the number of training samples, and m is the momentum coefficient. Furthermore, showed an equivalence of increasing batch sizes instead of a decreasing learning rate schedule. Importantly, these authors demonstrated that the noise scale g is relevant to training and not the learning rate or batch size. BID21 study the generalization gap between small and large mini-batches, stating that small mini-batch sizes lead to wide, flat minima and large batch sizes lead to sharp minima. They also suggest a batch size warm start for the first few epochs, then using a large batch size, which amounts to training with large gradient noise for a few epochs and then removing it. Our results contradicts this suggestion as we found it preferable to start training with little or no noise and let it increase (i.e., curriculum training), reach a noise peak, and reduce the noise level in the last part of training (i.e., simulated annealing). BID12 use a very large mini-batch size of up to 8,192 and adjust the learning rate linearly with the batch size. They also suggest a gradual warmup of the learning rate, which is a discretized version of CLR and matches our experience with an increasing learning rate. They make a point relevant to adjusting the batch size; if the network uses batch normalization, different mini-batch sizes leads to different statistics, which must be handled. BID17 made a similar point about batch norm and suggested using ghost statistics. Also, BID17 show that longer training lengths is a form of regularization that improves generalization. On the other hand, our results show a different form of regularization that comes from training with very large learning rates, which permits much shorter training lengths.Furthermore, this paper points the way towards new research directions, such as the following three:1. Characterizing ""good noise"" that improves the trained network's ability to generalize versus ""bad noise"" that interferes with finding a good solution (i.e., ). We find that there is a lack of a unified framework for treating SGD noise/diversity, such as architectural noise (e.g., dropout BID33 , dropconnect BID35 ), noise from hyper-parameter settings (e.g., learning rate, mini-batch size), adding gradient noise, adding noise to weights BID9 , and input diversity (e.g., data augmentation, noise). Gradient diversity has been shown to lead to flatter local minimum and better generalization. A unified framework should resolve conflicting claims in the literature on the value of each of these, such as for architectural noise BID33 ) versus Hoffer et al. (2017 ). Furthermore, many papers study each of these factors independently and by focusing on the trees, one might miss the forest. 2. Time dependent application of good noise during training: As described above, combining curriculum learning with simulated annealing leads to cyclical application. To the best of our knowledge, this has only been applied sporadically in a few methods such as CLR BID30 or cyclical batch sizes but these all fall under a single umbrella of time dependent gradient diversity (i.e., noise). Also, one might learn an optimal noise level while training the network. 3. Discovering new ways to stabilize optimization (i.e., SGD) with large noise levels: Our evidence indicates that normalization (and batch normalization in particular) is the catalyst enabling super-convergence in the face of destabilizing noise from the large learning rates. Normalization methods (batch norm, layer normalization BID2 , streaming normalization BID23 ) and new techniques (i.e., cyclical gradient clipping) to stabilize training need further investigation to discover better ways to keep SGD stable in the presence of enormous good noise.Classical physics was insufficient for explaining super-conductivity when it was discovered and pointed to the need for new theories, such as quantum mechanics. Similarly, super-convergence indicates a need for new theories of SGD and generalization.The Resnet-56 architecture used consists of three stages. Within each stage, the same residual block structure is sequentially repeated . This structure is given in TAB1 . Between stages, a different residual block structure is used to reduce the spatial dimension of the channels. TAB2 shows this structure. The overall architecture is described in TAB3 . Following the Caffe convention, each Batch Norm layer was followed by a scaling layer to achieve true batch normalization behavior. This and the other architectures necessary to replicate this work will be made available upon publication. We ran a wide variety of experiments and due to space limitations in the main article, we report some of the more interesting results here that did not fit in the main article.In the main text we only showed the results of super-convergence for the Cifar-10 dataset. In fact, the super-convergence phenomenon also occurs with Cifar-100, which implies an independence of this phenomenon on the number of classes. FIG0 shows the results of the LR range test for Resnet-56 with the Cifar-100 training data. The curve is smooth and accuracy remains high over the entire range from 0 to 3 indicating a potential for super-convergence. An example of super-convergence with Cifar-100 with Resnet-56 is given in FIG16 , where there is also a comparison to the results from a piecewise constant training regime. Furthermore, the final accuracy for the super-convergence curve is 68.6%, while the accuracy for the piecewise constant method is 59.8%, which is an 8.8% improvement.As discussed in the main text, we tested various adaptive learning rate methods with Resnet-56 training on Cifar-10 to determine if they are capable of recognizing the need for using very large learning rates. FIG0 shows the results of this training for Nesterov momentum BID34 BID27 , AdaDelta BID8 ), AdaGrad (Zeiler, 2012 , and Adam (Kingma BID22 . We found no sign that any of these methods discovered the utility of large learning rates nor any indication of super-convergence-like behavior. We also ran CLR with these adaptive learning methods and found that Nesterov, AdaDelta, and AdaGrad allowed super-convergence to occur, but we were unable to create this phenomenon with Adam. For example, FIG18 shows a comparison of super-convergence to a piecewise constant training regime with the Nesterov momentum method. Here super-convergence yields a final test accuracy after 10,000 iterations of 92.1% while the piecewise constant training regime at iteration 80,000 has an accuracy of 90.9%. FIG1 shows a comparison of runs of the super-convergence phenomenon, both with and without dropout. The LR range test with and without dropout is shown in FIG0 . FIG1 shows the results of training for 10,000 iterations . In both cases, the dropout ratio was set to 0.2 and the Figure shows a small improvement with dropout. We also ran with other values for the dropout ratio and consistently saw similar improvements.The effect of mini-batch size is discussed in the main paper but here we present a table containing the final accuracies of super-convergence training with various mini-batch sizes. One can see in Table 5 the final test accuracy results and this table shows that the larger the mini-batch size, the better the final accuracy, which differs from the results shown in the literature 4 . Most of results reported in this paper are with a total mini-batch size of 1,000.In addition, we ran experiments on Resnet-56 on Cifar-10 with modified values for momentum and weight decay to determine if they might hinder the super-convergence phenomenon. FIG0 shows the results for momentum set to 0.8, 0.85, 0.9, and 0.95 and the final test accuracies are listed in TAB5 . These results indicate only a small change in the results, with a setting of 0.9 being a bit better than the other values. In FIG1 are the results for weight decay values of 10 −3 , 10 −4 , 10 −5 , and 10 −6 . In this case, a weight decay value of 10 −3 prevents super-convergence, while the smaller values do not. This FIG0 shows that a weight decay value of 10 −4 performs well. Table 5 : Comparison of accuracy results for various total training batch sizes with Resnet-56 on Cifar-10 using CLR=0.1-3 and stepsize=5,000.","paper show phenomenon which we named super-convergence where residual networks can be trained using order magnitude fewer iterations is used standard training methods. existence super-convergence is relevant understanding why deep networks generalize well. One key elements super-convergence is training cyclical learning rates large maximum learning rate. Furthermore present evidence training large learning rates improves performance regularizing network. addition show super-convergence provides greater boost performance relative standard training when the amount labeled training data is limited. also derive simplification Hessian Free optimization method compute estimate optimal learning rate. architectures replicate work will be made available upon publication. deep neural networks have achieved amazing successes range applications understanding why stochastic gradient descent SGD works well remains open active area research. paper provides unique empirical evidence supports theories papers others. Specifically show certain datasets where residual network architectures BID15 hyper-parameter values using large learning rates cyclical learning rate CLR method BID29 BID30 can speed training order magnitude. Analogous phenomenon super-conductivity happens limited circumstances provides theoretical insights materials which we named phenomenon super-convergence super-convergence might practical value primary purpose paper is to provide empirical support theoretical insights active discussions literature SGD understanding generalization. FIG0 provides comparison test accuracies super-convergence example result typical piecewise constant training regime Cifar-10 using 56 layer residual network architecture. Piecewise constant training reaches peak accuracy 91.2 approximately 80,000 iterations super-convergence method reaches higher accuracy 92.4 10,000 iterations. FIG1 shows results range CLR stepsize values where training lasted one cycle. modified learning rate schedule achieves higher final test accuracy 92.1 typical training 91.2 6,000 iterations. addition total number iterations increases 2,000 20,000 final accuracy improves 89.7 92.7%.The contributions paper are:1 demonstrate new training phenomenon systematically investigate it. 2. show evidence large learning rates regularize trained network hypothesize allows SGD find flat local minima generalizes well. 3. derive simplification second order Hessian-free optimization method estimate optimal learning rates which demonstrates large learning rates find wide flat minima. 4. demonstrate effects super-convergence are increasingly dramatic when less labeled training data is available. is substantial discussion literature stochastic gradient descent SGD understanding why solutions generalize well.e Chaudharietal. FORMULA1 BID20 Super-convergence provides empirical evidence supports theories contradicts others points need theoretical understanding. hope response super-convergence is similar reaction initial report network memorization which sparked active discussion within deep learning research community better understanding factors SGD leading solutions generalize well.e.Our work impacts line research SGD importance noise generalization. paper focused use CLR large learning rates which adds noise middle part training. Recently stated higher levels noise lead SGD solutions better generalization. Specifically showed ratio learning rate batch size along variance gradients controlled width local minima found SGD. Independently BID6 show SGD performs regularization causing SGD equilibrium which is crucial obtain good generalization performance derive ratio learning rate batch size alone controls entropic regularization term. also state data augmentation increases diversity SGD's gradients leading better generalization. two papers provide theoretical support super-convergence phenomenon. addition are several papers literature which state wide flat local minima produce solutions generalize better sharp minima BID16 BID21 BID36. super-convergence results align results.In addition are several recent papers generalization gap small large minibatches relationship gradient noise learning rate batch size. results supplements work illustrating possibility time varying high noise levels training. mentioned showed SGD noise is proportional learning rate variance loss gradients divided batch size. Similarly Smith Le derived noise scale g≈N/B 1− whereg is the gradient noise learning rate N number training samples is momentum coefficient. Furthermore showed equivalence increasing batch sizes instead decreasing learning rate schedule. Importantly authors demonstrated noise scaleg is relevant training learning rate batch size. BID21 study generalization gap small large mini-batches stating small mini-batch sizes lead wide flat minima large batch sizes lead sharp minima. also suggest batch size warm start first epochs using large batch size which amounts training large gradient noise epochs removing it. results contradicts suggestion found preferable start training little noise let increase.e curriculum training reach noise peak reduce noise level last part training.e simulated annealing BID12 use large mini-batch size 8,192 adjust learning rate linearly batch size. also suggest gradual warmup learning rate which is a discretized version CLR matches experience increasing learning rate. make point relevant adjusting batch size;if the network uses batch normalization different mini-batch sizes leads different statistics which must handled. BID17 made similar point batch norm suggested using ghost statistics. Also BID17 show longer training lengths is a form regularization improves generalization. hand results show different form regularization comes training large learning rates which permits much shorter training lengths.Furthermore paper points way towards new research directions following three:1 Characterizing good noise improves trained network's ability generalize versus bad noise interferes finding good solution.e find is a lack unified framework treating SGD noise/diversity architectural noise e.g dropout BID33 dropconnect BID35 noise hyper-parameter settings e.g learning rate mini-batch size adding gradient noise adding noise weights BID9 input diversity e.g data augmentation noise Gradient diversity has been shown lead flatter local minimum better generalization. unified framework should resolve conflicting claims literature value architectural noise BID33 versus Hofferetal. 2017 Furthermore many papers study factors independently focusing trees one might miss forest. 2. Time dependent application good noise training:described combining curriculum learning simulated annealing leads cyclical application. best knowledge has only applied sporadically methods CLR BID30 cyclical batch sizes fall single umbrella time dependent gradient diversity.e noise Also one might learn optimal noise level training network. 3. Discovering new ways stabilize optimization.e SGD large noise levels:evidence indicates normalization batch normalization particular is the catalyst enabling super-convergence face destabilizing noise large learning rates. Normalization methods batch norm layer normalization BID2 streaming normalization BID23 new techniques.e cyclical gradient clipping stabilize training need investigation discover better ways keep SGD stable presence enormous good noise.Classical physics was insufficient explaining super-conductivity when it was discovered pointed need new theories quantum mechanics. Similarly super-convergence indicates need new theories SGD generalization.The Resnet-56 architecture used consists three stages. Within stage where residual block structure is sequentially repeated. structure is given TAB1. stages different residual block structure is used reduce spatial dimension channels. TAB2 shows structure. overall architecture is described TAB3. Following Caffe convention Batch Norm layer was followed scaling layer achieve true batch normalization behavior. architectures necessary replicate work will be made available upon publication. ran wide variety experiments due space limitations main article report interesting results did not fit main article.In main text showed results super-convergence Cifar-10 dataset. fact super-convergence phenomenon also occurs Cifar-100 which implies independence phenomenon number classes. FIG0 shows results LR range test Resnet-56 Cifar-100 training data. curve is smooth accuracy remains high entire range 0 3 indicating potential super-convergence example super-convergence Cifar-100 Resnet-56 is given FIG16 where there is also comparison results piecewise constant training regime. Furthermore final accuracy super-convergence curve is 68.6 68.6 accuracy piecewise constant method is 59.8 59.8 whichisan 8.8 improvement.As discussed main text tested various adaptive learning rate methods Resnet-56 training Cifar-10 determine if they are capable recognizing need using large learning rates. FIG0 shows results training Nesterov momentum BID34 BID27 AdaDelta BID8 AdaGrad Zeiler 2012 Adam Kingma BID22. found sign methods discovered utility large learning rates indication super-convergence-like behavior. also ran CLR adaptive learning methods found Nesterov AdaDelta AdaGrad allowed super-convergence occur were unable create phenomenon Adam. example FIG18 shows comparison super-convergence piecewise constant training regime Nesterov momentum method. super-convergence yields final test accuracy 10,000 iterations 92.1 piecewise constant training regime iteration 80,000 has an accuracy 90.9%. FIG1 shows comparison runs super-convergence phenomenon without dropout. LR range test without dropout is shown FIG0. FIG1 shows results training 10,000 iterations. cases dropout ratio was set 0.2 Figure shows small improvement dropout. also ran values dropout ratio consistently saw similar improvements.The effect mini-batch size is discussed main paper present table containing final accuracies super-convergence training various mini-batch sizes. One can see Table5 final test accuracy results table shows larger mini-batch size better final accuracy which differs results shown literature4. results reported paper are with a total mini-batch size 1 000.In addition ran experiments Resnet-56 Cifar-10 modified values momentum weight decay determine might hinder super-convergence phenomenon. FIG0 shows results momentum set 0.8 0.85 0.9 0.95 final test accuracies are listed TAB5. results indicate small change results setting 0.9 bit better values. FIG1 are the results weight decay values 10−3 10−4 10−5 10−6 case weight decay value 10 −3 prevents super-convergence smaller values do not. FIG0 shows weight decay value 10 −4 performs well. Table5:Comparison accuracy results various total training batch sizes Resnet-56 Cifar-10 using CLR=0.1-3 stepsize=5,000",2819,1906,913,0.044,1.479,2025/11/05 17:18:56,0.01,1.435,0.4641744548286605,953.248
"Infinite-width neural networks have been extensively used to study the theoretical properties underlying the extraordinary empirical success of standard, finite-width neural networks. Nevertheless, until now, infinite-width networks have been limited to at most two hidden layers. To address this shortcoming, we study the initialisation requirements of these networks and show that the main challenge for constructing them is defining the appropriate sampling distributions for the weights. Based on these observations, we propose a principled approach to weight initialisation that correctly accounts for the functional nature of the hidden layer activations and facilitates the construction of arbitrarily many infinite-width layers, thus enabling the construction of arbitrarily deep infinite-width networks. The main idea of our approach is to iteratively reparametrise the hidden-layer activations into appropriately defined reproducing kernel Hilbert spaces and use the canonical way of constructing probability distributions over these spaces for specifying the required weight distributions in a principled way. Furthermore, we examine the practical implications of this construction for standard, finite-width networks. In particular, we derive a novel weight initialisation scheme for standard, finite-width networks that takes into account the structure of the data and information about the task at hand. We demonstrate the effectiveness of this weight initialisation approach on the MNIST, CIFAR-10 and Year Prediction MSD datasets. While deep neural networks have achieved impressive empirical success on many tasks across a wide range of domains in recent years BID20 BID35 BID33 BID34 BID29 , they remain hard to interpret black boxes whose performance crucially depends on many heuristics. In an attempt to better understand them, significant research effort has been directed towards examining the theoretical properties of these models with one important line of research focusing on the profound connections between infinite-width networks and kernel methods. In particular, BID30 established a correspondence between single-layer infinite-width networks and Gaussian processes (GP) BID32 showing the equivalence of the prior over functions that is induced by the network and a GP with a particular covariance kernel. The appropriate covariance kernel has been analytically derived for a few particular activation functions and weight priors BID38 .Although there is a large body of research on infinite-width networks with surging recent interest in the topic BID13 BID24 BID27 , until now the construction of these networks has been limited to at most two hidden layers. In order to overcome this shortcoming and enable deep infinite-width networks, we propose a novel approach to the construction of networks with infinitely wide hidden layers. To the best of our knowledge, this is the first method that enables the construction of infinite-width networks with more than two hidden layers. The main challenge in constructing this type of networks lies in ensuring that the inner products between the hidden layer representations and the corresponding weights, which are both functions, are well-defined. In particular, this amounts to ensuring that the weights lie in the same function space as the hidden layer representations with which the inner product is taken. In other words, the weights connecting layers l and l + 1 need to be in the same function space as the activations of layer l. To construct the infinite-width layer l + 1, we need to construct infinitely many weights connecting layers l and l + 1 that fulfill this requirement, i.e. we need to define a probability distribution over the function space of activations of layer l. As the number of layers grows, the function spaces of activations grow increasingly more complex, thus making it increasingly more difficult to satisfy the requirements on the weights.In order to tackle this challenge, we propose a principled approach to weight initialisation that automatically ensures that the weights are in the appropriate function space. The main idea of our approach is to make use of the canonical way of defining probability distributions over reproducing kernel Hilbert spaces (RKHS) and iteratively define the appropriate weight distributions facilitating the composition of arbitrarily many layers of infinite width. To this end, we first construct a kernel corresponding to each hidden layer and examine the associated RKHS of functions that is induced by this kernel. Next, for every layer, we establish a correspondence between the space of activations at a layer and the corresponding RKHS by reparametrising the hidden layer activations of a datapoint with the RKHS function corresponding to that point. Establishing this correspondence allows us to use a principled approach to defining probability distributions over RKHSs for constructing the appropriate sampling distribution of the weights in the infinite-width network.We also examine some practical implications of this construction for the case of standard, finitewidth neural networks in terms of weight initialisation. Using Monte Carlo approximations, we derive a novel data-and task-dependent weight initialisation scheme for finite-width networks that incorporates the structure of the data and information about the task at hand into the network.The main contributions of this paper are• a novel approach to the construction of infinite-width networks that enables the construction of networks with arbitrarily many hidden layers of infinite-width,• a hierarchy of increasingly complex kernels that capture the geometry and inductive biases of individual layers in the network,• a novel weight initialisation scheme for deep neural networks with theoretical foundations established in the infinite-width case.The rest of the paper is organised as follows. Section 2 discusses related work and Section 3 introduces our proposed approach to the construction of deep infinite-width networks. In Section 4, we showcase the practical implications of our theoretical contribution for the case of standard, finite-width deep networks. Section 5 discusses the experimental results followed by a conclusion in Section 6. In this paper, we have studied the initialisation requirements of infinite-width networks and have shown that the main challenge in constructing these networks lies in defining the appropriate sampling distributions of the weights. To address this problem, we have presented a novel method for the construction of infinite-width networks that, unlike previous approaches, enables the construction of deep infinite-width networks with arbitrarily many hidden layers. In particular, we have proposed a principled approach to weight initialisation using the theory of reproducing kernel Hilbert spaces. In order to appropriately account for the functional form of the hidden layer activations and to facilitate the construction of arbitrarily many infinite-width layers, we proposed to construct the sampling distributions of the weights at every hidden layer as Gaussian processes with specific covariance kernels that take into account the geometry of the underlying space of activations. To achieve this, we have constructed a hierarchy of kernels that capture the geometry and inductive biases of individual layers in the neural network. Furthermore, using Monte Carlo approximations, we have examined the practical implications of this construction for standard, finite-width networks. In particular, we have derived a novel data-and task-dependent weight initialisation method for this type of network and showcased its competitive performance on three diverse datasets.7 SUPPLEMENTARY MATERIAL 7.1 PROOFS For completeness, we restate the proposition and lemma and provide the corresponding proofs.7.1.1 PROPOSITION 1 Proposition 1. Let x, x ∈ R d be inputs to an network with l infinite-width layers, k l be the kernel corresponding to the l-th layer with k l (·, x) the corresponding canonical feature maps and H k l the induced RKHS. We can extend the network with an (l + 1)-th layer of infinite width by sampling the weights w l connecting the l-th and (l + 1)-th layers from a Gaussian process with zero mean function and covariance function DISPLAYFORM0",Infinite-width neural networks have been extensively used study theoretical properties underlying extraordinary empirical success standard finite-width neural networks. Nevertheless infinite-width networks have been limited two hidden layers. address shortcoming study initialisation requirements networks show main challenge constructing is defining appropriate sampling distributions weights. Based observations propose principled approach weight initialisation correctly accounts functional nature hidden layer activations facilitates construction arbitrarily many infinite-width layers thus enabling construction arbitrarily deep infinite-width networks. main idea approach is to iteratively reparametrise hidden-layer activations appropriately defined reproducing kernel Hilbert spaces use canonical way constructing probability distributions spaces specifying required weight distributions principled way. Furthermore examine practical implications construction standard finite-width networks. particular derive novel weight initialisation scheme standard finite-width networks takes account structure data information task hand. demonstrate effectiveness weight initialisation approach MNIST CIFAR-10 Year Prediction MSD datasets. deep neural networks have achieved impressive empirical success many tasks across wide range domains recent years BID20 BID35 BID33 BID34 BID29 remain hard interpret black boxes whose performance crucially depends many heuristics. attempt better understand significant research effort has been directed towards examining theoretical properties models one important line research focusing profound connections infinite-width networks kernel methods. particular BID30 established correspondence single-layer infinite-width networks Gaussian processes GP BID32 showing equivalence prior functions is induced network GP particular covariance kernel. appropriate covariance kernel has been analytically derived particular activation functions weight priors BID38.Although is a large body research infinite-width networks surging recent interest topic BID13 BID24 BID27 construction networks has been limited two hidden layers. order overcome shortcoming enable deep infinite-width networks propose novel approach construction networks infinitely wide hidden layers. best knowledge is the first method enables construction infinite-width networks two hidden layers. main challenge constructing type networks lies ensuring inner products hidden layer representations corresponding weights which are both functions are well-defined well-defined particular amounts ensuring weights lie function space hidden layer representations which the inner product is taken. words weights connecting layersl l+1 need function space activations layerl. construct infinite-width layerl+1 need construct infinitely many weights connecting layersl l+1 fulfill requirement.e need define probability distribution function space activations layerl. number layers grows function spaces activations grow increasingly complex thus making increasingly difficult satisfy requirements weights.In order tackle challenge propose principled approach weight initialisation automatically ensures weights are in the appropriate function space. main idea approach is to make use canonical way defining probability distributions reproducing kernel Hilbert spaces RKHS iteratively define appropriate weight distributions facilitating composition arbitrarily many layers infinite width. end is the first construct kernel corresponding hidden layer examine associated RKHS functions is induced kernel. Next every layer establish correspondence space activations layer corresponding RKHS reparametrising hidden layer activations datapoint RKHS function corresponding point. Establishing correspondence allowsus use principled approach defining probability distributions RKHSs constructing appropriate sampling distribution weights infinite-width network.We also examine practical implications construction case standard finitewidth neural networks terms weight initialisation. Using Monte Carlo approximations derive novel data-and task-dependent weight initialisation scheme finite-width networks incorporates structure data information task hand network.The main contributions paper are• novel approach construction infinite-width networks enables construction networks arbitrarily many hidden layers infinite-width • hierarchy increasingly complex kernels capture geometry inductive biases individual layers network • novel weight initialisation scheme deep neural networks theoretical foundations established infinite-width case.The rest paper is organised follows. Section 2 discusses related work Section 3 introduces proposed approach construction deep infinite-width networks. Section4 showcase practical implications theoretical contribution case standard finite-width deep networks. Section 5 discusses experimental results followed conclusion Section6. paper have studied initialisation requirements infinite-width networks have shown main challenge constructing networks lies defining appropriate sampling distributions weights. address problem have presented novel method construction infinite-width networks unlike previous approaches enables construction deep infinite-width networks arbitrarily many hidden layers. particular have proposed principled approach weight initialisation using theory reproducing kernel Hilbert spaces. order appropriately account functional form hidden layer activations facilitate construction arbitrarily many infinite-width layers have proposed construct sampling distributions weights every hidden layer Gaussian processes specific covariance kernels take account geometry underlying space activations. achieve have constructed hierarchy kernels capture geometry inductive biases individual layers neural network. Furthermore using Monte Carlo approximations have examined practical implications construction standard finite-width networks. particular have derived novel data-and task-dependent weight initialisation method type network showcased competitive performance three diverse datasets.7 SUPPLEMENTARY MATERIAL 7.1 PROOFS completeness restate proposition lemma provide corresponding proofs.7.1.1 PROPOSITION1 Proposition1. Letx x∈R inputs network l infinite-width layers kl kernel corresponding l-th layer kl · x corresponding canonical feature maps Hkl induced RKHS. can extend network l+1 -th layer infinite width sampling weights w l connecting l-th l+1 -th layers Gaussian process zero mean function covariance function DISPLAYFORM0,1489,970,519,0.018,1.535,2025/11/05 17:18:56,0.01,1.577,0.6386292834890962,476.864
"Working memory requires information about external stimuli to be represented in the brain even after those stimuli go away. This information is encoded in the activities of neurons, and neural activities change over timescales of tens of milliseconds. Information in working memory, however, is retained for tens of seconds, suggesting the question of how time-varying neural activities maintain stable representations. Prior work shows that, if the neural dynamics are in the `  null space' of the representation - so that changes to neural activity do not affect the downstream read-out of stimulus information - then information can be retained for periods much longer than the time-scale of individual-neuronal activities. The prior work, however, requires precisely constructed synaptic connectivity matrices, without explaining how this would arise in a biological neural network. To identify mechanisms through which biological networks can self-organize to learn  memory function, we derived biologically plausible synaptic plasticity rules that dynamically modify the connectivity matrix to enable information storing. Networks implementing this plasticity rule can successfully learn to form memory representations even if only 10% of the synapses are plastic, they are robust to synaptic noise, and they can represent information about multiple stimuli. Working memory is a key cognitive function, and it relies on us retaining representations of external stimuli even after they go away. Stimulus-specific elevated firing rates have been observed in the prefrontal cortex during the delay period of working memory tasks, and are the main neural correlates of working memory BID6 BID7 . Perturbations to the delay period neural activities cause changes in the animal's subsequent report of the remembered stimulus representation BID12 BID19 . These elevated delay-period firing rates are not static but have time-varying dynamics with activities changing over timescales of tens of milliseconds BID0 BID18 ), yet information can be retained for tens of seconds FIG0 . This suggests the question of how time-varying neural activities keep representing the same information.Prior work from BID5 shows that, if the neural dynamics are in the ""null space"" of the representation -so that changes to neural activity do not affect the downstream read-out of stimulus information -then information can be retained for periods much longer than the timescale of individual neuronal activities (called the FEVER model; FIG0 . That model has a severe fine-tuning problem, discussed below. We identified a synaptic plasticity mechanism that overcomes this fine-tuning problem, enabling neural networks to learn to form stable representations.While the dynamics of neurons in the FEVER model match that which is observed in the monkey prefrontal cortex during a working memory task BID16 , the model itself requires that the network connectivity matrix have one or more eigenvalues very near to unity. According to the Gershgorin Circle Theorem, this will almost surely not happen in randomly-connected networks: fine-tuned connectivity is needed. BID5 suggest a mechanism of Hebbian learning by which this connectivity can be learned. That mechanism requires the read-out weights to form a 'tight frame' , which will not necessarily be true in biological circuits. Thus, the prior work leaves it unknown how synaptic plasticity can form and/or maintain functional working memory networks. Here, we identify biologically plausible synaptic plasticity rules that can solve this fine-tuning problem without making strong assumptions like 'tight frame' representations. Our plasticity rules dynamically re-tune the connectivity matrix to enable persistent representations of When presented with an external stimulus, s, neural activity patterns initially encode an internal representation of that stimulus,ŝ(t=0). These neural activity patterns change over time on timescales of tens of milliseconds, and yet somehow the same information is stored for up to tens of seconds. (B) While the firing rates, r i (t), change over time, information about stimulus,ŝ(t), can be remain unchanged as long as the projection of the firing rates onto the ""read-out"" vector d, remains constant BID5 .stimulus information. We specifically address parametric working memory, where the requirement is to remember continuous values describing several different variables or dimensions such as spatial locations or sound frequencies. For example, in the oculomotor delayed response task, subjects must remember the location of a target during a delay period BID6 . We perform experiments to demonstrate that networks using these plasticity rules are able to store information about multiple stimuli, work even if only a fraction of the synapses are tuned, and are robust to synaptic noise. We also show that these networks improve over time with multiple presented stimuli, and that the learning rules work within densely or sparsely connected networks. We derived biologically plausible synaptic plasticity rules through which networks self-organize to store information in working memory. Networks implementing these plasticity rules are robust to synaptic noise, to having only some of the synapses updated, and to partial connectivity. These networks can store multiple stimuli and have increased performance after previous training. We suggest two candidate sources for the global error signal necessary for the plasticity rule, and demonstrate that our networks can learn to store stimulus information while satisfying the added requirements imposed by these biological mechanisms. This flexibility suggests that other types of synaptic plasticity updates may also be able to organize working memory circuits.The results presented here were obtained for networks of 100 neurons -as opposed to larger networks -to speed up the simulations. Tests on networks with 10,000 neurons show that the update rule works in larger networks. The optimal learning rate, η, decreases as the network size increases. Aside from network size, a potential caveat in using a rate-based network model is losing information about spike-timing dependency. A future direction would be to create a spike-based model and determine what, if anything, must be adjusted to account for spike timing, and for the discretization that spiking neurons entail for the information shared between cells.Along with understanding how information is stored in working memory, this work may have implications in training recurrent neural networks (RNNs). Machine learning algorithms are generally unrealistic from a biological perspective: most rely on non-local synaptic updates or symmetric synapses. We show that recurrent networks can learn to store information using biologically plausible synaptic plasticity rules which require local information plus a global error signal (or signals), that can be calculated on the apical dendrite or via neuromodulators. This same setup could be utilized in RNNs to make them more biologically realistic. This would let us better understand how the brain learns, and could lead to novel biomimetic technologies: prior work on biologically realistic machine learning algorithms has led to hardware devices that use on-chip learning BID11 BID20 . Synaptically local updates do not have to be coordinated over all parts of the chip, enabling simpler and more efficient hardware implementations.","Working memory requires information external stimuli represented brain even stimuli go away. information is encoded activities neurons neural activities change timescales tens milliseconds. Information working memory however is retained tens seconds suggesting question how time-varying neural activities maintain stable representations. Prior work shows if the neural dynamics are in the null space' representation changes neural activity do not affect downstream read-out stimulus information information can be retained periods much longer time-scale individual-neuronal activities. prior work however requires precisely constructed synaptic connectivity matrices without explaining would arise biological neural network. identify mechanisms which biological networks can self-organize learn memory function derived biologically plausible synaptic plasticity rules dynamically modify connectivity matrix enable information storing. Networks implementing plasticity rule can successfully learn form memory representations even if only10% synapses are plastic are are robust synaptic noise can represent information multiple stimuli. Working memory is a key cognitive function relies us retaining representations external stimuli even go away. Stimulus-specific elevated firing rates have been observed prefrontal cortex delay period working memory tasks are the main neural correlates working memory BID6 BID7. Perturbations delay period neural activities cause changes animal's subsequent report remembered stimulus representation BID12 BID19. elevated delay-period firing rates are not static have time-varying dynamics activities changing timescales tens milliseconds BID0 BID18 yet information can be retained tens seconds FIG0. suggests question how time-varying neural activities keep representing information.Prior work BID5 shows if the neural dynamics are in the null space representation -so changes neural activity do not affect downstream read-out stimulus information -then information can be retained periods much longer timescale individual neuronal activities called FEVER model;FIG0. model has a severe fine-tuning problem discussed below. identified synaptic plasticity mechanism overcomes fine-tuning problem enabling neural networks learn form stable representations.While dynamics neurons FEVER model match which is observed monkey prefrontal cortex working memory task BID16 model requires network connectivity matrix have one eigenvalues near unity. According Gershgorin Circle Theorem will almost surely happen randomly-connected networks:fine-tuned connectivity is needed. BID5 suggest mechanism Hebbian learning which this connectivity can be learned. mechanism requires read-out weights form 'tight frame' which will not necessarily true biological circuits. Thus prior work leaves unknown how synaptic plasticity can form/maintain functional working memory networks. identify biologically plausible synaptic plasticity rules can solve fine-tuning problem without making strong assumptions like 'tight frame' representations. plasticity rules dynamically re-tune connectivity matrix enable persistent representations When presented external stimulus neural activity patterns initially encode internal representation stimulus ŝ t=0 neural activity patterns change time timescales tens milliseconds yet somehow information is stored tens seconds. B firing rates r change time information stimulus ŝ canbe remain unchanged long projection firing rates onto read-out vector remains constant BID5.stimulus information. specifically address parametric working memory where the requirement is to remember continuous values describing several different variables dimensions spatial locations sound frequencies. example oculomotor delayed response task subjects must remember location target delay period BID6. perform experiments demonstrate networks using plasticity rules are able store information multiple stimuli work even if only a fraction synapses are tuned are are robust synaptic noise. also show networks improve time multiple presented stimuli learning rules work within densely sparsely connected networks. derived biologically plausible synaptic plasticity rules which networks self-organize store information working memory. Networks implementing plasticity rules are robust synaptic noise synapses updated partial connectivity. networks can store multiple stimuli have increased performance previous training. suggest two candidate sources global error signal necessary plasticity rule demonstrate networks can learn store stimulus information satisfying added requirements imposed biological mechanisms. flexibility suggests types synaptic plasticity updates may also able organize working memory circuits.The results presented were obtained networks 100 neurons -as opposed larger networks -to speed simulations. Tests networks 10,000 neurons show update rule works larger networks. optimal learning rate η decreases network size increases. Aside network size potential caveat using rate-based network model is losing information spike-timing dependency. future direction would create spike-based model determine what,if anything must adjusted account spike timing discretization spiking neurons entail information shared cells.Along understanding how information is stored working memory work may have implications training recurrent neural networks RNNs Machine learning algorithms are generally unrealistic biological perspective:rely non-local synaptic updates symmetric synapses. show recurrent networks can learn store information using biologically plausible synaptic plasticity rules which require local information plus global error signal signals can calculated apical dendrite via neuromodulators. setup could utilized RNNs make biologically realistic. would let us better understand how the brain learns could lead novel biomimetic technologies:prior work biologically realistic machine learning algorithms has led hardware devices use on-chip learning BID11 BID20. Synaptically local updates do not haveto coordinated parts chip enabling simpler efficient hardware implementations.",1367,982,385,0.013,1.392,2025/11/05 17:18:56,0.01,1.491,0.1931464174454823,417.663
"Generative Adversarial Networks (GANs) have been proposed as an approach to learning generative models. While GANs have demonstrated promising performance on multiple vision tasks, their learning dynamics are not yet well understood, neither in theory nor in practice. In particular, the work in this domain has been focused so far only on understanding the properties of the stationary solutions that this dynamics might converge to, and of the behavior of that dynamics in this solutions’ immediate neighborhood.

 To address this issue, in this work we take a first step towards a principled study of the GAN dynamics itself. To this end, we propose a model that, on one hand, exhibits several of the common problematic convergence behaviors (e.g., vanishing gradient, mode collapse, diverging or oscillatory behavior), but on the other hand, is sufficiently simple to enable rigorous convergence analysis.

 This methodology enables us to exhibit an interesting phenomena: a GAN with an optimal discriminator provably converges, while guiding the GAN training using only a first order approximation of the discriminator leads to unstable GAN dynamics and mode collapse. This suggests that such usage of the first order approximation of the discriminator, which is a de-facto standard in all the existing GAN dynamics, might be one of the factors that makes GAN training so challenging in practice. Additionally, our convergence result constitutes the first rigorous analysis of a dynamics of a concrete parametric GAN. Generative modeling is a fundamental learning task of growing importance. As we apply machine learning to increasingly sophisticated problems, we often aim to learn functions with an output domain that is significantly more complex than simple class labels. Common examples include image ""translation"" BID12 , speech synthesis BID16 , and robot trajectory prediction BID6 . Due to progress in deep learning, we now have access to powerful architectures that can represent generative models over such complex domains. However, training these generative models is a key challenge. Simpler learning problems such as classification have a clear notion of ""right"" and ""wrong,"" and the approaches based on minimizing the corresponding loss functions have been tremendously successful. In contrast, training a generative model is far more nuanced because it is often unclear how ""good"" a sample from the model is.Generative Adversarial Networks (GANs) have recently been proposed to address this issue BID8 . In a nutshell, the key idea of GANs is to learn both the generative model and the loss function at the same time. The resulting training dynamics are usually described as a game between a generator (the generative model) and a discriminator (the loss function). The goal of the generator is to produce realistic samples that fool the discriminator, while the discriminator is trained to distinguish between the true training data and samples from the generator. GANs have shown promising results on a variety of tasks, and there is now a large body of work that explores the power of this framework BID9 .Unfortunately , reliably training GANs is a challenging problem that often hinders further research in this area. Practitioners have encountered a variety of obstacles such as vanishing gradients, mode collapse, and diverging or oscillatory behavior BID9 . At the same time , the theoretical underpinnings of GAN dynamics are not yet well understood. To date, there were no convergence proofs for GAN models, even in very simple settings. As a result, the root cause of frequent failures of GAN dynamics in practice remains unclear.In this paper, we take a first step towards a principled understanding of GAN dynamics. Our general methodology is to propose and examine a problem setup that exhibits all common failure cases of GAN dynamics while remaining sufficiently simple to allow for a rigorous analysis. Concretely, we introduce and study the GMM-GAN: a variant of GAN dynamics that captures learning a mixture of two univariate Gaussians. We first show experimentally that standard gradient dynamics of the GMM-GAN often fail to converge due to mode collapse or oscillatory behavior. Interestingly, this also holds for techniques that were recently proposed to improve GAN training such as unrolled GANs (Metz et al., 2017 ). In contrast, we then show that GAN dynamics with an optimal discriminator do converge, both experimentally and provably. To the best of our knowledge, our theoretical analysis of the GMM-GAN is the first global convergence proof for parametric and non-trivial GAN dynamics.Our results show a clear dichotomy between the dynamics arising from applying simultaneous gradient descent and the one that is able to use an optimal discriminator. The GAN with optimal discriminator provably converges from (essentially) any starting point. On the other hand, the simultaneous gradient GAN empirically often fails to converge, even when the discriminator is allowed many more gradient steps than the generator. These findings go against the common wisdom that first order methods are sufficiently strong for all deep learning applications. By carefully inspecting our models, we are able to pinpoint some of the causes of this, and we highlight a phenomena we call discriminator collapse which often causes first order methods to fail in our setting. We haven taken a step towards a principled understanding of GAN dynamics. We define a simple yet rich model of GAN training and prove convergence of the corresponding dynamics. To the best of our knowledge, our work is the first to establish global convergence guarantees for a parametric GAN. We find an interesting dichotomy: If we take optimal discriminator steps, the training dynamics provably converge. In contrast, we show experimentally that the dynamics often fail if we take first order discriminator steps. We believe that our results provide new insights into GAN training and point towards a rich algorithmic landscape to be explored in order to further understand GAN dynamics.",Generative Adversarial Networks GANs have been proposed approach learning generative models. GANs have demonstrated promising performance multiple vision tasks learning dynamics are not yet well understood neither theory practice. particular work domain has been focused far understanding properties stationary solutions dynamics might converge behavior dynamics solutions immediate neighborhood. address issue work take first step towards principled study GAN dynamics itself. end propose model one hand exhibits several common problematic convergence behaviors e.g vanishing gradient mode collapse diverging oscillatory behavior hand is sufficiently simple enable rigorous convergence analysis. methodology enablesus exhibit interesting phenomena:GAN optimal discriminator provably converges guiding GAN training using first order approximation discriminator leads unstable GAN dynamics mode collapse. suggests usage first order approximation discriminator which is a de-facto standard existing GAN dynamics might one factors makes GAN training challenging practice. Additionally were no convergence result constitutes first rigorous analysis dynamics concrete parametric GAN. Generative modeling is a fundamental learning task growing importance. apply machine learning increasingly sophisticated problems often aim learn functions output domain is significantly complex simple class labels. Common examples include image translation BID12 speech synthesis BID16 robot trajectory prediction BID6. Due progress deep learning have access powerful architectures can represent generative models complex domains. However training generative models is a key challenge. Simpler learning problems classification have a clear notion right wrong approaches based minimizing corresponding loss functions have been tremendously successful. contrast training generative model is far nuanced is often unclear how good sample model is.Generative Adversarial Networks GANs have recently proposed address issue BID8. nutshell key idea GANs is to learn generative model loss function time. resulting training dynamics are usually described game generator generative model discriminator loss function goal generator is to produce realistic samples fool discriminator discriminator is trained distinguish true training data samples generator. GANs have shown promising results variety tasks is large body work explores power framework BID9.Unfortunately reliably training GANs is a challenging problem often hinders research area. Practitioners have encountered variety obstacles vanishing gradients mode collapse diverging oscillatory behavior BID9. time theoretical underpinnings GAN dynamics are not yet well understood. date were no convergence proofs GAN models even simple settings. result root cause frequent failures GAN dynamics practice remains unclear.In paper take first step towards principled understanding GAN dynamics. general methodology is to propose examine problem setup exhibits common failure cases GAN dynamics remaining sufficiently simple allow rigorous analysis. Concretely introduce study GMM-GAN variant GAN dynamics captures learning mixture two univariate Gaussians. first show experimentally standard gradient dynamics GMM-GAN often fail converge due mode collapse oscillatory behavior. Interestingly also holds techniques were recently proposed improve GAN training unrolled GANs Metzetal. 2017 contrast show GAN dynamics optimal discriminator do converge experimentally provably. best knowledge theoretical analysis GMM-GAN is the first global convergence proof parametric non-trivial GAN dynamics.Our results show clear dichotomy dynamics arising applying simultaneous gradient descent one is able use optimal discriminator. GAN optimal discriminator provably converges essentially starting point. hand simultaneous gradient GAN empirically often fails converge even when the discriminator is allowed many gradient steps generator. findingsgo common wisdom first order methods are sufficiently strong deep learning applications. carefully inspecting models are able pinpoint causes highlight phenomena call discriminator collapse which often causes first order methods fail setting. taken step towards principled understanding GAN dynamics. define simple yet rich model GAN training prove convergence corresponding dynamics. best knowledge work is the first establish global convergence guarantees parametric GAN. find interesting dichotomy:If we take optimal discriminator steps training dynamics provably converge. contrast show experimentally dynamics often fail if we take first order discriminator steps. believe results provide new insights GAN training point towards rich algorithmic landscape explored order understand GAN dynamics.,1134,733,401,0.012,1.547,2025/11/05 17:18:56,0.01,1.474,0.6760124610591897,352.322
"The machine learning and computer vision community is witnessing an unprecedented rate of new tasks being proposed and addressed, thanks to the power of deep convolutional networks to find complex mappings from X to Y. The advent of each task often accompanies the release of a large-scale human-labeled dataset, for supervised training of the deep network. However, it is expensive and time-consuming to manually label sufficient amount of training data. Therefore, it is important to develop algorithms that can leverage off-the-shelf labeled dataset to learn useful knowledge for the target task. While previous works mostly focus on transfer learning from a single source, we study multi-source transfer across domains and tasks (MS-DTT), in a semi-supervised setting. We propose GradMix, a model-agnostic method applicable to any model trained with gradient-based learning rule. GradMix transfers knowledge via gradient descent, by weighting and mixing the gradients from all sources during training. Our method follows a meta-learning objective, by assigning layer-wise weights to the source gradients, such that the combined gradient follows the direction that can minimize the loss for a small set of samples from the target dataset. In addition, we propose to adaptively adjust the learning rate for each mini-batch based on its importance to the target task, and a pseudo-labeling method to leverage the unlabeled samples in the target domain. We perform experiments on two MS-DTT tasks: digit recognition and action recognition, and demonstrate the advantageous performance of the proposed method against multiple baselines. Deep convolutional networks (ConvNets) have significantly improved the state-of-the-art for visual recognition, by finding complex mappings from X to Y. Unfortunately, these impressive gains in performance come only when massive amounts of paired labeled data (x, y) s.t. x ∈ X , y ∈ Y are available for supervised training. For many application domains, it is often prohibitive to manually label sufficient training data, due to the significant amount of human efforts involved. Hence, there is strong incentive to develop algorithms that can reduce the burden of manual labeling, typically by leveraging off-the-shelf labeled datasets from other related domains and tasks.There has been a large amount of efforts in the research community to address adapting deep models across domains BID5 BID16 BID31 , to transfer knowledge across tasks BID17 BID7 BID34 , and to learn efficiently in a few shot manner BID4 BID22 BID23 . However, most works focus on a single-source and single-target scenario. Recently, some works BID33 BID19 propose deep approaches for multi-source domain adaptation, but they assume that the source and target domains have shared label space (task).In many computer vision applications, there often exist multiple labeled datasets available from different domains and/or tasks related to the target application. Hence , it is important and practically valuable that we can transfer knowledge from as many source datasets as possible. In this work, we formalize this problem as multi-source domain and task transfer (MS-DTT). Given a set of labeled source dataset, S = {S 1 , S 2 , ..., S k }, we aim to transfer knowledge to a sparsely labeled target dataset T . Each source dataset S i could come from a different domain compared to T , or from a different task, or different in both domain and task. We focus on a semi-supervised setting, where only few samples in T have labels.Most works achieve domain transfer by aligning the feature distribution of source domain and target domain BID15 BID5 BID30 BID19 BID33 . However, this method could be suboptimal for MS-DTT. The reason is that in MS-DTT, the distribution of source data p(x Si , y Si ) and target data p(x T , y T ) could be significantly different in both input space and label space, thus simply aligning their input space may generate indiscriminative features for the target classes. In addition, feature alignment introduces additional layers and loss terms, which require careful design to perform well.In this work, we propose a generic and scalable method, namely GradMix, for semi-supervised MS-DTT. GradMix is a model-agnostic method, applicable to any model that uses gradient-based learning rule. Our method does not introduce extra layers or loss functions for feature alignment. Instead, we perform knowledge transfer via gradient descent, by weighting and mixing the gradients from all the source datasets during training. We follow a meta-learning paradigm and model the most basic assumption: the combined gradient should minimize the loss for a set of unbiased samples from the target dataset. We propose an online method to weight and mix the source gradients at each training iteration, such that the knowledge most useful for the target task is preserved through the gradient update. Our method can adaptively adjust the learning rate for each mini-batch based on its importance to the target task. In addition, we propose a pseudo-labeling method based on model ensemble to learn from the unlabeled data in target domain. We perform extensive experiments on two sets of MS-DTT task, including digit recognition and action recognition, and demonstrate the advantageous performance of the proposed method compared to multiple baselines. Our code is available at https://www.url.com . In this work, we propose GradMix, a method for semi-supervised MS-DTT: multi-source domain and task transfer. GradMix assigns layer-wise weights to the gradients calculated from each source objective, in a way such that the combined gradient can optimize the target objective, measured by the loss on a small validation set. GradMix can adaptively adjust the learning rate for each mini-batch based on its importance to the target task. In addition, we assign pseudo-labels to the unlabeled samples using model ensembles, and consider the pseudo-labeled dataset as a source during training. We validate the effectiveness our method with extensive experiments on two MS-DTT settings, namely digit recognition and action recognition. GradMix is a generic framework applicable to any models trained with gradient descent. For future work, we intend to extend GradMix to other problems where labeled data for the target task is expensive to acquire, such as image captioning.",machine learning computer vision community is witnessing unprecedented rate new tasks proposed addressed thanks power deep convolutional networks find complex mappings X Y. advent task often accompanies release large-scale human-labeled dataset supervised training deep network. However is expensive time-consuming manually label sufficient amount training data. Therefore is important develop algorithms can leverage off-the-shelf labeled dataset learn useful knowledge target task. previous works mostly focus transfer learning single source study multi-source transfer across domains tasks MS-DTT semi-supervised setting. propose GradMix model-agnostic method applicable model trained gradient-based learning rule. GradMix transfers knowledge via gradient descent weighting mixing gradients sources training. method follows meta-learning objective assigning layer-wise weights source gradients combined gradient follows direction can minimize loss small set samples target dataset. addition propose adaptively adjust learning rate mini-batch based importance target task pseudo-labeling method leverage unlabeled samples target domain. perform experiments two MS-DTT tasks:digit recognition action recognition demonstrate advantageous performance proposed method multiple baselines. Deep convolutional networks ConvNets have significantly improved state-of-the-art visual recognition finding complex mappings X Y. Unfortunately impressive gains performance come when massive amounts paired labeled data x.tx∈X ∈ are available supervised training. many application domains is often prohibitive manually label sufficient training data due significant amount human efforts involved. Hence is strong incentive develop algorithms can reduce burden manual labeling typically leveraging off-the-shelf labeled datasets related domains tasks.There has been a large amount efforts research community address adapting deep models across domains BID5 BID16 BID31 transfer knowledge across tasks BID17 BID7 BID34 learn efficiently shot manner BID4 BID22 BID23. However works focus single-source single-target scenario. Recently works BID33 BID19 propose deep approaches multi-source domain adaptation assume source target domains have shared label space task.In many computer vision applications is often exist multiple labeled datasets available different domains/tasks related target application. Hence is important practically valuable can transfer knowledge many source datasets possible. work formalize problem multi-source domain task transfer MS-DTT Given set labeled source dataset 1 2... k aim transfer knowledge sparsely labeled target dataset T. source dataset could come different domain compared different task different domain task. focus semi-supervised setting where only few samples have labels.Most works achieve domain transfer aligning feature distribution source domain target domain BID15 BID5 BID30 BID19 BID33. However method could suboptimal MS-DTT reason is that in MS-DTT distribution source datap xSi Si target datap x could significantly different input space label space thus simply aligning input space may generate indiscriminative features target classes. addition feature alignment introduces additional layers loss terms which require careful design perform well.In work propose generic scalable method namely GradMix semi-supervised MS-DTT GradMix is a model-agnostic method applicable model uses gradient-based learning rule. method does not introduce extra layers loss functions feature alignment. Instead perform knowledge transfer via gradient descent weighting mixing gradients source datasets training. follow meta-learning paradigm model basic assumption:combined gradient should minimize loss set unbiased samples target dataset. propose online method weight mix source gradients training iteration knowledge useful target task is preserved gradient update. method can adaptively adjust learning rate mini-batch based importance target task. addition propose pseudo-labeling method based model ensemble learn unlabeled data target domain. perform extensive experiments two sets MS-DTT task including digit recognition action recognition demonstrate advantageous performance proposed method compared multiple baselines. code is available https://www.url.com work propose GradMix method semi-supervised MS-DTT multi-source domain task transfer. GradMix assigns layer-wise weights gradients calculated source objective way combined gradient can optimize target objective measured loss small validation set. GradMix can adaptively adjust learning rate mini-batch based importance target task. addition assign pseudo-labels unlabeled samples using model ensembles consider pseudo-labeled dataset source training. validate effectiveness method extensive experiments two MS-DTT settings namely digit recognition action recognition. GradMix is a generic framework applicable models trained gradient descent. future work intend extend GradMix problems where labeled data target task is expensive acquire image captioning.,1227,804,423,0.013,1.526,2025/11/05 17:18:56,0.01,1.321,0.6105919003115264,362.939
"Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo with simple mechanisms for proposing new states, which hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper we present an alternative approach: a variational framework for Bayesian phylogenetic analysis. We approximate the true posterior using an expressive graphical model for tree distributions, called a subsplit Bayesian network, together with appropriate branch length distributions. We train the variational approximation via stochastic gradient ascent and adopt multi-sample based gradient estimators for different latent variables separately to handle the composite latent space of phylogenetic models. We show that our structured variational approximations are flexible enough to provide comparable posterior estimation to MCMC, while requiring less computation due to a more efficient tree exploration mechanism enabled by variational inference. Moreover, the variational approximations can be readily used for further statistical analysis such as marginal likelihood estimation for model comparison via importance sampling. Experiments on both synthetic data and real data Bayesian phylogenetic inference problems demonstrate the effectiveness and efficiency of our methods. Bayesian phylogenetic inference is an essential tool in modern evolutionary biology. Given an alignment of nucleotide or amino acid sequences and appropriate prior distributions, Bayesian methods provide principled ways to assess the phylogenetic uncertainty by positing and approximating a posterior distribution on phylogenetic trees . In addition to uncertainty quantification, Bayesian methods enable integrating out tree uncertainty in order to get more confident estimates of parameters of interest, such as factors in the transmission of Ebolavirus BID4 . Bayesian methods also allow complex substitution models BID24 , which are important in elucidating deep phylogenetic relationships (Feuda et al., 2017) .Ever since its introduction to the phylogenetic community in the 1990s, Bayesian phylogenetic inference has been dominated by random-walk Markov chain Monte Carlo (MCMC) approaches BID43 BID26 ). However , this approach is fundamentally limited by the complexities of tree space. A typical MCMC method for phylogenetic inference involves two steps in each iteration: first, a new tree is proposed by randomly perturbing the current tree, and second, the tree is accepted or rejected according to the Metropolis-Hastings acceptance probability. Any such random walk algorithm faces obstacles in the phylogenetic case, in which the high-posterior trees are a tiny fraction of the combinatorially exploding number of trees. Thus, major modifications of trees are likely to be rejected, restricting MCMC tree movement to local modifications that may have difficulty moving between multiple peaks in the posterior distribution BID41 . Although recent MCMC methods for distributions on Euclidean space use intelligent proposal mechanisms such as Hamiltonian Monte Carlo BID30 , it is not straightforward to extend such algorithms to the composite structure of tree space, which includes both tree topology (discrete object) and branch lengths (continuous positive vector) BID3 .Variational inference (VI) is an alternative approximate inference method for Bayesian analysis which is gaining in popularity BID17 BID40 BID0 . Unlike MCMC methods that sample from the posterior, VI selects the best candidate from a family of tractable distributions to minimize a statistical distance measure to the target posterior, usually the Kullback-Leibler (KL) divergence. By reformulating the inference problem into an optimization problem, VI tends to be faster and easier to scale to large data (via stochastic gradient descent) BID0 . However, VI can also introduce a large bias if the variational distribution is insufficiently flexible. The success of variational methods , therefore, relies on having appropriate tractable variational distributions and efficient training procedures.To our knowledge, there have been no previous variational formulations of Bayesian phylogenetic inference. This has been due to the lack of an appropriate family of approximating distributions on phylogenetic trees. However the prospects for variational inference have changed recently with the introduction of subsplit Bayesian networks (SBNs) BID46 , which provide a family of flexible distributions on tree topologies (i.e. trees without branch lengths). SBNs build on previous work BID13 BID23 , but in contrast to these previous efforts, SBNs are sufficiently flexible for real Bayesian phylogenetic posteriors BID46 .In this paper, we develop a general variational inference framework for Bayesian phylogenetics. We show that SBNs, when combined with appropriate approximations for the branch length distribution, can provide flexible variational approximations over the joint latent space of phylogenetic trees with branch lengths. We use recently-proposed unbiased gradient estimators for the discrete and continuous components separately to enable efficient stochastic gradient ascent. We also leverage the similarity of local structures among trees to reduce the complexity of the variational parameterization for the branch length distributions and provide an extension to better capture the between-tree variation. Finally, we demonstrate the effectiveness and efficiency of our methods on both synthetic data and a benchmark of challenging real data Bayesian phylogenetic inference problems. In this work we introduced VBPI, a general variational framework for Bayesian phylogenetic inference. By combining subsplit Bayesian networks, a recent framework that provides flexible distributions of trees, and efficient structured parameterizations for branch length distributions, VBPI exhibits guided exploration (enabled by SBNs) in tree space and provides competitive performance to MCMC methods with less computation. Moreover, variational approximations provided by VBPI can be readily used for further statistical analysis such as marginal likelihood estimation for model comparison via importance sampling, which, compared to MCMC based methods, dramatically reduces the cost at test time. We report promising numerical results demonstrating the effectiveness and efficiency of VBPI on a benchmark of real data Bayesian phylogenetic inference problems.When the data are weak and posteriors are diffuse, support estimation of CPTs becomes challenging. However, compared to classical MCMC approaches in phylogenetics that need to traverse the enormous support of posteriors on complete trees to accurately evaluate the posterior probabilities, the SBN parameterization in VBPI has a natural advantage in that it alleviates this issue by factorizing the uncertainty of complete tree topologies into local structures.Many topics remain for future work: constructing more flexible approximations for the branch length distributions (e.g., using normalizing flow BID33 for within-tree approximation and deep networks for the modeling of between-tree variation), deeper investigation of support estimation approaches in different data regimes, and efficient training algorithms for general variational inference on discrete / structured latent variables.","Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo simple mechanisms proposing new states which hinders exploration efficiency often requires long runs deliver accurate posterior estimates. paper present alternative approach:variational framework Bayesian phylogenetic analysis. approximate true posterior using expressive graphical model tree distributions called subsplit Bayesian network together appropriate branch length distributions. train variational approximation via stochastic gradient ascent adopt multi-sample based gradient estimators different latent variables separately handle composite latent space phylogenetic models. show structured variational approximations are flexible enough provide comparable posterior estimation MCMC requiring less computation due efficient tree exploration mechanism enabled variational inference. Moreover variational approximations can be readily used statistical analysis marginal likelihood estimation model comparison via importance sampling. Experiments synthetic data real data Bayesian phylogenetic inference problems demonstrate effectiveness efficiency methods. Bayesian phylogenetic inference is an essential tool modern evolutionary biology. Given alignment nucleotide amino acid sequences appropriate prior distributions Bayesian methods provide principled ways assess phylogenetic uncertainty positing approximating posterior distribution phylogenetic trees. addition uncertainty quantification Bayesian methods enable integrating tree uncertainty order get confident estimates parameters interest factors transmission Ebolavirus BID4. Bayesian methods also allow complex substitution models BID24 which are important elucidating deep phylogenetic relationships Feudaetal. 2017.Ever since introduction phylogenetic community 1990s Bayesian phylogenetic inference has been dominated random-walk Markov chain Monte Carlo MCMC approaches BID43 BID26 However approach is fundamentally limited complexities tree space. typical MCMC method phylogenetic inference involves two steps iteration:first new tree is proposed randomly perturbing current tree second tree is accepted rejected according Metropolis-Hastings acceptance probability. random walk algorithm faces obstacles phylogenetic case which the high-posterior trees are a tiny fraction combinatorially exploding number trees. Thus major modifications trees are likely rejected restricting MCMC tree movement local modifications may have difficulty moving multiple peaks posterior distribution BID41. Although recent MCMC methods distributions Euclidean space use intelligent proposal mechanisms Hamiltonian Monte Carlo BID30 is not straightforward extend algorithms composite structure tree space which includes tree topology discrete object branch lengths continuous positive vector BID3.Variational inference VI is an alternative approximate inference method Bayesian analysis which is gaining popularity BID17 BID40 BID0. Unlike MCMC methods sample posterior VI selects best candidate family tractable distributions minimize statistical distance measure target posterior usually Kullback-Leibler KL divergence. reformulating inference problem optimization problem VI tends faster easier scale large data via stochastic gradient descent BID0. However VI can also introduce large bias if the variational distribution is insufficiently flexible. success variational methods therefore relies appropriate tractable variational distributions efficient training procedures.To knowledge have been previous variational formulations Bayesian phylogenetic inference. has been due lack appropriate family approximating distributions phylogenetic trees. However prospects variational inference have changed recently introduction subsplit Bayesian networks SBNs BID46 which can provide family flexible distributions tree topologies.e trees without branch lengths SBNs build previous work BID13 BID23 contrast previous efforts SBNs are sufficiently flexible real Bayesian phylogenetic posteriors BID46.In paper develop general variational inference framework Bayesian phylogenetics. show SBNs when combined appropriate approximations branch length distribution which can provide flexible variational approximations joint latent space phylogenetic trees branch lengths. use recently-proposed unbiased gradient estimators discrete continuous components separately enable efficient stochastic gradient ascent. also leverage similarity local structures among trees reduce complexity variational parameterization branch length distributions provide extension better capture between-tree variation. Finally demonstrate effectiveness efficiency methods synthetic data benchmark challenging real data Bayesian phylogenetic inference problems. work introduced VBPI general variational framework Bayesian phylogenetic inference. combining subsplit Bayesian networks recent framework provides flexible distributions trees efficient structured parameterizations branch length distributions VBPI exhibits guided exploration enabled SBNs tree space provides competitive performance MCMC methods less computation. Moreover variational approximations provided VBPI can be readily used statistical analysis marginal likelihood estimation model comparison via importance sampling which,compared MCMC based methods dramatically reduces cost test time. report promising numerical results demonstrating effectiveness efficiency VBPI benchmark real data Bayesian phylogenetic inference problems.When data are weak posteriors are diffuse support estimation CPTs becomes challenging. However which,compared classical MCMC approaches phylogenetics need traverse enormous support posteriors complete trees accurately evaluate posterior probabilities SBN parameterization VBPI has a natural advantage alleviates issue factorizing uncertainty complete tree topologies local structures.Many topics remain future work:constructing flexible approximations branch length distributions e.g using normalizing flow BID33 within-tree approximation deep networks modeling between-tree variation deeper investigation support estimation approaches different data regimes efficient training algorithms general variational inference discrete/structured latent variables.",1300,949,351,0.012,1.37,2025/11/05 17:18:56,0.01,1.438,0.1246105919003116,374.802
"This paper introduces HybridNet, a hybrid neural network to speed-up autoregressive
 models for raw audio waveform generation. As an example, we propose
 a hybrid model that combines an autoregressive network named WaveNet and a
 conventional LSTM model to address speech synthesis. Instead of generating
 one sample per time-step, the proposed HybridNet generates multiple samples per
 time-step by exploiting the long-term memory utilization property of LSTMs. In
 the evaluation, when applied to text-to-speech, HybridNet yields state-of-art performance.
 HybridNet achieves a 3.83 subjective 5-scale mean opinion score on
 US English, largely outperforming the same size WaveNet in terms of naturalness
 and provide 2x speed up at inference. Speech synthesis, also known as text-to-speech (TTS) has variety of applications in human-computer interactions, assistive technology and entertainment productions. The traditional TTS system, which is done with complex hand-engineered pipelines, transforms textual features into high temporal resolution waveforms (e.g., 16KHz). Recent work on neural TTS has demonstrated state-of-the-art results BID0 b; BID14 . In particular, various neural network architectures (e.g., BID12 have been proposed as neural vocoders for waveform synthesis.Recurrent neural network (RNN), especially long short-term memory (LSTM) BID6 , is well-suited to address speech synthesis as it can model long-term dependencies in audio data (e.g., BID3 BID16 BID4 . RNNs have been successfully applied in many state-of-the-art neural TTS systems (e.g., BID14 BID1 , and were proven to be more effective than the conventional hidden Markov model (HMM)-based synthesizer. However, RNNs are unsuitable for raw waveform generation at high sampling rate (e.g. 16,000 samples per second), because RNNs process each state sequentially and the computation cannot be paralleled over elements of a sequence at training. In practice, RNNs are usually operated on spectral or hand-engineered features of audio (e.g., BID14 BID5 , which have much fewer time steps than the raw waveform. Most recently, SampleRNN was proposed to tackle this difficulty by combining autoregressive multilayer perceptrons and RNNs in a hierarchical architecture, where different RNN modules operate at different clock rates.Another line of research investigates the convolutional autoregressive model (e.g., WaveNet BID12 ) for waveform synthesis, where the computation over different time-step can be fully parallelized during training. WaveNet can be efficiently trained on audio data with tens of thousands of samples per second. In order to model the long-range dependencies in audio data, WaveNet uses dilated convolution BID15 to increase the receptive fields of output units, and demonstrates very good performance in speech synthesis. Several state-of-the-art neural TTS systems, such as Deep Voice 1 BID0 and Deep Voice 2 BID1 , use WaveNet to synthesize waveform conditioned on acoustic features (e.g., phoneme duration and fundamental frequency). Despite its full parallelism at training, WaveNet poses daunting computational problem at inference due to the autoregressive nature of the model (see FIG0 for an illustration).In addition, although the dilated convolution is very effective at increasing receptive fields, the very long-range connections in deep layer could potentially result in high variance in the output sampling distribution. In practice, some buzz noises are commonly observed in the audio samples generated by WaveNet. We present a hybrid neural architecture to speed up autoregressive models for audio synthesis. As a demonstration of effectiveness, we design and implement a hybrid model that consists of an autoregressive network named WaveNet and a LSTM model. The hybrid model exploits the long-term memory utilization property and short inference time of LSTMs. We evaluate HybridNet with both Mean Opinion Score (MOS) and validation error, and find that it outperforms WaveNet with the same layer in terms of naturalness and validation error. In addition, HybridNet provides 2x-4x speed-up at inference with comparable generation quality compared to WaveNet. The technique used in HybridNet can be easily applied to another autoregressive model and can be combined with existing inference time reduction techniques.","paper introduces HybridNet hybrid neural network speed-up autoregressive models raw audio waveform generation. example propose hybrid model combines autoregressive network named WaveNet conventional LSTM model address speech synthesis. Instead generating one sample per time-step proposed HybridNet generates multiple samples per time-step exploiting long-term memory utilization property LSTMs. evaluation when applied text-to-speech HybridNet yields state-of-art performance. HybridNet achieves 3.83 subjective 5-scale mean opinion score US English largely outperforming size WaveNet terms naturalness provide 2x speed inference. Speech synthesis also known text-to-speech TTS has variety applications human-computer interactions assistive technology entertainment productions. traditional TTS system which is done complex hand-engineered pipelines transforms textual features high temporal resolution waveforms e.g 16KHz Recent work neural TTS has demonstrated state-of-the-art results BID0 b;BID14. particular various neural network architectures e.g BID12 have been proposed neural vocoders waveform synthesis.Recurrent neural network RNN especially long short-term memory LSTM BID6 is well-suited address speech synthesis can model long-term dependencies audio data e.g BID3 BID16 BID4. RNNs have been successfully applied many state-of-the-art neural TTS systems e.g BID14 BID1 were proven effective conventional hidden Markov model HMM -based synthesizer. However RNNs are unsuitable raw waveform generation high sampling rate e.g 16,000 samples per second RNNs process state sequentially computation cannot paralleled elements sequence training. practice RNNs are usually operated spectral hand-engineered features audio e.g BID14 BID5 which have much fewer time steps raw waveform. recently SampleRNN was proposed tackle difficulty combining autoregressive multilayer perceptrons RNNs hierarchical architecture where different RNN modules operate different clock rates.Another line research investigates convolutional autoregressive model e.g WaveNet BID12 waveform synthesis where the computation different time-step can be fully parallelized training. WaveNet can be efficiently trained audio data tens thousands samples per second. order model long-range dependencies audio data WaveNet uses dilated convolution BID15 increase receptive fields output units demonstrates good performance speech synthesis. Several state-of-the-art neural TTS systems Deep Voice 1 BID0 Deep Voice 2 BID1 use WaveNet synthesize waveform conditioned acoustic features e.g phoneme duration fundamental frequency Despite full parallelism training WaveNet poses daunting computational problem inference due autoregressive nature model see FIG0 illustration.In addition although dilated convolution is very effective increasing receptive fields long-range connections deep layer could potentially result high variance output sampling distribution. practice buzz noises are commonly observed audio samples generated WaveNet. present hybrid neural architecture speed autoregressive models audio synthesis. demonstration effectiveness design implement hybrid model consists autoregressive network named WaveNet LSTM model. hybrid model exploits long-term memory utilization property short inference time LSTMs. evaluate HybridNet Mean Opinion Score MOS validation error find outperforms WaveNet layer terms naturalness validation error. addition HybridNet provides 2x-4x speed-up inference comparable generation quality compared WaveNet. technique used HybridNet can be easily applied another autoregressive model can be combined existing inference time reduction techniques.",871,637,234,0.007,1.367,2025/11/05 17:18:56,0.0,1.476,0.1152647975077879,276.605
"Visual Interpretation and explanation of deep models is critical towards wide adoption of systems that rely on them. In this paper, we propose a novel scheme for both interpretation as well as explanation in which, given a pretrained model, we automatically identify internal features relevant for the set of classes considered by the model, without relying on additional annotations. We interpret the model through average visualizations of this reduced set of features. Then, at test time, we explain the network prediction by accompanying the predicted class label with supporting visualizations derived from the identified features. In addition, we propose a method to address the artifacts introduced by strided operations in deconvNet-based visualizations. Moreover, we introduce an8Flower , a dataset specifically designed for objective quantitative evaluation of methods for visual explanation. Experiments on the MNIST , ILSVRC 12, Fashion 144k and an8Flower datasets show that our method produces detailed explanations with good coverage of relevant features of the classes of interest. Methods based on deep neural networks (DNNs) have achieved impressive results for several computer vision tasks, such as image classification, object detection and image generation. Combined with the general tendency in the Computer Vision community of developing methods with a focus on high quantitative performance, this has motivated the wide adoption of DNN-based methods, despite the initial skepticism due to their black-box characteristics. In this work, we aim for more visuallydescriptive predictions and propose means to improve the quality of the visual feedback capabilities of DNN-based methods. Our goal is to bridge the gap between methods aiming at model interpretation, i.e., understanding what a given trained model has actually learned, and methods aiming at model explanation, i.e., justifying the decisions made by a model.Model interpretation of DNNs is commonly achieved in two ways: either by a) manually inspecting visualizations of every single filter (or a random subset thereof) from every layer of the network BID28 ; BID29 ) or, more recently, by b) exhaustively comparing the internal activations produced by a given model w.r.t. a dataset with pixel-wise annotations of possibly relevant concepts BID1 ; BID7 ). These two paths have provided useful insights into the internal representations learned by DNNs. However, they both have their own weaknesses. For the first case, the manual inspection of filter responses introduces a subjective bias, as was evidenced by BID8 . In addition, the inspection of every filter from every layer becomes a cognitive-expensive practice for deeper models, which makes it a noisy process. For the second case, as stated by BID1 , the interpretation capabilities over the network are limited by the concepts for which annotation is available. Moreover, the cost of adding annotations for new concepts is quite high due to its pixel-wise nature. A third weakness, shared by both cases, is inherited by the way in which they generate spatial filter-wise responses, i.e., either through deconvolution-based heatmaps BID23 ; BID29 ) or by up-scaling the activation maps at a given layer/filter to the image space BID1 ; BID32 ). On the one hand, deconvolution methods are able to produce heatmaps with high level of detail from any filter in Figure 1 : Left: Proposed training/testing pipeline. Center: Visual explanations generated by our method.Predicted class labels are enriched with heatmaps indicating the pixel locations, associated to the features, that contributed to the prediction. Note these features may come from the object itself as well as from the context. On top of each heatmap we indicate the number of the layer where the features come from. The layer type is color-coded (green for convolutional and pink for fully connected). Right: Visualization comparison. Note how our heatmaps attenuate the grid-like artifacts introduced by deconvnet-based methods at lower layers. At the same time, our method is able to produce a more detailed visual feedback than up-scaled activation maps. the network. However, as can be seen in Fig. 1 (right), they suffer from artifacts introduced by strided operations in the back-propagation process. Up-scaled activation maps, on the other hand, can significantly lose details when displaying the response of filters with large receptive field from deeper layers. Moreover, they have the weakness of only being computable for convolutional layers.In order to alleviate these issues, we start from the hypothesis proven by BID1 ; BID28 , that only a small subset of the internal filters of a network encode features that are important for the task that the network addresses. Based on that assumption, we propose a method which, given a trained DNN model, automatically identifies a set of relevant internal filters whose encoded features serve as indicators for the class of interest to be predicted (Fig. 1 left) . These filters can originate from any type of internal layer of the network, i.e., convolutional, fully connected, etc. Selecting them is formulated as a µ-lasso optimization problem in which a sparse set of filter-wise responses are linearly combined in order to predict the class of interest. At test time, we move from interpretation to explanation. Given an image, a set of identified relevant filters, and a class prediction, we accompany the predicted class label with heatmap visualizations of the top-responding relevant filters for the predicted class, see Fig. 1 (center). In addition, by improving the resampling operations within deconvnet-based methods, we are able to address the artifacts introduced in the backpropagation process, see Fig. 1 (right) . The code and models used to generate our visual explanations can be found in the following link 1 . Overall, the proposed method removes the requirement of additional expensive pixel-wise annotation, by relying on the same annotations used to train the initial model. Moreover, by using our own variant of a deconvolution-based method, our method is able to consider the spatial response from any filter at any layer while still providing visually pleasant feedback. This allows our method to reach some level of explanation by interpretation.Finally, recent approaches to evaluate explanation methods measure the validity of an explanation either via user studies BID29 BID20 ) or by measuring its effect on a proxy task, e.g. object detection/segmentation BID33 ; BID30 ). While user studies inherently add subjectivity, benchmarking through a proxy task steers the optimization of the explanation method towards such task. Here we propose an objective evaluation via an8Flower, a synthetic dataset where the discriminative feature between the classes of interest is controlled. This allows us to produce ground-truth masks for the regions to be highlighted by the explanation. Furthermore, it allows us to quantitatively measure the performance of methods for model explanation.The main contributions of this work are four-fold. First, we propose an automatic method based on feature selection to identify the network-encoded features that are important for the prediction of a given class. This alleviates the requirement of exhaustive manual inspection or additional expensive pixel-wise annotations required by existing methods. Second, the proposed method is able to provide visual feedback with higher-level of detail over up-scaled raw activation maps and improved quality over recent deconvolution+guided back-propagation methods. Third, the proposed method is general enough to be applied to any type of network, independently of the type of layers that compose it. Fourth, we release a dataset and protocol specifically designed for the evaluation of methods for model explanation. To the best of our knowledge this is the first dataset aimed at such task. This paper is organized as follows: in Sec. 2 we position our work w.r.t. existing work. Sec. 3 presents the pipeline and inner-workings of the proposed method. In Sec. 4, we conduct a series of experiments evaluating different aspects of the proposed method. We draw conclusions in Sec. 5. We propose a method to enrich the prediction made by DNNs by indicating the visual features that contributed to such prediction. Our method identifies features encoded by the network that are relevant for the task addressed by the DNN. It allows interpretation of these features by the generation of average feature-wise visualizations. In addition, we proposed a method to attenuate the artifacts introduced by strided operations in visualizations made by Deconvnet-based methods. This empowers our method with richer visual feedback with pixel-level precision without requiring additional annotations for supervision. Finally, we have proposed a novel dataset designed for the objective evaluation of methods for explanation of DNNs.","Visual Interpretation explanation deep models is critical towards wide adoption systems rely them. paper propose novel scheme interpretation well explanation which,given pretrained model automatically identify internal features relevant set classes considered model without relying additional annotations. interpret model average visualizations reduced set features. test time explain network prediction accompanying predicted class label supporting visualizations derived identified features. addition propose method address artifacts introduced strided operations deconvNet-based visualizations. Moreover introduce an8Flower dataset specifically designed objective quantitative evaluation methods visual explanation. Experiments MNIST ILSVRC12 Fashion 144k an8Flower datasets show method produces detailed explanations good coverage relevant features classes interest. Methods based deep neural networks DNNs have achieved impressive results several computer vision tasks image classification object detection image generation. Combined general tendency Computer Vision community developing methods focus high quantitative performance has motivated wide adoption DNN-based methods despite initial skepticism due black-box characteristics. work aim visuallydescriptive predictions propose means improve quality visual feedback capabilities DNN-based methods. goal is to bridge gap methods aiming model interpretation.e understanding what a given trained model has actually learned methods aiming model explanation.e justifying decisions made model.Model interpretation DNNs is commonly achieved two ways:either manually inspecting visualizations every single filter random subset thereof every layer network BID28;BID29 recently b exhaustively comparing internal activations produced given modelw.r.t dataset pixel-wise annotations possibly relevant concepts BID1;BID7 two paths have provided useful insights internal representations learned DNNs. However have weaknesses. first case manual inspection filter responses introduces subjective bias was evidenced BID8. addition inspection every filter every layer becomes cognitive-expensive practice deeper models which makes noisy process. second case stated BID1 interpretation capabilities network are limited concepts which annotation is available. Moreover cost adding annotations new concepts is quite high due pixel-wise nature. third weakness shared cases is inherited way which they generate spatial filter-wise responses.e either deconvolution-based heatmaps BID23;BID29 up-scaling activation maps given layer/filter image space BID1;BID32 one hand deconvolution methods are able produce heatmaps high level detail filter Figure1:Left:Proposed training/testing pipeline. Center:Visual explanations generated method.Predicted class labels are enriched heatmaps indicating pixel locations associated features contributed prediction. Note features may come object well context. top heatmap indicate number layer where the features come from. layer type is color-coded green convolutional pink fully connected Right:Visualization comparison. Note how our heatmaps attenuate grid-like artifacts introduced deconvnet-based methods lower layers. time method is able produce detailed visual feedback up-scaled activation maps. network. However can be seen Fig. 1 right suffer artifacts introduced strided operations back-propagation process. Up-scaled activation maps hand can significantly lose details when displaying response filters large receptive field deeper layers. Moreover have the weakness computable convolutional layers.In order alleviate issues start hypothesis proven BID1;BID28 small subset internal filters network encode features are important task network addresses. Based assumption propose method which,given trained DNN model automatically identifies set relevant internal filters whose encoded features serve indicators class interest predicted Fig. 1 left filters can originate type internal layer network.e convolutional fully connected etc. Selecting is formulated µ-lasso optimization problem which a sparse set filter-wise responses are linearly combined order predict class interest. test time move interpretation explanation. Given image set identified relevant filters class prediction accompany predicted class label heatmap visualizations top-responding relevant filters predicted class see Fig. 1 center addition improving resampling operations within deconvnet-based methods are able address artifacts introduced backpropagation process see Fig. 1 right code models used generate visual explanations can be found following link1. Overall have proposed method removes requirement additional expensive pixel-wise annotation relying annotations used train initial model. Moreover using variant deconvolution-based method method is able consider spatial response filter layer still providing visually pleasant feedback. allows method reach level explanation interpretation.Finally recent approaches evaluate explanation methods measure validity explanation either via user studies BID29 BID20 measuring effect proxy task e.g object detection/segmentation BID33;BID30 user studies inherently add subjectivity benchmarking proxy task steers optimization explanation method towards task. propose objective evaluation via an8Flower synthetic dataset where the discriminative feature classes interest is controlled. allowsus produce ground-truth masks regions highlighted explanation. Furthermore allowsus quantitatively measure performance methods model explanation.The main contributions work are four-fold four-fold First propose automatic method based feature selection identify network-encoded features are important prediction given class. alleviates requirement exhaustive manual inspection additional expensive pixel-wise annotations required existing methods. Second have proposed method is able provide visual feedback higher-level detail up-scaled raw activation maps improved quality recent deconvolution+guided back-propagation methods. Third have proposed method is general enough applied type network independently type layers compose it. Fourth release dataset protocol specifically designed evaluation methods model explanation. best knowledge is the first dataset aimed task. paper is organized follows:Sec. 2 position workw.r.t existing work. Sec. 3 presents pipeline inner-workings proposed method. Sec. 4 conduct series experiments evaluating different aspects proposed method. draw conclusions Sec. 5. propose method enrich prediction made DNNs indicating visual features contributed prediction. method identifies features encoded network are relevant task addressed DNN. allows interpretation features generation average feature-wise visualizations. addition have proposed method attenuate artifacts introduced strided operations visualizations made Deconvnet-based methods. empowers method richer visual feedback pixel-level precision without requiring additional annotations supervision. Finally have proposed novel dataset designed objective evaluation methods explanation DNNs.",1707,1125,582,0.02,1.517,2025/11/05 17:18:56,0.01,1.318,0.5825545171339559,544.78
"In this work we propose a simple and efficient framework for learning sentence representations from unlabelled data. Drawing inspiration from the distributional hypothesis and recent work on learning sentence representations, we reformulate the problem of predicting the context in which a sentence appears as a classification problem. Given a sentence and the context in which it appears, a classifier distinguishes context sentences from other contrastive sentences based on their vector representations. This allows us to efficiently learn different types of encoding functions, and we show that the model learns high-quality sentence representations. We demonstrate that our sentence representations outperform state-of-the-art unsupervised and supervised representation learning methods on several downstream NLP tasks that involve understanding sentence semantics while achieving an order of magnitude speedup in training time. Methods for learning meaningful representations of data have received widespread attention in recent years. It has become common practice to exploit these representations trained on large corpora for downstream tasks since they capture a lot of prior knowlege about the domain of interest and lead to improved performance. This is especially attractive in a transfer learning setting where only a small amount of labelled data is available for supervision.Unsupervised learning allows us to learn useful representations from large unlabelled corpora. The idea of self-supervision has recently become popular where representations are learned by designing learning objectives that exploit labels that are freely available with the data. Tasks such as predicting the relative spatial location of nearby image patches BID6 , inpainting BID30 and solving image jigsaw puzzles BID27 have been successfully used for learning visual feature representations. In the language domain, the distributional hypothesis has been integral in the development of learning methods for obtaining semantic vector representations of words BID24 . This is the assumption that the meaning of a word is characterized by the word-contexts in which it appears. Neural approaches based on this assumption have been successful at learning high quality representations from large text corpora.Recent methods have applied similar ideas for learning sentence representations Hill et al., 2016; BID8 . These are encoder-decoder models that learn to predict/reconstruct the context sentences of a given sentence. Despite their success, several modelling issues exist in these methods. There are numerous ways of expressing an idea in the form of a sentence. The ideal semantic representation is insensitive to the form in which meaning is expressed. Existing models are trained to reconstruct the surface form of a sentence, which forces the model to not only predict its semantics, but aspects that are irrelevant to the meaning of the sentence as well.The other problem associated with these models is computational cost. These methods have a word level reconstruction objective that involves sequentially decoding the words of target sentences. Training with an output softmax layer over the entire vocabulary is a significant source of slowdown in the training process. This further limits the size of the vocabulary and the model (Variations of the softmax layer such as hierarchical softmax BID26 , sampling based softmax BID9 and sub-word representations BID33 can help alleviate this issue).We circumvent these problems by proposing an objective that operates directly in the space of sentence embeddings. The generation objective is replaced by a discriminative approximation where the model attempts to identify the embedding of a correct target sentence given a set of sentence candidates. In this context, we interpret the 'meaning' of a sentence as the information in a sentence that allows it to predict and be predictable from the information in context sentences. We name our approach quick thoughts (QT), to mean efficient learning of thought vectors.Our key contributions in this work are the following:• We propose a simple and general framework for learning sentence representations efficiently. We train widely used encoder architectures an order of magnitude faster than previous methods, achieving better performance at the same time.• We establish a new state-of-the-art for unsupervised sentence representation learning methods across several downstream tasks that involve understanding sentence semantics.The pre-trained encoders will be made publicly available. We proposed a framework to learn generic sentence representations efficiently from large unlabelled text corpora. Our simple approach learns richer representations than prior unsupervised and supervised methods, consuming an order of magnitude less training time. We establish a new state-of-the-art for unsupervised sentence representation learning methods on several downstream tasks. We believe that exploring scalable approaches to learn data representations is key to exploit unlabelled data available in abundance.",work propose simple efficient framework learning sentence representations unlabelled data. Drawing inspiration distributional hypothesis recent work learning sentence representations reformulate problem predicting context which a sentence appears classification problem. Given sentence context which it appears classifier distinguishes context sentences contrastive sentences based vector representations. allowsus efficiently learn different types encoding functions show model learns high-quality sentence representations. demonstrate sentence representations outperform state-of-the-art unsupervised supervised representation learning methods several downstream NLP tasks involve understanding sentence semantics achieving order magnitude speedup training time. Methods learning meaningful representations data have received widespread attention recent years. has become common practice exploit representations trained large corpora downstream tasks since capture lot prior knowlege domain interest lead improved performance. is especially attractive transfer learning setting where only a small amount labelled data is available supervision.Unsupervised learning allowsus learn useful representations large unlabelled corpora. idea self-supervision has recently become popular where representations are learned designing learning objectives exploit labels are freely available data. Tasks predicting relative spatial location nearby image patches BID6 inpainting BID30 solving image jigsaw puzzles BID27 have been successfully used learning visual feature representations. language domain distributional hypothesis has been integral development learning methods obtaining semantic vector representations words BID24. is the assumption meaning word is characterized word-contexts which it appears. Neural approaches based assumption have been successful learning high quality representations large text corpora.Recent methods have applied similar ideas learning sentence representations Hill etal. 2016;BID8. are encoder-decoder models learn predict/reconstruct context sentences given sentence. Despite success several modelling issues exist methods. are numerous ways expressing idea form sentence. ideal semantic representation is insensitive form which meaning is expressed. Existing models are trained reconstruct surface form sentence which forces model predict semantics aspects are irrelevant meaning sentence well.The problem associated models is computational cost. methods have a word level reconstruction objective involves sequentially decoding words target sentences. Training output softmax layer entire vocabulary is a significant source slowdown training process. limits size vocabulary model Variations softmax layer hierarchical softmax BID26 sampling based softmax BID9 sub-word representations BID33 can help alleviate issue.We circumvent problems proposing objective operates directly space sentence embeddings. generation objective is replaced discriminative approximation where the model attempts identify embedding correct target sentence given set sentence candidates. context interpret 'meaning' sentence information which a sentence allows predict predictable information context sentences. name approach quick thoughts QT mean efficient learning thought vectors.Our key contributions work are the following:• propose simple general framework learning sentence representations efficiently. train widely used encoder architectures order magnitude faster previous methods achieving better performance time.• establish new state-of-the-art unsupervised sentence representation learning methods across several downstream tasks involve understanding sentence semantics.The pre-trained encoders will be made publicly available. proposed framework learn generic sentence representations efficiently large unlabelled text corpora. simple approach learns richer representations prior unsupervised supervised methods consuming order magnitude less training time. establish new state-of-the-art unsupervised sentence representation learning methods several downstream tasks. believe exploring scalable approaches learn data representations is key exploit unlabelled data available abundance.,857,607,250,0.009,1.412,2025/11/05 17:18:56,0.0,1.382,0.2554517133956382,295.146
"Many regularization methods have been proposed to prevent overfitting in neural networks. Recently, a regularization method has been proposed to optimize the variational lower bound of the Information Bottleneck Lagrangian. However, this method cannot be generalized to regular neural network architectures. We present the activation norm penalty that is derived from the information bottleneck principle and is theoretically grounded in a variation dropout framework. Unlike in previous literature, it can be applied to any general neural network. We demonstrate that this penalty can give consistent improvements to different state of the art architectures both in language modeling and image classification. We present analyses on the properties of this penalty and compare it to other methods that also reduce mutual information. Neural networks have been applied to many domains and are able to solve complex tasks such as image classification or machine translation, achieving higher performance than other families of learning algorithms. However, most neural networks used in these tasks are over-parameterized, and they are operating on inputs in high-dimensional space, thus prone to overfitting.For the task of supervised learning, the goal is to find a mapping from noisy input X to a set of corresponding labels Y . In the perspective of information theory, neural networks construct a mapping S and then decode from the resulting representation S(X) and obtain hypothesisŶ , forming the following Markov Chain: Y → X → S. By data processing inequality, I(Y ; X) ≥ I(Y ; S(X)). So if S captures the sufficient statistics of X, we have I(Y ; X) = I(Y ; S(X)) (Cover & BID2 . However, a trivial solution would satisfy this constraint: an identity mapping of X. To avoid this, we further require the minimum sufficient statistics of X to satisfy T * = arg min I(Y ;X)=I(Y ;S(X)) I(S(X); X). The minimum sufficient statistics should only capture the most relevant features in X. Intuitively, being able to compute T exactly would solve the overfitting problem.However, the minimum sufficient statistics does not exist for general distributions. BID16 relaxed the requirement and turn the problem into the Information Bottleneck Lagrangian: minimize βI(X; T ) − I(Y ; T ). We can work out a solution for P (T |X) if P (X, Y ) is known. We would also obtain a solution if we have deterministic mapping between T and X, namely for I(X; T ) = H(T ) − H(T |X), H(T |X) = 0, then minimizing the mutual information becomes minimizing the entropy of T . Since we don't know the distribution of T , we are not able to penalize towards this objective either.So we can only apply information bottleneck penalty in a principled way for probabilistic framework where T |X is a specified or known distribution. BID1 has proposed a variational lower bound of the information bottleneck objective when T |X ∼ N (µ(X), diag(σ 2 (X))) where both µ and σ are estimated by a neural network.We first extend BID1 's work naively to recurrent neural network. Then instead of relying on mean field approximation variational inference, which is not widely applicable to general neural network architecture, we extend the variational approximation of the information bottleneck objective to any neural network with dropout, which is shown to be mathematically equivalent to the lower bound of a Gaussian Process BID5 . We present an information bottleneck penalty that has a very simple equivalence in a neural network with dropout. From additional demonstration by BID6 , we can easily extend our case in recurrent neural networks as well.We validate this penalty on language modeling and image classification, we observe improvements over all near state of the art baselines. Finally, we show preliminary comparisons between this penalty and its variations. In this paper we present a simple way to extend information bottleneck principle to the training of recurrent neural network. We demonstrate how information bottleneck principle can be applied not only to Bayesian neural networks, but to general neural networks with dropout. We derived the activation norm penalty from the variational dropout framework, and observe consistent improvements to state of the art architectures when applied to language modeling and image classification.",Many regularization methods have been proposed prevent overfitting neural networks. Recently regularization method has been has proposed optimize variational lower bound Information Bottleneck Lagrangian. However method cannot generalized regular neural network architectures. present activation norm penalty is derived information bottleneck principle is theoretically grounded variation dropout framework. Unlike previous literature can be applied general neural network. demonstrate penalty can give consistent improvements different state art architectures language modeling image classification. present analyses properties penalty compare methods also reduce mutual information. Neural networks have been applied many domains are able solve complex tasks image classification machine translation achieving higher performance families learning algorithms. However neural networks used tasks are over-parameterized are operating inputs high-dimensional space thus prone overfitting.For task supervised learning goal is to find mapping noisy inputX set corresponding labels Y. perspective information theory neural networks construct mapping decode resulting representation X obtain hypothesisŶ forming following Markov Chain:→X→ S. data processing inequality haveIY;X ≥ Y;X ifS captures sufficient statistics X haveI Y;X Y;X Cover BID2. However trivial solution would satisfy constraint:identity mapping X. avoid require minimum sufficient statistics X satisfy * arg min Y;X =I Y;X X X minimum sufficient statistics should only capture relevant features X. Intuitively able compute exactly would solve overfitting problem.However minimum sufficient statistics does not exist general distributions. BID16 relaxed requirement turn problem Information Bottleneck Lagrangian:minimizeβI X;− Y;can work solution P |X ifP X is known. would also obtain solution if we have deterministic mapping X namely X;H −H |X H |X 0 minimizing mutual information becomes minimizing entropy T. Since know distribution are not able penalize towards objective either.So can only apply information bottleneck penalty principled way probabilistic framework whereT|X is a specified known distribution. BID1 has been has proposed variational lower bound information bottleneck objective whenT|X∼N µ X diag σ2 X where µ σ are estimated neural network.We first extend BID1 's work naively recurrent neural network. instead relying mean field approximation variational inference which is not widely applicable general neural network architecture extend variational approximation information bottleneck objective neural network dropout which is shown mathematically equivalent lower bound Gaussian Process BID5. present information bottleneck penalty has a very simple equivalence neural network dropout. additional demonstration BID6 can easily extend case recurrent neural networks well.We validate penalty language modeling image classification observe improvements near state art baselines. Finally show preliminary comparisons penalty variations. paper present simple way extend information bottleneck principle training recurrent neural network. demonstrate how information bottleneck principle can be applied Bayesian neural networks general neural networks dropout. derived activation norm penalty variational dropout framework observe consistent improvements state art architectures when applied language modeling image classification.,851,566,285,0.009,1.504,2025/11/05 17:18:56,0.0,1.647,0.542056074766355,291.354
"Unsupervised learning of timeseries data is a challenging problem in machine learning. Here, 
we propose a novel algorithm, Deep Temporal Clustering (DTC), a fully unsupervised method, to naturally integrate dimensionality reduction and temporal clustering into a single end to end learning framework. The algorithm starts with an initial cluster estimates using an autoencoder for dimensionality reduction and a novel temporal clustering layer for cluster assignment. Then it jointly optimizes the clustering objective and the dimensionality reduction objective. Based on requirement and application, the temporal clustering layer can be customized with any temporal similarity metric. Several similarity metrics are considered and compared.   To gain insight into features that the network has learned for its clustering, we apply a visualization method that generates a heat map of regions of interest in the timeseries. The viability of the algorithm is demonstrated using timeseries data from diverse domains, ranging from earthquakes to sensor data from spacecraft. In each case, we show that our algorithm outperforms traditional methods. This performance is attributed to fully integrated temporal dimensionality reduction and clustering criterion. Deep learning has become the dominant approach to supervised learning of labeled data BID12 BID17 . However, in many applications the data labels may not be available or be reliable. A variety of techniques have been developed for unsupervised learning where the algorithms draw inferences from unlabeled data. However, the progress in learning of complex structure in the data has so far been largely restricted to labeled datasets, while relatively little attention was paid to learning of complex, high-level structure and features of unlabeled data. The standard unsupervised techniques include clustering approaches which organize similar objects into clusters. Such techniques differ in the method for organizing the data as well as the metrics to measure similarity. While clustering techniques have been successfully applied to static data, their extension to time series data remains an open problem. This has left a gap in technology for accurate unsupervised learning of time series data which encompass many areas of science and engineering such as financial trading, medical monitoring, and event detection BID0 .The problem of unsupervised time series clustering is particularly challenging. Time series data from different domains exhibit considerable variations in important properties and features, temporal scales, and dimensionality. Further , time series data from real world applications often have temporal gaps as well as high frequency noise due to the data acquisition method and/or the inherent nature of the data BID1 ).To address the issues and limitations of using standard clustering techniques on time series data, we present a novel algorithm called deep temporal clustering (DTC) . A key element of DTC is the transformation of the time series data into a low dimensional latent space using a trainable network, which here we choose to be a deep autoencoder network that is fully integrated with a novel temporal clustering layer. The overview of our method is illustrated in Figure 1 . The latent representation is compatible with any temporal similarity metric.The proposed DTC algorithm was designed based on the observation that time series data have informative features on all time scales. To disentangle the data manifolds , i.e., to uncover the latent dimension(s) along which the temporal or spatio-temporal unlabeled data split into two or more classes, we propose the following three-level approach. The first level, implemented as a CNN, reduces the data dimensionality and learns the dominant short-time-scale waveforms. The second level, implemented as a BI-LSTM, reduces the data dimensionality further and learns the temporal connections between waveforms across all time scales. The third level performs non-parametric clustering of BI-LSTM latent representations, finding one or more spatio-temporal dimensions along which the data split into two or more classes. The unique ability of this approach to untangle the data manifolds without discarding the information provided by the time course of the data (e.g., in contrast to PCA-based methods) allows our approach to achieve high performance on a variety of real-life and benchmark datasets without any parameter adjustment.DTC also includes an algorithm to visualize the cluster-assignment activations across time, a feature not available in traditional clustering algorithms. This allows the localization of events in unlabeled time series data, and provides explanation (as opposed to black-box approaches) regarding the most informative data features for class assignment.To the best of our knowledge, this is the first work on the application of deep learning in temporal clustering. The main contribution of our study is the formulation of an end-to-end deep learning algorithm that implements objective formulation to achieve meaningful temporal clustering. We carefully formulated the objective to encompass two crucial aspects essential for high clustering accuracy: an effective latent representation and a similarity metric which can be integrated into the learning structure. We demonstrate that the end-to-end optimization of our network for both reconstruction loss and clustering loss offers superior performance compared to cases where these two objectives are optimized separately. We also show that DTC outperforms current state-of-theart , k-Shape BID15 and hierarchical clustering with complete linkage, when evaluated on various real world time series datasets. In this work we addressed the question of unsupervised learning of patterns in temporal sequences, unsupervised event detection and clustering. Post-hoc labeling of the clusters, and comparison to ground-truth labels not used in training, reveals high degree of agreement between our unsupervised clustering results and human-labeled categories, on several types of datasets. This indicates graceful dimensionality reduction from inputs with extensive and complex temporal structure to one or fewdimensional space spanned by the cluster centroids. As most natural stimuli are time-continuous and unlabeled, the approach promises to be of great utility in real-world applications. Generalization to multichannel spatio-temporal input is straightforward and has been carried out as well; it will be described in more detail in a separate paper.",Unsupervised learning timeseries data is a challenging problem machine learning. propose novel algorithm Deep Temporal Clustering DTC fully unsupervised method naturally integrate dimensionality reduction temporal clustering single end end learning framework. algorithm starts initial cluster estimates using autoencoder dimensionality reduction novel temporal clustering layer cluster assignment. jointly optimizes clustering objective dimensionality reduction objective. Based requirement application temporal clustering layer can be customized temporal similarity metric. Several similarity metrics are considered compared. gain insight features network has learned clustering apply visualization method generates heat map regions interest timeseries. viability algorithm is demonstrated using timeseries data diverse domains ranging earthquakes sensor data spacecraft. case show algorithm outperforms traditional methods. performance is attributed fully integrated temporal dimensionality reduction clustering criterion. Deep learning has become dominant approach supervised learning labeled data BID12 BID17. However many applications data labels may available reliable. variety techniques have been developed unsupervised learning where the algorithms draw inferences unlabeled data. However progress learning complex structure data has so far largely restricted labeled datasets relatively little attention was paid learning complex high-level structure features unlabeled data. standard unsupervised techniques include clustering approaches which organize similar objects clusters. techniques differ method organizing data well metrics measure similarity. clustering techniques have been successfully applied static data extension time series data remains open problem. has left gap technology accurate unsupervised learning time series data which encompass many areas science engineering financial trading medical monitoring event detection BID0.The problem unsupervised time series clustering is particularly challenging. Time series data different domains exhibit considerable variations important properties features temporal scales dimensionality. time series data real world applications often have temporal gaps well high frequency noise due data acquisition method/inherent nature data BID1.To address issues limitations using standard clustering techniques time series data present novel algorithm called deep temporal clustering DTC key element DTC is the transformation time series data low dimensional latent space using trainable network which here we choose deep autoencoder network is fully integrated novel temporal clustering layer. overview method is illustrated Figure1. latent representation is compatible temporal similarity metric.The proposed DTC algorithm was designed based observation time series data have informative features time scales. disentangle data manifolds.e uncover latent dimension along which the temporal spatio-temporal unlabeled data split two classes propose following three-level approach. first level implemented CNN reduces data dimensionality learns dominant short-time-scale waveforms. second level implemented BI-LSTM reduces data dimensionality learns temporal connections waveforms across time scales. third level performs non-parametric clustering BI-LSTM latent representations finding one spatio-temporal dimensions along which the data split two classes. unique ability approach untangle data manifolds without discarding information provided time course data e.g contrast PCA-based methods allows approach achieve high performance variety real-life benchmark datasets without parameter adjustment.DTC also includes algorithm visualize cluster-assignment activations across time feature available traditional clustering algorithms. allows localization events unlabeled time series data provides explanation opposed black-box approaches regarding informative data features class assignment.To best knowledge is the first work application deep learning temporal clustering. main contribution study is the formulation end-to-end deep learning algorithm implements objective formulation achieve meaningful temporal clustering. carefully formulated objective encompass two crucial aspects essential high clustering accuracy:effective latent representation similarity metric which can be integrated learning structure. demonstrate end-to-end optimization network reconstruction loss clustering loss offers superior performance compared cases where these two objectives are optimized separately. also show DTC outperforms current state-of-theart k-Shape BID15 hierarchical clustering complete linkage when evaluated various real world time series datasets. work addressed question unsupervised learning patterns temporal sequences unsupervised event detection clustering. Post-hoc labeling clusters comparison ground-truth labels used training reveals high degree agreement unsupervised clustering results human-labeled categories several types datasets. indicates graceful dimensionality reduction inputs extensive complex temporal structure one fewdimensional space spanned cluster centroids. natural stimuli are time-continuous unlabeled approach promises great utility real-world applications. Generalization multichannel spatio-temporal input is straightforward has been carried well;will be described detail separate paper.,1162,801,361,0.011,1.451,2025/11/05 17:18:56,0.01,1.5,0.3769470404984424,350.483
"We study many-class few-shot (MCFS) problem in both supervised learning and meta-learning scenarios. Compared to the well-studied many-class many-shot and few-class few-shot problems, MCFS problem commonly occurs in practical applications but is rarely studied. MCFS brings new challenges because it needs to distinguish between many classes, but only a few samples per class are available for training. In this paper, we propose ``memory-augmented hierarchical-classification network (MahiNet)'' for MCFS learning. It addresses the ``many-class'' problem by exploring the class hierarchy, e.g., the coarse-class label that covers a subset of fine classes, which helps to narrow down the candidates for the fine class and is cheaper to obtain. MahiNet uses a convolutional neural network (CNN) to extract features, and integrates a memory-augmented attention module with a multi-layer perceptron (MLP) to produce the probabilities over coarse and fine classes. While the MLP extends the linear classifier, the attention module extends a KNN classifier, both together targeting the ''`few-shot'' problem. We design different training strategies of MahiNet for supervised learning and meta-learning. Moreover, we propose two novel benchmark datasets ''mcfsImageNet'' (as a subset of ImageNet) and ''mcfsOmniglot'' (re-splitted Omniglot) specifically for MCFS problem. In experiments, we show that MahiNet outperforms several state-of-the-art models on MCFS classification tasks in both supervised learning and meta-learning scenarios. The representation power of deep neural networks (DNN) has dramatically improved in recent years, as deeper, wider and more complicated DNN architectures BID5 BID6 have emerged to match the increasing computation power of new hardwares. Although this brings hope for complex tasks that could be hardly solved by previous shallow models, more training data is usually required. Hence, the scarcity of annotated data has become a new bottleneck for training more powerful DNNs. For example, in image classification, the number of candidate classes can easily range from hundreds to tens of thousands (i.e., many-class), but the training samples available for each class can be less than 100 (i.e., few-shot). Additionally, in life-long learning, models are always updated once new training data becomes available, and those models are expected to quickly adapt to new classes with a few training samples. This ""many-class few-shot"" problem is very common in various applications, such as image search, robot navigation and video surveillance.Although enormous previous works have shown the remarkable power of DNN when ""many-class many-shot"" training data is available, their performance degrades dramatically when each class only has a few samples available for training. In practical applications, acquiring samples of rare species is usually difficult and often expensive. In these few-shot scenarios, the model's capacity cannot be fully utilized, and it becomes much harder to generalize the model to unseen data. Recently, several approaches have been proposed to address the few-shot learning problem. Most of them are based on the idea of ""meta-learning"", which trains a meta-learner that can generalize to different tasks. For classification, each task targets a different set of classes. Meta-learning can be categorized into two types: methods based on ""learning to optimize"", and methods based on metric learning. The former type adaptively modifies the optimizer (or some parts of it) applied to the training process. It includes methods that incorporate an RNN meta-learner BID0 BID13 BID16 , and model-agnostic meta-learning (MAML) methods aiming to learn a … Figure 1 : The MCFS problem with class hierarchy information. There are a few coarse classes (blue), but each coarse class contains a large number of fine classes (red), and the total number of fine classes is large. Only a few training samples are available for each fine class. The goal is to train a classifier to generate a prediction over all fine classes. In meta-learning, each task is an MCFS problem sampled from a certain distribution. The meta-learner's goal is to help train a classifier for any sampled task with better adaptation to few-shot data.generally compelling initialization BID4 . The latter type learns a similarity/distance metric BID22 or a support set of samples BID20 ) that can be generally used to build KNN classifiers for different tasks. Instead of using meta-learning, some other approaches, such as BID2 , address the few-shot learning problem through data augmentation by generating artificial samples for each class. However, most existing few-shot learning approaches only focus on ""few-class"" case (e.g., 5 or 10) per task, and performance usually collapses when the number of classes grows to hundreds or thousands. This is because the samples per class no longer provide enough information to distinguish them from other possible samples within a large number of other classes. And, in real-world problems, tasks are usually complicated involving many classes.Fortunately, in practice, class hierarchy is usually available or cheaper to obtain. As shown in Figure 1, coarse class labels might reveal the relationships among the targeted fine classes. Moreover, the samples per coarse class are sufficient to train a reliable coarse classifier, whose predictions are able to narrow down the candidates for fine classes. For example, a sheepdog with long hair could be easily mis-classified as mop when training samples of sheepdog are insufficient. However, if we could train a reliable dog classifier, it would be much simpler to predict an image as a sheepdog than a mop given a correct prediction of the coarse class as ""dog"". Hence, class hierarchy might provide weakly supervised information to help solve the ""many-class few-shot (MCFS)"" problem.",study many-class few-shot MCFS problem supervised learning meta-learning scenarios. Compared well-studied many-class many-shot few-class few-shot problems MCFS problem commonly occurs practical applications is rarely studied. MCFS brings new challenges needs distinguish many classes samples per class are available training. paper propose memory-augmented hierarchical-classification network MahiNet MCFS learning. addresses many-class problem exploring class hierarchy e.g coarse-class label covers subset fine classes which helps narrow candidates fine class is cheaper obtain. MahiNet uses convolutional neural network CNN extract features integrates memory-augmented attention module multi-layer perceptron MLP produce probabilities coarse fine classes. MLP extends linear classifier attention module extends KNN classifier together targeting few-shot problem. design different training strategies MahiNet supervised learning meta-learning Moreover propose two novel benchmark datasets mcfsImageNet subset ImageNet mcfsOmniglot re-splitted Omniglot specifically MCFS problem. experiments show MahiNet outperforms several state-of-the-art models MCFS classification tasks supervised learning meta-learning scenarios. representation power deep neural networks DNN has dramatically improved recent years deeper wider complicated DNN architectures BID5 BID6 have emerged match increasing computation power new hardwares. Although brings hope complex tasks could hardly solved previous shallow models training data is usually required. Hence scarcity annotated data has become new bottleneck training powerful DNNs. example image classification number candidate classes can easily range hundreds tens thousands.e many-class training samples available class can be less 100.e few-shot Additionally life-long learning models are always updated new training data becomes available models are expected quickly adapt new classes training samples. many-class few-shot problem is very common various applications image search robot navigation video surveillance.Although enormous previous works have shown remarkable power DNN when many-class many-shot training data is available performance degrades dramatically when each class has a few samples available training. practical applications acquiring samples rare species is usually difficult often expensive. few-shot scenarios model's capacity cannot fully utilized becomes much harder generalize model unseen data. Recently several approaches have been proposed address few-shot learning problem. are based idea meta-learning which trains meta-learner can generalize different tasks. classification task targets different set classes. Meta-learning can be categorized two types:methods based learning optimize methods based metric learning. former type adaptively modifies optimizer parts applied training process. includes methods incorporate RNN meta-learner BID0 BID13 BID16 model-agnostic meta-learning MAML methods aiming learn … Figure1:MCFS problem class hierarchy information. are a few coarse classes blue coarse class contains large number fine classes red total number fine classes is large. training samples are available fine class. goal is to train classifier generate prediction fine classes. meta-learning task is an MCFS problem sampled certain distribution. meta-learner's goal is to help train classifier sampled task better adaptation few-shot data.generally compelling initialization BID4. latter type learns similarity/distance metric BID22 support set samples BID20 can be generally used build KNN classifiers different tasks. Instead using meta-learning approaches BID2 address few-shot learning problem data augmentation generating artificial samples class. However existing few-shot learning approaches focus few-class case e.g 5 10 per task performance usually collapses when the number classes grows hundreds thousands. is because the samples per class longer provide enough information distinguish possible samples within large number classes. real-world problems tasks are usually complicated involving many classes.Fortunately practice class hierarchy is usually available cheaper obtain. shown Figure1 coarse class labels might reveal relationships among targeted fine classes. Moreover samples per coarse class are sufficient train reliable coarse classifier whose predictions are able narrow candidates fine classes. example sheepdog long hair could easily mis-classified mop when training samples sheepdog are insufficient. However could train reliable dog classifier would much simpler predict image sheepdog mop given correct prediction coarse class dog. Hence class hierarchy might provide weakly supervised information help solve many-class few-shot MCFS problem.,1171,790,381,0.011,1.482,2025/11/05 17:18:56,0.01,1.444,0.4735202492211836,345.739
"Learning a better representation with neural networks is a challenging problem, which has been tackled from different perspectives in the past few years. In this work, we focus on learning a representation that would be useful in a clustering task. We introduce two novel loss components that substantially improve the quality of produced clusters, are simple to apply to arbitrary models and cost functions, and do not require a complicated training procedure. We perform an extensive set of experiments, supervised and unsupervised, and evaluate the proposed loss components on two most common types of models, Recurrent Neural Networks and Convolutional Neural Networks, showing that the approach we propose consistently improves the quality of KMeans clustering in terms of mutual information scores and outperforms previously proposed methods. Representation learning is an important part of deep learning research, and the ability of deep neural networks to transform the input data into a space that is more suitable to the target task is one of the key reasons for their success. Consider the case of binary classification with a neural network with sigmoid activation function on the last layer, where a network transforms the input data x ∈ R n into a space R where two classes are linearly separable by applying a sequence of non-linear transformations f (x) : DISPLAYFORM0 Note that all representations, learned by the network in the sequence of transformations R i → R j , are devoted to one goal: binary classification. The learned intermediate representations can easily be used in tasks similar to the binary classification, but using them in a different task may be problematic.Consider the case of multivariate time series classification with an RNN model, depicted in Figure 1 with a sigmoid activation function in the last FC 2 layer and a ReLU activation function in the layer FC 1 . Note that ReLU activation produces non-negative vectors. During a regular training procedure with binary cross-entropy loss, the model will learn weights that produce two patterns of activation of the layer FC 1 : roughly orthogonal vectors for the samples that belong to different classes, and roughly parallel vectors for the samples that belong to the same class. Indeed, the value of the output scalar is the result of taking the dot product between the weights w of the final layer FC 2 (a single vector in this case) and the output h of the penultimate hidden layer FC 1 . Via the geometric interpretation of the dot product, this value is highest when the cosine between the vectors 1, and minimized when the cosine is −1. However, since the penultimate layer has the ReLU activation, the vectors cannot point in opposite directions, therefore, they must be orthogonal.",Learning better representation neural networks is a challenging problem which has been tackled different perspectives past years. work focus learning representation would useful clustering task. introduce two novel loss components substantially improve quality produced clusters are simple apply arbitrary models cost functions do not require complicated training procedure. perform extensive set experiments supervised unsupervised evaluate proposed loss components two common types models Recurrent Neural Networks Convolutional Neural Networks showing approach propose consistently improves quality KMeans clustering terms mutual information scores outperforms previously proposed methods. Representation learning is an important part deep learning research ability deep neural networks transform input data space is more suitable target task is one key reasons success. Consider case binary classification neural network sigmoid activation function last layer where a network transforms input datax∈ Rn spaceR where two classes are linearly separable applying sequence non-linear transformationsf x DISPLAYFORM0 Note representations learned network sequence transformationsR →Rj are devoted one goal:binary classification. learned intermediate representations can easily used tasks similar binary classification using different task may problematic.Consider case multivariate time series classification RNN model depicted Figure1 sigmoid activation function last FC 2 layer ReLU activation function layerFC1. Note ReLU activation produces non-negative vectors. regular training procedure binary cross-entropy loss model will learn weights produce two patterns activation layerFC1:roughly orthogonal vectors samples belong different classes roughly parallel vectors samples belong class. Indeed value output scalar is the result taking dot product weightsw final layerFC2 single vector case outputh penultimate hidden layerFC 1. Via geometric interpretation dot product value is highest when the cosine vectors1 minimized when the cosine is −1 −1 However since penultimate layer has the ReLU activation vectors cannot point opposite directions therefore must orthogonal.,526,345,181,0.005,1.525,2025/11/05 17:18:56,0.0,1.611,0.6074766355140183,180.288
"In high dimensions, the performance of nearest neighbor algorithms depends crucially on structure in the data.
 While traditional nearest neighbor datasets consisted mostly of hand-crafted feature vectors, an increasing number of datasets comes from representations learned with neural networks.
 We study the interaction between nearest neighbor algorithms and neural networks in more detail.
 We find that the network architecture can significantly influence the efficacy of nearest neighbor algorithms even when the classification accuracy is unchanged.
 Based on our experiments, we propose a number of training modifications that lead to significantly better datasets for nearest neighbor algorithms.
 Our modifications lead to learned representations that can accelerate nearest neighbor queries by 5x. Learning representations has become a major field of study over the past decade, with many succesful applications in computer vision, speech recognition, and natural language processing. The primary focus in these directions has been accuracy, usually with a focus on classification tasks. Here, the main goal is to learn a representation that enables a standard classifier (e.g., a linear model such as softmax regression) to correctly label the transformed data. However, as learned representations have achieved high accuracy in a wide range of applications, additional goals are becoming increasingly important. One such desideratum is computational efficiency: how quickly can we process the learned representations? This is question is particularly relevant in the context of large databases, where the goal is to store many millions or even billions of images, texts, and videos. Common instantiations of such settings include web search, recommender systems, near-duplicate detection (e.g., for copyrighted content), and large-scale face recognition.In this paper, we study the problem of learning representations through the lenss of similarity search. Similarity search, also known as Nearest Neighbor Search (NNS), is a fundamental algorithmic problem with a wide range of applications in machine learning and broader data science . The most common example is similarity search in large corpora such as the aforementioned image databases, segments of speech, or document collections. More recently, NNS has also appeared as a sub-routine in other algorithms such as optimization methods BID4 , cryptography (Laarhoven, 2015) , and large-scale classification (Vijayanarasimhan et al., 2015) . A key challenge in the design of efficient NNS methods is the interaction between the data and the algorithms: How can we exploit structure in the data to enable fast and accurate search? Research on NNS has established a large set of techniques such as kd-trees, locality-sensitive hashing, and quantization methods that utilize various forms of structure in the data.Traditionally, NNS is used on hand-crafted feature vectors: image similarity search is often performed on SIFT vectors, speakers are identified via their i-vector, and document similarity is computed via tfidf representations. However, recent progress in deep learning is replacing many of these hand-crafted feature vectors with learned representations. There is often a clear reason: learned representations often lead to higher accuracy and semantically more meaningful NNS results. However, this raises an important question: Do existing NNS algorithms perform well on these new classes of feature vectors? Moreover, learning the representations in NNS also offers an interesting new design space: Instead of adapting the algorithm to the dataset, can we learn a representation that is particularly well suited for fast NNS? We have demonstrated how to learn representations specifically for faster similarity search in large datasets. To this end, we have studied multiple modifications to neural network training and architecture that lead to a smaller angle between the learned representation vectors produced by the network and the class vectors in the softmax layer. This angle is a crucial measure of performance for approximate nearest neighbor algorithms and enables a 5× speed-up in query times. An interesting direction for future research is whether these insights can also lead to faster training of large multiclass networks, which are common in language models or recommender systems. Figure 7 : Effect of our training modifications on the query times of nearest neighbor algorithms. We report the relative accuracies, i.e., the probability of finding the correct nearest neighbor conditioned on the model being correct. For LSH as implemented in the FALCONN library (left), our training yields a 5× speed-up in the relevant high accuracy regime. The variant of kd-trees implemented in the Annoy library (right) does not reach relative accuracy 1 when the softmax is trained using the standard approach. In contrast, the softmax resulting from our training techniques is more amenable to the kd-tree algorithm. Again, we obtain faster query times for fixed accuracy. A RELATED WORK The paper (Liu et al., 2016) also proposes a method for training with larger angular distance gaps. In contrast to our approach, the authors modify the loss function, not the training process or network architecture. The focus of their paper is also on classification accuracy and not fast similarity search. The authors do not quantify the improvements in angular distance and train on datasets with a relatively small number of classes (100 or less). ? also modifies the loss function for learning representations with angular distance gaps. Again, the focus of their paper is on accuracy and not fast similarity search. In particular, the authors do not investigate the effect of their changes on the angular gap on large datasets. The focus of our paper is on fast similarity search and we evaluate various network modifications with end-to-end experiments using state-of-the art NNS methods.",high dimensions performance nearest neighbor algorithms depends crucially structure data. traditional nearest neighbor datasets consisted mostly hand-crafted feature vectors increasing number datasets comes representations learned neural networks. study interaction nearest neighbor algorithms neural networks detail. find network architecture can significantly influence efficacy nearest neighbor algorithms even when the classification accuracy is unchanged. Based experiments propose number training modifications lead significantly better datasets nearest neighbor algorithms. modifications lead learned representations can accelerate nearest neighbor queries 5x. Learning representations has become major field study past decade many succesful applications computer vision speech recognition natural language processing. primary focus directions has been accuracy usually focus classification tasks. main goal is to learn representation enables standard classifier e.g linear model softmax regression correctly label transformed data. However learned representations have achieved high accuracy wide range applications additional goals are becoming increasingly important. One desideratum is computational efficiency:how quickly can we process learned representations? is question is particularly relevant context large databases where the goal is to store many millions even billions images texts videos. Common instantiations settings include web search recommender systems near-duplicate detection e.g copyrighted content large-scale face recognition.In paper study problem learning representations lenss similarity search. Similarity search also known Nearest Neighbor Search NNS is a fundamental algorithmic problem wide range applications machine learning broader data science. common example is similarity search large corpora aforementioned image databases segments speech document collections. recently NNS has also appeared sub-routine algorithms optimization methods BID4 cryptography Laarhoven 2015 large-scale classification Vijayanarasimhanetal. 2015 key challenge design efficient NNS methods is the interaction data algorithms:How can we exploit structure data enable fast accurate search? Research NNS has established large set techniques kd-trees locality-sensitive hashing quantization methods utilize various forms structure data.Traditionally NNS is used hand-crafted feature vectors:image similarity search is often performed SIFT vectors speakers are identified via i-vector document similarity is computed via tfidf representations. However recent progress deep learning is replacing many hand-crafted feature vectors learned representations. is often clear reason:learned representations often lead higher accuracy semantically meaningful NNS results. However raises important question:Do existing NNS algorithms perform well new classes feature vectors? Moreover learning representations NNS also offers interesting new design space:Instead adapting algorithm dataset can we learn representation is particularly well suited fast NNS? have demonstrated how to learn representations specifically faster similarity search large datasets. end have studied multiple modifications neural network training architecture lead smaller angle learned representation vectors produced network class vectors softmax layer. angle is a crucial measure performance approximate nearest neighbor algorithms enables 5× speed-up query times. interesting direction future research is whether insights can also lead faster training large multiclass networks which are common language models recommender systems. Figure7:Effect training modifications query times nearest neighbor algorithms. report relative accuracies.e probability finding correct nearest neighbor conditioned model correct. LSH implemented FALCONN library left training yields 5× speed-up relevant high accuracy regime. variant kd-trees implemented Annoy library right does not reach relative accuracy1 when the softmax is trained using standard approach. contrast softmax resulting training techniques is more amenable kd-tree algorithm. obtain faster query times fixed accuracy. RELATED WORK paper Liuetal. 2016 also proposes method training larger angular distance gaps. contrast approach authors modify loss function training process network architecture. focus paper is also classification accuracy fast similarity search. authors do not quantify improvements angular distance train datasets relatively small number classes 100 less also modifies loss function learning representations angular distance gaps. focus paper is on accuracy fast similarity search. particular authors do not investigate effect changes angular gap large datasets. focus paper is on fast similarity search evaluate various network modifications end-to-end experiments using state-of-the art NNS methods.,1088,746,342,0.011,1.458,2025/11/05 17:18:56,0.01,1.447,0.3987538940809966,342.791
"Neural network quantization has become an important research area due to its great impact on deployment of large models on resource constrained devices. In order to train networks that can be effectively discretized without loss of performance, we introduce a differentiable quantization procedure. Differentiability can be achieved by transforming continuous distributions over the weights and activations of the network to categorical distributions over the quantization grid. These are subsequently relaxed to continuous surrogates that can allow for efficient gradient-based optimization. We further show that stochastic rounding can be seen as a special case of the proposed approach and that under this formulation the quantization grid itself can also be optimized with gradient descent. We experimentally validate the performance of our method on MNIST, CIFAR 10 and Imagenet classification. Neural networks excel in a variety of large scale problems due to their highly flexible parametric nature. However, deploying big models on resource constrained devices, such as mobile phones, drones or IoT devices is still challenging because they require a large amount of power, memory and computation. Neural network compression is a means to tackle this issue and has therefore become an important research topic.Neural network compression can be, roughly, divided into two not mutually exclusive categories: pruning and quantization. While pruning BID18 BID10 aims to make the model ""smaller"" by altering the architecture, quantization aims to reduce the precision of the arithmetic operations in the network. In this paper we focus on the latter. Most network quantization methods either simulate or enforce discretization of the network during training, e.g. via rounding of the weights and activations. Although seemingly straighforward, the discontinuity of the discretization makes the gradient-based optimization infeasible. The reason is that there is no gradient of the loss with respect to the parameters. A workaround to the discontinuity are the ""pseudo-gradients"" according to the straight-through estimator BID3 , which have been successfully used for training low-bit width architectures at e.g. BID13 ; Zhu et al. (2016) .The purpose of this work is to introduce a novel quantization procedure, Relaxed Quantization (RQ). RQ can bypass the non-differentiability of the quantization operation during training by smoothing it appropriately. The contributions of this paper are four-fold: First, we show how to make the set of quantization targets part of the training process such that we can optimize them with gradient descent. Second , we introduce a way to discretize the network by converting distributions over the weights and activations to categorical distributions over the quantization grid. Third , we show that we can obtain a ""smooth"" quantization procedure by replacing the categorical distributions with (a) (b)Figure 1: The proposed discretization process. (a) Given a distribution p(x) over the real line we partition it into K intervals of width α where the center of each of the intervals is a grid point g i . The shaded area corresponds to the probability ofx falling inside the interval containing that specific g i .(b) Categorical distribution over the grid obtained after discretization. The probability of each of the grid points g i is equal to the probability ofx falling inside their respective intervals.concrete BID22 BID15 equivalents. Finally we show that stochastic rounding BID8 , one of the most popular quantization techniques, can be seen as a special case of the proposed framework. We present the details of our approach in Section 2, discuss related work in Section 3 and experimentally validate it in Section 4. Finally we conclude and provide fruitful directions for future research in Section 5. We have introduced Relaxed Quantization (RQ), a powerful and versatile algorithm for learning low-bit neural networks using a uniform quantization scheme. As such, the models trained by this method can be easily transferred and executed on low-bit fixed point chipsets. We have extensively evaluated RQ on various image classification benchmarks and have shown that it allows for the better trade-offs between accuracy and bit operations per second.Future hardware might enable us to cheaply do non-uniform quantization, for which this method can be easily extended. BID17 BID25 for example, show the benefits of low-bit floating point weights that can be efficiently implemented in hardware. The floating point quantization grid can be easily learned with RQ by redefiningĜ. General non-uniform quantization, as described TAB4 in the Appendix. We compare against multiple works that employ fixed-point quantization: SR+DR BID8 BID9 , LR Net BID29 , , TWN BID19 , INQ BID40 , BWN BID28 , XNORnet BID28 , DoReFa (Zhou et al., 2016) , HWGQ BID4 , ELQ Zhou et al. (2018) , SYQ BID7 , Apprentice , QSM BID30 and rounding.for example in BID2 , is a natural extension to RQ, whose exploration we leave to future work. For example, we could experiment with a base grid that is defined as in . Currently, the bit-width of every quantizer is determined beforehand, but in future work we will explore learning the required bit precision within this framework. In our experiments, batch normalization was implemented as a sequence of convolution, batch normalization and quantization. On a low-precision chip, however, batch normalization would be ""folded"" into the kernel and bias of the convolution, the result of which is then rounded to low precision. In order to accurately reflect this folding at test time, future work on the proposed algorithm will emulate folded batchnorm at training time and learn the corresponding quantization grid of the modified kernel and bias. For fast model evaluation on low-precision hardware, quantization goes hand-in-hand with network pruning. The proposed method is orthogonal to pruning methods such as, for example, L 0 regularization BID21 , which allows for group sparsity and pruning of hidden units.","Neural network quantization has become important research area due great impact deployment large models resource constrained devices. order train networks can be effectively discretized without loss performance introduce differentiable quantization procedure. Differentiability can be achieved transforming continuous distributions weights activations network categorical distributions quantization grid. are subsequently relaxed continuous surrogates can allow efficient gradient-based optimization. show stochastic rounding can be seen special case proposed approach formulation quantization grid can also optimized gradient descent. experimentally validate performance method MNIST CIFAR10 Imagenet classification. Neural networks excel variety large scale problems due highly flexible parametric nature. However deploying big models resource constrained devices mobile phones drones IoT devices is still challenging require large amount power memory computation. Neural network compression is a means tackle issue has therefore become important research topic.Neural network compression can be,roughly divided two mutually exclusive categories:pruning quantization. pruning BID18 BID10 aims make model smaller altering architecture quantization aims reduce precision arithmetic operations network. paper focus latter. network quantization methods either simulate enforce discretization network training e.g via rounding weights activations. Although seemingly straighforward discontinuity discretization makes gradient-based optimization infeasible. reason is that thereis gradient loss respect parameters. workaround discontinuity are the pseudo-gradients according straight-through estimator BID3 which have been successfully used training low-bit width architectures e.g BID13;Zhuetal. 2016.The purpose work is to introduce novel quantization procedure Relaxed Quantization RQ RQ can bypass non-differentiability quantization operation training smoothing appropriately. contributions paper are four-fold four-fold First show how to make set quantization targets part training process can optimize gradient descent. Second introduce way discretize network converting distributions weights activations categorical distributions quantization grid. Third show can obtain smooth quantization procedure replacing categorical distributions b Figure1:proposed discretization process. Given distributionp x real line partition K intervals widthα where the center intervals is a grid pointg i. shaded area corresponds probability ofx falling inside interval containing specificg i. b Categorical distribution grid obtained discretization. probability grid pointsg is equal probability ofx falling inside respective intervals.concrete BID22 BID15 equivalents. Finally show stochastic rounding BID8 one popular quantization techniques can be seen special case proposed framework. present details approach Section2 discuss related work Section3 experimentally validate Section4. Finally conclude provide fruitful directions future research Section5. have introduced Relaxed Quantization RQ powerful versatile algorithm learning low-bit neural networks using uniform quantization scheme. models trained method can be easily transferred executed low-bit fixed point chipsets. have extensively evaluatedRQ various image classification benchmarks have shown allows better trade-offs accuracy bit operations per second.Future hardware might enableus cheaply do non-uniform quantization which this method can be easily extended. BID17 BID25 example show benefits low-bit floating point weights can be efficiently implemented hardware. floating point quantization grid can be easily learned RQ redefiningĜ. General non-uniform quantization described TAB4 Appendix. compare multiple works employ fixed-point quantization:SR+DR BID8 BID9 LR Net BID29 TWN BID19 INQ BID40 BWN BID28 XNORnet BID28 DoReFa Zhouetal. 2016 HWGQ BID4 ELQ Zhouetal. 2018 SYQ BID7 Apprentice QSM BID30 rounding.for example BID2 is a natural extension RQ whose exploration leave future work. example could experiment base grid is defined in. Currently bit-width every quantizer is determined beforehand future work will explore learning required bit precision within framework. experiments batch normalization was implemented sequence convolution batch normalization quantization. low-precision chip however batch normalization would folded kernel bias convolution result which is then rounded low precision. order accurately reflect folding test time future work proposed algorithm will emulate folded batchnorm training time learn corresponding quantization grid modified kernel bias. fast model evaluation low-precision hardware quantization goes hand-in-hand network pruning. proposed method is orthogonal pruning methods example L 0 regularization BID21 which allows group sparsity pruning hidden units.",1197,817,380,0.012,1.465,2025/11/05 17:18:56,0.01,1.6,0.4205607476635514,350.187
"In most current formulations of adversarial training, the discriminators can be expressed as single-input operators, that is, the mapping they define is separable over observations. In this work, we argue that this property might help explain the infamous mode collapse phenomenon in adversarially-trained generative models. Inspired by discrepancy measures and two-sample tests between probability distributions, we propose distributional adversaries that operate on samples, i.e., on sets of multiple points drawn from a distribution, rather than on single observations. We show how they can be easily implemented on top of existing models. Various experimental results show that generators trained in combination with our distributional adversaries are much more stable and are remarkably less prone to mode collapse than traditional models trained with observation-wise prediction discriminators. In addition, the application of our framework to domain adaptation results in strong improvement over recent state-of-the-art. Adversarial training of neural networks, especially Generative Adversarial Networks (GANs) BID10 , has proven to be a powerful tool for learning rich models, leading to outstanding results in various tasks such as realistic image generation, text to image synthesis, 3D object generation, and video prediction BID25 BID33 BID32 . Despite their success, GANs are known to be difficult to train. The generator and discriminator can oscillate significantly from iteration to iteration, and slight imbalances in their capacities frequently cause the training objective to diverge. Another common problem suffered by GANs is mode collapse, where the distribution learned by the generator concentrates on a few modes of the true data distribution, ignoring the rest of the space. In the case of images, this failure results in generated images that albeit realistic, lack diversity and reduce to a handful of prototypes.A flurry of recent research seeks to understand and address the causes of instability and mode collapse in adversarially-trained models. The first insights come from BID10 , who note that one of the main causes of training instability is saturation of the discriminator. BID1 formalize this idea by showing that if the two distributions have supports that are disjoint or concentrated on low-dimensional manifolds that do not perfectly align, then there exists an optimal discriminator with perfect classification accuracy almost everywhere and the usual divergences (Kullback-Leibler, Jensen-Shannon) max-out for this discriminator. In follow-up work, propose an alternative training scheme (WGAN) based on estimating the Wasserstein distance instead of the Jensen-Shannon divergence between real and generated distributions.In this work, we highlight a further view on mode collapse. The discriminator part of GANs and of variations like WGANs is separable over observations, which, as we will illustrate, can result in serious problems, even when minibatches are used. The underlying issue is that the stochastic gradients are essentially (sums of) functions of single observations (training points). Despite connections to two-sample tests based on Jensen-Shannon divergence, ultimately the updates based on gradients from different single observations are completely independent of each other. We show how this lack of sharing information between observations may explain mode collapses in GANs.Motivated by these insights, we take a different perspective on adversarial training and propose a framework that brings the discriminator closer to a truly distributional adversary, i.e., one that 1 (a set of observations) in its entirety, retaining and sharing global information between gradients. The key insight is that a carefully placed nonlinearity in the form of specific population comparisons can enable information-sharing and thereby stabilize training. We develop and test two such models, and also connect them to other popular ideas in deep learning and statistics.Contributions. The main contributions of this work are as follows:• We introduce a new distributional framework for adversarial training of neural networks that operates on a genuine sample, i.e., a collection of points, rather than an observation. This choice is orthogonal to modifications of the types of loss (e.g. logistic vs. Wasserstein) in the literature.• We show how off-the-shelf discriminator networks can be made distribution-aware via simple modifications to their architecture and how existing models can seamlessly fit into this framework.• Empirically, our distributional adversarial framework leads to more stable training and significantly better mode coverage than common single-observation methods. A direct application of our framework to domain adaptation results in strong improvements over state-of-the-art.","current formulations adversarial training discriminators can be expressed single-input operators is,mapping define is separable observations. work argue property might help explain infamous mode collapse phenomenon adversarially-trained generative models. Inspired discrepancy measures two-sample tests probability distributions propose distributional adversaries operate samples.e sets multiple points drawn distribution rather single observations. show how they can be easily implemented top existing models. Various experimental results show generators trained combination distributional adversaries are much stable are remarkably less prone mode collapse traditional models trained observation-wise prediction discriminators. addition application framework domain adaptation results strong improvement recent state-of-the-art Adversarial training neural networks especially Generative Adversarial Networks GANs BID10 has proven powerful tool learning rich models leading outstanding results various tasks realistic image generation text image synthesis 3D object generation video prediction BID25 BID33 BID32. Despite success GANs are known difficult train. generator discriminator can oscillate significantly iteration iteration slight imbalances capacities frequently cause training objective diverge. Another common problem suffered GANs is mode collapse where the distribution learned generator concentrates modes true data distribution ignoring rest space. case images failure results generated images albeit realistic lack diversity reduce handful prototypes.A flurry recent research seeks understand address causes instability mode collapse adversarially-trained models. first insights come BID10 who note one main causes training instability is saturation discriminator. BID1 formalize idea showing if the two distributions have supports are disjoint concentrated low-dimensional manifolds do not perfectly align exists optimal discriminator perfect classification accuracy almost everywhere usual divergences Kullback-Leibler Jensen-Shannon max-out discriminator. follow-up work propose alternative training scheme WGAN based estimating Wasserstein distance instead Jensen-Shannon divergence real generated distributions.In work highlight view mode collapse. discriminator part GANs variations like WGANs is separable observations which,as will illustrate can result serious problems even when minibatches are used. underlying issue is that the stochastic gradients are essentially sums functions single observations training points Despite connections two-sample tests based Jensen-Shannon divergence ultimately updates based gradients different single observations are completely independent other. show how this lack sharing information observations may explain mode collapses GANs.Motivated insights take different perspective adversarial training propose framework brings discriminator closer truly distributional adversary.e one 1 set observations entirety retaining sharing global information gradients. key insight is that a carefully placed nonlinearity form specific population comparisons can enable information-sharing thereby stabilize training. develop test two models also connect popular ideas deep learning statistics.Contributions. main contributions work are as follows:• introduce new distributional framework adversarial training neural networks operates genuine sample.e collection points rather observation. choice is orthogonal modifications types loss e.g logisticvs. Wasserstein literature.• show how off-the-shelf discriminator networks can be made distribution-aware via simple modifications architecture how existing models can seamlessly fit framework.• Empirically distributional adversarial framework leads stable training significantly better mode coverage common single-observation methods. direct application framework domain adaptation results strong improvements state-of-the-art",879,594,285,0.009,1.48,2025/11/05 17:18:56,0.0,1.5,0.467289719626168,301.273
"Chemical information extraction is to convert chemical knowledge in text into true chemical database, which is a text processing task heavily relying on chemical compound name identification and standardization. Once a systematic name for a chemical compound is given, it will naturally and much simply convert the name into the eventually required molecular formula. However, for many chemical substances, they have been shown in many other names besides their systematic names which poses a great challenge for this task. In this paper, we propose a framework to do the auto standardization from the non-systematic names to the corresponding systematic names by using the spelling error correction, byte pair encoding tokenization and neural sequence to sequence model. Our framework is trained end to end and is fully data-driven. Our standardization accuracy on the test dataset achieves 54.04% which has a great improvement compared to previous state-of-the-art result. There are more than 100 million named chemical substances in the world. In order to uniquely identify every chemical substance, there are elaborate rules for assigning names to them on the basis of their structures. These names are called systematic names. The rules for these names are defined by International Union of Pure and Applied Chemistry (IUPAC) BID1 .However , besides the systematic name, there can be also many other names for a chemical substance due to many reasons. Firstly , many chemical are so much a part of our life that we know them by their familiar names which we call them common names or trivial names for the sake of simplicity. For example , sucrose is a kind of sugar which we are very familiar with. Its systematic name is much more complicated, which is (2R,3R,4S,5S,6R)-2-[(2S,3S,4S,5R)-3,4-dihydroxy-2,5-bis(hydroxymethyl)oxolan-2-yl]oxy-6-(hydroxymethyl)oxane-3,4,5-triol.Secondly, in chemistry industry, especially in pharmaceutical industry, many producers always generate new names to a chemical substance in order to distinguish their products from those of their competitors. We call these kind of names proprietary names. The most famous example is Aspirin. Its systematic name is 2-Acetoxybenzoic acid. So due to the history reasons and idiomatic usages, a chemical substance can have many other names.Chemical information extraction is a research that extracts useful chemical knowledge in text and converts it into a database, which strongly relies on the unique standard chemical names. Nowadays, there are many chemical databases such as PubChem and SciFinder, which are designed to store chemical information including chemical names, chemical structures, molecular formulas and other relevant information. For these databases , it is still an ongoing work to extract chemical information from chemical papers to update the databases. If all the chemical substances are expressed by the systematic names, it is easy to generate other information. For example, we can nearly perfectly convert the systematic name to other representations such as Simplified Molecular-Input Line-Entry System (SMILES) BID13 and International Chemical Identifier (InCHI) BID9 and then generate the structural formulas. Some online systems are already well developed for converting automatically systematic names to SMILES string with a very high precision such as Open Parser for Systematic IUPAC Nomenclature (OPSIN) BID7 developed by In the following passage, we consider the differences between non-systematic names and systematic names as ""error"" 2 . In view of natural language processing, the error types of non-systematic names can be summarized by four types: 1. Spelling error. It means that non-systematic names just have slightly differences from systematic names in spelling; 2. Ordering error. It means that the groups in a non-systematic name are in wrong order; 3. Common name error. As mentioned above, many chemical substances have common names or proprietary names which look totally different from their systematic names; 4. Synonym error. It means that the words in the nonsystematic names are different from those in the systematic names but they share the same root of word. In fact, it is the error type which happens most often. For example, 2-(Acetyloxy)benzoic Acid has synonyms Acetylsalicylic Acid and Acetysal and these three words share the same root of word ""Acety"". Some examples of different types of errors are shown in TAB0 . What is worth mentioning is that several types of error can appear at the same time in a single non-systematic name, especially for the ordering error and synonym error. The mixed types of error make this task very challenging .Based on these four error types, we propose a framework to convert automatically the non-systematic names to systematic names. Our framework is structured as followed: 1. Spelling error correction. It aims to correct the spelling errors; 2. Byte pair encoding (BPE) tokenization. It aims to split a name into small parts; 3. Sequence to sequence model. It aims to fix all the remaining ordering errors, common name errors and synonym errors.Actually, due to its great challenge, few work has been done on the chemical name standardization. To our best knowledge, BID2 is the only work deserving a citation which developed an online system ChemHits to do the standardization basing on several transformation rules and the queries to online chemical databases. The work of BID2 severely depends on chemical knowledge, limiting its application potential and effectiveness to some extent.Differently, we adopt sequence to sequence model that has been widely used on neural machine translation. The reason why we apply the sequence to sequence model is that our task has some similarities with the machine translation problem. In machine translation, there are source language and target language which correspond to the non-systematic names and the systematic names in our task. Two different languages can be different in: 1. Vocabularies, which corresponds to the common name error and synonym error; 2. Word order, which corresponds to the ordering error. Our framework is trained end-to-end , fully data-driven and without using external chemical knowledge.With this approach, we achieve an accuracy of 54.04% in our test data set.Our work will be done on a corpus containing chemical names extracted from report of Chemical Journals with High Impact factors (CJHIF) 3 . The corpus is collected and checked by paid manual work. It is a parallel corpus which includes non-systematic names and systematic names of chemical substances . In the following passage, we call a non-systematic name and the corresponding systematic name of a chemical substance data pair. In our corpus, there are 384816 data pairs. In FIG1 , we give an overview of the distribution of the Levenshtein distance between the non-systematic names and the systematic names to show how different the non-systematic names and the systematic names are. In the experiment, we use 80%, 19% and 1% data as training set, test set and development set respectively. In this work, we propose a framework to automatically convert non-systematic names to systematic names . Our framework consists of spelling error correction, byte pair encoding tokenization and sequence to sequence model. Our framework achieves an accuracy of 54.04% on our dataset, which is far better than previous rule based system (nine times of accuracy) and thus enables the related chemical information extraction into more practical use stage. The advantage of our framework is that it is trained end to end, fully data-driven and independent of external chemical knowledge. This work starts a brand new research line for the related chemical information extraction as to our best knowledge.","Chemical information extraction is to convert chemical knowledge text true chemical database which is a text processing task heavily relying chemical compound name identification standardization. systematic name chemical compound is given will naturally much simply convert name eventually required molecular formula. However are many chemical substances have been shown many names besides systematic names which poses great challenge task. paper propose framework do the auto standardization non-systematic names corresponding systematic names using spelling error correction byte pair encoding tokenization neural sequence sequence model. framework is is that it is trained end end is fully fully data-driven standardization accuracy test dataset achieves 54.04 which has a great improvement compared previous state-of-the-art result. are more than 100 million named chemical substances world. order uniquely identify every chemical substance are elaborate rules assigning names basis structures. names are called systematic names. rules names are defined International Union Pure Applied Chemistry IUPAC BID1.However besides systematic name can be also many names chemical substance due many reasons. Firstly are many chemical are so much part life know familiar names which we call common names trivial names sake simplicity. example sucrose is a kind sugar which we are very familiar with. systematic name is much complicated which is(2R,3R,4S,5S,6R -2- 2S,3S,4S,5R -3,4-dihydroxy-2,5-bis hydroxymethyl oxolan-2-yl oxy-6- hydroxymethyl oxane-3,4 5-triol.Secondly chemistry industry especially pharmaceutical industry are many producers always generate new names chemical substance order distinguish products competitors. call kind names proprietary names. famous example is Aspirin. systematic name is 2-Acetoxybenzoic acid. due history reasons idiomatic usages chemical substance can have many names.Chemical information extraction is a research extracts useful chemical knowledge text converts database which strongly relies unique standard chemical names. Nowadays are many chemical databases PubChem SciFinder which are designed store chemical information including chemical names chemical structures molecular formulas relevant information. databases is still ongoing work extract chemical information chemical papers update databases. If all the chemical substances are expressed systematic names is easy generate information. example can nearly perfectly convert systematic name representations Simplified Molecular-Input Line-Entry System SMILES BID13 International Chemical Identifier InCHI BID9 generate structural formulas. online systems are already well developed converting automatically systematic names SMILES string high precision Open Parser Systematic IUPAC Nomenclature OPSIN BID7 developed following passage consider differences non-systematic names systematic names error2. view natural language processing is the error types non-systematic names can be summarized four types:1. Spelling error. means non-systematic names have slightly differences systematic names spelling;2. Ordering error. means groups non-systematic name are in wrong order;3. Common name error. mentioned many chemical substances have common names proprietary names which look totally different systematic names;4. Synonym error. means words nonsystematic names are different systematic names share root word. fact is the error type which happens often. example 2- Acetyloxy benzoic Acid has synonyms Acetylsalicylic Acid Acetysal three words share root word Acety. examples different types errors are shown TAB0. What is worth mentioning is that several types error can appear time single non-systematic name especially ordering error synonym error. mixed types error make task challenging.Based four error types propose framework convert automatically non-systematic names systematic names. framework is structured followed:1. Spelling error correction. aims correct spelling errors;2. Byte pair encoding BPE tokenization. aims split name small parts;3. Sequence sequence model. aims fix remaining ordering errors common name errors synonym errors.Actually due great challenge work has been done chemical name standardization. best knowledge BID2 is the only work deserving citation which developed online system ChemHits do the standardization basing several transformation rules queries online chemical databases. work BID2 severely depends chemical knowledge limiting application potential effectiveness extent.Differently adopt sequence sequence model has been widely used neural machine translation. reason why we apply sequence sequence model is that our task has some similarities machine translation problem. machine translation are source language target language which correspond non-systematic names systematic names task. Two different languages can be different in:1. Vocabularies which corresponds common name error synonym error;2. Word order which corresponds ordering error. framework is is that it is trained end-to-end fully data-driven without using external chemical knowledge.With approach achieve accuracy 54.04 test data set.Our work will be done corpus containing chemical names extracted report Chemical Journals High Impact factors CJHIF 3. corpus is collected checked paid manual work. is a parallel corpus which includes non-systematic names systematic names chemical substances. following passage call non-systematic name corresponding systematic name chemical substance data pair. corpus are 384816 data pairs. FIG1 give overview distribution Levenshtein distance non-systematic names systematic names show how different non-systematic names systematic names are. experiment use80% 19% 1% data training set test set development set respectively. work propose framework automatically convert non-systematic names systematic names. framework consists spelling error correction byte pair encoding tokenization sequence sequence model. framework achieves accuracy 54.04 dataset which is far better previous rule based system nine times accuracy thus enables related chemical information extraction practical use stage. advantage framework is is that it is trained end end fully data-driven independent external chemical knowledge. work starts brand new research line related chemical information extraction best knowledge.",1567,1117,450,0.016,1.403,2025/11/05 17:18:56,0.01,1.662,0.2274143302180684,473.568
"The training of deep neural networks with Stochastic Gradient Descent (SGD) with a large learning rate or a small batch-size typically ends in flat regions of the weight space, as indicated by small eigenvalues of the Hessian of the training loss. This was found to correlate with a good final generalization performance.   In this paper we extend previous work by investigating the curvature of the loss surface along the whole training trajectory, rather than only at the endpoint. We find that initially SGD visits increasingly sharp regions, reaching a maximum sharpness determined by both the learning rate and the batch-size of SGD. At this peak value SGD starts to fail to minimize the loss along directions in the loss surface corresponding to the largest curvature (sharpest directions). To further investigate the effect of these dynamics in the training process, we study a variant of SGD using a reduced learning rate along the sharpest directions which we show can improve training speed while finding both sharper and better generalizing solution, compared to vanilla SGD. Overall, our results show that the SGD dynamics in the subspace of the sharpest directions influence the regions that SGD steers to (where larger learning rate or smaller batch size result in wider regions visited), the overall training speed, and the generalization ability of the final model. Deep Neural Networks (DNNs) are often massively over-parameterized BID29 ), yet show state-of-the-art generalization performance on a wide variety of tasks when trained with Stochastic Gradient Descent (SGD). While understanding the generalization capability of DNNs remains an open challenge, it has been hypothesized that SGD acts as an implicit regularizer, limiting the complexity of the found solution BID17 BID0 BID24 BID9 .Various links between the curvature of the final minima reached by SGD and generalization have been studied BID15 BID16 . In particular , it is a popular view that models corresponding to wide minima of the loss in the parameter space generalize better than those corresponding to sharp minima BID8 BID10 BID9 . The existence of this empirical correlation between the curvature of the final minima and generalization motivates our study.Our work aims at understanding the interaction between SGD and the sharpest directions of the loss surface, i.e. those corresponding to the largest eigenvalues of the Hessian. In contrast to studies such as those by BID10 and BID9 our analysis focuses on the whole training trajectory of SGD rather than just on the endpoint. We will show in Sec. 3.1 that the evolution of the largest eigenvalues of the Hessian follows a Outline of the phenomena discussed in the paper. Curvature along the sharpest direction(s) initially grows (A to C). In most iterations , we find that SGD crosses the minimum if restricted to the subspace of the sharpest direction(s) by taking a too large step (B and C). Finally, curvature stabilizes or decays with a peak value determined by learning rate and batch size (C, see also right). Right two: Representative example of the evolution of the top 30 (decreasing, red to blue) eigenvalues of the Hessian for a SimpleCNN model during training (with η = 0.005, note that η is close to 1 λmax = 1 160 ).consistent pattern for the different networks and datasets that we explore. Initially, SGD is in a region of broad curvature, and as the loss decreases, SGD visits regions in which the top eigenvalues of the Hessian are increasingly large, reaching a peak value with a magnitude influenced by both learning rate and batch size. After that point in training, we typically observe a decrease or stabilization of the largest eigenvalues.To further understand this phenomenon, we study the dynamics of SGD in relation to the sharpest directions in Sec. 3.2 and Sec. 3.3. Projecting to the sharpest directions 1 , we see that the regions visited in the beginning resemble bowls with curvatures such that an SGD step is typically too large, in the sense that an SGD step cannot get near the minimum of this bowl-like subspace; rather it steps from one side of the bowl to the other, see FIG0 for an illustration.Finally in Sec. 4 we study further practical consequences of our observations and investigate an SGD variant which uses a reduced and fixed learning rate along the sharpest directions. In most cases we find this variant optimizes faster and leads to a sharper region, which generalizes the same or better compared to vanilla SGD with the same (small) learning rate. While we are not proposing a practical optimizer , these results may open a new avenue for constructing effective optimizers tailored to the DNNs' loss surface in the future.On the whole this paper exposes and analyses SGD dynamics in the subspace of the sharpest directions. In particular, we argue that the SGD dynamics along the sharpest directions influence the regions that SGD steers to (where larger learning rate or smaller batch size result in wider regions visited), the training speed, and the final generalization capability. The somewhat puzzling empirical correlation between the endpoint curvature and its generalization properties reached in the training of DNNs motivated our study. Our main contribution is exposing the relation between SGD dynamics and the sharpest directions, and investigating its importance for training. SGD steers from the beginning towards increasingly sharp regions of the loss surface, up to a level dependent on the learning rate and the batch-size. Furthermore, the SGD step is large compared to the curvature along the sharpest directions, and highly aligned with them.Our experiments suggest that understanding the behavior of optimization along the sharpest directions is a promising avenue for studying generalization properties of neural networks. Additionally, results such as those showing the impact of the SGD step length on the regions visited (as characterized by their curvature) may help design novel optimizers tailor-fit to neural networks.A Additional results for Sec. 3.1",training deep neural networks Stochastic Gradient Descent SGD large learning rate small batch-size typically ends flat regions weight space indicated small eigenvalues Hessian training loss. was found correlate good final generalization performance. paper extend previous work investigating curvature loss surface along whole training trajectory rather endpoint. find initially SGD visits increasingly sharp regions reaching maximum sharpness determined learning rate batch-size SGD. peak value SGD starts fail minimize loss along directions loss surface corresponding largest curvature sharpest directions investigate effect dynamics training process study variant SGD using reduced learning rate along sharpest directions which we show can improve training speed finding sharper better generalizing solution compared vanilla SGD. Overall results show SGD dynamics subspace sharpest directions influence regions SGD steers where larger learning rate smaller batch size result wider regions visited overall training speed generalization ability final model. Deep Neural Networks DNNs are often massively over-parameterized BID29 yet show state-of-the-art generalization performance wide variety tasks when trained Stochastic Gradient Descent SGD understanding generalization capability DNNs remains open challenge has been hypothesized SGD acts implicit regularizer limiting complexity found solution BID17 BID0 BID24 BID9.Various links curvature final minima reached SGD generalization have been studied BID15 BID16. particular is a popular view models corresponding wide minima loss parameter space generalize better corresponding sharp minima BID8 BID10 BID9. existence empirical correlation curvature final minima generalization motivates study.Our work aims understanding interaction SGD sharpest directions loss surface.e corresponding largest eigenvalues Hessian. contrast studies BID10 BID9 analysis focuses whole training trajectory SGD rather endpoint. will show Sec. 3.1 evolution largest eigenvalues Hessian follows Outline phenomena discussed paper. Curvature along sharpest direction initially grows C iterations find SGD crosses minimum if restricted subspace sharpest direction taking large step B C Finally curvature stabilizes decays peak value determined learning rate batch size C see also right Right two:Representative example evolution top30 decreasing red blue eigenvalues Hessian SimpleCNN model training η 0.005 note η is close 1 λmax 1 160.consistent pattern different networks datasets explore. Initially SGD is in a region broad curvature loss decreases SGD visits regions which the top eigenvalues Hessian are increasingly large reaching peak value magnitude influenced learning rate batch size. point training typically observe decrease stabilization largest eigenvalues.To understand phenomenon study dynamics SGD relation sharpest directions Sec. 3.2 Sec. 3.3 Projecting sharpest directions1 see regions visited beginning resemble bowls curvatures SGD step is typically large sense SGD step cannot get near minimum bowl-like subspace;rather steps one side bowl see FIG0 illustration.Finally Sec. 4 study practical consequences observations investigate SGD variant which uses reduced fixed learning rate along sharpest directions. cases find variant optimizes faster leads sharper region which generalizes better compared vanilla SGD small learning rate. are not proposing practical optimizer results may open new avenue constructing effective optimizers tailored DNNs' loss surface future.On whole paper exposes analyses SGD dynamics subspace sharpest directions. particular argue SGD dynamics along sharpest directions influence regions SGD steers where larger learning rate smaller batch size result wider regions visited training speed final generalization capability. somewhat puzzling empirical correlation endpoint curvature generalization properties reached training DNNs motivated study. main contribution is exposing relation SGD dynamics sharpest directions investigating importance training. SGD steers beginning towards increasingly sharp regions loss surface level dependent learning rate batch-size Furthermore SGD step is large compared curvature along sharpest directions highly aligned them.Our experiments suggest understanding behavior optimization along sharpest directions is a promising avenue studying generalization properties neural networks. Additionally results showing impact SGD step length regions visited characterized curvature may help design novel optimizers tailor-fit neural networks.A Additional results Sec. 3.1,1191,746,445,0.013,1.597,2025/11/05 17:18:56,0.01,1.409,0.8317757009345792,360.579
"We introduce a new approach to estimate continuous actions using actor-critic algorithms for reinforcement learning problems. Policy gradient methods usually predict one continuous action estimate or parameters of a presumed distribution (most commonly Gaussian) for any given state which might not be optimal as it may not capture the complete description of the target distribution. Our approach instead predicts M actions with the policy network (actor) and then uniformly sample one action during training as well as testing at each state. This allows the agent to learn a simple stochastic policy that has an easy to compute expected return. In all experiments, this facilitates better exploration of the state space during training and converges to a better policy. Reinforcement learning is a traditional branch of machine learning which focuses on learning complex tasks by assigning rewards to agents that interact with their environment. It has recently gained momentum thanks to the combination of novel algorithms for continuous control with deep learning models, sometimes even matching human performance in tasks such as playing video games and manipulating objects BID10 ; . Recent methods for continuous control problems like Deep Deterministic Policy Gradient (DDPG) , Asynchronous Advantage Actor Critic (A3C) BID11 use actor-critic architectures, where an action function is learned by mapping states to actions. DDPG works well on many tasks, but it does not model the uncertainty in actions as it produces a point estimate of the action distribution over states. The actor is forced to deterministically choose an action for every state. A3C and other stochastic policy gradient algorithms output distribution parameters (e.g. Gaussian distributions) instead of point estimate, which can be sampled for action values.As a simple example where this is sub-optimal, consider the inverted pendulum task, where a pendulum is attached to a cart and the agent needs to control the one dimensional movement of the cart to balance the pendulum upside down. A deterministic agent chooses a single action for every state. This breaks the inherent symmetry of the task. When the cart in not moving and the pendulum is hanging down, two actions are equally promising: either moving left or right. The distribution parameter estimation (e.g. A3C) might work better in this case as there are only two good options, but in cases when there are more than two good actions to select, this will not be optimal. In our approach we allow the agent to suggest multiple actions, which enables it to resolve cases like this easily.Further, we observe that a deterministic behavior of DDPG can lead to sub-optimal convergence during training. The main limitation is that, especially in the beginning of the learning procedure, the actor favors actions that lead to a good immediate reward but might end up being far from the globally optimal choice. This work is based on the intuition that if the actor is allowed to suggest, at each time step, multiple actions rather than a single one, this can render the resulting policy non-deterministic, leading to a better exploration of the entire solution space as well as a final solution of potentially higher quality. This can also eliminate the external exploration mechanisms required during training e.g. OrnsteinUhlenbeck process noise BID20 , parameter noise or differential entropy of normal distribution.Here, we introduce an algorithm, which we refer to as Multiple Action Policy Gradients (MAPG), that models a stochastic policy with several point estimates and allows to predict a pre-defined number M of actions at each time step, extending any policy gradient algorithm with little overhead. We will demonstrate the working of this algorithm by adapting DDPG Lillicrap et al. (2016) to use MAPG.Another benefit of the proposed method is that the variance of the predicted actions can give additional insights into the decision process during runtime. A low variance usually implies that the model only sees one way to act in a certain situation. A wider or even multi-modal distribution suggests that there exist several possibilities given the current state.We evaluate the proposed method on six continuous control problems of the OpenAI Gym BID0 as well as a deep driving scenario using the TORCS car simulator BID22 . For a fair evaluation we directly compare DDPG to our MAPG without changing hyper-parameters or modifying the training scheme. In all experiments, we show an improved performance using MAPG over DDPG. To verify if MAPG helps in better exploration during training, we also analyze MAPG under no external exploration policy. In this paper, we have proposed MAPG, a technique that leverages multiple action prediction to learn better policies in continuous control problems. The proposed method enables a better exploration of the state space and shows improved performance over DDPG. As indicated by exploration experiments, it can also be a used as a standalone exploration technique, although more work needs to be done in this direction. Last but not least, we conclude with interesting insights gained from the action variance. There are several interesting directions which we would like to investigate in the future. The number of actions M is a hyper-parameter in our model that needs to be selected and seems to be task specific. In general, the idea of predicting multiple action proposals can be extended to other on-or off-policy algorithms, such as NAF BID1 or TRPO. Evaluating MA-NAF and MA-TRPO will enable studying the generality of the proposed approach.","introduce new approach estimate continuous actions using actor-critic algorithms reinforcement learning problems. Policy gradient methods usually predict one continuous action estimate parameters presumed distribution commonly Gaussian given state might optimal may capture complete description target distribution. approach instead predicts actions policy network actor uniformly sample one action training well testing state. allows agent learn simple stochastic policy has an easy compute expected return. experiments facilitates better exploration state space training converges better policy. Reinforcement learning is a traditional branch machine learning which focuses learning complex tasks assigning rewards agents interact environment. has recently gained momentum thanks combination novel algorithms continuous control deep learning models sometimes even matching human performance tasks playing video games manipulating objects BID10;Recent methods continuous control problems like Deep Deterministic Policy Gradient DDPG Asynchronous Advantage Actor Critic A3C BID11 use actor-critic architectures where an action function is learned mapping states actions. DDPG works well many tasks does model uncertainty actions produces point estimate action distribution states. actor is forced deterministically choose action every state. A3C stochastic policy gradient algorithms output distribution parameters e.g Gaussian distributions instead point estimate which can be sampled action values.As simple example where this is sub-optimal consider inverted pendulum task where a pendulum is attached cart agent needs control one dimensional movement cart balance pendulum upside down. deterministic agent chooses single action every state. breaks inherent symmetry task. When the cart moving pendulum is hanging two actions are equally promising:either moving left right. distribution parameter estimation e.g A3C might work better case are only two good options cases when there are more two good actions select will not optimal. approach allow agent suggest multiple actions which enables resolve cases like easily.Further observe deterministic behavior DDPG can lead sub-optimal convergence training. main limitation is that,especially beginning learning procedure actor favors actions lead good immediate reward might end far globally optimal choice. work is based intuition if the actor is allowed suggest time step multiple actions rather single one can render resulting policy non-deterministic leading better exploration entire solution space well final solution potentially higher quality. can also eliminate external exploration mechanisms required training e.g OrnsteinUhlenbeck process noise BID20 parameter noise differential entropy normal distribution.Here introduce algorithm which we refer Multiple Action Policy Gradients MAPG models stochastic policy several point estimates allows predict pre-defined number actions time step extending policy gradient algorithm little overhead. will demonstrate working algorithm adapting DDPG Lillicrapet al. 2016 use MAPG.Another benefit proposed method is that the variance predicted actions can give additional insights decision process runtime. low variance usually implies model sees one way act certain situation. wider even multi-modal distribution suggests exist several possibilities given current state.We evaluate proposed method six continuous control problems OpenAI Gym BID0 well deep driving scenario using TORCS car simulator BID22. fair evaluation directly compare DDPG MAPG without changing hyper-parameters modifying training scheme. experiments show improved performance using MAPG DDPG. verify if MAPG helps better exploration training can also analyze MAPG external exploration policy. paper have proposed MAPG technique leverages multiple action prediction learn better policies continuous control problems. proposed method enables better exploration state space shows improved performance DDPG. indicated exploration experiments can also used standalone exploration technique although work needs done direction. Last least conclude interesting insights gained action variance. are several interesting directions would like investigate future. number actions is a hyper-parameter model needs selected seems task specific. general idea predicting multiple action proposals can be extended on-or off-policy algorithms NAF BID1 TRPO. Evaluating MA-NAF MA-TRPO will enable studying generality proposed approach.",1065,718,347,0.01,1.483,2025/11/05 17:18:56,0.01,1.595,0.4766355140186917,325.569
"Recently convolutional neural networks (CNNs) achieve great accuracy in visual recognition tasks. DenseNet becomes one of the most popular CNN models due to its effectiveness in feature-reuse. However, like other CNN models, DenseNets also face overfitting problem if not severer. Existing dropout method can be applied but not as effective due to the introduced nonlinear connections. In particular, the property of feature-reuse in DenseNet will be impeded, and the dropout effect will be weakened by the spatial correlation inside feature maps. To address these problems, we craft the design of a specialized dropout method from three aspects, dropout location, dropout granularity, and dropout probability. The insights attained here could potentially be applied as a general approach for boosting the accuracy of other CNN models with similar nonlinear connections. Experimental results show that DenseNets with our specialized dropout method yield better accuracy compared to vanilla DenseNet and state-of-the-art CNN models, and such accuracy boost increases with the model depth. Recent years have seen a rapid development of deep neural network in the computer vision area, especially for visual object recognition tasks. From AlexNet, the winner of ImageNet Large Scale Visual Recognition Challenge (ILSVRC) , to later VGG network BID14 and GoogLeNet , CNNs have shown significant success with its shocking improvement of accuracy.Researchers gradually realized that the depth of the network always plays an important role in the final accuracy of one model due to increased expressiveness BID2 BID3 . However, simply increasing the depth does not always help due to the induced vanishing gradient problem BID0 . ResNet BID4 has been proposed to promote the flow of information across layers without attenuation by introducing identity skip-connections, which sums together the input and the output of several convolutional layers. In 2016, Densely connected network (DenseNet) BID7 came out, which replaces the simple summation in ResNet with concatenation after realizing the summation may also impede the information flow.Despite the improved information flow, DenseNet still suffers from the overfitting problem, especially when the network goes deeper. Standard dropout BID16 has been used to combat such problem, but can not work effectively on DenseNet. The reasons are twofold: 1) Feature-reuse will be weakened by standard dropout as it could make features dropped at previous layers no longer be used at later layers. 2) Standard dropout method does not interact well with convolutional layers because of the spatial correlation inside feature maps BID19 . Since dense connectivity increases the number of feature maps tremendously -especially at deep layers -the effectiveness of standard dropout would further be reduced.In this paper, we design a specialized dropout method to resolve these problems. In particular, three aspects of dropout design are addressed: 1) Where to put dropout layers in the network? 2) What is the best dropout granularity? 3) How to assign appropriate dropout (or survival) probabilities for different layers? Meanwhile, we show that the idea to re-design the dropout method from the three aspects also applies to other CNN models like ResNet. The contributions of the paper can be summarized as follows:• First, we propose a new structure named pre-dropout to solve the possible feature-reuse obstruction when applying standard dropout method on DenseNet.• Second, we are the first to show that channel-wise dropout (compared to layer-wise and unit-wise) fit best for CNN through both detailed analysis and experimental results.• Third, we propose three distinct probability schedules, and via experiments we find out the best one for DenseNet.• Last, we provide a good insight for future practitioners, inspiring them regarding what should be considered and which is the best option when applying the dropout method on a CNN model.Experiments in our paper suggest that DenseNets with our proposed specialized dropout method outperforms other comparable DenseNet and state-of-art CNN models in terms of accuracy, and following the same idea dropout methods designed for other CNN models could also achieve consistent improvements over the standard dropout method. In this paper, first we show problems of applying standard dropout method on DenseNet. To deal with these problems, we come up with a new pre-dropout structure and adopt channel-wise dropout granularity. Specifically, we put dropout before convolutional layers to reinforce feature-reuse inside the model. Meanwhile we randomly drop some feature maps in inputs of convolutional layers to break dependence among them. Besides to further promote model generalization ability we introduce stochastic probability method to add various degrees of noise to different layers in DenseNet. Experiments show that in terms of accuracy DenseNets with our specialized dropout method outperform other CNN models.",Recently convolutional neural networks CNNs achieve great accuracy visual recognition tasks. DenseNet becomes one popular CNN models due effectiveness feature-reuse However like CNN models DenseNets also face overfitting problem if not severer. Existing dropout method can be applied effective due introduced nonlinear connections. particular property feature-reuse DenseNet will be impeded dropout effect will be weakened spatial correlation inside feature maps. address problems craft design specialized dropout method three aspects dropout location dropout granularity dropout probability. insights attained could potentially applied general approach boosting accuracy CNN models similar nonlinear connections. Experimental results show DenseNets specialized dropout method yield better accuracy compared vanilla DenseNet state-of-the-art CNN models accuracy boost increases model depth. Recent years have seen rapid development deep neural network computer vision area especially visual object recognition tasks. AlexNet winner ImageNet Large Scale Visual Recognition Challenge ILSVRC later VGG network BID14 GoogLeNet CNNs have shown significant success shocking improvement accuracy.Researchers gradually realized depth network always plays important role final accuracy one model due increased expressiveness BID2 BID3. However simply increasing depth does not always help due induced vanishing gradient problem BID0. ResNet BID4 has been proposed promote flow information across layers without attenuation introducing identity skip-connections which sums together input output several convolutional layers. 2016 Densely connected network DenseNet BID7 came which replaces simple summation ResNet concatenation realizing summation may also impede information flow.Despite improved information flow DenseNet still suffers overfitting problem especially when the network goes deeper. Standard dropout BID16 has been used combat problem can not work effectively DenseNet. reasons are twofold:1 Feature-reuse will be weakened standard dropout could make features dropped previous layers longer used later layers. 2 Standard dropout method does not interact well convolutional layers spatial correlation inside feature maps BID19. Since dense connectivity increases number feature maps tremendously -especially deep layers -the effectiveness standard dropout would reduced.In paper design specialized dropout method resolve problems. particular three aspects dropout design are addressed:1 Where to put dropout layers network? 2 What is the best dropout granularity? 3 How to assign appropriate dropout survival probabilities different layers? Meanwhile show idea re-design dropout method three aspects also applies CNN models like ResNet. contributions paper can be summarized follows:• First propose new structure named pre-dropout solve possible feature-reuse obstruction when applying standard dropout method DenseNet.• Second are the first show channel-wise dropout compared layer-wise unit-wise fit best CNN detailed analysis experimental results.• Third propose three distinct probability schedules via experiments find best one DenseNet.• Last provide good insight future practitioners inspiring regarding what should be considered which is the best option when applying dropout method CNN model.Experiments paper suggest DenseNets proposed specialized dropout method outperforms comparable DenseNet state-of-art CNN models terms accuracy following idea dropout methods designed CNN models could also achieve consistent improvements standard dropout method. paper are the first show problems applying standard dropout method DenseNet. deal problems come new pre-dropout structure adopt channel-wise dropout granularity. Specifically put dropout convolutional layers reinforce feature-reuse inside model. Meanwhile randomly drop feature maps inputs convolutional layers break dependence among them. Besides promote model generalization ability introduce stochastic probability method add various degrees noise different layers DenseNet. Experiments show terms accuracy DenseNets specialized dropout method outperform CNN models.,936,670,266,0.008,1.397,2025/11/05 17:18:56,0.0,1.833,0.2087227414330216,296.294
"While extremely successful in several applications, especially with low-level representations; sparse, noisy samples and structured domains (with multiple objects and interactions) are some of the open challenges in most deep models. Column Networks, a deep architecture, can succinctly capture such domain structure and interactions, but may still be prone to sub-optimal learning from sparse and noisy samples. Inspired by the success of human-advice guided learning in AI, especially in data-scarce domains, we propose Knowledge-augmented Column Networks that leverage human advice/knowledge for better learning with noisy/sparse samples. Our experiments demonstrate how our approach leads to either superior overall performance or faster convergence. The re-emergence of Deep Learning BID11 has found significant and successful applications in difficult real-world domains such as image BID17 , audio BID23 ) and video processing (Yue-Hei BID40 . Deep Learning has also been increasingly applied to structured domains, where the data is represented using richer symbolic or graph features to capture relational structure between entities and attributes in the domain. Intuitively, deep learning architectures are naturally suited to learning and reasoning over such multi-relational domains as they are able to capture increasingly complex interactions between features with deeper layers. However, the combinatorial complexity of reasoning over a large number of relations and objects has remained a significant bottleneck to overcome.Recent work in relational deep learning has sought to address this particular issue. This includes relational neural networks BID15 Šourek et al., 2015) , relational Restricted Boltzmann machines BID14 and neuro-symbolic architectures such as C-ILP BID7 . In our work, we focus upon the framework of Column Networks (CLNs) developed by BID31 . Column networks are composed of several (feedforward) mini-columns each of which represents an entity in the domain. Relationships between two entities are modeled through edges between mini-columns. These edges allow for the short-range exchange of information over successive layers of the column network; however, the true power of column networks emerges as the depth of interactions increases, which allows for the natural modeling of long-range interactions.Column networks are an attractive approach for several reasons: (1) hidden layers of a CLN share parameters, which means that making the network deeper does not introduce more parameters, (2) as the depth increases, the CLN can begin to model feature interactions of considerable complexity, which is especially attractive for relational learning, and (3) learning and inference are linear in the size of the network and the number of relations, which makes CLNs highly efficient. However, like other deep learning approaches, CLNs rely on vast amounts of data and incorporate little to no knowledge about the problem domain. While this may not be an issue for low-level applications such as image or video processing, it is a significant issue in relational domains, since the relational structure encodes rich, semantic information. This suggests that ignoring domain knowledge can considerably hinder generalization.It is well known that biasing learners is necessary in order to allow them to inductively leap from training instances to true generalization over new instances BID26 . Indeed, the inductive bias towards ""simplicity and generality"" leads to network architectures with simplifying assumptions through regularization strategies that aim to control the complexity of the neural/deep network.While deep learning does incorporate one such bias in the form of domain knowledge (for example, through parameter tying or convolution, which exploits neighborhood information), we are motivated to develop systems that can incorporate richer and more general forms of domain knowledge. This is especially germane for deep relational models as they inherently construct and reason over richer representations. Such domain-knowledge-based inductive biases have been applied to a diverse array of machine learning approaches, variously known as advice-based, knowledge-based or human-guided machine learning.One way in which a human can guide learning is by providing rules over training examples and features. The earliest such approaches combined explanation-based learning (EBL-NN, BID35 ) or symbolic domain rules with ANNs (KBANN, Towell & Shavlik (1994) ). Domain knowledge as rules over input features can also be incorporated into support vector machines (SVMs, BID2 ; BID34 BID9 ; BID21 ; BID19 ). Another natural way a human could guide learning is by expressing preferences and has been studied extensively within the preference-elicitation framework due to BID1 . We are inspired by this form of advice as they have been successful within the context of inverse reinforcement learning BID20 , imitation learning BID29 and planning BID3 .These approaches span diverse machine learning formalisms, and they all exhibit the same remarkable behavior: better generalization with fewer training examples because they effectively exploit and incorporate domain knowledge as an inductive bias. This is the prevailing motivation for our approach: to develop a framework that allows a human to guide deep learning by incorporating rules and constraints that define the domain and its aspects. Incorporation of prior knowledge into deep learning has begun to receive interest recently, for instance, the recent work on incorporating prior knowledge of color and scene information into deep learning for image classification BID5 . However, in many such approaches, the guidance is not through a human, but rather through a pre-processing algorithm to generate guidance. Our framework is much more general in that a human provides guidance during learning. Furthermore, the human providing the domain advice is not an AI/ML expert but rather a domain expert who provides rules naturally. We exploit the rich representation power of relational methods to capture, represent and incorporate such rules into relational deep learning models.We make the following contributions: (1) we propose the formalism of Knowledge-augmented Column Networks, (2) we present, inspired by previous work (such as KBANN), an approach to inject generalized domain knowledge in a CLN and develop the learning strategy that exploits this knowledge, and (3) we demonstrate, across four real problems in some of which CLNs have been previously employed, the effectiveness and efficiency of injecting domain knowledge. Specifically, our results across the domains clearly show statistically superior performance with small amounts of data. As far as we are aware, this is the first work on human-guided CLNs. We considered the problem of providing guidance for CLNs. Specifically, inspired by treating the domain experts as true domain experts and not CLN experts, we developed a formulation based on preferences. This formulation allowed for natural specification of guidance. We derived the gradients based on advice and outlined the integration with the original CLN formulation. Our experimental results across different domains clearly demonstrate the effectiveness and efficiency of the approach, specifically in knowledge-rich, data-scarce problems. Exploring other types of advice including feature importances, qualitative constraints, privileged information, etc. is a potential future direction. Scaling our approach to web-scale data is a natural extension. Finally, extending the idea to other deep models remains an interesting direction for future research.",extremely successful several applications which is especially low-level representations;sparse noisy samples structured domains multiple objects interactions are someof open challenges deep models. Column Networks deep architecture can succinctly capture domain structure interactions may still prone sub-optimal learning sparse noisy samples. Inspired success human-advice guided learning AI which is especially data-scarce domains propose Knowledge-augmented Column Networks leverage human advice/knowledge better learning noisy/sparse samples. experiments demonstrate how our approach leads either superior overall performance faster convergence. re-emergence Deep Learning BID11 has found significant successful applications difficult real-world domains image BID17 audio BID23 video processing Yue-Hei BID40. Deep Learning has also increasingly applied structured domains where the data is represented using richer symbolic graph features capture relational structure entities attributes domain. Intuitively deep learning architectures are naturally suited learning reasoning multi-relational domains are able capture increasingly complex interactions features deeper layers. However combinatorial complexity reasoning large number relations objects has remained significant bottleneck overcome.Recent work relational deep learning has sought address particular issue. includes relational neural networks BID15 Šoureketal. 2015 relational Restricted Boltzmann machines BID14 neuro-symbolic architectures C-ILP BID7. work focus upon framework Column Networks CLNs developed BID31. Column networks are composed several feedforward mini-columns which represents entity domain. Relationships two entities are modeled edges mini-columns edges allow short-range exchange information successive layers column network;however true power column networks emerges depth interactions increases which allows natural modeling long-range interactions.Column networks are an attractive approach several reasons:1 hidden layers CLN share parameters which means making network deeper does not introduce parameters 2 depth increases CLN can begin model feature interactions considerable complexity which is especially attractive relational learning 3 learning inference are linear size network number relations which makes CLNs highly efficient. However like deep learning approaches CLNs rely vast amounts data incorporate little knowledge problem domain. may issue low-level applications image video processing is a significant issue relational domains since relational structure encodes rich semantic information. suggests ignoring domain knowledge can considerably hinder generalization.It is well known biasing learners is necessary order allow inductively leap training instances true generalization new instances BID26. Indeed inductive bias towards simplicity generality leads network architectures simplifying assumptions regularization strategies aim control complexity neural/deep network.While deep learning does incorporate one bias form domain knowledge example parameter tying convolution which exploits neighborhood information are motivated develop systems can incorporate richer general forms domain knowledge. is especially germane deep relational models inherently construct reason richer representations. domain-knowledge-based inductive biases have been applied diverse array machine learning approaches variously known advice-based knowledge-based human-guided machine learning.One way which a human can guide learning is by providing rules training examples features. earliest approaches combined explanation-based learning EBL-NN BID35 symbolic domain rules ANNs KBANN Towell Shavlik 1994 Domain knowledge rules input features can also incorporated support vector machines SVMs BID2;BID34 BID9;BID21;BID19 Another natural way human could guide learning is by expressing preferences has been studied extensively within preference-elicitation framework due BID1. are inspired form advice have been successful within context inverse reinforcement learning BID20 imitation learning BID29 planning BID3.These approaches span diverse machine learning formalisms exhibit remarkable behavior:better generalization fewer training examples effectively exploit incorporate domain knowledge inductive bias. is the prevailing motivation approach:develop framework allows human guide deep learning incorporating rules constraints define domain aspects. Incorporation prior knowledge deep learning has begun receive interest recently instance recent work incorporating prior knowledge color scene information deep learning image classification BID5. However many approaches guidance is not through a human rather pre-processing algorithm generate guidance. framework is much general which a human provides guidance learning. Furthermore human providing domain advice is not an AI/ML expert rather domain expert who provides rules naturally. exploit rich representation power relational methods capture represent incorporate rules relational deep learning models.We make following contributions:1 propose formalism Knowledge-augmented Column Networks 2 present inspired previous work KBANN approach inject generalized domain knowledge CLN develop learning strategy exploits knowledge 3 demonstrate across four real problems which CLNs have been previously employed effectiveness efficiency injecting domain knowledge. Specifically results across domains clearly show statistically superior performance small amounts data. far are aware is the first work human-guided CLNs. considered problem providing guidance CLNs. Specifically inspired treating domain experts true domain experts CLN experts developed formulation based preferences. formulation allowed natural specification guidance. derived gradients based advice outlined integration original CLN formulation. experimental results across different domains clearly demonstrate effectiveness efficiency approach specifically knowledge-rich data-scarce problems. Exploring types advice including feature importances qualitative constraints privileged information etc. is a potential future direction. Scaling approach web-scale data is a natural extension. Finally extending idea deep models remains interesting direction future research.,1384,963,421,0.014,1.437,2025/11/05 17:18:56,0.01,1.462,0.3333333333333333,456.562
"Recent research has shown that one can train a neural network with binary weights and activations at train time by augmenting the weights with a high-precision continuous latent variable that accumulates small changes from stochastic gradient descent. However, there is a dearth of work to explain why one can effectively capture the features in data with binary weights and activations. Our main result is that the neural networks with binary weights and activations trained using the method of Courbariaux, Hubara et al. (2016) work because of the high-dimensional geometry of binary vectors. In particular, the ideal continuous vectors that extract out features in the intermediate representations of these BNNs are well-approximated by binary vectors in the sense that dot products are approximately preserved. Compared to previous research that demonstrated good classification performance with BNNs, our work explains why these BNNs work in terms of HD geometry.   Furthermore, the results and analysis used on BNNs are shown to generalize to neural networks with ternary weights and activations. Our theory serves as a foundation for understanding not only BNNs but a variety of methods that seek to compress traditional neural networks. Furthermore, a better understanding of multilayer binary neural networks serves as a starting point for generalizing BNNs to other neural network architectures such as recurrent neural networks. The rapidly decreasing cost of computation has driven many successes in the field of deep learning in recent years. Consequently, researchers are now considering applications of deep learning in resource limited hardware such as neuromorphic chips, embedded devices and smart phones , BID26 , BID2 ). A recent realization for both theoretical researchers and industry practitioners is that traditional neural networks can be compressed because they are highly over-parameterized. While there has been a large amount of experimental work dedicated to compressing neural networks (Sec. 2), we focus on the particular approach that replaces costly 32-bit floating point multiplications with cheap binary operations. Our analysis reveals a simple geometric picture based on the geometry of high dimensional binary vectors that allows us to understand the successes of the recent efforts to compress neural networks. and showed that one can efficiently train neural networks with binary weights and activations that have similar performance to their continuous counterparts. Such BNNs execute 7 times faster using a dedicated GPU kernel at test time. Furthermore, they argue that such BNNs require at least a factor of 32 fewer memory accesses at test time that should result in an even larger energy savings. There are two key ideas in their papers FIG0 . First, a continuous weight, w c , is associated with each binary weight, w b , that accumulates small changes from stochastic gradient descent. Second, the non-differentiable binarize function (θ(x) = 1 if x > 0 and −1 otherwise) is replaced with a continuous one during backpropagation. These modifications allow one to train neural networks that have binary weights and activations with stochastic gradient descent. While the work showed how to train such networks, the existence of neural networks with binary weights and activations needs to be reconciled with previous work that has sought to understand weight matrices as extracting out continuous features in data (e.g. BID30 ). Summary of contributions: Each oval corresponds to a tensor and the derivative of the cost with respect to that tensor. Rectangles correspond to transformers that specify forward and backward propagation functions. Associated with each binary weight, w b , is a continuous weight, w c , that is used to accumulate gradients. k denotes the kth layer of the network. (b) Each binarize transformer has a forward function and a backward function. The forward function simply binarizes the inputs. In the backward propagation step, one normally computes the derivative of the cost with respect to the input of a transformer via the Jacobian of the forward function and the derivative of the cost with respect to the output of that transformer (δu ≡ dC/du where C is the cost function used to train the network). Since the binarize function is non-differentiable, the straight-through estimator BID3 ), which is a smoothed version of the forward function, is used for the backward function . Neural networks with binary weights and activations have similar performance to their continuous counterparts with substantially reduced execution time and power usage. We provide an experimentally verified theory for understanding how one can get away with such a massive reduction in precision based on the geometry of HD vectors. First, we show that binarization of high-dimensional vectors preserves their direction in the sense that the angle between a random vector and its binarized version is much smaller than the angle between two random vectors (Angle Preservation Property). Second, we take the perspective of the network and show that binarization approximately preserves weight-activation dot products (Dot Product Proportionality Property). More generally, when using a network compression technique, we recommend looking at the weight activation dot product histograms as a heuristic to help localize the layers that are most responsible for performance degradation. Third, we discuss the impacts of the low effective dimensionality of the data on the first layer of the network. We recommend either using continuous weights for the first layer or a Generalized Binarization Transformation. Such a transformation may be useful for architectures like LSTMs where the update for the hidden state declares a particular set of axes to be important (e.g. by taking the pointwise multiply of the forget gates with the cell state). Finally, we show that neural networks with ternary weights and activations can also be understood with our approach. More broadly speaking, our theory is useful for analyzing a variety of neural network compression techniques that transform the weights, activations or both to reduce the execution cost without degrading performance.",Recent research has shown one can train neural network binary weights activations train time augmenting weights high-precision continuous latent variable accumulates small changes stochastic gradient descent. However is a dearth work explain why one can effectively capture features data binary weights activations. main result is that the neural networks binary weights activations trained using method Courbariaux Hubaraetal. 2016 work high-dimensional geometry binary vectors. particular ideal continuous vectors extract features intermediate representations BNNs are well-approximated binary vectors sense dot products are approximately preserved. Compared previous research demonstrated good classification performance BNNs work explains why these BNNs work terms HD geometry. Furthermore results analysis used BNNs are shown generalize neural networks ternary weights activations. theory serves foundation understanding BNNs variety methods seek compress traditional neural networks. Furthermore better understanding multilayer binary neural networks serves starting point generalizing BNNs neural network architectures recurrent neural networks. rapidly decreasing cost computation has driven many successes field deep learning recent years. Consequently researchers are now considering applications deep learning resource limited hardware neuromorphic chips embedded devices smart phones BID26 BID2 recent realization theoretical researchers industry practitioners is that traditional neural networks can be compressed are highly highly over-parameterized has been large amount experimental work dedicated compressing neural networks Sec. 2 focus particular approach replaces costly 32-bit floating point multiplications cheap binary operations. analysis reveals simple geometric picture based geometry high dimensional binary vectors allowsus understand successes recent efforts compress neural networks. showed one can efficiently train neural networks binary weights activations have similar performance continuous counterparts. BNNs execute 7 times faster using dedicated GPU kernel test time. Furthermore argue BNNs require least factor 32 fewer memory accesses test time should result even larger energy savings. are two key ideas papers FIG0. First is a continuous weight wc is associated binary weight wb accumulates small changes stochastic gradient descent. Second non-differentiable binarize function θ x 1 ifx 0 −1 otherwise is replaced continuous one backpropagation. modifications allow one train neural networks have binary weights activations stochastic gradient descent. work showed how to train networks existence neural networks binary weights activations needs reconciled previous work has sought understand weight matrices extracting continuous features data e.g BID30 Summary contributions:oval corresponds tensor derivative cost respect tensor. Rectangles correspond transformers specify forward backward propagation functions. Associated binary weight wb is a continuous weight wc is is used accumulate gradients. k denotes kth layer network. b binarize transformer has a forward function backward function. forward function simply binarizes inputs. backward propagation step one normally computes derivative cost respect input transformer via Jacobian forward function derivative cost respect output transformer δu≡dC/du whereC is the cost function used train network Since binarize function is non-differentiable straight-through estimator BID3 whichis smoothed version forward function is is used backward function. Neural networks binary weights activations have similar performance continuous counterparts substantially reduced execution time power usage. provide experimentally verified theory understanding how one can get away massive reduction precision based geometry HD vectors. First show binarization high-dimensional vectors preserves direction sense angle random vector binarized version is much smaller angle two random vectors Angle Preservation Property Second take perspective network show binarization approximately preserves weight-activation dot products Dot Product Proportionality Property generally when using network compression technique recommend looking weight activation dot product histograms heuristic help localize layers are most responsible performance degradation. Third discuss impacts low effective dimensionality data first layer network. recommend either using continuous weights first layer Generalized Binarization Transformation. transformation may useful architectures like LSTMs where the update hidden state declares particular set axes important e.g taking pointwise multiply forget gates cell state Finally show neural networks ternary weights activations can also understood approach. broadly speaking theory is useful analyzing variety neural network compression techniques transform weights activations reduce execution cost without degrading performance.,1159,783,376,0.013,1.48,2025/11/05 17:18:56,0.01,1.372,0.467289719626168,363.074
"In recent years Convolutional Neural Networks (CNN) have been used extensively for Superresolution (SR). In this paper, we use inverse problem and sparse representation solutions to form a mathematical basis for CNN operations. We show how a single neuron is able to provide the optimum solution for inverse problem, given a low resolution image dictionary as an operator. Introducing a new concept called Representation Dictionary Duality, we show that CNN elements (filters) are trained to be representation vectors and then, during reconstruction, used as dictionaries. In the light of theoretical work, we propose a new algorithm which uses two networks with different structures that are separately trained with low and high coherency image patches and show that it performs faster compared to the state-of-the-art algorithms while not sacrificing from performance. Recent years have witnessed an increased demand for superresolution (SR) algorithms. Increased number of video devices boosted the need for displaying high quality videos online with lower bandwidth. In addition, the social media required the storage of videos and images with lowest possible size for server optimization. Other areas include 4K video displaying from Full HD broadcasts, increasing the output size for systems that have limited sized sensors, such as medical imaging, thermal cameras and surveillance systems.SR algorithms aim to generate high-resolution (HR) image from single or ensemble of lowresolution (LR) images. The observation model of a real imaging system relating a high resolution image to the low resolution observation frame can be given as DISPLAYFORM0 where H models the blurring effects, S models the downsampling operation, and n models the system noise. The solution to this problem seeks a minimal energy of an energy functional comprised of the fidelity of the estimated imagef to the observational image f .State-of-the art algorithms that are addressing SR problem can be collected under Dictionary learning based methods (DLB) and Deep learning based methods (DLM) categories. Although SR problem is an inverse problem by nature, performance of other methods such as Bayesian and Example based methods have been surpassed which is the reason why they are not included in this work. Also the SR problem has never been directly dealt with inverse problem solutions as in BID3 BID4 DLB are generally solving optimization problems with sparsity constraints such as BID20 BID21 and L 2 norm regularization as in BID19 . The main concern of DLB is creation of a compact dictionary for reconstruction of high resolution (HR) image. Although useful, DLB methods become heavy and slow algorithms as reconstruction performance increases. Recent advances on GPUs have fueled the usage of convolutional neural networks (CNNs) for SR problem. CNN based algorithms such as BID5 and BID9 have used multi-layered networks which have successfully surpassed DLB methods in terms of run speed and performance. State-of-the art algorithms also use Perceptual Loss (PL) to generate new textures from LR images BID11 . By uniting PL and generative networks, photo realistic images can be generated BID10 . PL minimization based algorithms are visually superior to MSE minimization based ones. Stability of such algorithms have been improved since they have been first proposed BID7 . Although, stability issue is not yet completely addressed for generative networksIn BID1 authors have described representation learning as a manifold learning for which a higher dimensional data is represented compactly in a lower dimensional manifold. They have discussed that the variations in the input space is captured by the representations, for which we are explaining the mechanism at work.Though CNNs are successful for SR problem experimentally, their mathematical validation is still lacking. We summarized the contributions of this work.• We show that neurons solve an Iterative Shrinkage Thresholding (IST) equation during training for which the operator is dictionary matrix constructed from LR training data. The solution yields a representation vector as the neuron filters. Contrary to the discussion in literature for which an encoder-decoder structure is needed to obtain and use representations, we claim that the filters themselves become the representations.• We describe a new concept namely Representation Dictionary Duality (RDD) and show that neuron filters act as representation vectors during training phase. Then in the testing phase, filters start acting as dictionaries upon which the HR reconstruction is made layer by layer. This is a concept which helps us analyze CNNs with sparse representation and inverse problem mathematics.• After analyzing a neuron with inverse problem and DLB solutions and discussing how the entire network operates during training, we propose a new network structure which is able to recover certain details better, faster without sacrificing overall performance.Rest of the paper organized as follows: in section 2 we refer to related literature for different areas of research. Section 3 ties previous work into our analysis of CNNs . In section 4 we propose a new network for SR problem. In section 5 we give experimentation results.2 RELATED WORK 2.1 ANALYTIC APPROACHES Solution to eq. 1 is inherently ill-conditioned since a multiplicity of solutions exist for any given LR pixel. Thus proper prior regularization for the high resolution image is crucial. The regularization of the inversion is provided with a function , reg, which promotes the priori information from the desired output, reg takes different forms ranging from L 0 norm, Tikhonov regularization to orthogonal decomposition of the estimate. Denoting the SH matrix in eq. 2 by K, the regularized solution is given byf DISPLAYFORM1 In BID4 DISPLAYFORM2 Where a class of proximity operators are defined, the special function for the case of L 1 regularization is soft thresholding function also known as shrinkage operator. DISPLAYFORM3 Notice that K T (g − Kf n−1 ) is the negative gradient of data fidelity term in the original formulation. Therefore the solution for the inverse problem using IST iterations is obtained in a gradient descent type method thresholded by Moreau proximity mapping which is also named as Proximal Landweber Iterations. BID4 have proposed the usage of non-quadratic regularization constraints that promote sparsity by the help of an orthonormal (or overcomplete) basis ϕ l of a Hilbert space. For the problem defined in eq. 2 it is proposed to use a functional φ b, p as DISPLAYFORM4 For the case when p = 1, a straightforward variational equation can be obtained in an iterative way. DISPLAYFORM5 Iterations over the set of basis functions can be carried out in one formula DISPLAYFORM6 where DISPLAYFORM7 which can be seen as a method to file the elements of x in the direction of ϕ l . Daubechies et. al. have proven that the solution obtained by iterating f is the global minimum of the solution space. The solution will reach to an optimum point if K is a bounded operator satisfying ||Kf || ≤ C||f || for any vector f and some constant C.We will use this result in proving that neurons in a CNN architecture are able to reach to the optimum solution for SR problem by solving for the exact same eq. 7. A similar work is conducted by BID8 . They have proposed a Learned IST algorithm which can be seen as a time unfolded recurrent neural network. Later BID2 have discussed that LISTA and their own algorithms that extend LISTA are not mere approximations for an iterative algorithm but themselves are full featured sparse coders.Our work diverges from theirs in showing how a convolutional neural network is able to learn image representation and reconstruction for SR problem inside network parameters. We will unite inverse problem approaches, DLM and DLB methods in a representation-dictionary duality concept. We have proven that a neuron is able to solve an inverse problem optimally. By introducing RDD we have shown that CNN layers act as sparse representation solvers. We have proposed a method that addresses the texture recovery better. Experiments have shown that RDD is valid and proposed network recovers some texture components better and faster than state of the art algorithms while not sacrificing performance and speed. In the future we plan to investigate a content-aware aggregation method which might perform better than simple averaging. We will investigate ways of jointly training or optimizing two networks and including aggregation step inside a unified network. In parallel we are investigating a better network structure for texture recovery. Also we are going to incorporate the initial upsampling step into the network by allowing the network to learn its own interpolation kernels.A VISUAL RESULTS",recent years Convolutional Neural Networks CNN have been used extensively Superresolution SR paper use inverse problem sparse representation solutions form mathematical basis CNN operations. show how a single neuron is able provide optimum solution inverse problem given low resolution image dictionary operator. Introducing new concept called Representation Dictionary Duality show CNN elements filters are trained representation vectors reconstruction used dictionaries. light theoretical work propose new algorithm which uses two networks different structures are separately trained low high coherency image patches show performs faster compared state-of-the-art algorithms sacrificing performance. Recent years have witnessed increased demand superresolution SR algorithms. Increased number video devices boosted need displaying high quality videos online lower bandwidth. addition social media required storage videos images lowest possible size server optimization. areas include 4K video displaying Full HD broadcasts increasing output size systems have limited sized sensors medical imaging thermal cameras surveillance systems.SR algorithms aim generate high-resolution HR image single ensemble lowresolution LR images. observation model real imaging system relating high resolution image low resolution observation frame can be given DISPLAYFORM0 where H models blurring effects models downsampling operation n models system noise. solution problem seeks minimal energy energy functional comprised fidelity estimated imagef observational image f.State-of-the art algorithms are addressing SR problem can be collected Dictionary learning based methods DLB Deep learning based methods DLM categories. Although SR problem is an inverse problem nature performance methods Bayesian Example based methods have been surpassed which is the reason why they are not included work. Also SR problem has never directly dealt inverse problem solutions BID3 BID4 DLB are generally solving optimization problems sparsity constraints BID20 BID21 L 2 norm regularization BID19. main concern DLB is creation compact dictionary reconstruction high resolution HR image. Although useful DLB methods become heavy slow algorithms reconstruction performance increases. Recent advances GPUs have fueled usage convolutional neural networks CNNs SR problem. CNN based algorithms BID5 BID9 have used multi-layered networks which have successfully surpassed DLB methods terms run speed performance. State-of-the art algorithms also use Perceptual Loss PL generate new textures LR images BID11. unitingPL generative networks photo realistic images can be generated BID10. PL minimization based algorithms are visually superior MSE minimization based ones. Stability algorithms have been improved since have been first proposed BID7. Although stability issue is not yet completely addressed generative networksIn BID1 authors have described representation learning manifold learning which a higher dimensional data is represented compactly lower dimensional manifold. have discussed variations input space is captured representations whichwe are explaining mechanism work.Though CNNs are successful SR problem experimentally mathematical validation is still lacking. summarized contributions work.• show neurons solve Iterative Shrinkage Thresholding IST equation training which the operator is dictionary matrix constructed LR training data. solution yields representation vector neuron filters. Contrary discussion literature which an encoder-decoder structure is needed obtain use representations claim filters become representations.• describe new concept namely Representation Dictionary Duality RDD show neuron filters act representation vectors training phase. testing phase filters start acting dictionaries upon which the HR reconstruction is made layer layer. is a concept which helps us analyze CNNs sparse representation inverse problem mathematics.• analyzing neuron inverse problem DLB solutions discussing how the entire network operates training propose new network structure which is able recover certain details better faster without sacrificing overall performance.Rest paper organized follows:section2 refer related literature different areas research. Section 3 ties previous work analysis CNNs. section4 propose new network SR problem. section5 give experimentation results.2 RELATED WORK 2.1 ANALYTIC APPROACHES Solution eq. 1 is inherently ill-conditioned since multiplicity solutions exist given LR pixel. Thus proper prior regularization high resolution image is crucial. regularization inversion is provided function reg which promotes priori information desired output reg takes different forms ranging L 0 norm Tikhonov regularization orthogonal decomposition estimate. Denoting SH matrix eq. 2 K regularized solution is given byf DISPLAYFORM1 BID4 DISPLAYFORM2 Where a class proximity operators are defined special function case L 1 regularization is soft thresholding function also known shrinkage operator. DISPLAYFORM3 Notice K g − Kf n−1 is the negative gradient data fidelity term original formulation. Therefore solution inverse problem using IST iterations is obtained gradient descent type method thresholded Moreau proximity mapping which is also named Proximal Landweber Iterations. BID4 have proposed usage non-quadratic regularization constraints promote sparsity help orthonormal overcomplete basisϕl Hilbert space. problem defined eq. 2 is proposed use functionalφb p DISPLAYFORM4 case whenp 1 straightforward variational equation can be obtained iterative way. DISPLAYFORM5 Iterations set basis functions can be carried one formula DISPLAYFORM6 where DISPLAYFORM7 which can be seen method file elements x direction ϕl. Daubechieset. al. have proven solution obtained iteratingf is the global minimum solution space. solution will reach optimum point ifK is a bounded operator satisfying ||Kf || ≤ C||f|| vectorf constant C.We will use result proving neurons CNN architecture are able reach optimum solution SR problem solving exact eq. 7. similar work is conducted BID8. have proposed Learned IST algorithm which can be seen time unfolded recurrent neural network. Later BID2 have discussed LISTA algorithms extend LISTA are not mere approximations iterative algorithm are full featured sparse coders.Our work diverges showing how a convolutional neural network is able learn image representation reconstruction SR problem inside network parameters. will unite inverse problem approaches DLM DLB methods representation-dictionary duality concept. have proven neuron is able solve inverse problem optimally. introducing RDD have shown CNN layers act sparse representation solvers. have proposed method addresses texture recovery better. Experiments have shown RDD is valid proposed network recovers texture components better faster state art algorithms sacrificing performance speed. future plan investigate content-aware aggregation method might perform better simple averaging. will investigate ways jointly training optimizing two networks including aggregation step inside unified network. parallel are investigating better network structure texture recovery. Also are going incorporate initial upsampling step network allowing network learn interpolation kernels.A VISUAL RESULTS,1685,1221,464,0.017,1.38,2025/11/05 17:18:56,0.01,1.407,0.1557632398753888,542.793
"We consider the learning of algorithmic tasks by mere observation of input-output
 pairs. Rather than studying this as a black-box discrete regression problem with
 no assumption whatsoever on the input-output mapping, we concentrate on tasks
 that are amenable to the principle of divide and conquer, and study what are its
 implications in terms of learning.
 This principle creates a powerful inductive bias that we leverage with neural
 architectures that are defined recursively and dynamically, by learning two scale-
 invariant atomic operations: how to split a given input into smaller sets, and how
 to merge two partially solved tasks into a larger partial solution. Our model can be
 trained in weakly supervised environments, namely by just observing input-output
 pairs, and in even weaker environments, using a non-differentiable reward signal.
 Moreover, thanks to the dynamic aspect of our architecture, we can incorporate
 the computational complexity as a regularization term that can be optimized by
 backpropagation. We demonstrate the flexibility and efficiency of the Divide-
 and-Conquer Network on several combinatorial and geometric tasks: convex hull,
 clustering, knapsack and euclidean TSP. Thanks to the dynamic programming
 nature of our model, we show significant improvements in terms of generalization
 error and computational complexity. Algorithmic tasks can be described as discrete input-output mappings defined over variable-sized inputs, but this ""black-box"" vision hides all the fundamental questions that explain how the task can be optimally solved and generalized to arbitrary inputs. Indeed, many tasks have some degree of scale invariance or self-similarity, meaning that there is a mechanism to solve it that is somehow independent of the input size. This principle is the basis of recursive solutions and dynamic programming, and is ubiquitous in most areas of discrete mathematics, from geometry to graph theory. In the case of images and audio signals, invariance principles are also critical for success: CNNs exploit both translation invariance and scale separation with multilayer, localized convolutional operators. In our scenario of discrete algorithmic tasks, we build our model on the principle of divide and conquer, which provides us with a form of parameter sharing across scales akin to that of CNNs across space or RNNs across time.Whereas CNN and RNN models define algorithms with linear complexity, attention mechanisms BID1 generally correspond to quadratic complexity, with notable exceptions BID0 . This can result in a mismatch between the intrinsic complexity required to solve a given task and the complexity that is given to the neural network to solve it, which Figure 1: Divide and Conquer Network. The split phase is determined by a dynamic neural network S θ that splits each incoming set into two disjoint sets: {X j+1,l , X j+1,l+1 } = S θ (X j,m ), with X j,m = X j+1,l X j+1,l+1 . The merge phase is carried out by another neural network M φ that combines two partial solutions into a solution of the coarser scale: Y j,m = M φ (Y j+1,l , Y j+1,l+1 ); see Section 3 for more details. may impact its generalization performance. Our motivation is that learning cannot be 'complete' until these complexities match, and we start this quest by first focusing on problems for which the intrinsic complexity is well known and understood.Our Divide-and-Conquer Networks (DiCoNet ) contain two modules: a split phase that is applied recursively and dynamically to the input in a coarse-to-fine way to create a hierarchical partition encoded as a binary tree; and a merge phase that traces back that binary tree in a fine-to-coarse way by progressively combining partial solutions; see Figure 1 . Each of these phases is parametrized by a single neural network that is applied recursively at each node of the tree, enabling parameter sharing across different scales and leading to good sample complexity and generalisation.In this paper, we attempt to incorporate the scale-invariance prior with the desiderata to only require weak supervision. In particular, we consider two setups: learning from input-output pairs, and learning from a non-differentiable reward signal. Since our split block is inherently discrete, we resort to policy gradient to train the split parameters, while using standard backpropagation for the merge phase; see Section 5. An important benefit of our framework is that the architecture is dynamically determined, which suggests using the computational complexity as a regularization term. As shown in the experiments, computational complexity is a good proxy for generalisation error in the context of discrete algorithmic tasks. We demonstrate our model on algorithmic and geometric tasks with some degree of scale self-similarity: planar convex-hull, k-means clustering, Knapsack Problem and euclidean TSP. Our numerical results on these tasks reaffirm the fact that whenever the structure of the problem has scale invariance, exploiting it leads to improved generalization and computational complexity over non-recursive approaches. We have presented a novel neural architecture that can discover and exploit scale invariance in discrete algorithmic tasks, and can be trained with weak supervision. Our model learns how to split large inputs recursively, then learns how to solve each subproblem and finally how to merge partial solutions. The resulting parameter sharing across multiple scales yields improved generalization and sample complexity.Due to the generality of the DiCoNet , several very different problems have been tackled, some with large and others with weak scale invariance. In all cases, our inductive bias leads to better generalization and computational complexity. An interesting perspective is to relate our scale invariance with the growing paradigm of meta-learning; that is, to what extent one could supervise the generalization across problem sizes.In future work, we plan to extend the results of the TSP by increasing the number of splits J, by refining the supervised DiCoNet model with the non-differentiable TSP cost, and by exploring higher-order interactions using Graph Neural Networks defined over graph hierarchies BID17 . We also plan to experiment on other NP-hard combinatorial tasks.","consider learning algorithmic tasks mere observation input-output pairs. Rather studying black-box discrete regression problem assumption whatsoever input-output mapping concentrate tasks are amenable principle divide conquer study what are its implications terms learning. principle creates powerful inductive bias leverage neural architectures are defined recursively dynamically learning two scale- invariant atomic operations:how to split given input smaller sets how to merge two partially solved tasks larger partial solution. model can be trained weakly supervised environments namely observing input-output pairs even weaker environments using non-differentiable reward signal. Moreover thanks dynamic aspect architecture can incorporate computational complexity regularization term can be optimized backpropagation. demonstrate flexibility efficiency Divide- and-Conquer Network several combinatorial geometric tasks:convex hull clustering knapsack euclidean TSP. Thanks dynamic programming nature model show significant improvements terms generalization error computational complexity. Algorithmic tasks can be described discrete input-output mappings defined variable-sized inputs black-box vision hides fundamental questions explain how the task can be optimally solved generalized arbitrary inputs. Indeed many tasks have some degree scale invariance self-similarity meaning is a mechanism solve is somehow independent input size. principle is the basis recursive solutions dynamic programming is ubiquitous areas discrete mathematics geometry graph theory. case images audio signals invariance principles are also critical success:CNNs exploit translation invariance scale separation multilayer localized convolutional operators. scenario discrete algorithmic tasks build model principle divide conquer which providesus form parameter sharing across scales akin CNNs across space RNNs across time.Whereas CNN RNN models define algorithms linear complexity attention mechanisms BID1 generally correspond quadratic complexity notable exceptions BID0. can result mismatch intrinsic complexity required solve given task complexity is given neural network solve which Figure1:Divide Conquer Network. split phase is determined dynamic neural network θ splits incoming set two disjoint sets:Xj+1 l Xj+1 l+1 θ Xj Xj Xj+1 lXj+1 l+1. merge phase is carried another neural network φ combines two partial solutions solution coarser scale:j φ j+1 l j+1 l+1 see Section3 details. may impact generalization performance. motivation is that learning cannot 'complete' complexities match start quest first focusing problems which the intrinsic complexity is well known understood.Our Divide-and-Conquer Networks DiCoNet contain two modules:split phase is applied recursively dynamically input coarse-to-fine way create hierarchical partition encoded binary tree;merge phase traces back binary tree fine-to-coarse way progressively combining partial solutions;see Figure1. phases is parametrized single neural network is applied recursively node tree enabling parameter sharing across different scales leading good sample complexity generalisation.In paper attempt incorporate scale-invariance prior desiderata require weak supervision. particular consider two setups:learning input-output pairs learning non-differentiable reward signal. Since split block is inherently discrete resort policy gradient train split parameters using standard backpropagation merge phase;see Section5. important benefit framework is that the architecture is dynamically determined which suggests using computational complexity regularization term. shown experiments computational complexity is a good proxy generalisation error context discrete algorithmic tasks. demonstrate model algorithmic geometric tasks degree scale self-similarity planar convex-hull k-means clustering Knapsack Problem euclidean TSP. numerical results tasks reaffirm fact whenever structure problem has scale invariance exploiting leads improved generalization computational complexity non-recursive approaches. have presented novel neural architecture can discover exploit scale invariance discrete algorithmic tasks can be trained weak supervision. model learns how to split large inputs recursively learns how to solve subproblem finally how to merge partial solutions. resulting parameter sharing across multiple scales yields improved generalization sample complexity.Due generality DiCoNet several different problems have been tackled large others weak scale invariance. cases inductive bias leads better generalization computational complexity. interesting perspective is to relate scale invariance growing paradigm meta-learning is,to what extent one could supervise generalization across problem sizes.In future work plan extend results TSP increasing number splitsJ refining supervised DiCoNet model non-differentiable TSP cost exploring higher-order interactions using Graph Neural Networks defined graph hierarchies BID17. also plan experiment NP-hard combinatorial tasks.",1223,827,396,0.013,1.479,2025/11/05 17:18:56,0.01,1.558,0.4641744548286605,360.607
"Within many machine learning algorithms, a fundamental problem concerns efficient calculation of an unbiased gradient wrt parameters $\boldsymbol{\gamma}$ for expectation-based objectives $\mathbb{E}_{q_{\boldsymbol{\gamma}} (\boldsymbol{y})} [f (\boldsymbol{y}) ]$. Most existing methods either ($i$) suffer from high variance, seeking help from (often) complicated variance-reduction techniques; or ($ii$) they only apply to reparameterizable continuous random variables and employ a reparameterization trick. To address these limitations, we propose a General and One-sample (GO) gradient that ($i$) applies to many distributions associated with non-reparameterizable continuous {\em or} discrete random variables, and ($ii$) has the same low-variance as the reparameterization trick. We find that the GO gradient often works well in practice based on only one Monte Carlo sample (although one can of course use more samples if desired). Alongside the GO gradient, we develop a means of propagating the chain rule through distributions, yielding statistical back-propagation, coupling neural networks to common random variables. Neural networks, typically trained using back-propagation for parameter optimization, have recently demonstrated significant success across a wide range of applications. There has been interest in coupling neural networks with random variables, so as to embrace greater descriptive capacity. Recent examples of this include black-box variational inference (BBVI) BID17 BID33 BID29 BID11 BID32 BID31 Zhang et al., 2018) and generative adversarial networks (GANs) BID8 BID28 Zhao et al., 2016; BID1 BID20 . Unfortunately, efficiently backpropagating gradients through general distributions (random variables) remains a bottleneck. Most current methodology focuses on distributions with continuous random variables, for which the reparameterization trick may be readily applied BID17 BID9 .As an example, the aforementioned bottleneck greatly constrains the applicability of BBVI, by limiting variational approximations to reparameterizable distributions. This limitation excludes discrete random variables and many types of continuous ones. From the perspective of GAN, the need to employ reparameterization has constrained most applications to continuous observations. There are many forms of data that are more-naturally discrete.The fundamental problem associated with the aforementioned challenges is the need to efficiently calculate an unbiased low-variance gradient wrt parameters γ for an expectation objective of the form E qγ (y) [f (y)]1 . We are interested in general distributions q γ (y), for which the components of y may be either continuous or discrete. Typically the components of y have a hierarchical structure, and a subset of the components of y play a role in evaluating f (y).Unfortunately , classical methods for estimating gradients of E qγ (y) [f (y)] wrt γ have limitations. The REINFORCE gradient (Williams, 1992) , although generally applicable (e.g., for continuous and discrete random variables), exhibits high variance with Monte Carlo (MC) estimation of the expectation, forcing one to apply additional variance-reduction techniques. The reparameterization trick (Rep) BID38 BID17 BID33 works well, with as few as only one MC sample, but it is limited to continuous reparameterizable y. Many efforts have been devoted to improving these two formulations, as detailed in Section 6. However, none of these methods is characterized by generalization (applicable to general distributions) and efficiency (working well with as few as one MC sample).The key contributions of this work are based on the recognition that REINFORCE and Rep are seeking to solve the same objective, but in practice Rep yields lower-variance estimations, albeit for a narrower class of distributions. Recent work BID32 has made a connection between REINFORCE and Rep, recognizing that the former estimates a term the latter evaluates analytically. The high variance by which REINFORCE approximates this term manifests high variance in the gradient estimation. Extending these ideas, we make the following main contributions. (i) We propose a new General and One-sample (GO) gradient in Section 3, that principally generalizes Rep to many non-reparameterizable distributions and justifies two recent methods BID5 BID15 ; the ""One sample"" motivating the name GO is meant to highlight the low variance of the proposed method, although of course one may use more than one sample if desired. (ii) We find that the core of the GO gradient is something we term a variable-nabla, which can be interpreted as the gradient of a random variable wrt a parameter. (iii) Utilizing variablenablas to propagate the chain rule through distributions, we broaden the applicability of the GO gradient in Sections 4-5 and present statistical back-propagation, a statistical generalization of classic back-propagation BID36 . Through this generalization, we may couple neural networks to general random variables, and compute needed gradients with low variance. For expectation-based objectives, we propose a General and One-sample (GO) gradient that applies to continuous and discrete random variables. We further generalize the GO gradient to cases for which the underlying model is deep and has a marginal distribution corresponding to the latent variables of interest, and to cases for which the latent variables are hierarchical. The GO-gradient setup is demonstrated to yield the same low-variance estimation as the reparameterization trick, which is only applicable to reparameterizable continuous random variables. Alongside the GO gradient, we constitute a means of propagating the chain rule through distributions. Accordingly, we present statistical back-propagation, to flexibly integrate deep neural networks with general classes of random variables. A PROOF OF THEOREM 1We first prove (7) in the main manuscript, followed by its discrete counterpart, i.e., (8) in the main manuscript. Then, it is easy to verify Theorem 1.A.1 PROOF OF EQUATION FORMULA3 IN THE MAIN MANUSCRIPT Similar proof in one-dimension is also given in the supplemental materials of BID32 .We want to calculate DISPLAYFORM0 where y −v denotes y with y v excluded. Without loss of generality, we assume y v ∈ (−∞, ∞). DISPLAYFORM1 , and we have DISPLAYFORM2 where DISPLAYFORM3 , we then apply integration by parts (or partial integration) to get DISPLAYFORM4 With Q γ (∞) = 1 and Q γ (−∞) = 0, it's straightforward to verify that the first term is always zero for any Q γ (y v ), thus named the ""0"" term.",Within many machine learning algorithms fundamental problem concerns efficient calculation unbiased gradient wrt parameters $\boldsymbol \gamma expectation-based objectives $\mathbb E q_ \boldsymbol \gamma \boldsymbol f \boldsymbol $. existing methods either $i suffer high variance seeking help often complicated variance-reduction techniques;$ii apply reparameterizable continuous random variables employ reparameterization trick. address limitations propose General One-sample GO gradient $i applies many distributions associated non-reparameterizable continuous \em discrete random variables $ii has the same low-variance reparameterization trick. find GO gradient often works well practice based one Monte Carlo sample although one can of course use samples if desired Alongside GO gradient develop means propagating chain rule distributions yielding statistical back-propagation coupling neural networks common random variables. Neural networks typically trained using back-propagation parameter optimization have recently demonstrated significant success across wide range applications. has been interest coupling neural networks random variables embrace greater descriptive capacity. Recent examples include black-box variational inference BBVI BID17 BID33 BID29 BID11 BID32 BID31 Zhanget al. 2018 generative adversarial networks GANs BID8 BID28 Zhaoet al. 2016;BID1 BID20. Unfortunately efficiently backpropagating gradients general distributions random variables remains bottleneck. current methodology focuses distributions continuous random variables which the reparameterization trick may readily applied BID17 BID9.As example aforementioned bottleneck greatly constrains applicability BBVI limiting variational approximations reparameterizable distributions. limitation excludes discrete random variables many types continuous ones. perspective GAN need employ reparameterization has constrained applications continuous observations. are many forms data are more-naturally discrete.The fundamental problem associated aforementioned challenges is the need efficiently calculate unbiased low-variance gradient wrt parametersγ expectation objective formEqγ f 1. are interested general distributionsqγ which the components may either continuous discrete. Typically components have a hierarchical structure subset components play role evaluatingf.Unfortunately classical methods estimating gradients Eqγ f wrtγ have limitations. REINFORCE gradient Williams 1992 although generally applicable e.g continuous discrete random variables exhibits high variance Monte Carlo MC estimation expectation forcing one apply additional variance-reduction techniques. reparameterization trick Rep BID38 BID17 BID33 works well one MC sample is limited continuous reparameterizable y. Many efforts have been devoted improving two formulations detailed Section6. However none methods is characterized generalization applicable general distributions efficiency working well one MC sample.The key contributions work are based recognition REINFORCE Rep are seeking solve objective practice Rep yields lower-variance estimations albeit narrower class distributions. Recent work BID32 has made connection REINFORCE Rep recognizing former estimates term latter evaluates analytically. high variance which REINFORCE approximates term manifests high variance gradient estimation. Extending ideas make following main contributions. propose new General One-sample GO gradient Section3 principally generalizes Rep many non-reparameterizable distributions justifies two recent methods BID5 BID15;One sample motivating nameGO is meant highlight low variance proposed method although course one may use one sample if desired. ii find core GO gradient is something term variable-nabla which can be interpreted gradient random variable wrt parameter. iii Utilizing variablenablas propagate chain rule distributions broaden applicability GO gradient Sections 4-5 present statistical back-propagation statistical generalization classic back-propagation BID36. generalization may couple neural networks general random variables compute needed gradients low variance. expectation-based objectives propose General One-sample GO gradient applies continuous discrete random variables. generalize GO gradient cases which the underlying model is deep has a marginal distribution corresponding latent variables interest cases which the latent variables are hierarchical. GO-gradient setup is demonstrated yield low-variance estimation reparameterization trick which is only applicable reparameterizable continuous random variables. Alongside GO gradient constitute means propagating chain rule distributions. Accordingly present statistical back-propagation flexibly integrate deep neural networks general classes random variables. PROOF THEOREM 1We first prove 7 main manuscript followed discrete counterpart.e 8 main manuscript. is easy verify Theorem 1.A.1 PROOF EQUATION FORMULA3 MAIN MANUSCRIPT Similar proof one-dimension is also given supplemental materials BID32.We want calculate DISPLAYFORM0 where y −v denotes v excluded. Without loss generality assume v∈ −∞ ∞ DISPLAYFORM1 have DISPLAYFORM2 where DISPLAYFORM3 apply integration parts partial integration get DISPLAYFORM4 Qγ ∞ 1 Qγ −∞ 0 straightforward verify first term is always zero Qγ v thus named 0 term.,1354,918,436,0.014,1.475,2025/11/05 17:18:56,0.01,1.459,0.4517133956386294,414.059
"Quantum computers promise significant advantages over classical computers for a number of different applications. We show that the complete loss function landscape of a neural network can be represented as the quantum state output by a quantum computer. We demonstrate this explicitly for a binary neural network and, further, show how a quantum computer can train the network by manipulating this state using a well-known algorithm known as quantum amplitude amplification. We further show that with minor adaptation, this method can also represent the meta-loss landscape of a number of neural network architectures simultaneously. We search this meta-loss landscape with the same method to simultaneously train and design a binary neural network. Finding a suitable set of weights for a neural network has become one of the most studied problems of modern machine learning. It has presented a significant challenge to computer scientists for whom few successful alternatives to back-propagation are available. It can be difficult to explore very large search spaces efficiently and, worse, optimization may converge to a local minima far from global optimum BID2 . Understanding the cost function landscape is also hard, and choosing hyper-parameters and designing neural networks remains mostly a manual process. As Moore's law approaches its end, two new computing paradigms have been explored, neuromorphic and quantum computers. Quantum computing is based on quantum bits (or qbits) obeying the laws of quantum physics as opposed to the classical bits of today that are based on classical physics. Note that in physics the term classical is used to mean non-quantum and we use this terminology throughout. Quantum machine learning aims to find an advantage in applying quantum computing to machine learning. Current research into quantum machine learning falls into one of two catgeories. Some quantum algorithms promise a revolution in machine learning in theory, but contain many gaps in their implementation in practice. In contrast, others are more realistic in their method, but struggle to justify a place amongst the well-established methods of machine learning. In this paper, it is shown that a quantum computer can output a quantum state that represents the entire cost landscape for a given neural network. The method is shown to be versatile and even able to represent a meta-cost landscape of all possible hyperparameters and parameters. Applying it to the connectivities and weights of a binary neural network and simulating the quantum algorithm on a classical computer, we further show that this landscape state can be used for training and metatraining the binary neural network for a small toy problem using quantum amplitude amplification, a standard quantum algorithm. We show that quantum superposition can be used to represent many parameters of a neural network at once and efficiently encode entire loss landscapes in a quantum state using just a single run of a quantum circuit. We demonstrate this explicitly for both parameters and hyper-parameters of a BNN, and show that further processing of this state can lead to quantum advantage in training and metatraining. As a training method it possesses significant advantages as it is landscape-independent, has a quadratic speedup over a classical search of the same kind, and would be able to solve statistically neutral problems such as parity problems BID23 . It is not, however, without shortcomings. One potential criticism is the issue of over-fitting. Since our problem is so small, we chose to define a target state as one where the accuracy is 100% on the training set but this is rarely desirable in real machine learning. One solution may be to simply run the quantum algorithm and, upon finding a particular set of weights that represents an overfit, run the algorithm again but with a deselection of that particular set of weights. This can be done by simply changing the sign of the probability amplitude corresponding to that state during each iteration of the quantum amplitude amplification. A similar issue is that regular machine learning typically uses batch learning, whilst our method incorporates the entire dataset at once. This too can be fixed by altering our method to use a different batch of the data for each quantum amplitude amplification iteration. This works since no matter what batch we use, a good set of weights should still be amplified by the circuit. In fact, such an implementation is advantageous since it would allow us to use less qubits which in practical terms are limited in number in the near term. A significant limitation in our method is the requirement that the input is binary, and the poor scaling of the activation function. Both of these problems arise completely from our implementation of the sign function, which could either be improved or replaced entirely with a different binary activation function that could be implemented more efficiently on a quantum computer and would be compatible with non-binary input. There has been progress on creating effective non-linear activation functions by so-called repeat-until-success circuits BID1 ). An alternative approach would be to use floating point representations as in classical computing and the quantum equivalent of full-adders, but this would require an overhead in the number of qubits that would take us beyond the limit of classical simulation. Finally, we note that this method scales poorly compared to backpropagation and that the advantage only appears in like for like comparisons of unstructured classical/quantum searches. The cost function landscape is not unstructured and algorithms such as backpropagation take advantage of this. We conjecture that a quantum search method that applies quantum advantage to structured searches, if it exists, can be applied to the cost landscape in place of quantum amplitude amplification.Finding ways to harness quantum computers to aid classical machine learning methods in a meaningful way remains an open problem and we present the loss landscape state as a plausible candidate towards this goal. Whilst we used the example of quantum training, the most fruitful approach in the short term is to ask whether some property of the state can be used to glean useful information for classical machine learning methods. This might take the form of understanding the roughness of the landscape, identifying certain features, or even choosing an appropriate learning rate. Further work in investigating the relationship between the landscape as a quantum state and its features from a machine learning perspective would be a step forward in this direction.","Quantum computers promise significant advantages classical computers number different applications. show complete loss function landscape neural network can be represented quantum state output quantum computer. demonstrate explicitly binary neural network show how a quantum computer can train network manipulating state using well-known algorithm known quantum amplitude amplification. show minor adaptation method can also represent meta-loss landscape number neural network architectures simultaneously. search meta-loss landscape method simultaneously train design binary neural network. Finding suitable set weights neural network has become one studied problems modern machine learning. has presented significant challenge computer scientists successful alternatives back-propagation are available. can be difficult explore large search spaces efficiently worse optimization may converge local minima far global optimum BID2. Understanding cost function landscape is also hard choosing hyper-parameters designing neural networks remains mostly manual process. Moore's law approaches end two new computing paradigms have been explored neuromorphic quantum computers. Quantum computing is based quantum bits qbits obeying laws quantum physics opposed classical bits today are based classical physics. Note physics term classical is used mean non-quantum use terminology throughout. Quantum machine learning aims find advantage applying quantum computing machine learning. Current research quantum machine learning falls one two catgeories. quantum algorithms promise revolution machine learning theory contain many gaps implementation practice. contrast others are more realistic method struggle justify place amongst well-established methods machine learning. paper is shown quantum computer can output quantum state represents entire cost landscape given neural network. method is shown versatile even able represent meta-cost landscape possible hyperparameters parameters. Applying connectivities weights binary neural network simulating quantum algorithm classical computer show landscape state can be used training metatraining binary neural network small toy problem using quantum amplitude amplification standard quantum algorithm. show quantum superposition can be used represent many parameters neural network efficiently encode entire loss landscapes quantum state using single run quantum circuit. demonstrate explicitly parameters hyper-parameters BNN show processing state can lead quantum advantage training metatraining. training method possesses significant advantages is landscape-independent has a quadratic speedup classical search kind would able solve statistically neutral problems parity problems BID23. is not,however without shortcomings. One potential criticism is the issue over-fitting Since problem is so small chose define target state one where the accuracy is 100% training set is rarely desirable real machine learning. One solution may simply run quantum algorithm upon finding particular set weights represents overfit run algorithm deselection particular set weights. can be done simply changing sign probability amplitude corresponding state iteration quantum amplitude amplification. similar issue is that regular machine learning typically uses batch learning whilst method incorporates entire dataset once. can be fixed altering method use different batch data quantum amplitude amplification iteration. works since matter what batch use good set weights should still amplified circuit. fact implementation is advantageous since would allowus use less qubits which in practical terms are limited number near term. significant limitation method is the requirement input is binary poor scaling activation function. problems arise completely implementation sign function could either improved replaced entirely different binary activation function could implemented efficiently quantum computer would compatible non-binary input. has been progress creating effective non-linear activation functions so-called repeat-until-success circuits BID1 alternative approach would use floating point representations classical computing quantum equivalent full-adders would require overhead number qubits would take us beyond limit classical simulation. Finally note method scales poorly compared backpropagation advantage appears like like comparisons unstructured classical/quantum searches. cost function landscape is not unstructured algorithms backpropagation take advantage this. conjecture quantum search method applies quantum advantage structured searches if it exists can be applied cost landscape place quantum amplitude amplification.Finding ways harness quantum computers aid classical machine learning methods meaningful way remains open problem present loss landscape state plausible candidate towards goal. Whilst used example quantum training fruitful approach short term is to ask whether property state can be used glean useful information classical machine learning methods. might take form understanding roughness landscape identifying certain features even choosing appropriate learning rate. work investigating relationship landscape quantum state features machine learning perspective would step forward direction.",1192,773,419,0.014,1.542,2025/11/05 17:18:56,0.01,1.524,0.660436137071651,392.768
"Several recent works have developed methods for training classifiers that are certifiably robust against norm-bounded adversarial perturbations. These methods assume that all the adversarial transformations are equally important, which is seldom the case in real-world applications. We advocate for cost-sensitive robustness as the criteria for measuring the classifier's performance for tasks where some adversarial transformation are more important than others. We encode the potential harm of each adversarial transformation in a cost matrix, and propose a general objective function to adapt the robust training method of Wong & Kolter (2018) to optimize for cost-sensitive robustness. Our experiments on simple MNIST and CIFAR10 models with a variety of cost matrices show that the proposed approach can produce models with substantially reduced cost-sensitive robust error, while maintaining classification accuracy. Despite the exceptional performance of deep neural networks (DNNs) on various machine learning tasks such as malware detection BID24 , face recognition BID22 and autonomous driving BID2 , recent studies BID26 BID9 have shown that deep learning models are vulnerable to misclassifying inputs, known as adversarial examples, that are crafted with targeted but visually-imperceptible perturbations. While several defense mechanisms have been proposed and empirically demonstrated to be successful against existing particular attacks BID21 BID9 , new attacks BID3 BID27 BID1 are repeatedly found that circumvent such defenses. To end this arm race, recent works BID23 BID28 propose methods to certify examples to be robust against some specific norm-bounded adversarial perturbations for given inputs and to train models to optimize for certifiable robustness.However, all of the aforementioned methods aim at improving the overall robustness of the classifier. This means that the methods to improve robustness are designed to prevent seed examples in any class from being misclassified as any other class. Achieving such a goal (at least for some definitions of adversarial robustness) requires producing a perfect classifier, and has, unsurprisingly, remained elusive. Indeed, BID20 proved that if the metric probability space is concentrated, overall adversarial robustness is unattainable for any classifier with initial constant error.We argue that overall robustness may not be the appropriate criteria for measuring system performance in security-sensitive applications, since only certain kinds of adversarial misclassifications pose meaningful threats that provide value for potential adversaries. Whereas overall robustness places equal emphasis on every adversarial transformation, from a security perspective, only certain transformations matter. As a simple example, misclassifying a malicious program as benign results in more severe consequences than the reverse.In this paper, we propose a general method for adapting provable defenses against norm-bounded perturbations to take into account the potential harm of different adversarial class transformations. Inspired by cost-sensitive learning BID5 BID7 ) for non-adversarial contexts, we capture the impact of different adversarial class transformations using a cost matrix C, where each entry represents the cost of an adversary being able to take a natural example from the first class and perturb it so as to be misclassified by the model as the second class. Instead of reducing the overall robust error, our goal is to minimize the cost-weighted robust error (which we define for both binary and real-valued costs in C). The proposed method incorporates the specified cost matrix into the training objective function, which encourages stronger robustness guarantees on cost-sensitive class transformations, while maintaining the overall classification accuracy on the original inputs.Contributions. By encoding the consequences of different adversarial transformations into a cost matrix, we introduce the notion of cost-sensitive robustness (Section 3.1) as a metric to assess the expected performance of a classifier when facing adversarial examples. We propose an objective function for training a cost-sensitive robust classifier (Section 3.2). The proposed method is general in that it can incorporate any type of cost matrix, including both binary and real-valued. We demonstrate the effectiveness of the proposed cost-sensitive defense model for a variety of cost scenarios on two benchmark image classification datasets: MNIST (Section 4.1) and CIFAR10 (Section 4.2). Compared with the state-of-the-art overall robust defense model , our model achieves significant improvements in cost-sensitive robustness for different tasks, while maintaining approximately the same classification accuracy on both datasets.Notation. We use lower-case boldface letters such as x for vectors and capital boldface letters such as A to represent matrices. Let [m] be the index set {1, 2, . . . , m} and A ij be the (i, j)-th entry of matrix A. Denote the i-th natural basis vector, the all-ones vector and the identity matrix by e i , 1 and I respectively. For any vector x ∈ R d , the ∞ -norm of x is defined as DISPLAYFORM0 By focusing on overall robustness, previous robustness training methods expend a large fraction of the capacity of the network on unimportant transformations. We argue that for most scenarios, the actual harm caused by an adversarial transformation often varies depending on the seed and target class, so robust training methods should be designed to account for these differences. By incorporating a cost matrix into the training objective, we develop a general method for producing a cost-sensitive robust classifier. Our experimental results show that our cost-sensitive training method works across a variety of different types of cost matrices, so we believe it can be generalized to other cost matrix scenarios that would be found in realistic applications.There remains a large gap between the small models and limited attacker capabilities for which we can achieve certifiable robustness, and the complex models and unconstrained attacks that may be important in practice. The scalability of our techniques is limited to the toy models and simple attack norms for which certifiable robustness is currently feasible, so considerable process is needed before they could be applied to realistic scenarios. However, we hope that considering cost-sensitive robustness instead of overall robustness is a step towards achieving more realistic robustness goals.",Several recent works have developed methods training classifiers are certifiably robust norm-bounded adversarial perturbations. methods assume adversarial transformations are equally important which is seldom case real-world applications. advocate cost-sensitive robustness criteria measuring classifier's performance tasks where some adversarial transformation are more important others. encode potential harm adversarial transformation cost matrix propose general objective function adapt robust training method Wong Kolter 2018 optimize cost-sensitive robustness. experiments simple MNIST CIFAR10 models variety cost matrices show proposed approach can produce models substantially reduced cost-sensitive robust error maintaining classification accuracy. Despite exceptional performance deep neural networks DNNs various machine learning tasks malware detection BID24 face recognition BID22 autonomous driving BID2 recent studies BID26 BID9 have shown deep learning models are vulnerable misclassifying inputs known adversarial examples are crafted targeted visually-imperceptible perturbations. several defense mechanisms have been proposed empirically demonstrated successful existing particular attacks BID21 BID9 new attacks BID3 BID27 BID1 are repeatedly found circumvent defenses. end arm race recent works BID23 BID28 propose methods certify examples robust specific norm-bounded adversarial perturbations given inputs train models optimize which certifiable robustness.However aforementioned methods aim improving overall robustness classifier. means methods improve robustness are designed prevent seed examples class misclassified class. Achieving goal least definitions adversarial robustness requires producing perfect classifier unsurprisingly remained elusive. Indeed BID20 proved if the metric probability space is concentrated overall adversarial robustness is unattainable classifier initial constant error.We argue overall robustness may appropriate criteria measuring system performance security-sensitive applications since certain kinds adversarial misclassifications pose meaningful threats provide value potential adversaries. Whereas overall robustness places equal emphasis every adversarial transformation security perspective certain transformations matter. simple example misclassifying malicious program benign results severe consequences reverse.In paper propose general method adapting provable defenses norm-bounded perturbations take account potential harm different adversarial class transformations. Inspired cost-sensitive learning BID5 BID7 non-adversarial contexts capture impact different adversarial class transformations using cost matrixC where each entry represents cost adversary able take natural example first class perturb misclassified model second class. Instead reducing overall robust error goal is to minimize cost-weighted robust error which we define binary real-valued costs C proposed method incorporates specified cost matrix training objective function which encourages stronger robustness guarantees cost-sensitive class transformations maintaining overall classification accuracy original inputs.Contributions. encoding consequences different adversarial transformations cost matrix introduce notion cost-sensitive robustness Section 3.1 metric assess expected performance classifier when facing adversarial examples. propose objective function training cost-sensitive robust classifier Section 3.2 proposed method is general can incorporate type cost matrix including binary real-valued demonstrate effectiveness proposed cost-sensitive defense model variety cost scenarios two benchmark image classification datasets:MNIST Section 4.1 CIFAR10 Section 4.2 Compared state-of-the-art overall robust defense model model achieves significant improvements cost-sensitive robustness different tasks maintaining approximately classification accuracy datasets.Notation. use lower-case boldface letters x vectors capital boldface letters represent matrices. Let index set 1 2 ij j -th entry matrix A. Denote i-th natural basis vector all-ones vector identity matrix e 1 respectively. vectorx∈R ∞ -norm x is defined DISPLAYFORM0 focusing overall robustness previous robustness training methods expend large fraction capacity network unimportant transformations. argue scenarios actual harm caused adversarial transformation often varies depending seed target class robust training methods should be designed account differences. incorporating cost matrix training objective develop general method producing cost-sensitive robust classifier. experimental results show cost-sensitive training method works across variety different types cost matrices believe can be generalized cost matrix scenarios would found realistic applications.There remains large gap small models limited attacker capabilities which we can achieve certifiable robustness complex models unconstrained attacks may important practice. scalability techniques is limited toy models simple attack norms which certifiable robustness is currently feasible considerable process is needed could applied realistic scenarios. However hope considering cost-sensitive robustness instead overall robustness is a step towards achieving realistic robustness goals.,1184,792,392,0.012,1.495,2025/11/05 17:18:56,0.01,1.406,0.5140186915887852,351.906
"Retinal prostheses for treating incurable blindness are designed to electrically stimulate surviving retinal neurons,  causing them to send artificial visual signals to the brain. However, electrical stimulation generally cannot precisely reproduce  normal patterns of neural activity in the retina. Therefore, an electrical stimulus must be selected that produces a neural response as close as possible to the desired response. This requires a technique for computing a distance between the desired response and the achievable response that is meaningful in terms of the visual signal being conveyed. Here we propose a method to learn such a metric on neural responses, directly from recorded light responses of a population of retinal ganglion cells (RGCs) in the primate retina. The learned metric produces a measure of similarity of RGC population responses that accurately reflects the similarity of the visual input. Using data from electrical stimulation experiments, we demonstrate that this metric may improve the performance of a prosthesis. An important application of neuroscience research is the development of electronic devices to replace the function of diseased or damaged neural circuits BID57 BID39 . Artificial vision has been a particularly challenging modality due to the richness of visual information, its diverse uses in perception and behavior, and the complexity of fabricating a device that can interface effectively with neural circuitry BID47 BID56 BID20 .The most advanced example is a retinal prosthesis: a device that replaces the function of neural circuitry in the retina lost to degenerative disease. Most of the computational work related to this application has focused on building encoding models that use the visual image to accurately predict the spiking activity of populations of retinal ganglion cells (RGCs), the output neurons of the retina that convey visual information to the brain. Leading models include linear models BID7 , probabilistic point-process models BID33 and recently proposed models employing rich nonlinearities BID30 BID2 BID41 .However, an accurate encoding model, although valuable, is insufficient. Any retinal prosthesiswhether based on electrical stimulation BID40 or optical stimulation BID6 BID3 -is limited in its ability to create arbitrary desired patterns of neural activity, due to inefficiencies or lack of specificity in the stimulation modality BID1 BID20 . Thus, a given stimulation system can only achieve a limited vocabulary of elicited spike patterns. Although a powerful and accurate encoding model might indicate that a particular spike pattern would be the natural biological response to the incident visual stimulus, the desired spike pattern might not reside within the feasible set of the stimulation device FIG0 ).Previous studies BID21 have addressed this problem by selecting the electrical stimulation which minimizes the number of unmatched spikes across cells -equivalent to the Hamming distance between two binary vectors. Even though a Hamming distance is easy to compute, this solution is not necessarily optimal. The goal of a prosthetics device should be to instead select an Real recorded spiking activity in a two populations of primate retinal ganglion cells (RGCs) demonstrating the lack of specificity from electrical stimulation. The electrodes are in blue and the stimulated electrode is shaded green. C. The target firing pattern r often lies outside the set of firing patterns achievable with the prosthesis. The goal of the learned metric is to define a distance measure to identify the nearest feasible electrical stimulationr. R denotes the set of all neural population responses.electrical stimulation pattern that produces a response as close as possible to the desired pattern of activity in terms of the elicited visual sensation ( FIG0 ). In lieu of measuring the visual sensation produced by a prosthetic, we instead posit that one may infer a distance metric based on the signal and noise properties of individual and populations of neurons BID43 BID33 BID11 . In contrast, previous approaches to spike metrics have focused on user-specified, parameteric functions BID52 BID51 or unsupervised techniques to cluster nearby spike patterns BID50 BID9 BID14 .In this work, we propose a neural response metric learned directly from the statistics and structure of firing patterns in neural populations, with the aim of using it to select optimal electrical stimulation patterns in a prosthesis device. In particular, we learn a neural response metric by applying ideas from metric learning to recordings of RGC populations in non-human primate retina. We demonstrate that the learned metric provides an intuitive, meaningful representation of the similarity between spike patterns in the RGC population, capturing the statistics of neural responses as well as similarity between visual images. Finally, we use this metric to select the optimal electrical stimulation pattern within the constraints of the electrical interface to a population of RGCs. The learned metric approach has two major potential implications for visual neuroscience. First, it provides a novel method to find ""symbols"" in the neural code of the retina that are similar in the sense that they indicate the presence of similar stimuli BID14 . Second, it has an application to retinal prosthesis technology, in which hardware constraints demand that the set of neural responses that can be generated with a device be used to effectively transmit useful visual information. For this application, a metric on responses that reflects visual stimulus similarity could be extremely useful.The present approach differs from previously proposed spike train metrics (reviewed in BID51 ). Previous approaches have employed unsupervised techniques to cluster nearby spike patterns BID14 BID34 BID15 or employed user-specified, paramteric approaches BID53 BID0 . In the case of single snapshots in time used here, the latter approach (Victor-Purpura metric) has only one degree of freedom which is a user-specified cost associated with moving spikes from one cell to another. In our proposed method, the relative importance of cell identity is learned directly from the statistics of population firing patterns.The present work is a stepping stone towards building an encoding algorithm for retinal prostheses. In this paper, we learn the metric using light evoked responses. However, we need to estimate this metric in a blind retina, which has no light evoked responses. The convolutional metric is adaptable to any RGC population by merely noting cell types and center locations. Thus a convolutional metric could be trained on multiple healthy retinas and applied to a blind retina. Preliminary results in this direction indicate that a convolutional metric trained on half of the cells in a retinal recording (training data) generalizes to the other half (validation data), yielding performance higher than a quadratic metric (and comparable to a convolutional metric) trained directly on the validation data.Additional techniques may also be helpful in extending our method to data involving many cells, temporal responses, and additional response structure. For example, using recurrent neural networks BID26 to embed responses may help compute distances between spiking patterns consisting of multiple time bins, perhaps of unequal length. Boosting BID13 may help combine multiple efficiently learned metrics for a smaller, spatially localized groups of cells. Other metrics may be developed to capture invariances learned by commonly used encoding models BID7 BID33 . Also, triplet mining techniques (i.e., choosing hard negatives), a commonly used trick in computer vision, may improve efficiency BID38 BID32 . Novel metrics could also be learned with additional structure in population responses, such as the highly structured correlated activity in RGCs Mastronarde (1983); BID17 . This noise correlation structure may be learnable using negative examples that destroy the noise correlations in data while preserving light response properties, by taking responses of different cells from different repeats of the stimulus.Note that the convolutional metric outperforms the quadratic metric at both global (ROC curves) and local (precision recall curves) scales. However, using current retinal prosthesis technologies, we might be able to resolve information only up to a particular scale. For current retinal prostheses, capturing global structure may be of greatest importance, because state-of-the-art technology has a relatively coarse vocabulary for stimulating RGCs (Humayun et al., 2012; BID58 ) (see also FIG0 ). Specifically, the ""nearest"" elicited firing pattern is ""far"" in terms of the corresponding visual stimulus ( FIG5 ) . In terms of the proposed learned metric, the nearest feasible firing pattern achievable by electrical stimulation in our experiments is at the 10th percentile of all possible firing patterns. In this context, the average closest stimulation pattern, expressed as a percentile of the learned metric distances, provides a valuable benchmark to measure the performance of a prosthesis and how that performance is affected by advances in the underlying hardware and software. In particular, the network employs knowledge of the receptive field locations and firing rates of individual cells but the network is independent of the number of cells in the retina. The latter point is achieved by embedding the responses of neurons into pathways grouped by cell type. In our experiments, we focus on 2 cell types (ON and OFF parasols), thus we employ a 2 channel pathway BID22 .The network receives as input the spiking activity of ON and OFF parasols and embeds these spike patterns as one-hot vectors placed at the spatial locations of each cell's receptive field. The resulting pattern of activations is summed across all cells in the ON and OFF populations, respectively, and passed through several convolutional layers of a network. Successive layers shrink the spatial activation size of the representation, while increasing the number of filter channels BID24 BID44 . The final embedding response vector has 1/16th number of pixels in the stimulus and represents the flattened representation of the last layer of the network.Let c denote the number of different cells. The RGC population response is a vector r ∈ {0, 1} c .• Represent responses as vectors over {+1, −1} withr = 2(r − 0.5).• Compute the scale for each cell as a function of the mean firing rate: DISPLAYFORM0 • Map each cell to its center location on a grid with spatial dimensions same as those of visual stimulus. Let M i be grid embedding on cell i. So, M i has zero for all positions except center of cell.• Perform a separable 5 × 5 convolution of stride 1 on each M i to get RF estimate of cell,M i .• Add the activation of cells of the same type to get the total activation for a given cell type.Hence, activation map for each cell type A i = ir i s iMi . Subsequent layers receive input as a two layered activation map corresponding to ON and OFF parasol cells.• The convolutional layers further combine information accross multiple cells, of different types. The details of different layers are shown in FIG6 and Normalization Batch normalization after every convolution Optimizer Adam BID23 ) (α = 0.01, β 1 = 0.9, β 2 = 0.999) Parameter updates 20,000Batch size 100 Weight initialization Xavier initialization BID16","Retinal prostheses treating incurable blindness are designed electrically stimulate surviving retinal neurons causing send artificial visual signals brain. However electrical stimulation generally cannot precisely reproduce normal patterns neural activity retina. Therefore electrical stimulus must selected produces neural response close possible desired response. requires technique computing distance desired response achievable response is meaningful terms visual signal conveyed. propose method learn metric neural responses directly recorded light responses population retinal ganglion cells RGCs primate retina. learned metric produces measure similarity RGC population responses accurately reflects similarity visual input. Using data electrical stimulation experiments demonstrate metric may improve performance prosthesis. important application neuroscience research is the development electronic devices replace function diseased damaged neural circuits BID57 BID39. Artificial vision has been a particularly challenging modality due richness visual information diverse uses perception behavior complexity fabricating device can interface effectively neural circuitry BID47 BID56 BID20.The advanced example is a retinal prosthesis:device replaces function neural circuitry retina lost degenerative disease. computational work related application has focused building encoding models use visual image accurately predict spiking activity populations retinal ganglion cells RGCs output neurons retina convey visual information brain. Leading models include linear models BID7 probabilistic point-process models BID33 recently proposed models employing rich nonlinearities BID30 BID2 BID41.However accurate encoding model although valuable is insufficient. retinal prosthesiswhether based electrical stimulation BID40 optical stimulation BID6 BID3 -is limited ability create arbitrary desired patterns neural activity due inefficiencies lack specificity stimulation modality BID1 BID20. Thus given stimulation system can only achieve limited vocabulary elicited spike patterns. Although powerful accurate encoding model might indicate particular spike pattern would natural biological response incident visual stimulus desired spike pattern might reside within feasible set stimulation device FIG0.Previous studies BID21 have addressed problem selecting electrical stimulation which minimizes number unmatched spikes across cells -equivalent Hamming distance two binary vectors. Even though Hamming distance is easy compute solution is not necessarily optimal. goal prosthetics device should be to instead select Real recorded spiking activity two populations primate retinal ganglion cells RGCs demonstrating lack specificity electrical stimulation. electrodes are in blue stimulated electrode is shaded green. C. target firing patternr often lies outside set firing patterns achievable prosthesis. goal learned metric is to define distance measure identify nearest feasible electrical stimulationr. R denotes set neural population responses.electrical stimulation pattern produces response close possible desired pattern activity terms elicited visual sensation FIG0 lieu measuring visual sensation produced prosthetic instead posit one may infer distance metric based signal noise properties individual populations neurons BID43 BID33 BID11. contrast previous approaches spike metrics have focused user-specified parameteric functions BID52 BID51 unsupervised techniques cluster nearby spike patterns BID50 BID9 BID14.In work propose neural response metric learned directly statistics structure firing patterns neural populations aim using select optimal electrical stimulation patterns prosthesis device. particular learn neural response metric applying ideas metric learning recordings RGC populations non-human primate retina. demonstrate learned metric provides intuitive meaningful representation similarity spike patterns RGC population capturing statistics neural responses well similarity visual images. Finally use metric select optimal electrical stimulation pattern within constraints electrical interface population RGCs. learned metric approach has two major potential implications visual neuroscience. First provides novel method find symbols neural code retina are similar sense indicate presence similar stimuli BID14. Second has an application retinal prosthesis technology which hardware constraints demand set neural responses can be generated device used effectively transmit useful visual information. application metric responses reflects visual stimulus similarity could extremely useful.The present approach differs previously proposed spike train metrics reviewed BID51 Previous approaches have employed unsupervised techniques cluster nearby spike patterns BID14 BID34 BID15 employed user-specified paramteric approaches BID53 BID0. case single snapshots time used latter approach Victor-Purpura metric has only one degree freedom which is a user-specified cost associated moving spikes one cell another. proposed method relative importance cell identity is learned directly statistics population firing patterns.The present work is a stepping stone towards building encoding algorithm retinal prostheses. paper learn metric using light evoked responses. However need estimate metric blind retina which has no light evoked responses. convolutional metric is adaptable RGC population merely noting cell types center locations. Thus convolutional metric could trained multiple healthy retinas applied blind retina. Preliminary results direction indicate convolutional metric trained half cells retinal recording training data generalizes half validation data yielding performance higher quadratic metric comparable convolutional metric trained directly validation data.Additional techniques may also helpful extending method data involving many cells temporal responses additional response structure. example using recurrent neural networks BID26 embed responses may help compute distances spiking patterns consisting multiple time bins perhaps unequal length. Boosting BID13 may help combine multiple efficiently learned metrics smaller spatially localized groups cells. metrics may developed capture invariances learned commonly used encoding models BID7 BID33. Also triplet mining techniques.e choosing hard negatives commonly used trick computer vision may improve efficiency BID38 BID32. Novel metrics could also learned additional structure population responses highly structured correlated activity RGCs Mastronarde 1983 BID17. noise correlation structure may learnable using negative examples destroy noise correlations data preserving light response properties taking responses different cells different repeats stimulus.Note convolutional metric outperforms quadratic metric global ROC curves local precision recall curves scales. However using current retinal prosthesis technologies might able resolve information particular scale. current retinal prostheses capturing global structure may greatest importance state-of-the-art technology has a relatively coarse vocabulary stimulating RGCs Humayunetal. 2012;BID58 see also FIG0 Specifically nearest elicited firing pattern is far terms corresponding visual stimulus FIG5 terms proposed learned metric nearest feasible firing pattern achievable electrical stimulation experiments is at the 10th percentile possible firing patterns. context average closest stimulation pattern expressed percentile learned metric distances provides valuable benchmark measure performance prosthesis how that performance is affected advances underlying hardware software. particular network employs knowledge receptive field locations firing rates individual cells network is independent number cells retina. latter point is achieved embedding responses neurons pathways grouped cell type. experiments focus 2 cell types parasols thus employ 2 channel pathway BID22.The network receives input spiking activity parasols embeds spike patterns one-hot vectors placed spatial locations cell's receptive field. resulting pattern activations is summed across cells populations respectively passed several convolutional layers network. Successive layers shrink spatial activation size representation increasing number filter channels BID24 BID44. final embedding response vector has 1/16th number pixels stimulus represents flattened representation last layer network.Let c denote number different cells. RGC population response is a vectorr∈ 0 1 c.• Represent responses vectors+1 −1 withr 2 r − 0.5.• Compute scale cell function mean firing rate:DISPLAYFORM0 • Map cell center location grid spatial dimensions visual stimulus. Let grid embedding cell i. has zero positions except center cell.• Perform separable5×5 convolution stride1 get RF estimate cell.• Add activation cells type get total activation given cell type.Hence activation map cell type ir iMi. Subsequent layers receive input two layered activation map corresponding parasol cells.• convolutional layers combine information accross multiple cells different types. details different layers are shown FIG6 Normalization Batch normalization every convolution Optimizer Adam BID23 α 0.01 β1 0.9 β2 0.999 Parameter updates 20,000Batch size 100 Weight initialization Xavier initialization BID16",2159,1461,698,0.025,1.478,2025/11/05 17:18:56,0.01,1.548,0.4610591900311524,725.168
"We introduce a novel workflow, QCue, for providing textual stimulation during mind-mapping. Mind-mapping is a powerful tool whose intent is to allow one to externalize ideas and their relationships surrounding a central problem. The key challenge in mind-mapping is the difficulty in balancing the exploration of different aspects of the problem (breadth) with a detailed exploration of each of those aspects (depth). Our idea behind QCue is based on two mechanisms: (1) computer-generated automatic cues to stimulate the user to explore the breadth of topics based on the temporal and topological evolution of a mind-map and (2) user-elicited queries for helping the user explore the depth for a given topic. We present a two-phase study wherein the first phase provided insights that led to the development of our work-flow for stimulating the user through cues and queries. In the second phase, we present a between-subjects evaluation comparing QCue with a digital mind-mapping work-flow without computer intervention. Finally, we present an expert rater evaluation of the mind-maps created by users in conjunction with user feedback. Mind-maps are widely used for quick visual externalization of one's mental model around a central idea or problem. The underlying principle behind mind-mapping is to provide a means for associative thinking so as to foster the development of concepts that both explore different aspects around a given problem (breadth) and explore each of those aspects in a detailoriented manner (depth) [48] . The ideas in a mind-map spread out in a hierarchical/tree-like manner [35] , which allows for Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. the integration of diverse knowledge elements into a coherent pattern [8] to enable critical thinking and learning through making synaptic connections and divergent exploration [55, 74, 75, 41] . As a result, mind-maps are uniquely suitable for problem understanding/exploration prior to design conceptualization [8] . There are two main limitations in this work. First, a majority of the recruited users had little to no experience in mindmapping. While this allowed us to demonstrate the capability of QCue in guiding novices to explore problem spaces, we believe that including expert users in our future studies can help us (1) understand how differently they perform using this workflow and (2) lead to a richer discussion on how expertise can be transferred to our system toward better facilitation. Second, one of the key challenges we faced was the lack of robust methodology for determining the effect of cue-based stimulus during mind-mapping (how users may have used cues and queries without explicitly using them to add nodes). While we characterize it on the basis of the number of cues answered and the number of suggestions assimilated directly in the mind-map, we believe that a deeper qualitative study on the mind-mapping process can reveal valuable insights. We plan to conduct such an analysis as our immediate next step. Our intention in this research was to augment users' capability to discover more about a given problem during mind-mapping. For this, we introduced and investigated a new digital workflow (QCue) that provides cues to users based on the current state of the mind-map and also allows them to query suggestions. While our experiments demonstrated the potential of such mechanisms in stimulating idea exploration, the fundamental take-away is that such stimulation requires a balancing act between intervening the user's own line of thought with computer-generated cues and providing suggestions to the user's queries. Furthermore, our work shows the impact of computer-facilitated textual stimuli particularly for those with little practice in brainstorming-type tasks. We believe that QCue is only a step toward a much richer set of research directions in the domain of intelligent cognitive assistants.",introduce novel workflow QCue providing textual stimulation mind-mapping Mind-mapping is a powerful tool whose intent is to allow one externalize ideas relationships surrounding central problem. key challenge mind-mapping is the difficulty balancing exploration different aspects problem breadth detailed exploration aspects depth idea behind QCue is based two mechanisms:1 computer-generated automatic cues stimulate user explore breadth topics based temporal topological evolution mind-map 2 user-elicited queries helping user explore depth given topic. present two-phase study wherein first phase provided insights led development work-flow stimulating user cues queries. second phase present between-subjects evaluation comparing QCue digital mind-mapping work-flow without computer intervention. Finally present expert rater evaluation mind-maps created users conjunction user feedback. Mind-maps are widely used quick visual externalization one's mental model around central idea problem. underlying principle behind mind-mapping is to provide means associative thinking foster development concepts explore different aspects around given problem breadth explore aspects detailoriented manner depth 48 ideas mind-map spread hierarchical/tree-like manner 35 which allows Permission make digital hard copies part work personal classroom use is granted without fee provided copies are not made distributed profit commercial advantage copies bear notice full citation first page. Copyrights components work owned others author must honored. Abstracting credit is permitted. copy otherwise republish post servers redistribute lists requires prior specific permission/fee. Request permissions permissions@acm.org. integration diverse knowledge elements coherent pattern 8 enable critical thinking learning making synaptic connections divergent exploration 55 74 75 41 result mind-maps are uniquely suitable problem understanding/exploration prior design conceptualization 8 are two main limitations work. First majority recruited users had little experience mindmapping. allowedus demonstrate capability QCue guiding novices explore problem spaces believe including expert users future studies can helpus 1 understand how differently perform using workflow 2 lead richer discussion how expertise can be transferred system toward better facilitation. Second one key challenges faced was the lack robust methodology determining effect cue-based stimulus mind-mapping how users may have used cues queries without explicitly using add nodes characterize basis number cues answered number suggestions assimilated directly mind-map believe deeper qualitative study mind-mapping process can reveal valuable insights. plan conduct analysis immediate next step. intention research was to augment users' capability discover given problem mind-mapping introduced investigated new digital workflow QCue provides cues users based current state mind-map also allows query suggestions. experiments demonstrated potential mechanisms stimulating idea exploration fundamental take-away is that such stimulation requires balancing act intervening user's line thought computer-generated cues providing suggestions user's queries. Furthermore work shows impact computer-facilitated textual stimuli particularly little practice brainstorming-type tasks. believe QCue is only a step toward much richer set research directions domain intelligent cognitive assistants.,848,542,306,0.009,1.565,2025/11/05 17:18:56,0.0,1.5,0.73208722741433,287.836
"The ability to detect when an input sample was not drawn from the training distribution is an important  desirable property of deep neural networks. In this paper, we show that a simple ensembling of first and second order deep feature statistics can be exploited to effectively differentiate in-distribution and out-of-distribution samples. Specifically, we observe that  the mean and standard deviation within feature maps  differs greatly between in-distribution and out-of-distribution samples. Based on this observation, we propose a simple and  efficient plug-and-play detection procedure that does not require re-training, pre-processing or changes to the model.   The proposed method outperforms the state-of-the-art by a large margin in all standard benchmarking tasks, while being much simpler to implement and execute. Notably, our method improves the true negative rate from 39.6% to 95.3% when 95% of in-distribution (CIFAR-100) are correctly detected using a DenseNet and the out-of-distribution dataset is TinyImageNet resize. The source code of our method will be made publicly available. In the past few years, deep neural networks (DNNs) BID6 have settled as the state-of-the art-techniques in many difficult tasks in a plurality of domains, such as image classification BID18 , speech recognition BID9 , and machine translation BID2 BID28 . This recent progress has been mainly due to their high accuracy and good generalization ability when dealing with realworld data. Unfortunately, DNNs are also highly confident when tested against unseen samples, even if the samples are vastly different from the ones employed during training BID12 . Moreover, several works have shown that such deep networks are easily fooled by minor perturbations to the input BID5 BID27 . Obtaining a calibrated confidence score from a deep neural network is a problem under continuous investigation BID12 ) and a major thread in artificial intelligence (AI) safety BID1 . In fact, knowing when the model is wrong or inaccurate has a direct impact in many production systems, such as self-driving cars, authentication and disease identification BID0 BID7 , to name a few. BID8 showed that despite producing significantly low classification errors, DNNs confidence scores are not faithful estimates of the true certainty. Their experiments confirmed that depth, width, weight decay, and batch normalization are the main reasons for overconfident scores. Moreover, they demonstrated that a simple and yet powerful method of temperature scaling in the softmax scores is an effective way to improve calibrate a DNNs confidence. While calibrating the classifier's output to represent a faithful likelihood from the training (in-distribution) data has effective solutions, the problem of detecting whether or not the samples are generated from a known distribution (out-of-distribution), is still an open problem BID12 .One straightforward approach to calibrate the classifier's confidence in order to detect samples whose distribution differs from the training samples distribution is to train a secondary classifier that digests both in-distribution (ID) and out-of-distribution (OOD) data so that anomalies are scored differently from ID samples, as performed in BID13 . Re-training a network, however, can be computationally intensive and may even be intractable, since the number of OOD samples is virtually infinite. Other solutions rely on training both classification and generative neural net- Table 1 : Summary comparison of the characteristics of recent related methods. Test complexity refers to the required number of passes over the network. Training data is the number of samples for which the methods were calibrated against (with all standing for the whole training set). AUROC is the area under receiver characteristic curve (detailed in Section 4). Performance shown is for DenseNet trained on CIFAR-100 and using TinyImageNet (resized) as OOD dataset. Deep neural networks trained to maximize classification performance in a given dataset are extremely adapted to said dataset. The statistics of activations throughout the network for samples from the training distribution (in-distribution) are remarkably stable. However, when a sample from a different distribution (out-of-distribution) is given to the network, its activation statistics depart greatly from those of in-distribution samples. Based on this observation, we propose a very simple yet efficient method to detect out-of-distribution samples. Our method is based on computing averages of low-order statistics at the batch normalization layers of the network, and then use them as features in a linear classifier. This procedure is much simpler and efficient than current stateof-the-art methods, and outperforms them by a large margin in the traditional ID/OOD fitting task (as proposed in previous works). We evaluated all methods in the challenging task of fitting on a single OOD dataset and testing on samples from other (unseen) datasets. In this harder scenario, our method generalizes well to unseen OOD datasets, outperforming ODIN by an even larger margin. Moreover, we show some preliminary results that even in the extreme case where no OOD samples are used for the training (unsupervised) we get reasonable performance. tuning is carried out on each pair of in-and out-of-distribution samples, which is the same procedure presented in BID22 and BID21 . For reproducibility, a grid search is employed considering T ∈ {1, 1000} and with 21 linearly spaced values between 0 and 0.004 plus [0.00005, 0.0005, 0.0011].",ability detect when an input sample was not drawn training distribution is an important desirable property deep neural networks. paper show simple ensembling first second order deep feature statistics can be exploited effectively differentiate in-distribution out-of-distribution samples. Specifically observe mean standard deviation within feature maps differs greatly in-distribution out-of-distribution samples. Based observation propose simple efficient plug-and-play detection procedure does not require re-training pre-processing changes model. proposed method outperforms state-of-the-art large margin standard benchmarking tasks much simpler implement execute. Notably method improves true negative rate 39.6 95.3 when95% in-distribution CIFAR-100 are correctly detected using DenseNet out-of-distribution dataset is TinyImageNet resize. source code method will be made publicly available. past years deep neural networks DNNs BID6 have settled state-of-the art-techniques many difficult tasks plurality domains image classification BID18 speech recognition BID9 machine translation BID2 BID28. recent progress has been mainly due high accuracy good generalization ability when dealing realworld data. Unfortunately DNNs are also highly confident when tested unseen samples even if the samples are vastly different ones employed training BID12. Moreover several works have shown deep networks are easily fooled minor perturbations input BID5 BID27. Obtaining calibrated confidence score deep neural network is a problem continuous investigation BID12 major thread artificial intelligence AI safety BID1. fact knowing when the model is wrong inaccurate has a direct impact many production systems self-driving cars authentication disease identification BID0 BID7 name few. BID8 showed despite producing significantly low classification errors DNNs confidence scores are not faithful estimates true certainty. experiments confirmed depth width weight decay batch normalization are the main reasons overconfident scores. Moreover demonstrated simple yet powerful method temperature scaling softmax scores is an effective way improve calibrate DNNs confidence. calibrating classifier's output represent faithful likelihood training in-distribution data has effective solutions problem detecting whether samples are generated known distribution out-of-distribution is still open problem BID12.One straightforward approach calibrate classifier's confidence order detect samples whose distribution differs training samples distribution is to train secondary classifier digests in-distribution ID out-of-distribution OOD data anomalies are scored differently ID samples performed BID13. Re-training network however can be computationally intensive may even intractable since number OOD samples is virtually infinite. solutions rely training classification generative neural net- Table 1:Summary comparison characteristics recent related methods. Test complexity refers required number passes network. Training data is the number samples which the methods were calibrated standing whole training set AUROC is the area receiver characteristic curve detailed Section4 Performance shown is for DenseNet trained CIFAR-100 using TinyImageNet resized OOD dataset. Deep neural networks trained maximize classification performance given dataset are extremely adapted said dataset. statistics activations throughout network samples training distribution in-distribution are remarkably stable. However when a sample different distribution out-of-distribution is given network activation statistics depart greatly in-distribution samples. Based observation propose simple yet efficient method detect out-of-distribution samples. method is based computing averages low-order statistics batch normalization layers network use features linear classifier. procedure is much simpler efficient current stateof-the-art methods outperforms large margin traditional ID/OOD fitting task proposed previous works evaluated methods challenging task fitting single OOD dataset testing samples unseen datasets. harder scenario method generalizes well unseen OOD datasets outperforming ODIN even larger margin. Moreover show preliminary results even extreme case where no OOD samples are used training unsupervised get reasonable performance. tuning is carried pair in-and out-of-distribution samples which is the procedure presented BID22 BID21. reproducibility grid search is employed considering ∈ 1 1000 21 linearly spaced values 0 0.004 plus 0.00005 0.0005 0.0011,1106,768,338,0.011,1.44,2025/11/05 17:18:56,0.01,1.5,0.3426791277258563,330.213
"Due to the sharp increase in the severity of the threat imposed by software vulnerabilities, the detection of vulnerabilities in binary code has become an important concern in the software industry, such as the embedded systems industry, and in the field of computer security. However, most of the work in binary code vulnerability detection has relied on handcrafted features which are manually chosen by a select few, knowledgeable domain experts. In this paper, we attempt to alleviate this severe binary vulnerability detection bottleneck by leveraging recent advances in deep learning representations and propose the Maximal Divergence Sequential Auto-Encoder. In particular, latent codes representing vulnerable and non-vulnerable binaries are encouraged to be maximally divergent, while still being able to maintain crucial information from the original binaries. We conducted extensive experiments to compare and contrast our proposed methods with the baselines, and the results show that our proposed methods outperform the baselines in all performance measures of interest. Software vulnerabilities are specific flaws or oversights in a piece of software that allow attackers to perform malicious acts including exposing or altering sensitive information, disrupting or destroying a system, or taking control of a computer system or program BID5 . Due to the ubiquity of computer software, the growth and the diversity in its development process, a great amount of computer software potentially includes software vulnerabilities. This fact makes the problem of software security vulnerability identification an important concern in the software industry and in the field of computer security. Although a great effort has been made by the security community, the severity of the threat from software vulnerabilities has gradually increased over the years. Numerous exist of examples and incidents in the past two decades in which software vulnerabilities have imposed significant damages to companies and individuals BID6 . For example, vulnerabilities in popular browser plugins have threatened the security and privacy of millions of Internet users (e.g., Adobe Flash Player (US-CERT 2015; Adobe Security Bulletin 2015) and Oracle Java (US-CERT 2013)), vulnerabilities in popular and fundamental open-source software have also threatened the security of thousands of companies and their customers around the globe (e.g., Heartbleed (Codenomicon 2014) and ShellShock (Symantec Security Response 2014).Software vulnerability detection (SVD) can be categorized into source code and binary code vulnerability detection. Source code vulnerability detection has been widely studied in a variety of works BID20 BID17 BID22 BID13 BID9 BID14 . Most of the previous work in source code vulnerability detection BID17 BID20 BID22 BID13 BID9 has been based on handcrafted features which are manually chosen by a limited number of domain experts. To mitigate the dependency on handcrafted features, the use of automatic features in SVD has been studied recently in BID4 BID14 BID15 . In particular , BID4 ; BID15 employed a Recurrent Neural Network (RNN) to transform sequences of code tokens to vectorial features, which are further fed to a separate classifier, while BID14 combined learning the vector representation and the training of the classifier in a deep network.Compared with source code vulnerability detection, binary code vulnerability detection is significantly more difficult because much of the syntactic and semantic information provided by high-level programming languages is lost during the compilation process. The existence of such syntactic and semantic information makes it easier to reason how data and inputs drive the paths of execution. Unfortunately , a software binary, such as proprietary binary code (with no access to source code) or embedded systems code, is generally all that is made available for code analysis (together perhaps with the processor architecture such as x86 etc.). The ability to detect the presence or absence of vulnerabilities in binary code, without getting access to source code, is therefore a major importance in the context of computer security. Some work has been proposed to detect vulnerabilities at the binary code level when source code is not available, notably work based on fuzzing, symbolic execution BID2 BID1 BID16 , or techniques using handcrafted features extracted from dynamic analysis BID8 BID3 BID21 . To the best of our knowledge, there has been no work studying the use of automatically extracted features for binary code vulnerability detection, though there has been some work using automatic features in conjunction with deep learning methods for malware detection, notably BID19 BID18 . It is worth noting that binary code vulnerability detection and malware detection are two different tasks. In particular, binary code vulnerability detection aims to detect specific flaws or oversights in binary code, while malware detection aims to detect if a given binary is malicious or not. The former is arguably harder in the sense that vulnerable and non-vulnerable binaries might be only slightly different, while there might be a clearer difference in general between malware and benign binaries.In addition, a significant constraint in research on binary code vulnerability detection is the lack of suitable binaries labeled as either vulnerable or non-vulnerable. Although we have some source code datasets for software vulnerability detection, to the best of our knowledge, there exists no large public binary dataset for the purpose of binary code vulnerability detection. The reason is that most source code in source code vulnerability detection datasets is not compilable due to incompleteness, and they have important pieces missing (e.g., variables, data types) and relevant libraries -making the code compilable take a large effort in fixing a vast volume of source code. This arises from the nature of the process that involves collecting and labeling source code wherein we start from security reports in CVE 1 and navigate through relevant websites to obtain code snippets of vulnerable and non-vulnerable source code.In this work, we leverage recent advances in deep learning to derive the automatic features of binary code for vulnerability detection. In particular, we view a given binary as a sequence of machine instructions and then use the theory of Variational Auto-Encoders (VAE) BID11 to develop the Maximal Divergence Sequential Auto-Encoder (MDSAE) that can work out representations of binary code in such a way that representations of vulnerable and nonvulnerable binaries are encouraged to be maximally different for vulnerability detection purposes, while still preserving crucial information inherent in the original binaries. In contrast to the original VAE wherein the data prior is kept fixed, we propose using two learnable Gaussian priors, one for each class. Based on the VAE principle, latent codes (i.e., data representations) are absorbed (or compressed) into the data prior distribution, we further propose maximizing a divergence (e.g., Wasserstein (WS) distance or Kullback-Leibler (KL) divergence) between these two priors to separate representations of vulnerable and non-vulnerable binaries. Our MDSAE can be used to produce data representations for another independent classifier (e.g., Support Vector Machine or Random Forest) or incorporated with a shallow feedforward neural network built on top of the latent codes for simultaneously training both the mechanism to generate data representations and the classifier. The former is named MDSAE-R and the latter is named MDSAE-C. We summarize our contributions in this paper as follows:• We propose a novel method named Maximal Divergence Sequential Auto-Encoder (MDSAE) that leverages recent advances in deep learning representation (namely, VAE) for binary code vulnerability detection.• One of our most significant contributions is to create a labeled dataset for use in binary code vulnerability detection. In particular, we used the source code in the published NDSS18 dataset used in BID14 and then extracted vulnerable and non-vulnerable functions. We developed a tool that can automatically detect the syntactical errors in a given piece of source code, fix them, and finally compile the fixed source code into binaries for various platforms (both Windows OS and Linux OS) and architectures (both x86 and x86-64 processors). Specifically, after preprocessing and filtering out identical functions from the NDSS18 source code dataset, we obtain 13, 000 functions of which 9, 000 are able to be fixed and compiled to binaries. By compiling the source code of these functions under the various platform and architecture options, we obtain 32, 281 binary functions including 17, 977 binaries for Windows and 14, 304 binaries for Linux.• We conducted extensive experiments on the NDSS18 binary dataset. The experimental results show that the two variants MDSAE-R and MDSAE-C outperform the baselines in all performance measures of interest. It is not surprising that MDSAE-C achieves higher predictive performances compared with MDSAE-R, but the fact that MDSAE-R achieves good predictive performances confirms our hypothesis of encouraging the separation in representations of data in different classes so that a simple linear classifier subsequently trained on these data representations can obtain good predictive results. The detection of vulnerabilities in binary code is an important problem in the software industry and in the field of computer security. In this paper, we leverage recent advances in deep learning representation to propose the Maximal Divergence Sequential Auto-Encoder for binary vulnerability detection. Specifically, latent codes representing vulnerable and non-vulnerable binaries are encouraged to be maximally different, while still being able to maintain crucial information from the original binaries. To address the issue of limited labelled public binary datasets for this problem and to facilitate research in the application of machine learning and deep learning to the domain of binary vulnerability detection, we have created a labelled binary software dataset. Furthermore, our developed tool and approach can be reused to create other high-quality binary datasets. We conducted extensive experiments to compare our proposed methods with the baselines. The experimental results show that our proposed methods outperform the baselines in all performance measures of interest.",Due sharp increase severity threat imposed software vulnerabilities detection vulnerabilities binary code has become important concern which software industry embedded systems industry field computer security. However has been work binary code vulnerability detection has relied handcrafted features which are manually chosen select knowledgeable domain experts. paper attempt alleviate severe binary vulnerability detection bottleneck leveraging recent advances deep learning representations propose Maximal Divergence Sequential Auto-Encoder particular latent codes representing vulnerable non-vulnerable binaries are encouraged maximally divergent still able maintain crucial information original binaries. conducted extensive experiments compare contrast proposed methods baselines results show proposed methods outperform baselines performance measures interest. Software vulnerabilities are specific flaws oversights piece software allow attackers perform malicious acts including exposing altering sensitive information disrupting destroying system taking control computer system program BID5. Due ubiquity computer software growth diversity development process great amount computer software potentially includes software vulnerabilities. fact makes problem software security vulnerability identification important concern which software industry field computer security. Although great effort has been made security community severity threat software vulnerabilities has gradually increased years. Numerous exist examples incidents past two decades which software vulnerabilities have imposed significant damages companies individuals BID6. example vulnerabilities popular browser plugins have threatened security privacy millions Internet users e.g Adobe Flash Player US-CERT 2015;Adobe Security Bulletin 2015 Oracle Java US-CERT 2013 vulnerabilities popular fundamental open-source software have also threatened security thousands companies customers around globe e.g Heartbleed Codenomicon 2014 ShellShock Symantec Security Response 2014.Software vulnerability detection SVD can be categorized source code binary code vulnerability detection. Source code vulnerability detection has been widely studied variety works BID20 BID17 BID22 BID13 BID9 BID14. previous work source code vulnerability detection BID17 BID20 BID22 BID13 BID9 has been based handcrafted features which are manually chosen limited number domain experts. mitigate dependency handcrafted features use automatic features SVD has been studied recently BID4 BID14 BID15. particular BID4;BID15 employed Recurrent Neural Network RNN transform sequences code tokens vectorial features which are further fed separate classifier BID14 combined learning vector representation training classifier deep network.Compared source code vulnerability detection binary code vulnerability detection is significantly difficult much syntactic semantic information provided high-level programming languages is lost compilation process. existence syntactic semantic information makes easier reason how data inputs drive paths execution. Unfortunately software binary proprietary binary code access source code embedded systems code is generally is made available code analysis together perhaps processor architecture x86 etc. ability detect presence absence vulnerabilities binary code without getting access source code is therefore major importance context computer security. work has been proposed detect vulnerabilities binary code level when source code is not available notably work based fuzzing symbolic execution BID2 BID1 BID16 techniques using handcrafted features extracted dynamic analysis BID8 BID3 BID21. best knowledge has been work studying use automatically extracted features binary code vulnerability detection though has been some work using automatic features conjunction deep learning methods malware detection notably BID19 BID18. is worth noting binary code vulnerability detection malware detection are two different tasks. particular binary code vulnerability detection aims detect specific flaws oversights binary code malware detection aims detect if a given binary is malicious not. former is arguably harder sense vulnerable non-vulnerable binaries might slightly different might clearer difference general malware benign binaries.In addition significant constraint research binary code vulnerability detection is the lack suitable binaries labeled either vulnerable non-vulnerable Although have some source code datasets software vulnerability detection best knowledge exists large public binary dataset purpose binary code vulnerability detection. reason is that most source code source code vulnerability detection datasets is not compilable due incompleteness have important pieces missing e.g variables data types relevant libraries -making code compilable take large effort fixing vast volume source code. arises nature process involves collecting labeling source code wherein start security reports CVE1 navigate relevant websites obtain code snippets vulnerable non-vulnerable source code.In work leverage recent advances deep learning derive automatic features binary code vulnerability detection. particular view given binary sequence machine instructions use theory Variational Auto-Encoders VAE BID11 develop Maximal Divergence Sequential Auto-Encoder MDSAE can work representations binary code way representations vulnerable nonvulnerable binaries are encouraged maximally different vulnerability detection purposes still preserving crucial information inherent original binaries. contrast original VAE wherein data prior is kept fixed propose using two learnable Gaussian priors one class. Based VAE principle latent codes.e data representations are absorbed compressed data prior distribution propose maximizing divergence e.g Wasserstein WS distance Kullback-Leibler KL divergence two priors separate representations vulnerable non-vulnerable binaries. MDSAE can be used produce data representations another independent classifier e.g Support Vector Machine Random Forest incorporated shallow feedforward neural network built top latent codes simultaneously training mechanism generate data representations classifier. former is named is named MDSAE-R latter is named is named MDSAE-C summarize contributions paper follows:• propose novel method named Maximal Divergence Sequential Auto-Encoder MDSAE leverages recent advances deep learning representation namely VAE binary code vulnerability detection.• One significant contributions is to create labeled dataset use binary code vulnerability detection. particular used source code published NDSS18 dataset used BID14 extracted vulnerable non-vulnerable functions. developed tool can automatically detect syntactical errors given piece source code fix finally compile fixed source code binaries various platforms WindowsOS LinuxOS architectures x86 x86-64 processors Specifically preprocessing filtering identical functions NDSS18 source code dataset obtain13 000 functions which9 000 are able fixed compiled binaries. compiling source code functions various platform architecture options obtain32 281 binary functions including 17 977 binaries Windows 14 304 binaries Linux.• conducted extensive experiments NDSS18 binary dataset. experimental results show two variants MDSAE-R MDSAE-C outperform baselines performance measures interest. is not surprising MDSAE-C achieves higher predictive performances compared MDSAE-R fact MDSAE-R achieves good predictive performances confirms hypothesis encouraging separation representations data different classes simple linear classifier subsequently trained data representations can obtain good predictive results. detection vulnerabilities binary code is an important problem which software industry field computer security. paper leverage recent advances deep learning representation propose Maximal Divergence Sequential Auto-Encoder binary vulnerability detection. Specifically latent codes representing vulnerable non-vulnerable binaries are encouraged maximally different still able maintain crucial information original binaries. address issue limited labelled public binary datasets problem facilitate research application machine learning deep learning domain binary vulnerability detection have created labelled binary software dataset. Furthermore developed tool approach can be reused create high-quality binary datasets. conducted extensive experiments compare proposed methods baselines. experimental results show proposed methods outperform baselines performance measures interest.,1925,1301,624,0.025,1.48,2025/11/05 17:18:56,0.01,1.481,0.467289719626168,699.429
"Modern neural architectures critically rely on attention for mapping structured inputs to sequences. In this paper we show that prevalent attention architectures do not adequately model the dependence among the attention and output tokens across a predicted sequence.
 We present an alternative architecture called  Posterior Attention Models that after a principled factorization of the full joint distribution of the attention and output variables, proposes two major changes.   First, the position where attention is marginalized is changed from the input to the output. Second, the attention propagated to the next decoding stage is a posterior attention distribution conditioned on the output. Empirically on five translation and two morphological inflection tasks the proposed posterior attention models yield better BLEU score and alignment accuracy than existing attention models. Attention is a critical module of modern neural models for sequence to sequence learning as applied to tasks like translation, grammar error correction, morphological inflection, and speech to text conversion. Attention specifies what part of the input is relevant for each output. Many variants of attention have been proposed including soft BID1 BID14 , sparse BID15 , local BID14 , hard (Xu et al., 2015; Zaremba & Sutskever, 2015) , monotonic hard (Yu et al., 2016; BID0 , hard non-monotonic (Wu et al., 2018; , and variational BID6 , The most prevalent of these is soft attention that computes attention for each output as a multinomial distribution over the input states. The multinomial probabilities serve as weights, and an attention weighted sum of input states serves as relevant context for the output and subsequent attention. Soft attention is end to end differentiable, easy to implement, and hence widely popular. Hard attention and sparse attentions are difficult to implement and not popularly used.In this paper we revisit the statistical soundness of the way soft attention and other variants capture the dependence between attention and output variables, and among multiple attention variables along the length of the sequence. Our investigation leads to a more principled model that we call the Posterior Attention Model (PAM). We start with an explicit joint distribution of all output and attention variables in a predicted sequence. We then propose a tractable approximation that retains the advantages of forward dependence and token-level decomposition and thus leads to efficient training and inference. The computations performed at each decode step has two important differences with existing models. First, at each decoding step the probability of the output token is a mixture of output probability for each attention. In contrast, existing models take a mixture of the input, and compute a single output distribution from this diffused mixed input. We show that our direct coupling of output and attention gives the benefit of hard attention without its computational challenges. Second, we introduce the notion of a posterior attention distribution, that is, the attention distribution conditioned on the current output. We show that it is both statistically sounder and more accurate to condition subsequent attention on the output corrected posterior attention, rather than the output independent prior attention as in existing models.We evaluate the posterior attention model on five translation tasks and two morphological inflection tasks. We show that posterior attention provides improved BLEU score, higher alignment accuracy, and better input coverage. We also empirically analyze the reasons behind the improved performance of the posterior attention model. We discover that the entropy of posterior attention is much lower than entropy of soft attention. This is a significant finding that challenges the current practice of computing attention distribution without considering the output token. The running time overhead of posterior attention is only 40% over existing soft-attention. We show in this paper that none of the existing attention models adequately model the dependence of the output and attention along the length of the output for general sequence prediction tasks. We propose a factorization of the joint distribution, and develop practical approximations that allows the joint distribution to decompose over output tokens, much like in existing attention. Our more principled probabilistic joint modeling of the dependency structure leads to three important differences. First, the output token distribution is obtained by aggregating predictions across all attention. Second, the concept of conditioning attention on the current output i.e. a posterior attention for inferring the next output becomes important. Our experiments show that it is sounder, more meaningful and more accurate to condition subsequent attention distribution on the posterior attention. Thirdly, via directly exposing attention coupling, we have a principled way to directly incorporate task-specific structural biases and prior knowledge into attention. We experimented with some simple biases and found boosts in related tasks. Our work opens avenues for future work in scaling these techniques to large-scale models and multi-headed attention. Another promising line is to incorporate more complex biases like phrasal structure or image segments into joint attention models.","Modern neural architectures critically rely attention mapping structured inputs sequences. paper show prevalent attention architectures do not adequately model dependence among attention output tokens across predicted sequence. present alternative architecture called Posterior Attention Models principled factorization full joint distribution attention output variables proposes two major changes. First position where attention is marginalized is changed input output. Second is,attention propagated next decoding stage is a posterior attention distribution conditioned output. Empirically five translation two morphological inflection tasks proposed posterior attention models yield better BLEU score alignment accuracy existing attention models. Attention is a critical module modern neural models sequence sequence learning applied tasks like translation grammar error correction morphological inflection speech text conversion. Attention specifies what part input is relevant output. Many variants attention have been proposed including soft BID1 BID14 sparse BID15 local BID14 hard Xuetal. 2015;Zaremba Sutskever 2015 monotonic hard Yuetal. 2016;BID0 hard non-monotonic Wuetal. 2018;variational BID6 prevalent is soft attention computes attention output multinomial distribution input states. multinomial probabilities serve weights is,attention weighted sum input states serves relevant context output subsequent attention. Soft attention is end end differentiable easy implement hence widely popular. Hard attention sparse attentions are difficult implement popularly used.In paper revisit statistical soundness way soft attention variants capture dependence attention output variables among multiple attention variables along length sequence. investigation leads principled model call Posterior Attention Model PAM start explicit joint distribution output attention variables predicted sequence. propose tractable approximation retains advantages forward dependence token-level decomposition thus leads efficient training inference. computations performed decode step has two important differences existing models. First decoding step probability output token is a mixture output probability attention. contrast existing models take mixture input compute single output distribution diffused mixed input. show direct coupling output attention gives benefit hard attention without computational challenges. Second introduce notion posterior attention distribution is,attention distribution conditioned current output. show is both statistically sounder accurate condition subsequent attention output corrected posterior attention rather output independent prior attention existing models.We evaluate posterior attention model five translation tasks two morphological inflection tasks. show posterior attention provides improved BLEU score higher alignment accuracy better input coverage. also empirically analyze reasons behind improved performance posterior attention model. discover entropy posterior attention is much lower entropy is soft attention. is a significant finding challenges current practice computing attention distribution without considering output token. running time overhead posterior attention is only40% existing soft-attention show paper none existing attention models adequately model dependence output attention along length output general sequence prediction tasks. propose factorization joint distribution develop practical approximations allows joint distribution decompose output tokens much like existing attention. principled probabilistic joint modeling dependency structure leads three important differences. First output token distribution is obtained aggregating predictions across attention. Second concept conditioning attention current output.e posterior attention inferring next output becomes important. experiments show is sounder meaningful accurate condition subsequent attention distribution posterior attention. Thirdly via directly exposing attention coupling have a principled way directly incorporate task-specific structural biases prior knowledge attention. experimented simple biases found boosts related tasks. work opens avenues future work scaling techniques large-scale models multi-headed attention. Another promising line is to incorporate complex biases like phrasal structure image segments joint attention models.",943,645,298,0.009,1.462,2025/11/05 17:18:56,0.0,1.478,0.4112149532710277,305.365
"The growing interest to implement Deep Neural Networks (DNNs) on resource-bound hardware has motivated innovation of compression algorithms. Using these algorithms, DNN model sizes can be substantially reduced, with little to no accuracy degradation. This is achieved by either eliminating components from the model, or penalizing complexity during training. While both approaches demonstrate considerable compressions, the former often ignores the loss function during compression while the later produces unpredictable compressions. In this paper, we propose a technique that directly minimizes both the model complexity and the changes in the loss function. In this technique, we formulate compression as a constrained optimization problem, and then present a solution for it. We will show that using this technique, we can achieve competitive results. Deep Neural Networks have been rapidly improving in many classification tasks, even surpassing human accuracy for some problems BID12 . This high accuracy, however, is obtained by employing wider BID15 or deeper BID4 networks. Some prominent networks today even surpass 100 layers, store hundreds of millions of parameters, and require billions of operations per input sample BID4 ; BID13 . Such large networks are not well-suited for resource-bound, embedded and mobile platforms which are dominating the consumer market. This mismatch between computational requirements and available resources has motivated efforts to compress DNN models.Compression techniques exploit the redundancy inherent to neural networks that emerges due to the considerable number of parameters in them. These many parameters help learn highly informative features during training. However, they simultaneously learn multitudes of unnecessary, ineffectual ones. BID3 reduces these redundancies by pruning the network and quantizing the remaining parameters. Using these techniques, they were able to reduce the model size by more than an order of magnitude. Their success inspired other methodical approaches such as the soft weight-sharing BID14 . This method encodes model parameters using Bayesian prior and then penalizes this prior during training. As a result, it performs both pruning and quantization simultaneously and achieves superior compressions with negligible loss in accuracy.In this work, we take a similar, integrated approach with the twist that we directly minimize the complexity. Unlike soft weight-sharing, however, we encode the parameters using the k-means objective which imposes less computations. We further apply a hard constraint on the training loss to maintain sufficient accuracy. Such a constraint takes advantage of the fact that we have already obtained some information about the loss function during training. We then present a straightforward solution for this constrained optimization problem. Our solution iteratively minimizes the k-means objective, while satisfying the loss constraint. Consequently, it can compress the model progressively where the compression rate can be adjusted. Finally, we test the proposed technique on three popular datasets and show that this method can achieve state-of-the-art compression with minimal loss of accuracy.",growing interest implement Deep Neural Networks DNNs resource-bound hardware has motivated innovation compression algorithms. Using algorithms DNN model sizes can be substantially reduced little accuracy degradation. is achieved either eliminating components model penalizing complexity training. approaches demonstrate considerable compressions former often ignores loss function compression later produces unpredictable compressions. paper propose technique directly minimizes model complexity changes loss function. technique formulate compression constrained optimization problem present solution it. will show using technique can achieve competitive results. Deep Neural Networks have been rapidly improving many classification tasks even surpassing human accuracy problems BID12. high accuracy however is obtained employing wider BID15 deeper BID4 networks. prominent networks today even surpass 100 layers store hundreds millions parameters require billions operations per input sample BID4;BID13. large networks are not well-suited resource-bound embedded mobile platforms which are dominating consumer market. mismatch computational requirements available resources has motivated efforts compress DNN models.Compression techniques exploit redundancy inherent neural networks emerges due considerable number parameters them. many parameters help learn highly informative features training. However simultaneously learn multitudes unnecessary ineffectual ones. BID3 reduces redundancies pruning network quantizing remaining parameters. Using techniques were able reduce model size order magnitude. success inspired methodical approaches soft weight-sharing BID14. method encodes model parameters using Bayesian prior penalizes prior training. result performs pruning quantization simultaneously achieves superior compressions negligible loss accuracy.In work take similar integrated approach twist directly minimize complexity. Unlike soft weight-sharing however encode parameters using k-means objective which imposes less computations. apply hard constraint training loss maintain sufficient accuracy. constraint takes advantage fact have already obtained information loss function training. present straightforward solution constrained optimization problem. solution iteratively minimizes k-means objective satisfying loss constraint. Consequently can compress model progressively where the compression rate can be adjusted. Finally test proposed technique three popular datasets show method can achieve state-of-the-art compression minimal loss accuracy.,553,375,178,0.005,1.475,2025/11/05 17:18:56,0.0,1.375,0.4517133956386294,187.247
"Deep neural networks are able to solve tasks across a variety of domains and modalities of data. Despite many empirical successes, we lack the ability to clearly understand and interpret the learned mechanisms that contribute to such effective behaviors and more critically, failure modes. In this work, we present a general method for visualizing an arbitrary neural network's inner mechanisms and their power and limitations. Our dataset-centric method produces visualizations of how a trained network attends to components of its inputs. The computed ""attention masks"" support improved interpretability by highlighting which input attributes are critical in determining output. We demonstrate the effectiveness of our framework on a variety of deep neural network architectures in domains from computer vision and natural language processing. The primary contribution of our approach is an interpretable visualization of attention that provides unique insights into the network's underlying decision-making process irrespective of the data modality. Machine-learning systems are ubiquitous, even in safety-critical areas. Trained models used in self-driving cars, healthcare, and environmental science must not only strive to be error free but, in the face of failures, must be amenable to rapid diagnosis and recovery. This trend toward realworld applications is largely being driven by recent advances in the area of deep learning. Deep neural networks have achieved state-of-the-art performance on fundamental domains such as image classification BID15 , language modeling BID2 BID20 , and reinforcement learning from raw pixels BID22 . Unlike traditional linear models, deep neural networks offer the significant advantage of being able to learn their own feature representation for the completion of a given task. While learning such a representation removes the need for manual feature engineering and generally boosts performance, the resulting models are often hard to interpret, making it significantly more difficult to assign credit (or blame) to the model's behaviors. The use of deep learning models in increasingly important application areas underscores the need for techniques to gain insight into their failure modes, limitations, and decision-making mechanisms.Substantial prior work investigates methods for increasing interpretability of these systems. One body of work focuses on visualizing various aspects of networks or their relationship to each datum they take as input BID33 ; BID35 . Other work investigates algorithms for eliciting an explanation from trained machine-learning systems for each decision they make BID26 ; BID0 ; BID27 . A third line of work, of which our method is most aligned, seeks to capture and understand what networks focus on and what they ignore through attention mechanisms.Attention-based approaches focus on network architectures that specifically attend to regions of their input space. These ""explicit"" attention mechanisms were developed primarily to improve network behavior, but additionally offer increased interpretability of network decision making through highlighting key attributes of the input data BID30 BID12 BID25 BID16 . Crucially, these explicit attention mechanisms act as filters on the input. As such, the filtered components of the input could be replaced with reasonably generated noise without dramatically affecting the final network output. The ability to selectively replace irrelevant components of the input space is a direct consequence of the explicit attention mechanism. The insight at the heart of the present work is that it is possible to evaluate the property of ""selective replaceability"" to better understand a network that lacks any explicit attention mechanism. An architecture without explicit attention may still depend more on specific facets of its input data when constructing its learned, internal representation, resulting in a ""latent"" attention mechanism.In this work, we propose a novel approach for indirectly measuring latent attention mechanisms in arbitrary neural networks using the notion of selective replaceability. Concretely, we learn an auxiliary, ""Latent Attention Network"" (LAN) , that consumes an input data sample and generates a corresponding mask (of the same shape) indicating the degree to which each of the input's components are replaceable with noise. We train this LAN by corrupting the inputs to a pre-trained network according to generated LAN masks and observing the resulting corrupted outputs. We define a loss function that trades off maximizing the corruption of the input while minimizing the deviation between the outputs generated by the pre-trained network using the true and corrupted inputs, independently. The resultant LAN masks must learn to identify the components of the input data that are most critical to producing the existing network's output (i.e. those regions that are given the most attention by the existing network.)We empirically demonstrate that the LAN framework can provide unique insights into the inner workings of various pre-trained networks. Specifically, we show that classifiers trained on a Translated MNIST domain learn a two-stage process of first localizing a digit within the image before determining its class. We use this interpretation to predict regions on the screen where digits are less likely to be properly classified. Additionally, we use our framework to visualize the latent attention mechanisms of classifiers on both image classification (to learn the visual features most important to the network's prediction), and natural language document classification domains (to identify the words most relevant to certain output classes). Finally, we examine techniques for generating attention masks for specific samples, illustrating the capability of our approach to highlight salient features in individual members of a dataset. As deep neural networks continue to find application to a growing collection of tasks, understanding their decision-making processes becomes increasingly important. Furthermore, as this space of tasks grows to include areas where there is a small margin for error, the ability to explore and diagnose problems within erroneous models becomes crucial.In this work, we proposed Latent Attention Networks as a framework for capturing the latent attention mechanisms of arbitrary neural networks that draws parallels between noise-based input corruption and attention. We have shown that the analysis of these attention measurements can effectively diagnose failure modes in pre-trained networks and provide unique perspectives on the mechanism by which arbitrary networks perform their designated tasks.We believe there are several interesting research directions that arise from our framework. First, there are interesting parallels between this work and the popular Generative Adversarial Networks BID9 . It may be possible to simultaneously train F and A as adversaries. Since both F and A are differentiable, one could potentially exploit this property and use A to encourage a specific attention mechanism on F , speeding up learning in challenging domains and otherwise allowing for novel interactions between deep networks. Furthermore, we explored two types of noise for input corruption: η const and η boot . It may be possible to make the process of generating noise a part of the network itself by learning a nonlinear transformation and applying it to some standard variety of noise (such as Normal or Uniform). Since our method depends on being able to sample noise that is similar to the ""background noise"" of the domain, better mechanisms for capturing noise could potentially enhance the LAN's ability to pick out regions of attention and eliminate the need for choosing a specific type of noise at design time. Doing so would allow the LAN to pick up more specific features of the input space that are relevant to the decision-making process of arbitrary classifier networks.In the following experiment subsections we describe network architectures by sequentially listing their layers using an abbreviated notation: DISPLAYFORM0 for convolutional, convolutional-transpose and fully connected layers respectively. In all network architectures, -ReLU denotes the leaky-ReLU BID18 .We now describe each experiment in greater detail.",Deep neural networks are able solve tasks across variety domains modalities data. Despite many empirical successes lack ability clearly understand interpret learned mechanisms contribute effective behaviors critically failure modes. work present general method visualizing arbitrary neural network's inner mechanisms power limitations. dataset-centric method produces visualizations how a trained network attends components inputs. computed attention masks support improved interpretability highlighting which input attributes are critical determining output. demonstrate effectiveness framework variety deep neural network architectures domains computer vision natural language processing. primary contribution approach is an interpretable visualization attention provides unique insights network's underlying decision-making process irrespective data modality. Machine-learning systems are ubiquitous even safety-critical areas. Trained models used self-driving cars healthcare environmental science must strive error free face failures must amenable rapid diagnosis recovery. trend toward realworld applications is largely driven recent advances area deep learning. Deep neural networks have achieved state-of-the-art performance fundamental domains image classification BID15 language modeling BID2 BID20 reinforcement learning raw pixels BID22. Unlike traditional linear models deep neural networks offer significant advantage able learn feature representation completion given task. learning representation removes need manual feature engineering generally boosts performance resulting models are often hard interpret making significantly difficult assign credit blame model's behaviors. use deep learning models increasingly important application areas underscores need techniques gain insight failure modes limitations decision-making mechanisms.Substantial prior work investigates methods increasing interpretability systems. One body work focuses visualizing various aspects networks relationship datum take input BID33;BID35. work investigates algorithms eliciting explanation trained machine-learning systems decision make BID26;BID0;BID27. third line work which our method is most aligned seeks capture understand what networks focus what they ignore attention mechanisms.Attention-based approaches focus network architectures specifically attend regions input space. explicit attention mechanisms were developed primarily improve network behavior additionally offer increased interpretability network decision making highlighting key attributes input data BID30 BID12 BID25 BID16. Crucially explicit attention mechanisms act filters input. filtered components input could replaced reasonably generated noise without dramatically affecting final network output. ability selectively replace irrelevant components input space is a direct consequence explicit attention mechanism. insight heart present work is that it is possible evaluate property selective replaceability better understand network lacks explicit attention mechanism. architecture without explicit attention may still depend specific facets input data when constructing learned internal representation resulting latent attention mechanism.In work propose novel approach indirectly measuring latent attention mechanisms arbitrary neural networks using notion selective replaceability. Concretely learn auxiliary Latent Attention Network LAN consumes input data sample generates corresponding mask shape indicating degree which eachof input's components are replaceable noise. train LAN corrupting inputs pre-trained network according generated LAN masks observing resulting corrupted outputs. define loss function trades maximizing corruption input minimizing deviation outputs generated pre-trained network using true corrupted inputs independently. resultant LAN masks must learn identify components input data are most critical producing existing network's output.e regions are given attention existing network. empirically demonstrate LAN framework can provide unique insights inner workings various pre-trained networks. Specifically show classifiers trained Translated MNIST domain learn two-stage process first localizing digit within image determining class. use interpretation predict regions screen where digits are less likely properly classified. Additionally use framework visualize latent attention mechanisms classifiers image classification learn visual features important network's prediction natural language document classification domains identify words relevant certain output classes Finally examine techniques generating attention masks specific samples illustrating capability approach highlight salient features individual members dataset. deep neural networks continue find application growing collection tasks understanding decision-making processes becomes increasingly important. Furthermore space tasks grows include areas where there is a small margin error ability explore diagnose problems within erroneous models becomes crucial.In work proposed Latent Attention Networks framework capturing latent attention mechanisms arbitrary neural networks draws parallels noise-based input corruption attention. have shown analysis attention measurements can effectively diagnose failure modes pre-trained networks provide unique perspectives mechanism which arbitrary networks perform designated tasks.We believe are several interesting research directions arise framework. First are interesting parallels work popular Generative Adversarial Networks BID9. may possible simultaneously trainF adversaries. Since F are differentiable one could potentially exploit property use encourage specific attention mechanism F speeding learning challenging domains otherwise allowing novel interactions deep networks. Furthermore explored two types noise input corruption:η const η boot. may possible make process generating noise part network learning nonlinear transformation applying standard variety noise Normal Uniform Since method depends able sample noise is similar background noise domain better mechanisms capturing noise could potentially enhance LAN's ability pick regions attention eliminate need choosing specific type noise design time. would allow LAN pick specific features input space are relevant decision-making process arbitrary classifier networks.In following experiment subsections describe network architectures sequentially listing layers using abbreviated notation:DISPLAYFORM0 convolutional convolutional-transpose fully connected layers respectively. network architectures -ReLU denotes leaky-ReLU BID18.We describe experiment greater detail.,1426,932,494,0.015,1.53,2025/11/05 17:18:56,0.01,1.455,0.6230529595015576,489.526
"The design of small molecules with bespoke properties is of central importance to drug discovery.   However significant challenges yet remain for computational methods, despite recent advances such as deep recurrent networks and reinforcement learning strategies for sequence generation, and it can be difficult to compare results across different works.   This work proposes 19 benchmarks selected by subject experts, expands smaller datasets previously used to approximately 1.1 million training molecules, and explores how to apply new reinforcement learning techniques effectively for molecular design.   The benchmarks here, built as OpenAI Gym environments, will be open-sourced to encourage innovation in molecular design algorithms and to enable usage by those without a background in chemistry.   Finally, this work explores recent development in reinforcement-learning methods with excellent sample complexity (the A2C and PPO algorithms) and investigates their behavior in molecular generation, demonstrating significant performance gains compared to standard reinforcement learning techniques. Novel drugs are developed using design -make -test cycles: molecules are designed, synthesized in the laboratory, and then tested for their biological effect. The insights gained from these tests then inform the design for the next iteration. The objective of de novo design methodologies is to perform this cycle with computational methods BID4 BID29 . The test phase was the first to be automated, using the broad categorization of machine learning models known as quantitative structure-activity/property relationships (QSAR/QSPR) to predict the activity of a molecule against a certain biological target, or physicochemical properties. To make virtual molecules, symbolic approaches based on graph rewriting have been used, which are domain-specific and rely on extensive hand-engineering by experts. To optimize the properties of a molecule, for example its activity against a biological target (design), global optimization approaches such as evolutionary algorithms or ant colony optimization have been used BID4 BID29 . Symbolic approaches have been highlighted as either generating unrealistic molecules that would be difficult to synthesize, or for being too conservative, and therefore not sufficiently exploring the space of tractable molecules BID29 BID2 .Recently , generative models have been proposed to learn the distribution of real druglike molecules from data, and then to generate chemical structures that are appropriate for the application domain BID36 . Interestingly , the generation of molecules is related to natural language generation (NLG) . Two classic problems of NLG -preserving coherent long-range dependencies, and syntactic and semantic correctness -directly map to molecules. Current investigations draw heavily from tools developed for language tasks, including variational autoencoders (VAE) BID12 BID18 , recurrent neural network (RNN) models BID32 BID17 BID24 , generative adversarial networks (GAN) BID15 and Monte Carlo Tree Search (MCTS) BID38 .This work seeks to consolidate the growing body of recurrent models for molecular design that employ reinforcement learning. Here, we suggest a set of 19 benchmarks of relevance to de novo design. Furthermore, an implementation of these benchmarks as an OpenAI Gym is provided to the community to spur further innovation. Finally, we demonstrate state-of-the-art performance using new techniques drawing from recent advances in reinforcement learning.Under review as a conference paper at ICLR 2018 In this work, we proposed a large, standardized dataset and a set of 19 benchmarks to evaluate models for molecule generation and design. Several RL strategies were investigated on these benchmarks. Here, the results suggest that the Hillclimb-MLE model is a surprisingly robust technique with large datasets and deep models, outperforming PPO given sufficient compute times and sample evaluations. In the space of constrained compute and sample evaluations, PPO was shown to be an effective learning algorithm, converging an order of magnitude before other reinforcement-learning algorithms for molecule generation.Nevertheless, there is still tremendous need for more efficient and effective models for molecular design, which could have a profound impact on molecular design -including drug, materials and agrochemicals discovery -and thus immediately on human well-being. With the present, easily usable benchmark, we hope to inspire the machine learning community to pick up this challenge.",design small molecules bespoke properties is of central importance drug discovery. However significant challenges yet remain computational methods despite recent advances deep recurrent networks reinforcement learning strategies sequence generation can difficult compare results across different works. work proposes 19 benchmarks selected subject experts expands smaller datasets previously used approximately 1.1 million training molecules explores how to apply new reinforcement learning techniques effectively molecular design. benchmarks built OpenAI Gym environments will be open-sourced encourage innovation molecular design algorithms enable usage without background chemistry. Finally work explores recent development reinforcement-learning methods excellent sample complexity A2C PPO algorithms investigates behavior molecular generation demonstrating significant performance gains compared standard reinforcement learning techniques. Novel drugs are developed using design -make -test cycles:molecules are designed synthesized laboratory tested biological effect. insights gained tests inform design next iteration. objective de novo design methodologies is to perform cycle computational methods BID4 BID29. test phase was the first automated using broad categorization machine learning models known quantitative structure-activity/property relationships QSAR/QSPR predict activity molecule certain biological target physicochemical properties. make virtual molecules symbolic approaches based graph rewriting have been used which are domain-specific rely extensive hand-engineering experts. optimize properties molecule example activity biological target design global optimization approaches evolutionary algorithms ant colony optimization have been used BID4 BID29. Symbolic approaches have been highlighted either generating unrealistic molecules would difficult synthesize conservative therefore sufficiently exploring space tractable molecules BID29 BID2.Recently generative models have been proposed learn distribution real druglike molecules data generate chemical structures are appropriate application domain BID36. Interestingly generation molecules is related natural language generation NLG Two classic problems NLG -preserving coherent long-range dependencies syntactic semantic correctness -directly map molecules. Current investigations draw heavily tools developed language tasks including variational autoencoders VAE BID12 BID18 recurrent neural network RNN models BID32 BID17 BID24 generative adversarial networks GAN BID15 Monte Carlo Tree Search MCTS BID38.This work seeks consolidate growing body recurrent models molecular design employ reinforcement learning. suggest set 19 benchmarks relevance de novo design. Furthermore implementation benchmarks OpenAI Gym is provided community spur innovation. Finally demonstrate state-of-the-art performance using new techniques drawing recent advances reinforcement learning.Under review conference paper ICLR 2018 work proposed large standardized dataset set 19 benchmarks evaluate models molecule generation design. Several RL strategies were investigated benchmarks. results suggest Hillclimb-MLE model is a surprisingly robust technique large datasets deep models outperforming PPO given sufficient compute times sample evaluations. space constrained compute sample evaluations PPO was shown effective learning algorithm converging order magnitude reinforcement-learning algorithms molecule generation.Nevertheless is still tremendous need efficient effective models molecular design could have a profound impact molecular design -including drug materials agrochemicals discovery -and thus immediately human well-being present easily usable benchmark hope inspire machine learning community pick challenge.,805,555,250,0.008,1.45,2025/11/05 17:18:56,0.0,1.55,0.3738317757009343,270.999
"Analogical reasoning has been a principal focus of various waves of AI research. Analogy is particularly challenging for machines because it requires relational structures to be represented such that they can be flexibly applied across diverse domains of experience. Here, we study how analogical reasoning can be induced in neural networks that learn to perceive and reason about raw visual data. We find that the critical factor for inducing such a capacity is not an elaborate architecture, but rather, careful attention to the choice of data and the manner in which it is presented to the model. The most robust capacity for analogical reasoning is induced when networks learn analogies by contrasting abstract relational structures in their input domains, a training method that uses only the input data to force models to learn about important abstract features. Using this technique we demonstrate capacities for complex, visual and symbolic analogy making and generalisation in even the simplest neural network architectures. The ability to make analogies -that is, to flexibly map familiar relations from one domain of experience to another -is a fundamental ingredient of human intelligence and creativity BID10 BID14 BID16 BID20 . As noted, for instance, by BID15 , analogies gave Roman scientists a deeper understanding of sound when they leveraged knowledge of a familiar source domain (water waves in the sea) to better understand the structure of an unfamiliar target domain (acoustics). The Romans 'aligned' relational principles about water waves (periodicity, bending round corners, rebounding off solids) to phenomena observed in acoustics, in spite of the numerous perceptual and physical differences between water and sound. This flexible alignment, or mapping, of relational structure between source and target domains, independent of perceptual congruence, is a prototypical example of analogy making.It has proven particularly challenging to replicate processes of analogical thought in machines. Many classical or symbolic AI models lack the flexibility to apply predicates or operations across diverse domains, particularly those that may have never previously been observed. It is natural to consider, however, whether the strengths of modern neural network-based models can be exploited to solve difficult analogical problems, given their capacity to represent stimuli at different levels of abstraction and to enable flexible, context-dependent computation over noisy and ambiguous inputs.In this work we demonstrate that well-known neural network architectures can indeed learn to make analogies with remarkable generality and flexibility. This ability, however, is critically dependent on a method of training we call learning analogies by contrasting abstract relational structure (LABC). We show that simple architectures can be trained using this approach to apply abstract relations to never-before-seen source-target domain mappings, and even to entirely unfamiliar target domains.Our work differs from previous computational models of analogy in two important ways. First, unlike previous neural network models of analogy, we optimize a single model to perform both stimulus representation and cross-domain mapping jointly. This allows us to explore the potential benefit of interactions between perception, representation and inter-domain alignment, a question of some debate in the analogy literature BID8 The number of shapes increases as you go along the panels 2) Apply the relation from (1) to the target panels:The darkness of the lines increases as you go along the panels One shape Two shapes Three shapes These results demonstrate that LABC increases the ability of models to generalize beyond the distribution of their training data. This effect is observed for the prototypical analogical processes involving novel domain mappings and unfamiliar target domains FIG0 . Interestingly, it also results in moderate improvements to how well models extrapolate to perceptual input outside the range of their training experience (Experiment 3). Our experiments show that simple neural networks can learn to make analogies with visual and symbolic inputs, but this is critically contingent on the way in which they are trained; during training, the correct answers should be contrasted with alternative incorrect answers that are plausible at the level of relations rather than simple perceptual attributes. This is consistent with the SMT of human analogy-making, which highlights the importance of inter-domain comparison at the level of abstract relational structures. At the same time, in the visual analogy domain, our model reflects the idea of analogy as closely intertwined with perception itself. We find that models that are trained by LABC to reason better by analogy are, perhaps surprisingly, also better able to extrapolate to a wider range of input values. Thus, making better analogies seems connected to the ability of models to perceive and represent their raw experience.Recent literature has questioned whether neural networks can generalise in systematic ways to data drawn from outside the training distribution BID17 . Our results show that neural networks are not fundamentally limited in this respect. Rather, the capacity needs to be coaxed out through careful learning. The data with which these networks learn, and the manner in which they learn it, are of paramount importance. Such a lesson is not new; indeed, the task of one-shot learning was thought to be difficult, if not impossible to perform using neural networks, but was nonetheless ""solved"" using appropriate training objectives, models, and optimization innovations (e.g., BID28 BID6 ). The insights presented here may guide promising, general purpose approaches to obtain similar successes in flexible, generalisable abstract reasoning.Earlier work on analogical reasoning in AI and cognitive science employed constructed symbolic stimuli or pre-processed perceptual input (Carbonell ( BID21 show how analogies can be made via non-parametric operations on vector-spaces of text-based word representations. While the input to our visual analogy model is less naturalistic than these latter cases, this permits clear control over the semantics of training or test data when designing and evaluating hypotheses. Our study is nonetheless the only that we are aware to demonstrates such flexible, generalisable analogy making in neural networks learning end-to-end from raw perception. It is therefore a proof of principle that even very basic neural networks have the potential for strong analogical reasoning and generalization.As discussed in Sec. 5.3, in many machine-learning contexts it may not be possible to know exactly what a 'good quality' negative example looks like. The experiments there show that, in such cases, we might still achieve notable improvements in generalization via methods that learn to play the role of teacher by presenting alternatives to the main (student) model, as per BID31 . This underlines the fact that, for established learning algorithms involving negative examples such as (noise) contrastive estimation BID36 BID13 or negative sampling BID21 , the way in which negative examples are selected can be critical 3 . It may also help to explain the power of methods like self-play BID32 , in which a model is encouraged to continually challenge itself by posing increasingly difficult learning challenges.Analogies as the functions of the mind To check whether a plate is on a table we can look at the space above the table, but to find out whether a picture is on a wall or a person is on a train, the equivalent check would fail. A single on function operating in the same way on all input domains could not explain these entirely divergent outcomes of function evaluation. On the other hand, it seems implausible that our cognitive system encodes the knowledge underpinning these apparently distinct applications of the on relation in entirely independent representations. The findings of this work argue instead for a different perspective; that a single concept of on is indeed exploited in each of the three cases, but that its meaning and representation is sufficiently abstract to permit flexible interaction with, and context-dependent adaptation to, each particular domain of application. If we equate this process with analogy-making, then analogies are something like the functions of the mind. We believe that greater focus on analogy may be critical for replicating human-like cognitive processes, and ultimately human-like intelligent behaviour, in machines. It may now be time to revisit the insights from past waves of AI research on analogy, while bringing to bear the tools, perspectives and computing power of the present day. It is interesting to consider to what extent the effects reported in this work can transfer to a wider class of learning and reasoning problems beyond classical analogies. The importance of teaching concepts (to humans or models) by contrasting with negative examples is relatively established in both cognitive science BID31 BID35 and educational research BID34 BID0 . Our results underline the importance of this principle when training modern neural networks to replicate human-like cognitive processes and reasoning from raw perceptual input. In cases where expert understanding of potential data exists, for instance in the case of active learning with human interaction, it provides a recipe for achieving more robust representations leading to far greater powers of generalization. We should aspire to select as negative examples those examples that are plausible considering the most abstract principles that describe the data.A further notable property of our trained networks is the fact they can resolve analogies (even those involving with unfamiliar input domains) in a single rollout (forward pass) of a recurrent network. This propensity for fast reasoning has an interesting parallel with the fast and instinctive way in which humans can execute visual analogical reasoning BID23 BID24 .","Analogical reasoning has been a principal focus various waves AI research. Analogy is particularly challenging machines requires relational structures represented can flexibly applied across diverse domains experience. study how analogical reasoning can be induced neural networks learn perceive reason raw visual data. find critical factor inducing capacity is not an elaborate architecture rather careful attention choice data manner which it is presented model. robust capacity analogical reasoning is induced when networks learn analogies contrasting abstract relational structures input domains training method uses input data force models learn important abstract features. Using technique demonstrate capacities complex visual symbolic analogy making generalisation even simplest neural network architectures. ability make analogies -that is,to flexibly map familiar relations one domain experience another -is fundamental ingredient human intelligence creativity BID10 BID14 BID16 BID20. noted instance BID15 analogies gave Roman scientists deeper understanding sound when they leveraged knowledge familiar source domain water waves sea better understand structure unfamiliar target domain acoustics Romans 'aligned' relational principles water waves periodicity bending round corners rebounding solids phenomena observed acoustics spite numerous perceptual physical differences water sound. flexible alignment mapping relational structure source target domains independent perceptual congruence is a prototypical example analogy making.It has proven particularly challenging replicate processes analogical thought machines. Many classical symbolic AI models lack flexibility apply predicates operations across diverse domains particularly may have never previously observed. is natural consider however whether strengths modern neural network-based models can be exploited solve difficult analogical problems given capacity represent stimuli different levels abstraction enable flexible context-dependent computation noisy ambiguous inputs.In work demonstrate well-known neural network architectures can indeed learn make analogies remarkable generality flexibility. ability however is is critically dependent method training call learning analogies contrasting abstract relational structure LABC show simple architectures can be trained using approach apply abstract relations never-before-seen source-target domain mappings even entirely unfamiliar target domains.Our work differs previous computational models analogy two important ways. First unlike previous neural network models analogy optimize single model perform stimulus representation cross-domain mapping jointly. allowsus explore potential benefit interactions perception representation inter-domain alignment question debate analogy literature BID8 number shapes increases go along panels2 Apply relation 1 target panels:darkness lines increases go along panels One shape Two shapes Three shapes results demonstrate LABC increases ability models generalize beyond distribution training data. effect is observed prototypical analogical processes involving novel domain mappings unfamiliar target domains FIG0. Interestingly also results moderate improvements how well models extrapolate perceptual input outside range training experience Experiment3 experiments show simple neural networks can learn make analogies visual symbolic inputs is is critically contingent way which they are trained;training correct answers should be contrasted alternative incorrect answers are plausible level relations rather simple perceptual attributes. is consistent SMT human analogy-making which highlights importance inter-domain comparison level abstract relational structures. time visual analogy domain which a model reflects idea analogy closely intertwined perception itself. find models are trained LABC reason better analogy are,perhaps surprisingly also better able extrapolate wider range input values. Thus making better analogies seems connected ability models perceive represent raw experience.Recent literature has questioned whether neural networks can generalise systematic ways data drawn outside training distribution BID17. results show neural networks are not fundamentally limited respect. Rather capacity needs coaxed careful learning. data which these networks learn manner which they learn are of paramount importance. lesson is not new;indeed task one-shot learning was thought difficult if not impossible perform using neural networks was nonetheless solved using appropriate training objectives models optimization innovations e.g BID28 BID6 insights presented may guide promising general purpose approaches obtain similar successes flexible generalisable abstract reasoning.Earlier work analogical reasoning AI cognitive science employed constructed symbolic stimuli pre-processed perceptual input Carbonell BID21 show how analogies can be made via non-parametric operations vector-spaces text-based word representations. input visual analogy model is less naturalistic latter cases permits clear control semantics training test data when designing evaluating hypotheses. study is nonetheless are aware demonstrates flexible generalisable analogy making neural networks learning end-to-end raw perception. is therefore proof principle even basic neural networks have the potential strong analogical reasoning generalization.As discussed Sec. 5.3 many machine-learning contexts may possible know exactly what a 'good quality' negative example looks like. experiments show cases might still achieve notable improvements generalization via methods learn play role teacher presenting alternatives main student model per BID31. underlines fact established learning algorithms involving negative examples noise contrastive estimation BID36 BID13 negative sampling BID21 way which negative examples are selected can be critical3. may also help explain power methods like self-play BID32 which a model is encouraged continually challenge posing increasingly difficult learning challenges.Analogies functions mind check whether plate is on a table can look space table find whether picture is on a wall person is on a train equivalent check would fail. single function operating way input domains could explain entirely divergent outcomes function evaluation. hand seems implausible cognitive system encodes knowledge underpinning apparently distinct applications relation entirely independent representations. findings work argue instead different perspective;single concept is indeed exploited three cases meaning representation is sufficiently abstract permit flexible interaction context-dependent adaptation particular domain application. If we equate process analogy-making analogies are something like functions mind. believe greater focus analogy may critical replicating human-like cognitive processes ultimately human-like intelligent behaviour machines. may time revisit insights past waves AI research analogy bringing bear tools perspectives computing power present day. is interesting consider what extent effects reported work can transfer wider class learning reasoning problems beyond classical analogies. importance teaching concepts humans models contrasting negative examples is relatively established cognitive science BID31 BID35 educational research BID34 BID0. results underline importance principle when training modern neural networks replicate human-like cognitive processes reasoning raw perceptual input. cases where expert understanding potential data exists instance case active learning human interaction provides recipe achieving robust representations leading far greater powers generalization. should aspire select negative examples examples are plausible considering abstract principles describe data.A notable property trained networks is the fact can resolve analogies even involving unfamiliar input domains single rollout forward pass recurrent network. propensity fast reasoning has an interesting parallel fast instinctive way which humans can execute visual analogical reasoning BID23 BID24.",1802,1207,595,0.022,1.493,2025/11/05 17:18:57,0.01,1.5,0.5077881619937696,579.231
"Building chatbots that can accomplish goals such as booking a flight ticket is an unsolved problem in natural language understanding. Much progress has been made to build conversation models using techniques such as sequence2sequence modeling. One challenge in applying such techniques to building goal-oriented conversation models is that maximum likelihood-based models are not optimized toward accomplishing goals. Recently, many methods have been proposed to address this issue by optimizing a reward that contains task status or outcome. However, adding the reward optimization on the fly usually provides little guidance for language construction and the conversation model soon becomes decoupled from the language model. In this paper, we propose a new setting in goal-oriented dialogue system to tighten the gap between these two aspects by enforcing model level information isolation on individual models between two agents. Language construction now becomes an important part in reward optimization since it is the only way information can be exchanged. We experimented our models using self-play and results showed that our method not only beat the baseline sequence2sequence model in rewards but can also generate human-readable meaningful conversations of comparable quality. Building chatbots that can naturally interact with human users has long been an important challenge in artificial intelligence and computer science BID15 . Recently, there is growing interest in applying end-to-end neural networks to this task with promising results BID16 BID12 BID13 . A compelling aspect of these models is that they require fewer hand-crafted rules compared to traditional models. Their success is however limited to conversations with very few turns and without any goals (also known as ""chitchat"").The goal of this work is to build goal-oriented conversational models. Here we use ""goal-oriented"" to mean that the model must accomplish a particular desired goal in the dialogue. Depending on the nature of the task, conversations can be as simple as few-round dialogues such as resetting passwords or it can involve back and forth investigations in the case of travel recommendation and IT support. Different from chitchat based conversation models, whose goal is to generate response without task restrictions, goal-oriented models will have to direct the conversations in a way that facilitates the progress of the task. For example in the case of flight booking, customers are only interested in moving the conversation forward if the flight recommendations meet their expectations. Similarly, agents are only supposed to make responses that will resolve customers' requests.Building goal-oriented conversational models presents a fresh challenge to neural network-based conversational models because their success in chitchat dialogues can not be easily transferred into the world of goal-oriented dialogues. Firstly, chitchat models trend to remember the exact settings of the context-response pairs. Due to the high variance of deep models, slight changes in the context such as cities, time or names will likely change the response completely. Although one can provide more training data to cover different combinations of these pieces of information, acquiring dialogue data for the exhaustive set of conditions is difficult or in many cases infeasible. Secondly, the fact that most chitchat models optimize the likelihood of the utterances makes it hard for them to generate responses that are less likely in general but are appropriate given the context of the task. The progress of the dialogue can easily get lost during the conversation and agents might not be able to reach to the optimal conclusion. And finally, while in most chitchat models, diversity of the responses is one of the key metrics, goal-oriented conversation models focus on robustness and reliability of the response especially in it's roles to guide the conversation.To address these problems, in this paper we propose a two-party model for goal-oriented conversation with each sub-model being responsible for its own utterances. We define the goal oriented conversation problem to be a dialogue cooperation with two agents each having access to some pieces of hidden information that is only visible to itself. One of the agents is required to come up with a series of ""action"", which correctness relies solely on the understanding of the hidden information. Although the exact form of the hidden information is not visible, it can be interpreted using natural language and be exchanged to the other party. In order to achieve this, agents need to establish a protocol to talk and complete the task correctly.The two-party architecture makes it feasible to conduct self-play between agents, which enables two conversation models to talk to itself without human supervision. Different from previous proposed self-play dialogue models such as the negotiation chatbot BID4 , our setting enforces the isolation of information between the models of the two agents, which ensure the coupling between task reward and language models. And because hidden information is not directly visible , agents will need to guide and structure the conversation in a proper way in order to acquire the key pieces of information that is required to generate the correct actions. This process can be naturally strengthened using self-play with reinforcement learning.Another benefit of the self-play model is the ability to utilize large scale un-supervised knowledge that is otherwise difficult to leverage. Training of dialogue models require lots of data but supervised conversation data are usually hard to acquire. Fortunately, it is usually easy to generate the initial conditions of the dialogue such as user restrictions available information in the database. Based on those initial settings, a rule based program is usually enough to generate action states, which constitutes a perfect reinforcement learning environment to estimate rewards. Using self-play to exchange hidden information, we can potentially leverage knowledge of a much larger scale and train a much more reliable chatbot.To validate the performance of the model we first trained a supervised model based on fully supervised dialogue utterance, action states and hidden conditions. The supervised model is then used as a bootstrap to initialize a self-play training model based on initial conditions without supervised dialogues. We evaluated both models on a held-out self-play data sets and observed 37 % performances improvements on average rewards for the agent learned from self-play. In this paper, we proposed a new approach to model goal-oriented conversations based on information isolation and action states. By leveraging supervised learning with self-plays on actions states, we expanded the coverage of the training significantly and exposed the model with unseen data. By enforcing information isolation, we tightly coupled dialogue data with action states. Results indicated self-play under those settings significantly improved the reward function compares to the supervised learning baseline. Since dialogue data is usually hard to get while action states can be acquired easily, our approach can be easily applied in those scenario where the amount of the data is a bottleneck to the performance of the system.",Building chatbots can accomplish goals booking flight ticket is an unsolved problem natural language understanding. Much progress has been made build conversation models using techniques sequence2sequence modeling. One challenge applying techniques building goal-oriented conversation models is that maximum likelihood-based models are not optimized toward accomplishing goals. Recently many methods have been proposed address issue optimizing reward contains task status outcome. However adding reward optimization fly usually provides little guidance language construction conversation model soon becomes decoupled language model. paper propose new setting goal-oriented dialogue system tighten gap two aspects enforcing model level information isolation individual models two agents. Language construction becomes important part reward optimization since is the only way information can be exchanged. experimented models using self-play results showed method beat baseline sequence2sequence model rewards can also generate human-readable meaningful conversations comparable quality. Building chatbots can naturally interact human users has long important challenge artificial intelligence computer science BID15. Recently is growing interest applying end-to-end neural networks task promising results BID16 BID12 BID13. compelling aspect models is that they require fewer hand-crafted rules compared traditional models. success is however limited conversations turns without goals also known chitchat.The goal work is to build goal-oriented conversational models. use goal-oriented mean model must accomplish particular desired goal dialogue. Depending nature task conversations can be as simple few-round dialogues resetting passwords can involve back forth investigations case travel recommendation support. Different chitchat based conversation models whose goal is to generate response without task restrictions goal-oriented models will have to direct conversations way facilitates progress task. example case flight booking customers are only interested moving conversation forward if the flight recommendations meet expectations. Similarly agents are only supposed make responses will resolve customers' requests.Building goal-oriented conversational models presents fresh challenge neural network-based conversational models success chitchat dialogues can not be can can be easily transferred world goal-oriented dialogues. Firstly chitchat models trend remember exact settings context-response pairs. Due high variance deep models slight changes context cities time names will likely change response completely. Although one can provide training data cover different combinations pieces information acquiring dialogue data exhaustive set conditions is difficult many cases infeasible. Secondly fact chitchat models optimize likelihood utterances makes hard generate responses are less likely general are appropriate given context task. progress dialogue can not be can can be easily get lost conversation agents might able reach optimal conclusion. finally chitchat models diversity responses is one key metrics goal-oriented conversation models focus robustness reliability response especially roles guide conversation.To address problems paper propose two-party model goal-oriented conversation sub-model responsible utterances. define goal oriented conversation problem dialogue cooperation two agents access pieces hidden information is only visible itself. One agents is required come series action which correctness relies solely understanding hidden information. Although exact form hidden information is not visible can be interpreted using natural language exchanged party. order achieve agents need establish protocol talk complete task correctly.The two-party architecture makes feasible conduct self-play agents which enables two conversation models talk without human supervision. Different previous proposed self-play dialogue models negotiation chatbot BID4 setting enforces isolation information models two agents which ensure coupling task reward language models. hidden information is not directly visible agents will need guide structure conversation proper way order acquire key pieces information is required generate correct actions. process can be naturally strengthened using self-play reinforcement learning.Another benefit self-play model is the ability utilize large scale un-supervised knowledge is otherwise difficult leverage. Training dialogue models require lots data supervised conversation data are usually hard acquire. Fortunately is usually easy generate initial conditions dialogue user restrictions available information database. Based initial settings rule based program is usually enough generate action states which constitutes perfect reinforcement learning environment estimate rewards. Using self-play exchange hidden information can potentially leverage knowledge much larger scale train much reliable chatbot.To validate performance model first trained supervised model based fully supervised dialogue utterance action states hidden conditions. supervised model is then used bootstrap initialize self-play training model based initial conditions without supervised dialogues. evaluated models held-out self-play data sets observed37% performances improvements average rewards agent learned self-play paper proposed new approach model goal-oriented conversations based information isolation action states. leveraging supervised learning self-plays actions states expanded coverage training significantly exposed model unseen data. enforcing information isolation tightly coupled dialogue data action states. Results indicated self-play settings significantly improved reward function compares supervised learning baseline. Since dialogue data is usually hard get action states can be acquired easily approach can not be can can be easily applied scenario where the amount data is a bottleneck performance system.,1269,870,399,0.013,1.459,2025/11/05 17:18:57,0.01,1.593,0.4018691588785047,429.157
"Search engine users nowadays heavily depend on query completion and correction to shape their queries.  Typically, the completion is done by database lookup which does not understand the context and cannot generalize to prefixes not in the database . In the paper, we propose to use unsupervised deep language models to complete and correct the queries given an arbitrary prefix .  We show how to address two main challenges that renders this method practical for large-scale deployment : 1) we propose a method for integrating error correction into the language model completion via a edit-distance potential and a variant of beam search that can exploit these potential functions; and 2) we show how to efficiently perform CPU-based computation to complete the queries, with error correction, in real time (generating top 10 completions within 16 ms). Experiments show that the method substantially increases hit rate over standard approaches, and is capable of handling tail queries.
 Search completion is the problem of taking a prefix of a search query from a user and generating several candidate completions. This problem has enormous potential utility and monetary value to any search provider: the more accurately an engine can find the desired completions for a user (or indeed, potentially steer the user towards high-value completions), the more quickly it can lead the user to their desired goal. This paper proposes a realtime search completion architecture based upon deep character-level language models. The basic idea is that instead of looking up possible completions from a generic database, we perform search under a deep-network-based language model to find the most likely completions of a user's current input. This allows us to integrate the power of deep language models, that has been shown to perform extremely well on complex language modeling and prediction tasks, with the desired goal of finding a good completion. Although this is a conceptually simple strategy (and one which has been considered before, as we highlight in the literature below), there are two key elements required to make this of practical use for a search engine provider, which together make up the primary technical contributions of the paper: 1) The completion must be error correcting, able to handle small errors in the user's initial input and provide completions for the most likely ""correct"" input. We propose such an approach that combines a character-level language model with an edit-distance-based potential function, combining the two using a tree-based beam search algorithm;2) The completion must be realtime, able to produce high-quality potential completions in a time that is not even perceivable to the user. We achieve this by developing an efficient tree-based version of the error-correcting beam search, exploiting CPU-based computation for single queries (due to the high levels of branching in the beam search), and through numerous optimizations to the implementation that we discuss below.We evaluate the method on the AOL search data set, a dataset consisting of over 36 million total search queries. In total, the method substantially outperforms highly optimized standard search completion algorithms in terms of its hit rate (the benefit of the deep language model and the error correction), while being fast enough to execute in real time for search engines. Experiments and code are all available online, and a real-time demo of the approach is available at http: //www.deepquerycompletion.com. In this paper, we presented a search query completion approach based upon character-level deep language models. We proposed a method for integrating the approach with an error correction framework and showed that candidate completions with error correction can be efficiently generated using beam search. We further described several optimizations that enabled the system to work in real time, including a CPU-based custom LSTM implementation. The method is able to jointly produce better completions than simple prefix lookup, while simultaneously being able to generate the candidates in real time.",Search engine users nowadays heavily depend query completion correction shape queries. Typically completion is done database lookup which does not understand context cannot generalize prefixes database. paper propose use unsupervised deep language models complete correct queries given arbitrary prefix. show how to address two main challenges renders method practical large-scale deployment:1 propose method integrating error correction language model completion via edit-distance potential variant beam search can exploit potential functions;2 show how to efficiently perform CPU-based computation complete queries error correction real time generating top 10 completions within16ms Experiments show method substantially increases hit rate standard approaches is capable handling tail queries. Search completion is the problem taking prefix search query user generating several candidate completions. problem has enormous potential utility monetary value search provider:accurately engine can find desired completions user indeed potentially steer user towards high-value completions quickly can lead user desired goal. paper proposes realtime search completion architecture based upon deep character-level language models. basic idea is that instead looking possible completions generic database perform search deep-network-based language model find likely completions user's current input. allowsus integrate power deep language models has been shown perform extremely well complex language modeling prediction tasks desired goal finding good completion. Although is a conceptually simple strategy one which has been considered highlight literature are two key elements required make practical use search engine provider which together make primary technical contributions paper:1 completion must error correcting able handle small errors user's initial input provide completions likely correct input. propose approach combines character-level language model edit-distance-based potential function combining two using tree-based beam search algorithm;2 completion must realtime able produce high-quality potential completions time is not even perceivable user. achieve developing efficient tree-based version error-correcting beam search exploiting CPU-based computation single queries due high levels branching beam search numerous optimizations implementation discuss below.We evaluate method AOL search data set dataset consisting 36 million total search queries. total method substantially outperforms highly optimized standard search completion algorithms terms hit rate benefit deep language model error correction fast enough execute real time search engines. Experiments code are all available online real-time demo approach is available http://www.deepquerycompletion.com. paper presented search query completion approach based upon character-level deep language models. proposed method integrating approach error correction framework showed candidate completions error correction can be efficiently generated using beam search. described several optimizations enabled system work real time including CPU-based custom LSTM implementation. method is able jointly produce better completions simple prefix lookup simultaneously able generate candidates real time.,752,493,259,0.007,1.525,2025/11/05 17:18:57,0.0,1.619,0.6074766355140183,270.453
"RMSProp and ADAM continue to be extremely popular algorithms for training neural nets but their theoretical convergence properties have remained unclear. Further, recent work has seemed to suggest that these algorithms have worse generalization properties when compared to carefully tuned stochastic gradient descent or its momentum variants. In this work, we make progress towards a deeper understanding of ADAM and RMSProp in two ways. First, we provide proofs that these adaptive gradient algorithms are guaranteed to reach criticality for smooth non-convex objectives, and we give bounds on the running time.

 Next we design experiments to empirically study the convergence and generalization properties of RMSProp and ADAM against Nesterov's Accelerated Gradient method on a variety of common autoencoder setups and on VGG-9 with CIFAR-10. Through these experiments we demonstrate the interesting sensitivity that ADAM has to its momentum parameter \beta_1. We show that at very high values of the momentum parameter (\beta_1 = 0.99) ADAM outperforms a carefully tuned NAG on most of our experiments, in terms of getting lower training and test losses. On the other hand, NAG can sometimes do better when ADAM's \beta_1 is set to the most commonly used value: \beta_1 = 0.9, indicating the importance of tuning the hyperparameters of ADAM to get better generalization performance.

 We also report experiments on different autoencoders to demonstrate that NAG has better abilities in terms of reducing the gradient norms, and it also produces iterates which exhibit an increasing trend for the minimum eigenvalue of the Hessian of the loss function at the iterates. Many optimization questions arising in machine learning can be cast as a finite sum optimization problem of the form: min x f (x) where f (x) = 1 k k i=1 f i (x). Most neural network problems also fall under a similar structure where each function f i is typically non-convex. A well-studied algorithm to solve such problems is Stochastic Gradient Descent (SGD), which uses updates of the form: x t+1 := x t − α∇f it (x t ), where α is a step size, andf it is a function chosen randomly from {f 1 , f 2 , . . . , f k } at time t. Often in neural networks, ""momentum"" is added to the SGD update to yield a two-step update process given as: v t+1 = µv t − α∇f it (x t ) followed by x t+1 = x t + v t+1 . This algorithm is typically called the Heavy-Ball (HB) method (or sometimes classical momentum), with µ > 0 called the momentum parameter (Polyak, 1987) . In the context of neural nets, another variant of SGD that is popular is Nesterov's Accelerated Gradient (NAG), which can also be thought of as a momentum method (Sutskever et al., 2013) , and has updates of the form v t+1 = µv t − α∇f it (x t + µv t ) followed by x t+1 = x t + v t+1 (see Algorithm 1 for more details).Momentum methods like HB and NAG have been shown to have superior convergence properties compared to gradient descent in the deterministic setting both for convex and non-convex functions (Nesterov, 1983; Polyak, 1987; Zavriev & Kostyuk, 1993; Ochs, 2016; O'Neill & Wright, 2017; Jin et al., 2017) . While (to the best of our knowledge) there is no clear theoretical justification in the stochastic case of the benefits of NAG and HB over regular SGD in general (Yuan et al., 2016; Kidambi et al., 2018; Wiegerinck et al., 1994; Orr & Leen, 1994; Yang et al., 2016; Gadat et al., 2018) , unless considering specialized function classes (Loizou & Richtárik, 2017) ; in practice, these momentum methods, and in particular NAG, have been repeatedly shown to have good convergence and generalization on a range of neural net problems (Sutskever et al., 2013; Lucas et al., 2018; Kidambi et al., 2018) .The performance of NAG (as well as HB and SGD), however, are typically quite sensitive to the selection of its hyper-parameters: step size, momentum and batch size (Sutskever et al., 2013) . Thus, ""adaptive gradient"" algorithms such as RMSProp (Algorithm 2) (Tieleman & Hinton, 2012) and ADAM (Algorithm 3) (Kingma & Ba, 2014) have become very popular for optimizing deep neural networks (Melis et al., 2017; Xu et al., 2015; Denkowski & Neubig, 2017; Gregor et al., 2015; Radford et al., 2015; Bahar et al., 2017; Kiros et al., 2015) . The reason for their widespread popularity seems to be the fact that they are believed to be easier to tune than SGD, NAG or HB. Adaptive gradient methods use as their update direction a vector which is the image under a linear transformation (often called the ""diagonal pre-conditioner"") constructed out of the history of the gradients, of a linear combination of all the gradients seen till now. It is generally believed that this ""pre-conditioning"" makes these algorithms much less sensitive to the selection of its hyperparameters. A precursor to these RMSProp and ADAM was outlined in Duchi et al. (2011) .Despite their widespread use in neural net problems, adaptive gradients methods like RMSProp and ADAM lack theoretical justifications in the non-convex setting -even with exact/deterministic gradients (Bernstein et al., 2018) . Further, there are also important motivations to study the behavior of these algorithms in the deterministic setting because of usecases where the amount of noise is controlled during optimization, either by using larger batches (Martens & Grosse, 2015; De et al., 2017; Babanezhad et al., 2015) or by employing variance-reducing techniques (Johnson & Zhang, 2013; Defazio et al., 2014) .Further, works like Wilson et al. (2017) and Keskar & Socher (2017) have shown cases where SGD (no momentum) and HB (classical momentum) generalize much better than RMSProp and ADAM with stochastic gradients. Wilson et al. (2017) also show that ADAM generalizes poorly for large enough nets and that RMSProp generalizes better than ADAM on a couple of neural network tasks (most notably in the character-level language modeling task). But in general it's not clear and no heuristics are known to the best of our knowledge to decide whether these insights about relative performances (generalization or training) between algorithms hold for other models or carry over to the full-batch setting.A summary of our contributions In this work we try to shed some light on the above described open questions about adaptive gradient methods in the following two ways.• To the best of our knowledge, this work gives the first convergence guarantees for adaptive gradient based standard neural-net training heuristics. Specifically we show run-time bounds for deterministic RMSProp and ADAM to reach approximate criticality on smooth non-convex functions, as well as for stochastic RMSProp under an additional assumption. Recently, Reddi et al. (2018) have shown in the setting of online convex optimization that there are certain sequences of convex functions where ADAM and RMSprop fail to converge to asymptotically zero average regret. We contrast our findings with Theorem 3 in Reddi et al. (2018) . Their counterexample for ADAM is constructed in the stochastic optimization framework and is incomparable to our result about deterministic ADAM. Our proof of convergence to approximate critical points establishes a key conceptual point that for adaptive gradient algorithms one cannot transfer intuitions about convergence from online setups to their more common use case in offline setups.• Our second contribution is empirical investigation into adaptive gradient methods, where our goals are different from what our theoretical results are probing. We test the convergence and generalization properties of RMSProp and ADAM and we compare their performance against NAG on a variety of autoencoder experiments on MNIST data, in both full and mini-batch settings. In the full-batch setting, we demonstrate that ADAM with very high values of the momentum parameter (β 1 = 0.99) matches or outperforms carefully tuned NAG and RMSProp, in terms of getting lower training and test losses. We show that as the autoencoder size keeps increasing, RMSProp fails to generalize pretty soon. In the mini-batch experiments we see exactly the same behaviour for large enough nets. We further validate this behavior on an image classification task on CIFAR-10 using a VGG-9 convolutional neural network, the results to which we present in the Appendix E. We note that recently it has been shown by Lucas et al. (2018) , that there are problems where NAG generalizes better than ADAM even after tuning β 1 . In contrast our experiments reveal controlled setups where tuning ADAM's β 1 closer to 1 than usual practice helps close the generalization gap with NAG and HB which exists at standard values of β 1 .Remark. Much after this work was completed we came to know of a related paper ( Li & Orabona, 2018 ) which analyzes convergence rates of a modification of AdaGrad (not RMSPRop or ADAM).After the initial version of our work was made public, a few other analysis of adaptive gradient methods have also appeared like Chen et al. (2018) , Zhou et al. (2018) and Zaheer et al. (2018) . To the best of our knowledge, we present the first theoretical guarantees of convergence to criticality for the immensely popular algorithms RMSProp and ADAM in their most commonly used setting of optimizing a non-convex objective.By our experiments, we have sought to shed light on the important topic of the interplay between adaptivity and momentum in training nets. By choosing to study textbook autoencoder architectures where various parameters of the net can be changed controllably we highlight the following two aspects that (a) the value of the gradient shifting hyperparameter ξ has a significant influence on the performance of ADAM and RMSProp and (b) ADAM seems to perform particularly well (often supersedes Nesterov accelerated gradient method) when its momentum parameter β 1 is very close to 1. On VGG-9 with CIFAR-10 and for the task of training autoencoders on MNIST we have verified these conclusions across different widths and depths of nets as well as in the full-batch and the mini-batch setting (with large nets) and under compression of the input/out image size. Curiously enough, this regime of β 1 being close to 1 is currently not within the reach of our proof techniques of showing convergence for ADAM. Our experiments give strong reasons to try to advance theory in this direction in future work.Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. Now we give the proof of Theorem 3.1.Proof. We define σ t := max k=1,.. ,t ∇f i k (x k ) and we solve the recursion for v t as, DISPLAYFORM0 . This lets us write the following bounds, DISPLAYFORM1 i and this lets us get the following bounds, DISPLAYFORM2 Now we invoke the bounded gradient assumption about the f i functions and replace in the above equation the eigenvalue bounds of the pre-conditioner by worst-case estimates µ max and µ min defined as, DISPLAYFORM3 Using the L-smoothness of f between consecutive iterates x t and x t+1 we have, DISPLAYFORM4 We note that the update step of stochastic RMSProp is x t+1 = x t − α(V t ) − 1 2 g t where g t is the stochastic gradient at iterate x t . Let H t = {x 1 , x 2 , .., x t } be the set of random variables corresponding to the first t iterates. The assumptions we have about the stochastic oracle give us the following relations, DISPLAYFORM5 f . Now we can invoke these stochastic oracle's properties and take a conditional (on H t ) expectation over g t of the L−smoothness in equation to get, DISPLAYFORM6 We now separately analyze the middle term in the RHS above in Lemma A.1 below and we get, DISPLAYFORM7 We substitute the above into equation 1 and take expectations over H t to get, DISPLAYFORM8 Doing the above replacements to upperbound the RHS of equation 2 and summing the inequation over t = 1 to t = T and taking the average and replacing the LHS by a lowerbound of it, we get, DISPLAYFORM9 Replacing into the RHS above the optimal choice of, DISPLAYFORM10 Thus stochastic RMSProp with the above step-length is guaranteed is reach −criticality in number of iterations given by, T ≤ DISPLAYFORM11 Lemma A.1. At any time t, the following holds, DISPLAYFORM12 Proof. DISPLAYFORM13 Now we introduce some new variables to make the analysis easier to present. Let a pi := [∇f p (x t )] i where p indexes the training data set, p ∈ {1, . . . , k}. (conditioned on H t , a pi s are constants) This implies, DISPLAYFORM14 where the expectation is taken over the oracle call at the t th update step. Further our instantiation of the oracle is equivalent to doing the uniformly at random sampling, (g t ) i ∼ {a pi } p=1,...,k .Given that we have, DISPLAYFORM15 i +di where we have defined DISPLAYFORM16 This leads to an explicit form of the needed expectation over the t th −oracle call as, DISPLAYFORM17 Substituting the above (and the definition of the constants a pi ) back into equation 3 we have, DISPLAYFORM18 Substituting this, the above expression can be written as, DISPLAYFORM19 Note that with this substitution, the RHS of the claimed lemma becomes, DISPLAYFORM20 Therefore our claim is proved if we show that for all i, DISPLAYFORM21 To further simplify, we define DISPLAYFORM22 −µ min . We therefore need to show, DISPLAYFORM23 We first bound d i by recalling the definition of σ f (from which it follows that a 2 pi ≤ σ 2 f ), DISPLAYFORM24 The inequality follows since β 2 ∈ (0, 1]Putting this all together, we get, DISPLAYFORM25 Now our assumption that for all x, sign(∇f p (x)) = sign(∇f q (x)) for all p, q ∈ {1, . . . , k} leads to the conclusion that the term a pi a qi ≥ 0. And we had already shown in equation 5 that DISPLAYFORM26 Thus we have shown that (a i 1 k )(q i a i ) ≥ 0 and this finishes the proof.","RMSProp ADAM continue extremely popular algorithms training neural nets theoretical convergence properties have remained unclear. recent work has seemed suggest algorithms have worse generalization properties when compared carefully tuned stochastic gradient descent momentum variants. work make progress towards deeper understanding ADAM RMSProp two ways. First provide proofs adaptive gradient algorithms are guaranteed reach criticality smooth non-convex objectives give bounds running time. Next design experiments empirically study convergence generalization properties RMSProp ADAM Nesterov's Accelerated Gradient method variety common autoencoder setups VGG-9 CIFAR-10 experiments demonstrate interesting sensitivity ADAM has to its momentum momentum parameter \beta_1 show high values momentum parameter \beta_1 0.99 ADAM outperforms carefully tuned NAG experiments terms getting lower training test losses. hand NAG can sometimes do better when ADAM's \beta_1 is set commonly used value:\beta_1 0.9 indicating importance tuning hyperparameters ADAM get better generalization performance. also report experiments different autoencoders demonstrate NAG has better abilities terms reducing gradient norms also produces iterates which exhibit increasing trend minimum eigenvalue Hessian loss function iterates. Many optimization questions arising machine learning can be cast finite sum optimization problem form:minxf x wheref x 1 k k i=1 f x neural network problems also fall similar structure where each functionf is typically typically non-convex well-studied algorithm solve problems is Stochastic Gradient Descent SGD which uses updates form:x+1:x − α∇f x whereα is a step size andf is a function chosen randomly f1 f2 fk time t. Often neural networks momentum is added SGD update yield two-step update process given as:v+1 µv − α∇f x followed x+1 x+v+1. algorithm is typically called Heavy-Ball HB method sometimes classical momentum µ 0 called momentum parameter Polyak 1987 context neural nets another variant SGD is popular is Nesterov's Accelerated Gradient NAG which can also thought momentum method Sutskeveretal. 2013 has updates formv+1 µv − α∇f x+µv followed x+1 x+v+1 see Algorithm1 details.Momentum methods likeHB NAG have been shown have superior convergence properties compared gradient descent deterministic setting convex non-convex functions Nesterov 1983;Polyak 1987;Zavriev Kostyuk 1993;Ochs 2016;Neill Wright 2017;Jinetal. 2017 best knowledge is no clear theoretical justification stochastic case benefits NAG HB regular SGD general Yuanetal. 2016;Kidambietal. 2018;Wiegerincketal. 1994;Orr Leen 1994;Yangetal. 2016;Gadatetal. 2018 unless considering specialized function classes Loizou Richtárik 2017 practice momentum methods particular NAG have been repeatedly shown have good convergence generalization range neural net problems Sutskeveretal. 2013;Lucasetal. 2018;Kidambietal. 2018.The performance NAG well HB SGD however are typically quite sensitive selection hyper-parameters step size momentum batch size Sutskeveretal. 2013 Thus adaptive gradient algorithms RMSProp Algorithm2 Tieleman Hinton 2012 ADAM Algorithm3 Kingma Ba 2014 have become popular optimizing deep neural networks Melisetal. 2017;Xuetal. 2015;Denkowski Neubig 2017;Gregoretal. 2015;Radfordetal. 2015;Baharetal. 2017;Kirosetal. 2015 reason widespread popularity seems fact are believed easier tune SGD NAG HB. Adaptive gradient methods use update direction vector which is the image linear transformation often called diagonal pre-conditioner constructed history gradients linear combination gradients seen till now. is generally believed pre-conditioning makes algorithms much less sensitive selection hyperparameters. precursor RMSProp ADAM was outlined Duchietal. 2011.Despite widespread use neural net problems adaptive gradients methods like RMSProp ADAM lack theoretical justifications non-convex setting -even exact/deterministic gradients Bernsteinetal. 2018 which can are also important motivations study behavior algorithms deterministic setting usecases where the amount noise is controlled optimization either using larger batches Martens Grosse 2015;Deetal. 2017;Babanezhadetal. 2015 employing variance-reducing techniques Johnson Zhang 2013;Defazioetal. 2014.Further works like Wilsonet al. 2017 Keskar Socher 2017 have shown cases where SGD momentum HB classical momentum generalize much better RMSProp ADAM stochastic gradients. Wilsonetal. 2017 which can also show ADAM generalizes poorly large enough nets RMSProp generalizes better ADAM couple neural network tasks notably character-level language modeling task general clear heuristics are known best knowledge decide whether insights relative performances generalization training algorithms hold models carry full-batch setting.A summary contributions work try shed light described open questions adaptive gradient methods following two ways.• best knowledge work gives first convergence guarantees adaptive gradient based standard neural-net training heuristics. Specifically show run-time bounds deterministic RMSProp ADAM reach approximate criticality smooth non-convex functions well stochastic RMSProp additional assumption. Recently Reddietal. 2018 have shown setting online convex optimization are certain sequences convex functions where ADAM RMSprop fail converge asymptotically zero average regret. contrast findings Theorem3 Reddietal. 2018 counterexample ADAM is constructed stochastic optimization framework is incomparable result deterministic ADAM. proof convergence approximate critical points establishes key conceptual point adaptive gradient algorithms one cannot transfer intuitions convergence online setups common use case offline setups.• second contribution is empirical investigation adaptive gradient methods where our goals are different what our theoretical results are probing. test convergence generalization properties RMSProp ADAM compare performance NAG variety autoencoder experiments MNIST data full mini-batch settings. full-batch setting demonstrate ADAM high values momentum parameter β1 0.99 matches outperforms carefully tuned NAG RMSProp terms getting lower training test losses. show autoencoder size keeps increasing RMSProp fails generalize pretty soon. mini-batch experiments see exactly behaviour large enough nets. validate behavior image classification task CIFAR-10 using VGG-9 convolutional neural network results which we present AppendixE. note recently has been shown Lucasetal. 2018 are problems where NAG generalizes better ADAM even tuningβ1. contrast experiments reveal controlled setups where tuning ADAM'sβ1 closer 1 usual practice helps close generalization gap NAG HB which exists standard values β 1.Remark Much work was completed came know related paper Li Orabona 2018 which analyzes convergence rates modification AdaGrad RMSPRop ADAM.After initial version work was made public analysis adaptive gradient methods have also appeared like Chen etal. 2018 Zhouetal. 2018 Zaheeretal. 2018 best knowledge present first theoretical guarantees convergence criticality immensely popular algorithms RMSProp ADAM commonly used setting optimizing non-convex objective.By experiments have sought shed light important topic interplay adaptivity momentum training nets. choosing study textbook autoencoder architectures where various parameters net can be changed controllably highlight following two aspects value gradient shifting hyperparameterξ has a significant influence performance ADAM RMSProp b ADAM seems perform particularly well often supersedes Nesterov accelerated gradient method when its momentum parameterβ1 is very close 1. VGG-9 CIFAR-10 task training autoencoders MNIST have verified conclusions across different widths depths nets well full-batch mini-batch setting large nets compression input/image size. Curiously enough regime β1 close 1 is currently within reach proof techniques showing convergence ADAM. experiments give strong reasons try advance theory direction future work.Ilya Sutskever James Martens George Dahl Geoffrey Hinton. give proof Theorem3. 1.Proof. defineσ t:max k=1.. ∇f k xk solve recursion v DISPLAYFORM0. lets us write following bounds DISPLAYFORM1 lets us get following bounds DISPLAYFORM2 can invoke bounded gradient assumption f functions replace equation eigenvalue bounds pre-conditioner worst-case estimates µ max µ min defined DISPLAYFORM3 Using L-smoothness f consecutive iteratesx x+1 have,DISPLAYFORM4 note update step stochastic RMSProp isx+1 x −α V −12g whereg is the stochastic gradient iteratex t. LetH x1 x2.. x set random variables corresponding first iterates. assumptions have about the stochastic oracle giveus following relations DISPLAYFORM5f. can invoke stochastic oracle's properties take conditional H expectation g L−smoothness equation get DISPLAYFORM6 separately analyze middle term RHS Lemma A.1 get DISPLAYFORM7 substitute equation1 take expectations H get DISPLAYFORM8 replacements upperbound RHS equation2 summing inequation 1 taking average replacing LHS lowerbound get DISPLAYFORM9 Replacing RHS optimal choice DISPLAYFORM10 Thus stochastic RMSProp step-length is guaranteed is reach −criticality number iterations given ≤ DISPLAYFORM11 Lemma A.1 time following holds DISPLAYFORM12 Proof. DISPLAYFORM13 introduce new variables make analysis easier which we present. Let pi:∇fp x where p indexes training data set p∈ 1 k conditioned H pi are constants implies DISPLAYFORM14 where the expectation is taken oracle call th update step. instantiation oracle is equivalent uniformly random sampling g ∼ pi p=1... k.Given have,DISPLAYFORM15+di where we have defined DISPLAYFORM16 leads explicit form needed expectation th −oracle call DISPLAYFORM17 Substituting definition constants pi back equation3 have,DISPLAYFORM18 Substituting expression can be written DISPLAYFORM19 Note substitution RHS claimed lemma becomes DISPLAYFORM20 Therefore claim is proved if we show DISPLAYFORM21 simplify define DISPLAYFORM22 −µ min. therefore need show DISPLAYFORM23 first bound recalling definition σf which it follows 2pi≤σ 2f DISPLAYFORM24 inequality follows sinceβ 2∈ 0 1 Putting together get DISPLAYFORM25 assumption x sign ∇fp x sign ∇fq x p q∈ 1 k leads conclusion term pi qi≥0. had already shown equation5 DISPLAYFORM26 Thus have shown 1k q ≥0 finishes proof.",3228,2116,1112,0.065,1.526,2025/11/05 17:18:57,0.02,1.376,0.6105919003115264,1050.363
"Recent advances in adversarial Deep Learning (DL) have opened up a new and largely unexplored surface for malicious attacks jeopardizing the integrity of autonomous DL systems. We introduce a novel automated countermeasure called Parallel Checkpointing Learners (PCL) to thwart the potential adversarial attacks and significantly improve the reliability (safety) of a victim DL model. The proposed PCL methodology is unsupervised, meaning that no adversarial sample is leveraged to build/train parallel checkpointing learners. We formalize the goal of preventing adversarial attacks as an optimization problem to minimize the rarely observed regions in the latent feature space spanned by a DL network. To solve the aforementioned minimization problem, a set of complementary but disjoint checkpointing modules are trained and leveraged to validate the victim model execution in parallel. Each checkpointing learner explicitly characterizes the geometry of the input data and the corresponding high-level data abstractions within a particular DL layer. As such, the adversary is required to simultaneously deceive all the defender modules in order to succeed. We extensively evaluate the performance of the PCL methodology against the state-of-the-art attack scenarios, including Fast-Gradient-Sign (FGS), Jacobian Saliency Map Attack (JSMA), Deepfool, and Carlini&WagnerL2 algorithm. Extensive proof-of-concept evaluations for analyzing various data collections including MNIST, CIFAR10, and ImageNet corroborate the effectiveness of our proposed defense mechanism against adversarial samples. Security and safety consideration is a major obstacle to the wide-scale adoption of emerging learning algorithms in sensitive scenarios, such as intelligent transportation, healthcare, and video surveillance applications BID18 ; BID5 ; BID12 ). While advanced learning technologies are essential for enabling coordination and interaction between the autonomous agents and the environment, a careful analysis of their decision reliability in the face of carefully crafted adversarial samples ; ; BID22 ; BID3 ) and thwarting their vulnerabilities are still in their infancy.Consider a traffic sign classifier employed in self-driving cars. In this setting, an adversary can carefully add imperceptible perturbation to a legitimate ""stop"" sign sample and fool the DL model to classify it as a ""yield"" sign; thus, jeopardizes the safety of the vehicle as shown in BID18 ). As such, it is highly important to reject risky adversarial samples to ensure the integrity of DL models used in autonomous systems such as unmanned vehicles and drones. In this paper, we aim to answer two open questions regarding the adversarial attacks.(i ) Why are machine learning models vulnerable to adversarial samples? Our hypothesis is that the vulnerability of neural networks to adversarial samples originates from the existence of rarely explored sub-spaces in each feature map. This phenomenon is particularly caused by the limited access to the labeled data and/or inefficiency of regularization algorithms BID30 ; BID7 ). Figure 1 provides a simple illustration of the partially explored space in a twodimensional setup. We analytically and empirically back up our hypothesis by extensive evaluations on the state-of-the-art attacks, including Fast-Gradient-Sign ), Jacobian Saliency Map Attack ), Deepfool BID22 ), and Carlini&WagnerL2 BID3 ).(ii) How can we characterize and thwart the underlying space for unsupervised model assurance as well as defend against the adversaries? A line of research has shown that there is a trade-off between the robustness of a model and its accuracy BID17 ; BID25 ). Taking this into account , instead of making a single model that is both robust and accurate, we introduce a new defense mechanism called Parallel Checkpointing Learners (PCL) . In this setting, the victim model is kept as is while separate defender modules are trained to checkpoint the data abstractions and assess the reliability of the victim's prediction. Each defender module characterizes the explored sub-space in the pertinent layer by learning the probability density function (pdf) of legitimate data points and marking the complement sub-spaces as rarely observed regions. Once such characterization is obtained , the checkpointing modules 1 evaluate the input sample in parallel with the victim model and raise alarm flags for data points that lie within the rarely explored regions ( Figure 1c ). As we demonstrate in Section 4, adversarial samples created by various attack methods mostly lie within the sub-spaces marked as partially explored sectors.We consider a white-box attack model in which the attacker knows everything about the victim model including its architecture, learning algorithm, and parameters. This threat model represents the most powerful attacker that can endanger the real-world applications. We validate the security of our proposed approach for different DL benchmarks including MNIST, CIFAR10, and a subset of ImageNet data. Based on the result of our analysis, we provide new insights on the reason behind the existence of adversarial transferability. We open-source our API to ensure ease of use by the users (the link is omitted for blind review purposes) and invite the community to attempt attacks against our provided benchmarks in the form of a challenge.The explicit contribution of this paper is as follows: (i) Devising an automated end-to-end framework for unsupervised model assurance as well as defending against the adversaries. (ii) Incepting the idea of parallel checkpointing learners to validate the legitimacy of data abstractions at each intermediate DL layer. (iii) Performing extensive proof-of-concept evaluations against state-of-the-art attack methods. (iv) Providing new insights regarding the transferability of adversarial samples in between different models. Figure 1: (a) In this example, data points (denoted by green and blue squares) can be easily separated in one-dimensional space. Having extra dimensions adds ambiguity in choosing the pertinent decision boundaries. For instance, all the shown boundaries (dashed lines) are sufficient to classify the raw data with full accuracy in two-dimensional space but are not equivalent in terms of robustness to noise. (b) The rarely explored space (region specified by diagonal striped) in a learning model leaves room for adversaries to manipulate the nuisance (non-critical) variables and mislead the model by crossing the decision boundaries. (c) In PCL methodology, a set of defender (checkpoint) modules is trained to characterize the data density distribution in the space spanned by the victim model. The defender modules are then used in parallel to checkpoint the reliability of the ultimate prediction and raise an alarm flag for risky samples. Note that the remaining adversarial samples that are not detected in this experiment are crafted from legitimate samples that are inherently hard to classify even by a human observer due to the closeness of decision boundaries corresponding to such classes. For instance, in the MNIST application, such adversarial samples mostly belong to class 5 that is misclassified to class 3 or class 4 misclassified as 9. Such misclassifications are indeed the model approximation error which is well-understood to the statistical nature of the models. As such, a more precise definition of adversarial samples DISPLAYFORM0 Figure 9: Example adversarial confusion matrix (a) without PCL defense mechanism, and (b) with PCL defense and a security parameter of (1%). (c) Example adversarial samples for which accurate detection is hard due to the closeness of decision boundaries for the corresponding classes.is extremely required to distinguish malicious samples form those that simply lie near the decision boundaries.We emphasize that the PCL defenders are trained in an unsupervised setting independent of the attack strategy, meaning that no adversarial sample is used to train the defender models. This is particularly important as it corroborates the effectiveness of the proposed countermeasure in the face of generic attack scenarios including possible future adversarial DL algorithms. Nevertheless, one might question the effectiveness of the proposed approach for adaptive attack algorithms that target the defender modules. A comprehensive study of possible adaptive attack algorithms is yet to be performed if such attacks are developed in the future. We emphasize that, thus far, we have been able to significantly thwart all the existing attacks with only one checkpoint model approximating the data distribution in the second-to-last layer of the corresponding models. Our proposed PCL methodology, however, provides a rather more generic approach that can be adapted/modified against potential future attacks by training parallel disjoint models (with diverse objectives/parameters) to further strengthen the defense.Figure 10 demonstrate how using multiple checkpoints with a negative correlation in parallel can effectively reduce the number of false alarms while increasing the detection rate of adversarial samples. In this experiment, we have considered MNIST data classification using LeNet model with 4 layers and FGS attack. The checkpoints are inserted in different layers of the pertinent neural network (first layer up to the second-to-last layer). We empirically select the mixing coefficients to aggregate the confidence of the checkpoint defenders for rejecting an incoming sample. Note that, there is a trade-off between the computational complexity (e.g., runtime overhead) of the PCL defenders and the reliability of the overall system. On the one hand, a high number of validation checkpoints increases the reliability of the systems, but it also increases the computational load as each input sample should be validated by more defender networks. On the other hand, a small number of checkpoints may degrade the defense mechanism performance by treating adversarial samples as legitimate ones. We are looking into automated techniques to customize the number of checkpoint modules and their corresponding mixing coefficients based on application data and physical constraints such as real-time analysis requirement as future work. This paper proposes a novel end-to-end methodology for characterizing and thwarting adversarial DL space. We introduce the concept of parallel checkpointing learners as a viable countermeasure to significantly reduce the risk of integrity attacks. The proposed PCL methodology explicitly characterizes statistical properties of the features within different layers of a neural network by learning a set of complementary dictionaries and corresponding probability density functions. The effectiveness of the PCL approach is evaluated against the state-of-the-art attack models including FGS, JSMA, Deepfool, and Carlini&WagnerL2. Proof-of-concept experiments for analyzing various data collections including MNIST, CIFAR10, and a subset of the ImageNet dataset corroborate successful detection of adversarial samples with relatively small false-positive rates.We devise an open-source API for the proposed countermeasure and invite the community to attempt attacks against the provided benchmarks in the form of a challenge. Table 2 presents the neural network architectures for the victim models used in each benchmark. The network for MNIST is the popular LeNet-3 architecture, the CIFAR-10 architecture is taken from BID4 , and the ImageNet model is inspired by the AlexNet architecture BID14 ). Table 2 : Baseline (victim) network architectures for evaluated benchmarks. Here, 128C3(2) denotes a convolutional layer with 128 maps and 3 × 3 filters applied with a stride of 2, MP3(2) indicates a max-pooling layer over regions of size 3 × 3 and stride of 2, and 300FC is a fully-connected layer consisting of 300 neurons. All convolution and fully connected layers (except the last layer) are followed by ReLU activation. A Softmax activation is applied to the last layer of each network. We visually evaluate the perturbed examples to determine the attack parameters (e.g., perturbation level ε and n iters ) such that the perturbations cannot be recognized by a human observer. Table 3 details the parameters used for the realization of different attack algorithms. The JSMA attack for the ImageNet benchmark is computationally expensive (e.g., it took more than 20min to generate one adversarial sample on an NVIDIA TITAN Xp GPU). As such, we could not generate the adversarial samples of this attack using the JSMA library provided by (Nicolas Papernot (2017) ). Table 3 : Details of attack algorithms for each evaluated application. The FGS method ) is characterized with a single ε parameter. The JSMA attack ) has two parameters: γ specifies the maximum percentage of perturbed features and θ denotes the value added to each selected feature. The Deepfool attack BID22 ) is characterized by the number of iterative updates, which we denote by n iters in this table. For the Carlini&WagnerL2 attack BID3 ), ""C"" denotes the confidence, ""LR"" is the learning rate, ""steps"" is the number of binary search steps, and ""iterations"" stands for the maximum number of iterations.",Recent advances adversarial Deep Learning DL have opened new largely unexplored surface malicious attacks jeopardizing integrity autonomous DL systems. introduce novel automated countermeasure called Parallel Checkpointing Learners PCL thwart potential adversarial attacks significantly improve reliability safety victim DL model. proposed PCL methodology is unsupervised meaning adversarial sample is leveraged build/train parallel checkpointing learners. formalize goal preventing adversarial attacks optimization problem minimize rarely observed regions latent feature space spanned DL network. solve aforementioned minimization problem set complementary disjoint checkpointing modules are trained leveraged validate victim model execution parallel. checkpointing learner explicitly characterizes geometry input data corresponding high-level data abstractions within particular DL layer. adversary is required simultaneously deceive defender modules order succeed. extensively evaluate performance PCL methodology state-of-the-art attack scenarios including Fast-Gradient-Sign FGS Jacobian Saliency Map Attack JSMA Deepfool Carlini WagnerL2 algorithm. Extensive proof-of-concept evaluations analyzing various data collections including MNIST CIFAR10 ImageNet corroborate effectiveness proposed defense mechanism adversarial samples. Security safety consideration is a major obstacle wide-scale adoption emerging learning algorithms sensitive scenarios intelligent transportation healthcare video surveillance applications BID18;BID5;BID12 advanced learning technologies are essential enabling coordination interaction autonomous agents environment careful analysis decision reliability face carefully crafted adversarial samples;BID22;BID3 thwarting vulnerabilities are still infancy.Consider traffic sign classifier employed self-driving cars. setting adversary can carefully add imperceptible perturbation legitimate stop sign sample fool DL model classify yield sign;thus jeopardizes safety vehicle shown BID18 is highly important reject risky adversarial samples ensure integrity DL models used autonomous systems unmanned vehicles drones. paper aim answer two open questions regarding adversarial attacks. Why are machine learning models vulnerable adversarial samples? hypothesis is that the vulnerability neural networks adversarial samples originates existence rarely explored sub-spaces feature map. phenomenon is particularly caused limited access labeled data/inefficiency regularization algorithms BID30;BID7 Figure 1 provides simple illustration partially explored space twodimensional setup. analytically empirically back hypothesis extensive evaluations state-of-the-art attacks including Fast-Gradient-Sign Jacobian Saliency Map Attack Deepfool BID22 Carlini WagnerL2 BID3 ii How can we characterize thwart underlying space unsupervised model assurance well defend adversaries? line research has shown is a is trade-off robustness model accuracy BID17;BID25 Taking account instead making single model is both robust accurate introduce new defense mechanism called Parallel Checkpointing Learners PCL setting victim model is kept is while separate defender modules are trained checkpoint data abstractions assess reliability victim's prediction. defender module characterizes explored sub-space pertinent layer learning probability density function pdf legitimate data points marking complement sub-spaces rarely observed regions. characterization is obtained checkpointing modules 1 evaluate input sample parallel victim model raise alarm flags data points lie within rarely explored regions Figure1c demonstrate Section4 adversarial samples created various attack methods mostly lie within sub-spaces marked partially explored sectors.We consider white-box attack model which the attacker knows everything victim model including architecture learning algorithm parameters. threat model represents powerful attacker can endanger real-world applications. validate security proposed approach different DL benchmarks including MNIST CIFAR10 subset ImageNet data. Based result analysis provide new insights reason behind existence adversarial transferability. open-source API ensure ease use users link is omitted blind review purposes invite community attempt attacks provided benchmarks form challenge.The explicit contribution paper is as follows:Devising automated end-to-end framework unsupervised model assurance well defending adversaries. ii Incepting idea parallel checkpointing learners validate legitimacy data abstractions intermediate DL layer. iii Performing extensive proof-of-concept evaluations state-of-the-art attack methods. iv Providing new insights regarding transferability adversarial samples different models. Figure1:example data points denoted green blue squares can be easily separated one-dimensional space. extra dimensions adds ambiguity choosing pertinent decision boundaries. instance shown boundaries dashed lines are sufficient classify raw data full accuracy two-dimensional space are not equivalent terms robustness noise. b rarely explored space region specified diagonal striped learning model leaves room adversaries manipulate nuisance non-critical variables mislead model crossing decision boundaries. c PCL methodology set defender checkpoint modules is trained characterize data density distribution space spanned victim model. defender modules are then used parallel checkpoint reliability ultimate prediction raise alarm flag risky samples. Note remaining adversarial samples are not detected experiment are crafted legitimate samples are inherently hard classify even human observer due closeness decision boundaries corresponding classes. instance MNIST application adversarial samples mostly belong class5 is misclassified class3 class 4 misclassified 9. misclassifications are indeed model approximation error which is well-understood statistical nature models. precise definition adversarial samples DISPLAYFORM0 Figure 9:Example adversarial confusion matrix without PCL defense mechanism b PCL defense security parameter 1% c Example adversarial samples which accurate detection is hard due closeness decision boundaries corresponding classes.is extremely required distinguish malicious samples form simply lie near decision boundaries.We emphasize PCL defenders are trained unsupervised setting independent attack strategy meaning adversarial sample is used train defender models. is particularly important corroborates effectiveness proposed countermeasure face generic attack scenarios including possible future adversarialDL algorithms. Nevertheless one might question effectiveness proposed approach adaptive attack algorithms target defender modules. comprehensive study possible adaptive attack algorithms is yet performed if such attacks are developed future. emphasize thus far have been able significantly thwart existing attacks one checkpoint model approximating data distribution second-to-last layer corresponding models. proposed PCL methodology however provides rather generic approach can be adapted/modified potential future attacks training parallel disjoint models diverse objectives/parameters strengthen defense.Figure 10 demonstrate how using multiple checkpoints negative correlation parallel can effectively reduce number false alarms increasing detection rate adversarial samples. experiment have considered MNIST data classification using LeNet model 4 layers FGS attack. checkpoints are inserted different layers pertinent neural network first layer second-to-last layer empirically select mixing coefficients aggregate confidence checkpoint defenders rejecting incoming sample. Note isais trade-off computational complexity e.g runtime overhead PCL defenders reliability overall system. one hand high number validation checkpoints increases reliability systems also increases computational load input sample should be validated defender networks. hand small number checkpoints may degrade defense mechanism performance treating adversarial samples legitimate ones. are looking automated techniques customize number checkpoint modules corresponding mixing coefficients based application data physical constraints real-time analysis requirement future work. paper proposes novel end-to-end methodology characterizing thwarting adversarial DL space. introduce concept parallel checkpointing learners viable countermeasure significantly reduce risk integrity attacks. proposed PCL methodology explicitly characterizes statistical properties features within different layers neural network learning set complementary dictionaries corresponding probability density functions. effectiveness PCL approach is evaluated state-of-the-art attack models including FGS JSMA Deepfool Carlini WagnerL2. Proof-of-concept experiments analyzing various data collections including MNIST CIFAR10 subset ImageNet dataset corroborate successful detection adversarial samples relatively small false-positive rates.We devise open-source API proposed countermeasure invite community attempt attacks provided benchmarks form challenge. Table 2 presents neural network architectures victim models used benchmark. network MNIST is the popular LeNet-3 architecture CIFAR-10 architecture is taken BID4 ImageNet model is inspired AlexNet architecture BID14 Table2:Baseline victim network architectures evaluated benchmarks. 128C3 2 denotes convolutional layer 128 maps 3 × 3 filters applied stride 2 MP3 2 indicates max-pooling layer regions size3×3 stride 2 300FC is a fully-connected layer consisting 300 neurons. convolution fully connected layers except last layer are followed ReLU activation. Softmax activation is applied last layer network. visually evaluate perturbed examples determine attack parameters e.g perturbation levelε n iters perturbations cannot recognized human observer. Table 3 details parameters used realization different attack algorithms. JSMA attack ImageNet benchmark is computationally expensive e.g took 20min generate one adversarial sample NVIDIA TITAN Xp GPU could generate adversarial samples attack using JSMA library provided Nicolas Papernot 2017 Table3:Details attack algorithms evaluated application. FGS method is characterized single ε parameter. JSMA attack has two parameters:γ specifies maximum percentage perturbed features θ denotes value added selected feature. Deepfool attack BID22 is characterized number iterative updates which we denote n iters table. Carlini WagnerL2 attack BID3 C denotes confidence LR is the learning rate steps is the number binary search steps iterations stands maximum number iterations.,2522,1698,824,0.037,1.485,2025/11/05 17:18:57,0.01,1.369,0.4828660436137073,803.048
"Neural architecture search (NAS) has a great impact by automatically designing effective neural network architectures. However, the prohibitive computational demand of conventional NAS algorithms (e.g. 10 4 GPU hours) makes it difficult to directly search the architectures on large-scale tasks (e.g. ImageNet). Differentiable NAS can reduce the cost of GPU hours via a continuous representation of network architecture but suffers from the high GPU memory consumption issue (grow linearly w.r.t. candidate set size). As a result, they need to utilize proxy tasks, such as training on a smaller dataset, or learning with only a few blocks, or training just for a few epochs. These architectures optimized on proxy tasks are not guaranteed to be optimal on the target task. In this paper, we present ProxylessNAS that can directly learn the architectures for large-scale target tasks and target hardware platforms. We address the high memory consumption issue of differentiable NAS and reduce the computational cost (GPU hours and GPU memory) to the same level of regular training while still allowing a large candidate set. Experiments on CIFAR-10 and ImageNet demonstrate the effectiveness of directness and specialization. On CIFAR-10, our model achieves 2.08% test error with only 5.7M parameters, better than the previous state-of-the-art architecture AmoebaNet-B, while using 6× fewer parameters. On ImageNet, our model achieves 3.1% better top-1 accuracy than MobileNetV2, while being 1.2× faster with measured GPU latency. We also apply ProxylessNAS to specialize neural architectures for hardware with direct hardware metrics (e.g. latency) and provide insights for efficient CNN architecture design.",Neural architecture search NAS has a great impact automatically designing effective neural network architectures. However prohibitive computational demand conventional NAS algorithms e.g104 GPU hours makes difficult directly search architectures large-scale tasks e.g ImageNet Differentiable NAS can reduce cost GPU hours via continuous representation network architecture suffers high GPU memory consumption issue grow linearlyw.r.t candidate set size result need utilize proxy tasks training smaller dataset learning blocks training epochs. architectures optimized proxy tasks are not guaranteed optimal target task. paper present ProxylessNAS can directly learn architectures large-scale target tasks target hardware platforms. address high memory consumption issue differentiable NAS reduce computational cost GPU hours GPU memory level regular training still allowing large candidate set. Experiments CIFAR-10 ImageNet demonstrate effectiveness directness specialization. CIFAR-10 model achieves 2.08 test error 5.7M parameters better previous state-of-the-art architecture AmoebaNet-B using 6× fewer parameters. ImageNet model achieves 3.1 better top-1 accuracy MobileNetV2 1.2× faster measured GPU latency. also apply ProxylessNAS specialize neural architectures hardware direct hardware metrics e.g latency provide insights efficient CNN architecture design.,347,234,113,0.003,1.483,2025/11/05 17:18:57,0.0,1.5,0.4766355140186917,103.817
"With the recently rapid development in deep learning, deep neural networks have been widely adopted in many real-life applications. However, deep neural networks are also known to have very little control over its uncertainty for test examples, which potentially causes very harmful and annoying consequences in practical scenarios. In this paper, we are particularly interested in designing a higher-order uncertainty metric for deep neural networks and investigate its performance on the out-of-distribution detection task proposed by~\cite{hendrycks2016baseline}. Our method first assumes there exists a underlying higher-order distribution $\mathcal{P}(z)$ , which generated label-wise distribution $\mathcal{P}(y)$ over classes on the K-dimension simplex, and then approximate such higher-order distribution via parameterized posterior function $p_{\theta}(z|x)$ under variational inference framework, finally we use the entropy of learned posterior distribution $p_{\theta}(z|x)$ as uncertainty measure to detect out-of-distribution examples. However , we identify the overwhelming over-concentration issue in such a framework, which greatly hinders the detection performance. Therefore , we further design a log-smoothing function to alleviate such issue to greatly increase the robustness of the proposed entropy-based uncertainty measure. Through comprehensive experiments on various datasets and architectures, our proposed variational Dirichlet framework with entropy-based uncertainty measure is consistently observed to yield significant improvements over many baseline systems. Recently, deep neural networks BID18 have surged and replaced the traditional machine learning algorithms to demonstrate its potentials in many real-life applications like speech recognition BID10 , image classification BID11 , and machine translation BID34 BID32 , reading comprehension BID27 , etc. However, unlike the traditional machine learning algorithms like Gaussian Process, Logistic Regression, etc, deep neural networks are very limited in their capability to measure their uncertainty over the unseen test cases and tend to produce over-confident predictions. Such overconfidence issue BID1 ) is known to be harmful or offensive in real-life applications. Even worse, such models are prone to adversarial attacks and raise concerns in AI safety BID9 BID23 . Therefore, it is very essential to design a robust and accurate uncertainty metric in deep neural networks in order to better deploy them into real-world applications. Recently, An out-of-distribution detection task has been proposed in BID12 as a benchmark to promote the uncertainty research in the deep learning community. In the baseline approach, a simple method using the highest softmax score is adopted as the indicator for the model's confidence to distinguish in-from out-ofdistribution data. Later on, many follow-up algorithms BID21 BID19 BID30 BID4 have been proposed to achieve better performance on this benchmark. In ODIN BID21 , the authors follow the idea of temperature scaling and input perturbation BID25 to widen the distance between in-and out-of-distribution examples. Later on, adversarial training BID19 ) is introduced to explicitly introduce boundary examples as negative training data to help increase the model's robustness. In BID4 , the authors proposed to directly output a real value between [0, 1] as the confidence measure. The most recent paper BID30 leverages the semantic dense representation into the target labels to better separate the label space and uses the cosine similarity score as the confidence measure.These methods though achieve significant results on out-of-distribution detection tasks, they conflate different levels of uncertainty as pointed in BID22 . For example, when presented with two pictures, one is faked by mixing dog, cat and horse pictures, the other is a real but unseen dog, the model might output same belief as {cat:34%, dog:33%, horse:33%}. Under such scenario, the existing measures like maximum probability or label-level entropy BID21 BID30 BID12 will misclassify both images as from out-of-distribution because they are unable to separate the two uncertainty sources: whether the uncertainty is due to the data noise (class overlap) or whether the data is far from the manifold of training data. More specifically, they fail to distinguish between the lower-order (aleatoric) uncertainty BID5 , and higherorder (episdemic) uncertainty BID5 , which leads to their inferior performances in detecting out-domain examples. In order to resolve the issues presented by lower-order uncertainty measures, we are motivated to design an effective higher-order uncertainty measure for out-of-distribution detection. Inspired by Subjective Logic BID14 BID37 BID29 , we first view the label-wise distribution P(y ) as a K-dimensional variable z generated from a higher-order distribution P(z ) over the simplex S k , and then study the higher-order uncertainty by investigating the statistical properties of such underlying higher-order distribution. Under a Bayesian framework with data pair D = (x, y), we propose to use variational inference to approximate such ""true"" latent distribution P(z) = p(z|y ) by a parameterized Dirichlet posterior p θ (z|x), which is approximated by a deep neural network. Finally, we compute the entropy of the approximated posterior for outof-distribution detection. However, we have observed an overwhelming over-concentration problem in our experiments, which is caused by over-confidence problem of the deep neural network to greatly hinder the detection accuracy. Therefore, we further propose to smooth the Dirichlet distribution by a calibration algorithm. Combined with the input perturbation method BID21 BID16 , our proposed variational Dirichlet framework can greatly widen the distance between in-and out-of-distribution data to achieve significant results on various datasets and architectures.The contributions of this paper are described as follows:• We propose a variational Dirichlet algorithm for deep neural network classification problem and define a higher-order uncertainty measure.• We identify the over-concentration issue in our Dirichlet framework and propose a smoothing method to alleviate such problem. In this paper, we aim at finding an effective way for deep neural networks to express their uncertainty over their output distribution. Our variational Dirichlet framework is empirically demonstrated to yield better results, but its detection accuracy on a more challenging setup like CIFAR100 is still very compromised. We conjecture that better prior Dirichlet distribution or smoothing function could help further improve the performance. In the future work, we plan to apply our method to broader applications like natural language processing tasks or speech recognition tasks.• LSUN (out-of-distribution): The Large-scale Scene UNderstanding dataset (LSUN) BID38 has a test set consisting of 10,000 images from 10 different scene classes, such as bedroom, church, kitchen, and tower. We downsample LSUN's original image and create 32 × 32 images as an out-of-distribution dataset.• iSUN (out-of-distribution): The iSUN dataset BID35 ) is a subset of the SUN dataset, containing 8,925 images. All images are downsampled to 32 × 32 pixels.","recently rapid development deep learning deep neural networks have been widely adopted many real-life applications. However deep neural networks are also known have very little control uncertainty test examples which potentially causes harmful annoying consequences practical scenarios. paper are particularly interested designing higher-order uncertainty metric deep neural networks investigate performance out-of-distribution detection task proposed by~\cite hendrycks2016baseline method first assumes exists underlying higher-order distribution $\mathcal P z which generated label-wise distribution $\mathcal P classes K-dimension simplex approximate higher-order distribution via parameterized posterior function $p_ \theta z|x variational inference framework finally use entropy learned posterior distribution $p_ \theta z|x uncertainty measure detect out-of-distribution examples. However identify overwhelming over-concentration issue framework which greatly hinders detection performance. Therefore design log-smoothing function alleviate issue greatly increase robustness proposed entropy-based uncertainty measure. comprehensive experiments various datasets architectures proposed variational Dirichlet framework entropy-based uncertainty measure is consistently observed yield significant improvements many baseline systems. Recently deep neural networks BID18 have surged replaced traditional machine learning algorithms demonstrate potentials many real-life applications like speech recognition BID10 image classification BID11 machine translation BID34 BID32 reading comprehension BID27 etc. However unlike traditional machine learning algorithms like Gaussian Process Logistic Regression etc deep neural networks are very limited capability measure uncertainty unseen test cases tend produce over-confident predictions. overconfidence issue BID1 is known harmful offensive real-life applications. Even worse models are prone adversarial attacks raise concerns AI safety BID9 BID23. Therefore is very essential design robust accurate uncertainty metric deep neural networks order better deploy real-world applications. Recently out-of-distribution detection task has been proposed BID12 benchmark promote uncertainty research deep learning community. baseline approach simple method using highest softmax score is adopted indicator model's confidence distinguish in-from out-ofdistribution data. Later many follow-up algorithms BID21 BID19 BID30 BID4 have been proposed achieve better performance benchmark. ODIN BID21 authors follow idea temperature scaling input perturbation BID25 widen distance in-and out-of-distribution examples. Later adversarial training BID19 is introduced explicitly introduce boundary examples negative training data help increase model's robustness. BID4 authors proposed directly output real value 0 1 confidence measure. recent paper BID30 leverages semantic dense representation target labels better separate label space uses cosine similarity score confidence measure.These methods though achieve significant results out-of-distribution detection tasks conflate different levels uncertainty pointed BID22. example when presented two pictures one is faked mixing dog cat horse pictures is real unseen dog model might output belief cat:34 dog:33 horse:33 scenario existing measures like maximum probability label-level entropy BID21 BID30 BID12 will misclassify images out-of-distribution are unable separate two uncertainty sources:whether uncertainty is due data noise class overlap whether data is far manifold training data. specifically fail distinguish lower-order aleatoric uncertainty BID5 higherorder episdemic uncertainty BID5 which leads inferior performances detecting out-domain examples. order resolve issues presented lower-order uncertainty measures are motivated design effective higher-order uncertainty measure out-of-distribution detection. Inspired Subjective Logic BID14 BID37 BID29 first view label-wise distributionP K-dimensional variable z generated higher-order distributionP z simplex k study higher-order uncertainty investigating statistical properties underlying higher-order distribution. Bayesian framework data pair x propose use variational inference approximate true latent distributionP z p z|y parameterized Dirichlet posteriorp θ z|x which is approximated deep neural network. Finally compute entropy approximated posterior outof-distribution detection. However have observed overwhelming over-concentration problem experiments which is caused over-confidence problem deep neural network greatly hinder detection accuracy. Therefore propose smooth Dirichlet distribution calibration algorithm. Combined input perturbation method BID21 BID16 proposed variational Dirichlet framework can greatly widen distance in-and out-of-distribution data achieve significant results various datasets architectures.The contributions paper are described follows:• propose variational Dirichlet algorithm deep neural network classification problem define higher-order uncertainty measure.• identify over-concentration issue Dirichlet framework propose smoothing method alleviate problem. paper aim finding effective way deep neural networks express uncertainty output distribution. variational Dirichlet framework is empirically demonstrated yield better results detection accuracy challenging setup like CIFAR100 is still compromised. conjecture better prior Dirichlet distribution smoothing function could help improve performance. future work plan apply method broader applications like natural language processing tasks speech recognition tasks.• LSUN out-of-distribution Large-scale Scene UNderstanding dataset LSUN BID38 has a test set consisting 10,000 images 10 different scene classes bedroom church kitchen tower. downsample LSUN's original image create32×32 images out-of-distribution dataset.• iSUN out-of-distribution iSUN dataset BID35 is a subset SUN dataset containing 8,925 images. images are downsampled 32 × 32 pixels.",1388,972,416,0.013,1.428,2025/11/05 17:18:57,0.01,1.278,0.3052959501557628,414.115
"Intelligent agents can learn to represent the action spaces of other agents simply by observing them act. Such representations help agents quickly learn to predict the effects of their own actions on the environment and to plan complex action sequences. In this work, we address the problem of learning an agent’s action space purely from visual observation. We use stochastic video prediction to learn a latent variable that captures the scene's dynamics while being minimally sensitive to the scene's static content. We introduce a loss term that encourages the network to capture the composability of visual sequences and show that it leads to representations that disentangle the structure of actions. We call the full model with composable action representations Composable Learned Action Space Predictor (CLASP). We show the applicability of our method to synthetic settings and its potential to capture action spaces in complex, realistic visual settings. When used in a semi-supervised setting, our learned representations perform comparably to existing fully supervised methods on tasks such as action-conditioned video prediction and planning in the learned action space, while requiring orders of magnitude fewer action labels. Project website: https://daniilidis-group.github.io/learned_action_spaces Agents behaving in real-world environments rely on perception to judge what actions they can take and what effect these actions will have. Purely perceptual learning may play an important role in how these action representations are acquired and used. In this work, we focus on the problem of learning an agent's action space from unlabeled visual observations. To see the usefulness of this strategy, consider an infant that is first learning to walk. From around 10 months of age, infants rapidly progress from crawling, to irregular gaits with frequent falling, and finally to reliable locomotion (Adolph et al. (2012) ). But before they first attempt to walk, infants have extensive sensory exposure to adults walking. Unsupervised learning from sensory experience of this type appears to play a critical role in how humans acquire representations of actions before they can reliably reproduce the corresponding behaviour BID33 ). Infants need to relate the set of motor primitives they can generate to the action spaces exploited by adults (Dominici et al. (2011)) , and a representation acquired by observation may allow an infant to more efficiently learn to produce natural, goal-directed walking behavior.Reinforcement learning (RL) provides an alternative to the (passive) unsupervised learning approach as it implicitly discovers an agent's action space and the consequences of its actions. Recent breakthroughs in model-free and model-based RL suggest that end-to-end training can be used to learn mappings between sensory input and actions BID14 ; BID12 ; BID11 ; Finn & Levine (2017) ; BID25 ). However, these methods require active observations and the sensorimotor mappings learned in this way cannot be easily generalized to new agents with different control interfaces. Methods for sensorimotor learning from purely visual Using latent composition to recover actions from passive data. a) Two sequences starting from different initial states but changing according to the same actions. Without requiring labels, our model learns to represent the action in sequences like these identically. We train a representation z to capture the dynamics of the scene and its compositional structure: applying (z 1 and z 2 ) should have the same effect as applying the composed representation g(z 1 , z 2 ). These properties capture the fact that effector systems, such as a robot arm, use the same composable action space in many different states. b) The learned action space z recovered by our method (PCA visualization). Points are colored by the true action u: true actions can be easily decoded from z, validating that the structure of the action space has been captured.data may facilitate learning where action information is not available, such as when using video data collected from the Internet. Such methods may also be useful for imitation learning, where ground truth actions are often hard or impossible to collect other than by visual observation (Finn et al. (2017) ; BID18 ). More generally, learning from passive observations may make it easier to reuse action representations between systems with different effectors and goals. The representations learned by unsupervised methods are invariant to these choices because the model does not have access to motor commands or goals during training.In this work, we evaluate the proposal that learning what you can do before doing anything can lead to action space representations that make subsequent learning more efficient. To this end, we develop a model that learns to represent an agent's action space given only unlabeled videos of the agent. The resulting representation enables direct planning in the latent space. Given a small number of action-labeled sequences we can execute the plan by learning a simple mapping from latent action representations to the agent's controls. This representation may be analogous to those in the parietal and premotor areas of cortex, which include populations of neurons that represent the structure of actions produced both by the self and by others BID20 ; BID21 ) and that are critical for reliably producing flexible, voluntary motor control (see BID6 , Chapter 38). In the brain, representations of this kind could plausibly be learned using specialized loss functions BID13 ) whose effect is to induce the prior needed to determine the structure of actions in observation data.In contrast to most approaches to unsupervised learning of dynamics, which focus on learning the statistical structure of the environment, we focus on disentangling action information from the instantaneous state of the environment FIG0 . We base our work on recent stochastic video prediction methods (Babaeizadeh et al. (2018); Denton & Fergus (2018) ; BID10 ) and impose two properties on the latent representation. First, we train the representation to be minimal, i.e. containing minimal information about the current world state. This forces the representation to focus on dynamic properties of the sensory input. A similar objective has been used in previous work to constrain the capacity of video prediction models (Denton & Fergus (2018) ). Second, we train the representation to be composable by introducing a novel loss term that enforces that the cumulative effect of a sequence of actions can be computed from the individual actions' representations ( FIG0 . Composability encourages disentangling: as a composed representation does not have access to the static content of the intermediate frames, a representation is composable only if the individual action representations are disentangled from the static content. Taken together, these two properties lead to a representation of sensory dynamics that captures the structure of the agent's actions.We make the following three contributions. First, we introduce a method for unsupervised learning of an agent's action space by training the latent representation of a stochastic video prediction model for the desiderata of minimality and composability. Second, we show that our method learns a representation of actions that is independent of scene content and visual characteristics on (i) a simulated robot with one degree of freedom and (ii) the BAIR robot pushing dataset (Ebert et al. (2017) ). Finally, we demonstrate that the learned representation can be used for action-conditioned video prediction and planning in the learned action space, while requiring orders of magnitude fewer action-labeled videos than extant supervised methods. We have shown a way of learning the structure of an agent's action space from visual observations alone by imposing the properties of minimality and composability on a latent variable for stochastic video prediction. This strategy offers a data-efficient alternative to approaches that rely on fully supervised action-conditioned methods. The resulting representation can be used for a range of tasks, such as action-conditioned video prediction and planning in the learned latent action space. The representation is insensitive to the static scene content and visual characteristics of the environment. It captures meaningful structure in synthetic settings and achieves promising results in realistic visual settings.",Intelligent agents can learn represent action spaces agents simply observing act. representations help agents quickly learn predict effects actions environment plan complex action sequences. work address problem learning agents action space purely visual observation. use stochastic video prediction learn latent variable captures scene's dynamics minimally sensitive scene's static content. introduce loss term encourages network capture composability visual sequences show leads representations disentangle structure actions. call full model composable action representations Composable Learned Action Space Predictor CLASP show applicability method synthetic settings potential capture action spaces complex realistic visual settings. When used semi-supervised setting learned representations perform comparably existing fully supervised methods tasks action-conditioned video prediction planning learned action space requiring orders magnitude fewer action labels. Project website:https://daniilidis-group.github.io/learned_action_spaces Agents behaving real-world environments rely perception judge what actions can take what effect actions have. Purely perceptual learning may play important role how these action representations are acquired used. work which focus problem learning agent's action space unlabeled visual observations. see usefulness strategy consider infant is first learning walk. around 10 months age infants rapidly progress crawling irregular gaits frequent falling finally reliable locomotion Adolphetal. 2012 first attempt walk infants have extensive sensory exposure adults walking. Unsupervised learning sensory experience type appears play critical role how humans acquire representations actions can reliably reproduce corresponding behaviour BID33 Infants need relate set motor primitives can generate action spaces exploited adults Dominicietal. 2011 representation acquired observation may allow infant efficiently learn produce natural goal-directed walking behavior.Reinforcement learning RL provides alternative passive unsupervised learning approach implicitly discovers agent's action space consequences actions. Recent breakthroughs model-free model-based RL suggest end-to-end training can be used learn mappings sensory input actions BID14;BID12;BID11;Finn Levine 2017 BID25 However methods require active observations sensorimotor mappings learned way cannot easily generalized new agents different control interfaces. Methods sensorimotor learning purely visual Using latent composition recover actions passive data. Two sequences starting different initial states changing according actions. Without requiring labels model learns represent action sequences like identically. train representationz capture dynamics scene compositional structure:applying z1 z2 should have the effect applying composed representationg z1 z2 properties capture fact effector systems robot arm use composable action space many different states. b learned action spacez recovered method PCA visualization Points are colored true actionu:true actions can be easily decoded z validating structure action space has been captured.data may facilitate learning where action information is not available when using video data collected Internet. methods may also useful imitation learning where ground truth actions are often hard impossible collect visual observation Finnetal. 2017 BID18 generally learning passive observations may make easier reuse action representations systems different effectors goals. representations learned unsupervised methods are invariant choices model does not have access motor commands goals training.In work evaluate proposal learning what you cando anything can lead action space representations make subsequent learning efficient. end develop model learns represent agent's action space given unlabeled videos agent. resulting representation enables direct planning latent space. Given small number action-labeled sequences can execute plan learning simple mapping latent action representations agent's controls. representation may analogous parietal premotor areas cortex which include populations neurons represent structure actions produced self others BID20;BID21 are critical reliably producing flexible voluntary motor control see BID6 Chapter38 brain representations kind could plausibly learned using specialized loss functions BID13 whose effect is to induce prior needed determine structure actions observation data.In contrast approaches unsupervised learning dynamics which focus learning statistical structure environment which focus disentangling action information instantaneous state environment FIG0. base work recent stochastic video prediction methods Babaeizadehetal. 2018 Denton Fergus 2018 BID10 impose two properties latent representation. First train representation minimal.e containing minimal information current world state. forces representation focus dynamic properties sensory input. similar objective has been used previous work constrain capacity video prediction models Denton Fergus 2018 Second train representation composable introducing novel loss term enforces cumulative effect sequence actions can be computed individual actions' representations FIG0. Composability encourages disentangling:composed representation does not have access static content intermediate frames representation is composable if the individual action representations are disentangled static content. Taken together two properties lead representation sensory dynamics captures structure agent's actions.We make following three contributions. First introduce method unsupervised learning agent's action space training latent representation stochastic video prediction model desiderata minimality composability. Second show method learns representation actions is independent scene content visual characteristics simulated robot one degree freedom ii BAIR robot pushing dataset Ebertetal. 2017 Finally demonstrate learned representation can be used action-conditioned video prediction planning learned action space requiring orders magnitude fewer action-labeled videos extant supervised methods. have shown way learning structure agent's action space visual observations alone imposing properties minimality composability latent variable stochastic video prediction. strategy offers data-efficient alternative approaches rely fully supervised action-conditioned methods. resulting representation can be used range tasks action-conditioned video prediction planning learned latent action space. representation is insensitive static scene content visual characteristics environment. captures meaningful structure synthetic settings achieves promising results realistic visual settings.,1563,1029,534,0.018,1.519,2025/11/05 17:18:57,0.01,1.41,0.5887850467289715,510.5
"When autonomous agents interact in the same environment, they must often cooperate to achieve their goals. One way for agents to cooperate effectively is to form a team, make a binding agreement on a joint plan, and execute it. However, when agents are self-interested, the gains from team formation must be allocated appropriately to incentivize agreement. Various approaches for multi-agent negotiation have been proposed, but typically only work for particular negotiation protocols. More general methods usually require human input or domain-specific data, and so do not scale. To address this, we propose a framework for training agents to negotiate and form teams using deep reinforcement learning. Importantly, our method makes no assumptions about the specific negotiation protocol, and is instead completely experience driven. We evaluate our approach on both non-spatial and spatially extended team-formation negotiation environments, demonstrating that our agents beat hand-crafted bots and reach negotiation outcomes consistent with fair solutions predicted by cooperative game theory. Additionally, we investigate how the physical location of agents influences negotiation outcomes. Multiple agents inhabiting the same environment affect each other, and may gain by coordinating their actions. Indeed, many tasks are effectively intractable for any single agent, and so can only be solved by a team of collaborators. Examples include search and rescue BID27 , multirobot patrolling BID1 , security BID56 and multiplayer first-person video games BID24 . Despite the need to cooperate, stakeholders have different abilities and preferences which affect the chosen course of action. Agents must therefore negotiate to form teams that are both fairly aligned with individual interests and capable of achieving the task at hand. This problem can formalized as a team-formation negotiation task as follows BID29 BID51 . By definition, no single agent can perform the task on their own, but there may be several teams of agents who are capable of doing so, so each agent must decide who to collaborate with. The reward for accomplishing the task is awarded to the first team that solves it. Hence, agents need to interact with one another to simultaneously form a team and agree on how to share the joint reward. To solve this abstract problem, one must provide a concrete environment where agents can negotiate and reach an agreement; We must specify a negotiation protocol that encodes the allowed negotiation actions and determines the agreement reached BID46 .Team-formation negotiation tasks are natural objects of study in game theory. More precisely , cooperative game theory focuses on interactions between agents who form teams and make enforceable agreements about outcomes BID7 BID11 .1 Weighted voting games are an archetypal problem, in which every agent has a weight and a team of agents is successful if the sum of the weights of its participants exceeds a fixed threshold BID5 BID21 . Weighted voting games also offer a simple model of coalition formation in legislative bodies BID31 BID17 . Cooperative game theory seeks to predict the agreements negotiated by agents in such settings, proposing several solution concepts. Some solutions, such as the core and nucleolus BID47 , have focused on identifying stable agreements. Other solutions , known as power indices, have tried to measure the objective negotiation position of agents, quantifying their relative ability to affect the outcome of the game, or the fair share of the joint reward they should receive BID11 . The most prominent of these is the Shapley value BID49 which has been widely studied for weighted voting games BID50 BID54 . In particular, it has been used to estimate political power BID31 BID17 . In Appendix A we provide a detailed motivating example, showing how the Shapley value fairly measures power in such settings.There remains a pragmatic question for the design of multi-agent systems. How should one construct a negotiating agent that maximizes the reward obtained? Many researchers have borrowed ideas from cooperative game theory to hand-craft bots (Zlotkin & Rosenschein, 1989; BID2 BID23 , often requiring additional human data BID43 BID35 . Such bots are tailored to specific negotiation protocols, so modifying the protocol or switching to a different protocol requires manually re-writing the bot BID25 . As a result, algorithms based purely on cooperative game theory are neither generally applicable nor scalable.Moreover, negotiation and team formation in the real world is significantly more complex than in the game theoretic setting, for several reasons: (1) negotiation protocols can be arbitrarily complicated and are rarely fixed; (2) enacting a negotiation requires a temporally extended policy; (3) the idiosyncrasies of the environment affect the negotiation mechanics; (4) Players must make decisions based on incomplete information about others' policies.We propose multi-agent reinforcement learning as an alternative paradigm which may be applied to arbitrary negotiation protocols in complex environments. Here, individual agents must learn how to solve team formation tasks based on their experiences interacting with others, rather than via hand-crafted algorithms. Our RL approach is automatically applicable to Markov games BID48 Littman, 1994) , which are temporally and spatially extended, similar to recent work in the non-cooperative case BID33 Foerster et al., 2017) . In contrast to earlier work on multi-agent RL in non-cooperative games, the key novelty of our work is comparing the behaviour of negotiating RL agents with solutions from cooperative game theory.Some previous work in multi-agent (deep) reinforcement learning for negotiation has cast the problem as one of communication, rather than team formation (e.g. BID19 ; BID34 BID9 ). In particular, the environments considered involved only two agents, sidestepping the issue of coalition selection. Closer to our perspective is the work of Chalkiadakis & Boutilier (2004); BID40 , which propose a Bayesian reinforcement learning framework for team formation. However, they do not consider spatially extended environments and the computational cost of the Bayesian calculation is significant. We evaluate our approach on a team formation negotiation task using a direct negotiation protocol, showing that agents trained via independent reinforcement learning outperform hand-crafted bots based on game-theoretic principles. We analyze the reward distribution, showing a high correspondence with the Shapley value solution from cooperative game theory. We show that the slight deviation is not due to lack of neural network capacity by training a similar-sized supervised model to predict the Shapley value. We also introduce a more complicated spatial grid-world environment in which agents must move around to form teams. We show that the correspondence with the Shapley value persists in this case, and investigate how spatial perturbations influence agents' rewards. Team formation is an important problem for multi-agent systems, since many real-world tasks are impossible without the cooperation and coordination of multiple agents. Our contributions are as follows: FORMULA0 we introduced a scalable method for team-formation negotiation based on deep reinforcement learning which generalizes to new negotiation protocols and does not require human data, (2) we showed that negotiator agents derived by this method outperform simple hand-crafted bots, and produce results consistent with cooperative game theory, 3) we applied our method to spatially and temporally extended team-formation negotiation environments, where solving for the equilibrium behavior is hard, and (4) we showed that our method makes sensible predictions about the effect of spacial changes on agent behavioral and negotiation outcomes.This work opens up a new avenue of research applying deep learning to team-formation negotiation tasks. In particular, it would be interesting to analyze how team formation dynamics affect emergent language in reinforcement learning agents, naturally extending the work of BID8 and BID30 . Indeed, it has been suggested that the human ability to negotiate and form teams was critical in the evolution of language (Thomas & Kirby, 2018) . One might also consider creating tasks that interpolate between the fully cooperative game-theoretic setting and the purely non-cooperative one. Fundamentally, binding contracts are managed by dynamic institutions, whose behavior is also determined by learning. In principle, we could extend our method to this hierarchical case, perhaps along the lines of BID20",When autonomous agents interact environment must often cooperate achieve goals. One way agents cooperate effectively is to form team make binding agreement joint plan execute it. However when agents are self-interested gains team formation must allocated appropriately incentivize agreement. Various approaches multi-agent negotiation have been proposed typically work particular negotiation protocols. general methods usually require human input domain-specific data do scale. address propose framework training agents negotiate form teams using deep reinforcement learning. Importantly method makes assumptions specific negotiation protocol is instead completely experience driven. evaluate approach non-spatial spatially extended team-formation negotiation environments demonstrating agents beat hand-crafted bots reach negotiation outcomes consistent fair solutions predicted cooperative game theory. Additionally investigate how the physical location agents influences negotiation outcomes. Multiple agents inhabiting environment affect may gain coordinating actions. Indeed many tasks are effectively intractable single agent can solved team collaborators. Examples include search rescue BID27 multirobot patrolling BID1 security BID56 multiplayer first-person video games BID24. Despite need cooperate stakeholders have different abilities preferences which affect chosen course action. Agents must therefore negotiate form teams are both fairly aligned individual interests capable achieving task hand. problem can formalized team-formation negotiation task follows BID29 BID51. definition single agent can perform task may several teams agents who are capable agent must decide who to collaborate with. reward accomplishing task is awarded first team solves it. Hence when agents need interact one another simultaneously form team agree how to share joint reward. solve abstract problem one must provide concrete environment where agents can negotiate reach agreement;must specify negotiation protocol encodes allowed negotiation actions determines agreement reached BID46.Team-formation negotiation tasks are natural objects study game theory. precisely cooperative game theory focuses interactions agents who form teams make enforceable agreements outcomes BID7 BID11.1 Weighted voting games are an archetypal problem which every agent has a weight team agents is successful if the sum weights participants exceeds fixed threshold BID5 BID21. Weighted voting games also offer simple model coalition formation legislative bodies BID31 BID17. Cooperative game theory seeks predict agreements negotiated agents settings proposing several solution concepts. solutions core nucleolus BID47 have focused identifying stable agreements. solutions known power indices have tried measure objective negotiation position agents quantifying relative ability affect outcome game fair share joint reward should receive BID11. prominent is the Shapley value BID49 which has been widely studied weighted voting games BID50 BID54. particular has been used estimate political power BID31 BID17. Appendix provide detailed motivating example showing how the Shapley value fairly measures power settings.There remains pragmatic question design multi-agent systems. How should one construct negotiating agent maximizes reward obtained? Many researchers have borrowed ideas cooperative game theory hand-craft bots Zlotkin Rosenschein 1989;BID2 BID23 often requiring additional human data BID43 BID35. bots are tailored specific negotiation protocols modifying protocol switching different protocol requires manually re-writing bot BID25. result algorithms based purely cooperative game theory are neither generally applicable scalable.Moreover negotiation team formation real world is significantly complex game theoretic setting several reasons:1 negotiation protocols can be arbitrarily complicated are rarely fixed;2 enacting negotiation requires temporally extended policy;3 idiosyncrasies environment affect negotiation mechanics;4 Players must make decisions based incomplete information others' policies.We propose multi-agent reinforcement learning alternative paradigm may applied arbitrary negotiation protocols complex environments. individual agents must learn how to solve team formation tasks based experiences interacting others rather via hand-crafted algorithms. RL approach is automatically applicable Markov games BID48 Littman 1994 which are temporally spatially extended similar recent work non-cooperative case BID33 Foerster etal. 2017 contrast earlier work multi-agentRL non-cooperative games key novelty work is comparing behaviour negotiating RL agents solutions cooperative game theory.Some previous work multi-agent deep reinforcement learning negotiation has cast problem one communication rather team formation e.g BID19;BID34 BID9 particular environments considered involved two agents sidestepping issue coalition selection. Closer perspective is the work Chalkiadakis Boutilier 2004 BID40 which propose Bayesian reinforcement learning framework team formation. However do not consider spatially extended environments computational cost Bayesian calculation is significant. evaluate approach team formation negotiation task using direct negotiation protocol showing agents trained via independent reinforcement learning outperform hand-crafted bots based game-theoretic principles. analyze reward distribution showing high correspondence Shapley value solution cooperative game theory. show slight deviation is not due lack neural network capacity training similar-sized supervised model predict Shapley value. also introduce complicated spatial grid-world environment which agents must move around form teams. show correspondence Shapley value persists case investigate how spatial perturbations influence agents' rewards. Team formation is an important problem multi-agent systems since many real-world tasks are impossible without cooperation coordination multiple agents. contributions are as follows:FORMULA0 introduced scalable method team-formation negotiation based deep reinforcement learning which generalizes new negotiation protocols does not require human data 2 showed negotiator agents derived method outperform simple hand-crafted bots produce results consistent cooperative game theory 3 applied method spatially temporally extended team-formation negotiation environments where solving equilibrium behavior is hard 4 showed method makes sensible predictions effect spacial changes agent behavioral negotiation outcomes.This work opens new avenue research applying deep learning team-formation negotiation tasks. particular would interesting analyze how team formation dynamics affect emergent language reinforcement learning agents naturally extending work BID8 BID30. Indeed has been suggested human ability negotiate form teams was critical evolution language Thomas Kirby 2018 One might also consider creating tasks interpolate fully cooperative game-theoretic setting purely non-cooperative one. Fundamentally binding contracts are managed dynamic institutions whose behavior is also determined learning. principle could extend method hierarchical case perhaps along lines BID20,1593,1130,463,0.017,1.41,2025/11/05 17:18:57,0.01,1.394,0.2492211838006226,515.961
"Neural machine translation (NMT) models learn representations containing substantial linguistic information. However, it is not clear if such information is fully distributed or if some of it can be attributed to individual neurons. We develop unsupervised methods for discovering important neurons in NMT models. Our methods rely on the intuition that different models learn similar properties, and do not require any costly external supervision. We show experimentally that translation quality depends on the discovered neurons, and find that many of them capture common linguistic phenomena. Finally, we show how to control NMT translations in predictable ways, by modifying activations of individual neurons. Neural machine translation (NMT) systems achieve state-of-the-art results by learning from large amounts of example translations, typically without additional linguistic information. Recent studies have shown that representations learned by NMT models contain a non-trivial amount of linguistic information on multiple levels: morphological BID4 BID7 , syntactic BID31 , and semantic BID16 . These studies use trained NMT models to generate feature representations for words, and use these representations to predict certain linguistic properties. This approach has two main limitations. First, it targets the whole vector representation and fails to analyze individual dimensions in the vector space. In contrast, previous work found meaningful individual neurons in computer vision BID34 BID36 Bau et al., 2017, among others) and in a few NLP tasks BID18 BID27 BID25 . Second, these methods require external supervision in the form of linguistic annotations. They are therefore limited by available annotated data and tools.In this work, we make initial progress towards addressing these limitations by developing unsupervised methods for analyzing the contribution of individual neurons to NMT models. We aim to answer the following questions:• How important are individual neurons for obtaining high-quality translations?• Do individual neurons in NMT models contain interpretable linguistic information?• Can we control MT output by intervening in the representation at the individual neuron level?To answer these questions, we develop several unsupervised methods for ranking neurons according to their importance to an NMT model. Inspired by work in machine vision BID22 , we hypothesize that different NMT models learn similar properties, and therefore similar important neurons should emerge in different models. To test this hypothesis, we map neurons between pairs of trained NMT models using several methods: correlation analysis, regression analysis, and SVCCA, a recent method combining singular vectors and canonical correlation analysis BID28 . Our mappings yield lists of candidate neurons containing shared information across models. We then evaluate whether these neurons carry important information to the NMT model by masking their activations during testing. We find that highly-shared neurons impact translation quality much more than unshared neurons, affirming our hypothesis that shared information matters.Given the list of important neurons, we then investigate what linguistic properties they capture, both qualitatively by visualizing neuron activations and quantitatively by performing supervised classification experiments. We were able to identify neurons corresponding to several linguistic phenomena, including morphological and syntactic properties.Finally, we test whether intervening in the representation at the individual neuron level can help control the translation. We demonstrate the ability to control NMT translations on three linguistic properties-tense, number, and gender-to varying degrees of success. This sets the ground for controlling NMT in desirable ways, potentially reducing system bias to properties like gender.Our work indicates that not all information is distributed in NMT models, and that many humaninterpretable grammatical and structural properties are captured by individual neurons. Moreover, modifying the activations of individual neurons allows controlling the translation output according to specified linguistic properties. The methods we develop here are task-independent and can be used for analyzing neural networks in other tasks. More broadly, our work contributes to the localist/distributed debate in artificial intelligence and cognitive science BID13 by investigating the important case of neural machine translation. Neural machine translation models learn vector representations that contain linguistic information while being trained solely on example translations. In this work, we developed unsupervised methods for finding important neurons in NMT, and evaluated how these neurons impact translation quality. We analyzed several linguistic properties that are captured by individual neurons using quantitative prediction tasks and qualitative visualizations. We also designed a protocol for controlling translations by modifying neurons that capture desired properties.Our analysis can be extended to other NMT components (e.g. the decoder) and architectures BID14 BID33 , as well as other tasks. We believe that more work should be done to analyze the spectrum of localized vs. distributed information in neural language representations. We would also like to expand the translation control experiments to other architectures and components (e.g. the decoder), and to develop more sophisticated ways to control translation output, for example by modifying representations in variational NMT architectures BID35 BID32 . Our code is publicly available as part of the NeuroX toolkit BID9 .",Neural machine translation NMT models learn representations containing substantial linguistic information. However is not clear if such information is fully distributed if someof canbe attributed individual neurons. develop unsupervised methods discovering important neurons NMT models. methods rely intuition different models learn similar properties do not require costly external supervision. show experimentally translation quality depends discovered neurons find many capture common linguistic phenomena. Finally show how to control NMT translations predictable ways modifying activations individual neurons. Neural machine translation NMT systems achieve state-of-the-art results learning large amounts example translations typically without additional linguistic information. Recent studies have shown representations learned NMT models contain non-trivial amount linguistic information multiple levels:morphological BID4 BID7 syntactic BID31 semantic BID16. studies use trained NMT models generate feature representations words use representations predict certain linguistic properties. approach has two main limitations. First targets whole vector representation fails analyze individual dimensions vector space. contrast previous work found meaningful individual neurons computer vision BID34 BID36 Bauetal. 2017 among others NLP tasks BID18 BID27 BID25. Second methods require external supervision form linguistic annotations. are therefore limited available annotated data tools.In work make initial progress towards addressing limitations developing unsupervised methods analyzing contribution individual neurons NMT models. aim answer following questions:• How important are individual neurons obtaining high-quality translations? • Do individual neurons NMT models contain interpretable linguistic information? • Can we control MT output intervening representation individual neuron level? answer questions develop several unsupervised methods ranking neurons according importance NMT model. Inspired work machine vision BID22 hypothesize different NMT models learn similar properties therefore similar important neurons should emerge different models. test hypothesis map neurons pairs trained NMT models using several methods:correlation analysis regression analysis SVCCA recent method combining singular vectors canonical correlation analysis BID28. mappings yield lists candidate neurons containing shared information across models. evaluate whether neurons carry important information NMT model masking activations testing. find highly-shared neurons impact translation quality much unshared neurons affirming hypothesis shared information matters.Given list important neurons investigate what linguistic properties capture qualitatively visualizing neuron activations quantitatively performing supervised classification experiments. were able identify neurons corresponding several linguistic phenomena including morphological syntactic properties.Finally test whether intervening representation individual neuron level can help control translation. demonstrate ability control NMT translations three linguistic properties-tense number gender-to varying degrees success. sets ground controlling NMT desirable ways potentially reducing system bias properties like gender.Our work indicates information is distributed NMT models many humaninterpretable grammatical structural properties are captured individual neurons. Moreover modifying activations individual neurons allows controlling translation output according specified linguistic properties. methods develop are task-independent can be used analyzing neural networks tasks. broadly work contributes localist/distributed debate artificial intelligence cognitive science BID13 investigating important case neural machine translation. Neural machine translation models learn vector representations contain linguistic information trained solely example translations. work developed unsupervised methods finding important neurons NMT evaluated how these neurons impact translation quality. analyzed several linguistic properties are captured individual neurons using quantitative prediction tasks qualitative visualizations. also designed protocol controlling translations modifying neurons capture desired properties.Our analysis can be extended NMT components e.g decoder architectures BID14 BID33 well tasks. believe work should be done analyze spectrum localizedvs. distributed information neural language representations. would also like expand translation control experiments architectures components e.g decoder develop sophisticated ways control translation output example modifying representations variational NMT architectures BID35 BID32. code is publicly available part NeuroX toolkit BID9.,966,695,271,0.009,1.39,2025/11/05 17:18:57,0.0,1.444,0.1869158878504667,298.108
"Recent state-of-the-art reinforcement learning algorithms are trained under the goal of excelling in one specific task. Hence, both environment and task specific knowledge are entangled into one framework. However, there are often scenarios where the environment (e.g. the physical world) is fixed while only the target task changes. Hence, borrowing the idea from hierarchical reinforcement learning, we propose a framework that disentangles task and environment specific knowledge by separating them into two units. The environment-specific unit handles how to move from one state to the target state; and the task-specific unit plans for the next target state given a specific task. The extensive results in simulators indicate that our method can efficiently separate and learn two independent units, and also adapt to a new task more efficiently than the state-of-the-art methods. Let's imagine ourselves learning how to play tennis for the first time. Even though we have never played tennis before, we already have a good understanding of agent and environment dynamics related to tennis. For example, we know how to move our arm from one position to another and that a ball will slow down and bounce back from the ground. Hence, we just need to learn the tennis specific knowledge (e.g. its game rule and a relationship between an arm control and a tennis racket). Just like this example, when we learn to complete a new task, we utilize the prior knowledge that is disentangled from the task and acquired over our lifetime. Figure 1: Our model disentangles environment-specific information (e.g. transition dynamics) and task-specific knowledge (e.g. task rewards) for training efficiency and interpretability.From a reinforcement learning perspective, this brings a very interesting question -how can agents also obtain and utilize such disentangled prior knowledge about the environment? Most of today's deep reinforcement learning (DRL) models BID14 ; BID25 are trained with entangled environment-specific knowledge (e.g. transition dynamics) and taskspecific knowledge (e.g. rewards), as described in Figure 1a However, as described earlier, humans τ τ Figure 2 : Proposed universal agent, which consists of three parts: a φ function mapping raw observation to feature space, a PATH function as an environment actor, and a τ function for future state planning.have an innate ability to obtain a good understanding about the environment dynamics, and utilize them in a newly given task. Motivated from this, we introduce a new scheme to disentangle the learning procedure of task-independent transition dynamics and task-specific rewards, as described in Figure 2 . This will help an agent to adapt to a new task more efficiently and also provides an extra interpretability.The idea of disentangling a model into two components can be related to hierarchical RL approaches BID29 ; BID17 ; BID16 . However, to the best of our knowledge, there has not been a work that separating units by the natural criteria of environment and task specific knowledge, for the goal of transfer learning.To this end, we introduce a model that consists of two major units: a PATH function and a goal generator. This is illustrated in Figure 2 . The key intuition is as the following. PATH function handles the environment specific knowledge, and a goal function handles the task specific knowledge. We design (1) PATH function to learn how to move from one state to another -a lower-level controller, which is independent from the task and only depends on the environment, and (2) the goal function τ to determine the next state given a target task -a higher-level planner. Thus, PATH function can be shared across different tasks as long as it is under the same environment (e.g. the physical world).We evaluate our method to answer the following two questions: (1) how a good PATH unit can benefit the task learning, and (2) how efficient is our model for learning a new task in the same environment. We analyze the behavior of our method on various environments including a maze world and multiple Atari 2600 games. Our study shows that a good PATH unit can be trained, and our model has a faster convergence compared to the state-of-the-art method BID15 in most of the tasks, especially on transfer learning tasks.In summary, we introduce an RL model with disentangled units for task-specific and environmentspecific knowledge. We demonstrate in multiple environments that our method learns environmentspecific knowledge, which further enables an agent adapting to a new task in the same environment. Model-based reinforcement learning Typical model-based RL frameworks aim to model the dynamics of the environment. They usually involve search-based algorithms (e.g., Monte Carlo Tree Search) as part of the policy Sutton & Barto (1998) (e.g., Alpha GO with a simulator , Scheme-networks with learned forward dynamics BID11 ). In this paper, we address the problem of representing the knowledge about the environment by learning skills (how to reach a given state). As a cognitive science motivation described in BID6 , humans also store the knowledge of movements or actions by their end-states. Most importantly, this knowledge can be easily utilized by a task-specific module (the goal generator) to exploit novel tasks.Multi-task learning and transfer learning Multi-task learning and transfer learning BID2 ; BID0 ; Taylor & Stone (2009) provide approaches to transfer knowledge among multiple agents. The methods include the decomposition of value function or task and direct multi-task learning where agents learn several tasks jointly. Contrary to them, universal agent is able to obtain the environment specific knowledge without any specific task supervision. (2015) ; BID32 , the τ function does not perform option selection but directly composes target state since a general-purpose PATH function is utilized. We do not follow typical HRL methods where once the subtask is selected, the low-level controller will be executed for multiple time steps. In universal agent, for simplicity now, τ function plans the future state at every time step. We leave its adaption to HRL frameworks as a future work. We present a new reinforcement learning scheme that disentangles the learning procedure of taskindependent transition dynamics and task-specific rewards. The main advantage of this is efficiency of task adaptation and interpretability. For this we simply introduce two major units: a PATH function and a goal generator. Our study shows that a good PATH unit can be trained, and our model outperforms the state-of-the-art method BID15 in most of tasks, especially on transfer learning tasks.The proposed framework is a novel step towards the knowledge representation learning for deep reinforcement learning (DRL). There are a variety of future research directions. For example, how PATH function can be learned (e.g., in a continual learning manner BID22 , with less requirement such as state restoration), how it can better cooperate with the goal generator (e.g., incorporating explicit future planning) and how it can be used for other tasks (e.g., learning from demonstration).",Recent state-of-the-art reinforcement learning algorithms are trained goal excelling one specific task. Hence environment task specific knowledge are entangled one framework. However are often scenarios where the environment e.g physical world is fixed target task changes. Hence borrowing idea hierarchical reinforcement learning propose framework disentangles task environment specific knowledge separating two units. environment-specific unit handles how to move one state target state;task-specific unit plans next target state given specific task. extensive results simulators indicate method can efficiently separate learn two independent units also adapt new task efficiently state-of-the-art methods. Let's imagine learning how to play tennis first time. Even though have never played tennis already have a good understanding agent environment dynamics related tennis. example know how to move arm one position another ball will slow bounce back ground. Hence need learn tennis specific knowledge e.g game rule relationship arm control tennis racket like example when we learn complete new task utilize prior knowledge is disentangled task acquired lifetime. Figure1:model disentangles environment-specific information e.g transition dynamics task-specific knowledge e.g task rewards training efficiency interpretability.From reinforcement learning perspective brings interesting question -how can agents also obtain utilize disentangled prior knowledge environment? today's deep reinforcement learning DRL models BID14;BID25 are trained entangled environment-specific knowledge e.g transition dynamics taskspecific knowledge e.g rewards described Figure 1a However described earlier humans τ τ Figure 2:Proposed universal agent which consists three parts:φ function mapping raw observation feature space how PATH function is under environment actor τ function future state planning.have innate ability obtain good understanding environment dynamics utilize newly given task. Motivated introduce new scheme disentangle learning procedure task-independent transition dynamics task-specific rewards described Figure2. will help agent adapt new task efficiently also provides extra interpretability.The idea disentangling model two components can be related hierarchical RL approaches BID29;BID17;BID16. However best knowledge has not work separating units natural criteria environment task specific knowledge goal transfer learning.To end introduce model consists two major units:PATH function goal generator. is illustrated Figure2. key intuition is as the following. PATH function handles environment specific knowledge goal function handles task specific knowledge. design 1 PATH function learn how to move one state another -a lower-level controller which is independent task depends environment 2 goal functionτ determine next state given target task -a higher-level planner. Thus how PATH function can be shared across different tasks long is under environment e.g physical world.We evaluate method answer following two questions:1 how a good PATH unit can benefit task learning 2 how efficient is our model learning new task environment. analyze behavior method various environments including maze world multiple Atari 2600 games. study shows good PATH unit can be trained model has a faster convergence compared state-of-the-art method BID15 tasks especially transfer learning tasks.In summary introduce RL model disentangled units task-specific environmentspecific knowledge. demonstrate multiple environments method learns environmentspecific knowledge which further enables agent adapting new task environment. Model-based reinforcement learning Typical model-based RL frameworks aim model dynamics environment. usually involve search-based algorithms e.g Monte Carlo Tree Search part policy Sutton Barto 1998 e.g AlphaGO simulator Scheme-networks learned forward dynamics BID11 paper address problem representing knowledge environment learning skills how to reach given state cognitive science motivation described BID6 humans also store knowledge movements actions end-states importantly knowledge can be easily utilized task-specific module goal generator exploit novel tasks.Multi-task learning transfer learning Multi-task learning transfer learning BID2;BID0;Taylor Stone 2009 provide approaches transfer knowledge among multiple agents. methods include decomposition value function task direct multi-task learning where agents learn several tasks jointly. Contrary universal agent is able obtain environment specific knowledge without specific task supervision. 2015 BID32 τ function does not perform option selection directly composes target state since general-purpose PATH function is utilized. do not follow typical HRL methods where once the subtask is selected low-level controller will be executed multiple time steps. universal agent simplicity τ function plans future state every time step. leave adaption HRL frameworks future work. present new reinforcement learning scheme disentangles learning procedure taskindependent transition dynamics task-specific rewards. main advantage is efficiency task adaptation interpretability. simply introduce two major units:PATH function goal generator. study shows good PATH unit can be trained model outperforms state-of-the-art method BID15 tasks especially transfer learning tasks.The proposed framework is a novel step towards knowledge representation learning deep reinforcement learning DRL are variety future research directions. example how PATH function can be learned e.g continual learning manner BID22 less requirement state restoration howit can better cooperate goal generator e.g incorporating explicit future planning howit canbe used tasks e.g learning demonstration,1375,932,443,0.016,1.475,2025/11/05 17:18:57,0.01,1.592,0.4517133956386294,451.776
"Modelling 3D scenes from 2D images is a long-standing problem in computer vision with implications in, e.g., simulation and robotics. We propose pix2scene, a deep generative-based approach that implicitly models the geometric properties of a scene from images. Our method learns the depth and orientation of scene points visible in images. Our model can then predict the structure of a scene from various, previously unseen view points. It relies on a bi-directional adversarial learning mechanism to generate scene representations from a latent code, inferring the 3D representation of the underlying scene geometry. We showcase a novel differentiable renderer to train the 3D model in an end-to-end fashion, using only images. We demonstrate the generative ability of our model qualitatively on both a custom dataset and on ShapeNet. Finally, we evaluate the effectiveness of the learned 3D scene representation in supporting a 3D spatial reasoning. Understanding the 3-dimensional (3D) world from its 2-dimensional (2D) projections is a fundamental problem in computer vision with a broad range of application in robotics, simulation and design. Given that the majority natural scene data is available exclusively in the form of 2D images, the ability to directly infer knowledge about 3D structure from these images would be of great utility in scene understanding.Inferring the 3D structure from multiple images of a scene has been pursued extensively, such as in stereo or structure from motion tasks BID9 . Since most available natural image data informative about the real world comes with only a single view of a given scene, it is perhaps more important to explore the development of models which can infer the 3D structural properties from a single image. On the other hand, single image 3D recovery is an extremely challenging and heavily under constrained task. The system has to rely on prior knowledge and 2D visual cues such as textures, shadows or occlusions in order to provide hints to the 3D structure of the scene. Practically, building a machine learning model that learns to infer 3D structure from images requires either a strong inductive bias or supervision. While some have used the 3D ground truth as explicit supervision BID34 , in most cases of interest, such supervision will not be available. Consequently, our long term goal is to infer the 3D structure of realistic scenes from single images. In this paper we take a step towards this direction via a method of unsupervised learning of the 3D structure, directly from a single 2D image of each scene. Our method based on the adversarial learning framework BID6 and exploits a uniquely suitable 3D representation (i.e., surfels BID24 ) and a differentiable renderer.Most 3D reconstruction methods rely on representing 3D objects explicitly using either voxels BID26 BID36 or meshes BID14 BID31 . Explicit representations store all the rendering-relevant information from a given 3D space and are easily transferable, i.e., they can be loaded with any 3D modeling software and viewed from any angle. However, approaches using explicit representations typically scale very poorly (O(n 3 ) or require a sparse/discrete representation which can be challenging for deep learning methods. As a result, these representations have only been applied to the reconstruction of single objects. As an alternative we propose to learn an implicit 3D representation which produces only the 3D geometry which is directly relevant for a particular viewpoint. Our viewpoint-specific 3D geometry is captured Figure 1: Implicit vs explicit representations. Explicit voxel and mesh representations are viewpoint-independent and constitutes the complete scene. Our implicit surfel-based representation is viewpoint-dependent and it adapts the resolution to the viewpoint. The full scene is contained in a high-dimensional latent variable and only when the scene is to be rendered, the latent variable is serialized to surfels for a specific view.using camera facing surfels BID24 which are surface elements defined by its position, orientation and material properties. Given an image we can infer its implicit 3D representation and then recreate novel surfel representations of the underlying scene from unobserved viewpoints. In general, we note that in a 3D scene, only a small fraction of the entities are perceivable from the camera. As the camera moves, and the occluded regions become visible, our method then generates surfels for those newly unoccluded regions. Another advantage of this approach is that minimal number of primitives (surfels) are required to obtain a high-resolution image as the camera moves closer to a part of the scene. Moreover this representation fits well with image based convolutional architectures.Our model, Pix2Scene, is a deep generative-based approach for modelling the 3D structure of a scene directly from images. This model is unsupervised in the sense that it does not require 3D groundtruth or any other kind of image annotations. We base our model on Adversarially Learned Inference (ALI) approach BID5 . ALI extends the GAN BID6 framework by learning to infer the latent representation of a given image. In pix2scene the learned latent space embeds the 3D information of the underlying scene. The latent representation is mapped via a decoder network to a view-dependent 3D surface and then projected to image space by a differentiable renderer. The resulting image is then evaluated by an adversarial critic.While our long-term goal is to be able to infer the 3D structure of a real-world photograph, in this paper we experiment exclusively with synthetically-constructed scenes and adopt several simplifying assumptions. In particular, we assume that the world is piece-wise smooth and that for each input image the illumination, view and object materials are known.This work has the following main contributions, (1) we propose a novel unsupervised method for 3D understanding from a single image; (2) we propose a new implicit 3D representation based on view-space surfels; (3) we propose a surfel-based differentiable 3D renderer that can be used as a layer of a neural network; and (4) we propose 3D-IQTT a new 3D understanding evaluation benchmark. This task evaluates the model's ability to perform mental rotation by obtaining comprehensive understanding of underlying 3D structure. We also estimate the camera pose as part of the learnt latent variable for this particular task. In this paper we proposed a generative approach to learn 3D structural properties from single images in an unsupervised and implicit fashion. Our model receives an image of a scene with uniform material as input, estimates the depth of the scene points and then reconstructs the input scene. We also provided quantitative evidence that support our argument by introducing a novel IQ-task in a semi-supervised setup. We hope that this evaluation metric will be used as a standard benchmark to measure the 3D understanding capability of the models across different 3D representations. The main drawback of our current model is that it requires the knowledge of lighting and material properties. Future work will focus on tackling the more ambitious setting of learning complex materials and texture along with modelling the lighting properties of the scene.",Modelling 3D scenes 2D images is a long-standing problem computer vision implications e.g simulation robotics. propose pix2scene is a deep generative-based approach implicitly models geometric properties scene images. method learns depth orientation scene points visible images. model can then predict structure scene various previously unseen view points. relies bi-directional adversarial learning mechanism generate scene representations latent code inferring 3D representation underlying scene geometry. showcase novel differentiable renderer train 3D model end-to-end fashion using images. demonstrate generative ability model qualitatively custom dataset ShapeNet. Finally evaluate effectiveness learned 3D scene representation supporting 3D spatial reasoning. Understanding 3-dimensional 3D world 2-dimensional 2D projections is a fundamental problem computer vision broad range application robotics simulation design. Given majority natural scene data is available exclusively form 2D images ability directly infer knowledge 3D structure images would great utility scene understanding.Inferring 3D structure multiple images scene has been pursued extensively stereo structure motion tasks BID9. Since available natural image data informative real world comes single view given scene is perhaps important explore development models which can infer 3D structural properties single image. hand single image 3D recovery is an extremely challenging heavily constrained task. system has to rely prior knowledge 2D visual cues textures shadows occlusions order provide hints 3D structure scene. Practically building machine learning model learns infer 3D structure images requires either strong inductive bias supervision. have used 3D ground truth explicit supervision BID34 cases interest supervision will not be available. Consequently long term goal is to infer 3D structure realistic scenes single images. paper take step towards direction via method unsupervised learning 3D structure directly single 2D image scene. method based adversarial learning framework BID6 exploits uniquely suitable 3D representation.e surfels BID24 differentiable renderer.Most 3D reconstruction methods rely representing 3D objects explicitly using either voxels BID26 BID36 meshes BID14 BID31. Explicit representations store rendering-relevant information given 3D space are easily transferable.e can be loaded 3D modeling software viewed angle. However approaches using explicit representations typically scale poorly n3 require sparse/discrete representation which can be challenging deep learning methods. result representations have only been applied reconstruction single objects. alternative propose learn implicit 3D representation which produces 3D geometry which is directly relevant particular viewpoint. viewpoint-specific 3D geometry is captured Figure1:Implicit vs explicit representations. Explicit voxel mesh representations are viewpoint-independent constitutes complete scene. implicit surfel-based representation is viewpoint-dependent adapts resolution viewpoint. full scene is contained high-dimensional latent variable when the scene is to be rendered latent variable is serialized surfels specific view.using camera facing surfels BID24 which are surface elements defined position orientation material properties. Given image can infer implicit 3D representation recreate novel surfel representations underlying scene unobserved viewpoints. general note 3D scene small fraction entities are perceivable camera. camera moves occluded regions become visible method generates surfels newly unoccluded regions. Another advantage approach is that minimal number primitives surfels are required obtain high-resolution image camera moves closer part scene. Moreover representation fits well image based convolutional architectures.Our model Pix2Scene is a deep generative-based approach modelling 3D structure scene directly images. model is unsupervised sense does not require 3D groundtruth kind image annotations. base model Adversarially Learned Inference ALI approach BID5. ALI extends GAN BID6 framework learning infer latent representation given image. pix2scene learned latent space embeds 3D information underlying scene. latent representation is mapped via decoder network view-dependent 3D surface projected image space differentiable renderer. resulting image is then evaluated adversarial critic.While long-term goal is to be able infer 3D structure real-world photograph paper experiment exclusively synthetically-constructed scenes adopt several simplifying assumptions. particular assume world is piece-wise smooth input image illumination view object materials are known.This work has the following main contributions 1 propose novel unsupervised method 3D understanding single image;2 propose new implicit 3D representation based view-space surfels;3 propose surfel-based differentiable 3D renderer can be used layer neural network;4 propose 3D-IQTT new 3D understanding evaluation benchmark. task evaluates model's ability perform mental rotation obtaining comprehensive understanding underlying 3D structure. also estimate camera pose part learnt latent variable particular task. paper proposed generative approach learn 3D structural properties single images unsupervised implicit fashion. model receives image scene uniform material input estimates depth scene points reconstructs input scene. also provided quantitative evidence support argument introducing novel IQ-task semi-supervised setup. hope evaluation metric will be used standard benchmark measure 3D understanding capability models across different3D representations. main drawback current model is that it requires knowledge lighting material properties. Future work will focus tackling ambitious setting learning complex materials texture along modelling lighting properties scene.,1452,1004,448,0.015,1.446,2025/11/05 17:18:57,0.01,1.721,0.3613707165109031,451.754
"Identifying the relations that connect words is an important step towards understanding human languages and is useful for various NLP tasks such as knowledge base completion and analogical reasoning. Simple unsupervised operators such as vector offset between two-word embeddings have shown to recover some specific relationships between those words, if any. Despite this, how to accurately learn generic relation representations from word representations remains unclear. We model relation representation as a supervised learning problem and learn parametrised operators that map pre-trained word embeddings to relation representations. We propose a method for learning relation representations using a feed-forward neural network that performs relation prediction. Our evaluations on two benchmark datasets reveal that the penultimate layer of the trained neural network-based relational predictor acts as a good representation for the relations between words. Different types of relations exist between words in a language such as Hypernym, Meronym, Synonym, etc. Representing relations between words is important for various NLP tasks such as questions answering BID43 , knowledge base completion BID35 and relational information retrieval BID7 .Two main approaches have been proposed in the literature to represent relations between words. In the first approach, a pair of words is represented by a vector derived from a statistical analysis of a text corpus BID39 . In a text corpus, a relationship between two words X and Y can be expressed using lexical patterns containing X and Y as slot variables. For example, ""X is a Y"" or ""Y such as X"" indicate that Y is a Hypernym of X BID34 . The elements of the vector representing the relation between two words correspond to the number of times those two words co-occur with a particular pattern in a corpus. Given such a relation representation, the relational similarity between the relations that exist between the two words in two word-pairs can be measured by the cosine of the angle between the corresponding vectors. We call this the holistic approach because a pair of words is treated as a whole rather than the two constituent words separately when creating a relation representation . Sparsity is a well-known problem for the holistic approach as two words have to co-occur enough in a corpus, or else no relation can be represented for rare or unseen word-pairs.In contrast, the second approach for relation representation directly computes a relation representation from pre-trained word representations (i.e. word embeddings) using some relational operators. Prediction-based word embedding learning methods BID27 BID24 represent the meaning of individual words by dense, low-dimensional real-valued vectors by optimising different language modelling objectives. Although no explicit information is provided to the word embedding learning algorithms regarding the semantic relations that exist among words, prior work BID25 has shown that the learnt word embeddings encode remarkable structural properties pertaining to semantic relations. They showed that the difference (vector offset) between two word vectors (here-onwards denoted by PairDiff) is an accurate method for solving analogical questions in the form ""a is to b as c is to ?"". For example, king − man + woman results in a vector that is closest to the queen vector. We call this approach compositional because the way in which the relation representation is composed by applying some linear algebraic relational operator on the the semantic representations of the the words that participate in a relation. This interesting property of word embeddings sparked a renewed interest in methods that compose relation representations using word embeddings and besides PairDiff, several other unsupervised methods have been proposed such as 3CosAdd and 3CosMult BID19 .Despite the initial hype, recently, multiple independent works have raised concerns about of word embeddings capturing relational structural properties BID22 BID32 BID23 BID29 . Although PairDiff performs well on the Google analogy dataset, its performance for other relation types has been poor BID3 BID41 BID18 . BID41 tested for the generalisation ability of PairDiff using different relation types and found that semantic relations are captured less accurately compared to syntactic relations. Likewise, BID18 showed that word embeddings are unable to detect paradigmatic relations such as Hypernym, Synonym and Antonyms. Methods such as PairDiff are biased towards attributional similarities between individual words than relational similarities and fails in the presence of nearest neighbours. We further discuss various limitations of the existing unsupervised relation composition methods in Section 2.2.Considering the above-mentioned limitations of the unsupervised relation composition methods, a natural question that arises is whether it is possible to learn supervised relation composition methods to overcome those limitations. In this paper, we model relation representation as learning a parametrised operator f (a, b; θ) such that we can accurately represent the relation between two given words a and b from their word representations a and b, without modifying the input word embeddings. For this purpose, we propose a Multi-class Neural Network Penultimate Layer (MnnPl), a simple and effective parametrised operator for computing relation representations from word representations. Specifically, we train a nonlinear multilayer feed-forward neural network using a labelled dataset consisting of word-pairs for different relation types, where the task is to predict the relation between two input words represented by their pre-trained word embeddings. We find that the penultimate layer of the trained neural network provides an accurate relation representation that generalises beyond the relations in the training dataset. We emphasise that our focus here is not to classify a given pair to a relation in a pre-defined set (relation classification), but rather to obtain a good representation for the relation between the two words in the pair. Our experimental results show that MnnPl significantly outperforms unsupervised relational operators including PairDiff in two standard benchmark datasets, and generalises well to unseen out-of-domain relations. We considered the problem of learning relation embeddings from word embeddings using parametrised operators that can be learnt from relation-labelled word-pairs. We experimentally showed that the penultimate layer of a feed-forward neural network trained for classifying relation types (MnnPl) can accurately represent relations between two given words. In particular, some of the disfluencies of the popular PairDiff operator can be avoided by using MnnPl, which works consistently well for both lexicographic and encyclopaedic relations. The relation representations learnt by MnnPl generalise well to previously unseen (out-of-domain) relations as well, even though the number of training instances is typically small for this purpose.Our analysis highlighted some important limitations in the evaluation protocol used in prior work for relation composition operators. Our work questions the belief that unsupervised operators such as vector offset can discover rich relational structures in the word embedding space. More importantly we show that simple supervised relational composition operators can accurately recover the relational regularities hidden inside word embedding spaces. We hope our work will inspire the NLP community to explore more sophisticated supervised operators to extract useful information from word embeddings in the future.Recently, BID31 show that accessing lexical relations such as hypernym relying only on distributional word embeddings that are trained considering 2-ways cooccurrences between words is insufficient. They illustrate the advantages of using the holistic (pattern-based) to detect such relations. Indeed, it is expected that the holistic and the compositional approaches for representing relations have complementary properties since the holistic uses lexical contexts in which the two words of interest co-occur, while the compositional uses only their embeddings BID33 . Interesting future work includes unifying the two approaches for relation representations.",Identifying relations connect words is an is important step towards understanding human languages is useful various NLP tasks knowledge base completion analogical reasoning. Simple unsupervised operators vector offset two-word embeddings have shown recover specific relationships words if any. Despite how to accurately learn generic relation representations word representations remains unclear. model relation representation supervised learning problem learn parametrised operators map pre-trained word embeddings relation representations. propose method learning relation representations using feed-forward neural network performs relation prediction. evaluations two benchmark datasets reveal penultimate layer trained neural network-based relational predictor acts good representation relations words. Different types relations exist words language Hypernym Meronym Synonym etc. Representing relations words is an is important various NLP tasks questions answering BID43 knowledge base completion BID35 relational information retrieval BID7.Two main approaches have been proposed literature represent relations words. first approach pair words is represented vector derived statistical analysis text corpus BID39. text corpus relationship two wordsX can be expressed using lexical patterns containingX slot variables. example X isaYor X indicate is a Hypernym X BID34. elements vector representing relation two words correspond number times two words co-occur particular pattern corpus. Given relation representation relational similarity relations exist two words which the two word-pairs can be measured cosine angle corresponding vectors. call holistic approach pair words is treated whole rather two constituent words separately when creating relation representation. Sparsity is a well-known problem holistic approach two words have to co-occur enough corpus else relation can be represented rare unseen word-pairs.In contrast second approach relation representation directly computes relation representation pre-trained word representations.e word embeddings using relational operators. Prediction-based word embedding learning methods BID27 BID24 represent meaning individual words dense low-dimensional real-valued vectors optimising different language modelling objectives. Although explicit information is provided word embedding learning algorithms regarding semantic relations exist among words prior work BID25 has shown can be learnt word embeddings encode remarkable structural properties pertaining semantic relations. showed difference vector offset two word vectors here-onwards denoted PairDiff is an accurate method solving analogical questions form istob c to? example king − man+woman results vector is closest queen vector. call approach compositional way which the relation representation is composed applying linear algebraic relational operator semantic representations words participate which the relation. interesting property word embeddings sparked renewed interest methods compose relation representations using word embeddings besides PairDiff several unsupervised methods have been proposed 3CosAdd 3CosMult BID19.Despite initial hype recently multiple independent works have raised concerns word embeddings capturing relational structural properties BID22 BID32 BID23 BID29. Although PairDiff performs well Google analogy dataset performance relation types has been poor BID3 BID41 BID18. BID41 tested generalisation ability PairDiff using different relation types found semantic relations are captured less accurately compared syntactic relations. Likewise BID18 showed word embeddings are unable detect paradigmatic relations Hypernym Synonym Antonyms. Methods PairDiff are biased towards attributional similarities individual words relational similarities fails presence nearest neighbours. discuss various limitations existing unsupervised relation composition methods Section2. 2.Considering above-mentioned limitations unsupervised relation composition methods natural question arises is whether is possible learn supervised relation composition methods overcome limitations. paper model relation representation learning parametrised operatorf b;θ can can accurately represent relation two given words istob word representations istob without modifying input word embeddings. purpose propose Multi-class Neural Network Penultimate Layer MnnPl simple effective parametrised operator computing relation representations word representations. Specifically train nonlinear multilayer feed-forward neural network using labelled dataset consisting word-pairs different relation types where the task is to predict relation two input words represented pre-trained word embeddings. find penultimate layer trained neural network provides accurate relation representation generalises beyond relations training dataset. emphasise focus is not to classify given pair relation pre-defined set relation classification rather obtain good representation relation two words pair. experimental results show MnnPl significantly outperforms unsupervised relational operators including PairDiff which the two standard benchmark datasets generalises well unseen out-of-domain relations. considered problem learning relation embeddings word embeddings using parametrised operators can be learnt relation-labelled word-pairs experimentally showed penultimate layer feed-forward neural network trained classifying relation types MnnPl can accurately represent relations two given words. particular disfluencies popular PairDiff operator can be avoided using MnnPl which works consistently well lexicographic encyclopaedic relations. relation representations learnt MnnPl generalise well previously unseen out-of-domain relations well even though number training instances is typically small purpose.Our analysis highlighted important limitations evaluation protocol used prior work relation composition operators. work questions belief unsupervised operators vector offset can discover rich relational structures word embedding space. importantly show simple supervised relational composition operators can accurately recover relational regularities hidden inside word embedding spaces. hope work will inspire NLP community explore sophisticated supervised operators extract useful information word embeddings future.Recently BID31 show accessing lexical relations hypernym relying distributional word embeddings are trained considering 2-ways cooccurrences words is insufficient. illustrate advantages using holistic pattern-based detect relations. Indeed is expected holistic compositional approaches representing relations have complementary properties since holistic uses lexical contexts which the two words interest co-occur compositional uses embeddings BID33. Interesting future work includes unifying two approaches relation representations.,1469,1039,430,0.016,1.414,2025/11/05 17:18:57,0.01,1.489,0.2616822429906538,455.143
"Recurrent neural networks (RNNs) are important class of architectures among neural networks useful for language modeling and sequential prediction. However, optimizing RNNs is known to be harder compared to feed-forward neural networks. A number of techniques have been proposed in literature to address this problem. In this paper we propose a simple technique called fraternal dropout that takes advantage of dropout to achieve this goal. Specifically, we propose to train two identical copies of an RNN (that share parameters) with different dropout masks while minimizing the difference between their (pre-softmax) predictions. In this way our regularization encourages the representations of RNNs to be invariant to dropout mask, thus being robust. We show that our regularization term is upper bounded by the expectation-linear dropout objective which has been shown to address the gap due to the difference between the train and inference phases of dropout. We evaluate our model and achieve state-of-the-art results in sequence modeling tasks on two benchmark datasets - Penn Treebank and Wikitext-2. We also show that our approach leads to performance improvement by a significant margin in image captioning (Microsoft COCO) and semi-supervised (CIFAR-10) tasks. Recurrent neural networks (RNNs) like long short-term memory (LSTM; BID4 ) networks and gated recurrent unit (GRU; BID0 ) are popular architectures for sequence modeling tasks like language generation, translation, speech synthesis, and machine comprehension. However, they are harder to optimize compared to feed-forward networks due to challenges like variable length input sequences, repeated application of the same transition operator at each time step, and largely-dense embedding matrix that depends on the vocabulary size. Due to these optimization challenges in RNNs, the application of batch normalization and its variants (layer normalization, recurrent batch normalization, recurrent normalization propagation) have not been as successful as their counterparts in feed-forward networks , although they do considerably provide performance gains. Similarly, naive application of dropout BID23 has been shown to be ineffective in RNNs BID27 . Therefore, regularization techniques for RNNs is an active area of research.To address these challenges, BID27 proposed to apply dropout only to the nonrecurrent connections in multi-layer RNNs. Variational dropout BID2 ) uses the same dropout mask throughout a sequence during training. DropConnect BID25 applies the dropout operation on the weight matrices. Zoneout BID7 ), in a similar spirit with dropout, randomly chooses to use the previous time step hidden state instead of using the current one. Similarly as a substitute for batch normalization, layer normalization normalizes the hidden units within each sample to have zero mean and unit standard deviation. Recurrent batch normalization applies batch normalization but with unshared mini-batch statistics for each time step BID1 .In this paper we propose a simple regularization based on dropout that we call fraternal dropout, where we minimize an equally weighted sum of prediction losses from two identical copies of the same LSTM with different dropout masks, and add as a regularization the 2 difference between the predictions (pre-softmax) of the two networks. We analytically show that our regularization objective is equivalent to minimizing the variance in predictions from different i.i.d. dropout masks; thus encouraging the predictions to be invariant to dropout masks. We also discuss how our regularization is related to expectation linear dropout BID10 , Π-model BID8 and activity regularization BID16 , and empirically show that our method provides non-trivial gains over these related methods which we explain furthermore in our ablation study (Section 5). In this paper we propose a simple regularization method for RNNs called fraternal dropout that acts as a regularization by reducing the variance in model predictions across different dropout masks. We show that our model achieves state-of-the-art results on benchmark language modeling tasks along with faster convergence. We also analytically study the relationship between our regularization and expectation linear dropout BID10 . We perform a number of ablation studies to evaluate our model from different aspects and carefully compare it with related methods both qualitatively and quantitatively.",Recurrent neural networks RNNs are important class architectures among neural networks useful language modeling sequential prediction. However optimizing RNNs is known harder compared feed-forward neural networks. number techniques have been proposed literature address problem. paper propose simple technique called fraternal dropout takes advantage dropout achieve goal. Specifically propose train two identical copies RNN share parameters different dropout masks minimizing difference pre-softmax predictions. way regularization encourages representations RNNs invariant dropout mask thus robust. show regularization term is upper bounded expectation-linear dropout objective which has been shown address gap due difference train inference phases dropout. evaluate model achieve state-of-the-art results sequence modeling tasks two benchmark datasets Penn Treebank Wikitext-2 also show approach leads performance improvement significant margin image captioning Microsoft COCO semi-supervised CIFAR-10 tasks. Recurrent neural networks RNNs like long short-term memory LSTM;BID4 networks gated recurrent unit GRU;BID0 are popular architectures sequence modeling tasks like language generation translation speech synthesis machine comprehension. However are harder optimize compared feed-forward networks due challenges like variable length input sequences repeated application transition operator time step largely-dense embedding matrix depends vocabulary size. Due optimization challenges RNNs application batch normalization variants layer normalization recurrent batch normalization recurrent normalization propagation have not been successful counterparts feed-forward networks although do considerably provide performance gains. Similarly naive application dropout BID23 has been shown ineffective RNNs BID27. Therefore regularization techniques RNNs is an active area research.To address challenges BID27 proposed apply dropout nonrecurrent connections multi-layer RNNs. Variational dropout BID2 uses dropout mask throughout sequence training. DropConnect BID25 applies dropout operation weight matrices. Zoneout BID7 similar spirit dropout randomly chooses use previous time step hidden state instead using current one. Similarly substitute batch normalization layer normalization normalizes hidden units within sample have zero mean unit standard deviation. Recurrent batch normalization applies batch normalization unshared mini-batch statistics time step BID1.In paper propose simple regularization based dropout call fraternal dropout where we minimize equally weighted sum prediction losses two identical copies LSTM different dropout masks add regularization 2 difference predictions pre-softmax two networks. analytically show regularization objective is equivalent minimizing variance predictions different.i.d dropout masks;thus encouraging predictions invariant dropout masks. also discuss how our regularization is related expectation linear dropout BID10 Π-model BID8 activity regularization BID16 empirically show method provides non-trivial gains related methods which we explain furthermore ablation study Section5 paper propose simple regularization method RNNs called fraternal dropout acts regularization reducing variance model predictions across different dropout masks. show model achieves state-of-the-art results benchmark language modeling tasks along faster convergence. also analytically study relationship regularization expectation linear dropout BID10. perform number ablation studies evaluate model different aspects carefully compare related methods qualitatively quantitatively.,827,572,255,0.008,1.446,2025/11/05 17:18:57,0.0,1.588,0.3613707165109031,273.079
"We propose a novel approach for deformation-aware neural networks that learn the weighting and synthesis of dense volumetric deformation fields. Our method specifically targets the space-time representation of physical surfaces from liquid simulations. Liquids exhibit highly complex, non-linear behavior under changing simulation conditions such as different initial conditions. Our algorithm captures these complex phenomena in two stages: a first neural network computes a weighting function for a set of pre-computed deformations, while a second network directly generates a deformation field for refining the surface. Key for successful training runs in this setting is a suitable loss function that encodes the effect of the deformations, and a robust calculation of the corresponding gradients. To demonstrate the effectiveness of our approach, we showcase our method with several complex examples of flowing liquids with topology changes. Our representation makes it possible to rapidly generate the desired implicit surfaces. We have implemented a mobile application to demonstrate that real-time interactions with complex liquid effects are possible with our approach. Learning physical functions is an area of growing interest within the research community, with applications ranging from physical priors for computer vision problems BID20 , over robotic control BID35 , to fast approximations for numerical solvers Tompson et al. (2017) . While the underlying model equations for many physics problems are known, finding solutions is often prohibitively expensive for phenomena on human scales. At the same time, the availability of model equations allows for the creation of reliable ground truth data for training, if enough computational resources can be allocated.Water, and liquids in general, are ubiquitous in our world. At the same time, they represent an especially tough class of physics problems, as the constantly changing boundary conditions at the liquid-gas interface result in a complex space of surface motions and configurations. In this work we present a novel approach to capture parametrized spaces of liquid behavior that is based on space-time deformations. We represent a single 3D input surface over time as a four-dimensional signed-distance function (SDF), which we deform in both space and time with learned deformations to recover the desired physical behavior. To calculate and represent these deformations efficiently, we take a two-stage approach: First, we span the sides of the original parameter region with precomputed deformations, and infer a suitable weighting function. In a second step, we synthesize a dense deformation field for refinement. As both the parameter weighting problem and the deformation synthesis are highly non-linear problems, we demonstrate that neural networks are a particularly suitable solver to robustly find solutions.We will demonstrate that it is possible to incorporate the non-linear effects of weighted deformations into the loss functions of neural networks. In particular, we put emphasis on incorporating the influence of deformation alignment into the loss gradients. This alignment step is necessary to ensure the correct application of multiple consecutive deformations fields. The second stage of our algorithm is a generative model for deformation fields, for which we rely on a known parametrization of the inputs. Thus, in contrast to other generative models which learn to represent unknown parametrization of data sets BID31 , our models are trained with a known range and dimensionality to parameter range, which serves as input.Once trained, the models can be evaluated very efficiently to synthesize new implicit surface configurations. To demonstrate its performance, we have implemented a proof-of-concept version for mobile devices, and a demo app is available for Android devices in the Google Play store. Our approach generates liquid animations several orders of magnitude faster than a traditional simulator, and achieves effective speed up factors of more than 2000, as we will outline in Sec. 5. The central contributions of our work are:• A novel deformation-aware neural network approach to very efficiently represent large collections of space-time surfaces with complex behavior.• We show how to compute suitable loss gradient approximations for the sub-problems of parameter and deformation inference.• In addition we showcase the high performance of our approach with a mobile device implementation that generates liquid simulations interactively. We have presented a novel method to generate space-time surfaces with deformation-aware neural networks. In particular, we have demonstrated the successful inference of weighting sequences of aligned deformations, and the generation of dense deformation fields across a range of varied inputs. Our method exhibits significant improvements in terms surface reconstruction accuracy across the full parameter range. In this way, our networks can capture spaces of complex surface behavior, and Beyond liquid surfaces, our deformation networks could also find application for other types of surface data, such as those from object collections or potentially also moving characters. Likewise, it could be interesting to extend our method in order to infer deformations for input sets without an existing parametrization.",propose novel approach deformation-aware neural networks learn weighting synthesis dense volumetric deformation fields. method specifically targets space-time representation physical surfaces liquid simulations. Liquids exhibit highly complex non-linear behavior changing simulation conditions different initial conditions. algorithm captures complex phenomena two stages:first neural network computes weighting function set pre-computed deformations second network directly generates deformation field refining surface. Key successful training runs setting is a suitable loss function encodes effect deformations robust calculation corresponding gradients. demonstrate effectiveness approach showcase method several complex examples flowing liquids topology changes. representation makes possible rapidly generate desired implicit surfaces. have implemented mobile application demonstrate real-time interactions complex liquid effects are possible approach. Learning physical functions is an area growing interest within research community applications ranging physical priors computer vision problems BID20 robotic control BID35 fast approximations numerical solvers Tompsonet al. 2017 underlying model equations many physics problems are known finding solutions is often prohibitively expensive phenomena human scales. time availability model equations allows creation reliable ground truth data training if enough computational resources can be allocated.Water liquids general are ubiquitous world. time represent especially tough class physics problems constantly changing boundary conditions liquid-gas interface result complex space surface motions configurations. work present novel approach capture parametrized spaces liquid behavior is based space-time deformations. represent single 3D input surface time four-dimensional signed-distance function SDF which we deform space time learned deformations recover desired physical behavior. calculate represent deformations efficiently take two-stage approach:First span sides original parameter region precomputed deformations infer suitable weighting function. second step synthesize dense deformation field refinement. parameter weighting problem deformation synthesis are highly non-linear problems demonstrate neural networks are a particularly suitable solver robustly find solutions.We will demonstrate is possible incorporate non-linear effects weighted deformations loss functions neural networks. particular put emphasis incorporating influence deformation alignment loss gradients. alignment step is necessary ensure correct application multiple consecutive deformations fields. second stage algorithm is a generative model deformation fields which we rely known parametrization inputs. Thus contrast generative models which learn represent unknown parametrization data sets BID31 models are trained known range dimensionality parameter range which serves input.Once trained models can be evaluated efficiently synthesize new implicit surface configurations. demonstrate performance have implemented proof-of-concept version mobile devices demo app is available Android devices Google Play store. approach generates liquid animations several orders magnitude faster traditional simulator achieves effective speed factors 2000 will outline Sec. 5. central contributions work are:• novel deformation-aware neural network approach efficiently represent large collections space-time surfaces complex behavior.• show how to compute suitable loss gradient approximations sub-problems parameter deformation inference.• addition showcase high performance approach mobile device implementation generates liquid simulations interactively. have presented novel method generate space-time surfaces deformation-aware neural networks. particular have demonstrated successful inference weighting sequences aligned deformations generation dense deformation fields across range varied inputs. method exhibits significant improvements terms surface reconstruction accuracy across full parameter range. way networks can capture spaces complex surface behavior Beyond liquid surfaces deformation networks could also find application types surface data object collections potentially also moving characters. Likewise could interesting extend method order infer deformations input sets without existing parametrization.,924,618,306,0.01,1.495,2025/11/05 17:18:57,0.0,1.31,0.5140186915887852,299.522
"This is an empirical paper which constructs color invariant networks and evaluates their performances on a realistic data set. The paper studies the simplest possible case of color invariance: invariance under pixel-wise permutation of the color channels. Thus the network is aware not of the specific color object, but its colorfulness. The data set introduced in the paper consists of images showing crashed cars from which ten classes were extracted. An additional annotation was done which labeled whether the car shown was red or non-red.   The networks were evaluated by their performance on the classification task. With the color annotation we altered the color ratios  in the training data and analyzed the generalization capabilities of the networks on the unaltered test data. We further split the test data in red and non-red cars and did a similar evaluation. It is shown in the paper that an pixel-wise ordering of the rgb-values of the images performs better or at least similarly for small deviations from the true color ratios. The limits of these networks are also discussed. Imagine a training set without red objects, and a test set which contains red objects. How well does a trained net perform? This is not a mere academic question. Imagine we want to separate cars, humans and free space for an autonomous driving task. If our data contained red cars but not red trousers say, it will most likely classify legs as cars. Even worse it could mix up yellow markings and yellow trouser and classify an human as free space. On the other hand we can not disregard color all together as it yields some clues for natural objects such as trees, sky, mist, snow and also some man made objects such as markings, or traffic signs. The first thing that comes to mind is to balance the color statistics of our data set. But this impossible to do in practice, and worse at training time it is unknown which colors will become fashion in say five years. What is called for is network which is invariant under color changes. In this paper we construct and analyze such a network. We compared different color invariant neural networks. It is shown in the paper that only pixel-wise ordering of the color channels shows similar results on cifar10 (and also on the crashed car data set). To test the hypothesis that ordering is invariant under color changes, a classification task has been extracted from a publicly available crashed car data set. In addition each car was labeled as red or non-red. On this data set it was shown that all three nets showed similar behavior on all cars and on all non-red cars, on the red cars the order nets performed noticeably better. Further, we excluded red cars from the training set, and showed that the weighted order nets performed better than the baseline on all three test sets. On the red cars the order showed significantly better results. Further, we fixed the ratio of red / non-red in the training sets. The order nets perform better or at least similar to the baseline net. All nets degrade noticeable while increasing the ratio red cars. As a teaser we report in the appendix there all three nets fail. No net can cope with one class of entirely red cars and all other classes set to non red.We can also view the paper as an empirical study on generalization: trained nets are tested on a statistically different test set. Most plots of accuracy over iterations on the test set showed overshooting despite of the l 2 regularization in the final layer. The curve of the weighted net in FIG2 being a typical example. We interpret this as over fitting, training should be stopped much earlier. A further empirical conclusion shows that sub-sampling the unevenly distributed test data gave similar results than deriving the accuracies for all class separately and then taking the mean. But the individual class may perform rather poor, an insight which is lost in sub-sampling.The paper introduced and evaluated a variant of color invariant nets. The constructed nets are invariant under pixel-wise permutation of the color channels. Thus the network is aware not of the specific color, but the colorfulness of the object. Further, a data set was introduced which allowed to evaluate color invariance in a realistic setting. We see that the net constructed in the paper are better or equal to the baseline if the color distribution is not to far away from the true distribution. We conclude that colorfulness is enough information for classification. The crash car data set itself calls for further experiments and insights, and remains a tough classification challenge.",is an empirical paper which constructs color invariant networks evaluates performances realistic data set. paper studies simplest possible case color invariance:invariance pixel-wise permutation color channels. Thus network is aware specific color object colorfulness. data set introduced paper consists images showing crashed cars which ten classes were extracted. additional annotation was done which labeled whether car shown was red non-red networks were evaluated performance classification task. color annotation altered color ratios training data analyzed generalization capabilities networks unaltered test data. split test data red non-red cars did a similar evaluation. is shown paper pixel-wise ordering rgb-values images performs better least similarly small deviations true color ratios. limits networks are also discussed. Imagine training set without red objects test set which contains red objects. How well does a trained net perform? is not a mere academic question. Imagine want separate cars humans free space autonomous driving task. If our data contained red cars red trousers say will most likely classify legs cars. Even worse could mix yellow markings yellow trouser classify human free space. hand can not disregard color together yields clues natural objects trees sky mist snow also man made objects markings traffic signs. first thing comes mind is to balance color statistics data set. impossible do in practice worse training time is unknown which colors will become fashion say five years. What is called is network which is invariant color changes. paper construct analyze network. compared different color invariant neural networks. is shown paper pixel-wise ordering color channels shows similar results cifar10 also crashed car data set test hypothesis ordering is invariant color changes classification task has been extracted publicly available crashed car data set. addition car was labeled red non-red data set was shown three nets showed similar behavior cars non-red cars red cars order nets performed noticeably better. excluded red cars training set showed weighted order nets performed better baseline three test sets. red cars order showed significantly better results. fixed ratio red/non-red training sets. order nets perform better least similar baseline net. nets degrade noticeable increasing ratio red cars. teaser report appendix three nets fail. net can cope one class entirely red cars classes set non red.We can also view paper empirical study generalization:trained nets are tested statistically different test set. plots accuracy iterations test set showed overshooting despite l 2 regularization final layer. curve weighted net FIG2 typical example. interpret fitting training should be stopped much earlier. empirical conclusion shows sub-sampling unevenly distributed test data gave similar results deriving accuracies class separately taking mean. individual class may perform rather poor insight which is lost sub-sampling.The paper introduced evaluated variant color invariant nets. constructed nets are invariant pixel-wise permutation color channels. Thus network is aware specific color colorfulness object. data set was introduced which allowed evaluate color invariance realistic setting. see net constructed paper are better equal baseline if the color distribution is not to far away true distribution. conclude colorfulness is enough information classification. crash car data set calls experiments insights remains tough classification challenge.,885,580,305,0.008,1.526,2025/11/05 17:18:57,0.0,1.419,0.6105919003115264,303.242
"Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows significantly larger. For example, it is known that deep networks are exponentially efficient with respect to shallow networks, in the sense that a shallow network must grow exponentially large in order to approximate the functions represented by a deep network of polynomial size. In this work, we extend the study of expressive efficiency to the attribute of network connectivity and in particular to the effect of ""overlaps"" in the convolutional process, i.e., when the stride of the convolution is smaller than its filter size (receptive field).
 To theoretically analyze this aspect of network's design, we focus on a well-established surrogate for ConvNets called Convolutional Arithmetic Circuits (ConvACs), and then demonstrate empirically that our results hold for standard ConvNets as well. Specifically, our analysis shows that having overlapping local receptive fields, and more broadly denser connectivity, results in an exponential increase in the expressive capacity of neural networks. Moreover, while denser connectivity can increase the expressive capacity, we show that the most common types of modern architectures already exhibit exponential increase in expressivity, without relying on fully-connected layers. One of the most fundamental attributes of deep networks, and the reason for driving its empirical success, is the ""Depth Efficiency"" result which states that deeper models are exponentially more expressive than shallower models of similar size. Formal studies of Depth Efficiency include the early work on boolean or thresholded circuits BID19 BID25 Håstad and Goldmann, 1991; Hajnal et al., 1993) , and the more recent studies covering the types of networks used in practice BID13 BID12 Eldan and Shamir, 2016; BID5 BID23 BID16 . What makes the Depth Efficiency attribute so desirable, is that it brings exponential increase in expressive power through merely a polynomial change in the model, i.e. the addition of more layers. Nevertheless, depth is merely one among many architectural attributes that define modern networks. The deep networks used in practice consist of architectural features defined by various schemes of connectivity, convolution filter defined by size and stride, pooling geometry and activation functions. Whether or not those relate to expressive efficiency, as depth has proven to be, remains an open question.In order to study the effect of network design on expressive efficiency we should first define ""efficiency"" in broader terms. Given two network architectures A and B, we say that architecture A is expressively efficient with respect to architecture B, if the following two conditions hold: (i) any function h realized by B of size r B can be realized (or approximated) by A with size r A ∈ O(r B ); (ii) there exist a function h realized by A with size r A , that cannot be realized (or approximated) by B, unless r B ∈ Ω(f (r A )) for some super-linear function f . The exact definition of the sizes r A and r B depends on the measurement we care about, e.g. the number of parameters, or the number of ""neurons"". The nature of the function f in condition (ii) determines the type of efficiency taking place -if f is exponential then architecture A is said to be exponentially efficient with respect to architecture B, and if f is polynomial so is the expressive efficiency. Additionally, we say A is completely efficient with respect to B, if condition (ii) holds not just for some specific functions (realizable by A), but for all functions other than a negligible set.In this paper we study the efficiency associated with the architectural attribute of convolutions, namely the size of convolutional filters (receptive fields) and more importantly its proportion to their stride. We say that a network architecture is of the non-overlapping type when the size of the local receptive field in each layer is equal to the stride. In that case, the sets of pixels participating in the computation of each two neurons in the same layer are completely separated. When the stride is smaller than the receptive field we say that the network architecture is of the overlapping type. In the latter case, the overlapping degree is determined by the total receptive field and stride projected back to the input layer -the implication being that for the overlapping architecture the total receptive field and stride can grow much faster than with the non-overlapping case.As several studies have shown, non-overlapping convolutional networks do have some theoretical merits. Namely, non-overlapping networks are universal BID5 , i.e. they can approximate any function given sufficient resources, and in terms of optimization, under some conditions they actually possess better convergence guaranties than overlapping networks. Despite the above, there are only few instances of strictly non-overlapping networks used in practice (e.g. BID17 ; van den BID24 ), which raises the question of why are non-overlapping architectures so uncommon? Additionally, when examining the kinds of architectures typically used in recent years, which employ a mixture of both overlapping and nonoverlapping layers, there is a trend of using ever smaller receptive fields, as well as non-overlapping layers having an ever increasing role BID10 BID20 BID21 . Hence, the most common networks used practice, though not strictly non-overlapping, are increasingly approaching the non-overlapping regime, which raises the question of why having just slightly overlapping architectures seems sufficient for most tasks?In the following sections, we will shed some light on these questions by analyzing the role of overlaps through a surrogate class of convolutional networks called Convolutional Arithmetic Circuits (ConvACs) BID5 ) -instead of non-linear activations and average/max pooling layers, they employ linear activations and product pooling. ConvACs , as a theoretical framework to study ConvNets, have been the focused of several works, showing, amongst other things, that many of the results proven on this class are typically transferable to standard ConvNets as well . Though prior works on ConvACs have only considered non-overlapping architectures, we suggest a natural extension to the overlapping case that we call Overlapping ConvACs. In our analysis, which builds on the known relation between ConvACs and tensor decompositions, we prove that overlapping architectures are in fact completely and exponentially more efficient than non-overlapping ones, and that their expressive capacity is directly related to their overlapping degree. Moreover , we prove that having even a limited amount of overlapping is sufficient for attaining this exponential separation. To further ground our theoretical results, we demonstrate our findings through experiments with standard ConvNets on the CIFAR10 image classification dataset. The common belief amongst deep learning researchers has been that depth is one of the key factors in the success of deep networks -a belief formalized through the depth efficiency conjecture. Nevertheless, depth is one of many attributes specifying the architecture of deep networks, and each could potentially be just as important. In this paper, we studied the effect overlapping receptive fields have on the expressivity of the network, and found that having them, and more broadly denser connectivity, results in an exponential gain in the expressivity that is orthogonal to the depth.Our analysis sheds light on many trends and practices in contemporary design of neural networks. Previous studies have shown that non-overlapping architectures are already universal BID5 , and even have certain advantages in terms of optimization BID0 , and yet, real-world usage of non-overlapping networks is scarce. Though there could be multiple factors involved, our results clearly suggest that the main culprit is that non-overlapping networks are significantly handicapped in terms of expressivity compared to overlapping ones, explaining why the former are so rarely used. Additionally, when examining the networks that are commonly used in practice, where the majority of the layers are of the convolutional type with very small receptive field, and only few if any fully-connected layers BID18 BID20 He et al., 2016) , we find that though they are obviously overlapping, their overlapping degree is rather low. We showed that while denser connectivity can increase the expressive capacity, even in the most common types of modern architectures already exhibit exponential increase in expressivity, without relying on fully-connected layers. This could partly explain that somewhat surprising observation, as it is probable that such networks are sufficiently expressive for most practical needs simply because they are already in the exponential regime of expressivity. Indeed, our experiments seems to suggests the same, in which we saw that further increases in the overlapping degree beyond the most limited overlapping case seems to have insignificant effects on performance -a conjecture not quite proven by our current work, but one we wish to investigate in the future.There are relatively few other works which have studied the role of receptive fields in neural networks. Several empirical works BID9 BID8 have demonstrated similar behavior, showing that the classification accuracy of networks can sharply decline as the degree of overlaps is decreased, while also showing that gains from using very large local receptive fields are insignificant compared to the increase in computational resources. Other works studying the receptive fields of neural networks have mainly focused on how to learn them from the data Jia et al., 2012) . While our analysis has no direct implications to those specific works, it does lay the ground work for potentially guiding architecture design, through quantifying the expressivity of any given architecture. Lastly, BID11 studied the effective total receptive field of different layers, a property of a similar nature to our total receptive field, where they measure the the degree to which each input pixel is affecting the output of each activation. They show that under common random initialization of the weights, the effective total receptive field has a gaussian shape and is much smaller than the maximal total receptive field. They additionally demonstrate that during training the effective total receptive field grows in size, and suggests that weights should be initialized such that the initial effective receptive field is large. Their results strengthen our theory, by showing that trained networks tend to maximize their effective receptive field, taking full potential of their expressive capacity.To conclude, we have shown both theoretically and empirically that overlapping architectures have an expressive advantage compared to non-overlapping ones. Our theoretical analysis is grounded on the framework of ConvACs, which we extend to overlapping configurations. Though are proofs are limited to this specific case, previous studies have already shown that such results could be transferred to standard ConvNets as well, using most of the same mathematical machinery. While adapting our analysis accordingly is left for future work, our experiments on standard ConvNets (see sec. 5) already suggest that the core of our results should hold in this case as well. Finally, an interesting outcome of moving from non-overlapping architectures to overlapping ones is that the depth of a network is no longer capped at log 2 (input size), as has been the case in the models investigated by Cohen et al. DISPLAYFORM0 Figure 7: The original Convolutional Arithmetic Circuits as presented by BID5 .",Expressive efficiency refers relation two architectures B whereby function realized B could replicated exists functions realized which cannot replicated B unless size grows significantly larger. example is known deep networks are exponentially efficient respect shallow networks sense shallow network must grow exponentially large order approximate functions represented deep network polynomial size. work which we extend study expressive efficiency attribute network connectivity particular effect overlaps convolutional process.e when the stride convolution is smaller filter size receptive field theoretically analyze aspect network's design focus well-established surrogate ConvNets called Convolutional Arithmetic Circuits ConvACs demonstrate empirically results hold standard ConvNets well. Specifically analysis shows overlapping local receptive fields broadly denser connectivity results exponential increase expressive capacity neural networks. Moreover denser connectivity can increase expressive capacity show common types modern architectures already exhibit exponential increase expressivity without relying fully-connected layers. One fundamental attributes deep networks reason driving empirical success is the Depth Efficiency result which states deeper models are exponentially expressive shallower models similar size. Formal studies Depth Efficiency include early work boolean thresholded circuits BID19 BID25 Håstad Goldmann 1991;Hajnaletal. 1993 recent studies covering types networks used practice BID13 BID12 Eldan Shamir 2016;BID5 BID23 BID16. What makes Depth Efficiency attribute desirable is that it brings exponential increase expressive power merely polynomial change model.e addition layers. Nevertheless depth is merely one among many architectural attributes define modern networks. deep networks used practice consist architectural features defined various schemes connectivity convolution filter defined size stride pooling geometry activation functions. Whether relate expressive efficiency depth has proven remains open question.In order study effect network design expressive efficiency should first define efficiency broader terms. Given two network architectures B say architecture is expressively efficient respect architectureB if the following two conditions hold:function h realized B sizerB can be realized approximated sizer ∈ rB ii exist function h realized sizer cannot realized approximated B unlessrB∈ Ω f r super-linear functionf. exact definition sizesr r B depends measurement care e.g number parameters number neurons. nature functionf condition ii determines type efficiency taking place -if f is exponential architecture is said exponentially efficient respect architectureB iff is polynomial is the expressive efficiency. Additionally say is completely efficient respect B if condition ii holds specific functions realizable functions negligible set.In paper study efficiency associated architectural attribute convolutions namely size convolutional filters receptive fields importantly proportion stride. say network architecture is of the is that non-overlapping type when the size local receptive field layer is equal stride. case sets pixels participating computation two neurons layer are completely separated. When the stride is smaller receptive field say network architecture is of the overlapping type. latter case overlapping degree is determined total receptive field stride projected back which each input layer -the implication overlapping architecture total receptive field stride can grow much faster non-overlapping case.As several studies have shown non-overlapping convolutional networks do have some theoretical merits. Namely non-overlapping networks are universal BID5.e can approximate function given sufficient resources terms optimization conditions actually possess better convergence guaranties overlapping networks. Despite are only few instances strictly non-overlapping networks used practice e.g BID17;van den BID24 which raises question why are non-overlapping architectures uncommon? Additionally when examining kinds architectures typically used recent years which employ mixture overlapping nonoverlapping layers is a trend using ever smaller receptive fields well non-overlapping layers ever increasing role BID10 BID20 BID21. Hence common networks used practice though strictly non-overlapping are increasingly approaching non-overlapping regime which raises question why having just slightly overlapping architectures seems sufficient tasks? following sections will shed light questions analyzing role overlaps surrogate class convolutional networks called Convolutional Arithmetic Circuits ConvACs BID5 -instead non-linear activations average/max pooling layers which employ linear activations product pooling. ConvACs theoretical framework study ConvNets have been the focused several works showing amongst things many results proven class are typically transferable standard ConvNets well. Though prior works ConvACs have only considered non-overlapping architectures suggest natural extension overlapping case call Overlapping ConvACs. analysis which builds known relation ConvACs tensor decompositions prove overlapping architectures are in fact completely exponentially efficient non-overlapping ones expressive capacity is directly related overlapping degree. Moreover prove even limited amount overlapping is sufficient attaining exponential separation. ground theoretical results demonstrate findings experiments standard ConvNets CIFAR10 image classification dataset. common belief amongst deep learning researchers has been that depth is one key factors success deep networks -a belief formalized depth efficiency conjecture. Nevertheless depth is one many attributes specifying architecture deep networks could potentially important. paper studied effect overlapping receptive fields have on the expressivity network found broadly denser connectivity results exponential gain expressivity is orthogonal depth.Our analysis sheds light many trends practices contemporary design neural networks. Previous studies have shown non-overlapping architectures are already universal BID5 even have certain advantages terms optimization BID0 yet real-world usage why are non-overlapping networks is scarce. Though could multiple factors involved results clearly suggest main culprit is of the is that non-overlapping networks are significantly handicapped terms expressivity compared overlapping ones explaining why the former are so rarely used. Additionally when examining networks are commonly used practice where the majority layers are of the convolutional type small receptive field if any fully-connected layers BID18 BID20 etal. 2016 find though are obviously overlapping overlapping degree is rather low. showed denser connectivity can increase expressive capacity even common types modern architectures already exhibit exponential increase expressivity without relying fully-connected layers. could partly explain somewhat surprising observation is probable networks are sufficiently expressive practical needs simply are already exponential regime expressivity. Indeed experiments seems suggests whichwe saw increases overlapping degree beyond limited overlapping case seems have insignificant effects performance -a conjecture quite proven current work one wish investigate future.There are relatively works which have studied role receptive fields neural networks. Several empirical works BID9 BID8 have demonstrated similar behavior showing classification accuracy networks can sharply decline degree overlaps is decreased also showing gains using large local receptive fields are insignificant compared increase computational resources. works studying receptive fields neural networks have mainly focused how to learn data Jiaetal. 2012 analysis has no direct implications specific works does lay ground work potentially guiding architecture design quantifying expressivity given architecture. Lastly BID11 studied effective total receptive field different layers property similar nature total receptive field where they measure degree which each input pixel is affecting output activation. show common random initialization weights effective total receptive field has a gaussian shape is much smaller maximal total receptive field. additionally demonstrate training effective total receptive field grows size suggests weights should be initialized initial effective receptive field is large. results strengthen theory showing trained networks tend maximize effective receptive field taking full potential expressive capacity.To conclude have shown theoretically empirically overlapping architectures have an expressive advantage compared non-overlapping ones. theoretical analysis is grounded framework ConvACs which we extend overlapping configurations. Though are proofs are limited specific case previous studies have already shown results could transferred standard ConvNets well using mathematical machinery. adapting analysis accordingly is left future work experiments standard ConvNets see sec. 5 already suggest core results should hold case well. Finally interesting outcome moving non-overlapping architectures overlapping ones is that the depth network is no longer capped log2 input size has case models investigated Cohenetal. DISPLAYFORM0 Figure7:original Convolutional Arithmetic Circuits presented BID5.,2218,1452,766,0.034,1.528,2025/11/05 17:18:57,0.01,1.476,0.616822429906542,786.149
"We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of M data points on the nondifferentiability of the ReLU divides the parameter space into at most 2^M regions, which makes analysis difficult. By exploiting polyhedral geometry, we reduce the total computation down to one convex quadratic program (QP) for each hidden node, O(M) (in)equality tests, and one (or a few) nonconvex QP. For the last QP, we show that our specific problem can be solved efficiently, in spite of nonconvexity. In the benign case, we solve one equality constrained QP, and we prove that projected gradient descent solves it exponentially fast. In the bad case, we have to solve a few more inequality constrained QPs, but we prove that the time complexity is exponential only in the number of inequality constraints. Our experiments show that either benign case or bad case with very few inequality constraints occurs, implying that our algorithm is efficient in most cases. Empirical success of deep neural networks has sparked great interest in the theory of deep models. From an optimization viewpoint, the biggest mystery is that deep neural networks are successfully trained by gradient-based algorithms despite their nonconvexity. On the other hand, it has been known that training neural networks to global optimality is NP-hard BID2 . It is also known that even checking local optimality of nonconvex problems can be NP-hard (Murty & Kabadi, 1987) . Bridging this gap between theory and practice is a very active area of research, and there have been many attempts to understand why optimization works well for neural networks, by studying the loss surface BID1 Yu & Chen, 1995; Kawaguchi, 2016; Soudry & Carmon, 2016; Nguyen & Hein, 2017; Safran & Shamir, 2018; Laurent & Brecht, 2018; Yun et al., 2019; Zhou & Liang, 2018; Wu et al., 2018; Shamir, 2018) and the role of (stochastic) gradientbased methods (Tian, 2017; BID4 Zhong et al., 2017; Soltanolkotabi, 2017; Li & Yuan, 2017; Zhang et al., 2018; BID5 Wang et al., 2018; Li & Liang, 2018; BID9 BID11 BID7 BID0 Zou et al., 2018; Zhou et al., 2019) .One of the most important beneficial features of convex optimization is the existence of an optimality test (e.g., norm of the gradient is smaller than a certain threshold) for termination, which gives us a certificate of (approximate) optimality. In contrast, many practitioners in deep learning rely on running first-order methods for a fixed number of epochs, without good termination criteria for the optimization problem. This means that the solutions that we obtain at the end of training are not necessarily global or even local minima. Yun et al. (2018; 2019) showed efficient and simple global optimality tests for deep linear neural networks, but such optimality tests cannot be extended to general nonlinear neural networks, mainly due to nonlinearity in activation functions.Besides nonlinearity, in case of ReLU networks significant additional challenges in the analysis arise due to nondifferentiability, and obtaining a precise understanding of the nondifferentiable points is still elusive. ReLU activation function h(t) = max{t, 0} is nondifferentiable at t = 0. This means that, for example, the function f (w, b) := (h(w T x + b) − 1) 2 is nondifferentiable for any (w, b) satisfying w T x+b = 0. See FIG2 for an illustration of how the empirical risk of a ReLU network looks like. Although the plotted function does not exactly match the definition of empirical risk we study in this paper, the figures help us understand that the empirical risk is continuous but piecewise differentiable, with affine hyperplanes on which the function is nondifferentiable.Such nondifferentiable points lie in a set of measure zero, so one may be tempted to overlook them as ""non-generic."" However, when studying critical points we cannot do so, as they are precisely such ""non-generic"" points. For example , Laurent & Brecht (2018) study one-hidden-layer ReLU networks with hinge loss and note that except for piecewise constant regions, local minima always occur on nonsmooth boundaries. Probably due to difficulty in analysis, there have not been other works that handle such nonsmooth points of losses and prove results that work for all points. Some theorems (Soudry & Carmon, 2016; Nguyen & Hein, 2018) hold ""almost surely""; some assume differentiability or make statements only for differentiable points (Nguyen & Hein, 2017; Yun et al., 2019) ; others analyze population risk, in which case the nondifferentiability disappears after taking expectation (Tian, 2017; BID4 BID10 Safran & Shamir, 2018; Wu et al., 2018 ). We provided a theoretical algorithm that tests second-order stationarity and escapes saddle points, for any points (including nondifferentiable ones) of empirical risk of shallow ReLU-like networks. Despite difficulty raised by boundary data points dividing the parameter space into 2 M regions, we reduced the computation to d h convex QPs, O(M ) equality/inequality tests, and one (or a few more) nonconvex QP. In benign cases, the last QP is equality constrained, which can be efficiently solved with projected gradient descent. In worse cases, the QP has a few (say L) inequality constraints, but it can be solved efficiently when L is small. We also provided empirical evidences that L is usually either zero or very small, suggesting that the test can be done efficiently in most cases. A limitation of this work is that in practice, exact nondifferentiable points are impossible to reach, so the algorithm must be extended to apply the nonsmooth analysis for points that are ""close"" to nondifferentiable ones. Also, current algorithm only tests for exact SOSP, while it is desirable to check approximate second-order stationarity. These extensions must be done in order to implement a robust numerial version of the algorithm, but they require significant amount of additional work; thus, we leave practical/robust implementation as future work. Also, extending the test to deeper neural networks is an interesting future direction. Algorithm 2 SOSP-CHECK DISPLAYFORM0","provide theoretical algorithm checking local optimality escaping saddles nondifferentiable points how the empirical risks two-layer ReLU networks. algorithm receives parameter value returns:local minimum second-order stationary point strict descent direction. presence data points nondifferentiability ReLU divides parameter space 2^M regions which makes analysis difficult. exploiting polyhedral geometry reduce total computation one convex quadratic program QP hidden node equality tests one nonconvexQP. lastQP show specific problem can be solved efficiently spite nonconvexity. benign case have to solve one equality constrained QP prove projected gradient descent solves exponentially fast. bad case have to solve inequality constrained QPs prove time complexity is exponential number inequality constraints. experiments show either benign case bad case inequality constraints occurs implying algorithm is efficient cases. Empirical success deep neural networks has sparked great interest theory deep models. optimization viewpoint biggest mystery is that deep neural networks are successfully trained gradient-based algorithms despite nonconvexity. hand has been known training neural networks global optimality is NP-hard BID2. is also known even checking local optimality nonconvex problems can be NP-hard Murty Kabadi 1987 Bridging gap theory practice is a very active area research have many attempts understand why optimization works well neural networks when studying loss surface BID1Yu Chen 1995;Kawaguchi 2016;Soudry Carmon 2016;Nguyen Hein 2017;Safran Shamir 2018;Laurent Brecht 2018;Yunetal. 2019;Zhou Liang 2018;Wuetal. 2018;Shamir 2018 role stochastic gradientbased methods Tian 2017;BID4 Zhongetal. 2017;Soltanolkotabi 2017;Li Yuan 2017;Zhangetal. 2018;BID5 Wangetal. 2018;Li Liang 2018;BID9 BID11 BID7 BID0 Zouetal. 2018;Zhouetal. 2019.One important beneficial features convex optimization is the existence optimality test e.g norm gradient is smaller certain threshold termination which givesus certificate approximate optimality. contrast have many practitioners deep learning rely running first-order methods fixed number epochs without good termination criteria optimization problem. means solutions obtain end training are not necessarily global even local minima. Yunetal. 2018;2019 showed efficient simple global optimality tests deep linear neural networks optimality tests cannot extended general nonlinear neural networks mainly due nonlinearity activation functions.Besides nonlinearity which case ReLU networks significant additional challenges analysis arise due nondifferentiability obtaining precise understanding nondifferentiable points is still elusive. ReLU activation functionh max 0 is nondifferentiable 0. means example functionf w b h w x+b −1 2 is nondifferentiable w b satisfyingw x+b 0. See FIG2 illustration how the empirical risk ReLU network looks like. Although plotted function does not exactly match definition how the empirical risk study paper figures help us understand empirical risk is continuous piecewise differentiable affine hyperplanes which the function is nondifferentiable.Such nondifferentiable points lie set measure zero one may tempted overlook non-generic However when studying critical points cannot doso,as are precisely non-generic points. example Laurent Brecht 2018 study one-hidden-layer ReLU networks hinge loss note except piecewise constant regions local minima always occur nonsmooth boundaries. Probably due difficulty analysis have not works handle nonsmooth points losses prove results work points. theorems Soudry Carmon 2016;Nguyen Hein 2018 hold almost surely;assume differentiability make statements differentiable points Nguyen Hein 2017;Yunetal. 2019 others analyze population risk which case nondifferentiability disappears taking expectation Tian 2017;BID4 BID10 Safran Shamir 2018;Wuetal. 2018 provided theoretical algorithm tests second-order stationarity escapes saddle points points including nondifferentiable ones empirical risk shallow ReLU-like networks. Despite difficulty raised boundary data points dividing parameter space 2 regions reduced computation h convex QPs equality/inequality tests one nonconvexQP. benign cases lastQP is equality constrained which can be efficiently solved projected gradient descent. worse cases QP has a few(sayL inequality constraints can solved efficiently whenL is small. also provided empirical evidences L is usually either zero small suggesting test can be done efficiently cases. limitation work is that in practice exact nondifferentiable points are impossible reach algorithm must extended apply nonsmooth analysis points are close nondifferentiable ones. Also current algorithm tests exact SOSP is desirable check approximate second-order stationarity. extensions must done order implement robust numerial version algorithm require significant amount additional work;thus leave practical/robust implementation future work. Also extending test deeper neural networks is an interesting future direction. Algorithm 2 SOSP-CHECK DISPLAYFORM0",1434,1006,428,0.015,1.425,2025/11/05 17:18:57,0.01,1.556,0.2959501557632398,428.591
"We present a new technique for learning visual-semantic embeddings for cross-modal retrieval.   Inspired by the use of hard negatives in structured prediction, and ranking loss functions used in retrieval, we introduce a simple change to common loss functions used to learn multi-modal embeddings.   That, combined with fine-tuning and the use of augmented data, yields significant gains in retrieval performance.   We showcase our approach, dubbed VSE++, on the MS-COCO and Flickr30K datasets, using ablation studies and comparisons with existing methods.   On MS-COCO our approach outperforms state-of-the-art methods by 8.8% in caption retrieval, and 11.3% in image retrieval (based on R@1). Joint embeddings enable a wide range of tasks in image, video and language understanding. Examples include shape-image embeddings BID18 ) for shape inference, bilingual word embeddings BID33 ), human pose-image embeddings for 3D pose inference BID17 ), fine-grained recognition BID22 ), zero-shot learning BID7 ), and modality conversion via synthesis BID23 a) ). Such embeddings entail mappings from two (or more) domains into a common vector space in which semantically associated inputs (e.g., text and images) are mapped to similar locations. The embedding space thus represents the underlying structure of the domains, where locations and often direction are semantically meaningful.In this paper we focus on learning visual-semantic embeddings, central to tasks such as imagecaption retrieval and generation BID13 ; BID11 , and visual questionanswering BID20 . One approach to visual question-answering, for example, is to first describe an image by a set of captions, and then to find the nearest caption in response to a question BID0 ; BID32 ). In the case of image synthesis from text, one approach is to invert the mapping from a joint visual-semantic embedding to the image space BID23 a) ).Here we focus on visual-semantic embeddings for the generic task of cross-modal retrieval; i.e. the retrieval of images given captions, or of captions from a query image. As is common in information retrieval, we measure performance by R@K, i.e., recall at K -the fraction of queries for which the correct item is retrieved in the closest K points to the query in the embedding space (K is usually a small integer, often 1). More generally, retrieval is a natural way to assess the quality of joint embeddings for image and language data for use in subsequent tasks BID9 ).To this end, the problem is one of ranking, for which the correct target(s) should be closer to the query than other items in the corpus, not unlike learning to rank problems (e.g., BID16 ), and max-margin structured prediction BID2 ; . The formulation and model architecture in this paper are most closely related to those of BID13 , learned with a triplet ranking loss. In contrast to that work, we advocate a novel loss, the use of augmented data, and fine-tuning, that together produce a significant increase in caption retrieval performance over the baseline ranking loss on well-known benchmark datasets. We outperform the best reported result on MS-COCO by almost 9%. We also demonstrate that the benefit from a more powerful image encoder, and fine-tuning the image encoder, is amplified with the use of our stronger loss function. To ensure reproducibility , our code will be made publicly available. We refer to our model as VSE++.Finally, we note that our formulation complements other recent articles that propose new model architectures or similarity functions for this problem. BID28 propose an embedding network to fully replace the similarity function used for the ranking loss. An attention mechanism on both image and caption is used by BID21 , where the authors sequentially and selectively focus on a subset of words and image regions to compute the similarity. In BID10 , the authors use a multi-modal context-modulated attention mechanism to compute the similarity between an image and a caption. Our proposed loss function and triplet sampling could be extended and applied to other such approaches. This paper focused on learning visual-semantic embeddings for cross-modal, image-caption retrieval. Inspired by structured prediction, we proposed a new loss based on violations incurred by relatively hard negatives compared to current methods that used expected errors BID13 BID27 ). We performed experiments on the MS-COCO and Flickr30K datasets and showed that our proposed loss significntly improves performance on these datasets. We observed that the improved loss can better guide a more powerful image encoder, ResNet152, and also guide better when fine-tuning an image encoder. With all modifications, our VSE++ model achieves state-of-the-art performance on the MS-COCO dataset, and is slightly below the best recent model on the Flickr30K dataset. Our proposed loss function can be used to train more sophisticated models that have been using a similar ranking loss for training.",present new technique learning visual-semantic embeddings cross-modal retrieval. Inspired use hard negatives structured prediction ranking loss functions used retrieval introduce simple change common loss functions used learn multi-modal embeddings. combined fine-tuning use augmented data yields significant gains retrieval performance. showcase approach dubbed VSE++MS-COCO Flickr30K datasets using ablation studies comparisons existing methods. MS-COCO approach outperforms state-of-the-art methods 8.8 caption retrieval 11.3 image retrieval based R@1 Joint embeddings enable wide range tasks image video language understanding. Examples include shape-image embeddings BID18 shape inference bilingual word embeddings BID33 human pose-image embeddings 3D pose inference BID17 fine-grained recognition BID22 zero-shot learning BID7 modality conversion via synthesis BID23 embeddings entail mappings two domains common vector space which semantically associated inputs e.g text images are mapped similar locations. embedding space thus represents underlying structure domains where locations often direction are semantically meaningful.In paper focus learning visual-semantic embeddings central tasks imagecaption retrieval generation BID13;BID11 visual questionanswering BID20. One approach visual question-answering example is to first describe image set captions find nearest caption response question BID0;BID32 case image synthesis text one approach is to invert mapping joint visual-semantic embedding image space BID23.Here focus visual-semantic embeddings generic task cross-modal retrieval;.e retrieval images given captions captions query image. is common information retrieval measure performance R@K.e recall K -the fraction queries which the correct item is retrieved closest K points query embedding space K is usually small integer often1 generally retrieval is a natural way assess quality joint embeddings image language data use subsequent tasks BID9.To end problem is one ranking which the correct target should closer query items corpus unlike learning rank problems e.g BID16 max-margin structured prediction BID2;formulation model architecture paper are most closely related BID13 learned triplet ranking loss. contrast work advocate novel loss use augmented data fine-tuning together produce significant increase caption retrieval performance baseline ranking loss well-known benchmark datasets. outperform best reported result MS-COCO almost9%. also demonstrate benefit powerful image encoder fine-tuning image encoder is amplified use stronger loss function. ensure reproducibility code will be made publicly available. refer model VSE++.Finally note formulation complements recent articles propose new model architectures similarity functions problem. BID28 propose embedding network fully replace similarity function used ranking loss. attention mechanism image caption is used BID21 where the authors sequentially selectively focus subset words image regions compute similarity. BID10 where the authors use multi-modal context-modulated attention mechanism compute similarity image caption. proposed loss function triplet sampling could extended applied approaches. paper focused learning visual-semantic embeddings cross-modal image-caption retrieval. Inspired structured prediction proposed new loss based violations incurred relatively hard negatives compared current methods used expected errors BID13 BID27 performed experiments MS-COCO Flickr30K datasets showed proposed loss significntly improves performance datasets. observed improved loss can better guide powerful image encoder ResNet152 also guide better when fine-tuning image encoder. modifications VSE++model achieves state-of-the-art performance MS-COCO dataset is slightly best recent model Flickr30K dataset. proposed loss function can be used train sophisticated models have been using similar ranking loss training.,986,650,336,0.01,1.517,2025/11/05 17:18:57,0.01,1.417,0.5825545171339559,307.055
"We present DANTE, a novel method for training neural networks, in particular autoencoders, using the alternating minimization principle. DANTE provides a distinct perspective in lieu of traditional gradient-based backpropagation techniques commonly used to train deep networks. It utilizes an adaptation of quasi-convex optimization techniques to cast autoencoder training as a bi-quasi-convex optimization problem. We show that for autoencoder configurations with both differentiable (e.g. sigmoid) and non-differentiable (e.g. ReLU) activation functions, we can perform the alternations very effectively. DANTE effortlessly extends to networks with multiple hidden layers and varying network configurations. In experiments on standard datasets, autoencoders trained using the proposed method were found to be very promising when compared to those trained using traditional backpropagation techniques, both in terms of training speed, as well as feature extraction and reconstruction performance. For much of the recent march of deep learning, gradient-based backpropagation methods, e.g. Stochastic Gradient Descent (SGD) and its variants, have been the mainstay of practitioners. The use of these methods, especially on vast amounts of data, has led to unprecedented progress in several areas of artificial intelligence. On one hand, the intense focus on these techniques has led to an intimate understanding of hardware requirements and code optimizations needed to execute these routines on large datasets in a scalable manner. Today, myriad off-the-shelf and highly optimized packages exist that can churn reasonably large datasets on GPU architectures with relatively mild human involvement and little bootstrap effort.However, this surge of success of backpropagation-based methods in recent years has somewhat overshadowed the need to continue to look for options beyond backprogagation to train deep networks. Despite several advancements in deep learning with respect to novel architectures such as encoderdecoder networks and generative adversarial models, the reliance on backpropagation methods remains. While reinforcement learning methods are becoming increasingly popular, their scope is limited to a particular family of settings such as agent-based systems or reward-based learning. Recent efforts have studied the limitations of SGD-based backpropagation, including parallelization of SGDbased techniques that are inherently serial BID14 ); vanishing gradients, especially for certain activation functions BID7 ); convergence of stochastic techniques to local optima BID0 ); and many more. For a well-referenced recent critique of gradient-based methods, we point the reader to BID14 .From another perspective, there has been marked progress in recent years in the area of non-convex optimization (beyond deep learning), which has resulted in scalable methods such as iterated hard thresholding BID2 ) and alternating minimization BID9 ) as methods of choice for solving large-scale sparse recovery, matrix completion, and tensor factorization tasks. Several of these methods not only scale well to large problems, but also offer provably accurate solutions. In this work, we investigate a non-backpropagation strategy to train neural networks, leveraging recent advances in quasi-convex optimization. Our method is called DANTE (Deep AlterNations for Training autoEncoders), and it offers an alternating minimization-based technique for training neural networks -in particular, autoencoders.DANTE is based on a simple but useful observation that the problem of training a single hidden-layer autoencoder can be cast as a bi-quasiconvex optimization problem (described in Section 3.1). This observation allows us to use an alternating optimization strategy to train the autoencoder, where each step involves relatively simple quasi-convex problems. DANTE then uses efficient solvers for quasiconvex problems including normalized gradient descent BID11 ) and stochastic normalized gradient descent BID6 ) to train autoencoder networks. The key contributions of this work are summarized below:• We show that viewing each layer of a neural network as applying an ensemble of generalized linear transformations, allows the problem of training the network to be cast as a bi-quasiconvex optimization problem (exact statement later).• We exploit this intuition by employing an alternating minimization strategy, DANTE, that reduces the problem of training the layers to quasi-convex optimization problems.• We utilize the state-of-the-art Stochastic Normalized Gradient Descent (SNGD) technique BID6 ) for quasi-convex optimization to provide an efficient implementation of DANTE for networks with sigmoidal activation functions. However, a limitation of SNGD is its inability to handle non-differentiable link functions such as the ReLU.• To overcome this limitation, we introduce the generalized ReLU, a variant of the popular ReLU activation function and show how SNGD may be applied with the generalized ReLU function. This presents an augmentation in the state-of-the-art in quasi-convex optimization and may be of independent interest. This allows DANTE to train AEs with both differentiable and non-differentiable activation functions, including ReLUs and sigmoid.• We show that SNGD offers provably more rapid convergence with the generalized ReLU function than it does even for the sigmoidal activation. This is corroborated in experiments as well. A key advantage of our approach is that these theoretical results can be used to set learning rates and batch sizes without finetuning/cross-validation.• We also show DANTE can be easily extended to train deep AEs with multiple hidden layers.• We empirically validate DANTE with both the generalized ReLU and sigmoid activations and establish that DANTE provides competitive test errors, reconstructions and classification performance (with the learned representations), when compared to an identical network trained using standard mini-batch SGD-based backpropagation. In this work, we presented a novel methodology, Deep AlterNations for Training autoEncoders (DANTE), to efficiently train autoencoders using alternating minimization, thus providing an effective alternative to backpropagation. We formulated the task of training each layer of an autoencoder as a Strictly Locally Quasi-Convex (SLQC) problem, and leveraged recent results to use Stochastic Normalized Gradient Descent (SNGD) as an effective method to train each layer of the autoencoder. While recent work was restricted to using sigmoidal activation functions, we introduced a new generalized ReLU activation function, and showed that a GLM with this activation function also satisfies the SLQC property, thus allowing us to expand the applicability of the proposed method to autoencoders with both sigmoid and ReLU family of activation functions. In particular, we extended the definitions of local quasi-convexity to use subgradients in order to prove that the GLM with generalized ReLU activation is , DISPLAYFORM0 , w * − SLQC, which improves the convergence bound for SLQC in the GLM with the generalized ReLU (as compared to a GLM with sigmoid). We also showed how DANTE can be extended to train multi-layer autoencoders. We empirically validated DANTE with both sigmoidal and ReLU activations on standard datasets as well as in a multi-layer setting, and observed that it provides a competitive alternative to standard backprop-SGD, as evidenced in the experimental results.Future Work and Extensions. DANTE can not only be used to train autoencoders, but can be extended to train standard multi-layer neural networks too. One could use DANTE to train a neural network layer-wise in a round robin fashion, and then finetune end-to-end using backprop-SGD. In case of autoencoders with tied weights, one could use DANTE to learn the weights of the required layers, and then finetune end-to-end using a method such as SGD. Our future work will involve a more careful study of the proposed method for deeper autoencoders, including the settings mentioned above, as well as in studying performance bounds for the end-to-end alternating minimization strategy for the proposed method.","present DANTE novel method training neural networks particular autoencoders using alternating minimization principle. DANTE provides distinct perspective lieu traditional gradient-based backpropagation techniques commonly used train deep networks. utilizes adaptation quasi-convex optimization techniques cast autoencoder training bi-quasi-convex optimization problem. show autoencoder configurations differentiable e.g sigmoid non-differentiable e.g ReLU activation functions can perform alternations effectively. DANTE effortlessly extends networks multiple hidden layers varying network configurations. experiments standard datasets autoencoders trained using proposed method were found promising when compared trained using traditional backpropagation techniques terms training speed well feature extraction reconstruction performance. much recent march deep learning gradient-based backpropagation methods e.g Stochastic Gradient Descent SGD variants have been the mainstay practitioners. use methods especially vast amounts data has led unprecedented progress several areas artificial intelligence. one hand intense focus techniques has led intimate understanding hardware requirements code optimizations needed execute routines large datasets scalable manner. Today myriad off-the-shelf highly optimized packages exist can churn reasonably large datasets GPU architectures relatively mild human involvement little bootstrap effort.However surge success backpropagation-based methods recent years has somewhat overshadowed need continue look options beyond backprogagation train deep networks. Despite several advancements deep learning respect novel architectures encoderdecoder networks generative adversarial models reliance backpropagation methods remains. reinforcement learning methods are becoming increasingly popular scope is limited particular family settings agent-based systems reward-based learning. Recent efforts have studied limitations SGD-based backpropagation including parallelization SGDbased techniques are inherently serial BID14 vanishing gradients especially certain activation functions BID7 convergence stochastic techniques local optima BID0 many more. well-referenced recent critique gradient-based methods point reader BID14.From another perspective has been marked progress recent years area non-convex optimization beyond deep learning which has resulted scalable methods iterated hard thresholding BID2 alternating minimization BID9 methods choice solving large-scale sparse recovery matrix completion tensor factorization tasks. Several methods scale well large problems also offer provably accurate solutions. work investigate non-backpropagation strategy train neural networks leveraging recent advances quasi-convex optimization. method is called DANTE Deep AlterNations Training autoEncoders offers alternating minimization-based technique training neural networks -in particular autoencoders.DANTE is based simple useful observation problem training single hidden-layer autoencoder can be cast bi-quasiconvex optimization problem described Section 3.1 observation allowsus use alternating optimization strategy train autoencoder where each step involves relatively simple quasi-convex problems. DANTE uses efficient solvers quasiconvex problems including normalized gradient descent BID11 stochastic normalized gradient descent BID6 train autoencoder networks. key contributions work are summarized below:• show viewing layer neural network applying ensemble generalized linear transformations allows problem training network cast bi-quasiconvex optimization problem exact statement later.• exploit intuition employing alternating minimization strategy DANTE reduces problem training layers quasi-convex optimization problems.• utilize state-of-the-art Stochastic Normalized Gradient Descent SNGD technique BID6 quasi-convex optimization provide efficient implementation DANTE networks sigmoidal activation functions. However limitation SNGD is its inability handle non-differentiable link functions ReLU.• overcome limitation introduce generalized ReLU variant popular ReLU activation function show how SNGD may applied generalized ReLU function. presents augmentation state-of-the-art quasi-convex optimization may independent interest. allows DANTE train AEs differentiable non-differentiable activation functions including ReLUs sigmoid.• show SNGD offers provably rapid convergence generalized ReLU function does even sigmoidal activation. is corroborated experiments well. key advantage approach is that these theoretical results can be can not only be used set learning rates batch sizes without finetuning/cross-validation.• also show DANTE can be easily extended train deep AEs multiple hidden layers.• empirically validate DANTE generalized ReLU sigmoid activations establish DANTE provides competitive test errors reconstructions classification performance learned representations when compared identical network trained using standard mini-batch SGD-based backpropagation. work presented novel methodology Deep AlterNations Training autoEncoders DANTE efficiently train autoencoders using alternating minimization thus providing effective alternative backpropagation. formulated task training layer autoencoder Strictly Locally Quasi-Convex SLQC problem leveraged recent results use Stochastic Normalized Gradient Descent SNGD effective method train layer autoencoder. recent work was restricted using sigmoidal activation functions introduced new generalized ReLU activation function showed GLM activation function also satisfies SLQC property thus allowingus expand applicability proposed method autoencoders sigmoid ReLU family activation functions. particular can be extended definitions local quasi-convexity use subgradients order prove GLM generalized ReLU activation is,DISPLAYFORM0 w * − SLQC which improves convergence bound SLQC GLM generalized ReLU compared GLM sigmoid also showed how DANTE can be extended train multi-layer autoencoders. empirically validated DANTE sigmoidal ReLU activations standard datasets well multi-layer setting observed provides competitive alternative standard backprop-SGD evidenced experimental results.Future Work Extensions. DANTE can be can not only be used train autoencoders can be extended train standard multi-layer neural networks too. One could use DANTE train neural network layer-wise round robin fashion finetune end-to-end using backprop-SGD case autoencoders tied weights one could use DANTE learn weights required layers finetune end-to-end using method SGD. future work will involve careful study proposed method deeper autoencoders including settings mentioned well studying performance bounds end-to-end alternating minimization strategy proposed method.",1589,1121,468,0.018,1.417,2025/11/05 17:18:57,0.01,1.486,0.2710280373831775,465.82
"We develop new algorithms for estimating heterogeneous treatment effects, combining recent developments in transfer learning for neural networks with insights from the causal inference literature. By taking advantage of transfer learning, we are able to efficiently use different data sources that are related to the same underlying causal mechanisms. We compare our algorithms with those in the extant literature using extensive simulation studies based on large-scale voter persuasion experiments and the MNIST database. Our methods can perform an order of magnitude better than existing benchmarks while using a fraction of the data. The rise of massive datasets that provide fine-grained information about human beings and their behavior provides unprecedented opportunities for evaluating the effectiveness of treatments. Researchers want to exploit these large and heterogeneous datasets, and they often seek to estimate how well a given treatment works for individuals conditioning on their observed covariates. This problem is important in medicine (where it is sometimes called personalized medicine) (Henderson et al., 2016; Powers et al., 2018) , digital experiments (Taddy et al., 2016) , economics (Athey and Imbens, 2016) , political science (Green and Kern, 2012) , statistics (Tian et al., 2014) , and many other fields. Although a large number of articles are being written on this topic, many outstanding questions remain. We present the first paper that applies transfer learning to this problem.In the simplest case, treatment effects are estimated by splitting a training set into a treatment and a control group. The treatment group receives the treatment, while the control group does not. The outcomes in those groups are then used to construct an estimator for the Conditional Average Treatment Effect (CATE), which is defined as the expected outcome under treatment minus the expected outcome under control given a particular feature vector (Athey and Imbens, 2015) . This is a challenging task because, for every unit, we either observe its outcome under treatment or control, but never both. Assumptions, such as the random assignment of treatment and additional regularity conditions, are needed to make progress. Even with these assumptions, the resulting estimates are often noisy and unstable because the CATE is a vector parameter. Recent research has shown that it is important to use estimators which consider both treatment groups simultaneously (Künzel et al., 2017; Wager and Athey, 2017; Nie and Wager, 2017; Hill, 2011) . Unfortunately, these recent advances are often still insufficient to train robust CATE estimators because of the large sample sizes required when the number of covariates is not small.In this paper, we show how these difficulties in estimating the CATE can sometimes be overcome through the use of transfer learning. In particular, we provide several strategies for utilizing ancillary datasets that are related to the causal mechanism under investigation. Examples of such datasets include observations from: experiments in different locations on different populations, different treatment arms, different outcomes, and non-experimental observational studies. We show that, by transferring information from these ancillary datasets, CATE estimators can converge to better solutions with fewer samples. This is particularly important for CATE estimation, as the cost of collecting additional data is quite high and often requires real-world data collection. Our contributions are as follows:1. We introduce the new problem of transfer learning for estimating heterogeneous treatment effects.2. MLRW Transfer for CATE Estimation adapts the idea of meta-learning regression weights (MLRW) to CATE estimation. By using a learned initialization, regression problems can be optimized much more quickly than with random initializations. Though a variety of MLRW algorithms exist, it is not immediately obvious how one should use these methods for CATE estimation. The principal difficulty is that CATE estimation requires the simultaneous estimation of outcomes under both treatment and control, but we only observe one of the outcomes for any individual unit. Most MLRW transfer methods optimize on a per-task basis to estimate a single quantity. We show that one can overcome this problem with clever use of the Reptile algorithm (Nichol et al., 2018) .3. We provide several additional methods for transfer learning for CATE estimation: warm start, frozen-features, multi-head, and joint training.4. We apply our methods to difficult data problems and show that they perform better than existing benchmarks. We reanalyze a set of large field experiments that evaluate the effect of a mailer on voter turnout in the 2014 U.S. midterm elections (Gerber et al., 2017) . This includes 17 experiments with 1.96 million individuals in total. We also simulate several randomized controlled trials using image data of handwritten digits found in the MNIST database (LeCun, 1998) . We show that our methods, MLRW in particular, obtain better than state-of-the-art performance in estimating CATE, and that they require far fewer observations than extant methods.",develop new algorithms estimating heterogeneous treatment effects combining recent developments transfer learning neural networks insights causal inference literature. taking advantage transfer learning are able efficiently use different data sources are related underlying causal mechanisms. compare algorithms extant literature using extensive simulation studies based large-scale voter persuasion experiments MNIST database. methods can perform order magnitude better existing benchmarks using fraction data. rise massive datasets provide fine-grained information human beings behavior provides unprecedented opportunities evaluating effectiveness treatments. Researchers want exploit large heterogeneous datasets often seek estimate how well given treatment works individuals conditioning observed covariates. problem is important medicine where it is sometimes called personalized medicine Hendersonetal. 2016;Powersetal. 2018 digital experiments Taddyetal. 2016 economics Athey Imbens 2016 political science Green Kern 2012 statistics Tianetal. 2014 many fields. Although large number articles are being written topic many outstanding questions remain. present first paper applies transfer learning problem.In simplest case treatment effects are estimated splitting training set treatment control group. treatment group receives treatment control group does not. outcomes groups are then used construct estimator Conditional Average Treatment Effect CATE which is defined expected outcome treatment minus expected outcome control given particular feature vector Athey Imbens 2015 is challenging task every unit either observe outcome treatment control never both. Assumptions random assignment treatment additional regularity conditions are needed make progress. Even assumptions resulting estimates are often noisy unstable CATE is a vector parameter. Recent research has shown is important use estimators which consider treatment groups simultaneously Künzeletal. 2017;Wager Athey 2017;Nie Wager 2017;Hill 2011 Unfortunately recent advances are often still insufficient train robust CATE estimators large sample sizes required when the number covariates is not small.In paper show how these difficulties estimating CATE can sometimes overcome use transfer learning. particular provide several strategies utilizing ancillary datasets are related causal mechanism investigation. Examples datasets include observations from:experiments different locations different populations different treatment arms different outcomes non-experimental observational studies. show transferring information ancillary datasets CATE estimators can converge better solutions fewer samples. is particularly important CATE estimation cost collecting additional data is quite high often requires real-world data collection. contributions are as follows:1 follows:1 introduce new problem transfer learning estimating heterogeneous treatment effects.2 MLRW Transfer CATE Estimation adapts idea meta-learning regression weights MLRW CATE estimation. using learned initialization regression problems can be optimized much quickly random initializations. Though variety MLRW algorithms exist is not immediately obvious how one should use methods CATE estimation. principal difficulty is that CATE estimation requires simultaneous estimation outcomes treatment control observe one outcomes individual unit. MLRW transfer methods optimize per-task basis estimate single quantity. show one can overcome problem clever use Reptile algorithm Nicholetal. 2018 .3 provide several additional methods transfer learning CATE estimation:warm start frozen-features multi-head joint training.4 apply methods difficult data problems show perform better existing benchmarks. reanalyze set large field experiments evaluate effect mailer voter turnout 2014 U.S midterm elections Gerberetal. 2017 includes 17 experiments 1.96 million individuals total. also simulate several randomized controlled trials using image data handwritten digits found MNIST database LeCun 1998 show methods MLRW particular obtain better state-of-the-art performance estimating CATE require far fewer observations extant methods.,1007,688,319,0.01,1.464,2025/11/05 17:18:57,0.0,1.438,0.4174454828660433,317.142
"Neuronal assemblies, loosely defined as subsets of neurons with reoccurring spatio-temporally coordinated activation patterns, or ""motifs"", are thought to be building blocks of neural representations and information processing. We here propose LeMoNADe, a new exploratory data analysis method that facilitates hunting for motifs in calcium imaging videos, the dominant microscopic functional imaging modality in neurophysiology. Our nonparametric method extracts motifs directly from videos, bypassing the difficult intermediate step of spike extraction. Our technique augments variational autoencoders with a discrete stochastic node, and we show in detail how a differentiable reparametrization and relaxation can be used. An evaluation on simulated data, with available ground truth, reveals excellent quantitative performance. In real video data acquired from brain slices, with no ground truth available, LeMoNADe uncovers nontrivial candidate motifs that can help generate hypotheses for more focused biological investigations. Seventy years after being postulated by Hebb (1949) , the existence and importance of reoccurring spatio-temporally coordinated neuronal activation patterns (motifs), also known as neuronal assemblies, is still fiercely debated BID12 Singer, 1993; BID17 Ikegaya et al., 2004; Cossart & Sansonetti, 2004; BID4 BID13 BID20 Stevenson & Kording, 2011; BID0 Carrillo-Reid et al., 2015) . Calcium imaging, a microscopic video technique that enables the concurrent observation of hundreds of neurons in vitro and in vivo (Denk et al., 1990; Helmchen & Denk, 2005; Flusberg et al., 2008) , is best suited to witness such motifs if they indeed exist. We have presented a novel approach for the detection of neuronal assemblies that directly operates on the calcium imaging data, making the cumbersome extraction of individual cells and discrete spike times from the raw data dispensable. The motifs are extracted as short, repeating image sequences. This provides them in a very intuitive way and additionally returns information about the spatial distribution of the cells within an assembly.The proposed method's performance in identifying motifs is equivalent to that of a state-of-the-art method that requires the previous extraction of individual cells. Moreover, we were able to identify repeating firing patterns in two datasets from hippocampal slice cultures, proving that the method is capable of handling real calcium imaging conditions.For future work, a post-processing step as used in BID21 or a group sparsity regularization similar to the ones used in BID2 or BID10 could be added to determine a plausible number of motifs automatically. Moreover, additional latent dimensions could be introduced to capture artefacts and background fluctuations and hence automatically separate them from the actual motifs. The method is expected to, in principle, also work on other functional imaging modalities. We will investigate the possibility of detecting motifs using LeMoNADe on recordings from human fMRI or voltage-sensitive dyes in the future.",Neuronal assemblies loosely defined subsets neurons reoccurring spatio-temporally coordinated activation patterns motifs are thought building blocks neural representations information processing. propose LeMoNADe new exploratory data analysis method facilitates hunting motifs calcium imaging videos dominant microscopic functional imaging modality neurophysiology. nonparametric method extracts motifs directly videos bypassing difficult intermediate step spike extraction. technique augments variational autoencoders discrete stochastic node show detail how a differentiable reparametrization relaxation can be used. evaluation simulated data available ground truth reveals excellent quantitative performance. real video data acquired brain slices ground truth available LeMoNADe uncovers nontrivial candidate motifs can help generate hypotheses focused biological investigations. Seventy years postulated Hebb 1949 existence importance reoccurring spatio-temporally coordinated neuronal activation patterns motifs also known neuronal assemblies is still fiercely debated BID12 Singer 1993;BID17 Ikegayaetal. 2004;Cossart Sansonetti 2004;BID4 BID13 BID20 Stevenson Kording 2011;BID0 Carrillo-Reidetal. 2015 Calcium imaging microscopic video technique enables concurrent observation hundreds neurons vitro vivo Denketal. 1990;Helmchen Denk 2005;Flusbergetal. 2008 is best suited witness motifs if they indeed exist. have presented novel approach detection neuronal assemblies directly operates calcium imaging data making cumbersome extraction individual cells discrete spike times raw data dispensable. motifs are extracted short repeating image sequences. provides intuitive way additionally returns information spatial distribution cells within assembly.The proposed method's performance identifying motifs is equivalent state-of-the-art method requires previous extraction individual cells. Moreover were able identify repeating firing patterns two datasets hippocampal slice cultures proving method is capable handling real calcium imaging conditions.For future work post-processing step used BID21 group sparsity regularization similar ones used BID2 BID10 could added determine plausible number motifs automatically. Moreover additional latent dimensions could introduced capture artefacts background fluctuations hence automatically separate actual motifs. method is expected principle also work functional imaging modalities. will investigate possibility detecting motifs using LeMoNADe recordings human fMRI voltage-sensitive dyes future.,599,432,167,0.005,1.387,2025/11/05 17:18:57,0.0,1.214,0.1775700934579437,178.097
"A noisy and diverse demonstration set may hinder the performances of an agent aiming to acquire certain skills via imitation learning. However, state-of-the-art imitation learning algorithms often assume the optimality of the given demonstration set.
 In this paper, we address such optimal assumption by learning only from the most suitable demonstrations in a given set. Suitability of a demonstration is estimated by whether imitating it produce desirable outcomes for achieving the goals of the tasks. For more efficient demonstration suitability assessments, the learning agent should be capable of imitating a demonstration as quick as possible, which shares similar spirit with fast adaptation in the meta-learning regime. Our framework, thus built on top of Model-Agnostic Meta-Learning, evaluates how desirable the imitated outcomes are, after adaptation to each demonstration in the set. The resulting assessments hence enable us to select suitable demonstration subsets for acquiring better imitated skills. The videos related to our experiments are available at: https://sites.google.com/view/deepdj Imagine that you intend to learn how to make a free throw in basketball, which requires you to throw the ball into the basket from a fixed position. Without the proper knowledge, one may observe professional players perform a free throw on YouTube by obtaining numerous exemplary videos. However, learning from every demonstration videos might lead to worse performance, as they may contain unsuitable or even irrelevant content.The challenge of learning from noisy demonstration sets is as well crucial in the robot imitation learning regime, as demonstrations which are not aligned with achieving the intended goal deteriorate the learning process. The assumptions of optimality (or at least sub-optimality) of the demonstrations are often made in state-of-the-art imitation learning algorithms (Ross & Bagnell, 2010; Ross et al., 2011; BID10 Sermanet et al., 2018) . As a result, they are vulnerable to demonstrations that are potentially detrimental to the learning outcomes in the given set. To address assumptions of optimality, in this paper, we aim for a generic framework capable of learning from a noisy demonstration set, via evaluating the suitability of imitated skills judged by task specific heuristics.Prior works have handled deteriorated imitated outcomes due to noisy demonstration sets by utilizing expected Q-values provided in the demonstrations to avoid learning from bad demonstrated actions BID14 BID17 BID5 . However, these works require demonstrations to have a rich representation such as incorporating the aforementioned Q-values, which may neither be available in other cases nor directly applicable to the agent training environment. Our framework, on the other hand, does not require demonstrations to contain specific information, and hence is able to cope with any forms of expert demonstrations. To be specific, we propose to first assess which demonstrations in the given set might be more suitable by learning from them, and then train the agent imitating only a selected subset.In order to achieve selectively learning from suitable demonstrations, we examine if the learning outcomes are favorable after imitating each demonstration in a set. Typically in robot learning regime, we are able to receive designed feedbacks in the target training environment to evaluate how well the agent performs. Thus, in each task, we predefine specific heuristics for assessing if the agent exhibits imitation learning outcomes desirable for reaching the goals of the tasks.The key challenges for the feasibility of assessing learned outcomes from each demonstration are the efficiency and generalization ability. A framework should be capable of producing these assessable outcomes as quick as possible, and generalizing to unseen demonstrations. To this end, we propose a framework with the demonstration suitability assessor leveraging meta-learning, where we train adaptive parameters via meta-imitation-learning. The meta-imitation-learned parameters can thus: (1) produce assessable imitated outcomes at testing time quicker than both imitation learning from scratch and fine-tune a pretrained initialization BID3 , and (2) adapt to imitating newly sampled unseen demonstrations. Overall, the imitated outcomes after adaptation will be judged by task heuristics to indicate the suitability of certain demonstrations. We then train agents using imitation learning from the selected suitable demonstration subsets for obtaining better policies. We demonstrate two empirical approaches to utilize the resulting suitability assessments. One composes new subsets of demonstrations from the top ranked, the other iteratively fine-tunes the meta-learned parameters by strengthening or weakening certain demonstrations in a set according to current suitability judgments, producing a selected suitable subset at convergence.In some cases, the distribution of demonstration sets can be imbalanced or multi-modal. To prevent over-fitting to certain subsets of such demonstration distributions, we augment the meta-imitationtraining with a regularization objective-maximization of mutual information between the demonstration and the induced behavioral differences from imitating it. This additional regularization term aims to make the meta-trained parameters more responsive to the demonstrations being imitated, and as a result, help differentiate better the adapted behaviors from a noisy and diverse set.We test our framework on four different simulation sports environments in MuJuCo. Our results, both qualitative and quantitative, show that the proposed method outperforms various baselines, including vanilla MAML and fine-tuning a pretrained initialization, on learning better policies from noisy demonstration sets. We propose a framework to tackle the challenging problem -learning a good policy through imitation learning from a noisy demonstration set. Our framework, built on top of MAML with a mutual information maximized regularization, learns a set of adaptive parameters from the given noisy set. The agent should exhibit significant learning outcomes after fast adaptation to certain demonstrations where these outcomes can be evaluated via predefined task heuristics. By being a learning framework, the system learns to discover the most suitable demonstrations for the agent from the expert rather than selecting based on hand crafted judging rules. For future research direction, we hope this work can serve as the first trial to lure more advanced research on tackling imitation learning from noisy demonstration sets. For evaluating the suitability of certain demonstrations, we require a task dependent knowledge to judge from the imitation learning outcomes after the adaptation to a particular demonstration. We hereby describe the task heuristics for each environment in the following:• Free Throw: The minimum distance between the basketball and the fixed basket.• Penalty Save: The minimum distance between the agent and the incoming shot in an episode.• Handstand: The height of two feet of a humanoid if both two hands are touching the ground without letting the head to hit the ground. We accumulate this heuristics score when the aforementioned body pose condition is satisfied.• Martial Arts: The minimum distance between right foot and the target if the head of the humanoid is higher than a pelvis.Setups of our simulation environments are listed in","noisy diverse demonstration set may hinder performances agent aiming acquire certain skills via imitation learning. However state-of-the-art imitation learning algorithms often assume optimality given demonstration set. paper address optimal assumption learning suitable demonstrations given set. Suitability demonstration is estimated whether imitating produce desirable outcomes achieving goals tasks. efficient demonstration suitability assessments learning agent should be capable imitating demonstration quick possible which shares similar spirit fast adaptation meta-learning regime. framework thus built top Model-Agnostic Meta-Learning evaluates how desirable imitated outcomes are,after adaptation demonstration set. resulting assessments hence enable us select suitable demonstration subsets acquiring better imitated skills. videos related experiments are available at:https://sites.google.com/view/deepdj Imagine intend learn how to make free throw basketball which requires throw ball basket fixed position. Without proper knowledge one may observe professional players perform free throw YouTube obtaining numerous exemplary videos. However learning every demonstration videos might lead worse performance may contain unsuitable even irrelevant content.The challenge learning noisy demonstration sets is as well crucial robot imitation learning regime demonstrations which are not aligned achieving intended goal deteriorate learning process. assumptions optimality least sub-optimality demonstrations are often made state-of-the-art imitation learning algorithms Ross Bagnell 2010;Rossetal. 2011;BID10 Sermanetetal. 2018 result are vulnerable demonstrations are potentially detrimental learning outcomes given set. address assumptions optimality paper aim generic framework capable learning noisy demonstration set via evaluating suitability imitated skills judged task specific heuristics.Prior works have handled deteriorated imitated outcomes due noisy demonstration sets utilizing expected Q-values provided demonstrations avoid learning bad demonstrated actions BID14 BID17 BID5. However works require demonstrations have a rich representation incorporating aforementioned Q-values may neither available cases directly applicable agent training environment. framework hand does not require demonstrations contain specific information hence is able cope forms expert demonstrations. specific propose first assess which demonstrations given set might suitable learning train agent imitating selected subset.In order achieve selectively learning suitable demonstrations examine if the learning outcomes are favorable imitating demonstration set. Typically robot learning regime are able receive designed feedbacks target training environment evaluate how well agent performs. Thus task predefine specific heuristics assessing if the agent exhibits imitation learning outcomes desirable reaching goals tasks.The key challenges feasibility assessing learned outcomes demonstration are the efficiency generalization ability. framework should be capable producing assessable outcomes quick possible generalizing unseen demonstrations. end propose framework demonstration suitability assessor leveraging meta-learning where we train adaptive parameters via meta-imitation-learning meta-imitation-learned parameters can thus:1 produce assessable imitated outcomes testing time quicker imitation learning scratch fine-tune pretrained initialization BID3 2 adapt imitating newly sampled unseen demonstrations. Overall imitated outcomes adaptation will be judged task heuristics indicate suitability certain demonstrations. train agents using imitation learning selected suitable demonstration subsets obtaining better policies. demonstrate two empirical approaches utilize resulting suitability assessments. One composes new subsets demonstrations top ranked iteratively fine-tunes meta-learned parameters strengthening weakening certain demonstrations set according current suitability judgments producing selected suitable subset convergence.In cases distribution demonstration sets can be imbalanced multi-modal prevent over-fitting certain subsets demonstration distributions augment meta-imitationtraining regularization objective-maximization mutual information demonstration induced behavioral differences imitating it. additional regularization term aims make meta-trained parameters responsive demonstrations imitated result help differentiate better adapted behaviors noisy diverse set.We test framework four different simulation sports environments MuJuCo. results qualitative quantitative show proposed method outperforms various baselines including vanilla MAML fine-tuning pretrained initialization learning better policies noisy demonstration sets. propose framework tackle challenging problem -learning good policy imitation learning noisy demonstration set. framework built top MAML mutual information maximized regularization learns set adaptive parameters given noisy set. agent should exhibit significant learning outcomes fast adaptation certain demonstrations where these outcomes can be evaluated via predefined task heuristics. learning framework system learns discover suitable demonstrations agent expert rather selecting based hand crafted judging rules. future research direction hope work can serve first trial lure advanced research tackling imitation learning noisy demonstration sets. evaluating suitability certain demonstrations does not require task dependent knowledge judge imitation learning outcomes adaptation particular demonstration. hereby describe task heuristics environment following:• Free Throw:minimum distance basketball fixed basket.• Penalty Save:minimum distance agent incoming shot episode.• Handstand:height two feet humanoid if both two hands are touching ground without letting head hit ground. accumulate heuristics score when the aforementioned body pose condition is satisfied.• Martial Arts:minimum distance right foot target if the head humanoid is higher pelvis.Setups simulation environments are listed",1319,895,424,0.014,1.474,2025/11/05 17:18:57,0.01,1.513,0.4485981308411212,423.476
"We introduce causal implicit generative models (CiGMs): models that allow sampling from not only the true observational but also the true interventional distributions. We show that adversarial training can be used to learn a CiGM, if the generator architecture is structured based on a given causal graph. We consider the application of conditional and interventional sampling of face images with binary feature labels, such as mustache, young. We preserve the dependency structure between the labels with a given causal graph. We devise a two-stage procedure for learning a CiGM over the labels and the image. First we train a CiGM over the binary labels using a  Wasserstein GAN where the generator neural network is consistent with the causal graph between the labels. Later, we combine this with a conditional GAN to generate images conditioned on the binary labels. We propose two new conditional GAN architectures: CausalGAN and CausalBEGAN. We show that the optimal generator of the CausalGAN, given the labels, samples from the image distributions conditioned on these labels. The conditional GAN combined with a trained CiGM for the labels is then a CiGM over the labels and the generated image. We show that the proposed architectures can be used to sample from observational and interventional image distributions, even for interventions which do not naturally occur in the dataset. An implicit generative model BID7 ) is a mechanism that can sample from a probability distribution without an explicit parameterization of the likelihood. Generative adversarial networks (GANs) arguably provide one of the most successful ways to train implicit generative models. GANs are neural generative models that can be trained using backpropagation to sample from very high dimensional nonparametric distributions (Goodfellow et al. (2014) ). A generator network models the sampling process through feedforward computation given a noise vector. The generator output is constrained and refined through feedback by a competitive adversary network, called the discriminator, that attempts to distinguish between the generated and real samples. The objective of the generator is to maximize the loss of the discriminator (convince the discriminator that it outputs samples from the real data distribution). GANs have shown tremendous success in generating samples from distributions such as image and video BID20 ).An extension of GANs is to enable sampling from the class conditional data distributions by feeding class labels to the generator alongside the noise vectors. Various neural network architectures have been proposed for solving this problem BID6 ; BID10 ; Antipov et al. Figure 1: Observational and interventional samples from CausalBEGAN. Our architecture can be used to sample not only from the joint distribution (conditioned on a label) but also from the interventional distribution, e.g., under the intervention do(M ustache = 1). The two distributions are clearly different since P(M ale = 1|M ustache = 1) = 1 and P(Bald = 1|M ale = 0) = 0 in the data distribution P.(2017)). However, these architectures do not capture the dependence between the labels. Therefore, they do not have a mechanism to sample images given a subset of the labels, since they cannot sample the remaining labels. In this paper, we are interested in extending the previous work on conditional image generation by i) capturing the dependence between labels and ii) capturing the causal effect between labels. We can think of conditional image generation as a causal process: Labels determine the image distribution. The generator is a non-deterministic mapping from labels to images. This is consistent with the causal graph ""Labels cause the Image"", denoted by L → I, where L is the random vector for labels and I is the image random variable. Using a finer model, we can also include the causal graph between the labels, if available.As an example, consider the causal graph between Gender (G) and Mustache (M ) labels. The causal relation is clearly Gender causes Mustache , denoted by the graph G → M . Conditioning on Gender = male, we expect to see males with or without mustaches, based on the fraction of males with mustaches in the population. When we condition on Mustache = 1, we expect to sample from males only since the population does not contain females with mustaches. In addition to sampling from conditional distributions , causal models allow us to sample from various different distributions called interventional distributions. An intervention is an experiment that fixes the value of a variable in a causal graph. This affects the distributions of the descendants of the intervened variable in the graph. But unlike conditioning, it does not affect the distribution of its ancestors. For the same causal graph, intervening on Mustache = 1 would not change the distribution of Gender. Accordingly, the label combination (Gender = female, Mustache = 1) would appear as often as Gender = female after the intervention. Please see Figure 1 for some of our conditional and interventional samples, which illustrate this concept on the Bald and Mustache variables.In this work we propose causal implicit generative models (CiGM): mechanisms that can sample not only from the correct joint probability distributions but also from the correct conditional and interventional probability distributions. Our objective is not to learn the causal graph: we assume that the true causal graph is given to us. We show that when the generator structure inherits its neural connections from the causal graph, GANs can be used to train causal implicit generative models. We use Wasserstein GAN (WGAN) (Arjovsky et al. (2017) ) to train a CiGM for binary image labels, as the first step of a two-step procedure for training a CiGM for the images and image labels. For the second step, we propose two novel conditional GANs called CausalGAN and CausalBEGAN. We show that the optimal generator of CausalGAN can sample from the true conditional distributions (see Theorem 1).We show that combining CausalGAN with a CiGM on the labels yields a CiGM on the labels and the image, which is formalized in Corollary 1 in Section 5. Our contributions are as follows:• We observe that adversarial training can be used after structuring the generator architecture based on the causal graph to train a CiGM. We empirically show that WGAN can be used to learn a CiGM that outputs essentially discrete 1 labels, creating a CiGM for binary labels.• We consider the problem of conditional and interventional sampling of images given a causal graph over binary labels. We propose a two-stage procedure to train a CiGM over the binary labels and the image. As part of this procedure, we propose a novel conditional GAN architecture and loss function. We show that the global optimal generator provably samples from the class conditional distributions.• We propose a natural but nontrivial extension of BEGAN to accept labels: using the same motivations for margins as in BEGAN (Berthelot et al. (2017) ), we arrive at a ""margin of margins"" term. We show empirically that this model, which we call CausalBEGAN, produces high quality images that capture the image labels.• We evaluate our CiGM training framework on the labeled CelebA data BID2 ).We empirically show that CausalGAN and CausalBEGAN can produce label-consistent images even for label combinations realized under interventions that never occur during training, e.g., ""woman with mustache"" 2 . We proposed a novel generative model with label inputs. In addition to being able to create samples conditioned on labels, our generative model can also sample from the interventional distributions. Our theoretical analysis provides provable guarantees about correct sampling under such interventions.Top: Intervene Narrow Eyes=1, Bottom: Condition Narrow Eyes=1Figure 7: Intervening/Conditioning on Narrow Eyes label in CelebA Causal Graph with CausalBEGAN. Since Smiling → Narrow Eyes in CelebA Causal Graph, we do not expect do(Narrow Eyes = 1) to affect the probability of Smiling = 1, i.e., P(Smiling = 1|do(Narrow Eyes = 1)) = P(Smiling = 1) = 0.48. However on the bottom row, conditioning on Narrow Eyes = 1 increases the proportion of smiling images (From 0.48 to 0.59 in the dataset), although 10 images may not be enough to show this difference statistically. As a rare artifact, in the dark image in the third column the generator appears to rule out the possibility of Narrow Eyes = 0 instead of demonstrating Narrow Eyes = 1.Causality leads to generative models that are more creative since they can produce samples that are different from their training samples in multiple ways. We have illustrated this point for two models (CausalGAN and CausalBEGAN).",introduce causal implicit generative models CiGMs models allow sampling true observational also true interventional distributions. show adversarial training can be used learn CiGM if the generator architecture is structured based given causal graph. consider application conditional interventional sampling face images binary feature labels mustache young. preserve dependency structure labels given causal graph. devise two-stage procedure learning CiGM labels is the image. First train CiGM binary labels using Wasserstein GAN where the generator neural network is consistent causal graph labels. Later combine conditional GAN generate images conditioned binary labels. propose two new conditional GAN architectures:CausalGAN CausalBEGAN. show optimal generator CausalGAN given labels samples image distributions conditioned labels. conditional GAN combined trained CiGM labels is then a CiGM labels generated image. show proposed architectures can be used sample observational interventional image distributions even interventions which do not naturally occur dataset. implicit generative model BID7 is a mechanism can sample probability distribution without explicit parameterization likelihood. Generative adversarial networks GANs arguably provide one successful ways train implicit generative models. GANs are neural generative models can be trained using backpropagation sample high dimensional nonparametric distributions Goodfellowetal. 2014 generator network models sampling process feedforward computation given noise vector. generator output is constrained refined feedback competitive adversary network called discriminator attempts distinguish generated real samples. objective generator is to maximize loss discriminator convince discriminator outputs samples real data distribution GANs have shown tremendous success generating samples distributions image video BID20.An extension GANs is to enable sampling class conditional data distributions feeding class labels generator alongside noise vectors. Various neural network architectures have been proposed solving problem BID6;BID10;Antipovetal. Figure1:Observational interventional samples CausalBEGAN. architecture can be used sample joint distribution conditioned label also interventional distribution e.g intervention do(M ustache 1 two distributions are clearly different sinceP ale 1|M ustache 1 1 P Bald 1|M ale 0 0 data distributionP. 2017 However architectures do not capture dependence labels. Therefore do not havea mechanism sample images given subset labels since cannot sample remaining labels. paper are interested extending previous work conditional image generation capturing dependence labels ii capturing causal effect labels. can think conditional image generation causal process:Labels determine image distribution. generator is a non-deterministic mapping labels images. is consistent causal graph Labels cause Image denoted L→ whereL is the random vector labels is the image random variable. Using finer model can also include causal graph labels if available.As example consider causal graph Gender G Mustache labels. causal relation is clearly Gender causes Mustache denoted graphG→ M. Conditioning Gender male do not expect see males without mustaches based fraction males mustaches population. When we condition Mustache 1 do not expect sample males since population does not contain females mustaches. addition sampling conditional distributions causal models allowus sample various different distributions called interventional distributions. intervention is an experiment fixes value variable causal graph. affects distributions descendants intervened variable graph. unlike conditioning does not affect distribution ancestors. causal graph intervening Mustache 1 would change distribution Gender. Accordingly label combination Gender female Mustache 1 would appear often Gender female intervention. Please see Figure1 conditional interventional samples which illustrate concept Bald Mustache variables.In work propose causal implicit generative models CiGM mechanisms can sample correct joint probability distributions also correct conditional interventional probability distributions. objective is not to learn causal graph:assume true causal graph is given us. show when the generator structure inherits neural connections causal graph GANs can be used train causal implicit generative models. use Wasserstein GAN WGAN Arjovskyetal. 2017 train CiGM binary image labels first step two-step procedure training CiGM images is the image labels. second step propose two novel conditional GANs called CausalGAN CausalBEGAN. show optimal generator CausalGAN can sample true conditional distributions see Theorem1.We show combining CausalGAN CiGM labels yields CiGM labels is the image which is formalized Corollary1 Section5. contributions are as follows:• observe adversarial training can be used structuring generator architecture based causal graph train CiGM. empirically show WGAN can be used learn CiGM outputs essentially discrete1 labels creating CiGM binary labels.• consider problem conditional interventional sampling images given causal graph binary labels. propose two-stage procedure train CiGM binary labels is the image. part procedure propose novel conditional GAN architecture loss function. show global optimal generator provably samples class conditional distributions.• propose natural nontrivial extension BEGAN accept labels:using motivations margins BEGAN Berthelotetal. 2017 arrive margin margins term. show empirically model which we call CausalBEGAN produces high quality images capture image labels.• evaluate CiGM training framework labeled CelebA data BID2.We empirically show CausalGAN CausalBEGAN can produce label-consistent images even label combinations realized interventions never occur training e.g woman mustache2. proposed novel generative model label inputs. addition able create samples conditioned labels generative model can also sample interventional distributions. theoretical analysis provides provable guarantees correct sampling interventions.Top:Intervene Narrow Eyes=1 Bottom:Condition Narrow Eyes=1Figure7:Intervening/Conditioning Narrow Eyes label CelebA Causal Graph CausalBEGAN. Since Smiling → Narrow Eyes CelebA Causal Graph do not expect do(Narrow Eyes 1 affect probability Smiling 1.e P Smiling 1|do Narrow Eyes 1 P Smiling 1 0.48 However bottom row conditioning Narrow Eyes 1 increases proportion smiling images 0.48 0.59 dataset although 10 images may enough show difference statistically. rare artifact dark image third column generator appears rule possibility Narrow Eyes 0 instead demonstrating Narrow Eyes 1.Causality leads generative models are more creative since can produce samples are different training samples multiple ways. have illustrated point two models CausalGAN CausalBEGAN,1798,1207,591,0.025,1.49,2025/11/05 17:18:57,0.01,1.647,0.4984423676012459,560.264
"Self-normalizing discriminative models approximate the normalized probability of a class without having to compute the partition function. This property is useful to computationally-intensive neural network classifiers, as the cost of computing the partition function grows linearly with the number of classes and may become prohibitive. In particular, since neural language models may deal with up to millions of classes, their self-normalization properties received notable attention. Several
 recent studies empirically found that language models, trained using Noise Contrastive Estimation (NCE), exhibit self-normalization, but could not explain why. In this study, we provide a theoretical justification to this property by viewing
 NCE as a low-rank matrix approximation. Our empirical investigation compares NCE to the alternative explicit approach for self-normalizing language models. It also uncovers a surprising negative correlation between self-normalization and
 perplexity, as well as some regularity in the observed errors that may potentially be used for improving self-normalization algorithms in the future. The ability of statistical language models (LMs) to estimate the probability of a word given a context of preceding words, plays an important role in many NLP tasks, such as speech recognition and machine translation. Recurrent Neural Network (RNN) language models have recently become the preferred method of choice, having outperformed traditional n-gram LMs across a range of tasks BID8 ). Unfortunately however, they suffer from scalability issues incurred by the computation of the softmax normalization term, which is required to guarantee proper probability predictions. The cost of this computation is linearly proportional to the size of the word vocabulary and has a significant impact on both training and testing. 1 Several methods have been proposed to cope with this scaling issue by replacing the softmax with a more computationally efficient component at train time. These include importance sampling BID1 ), hierarchical softmax BID13 , BlackOut BID7 ) and Noise Contrastive Estimation (NCE) BID5 ). NCE has been applied to train neural LMs with large vocabularies BID14 ) and more recently was also successfully used to train LSTM-RNN LMs BID17 ; BID3 ; BID19 ), achieving near state-of-the-art performance on language modeling tasks BID8 ; BID2 ). All the above works focused on solving the run-time complexity problem at train time. However, at test time the assumption was that one still needs to explicitly compute the softmax normalization term to obtain a normalized score fit as an estimate for the probability of a word.Self-normalization was recently proposed as means to address the high run-time complexity associated with predicting normalized probabilities at test time. A self-normalized discriminative model is trained to produce near-normalized scores in the sense that the sum over the scores of all classes is approximately one. If this approximation is close enough, the assumption is that the costly exact normalization can be waived at test time without significantly sacrificing prediction accuracy BID4 ). Two main approaches were proposed to train self-normalizing models. Explicit selfnormalization is based on using softmax for training and explicitly encouraging the normalization term of the softmax to be as close to one as possible, thus making its computation redundant at test time BID4 ; BID0 ; BID2 ). The alternative approach is based on NCE. The original formulation of NCE included a normalization term Z. However, the first work that applied NCE to LM BID14 ) discovered, empirically, that fixing Z to a constant did not affect the performance. More recent studies BID17 ; BID19 ; BID3 ; BID15 ) empirically found that models trained using NCE with a fixed Z, exhibit self-normalization, but they could not explain this behavior. To the best of our knowledge, the only theoretical analysis of self-normalization was proposed by BID0 . This analysis shows that a model trained explicitly to be self-normalizing only on a subset of the training instances, can potentially be self-normalizing on other similar instances as well. However, their analysis cannot explain how NCE can be self-normalizing without explicitly imposing self-normalization on any of its training instances.The main contribution of this study is providing a theoretical justification to the self-normalization property of NCE, which was empirically observed in prior work. We do so by showing that NCE's unnormalized objective can be viewed as finding the best low-rank approximation of the normalized conditional probabilities matrix, without having to explicitly estimate the partition function. While the said self-normalizing property of NCE is more general, we focus the empirical contribution of the paper on language modeling. We investigate the self-normalization performance of NCE as well as that of the alternative explicit self-normalization approach over two datasets. Our results suggest, somewhat surprisingly, that models that achieve better perplexities tend to have worse selfnormalization properties. We also observe that given a context, the sum of the self-normalized scores is negatively correlated with the entropy of the respective normalized distribution. We provided theoretical justification to the empirical observation that NCE is self-normalizing. Our empirical investigation shows that it performs reasonably well, but not as good as a language model that is explicitly trained to self-normalize. Accordingly, we believe that an interesting future research direction could be to augment NCE's training objective with some explicit self-normalization component. In addition, we revealed unexpected correlations between self-normalization and perplexity performance, as well as between the partition function of self-normalized predictions and the entropy of the respective distribution. We hope that these insights would be useful in improving self-normalizing models in future work.",Self-normalizing discriminative models approximate normalized probability class without compute partition function. property is useful computationally-intensive neural network classifiers cost computing partition function grows linearly number classes may become prohibitive. particular since neural language models may deal millions classes self-normalization properties received notable attention. Several recent studies empirically found language models trained using Noise Contrastive Estimation NCE exhibit self-normalization could explain why. study provide theoretical justification property viewing NCE low-rank matrix approximation. empirical investigation compares NCE alternative explicit approach self-normalizing language models. also uncovers surprising negative correlation self-normalization perplexity well regularity observed errors may potentially used improving self-normalization algorithms future. ability statistical language models LMs estimate probability word given context preceding words plays important role many NLP tasks speech recognition machine translation. Recurrent Neural Network RNN language models have recently become preferred method choice outperformed traditional n-gram LMs across range tasks BID8 Unfortunately however suffer scalability issues incurred computation softmax normalization term which is required guarantee proper probability predictions. cost computation is linearly proportional size word vocabulary has a significant impact training testing. 1 Several methods have been proposed cope scaling issue replacing softmax computationally efficient component train time. include importance sampling BID1 hierarchical softmax BID13 BlackOut BID7 Noise Contrastive Estimation NCE BID5 NCE has been applied train neural LMs large vocabularies BID14 recently was also successfully used train LSTM-RNN LMs BID17;BID3;BID19 achieving near state-of-the-art performance language modeling tasks BID8;BID2 works focused solving run-time complexity problem train time. However test time assumption was that one still needs explicitly compute softmax normalization term obtain normalized score fit estimate probability word.Self-normalization was recently proposed means address high run-time complexity associated predicting normalized probabilities test time. self-normalized discriminative model is trained produce near-normalized scores sense sum scores classes is approximately one. If this approximation is close enough assumption is that the costly exact normalization can be waived test time without significantly sacrificing prediction accuracy BID4 Two main approaches were proposed train self-normalizing models. Explicit selfnormalization is based using softmax training explicitly encouraging normalization term softmax close one possible thus making computation redundant test time BID4;BID0;BID2 alternative approach is based NCE. original formulation NCE included normalization termZ. However first work applied NCE LM BID14 discovered which was empirically fixingZ constant did not affect performance. recent studies BID17;BID19;BID3;BID15 empirically found models trained using NCE fixedZ exhibit self-normalization could explain behavior. best knowledge theoretical analysis self-normalization was proposed BID0. analysis shows model trained explicitly self-normalizing subset training instances can potentially self-normalizing similar instances well. However analysis cannot explain how NCE can be self-normalizing without explicitly imposing self-normalization training instances.The main contribution study is providing theoretical justification self-normalization property NCE which was empirically observed prior work. do so by showing NCE's unnormalized objective can be viewed finding best low-rank approximation normalized conditional probabilities matrix without explicitly estimate partition function. said self-normalizing property NCE is more general focus empirical contribution paper language modeling. investigate self-normalization performance NCE well alternative explicit self-normalization approach two datasets. results suggest somewhat surprisingly models achieve better perplexities tend have worse selfnormalization properties. also observe given context sum self-normalized scores is negatively correlated entropy respective normalized distribution. provided theoretical justification empirical observation NCE is self-normalizing self-normalizing empirical investigation shows performs reasonably well good language model is explicitly trained self-normalize Accordingly believe interesting future research direction could augment NCE's training objective explicit self-normalization component. addition revealed unexpected correlations self-normalization perplexity performance well partition function self-normalized predictions entropy respective distribution. hope insights would useful improving self-normalizing models future work.,1117,784,333,0.011,1.425,2025/11/05 17:18:57,0.0,1.531,0.2959501557632398,325.235
"Learning word representations from large available corpora relies on the distributional hypothesis that words present in similar contexts tend to have similar meanings. Recent work has shown that word representations learnt in this manner lack sentiment information which, fortunately, can be leveraged using external knowledge. Our work addresses the question: can affect lexica improve the word representations learnt from a corpus? In this work, we propose techniques to incorporate affect lexica, which capture fine-grained information about a word's psycholinguistic and emotional orientation, into the training process of Word2Vec SkipGram, Word2Vec CBOW and GloVe methods using a joint learning approach. We use affect scores from Warriner's affect lexicon to regularize the vector representations learnt from an unlabelled corpus. Our proposed method outperforms previously proposed methods on standard tasks for word similarity detection, outlier detection and sentiment detection. We also demonstrate the usefulness of our approach for a new task related to the prediction of formality, frustration and politeness in corporate communication. In natural language research, words, sentences and paragraphs are considered in context through vector space representations, rather than as atomic units with no relational information among them. Although n-gram based methods trained on large volumes of data have been found to outperform more complex approaches both on computational cost and accuracy, the techniques do not scale well in cases where the corpus size is limited(for example, for labeled speech or affect corpora with a size of a few millions of words). Recent work has attempted to improve the performance of word distributions for downstream tasks such as sentiment analysis BID27 and knowledge base completion BID16 using lexical knowledge to enrich word embeddings, by performing methods such as regularization or introducing a loss term in the learning objective.Sentiment relationships between words can be considered transitive, where 'good' < 'better' < 'best' implies that 'good' < 'best'. However, word representations based on traditional approaches such as Word2Vec BID19 and GloVe BID23 are agnostic to the associated sentiments, emotions, or more generally affects BID4 . Furthermore, although words such as delighted and disappointed share similar vector representations given their similar contexts, these words are associated with opposite reactions (or sentiments) as well as have a fairly different interpreted meaning. The challenge in using syntactic relational information for sentiment detection, is that sentiment relations are transitive and symmetric (i.e., if 'delighted' is the opposite of 'disappointed', then 'disappointed' is the opposite of 'delighted'.) Ignoring the bipolar nature of words could lead to spurious results, especially in predictive tasks related to synonyms and antonyms and sentiment analysis. On the other hand, incorporating affect-related information would make word distributions homogeneous and suitable for speech and text generation tasks that aim at capturing author or reader reactions. Furthermore, by using a small sentiment lexicon, it is possible to develop an automatic way to rate words based on their vector space representations. This could help reduce the time and cost required to gather word ratings, as well as eliminate the implicit biases that may be introduced in annotations, such as the high correlation between high valence ratings with high arousal reported by BID27 .We present an approach to build affect-enriched word representations. In other words, we enhance word distributions by incorporating reactions and affect dimensions. The output of this work produces word distributions that capture human reactions by modeling the affect information in the words. The affective word representations distinguish between semantically similar words that have varying affective interpretations. Affect is represented as a weighted relational information between two words, following the approach used by existing work. BID27 identify words of opposite polarity by performing signed spectral clustering on pre-trained embeddings. We present an approach to incorporate external affect and reaction signals in the pre-training step, using the hand-annotated affect lexica to learn from. Our experiments are based on using the state-of-the-art Warriner's affect lexicon BID30 as the input. The proposed approach builds on the intuition that relationships between synonyms and antonyms can be characterized using semantic dictionaries and the relationship can then be deterministically captured into the training loss functions.We evaluate the proposed enriched word distributions on standard natural language tasks. We predict formality, frustration and politeness on a labeled dataset and show improved results using the enriched word embeddings. Further, we outperform the state-of-the-art for sentiment prediction on standard datasets. The key contributions of this paper include:• Algorithm to incorporate affect sensors in the cost functions of distributional word representations (including Word2Vec SkipGram, Word2Vec CBOW, and GloVe) during training using semantic and external affect signals.• Establish the utility of affect enriched word-embeddings for linguistic tasks such as Sentiment and Formality prediction in text data. Our method out performs the state-of-the-art with an 20% improvement in accuracy for the outlier detection methods. Detailed results are reported in table 1.• Introduce a workflow to incorporate affective and reaction signals to word representations during pre-training. We show the generalizability of the workflow through experiments on 3 existing embeddings; Word2Vec-CBOW, Word2Vec-SkipGram, and GloVe.Section 2 covers the prior art in both pre-training and post-training approaches for distributional word representations. Section 3 presents the proposed approach and detailed experiments are discussed in section 4. We conclude with a discussion on the learnings and the observations through this process 5. We find reasonable improvements by our proposed approaches in all the task-based evaluations. SkipGram based methods perform poorly in word similarity prediction and outlier detection, but do well on sentiment and affect prediction. This difference in performance on downstream tasks, has been discussed before in BID9 and BID6 , who point out various issues with word similarity based evaluations such as task subjectivity, low inter annotator agreements and low correlations between the performance of word vectors on word similarity and NLP tasks like text classification, parsing and sentiment analysis. Performance differences can also be attributed to corpus size, which are examined in the Appendix section. Table 3 : Performance of proposed approaches on affect prediction task: (a) In terms of Mean Square Error (MSE) values for affect prediction on a labeled email corpus, (b) Comparison with prior work. The baseline model refers to the corpus only approach, with λ = 0. λ is set to 2 for all other approaches: using Valence list(+V), Arousal(+A), Dominance(+D) and average strength(+VAD).(a ) The results suggest that different embeddings perform well for different tasks. In word similarity tasks, the +V model performs well in GloVe setting but the +A model seems to perform the best for CBOW. Similar results are observed in sentiment prediction: for binary sentiment prediction, arousal scores give the best performance with CBOW embeddings but dominance and valence give the best performance with skip-gram and GloVe embeddings respectively. This suggests that the most flexible method could be an ensemble implementation that considers all these inputs before predicting a final class. Also note that given the vocabulary of our ukWaC corpus as 569, 574 words, our affect lexica with 13, 915 words is relatively small. We plan to take this work forward by further analysis in the future. At the least, we expect superior word embeddings with better quality and larger affect lexica. This work proposes methods to incorporate information from an affect lexicon into Word2Vec and GloVe training process. In a nutshell, we first use WordNet to identify word pairs in the affect lexicon which are semantically related. We define the strength of this relationship using available affect scores. Finally, we modify the training objectives to incorporate this information. In order to evaluate our embeddings, we compare them with baseline approaches where the training completely ignores the affect information. Our embeddings show improvements over baselines on not only Word Similarity benchmarks but also on a more complex, Outlier Detection task. We also do this comparison extrinsically and show that our modified embeddings perform better over prior work in predicting sentiment and predicting formality, frustration and politeness in emails. Among models using Valence, Arousal or Dominance score lists, there is no clear winner but overall addition of valence scores does a reasonable job in almost all of the cases.1. Choosing an appropriate value for hyper-parameter λ:In order to choose a suitable value for λ, we take a 100 MB sample of ukWaC corpus. The sample has close to 20 million tokens, with a vocabulary size of 27,978 words, eliminating all the words having the frequency count of less than 20. We choose a smaller corpus for tuning as it is more manageable with respect to space and time resources.We train a Word2Vec SkipGram model on the above 100MB sample and Valence affect lists by using all the λ value from the set (0, 0.5, 1, 2, 10, 100, 1000) one by one.To pick the most suitable value, we compare the results on word similarity task on the Rubenstein-Goodenough(RG) dataset BID26 . The results are given in FIG2 . Since λ = 2.0 performs the best, we fix this value for all our experiments.","Learning word representations large available corpora relies distributional hypothesis words present similar contexts tend have similar meanings. Recent work has shown word representations learnt manner lack sentiment information which,fortunately can be leveraged using external knowledge. work addresses question:can affect lexica improve word representations learnt corpus? work propose techniques incorporate affect lexica which capture fine-grained information word's psycholinguistic emotional orientation training process Word2Vec SkipGram Word2Vec CBOW GloVe methods using joint learning approach. use affect scores Warriner's affect lexicon regularize vector representations learnt unlabelled corpus. proposed method outperforms previously proposed methods standard tasks word similarity detection outlier detection sentiment detection. also demonstrate usefulness approach new task related prediction formality frustration politeness corporate communication. natural language research words sentences paragraphs are considered context vector space representations rather atomic units relational information among them. Although n-gram based methods trained large volumes data have been found outperform complex approaches computational cost accuracy techniques do not scale well cases where the corpus size is limited example labeled speech affect corpora size millions words Recent work has attempted improve performance word distributions downstream tasks sentiment analysis BID27 knowledge base completion BID16 using lexical knowledge enrich word embeddings performing methods regularization introducing loss term learning objective.Sentiment relationships words can be considered transitive where 'good' 'better' 'best' implies 'good' 'best'. However word representations based traditional approaches Word2Vec BID19 GloVe BID23 are agnostic associated sentiments emotions generally affects BID4. Furthermore although words delighted disappointed share similar vector representations given similar contexts words are associated opposite reactions sentiments well have a fairly different interpreted meaning. challenge using syntactic relational information sentiment detection is that sentiment relations are transitive symmetric.e if 'delighted' is the opposite 'disappointed' 'disappointed' is the opposite 'delighted'. Ignoring bipolar nature words could lead spurious results especially predictive tasks related synonyms antonyms sentiment analysis. hand incorporating affect-related information would make word distributions homogeneous suitable speech text generation tasks aim capturing author reader reactions. Furthermore using small sentiment lexicon is possible develop automatic way rate words based vector space representations. could help reduce time cost required gather word ratings do well eliminate implicit biases may introduced annotations high correlation high valence ratings high arousal reported BID27.We present approach build affect-enriched word representations. words enhance word distributions incorporating reactions affect dimensions. output work produces word distributions capture human reactions modeling affect information words. affective word representations distinguish semantically similar words have varying affective interpretations. Affect is represented weighted relational information two words following approach used existing work. BID27 identify words opposite polarity performing signed spectral clustering pre-trained embeddings. present approach incorporate external affect reaction signals pre-training step using hand-annotated affect lexica learn from. experiments are based using state-of-the-art Warriner's affect lexicon BID30 input. proposed approach builds intuition relationships synonyms antonyms can be characterized using semantic dictionaries relationship can then be deterministically captured training loss functions.We evaluate proposed enriched word distributions standard natural language tasks. predict formality frustration politeness labeled dataset show improved results using enriched word embeddings. outperform state-of-the-art sentiment prediction standard datasets. key contributions paper include:• Algorithm incorporate affect sensors cost functions distributional word representations including Word2Vec SkipGram Word2Vec CBOW GloVe training using semantic external affect signals.• Establish utility affect enriched word-embeddings linguistic tasks Sentiment Formality prediction text data. method performs state-of-the-art 20% improvement accuracy outlier detection methods. Detailed results are reported table 1.• Introduce workflow incorporate affective reaction signals word representations pre-training show generalizability workflow experiments 3 existing embeddings;Word2Vec-CBOW Word2Vec-SkipGram GloVe.Section 2 covers prior art pre-training post-training approaches distributional word representations. Section 3 presents proposed approach detailed experiments are discussed section4. conclude discussion learnings observations process5. find reasonable improvements proposed approaches task-based evaluations. SkipGram based methods perform poorly word similarity prediction outlier detection do well sentiment affect prediction. difference performance downstream tasks has been discussed BID9 BID6 who point various issues word similarity based evaluations task subjectivity low inter annotator agreements low correlations performance word vectors word similarity NLP tasks like text classification parsing sentiment analysis. Performance differences can also attributed corpus size which are examined Appendix section. Table3:Performance proposed approaches affect prediction task:terms Mean Square Error MSE values affect prediction labeled email corpus b Comparison prior work. baseline model refers corpus approach λ 0. λ is set 2 approaches:using Valence list+V Arousal+Dominance+average strength+VAD results suggest different embeddings perform well different tasks. word similarity tasks+V model performs well GloVe setting+model seems perform best CBOW. Similar results are observed sentiment prediction:binary sentiment prediction arousal scores give best performance CBOW embeddings dominance valence give best performance skip-gram GloVe embeddings respectively. suggests flexible method could ensemble implementation considers inputs predicting final class. Also note given vocabulary ukWaC corpus 569 574 words affect lexica 13 915 words is relatively small. plan take work forward analysis future. least expect superior word embeddings better quality larger affect lexica. work proposes methods incorporate information affect lexicon Word2Vec GloVe training process. nutshell first use WordNet identify word pairs affect lexicon which are semantically related. define strength relationship using available affect scores. Finally modify training objectives incorporate information. order evaluate embeddings compare baseline approaches where the training completely ignores affect information. embeddings show improvements baselines Word Similarity benchmarks also complex Outlier Detection task. also do this comparison extrinsically show modified embeddings perform better prior work predicting sentiment predicting formality frustration politeness emails. Among models using Valence Arousal Dominance score lists is no clear winner overall addition valence scores does a reasonable job almost cases.1 Choosing appropriate value hyper-parameterλ:order choose suitable value λ take 100 MB sample ukWaC corpus. sample has close 20 million tokens vocabulary size 27,978 words eliminating words frequency count less 20. choose smaller corpus tuning is more manageable respect space time resources.We train Word2Vec SkipGram model 100MB sample Valence affect lists using λ value set 0 0.5 1 2 10 100 1000 one one.To pick suitable value compare results word similarity task Rubenstein-Goodenough RG dataset BID26. results are given FIG2. Sinceλ 2.0 performs best fix value experiments.",1896,1312,584,0.022,1.445,2025/11/05 17:18:57,0.01,1.444,0.3582554517133957,568.613
"Different kinds of representation learning techniques on graph have shown significant effect in downstream machine learning tasks. Recently, in order to inductively learn representations for graph structures that is unobservable during training, a general framework with sampling and aggregating (GraphSAGE) was proposed by Hamilton and Ying and had been proved more efficient than transductive methods on fileds like transfer learning or evolving dataset. However, GraphSAGE is uncapable of selective neighbor sampling and lack of memory of known nodes that've been trained. To address these problems, we present an unsupervised method that samples neighborhood information attended by co-occurring structures and optimizes a trainable global bias as a representation expectation for each node in the given graph. Experiments show that our approach outperforms the state-of-the-art inductive and unsupervised methods for representation learning on graphs. Graphs and networks, e.g., social network analysis BID7 , molecule screening BID4 , knowledge base reasoning BID19 , and biological proteinprotein networks BID24 ), emerge in many real-world applications. Learning low-dimensional vector embeddings of nodes in large graphs has been proved effective for a wide variety of prediction and graph analysis tasks BID5 ; BID18 ). The high-level idea of node embedding is to explore high-dimensional information about the neighborhood of a node with a dense vector embedding, which can be fed to off-the-shelf machine learning approaches to tasks such as node classification and link prediction BID14 ).Whereas previous approaches BID14 ; BID5 ; BID18 ) can transductively learn embeddings on graphs, without re-training they cannot generalize to new nodes that are newly added to graphs. It is ubiquitous in real-world evolving networks, e.g., new users joining in a social friendship circle such as facebook. To address the problem , BID8 propose an approach, namely GraphSAGE, to leverage node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen nodes. Despite the success of GraphSAGE, it randomly and uniformly samples neighbors of nodes, which suggests it is difficult to explore the most useful neighbor nodes. It could be helpful if we can take advantage of the most relevant neighbors and ignore irrelevant neighbors of the target node. Besides, GraphSAGE only focuses on training parameters of the hierarchical aggregator functions, but lose sight of preserving the memory of the training nodes, which means when training is finished, those nodes that have been trained over and over again would still be treated like unseen nodes, which causes a huge waste.To address the first issue, inspired by GAT BID20 ), a supervised approach that assigns different weights to all neighbors of each node in each aggregating layer, we introduce a bi-attention architecture BID16 ) to perform selective neighbor sampling in unsupervised learning scenarios. In unsupervised representation learning, when encoding embeddings of a positive 1 node pair before calculating their proximity loss BID7 ), we assume that neighbor nodes positive to both of the pair should have larger chance to be selected, since they are statistically more relevant to the current positive pair than other neighbors. For example, when embedding words like ""mouse"", in FIG0 , it's more reasonable to choose ""keyboard"" rather than ""cat"" as sampled neighbor while maximizing co-occrrence probability between ""mouse"" and ""PC"", because ""keyboard"" also tends to co-occurr with ""PC"", which means its imformation should be more relevant. We thus stack a bi-attention architecture BID16 ) on representations aggregated from both side in a positive node pair. In this way, we learn the most relevant representations for each positive node pair corresponding to their most relevant neighbors, and simply use a fixed-size uniform sampling which allows us to efficiently generate node embeddings in batches.To address the second issue, we combine the idea behind transductive approaches and inductive approaches, by intuitively applying an additive global embedding bias to each node's aggregated embedding. The global embedding biases are trainable as well as parameters of aggregator functions and can be considered as a memorable global identification of each node in training sets. When the training is completed, we generate the embedding for each node by calculating an average of multiple embedding outputs corresponding to different sampled neighbors with respect to different positive nodes. In this way, nodes that tend to co-occur in short random-walks will have more similar embeddings based on our bi-attention mechanism.Based on the above-mentioned two techniques, we propose a novel approach, called BIGSAGE (which stands for the BI-attention architeture, global BIas and the original framework GraphSAGE,) to explore most relevant neighbors and preserve previously learnt knowledge of nodes by utilizing bi-attention architecture and introducing global bias, respectively. In this paper, we proposed BIGSAGE, an unsupervised and inductive network embedding approach which is able to preserve local proximity wisely as well as learn and memorize global identities for seen nodes while generalizing to unseen nodes or networks. We apply a bi-attention architeture upon hierarchical aggregating layers to directly capture the most relevant representations of co-occurring nodes. We also present an efficient way of combining inductive and transductive approaches by allowing trainable global embedding bias to be retrieved in all layers within the hierarchical aggregating framework. Experiments demenstrate the superiority of BIGSAGE over the state-of-art baselines on unsupervised and inductive tasks.",Different kinds representation learning techniques graph have shown significant effect downstream machine learning tasks. Recently order inductively learn representations graph structures is unobservable training general framework sampling aggregating GraphSAGE was proposed Hamilton Ying had been proved efficient transductive methods fileds like transfer learning evolving dataset. However GraphSAGE is uncapable selective neighbor sampling lack memory known nodes that've trained. address problems present unsupervised method samples neighborhood information attended co-occurring structures optimizes trainable global bias representation expectation node given graph. Experiments show approach outperforms state-of-the-art inductive unsupervised methods representation learning graphs. Graphs networks e.g social network analysis BID7 molecule screening BID4 knowledge base reasoning BID19 biological proteinprotein networks BID24 emerge many real-world applications. Learning low-dimensional vector embeddings nodes large graphs has been proved effective wide variety prediction graph analysis tasks BID5;BID18 high-level idea node embedding is to explore high-dimensional information neighborhood node dense vector embedding which can be fed off-the-shelf machine learning approaches tasks node classification link prediction BID14.Whereas previous approaches BID14;BID5;BID18 can transductively learn embeddings graphs without re-training cannot generalize new nodes are newly added graphs. is ubiquitous real-world evolving networks e.g new users joining social friendship circle facebook. address problem BID8 propose approach namely GraphSAGE leverage node feature information e.g text attributes efficiently generate node embeddings previously unseen nodes. Despite success GraphSAGE randomly uniformly samples neighbors nodes which suggests is difficult explore useful neighbor nodes. could helpful if we can take advantage relevant neighbors ignore irrelevant neighbors target node. Besides GraphSAGE focuses training parameters hierarchical aggregator functions lose sight preserving memory training nodes which means when training is finished nodes have been trained would still treated like unseen nodes which causes huge waste.To address first issue inspired GAT BID20 supervised approach assigns different weights neighbors node aggregating layer introduce bi-attention architecture BID16 perform selective neighbor sampling unsupervised learning scenarios. unsupervised representation learning when encoding embeddings positive 1 node pair calculating proximity loss BID7 assume neighbor nodes positive pair should have larger chance selected since are statistically relevant current positive pair neighbors. example when embedding words like mouse FIG0 reasonable choose keyboard rather cat sampled neighbor maximizing co-occrrence probability mouse PC keyboard also tends co-occurr PC which means imformation should be more relevant. thus stack bi-attention architecture BID16 representations aggregated side positive node pair. way learn relevant representations positive node pair corresponding relevant neighbors simply use fixed-size uniform sampling which allowsus efficiently generate node embeddings batches.To address second issue combine idea behind transductive approaches inductive approaches intuitively applying additive global embedding bias node's aggregated embedding. global embedding biases are trainable well parameters aggregator functions can be considered memorable global identification node training sets. When the training is completed generate embedding node calculating average multiple embedding outputs corresponding different sampled neighbors respect different positive nodes. way nodes tend co-occur short random-walks will have more similar embeddings based bi-attention mechanism.Based above-mentioned two techniques propose novel approach called BIGSAGE which stands BI-attention architeture global BIas original framework GraphSAGE explore relevant neighbors preserve previously learnt knowledge nodes utilizing bi-attention architecture introducing global bias respectively. paper proposed BIGSAGE unsupervised inductive network embedding approach which is able preserve local proximity wisely well learn memorize global identities seen nodes generalizing unseen nodes networks. apply bi-attention architeture upon hierarchical aggregating layers directly capture relevant representations co-occurring nodes. also present efficient way combining inductive transductive approaches allowing trainable global embedding bias retrieved layers within hierarchical aggregating framework. Experiments demenstrate superiority BIGSAGE state-of-art baselines unsupervised inductive tasks.,1080,745,335,0.01,1.45,2025/11/05 17:18:57,0.01,1.5,0.3738317757009343,319.896
"Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both positive and negative edges while constraining the dimension of the embedding vectors. We argue that the generalization performance of these methods is not due to the dimensionality constraint as commonly believed, but rather the small norm of embedding vectors. Both theoretical and empirical evidence are provided to support this argument: (a) we prove that the generalization error of these methods can be bounded by limiting the norm of vectors, regardless of the embedding dimension; (b) we show that the generalization performance of linear graph embedding methods is correlated with the norm of embedding vectors, which is small due to the early stopping of SGD and the vanishing gradients. We performed extensive experiments to validate our analysis and showcased the importance of proper norm regularization in practice. Graphs have long been considered as one of the most fundamental structures that can naturally represent interactions between numerous real-life objects (e.g., the Web, social networks, proteinprotein interaction networks). Graph embedding, whose goal is to learn distributed representations for nodes while preserving the structure of the given graph, is a fundamental problem in network analysis that underpins many applications. A handful of graph embedding techniques have been proposed in recent years BID10 BID15 BID2 , along with impressive results in applications like link prediction, text classification BID14 , and gene function prediction BID18 .Linear graph embedding methods preserve graph structures by converting the inner products of the node embeddings into probability distributions with a softmax function BID10 BID15 BID2 . Since the exact softmax objective is computationally expensive to optimize, the negative sampling technique BID8 is often used in these methods: instead of optimizing the softmax objective function, we try to maximize the probability of positive instances while minimizing the probability of some randomly sampled negative instances. It has been shown that by using this negative sampling technique, these graph embedding methods are essentially computing a factorization of the adjacency (or proximity) matrix of graph BID7 . Hence, it is commonly believed that the key to the generalization performance of these methods is the dimensionality constraint.However, in this paper we argue that the key factor to the good generalization of these embedding methods is not the dimensionality constraint, but rather the small norm of embedding vectors. We provide both theoretical and empirical evidence to support this argument:• Theoretically, we analyze the generalization error of two linear graph embedding hypothesis spaces (restricting embedding dimension/norm), and show that only the norm-restricted hypothesis class can theoretically guarantee good generalization in typical parameter settings.• Empirically , we show that the success of existing linear graph embedding methods BID10 BID15 BID2 are due to the early stopping of stochastic gradient descent (SGD), which implicitly restricts the norm of embedding vectors. Furthermore, with prolonged SGD execution and no proper norm regularization, the embedding vectors can severely overfit the training data. So far, we have seen many pieces of evidence supporting our argument, suggesting that the generalization of embedding vectors in linear graph embedding is determined by the vector norm. Intuitively, it means that these embedding methods are trying to embed the vertices onto a small sphere centered around the origin point. The radius of the sphere controls the model capacity, and choosing proper embedding dimension allows us to control the trade-off between the expressive power of the model and the computation efficiency.Note that the connection between norm regularization and generalization performance is actually very intuitive. To see this, let us consider the semantic meaning of embedding vectors: the probability of any particular edge (u, v) being positive is equal to DISPLAYFORM0 As we can see, this probability value is determined by three factors: DISPLAYFORM1 , the cosine similarity between x u and x v , evaluates the degree of agreement between the directions of x u and x v .• ||x u || 2 and ||x v || 2 on the other hand, reflects the degree of confidence we have regarding the embedding vectors of u and v.Therefore, by restricting the norm of embedding vectors, we are limiting the confidence level that we have regarding the embedding vectors, which is indeed intuitively helpful for preventing overfitting.It is worth noting that our results in this paper do not invalidate the analysis of BID7 , but rather clarifies on some key points: as pointed out by BID7 , linear graph embedding methods are indeed approximating the factorization of PMI matrices. However , as we have seen in this paper, the embedding vectors are primarily constrained by their norm instead of embedding dimension, which implies that the resulting factorization is not really a standard low-rank one, but rather a low-norm factorization: DISPLAYFORM2 The low-norm factorization represents an interesting alternative to the standard low-rank factorization, and our current understanding of such factorization is still very limited. Given the empirical success of linear graph embedding methods, it would be really helpful if we can have a more in-depth analysis of such factorization, to deepen our understanding and potentially inspire new algorithms. We have shown that the generalization of linear graph embedding methods are not determined by the dimensionality constraint but rather the norm of embedding vectors. We proved that limiting the norm of embedding vectors would lead to good generalization, and showed that the generalization of existing linear graph embedding methods is due to the early stopping of SGD and vanishing gradients. We experimentally investigated the impact embedding dimension choice, and demonstrated that such choice only matters when there is no norm regularization. In most cases, the best generalization performance is obtained by choosing the optimal value for the norm regularization coefficient, and in such case the impact of embedding dimension case is negligible. Our findings combined with the analysis of BID7 suggest that linear graph embedding methods are probably computing a low-norm factorization of the PMI matrix, which is an interesting alternative to the standard low-rank factorization and calls for further study.",Learning distributed representations nodes graphs is a crucial primitive network analysis wide spectrum applications. Linear graph embedding methods learn representations optimizing likelihood positive negative edges constraining dimension embedding vectors. argue generalization performance methods is not is due dimensionality constraint commonly believed rather small norm embedding vectors. theoretical empirical evidence are provided support argument:prove generalization error methods can be bounded limiting norm vectors regardless embedding dimension;b show generalization performance linear graph embedding methods is correlated norm embedding vectors which is small due early stopping SGD vanishing gradients. performed extensive experiments validate analysis showcased importance proper norm regularization practice. Graphs have long considered one fundamental structures can naturally represent interactions numerous real-life objects e.g Web social networks proteinprotein interaction networks Graph embedding whose goal is to learn distributed representations nodes preserving structure given graph is a fundamental problem network analysis underpins many applications. handful graph embedding techniques have been proposed recent years BID10 BID15 BID2 along impressive results applications like link prediction text classification BID14 gene function prediction BID18.Linear graph embedding methods preserve graph structures converting inner products node embeddings probability distributions softmax function BID10 BID15 BID2. Since exact softmax objective is computationally expensive optimize negative sampling technique BID8 is often used methods:instead optimizing softmax objective function try maximize probability positive instances minimizing probability randomly sampled negative instances. has been shown using negative sampling technique graph embedding methods are essentially computing factorization adjacency proximity matrix graph BID7. Hence is commonly believed key generalization performance methods is the is not the dimensionality constraint.However paper argue key factor good generalization embedding methods is the is not the dimensionality constraint rather small norm embedding vectors. provide theoretical empirical evidence support argument:• Theoretically analyze generalization error two linear graph embedding hypothesis spaces restricting embedding dimension/norm show norm-restricted hypothesis class can theoretically guarantee good generalization typical parameter settings.• Empirically show success existing linear graph embedding methods BID10 BID15 BID2 are due early stopping stochastic gradient descent SGD which implicitly restricts norm embedding vectors. Furthermore prolonged SGD execution proper norm regularization embedding vectors can severely overfit training data. far have have seen many pieces evidence supporting argument suggesting generalization embedding vectors linear graph embedding is determined vector norm. Intuitively means embedding methods are trying embed vertices onto small sphere centered around origin point. radius sphere controls model capacity choosing proper embedding dimension allowsus control trade-off expressive power model computation efficiency.Note connection norm regularization generalization performance is actually intuitive. see let us consider semantic meaning embedding vectors:probability particular edge u v positive is equal DISPLAYFORM0 can see probability value is determined three factors:DISPLAYFORM1 cosine similarity xu xv evaluates degree agreement directions xu x v.• ||x u||2 ||xv||2 hand reflects degree confidence have regarding embedding vectors u v.Therefore restricting norm embedding vectors are limiting confidence level have regarding embedding vectors which is indeed intuitively helpful preventing overfitting.It is worth noting results paper do not invalidate analysis BID7 rather clarifies key points:pointed BID7 linear graph embedding methods are indeed approximating factorization PMI matrices. However have have seen paper embedding vectors are primarily constrained norm instead embedding dimension which implies resulting factorization is not really standard low-rank one rather low-norm factorization:DISPLAYFORM2 low-norm factorization represents interesting alternative standard low-rank factorization current understanding factorization is still limited. Given empirical success linear graph embedding methods would really helpful if we can have in-depth analysis factorization deepen understanding potentially inspire new algorithms. have shown generalization linear graph embedding methods are not determined dimensionality constraint rather norm embedding vectors. proved limiting norm embedding vectors would lead good generalization showed generalization existing linear graph embedding methods is not is due early stopping SGD vanishing gradients. experimentally investigated impact embedding dimension choice demonstrated choice matters when there is no norm regularization. cases best generalization performance is obtained choosing optimal value norm regularization coefficient case impact embedding dimension case is negligible. findings combined analysis BID7 suggest linear graph embedding methods are probably computing low-norm factorization PMI matrix which is an interesting alternative standard low-rank factorization calls study.,1207,811,396,0.014,1.488,2025/11/05 17:18:57,0.01,1.469,0.4922118380062303,404.587
"Momentum-based acceleration of stochastic gradient descent (SGD) is widely used in deep learning. We propose the quasi-hyperbolic momentum algorithm (QHM) as an extremely simple alteration of momentum SGD, averaging a plain SGD step with a momentum step. We describe numerous connections to and identities with other algorithms, and we characterize the set of two-state optimization algorithms that QHM can recover. Finally, we propose a QH variant of Adam called QHAdam, and we empirically demonstrate that our algorithms lead to significantly improved training in a variety of settings, including a new state-of-the-art result on WMT16 EN-DE. We hope that these empirical results, combined with the conceptual and practical simplicity of QHM and QHAdam, will spur interest from both practitioners and researchers. Code is immediately available. Stochastic gradient descent (SGD) serves as the optimizer of choice for many recent advances in deep learning across domains (Krizhevsky et al., 2012; He et al., 2016a; . SGD for deep learning is typically augmented with either the ""heavy ball"" momentum technique of Polyak (1964) or the accelerated gradient of Nesterov (1983) . In the deterministic setting, these methods provably yield faster convergence in fairly general settings. In the stochastic setting, these methods lose many theoretical advantages. However, due to its implicit gradient averaging, momentum can confer the benefit of variance reduction, applying less noisy parameter updates than plain SGD. Recent work has explicitly shown the use of momentum as a variance reducer (Roux et al., 2018) .Algorithms Starting with gradient variance reduction as an informal and speculative motivation, we introduce the quasi-hyperbolic momentum (QHM) optimization algorithm in Section 3. Put as simply as possible, QHM's update rule is a weighted average of momentum's and plain SGD's update rule. We later propose a similar variant of Adam (QHAdam) in Section 5.Connecting the dots QHM is simple yet expressive. In Section 4, we connect QHM with plain SGD, momentum, Nesterov's accelerated gradient, PID control algorithms (Recht, 2018; , synthesized Nesterov variants (Lessard et al., 2016) , noise-robust momentum (Cyrus et al., 2018) , Triple Momentum (Scoy et al., 2018) , and least-squares acceleration of SGD (Kidambi et al., 2018) . Such connections yield reciprocal benefits -these algorithms aid in analyzing QHM, and conversely QHM recovers many of these algorithms in a more efficient and conceptually simpler manner. We then characterize the set of optimization algorithms that QHM recovers. Theoretical convergence results We note that various convergence results follow simply via these connections. In the deterministic (full-batch) case, since QHM recovers Triple Momentum, QHM also recovers the global linear convergence rate of 1 − 1/ √ κ for strongly convex, smooth loss functions.6 For first-order methods, this is the fastest known global convergence rate for such functions. In the stochastic (minibatch) case, QHM's recovery of AccSGD gives QHM the same convergence results as in Kidambi et al. (2018) 's least-squares regression setting, of O( √ κ · log κ · log 1 ) iterations for -approximation of the minimal loss.Unifying two-state optimization algorithms These connections demonstrate that many two-state optimization algorithms are functionally similar or equivalent to each other. However, they are often implemented inefficiently and their parameterizations can be inaccessible to practitioners. QHM yields a highly accessible and efficient version of these algorithms. Polyak, 1964) subfamily better recovered by QHM with ν = 1 NAG (Nesterov, 1983) subfamily same recovered by QHM with ν = β PID (Recht, 2018) parent worse QHM's β restricts PID's k P /k D PID bijective worse degenerate; either ""PI"" or ""PD"" SNV (Lessard et al., 2016) bijective worse used in handling multiplicative noise Robust M. (Cyrus et al., 2018) subfamily worse SNV w/ convergence guarantees Triple M. (Scoy et al., 2018) subfamily worse ""fastest"" for str. convex, smooth L(·) AccSGD (Kidambi et al., 2018) subfamily worse acceleration for least-squares SGD * ""subfamily"" means that QHM recovers the algorithm but not vice-versa. ""parent"" means that the algorithm recovers QHM but not vice-versa. ""bijective"" means that the algorithms recover each other. † Efficiency (compute and/or memory) vs. QHM.In Appendix D, we characterize the set of two-state optimization algorithms recoverable by QHM. Our hope here is to provide future work with a routine conversion to QHM so that they may leverage the accessibility and efficiency benefits, as well as the many connections to other algorithms.Many-state optimization algorithms Going beyond a single momentum buffer, it is possible to recover many-state algorithms by linearly combining many momentum buffers (with different discount factors) in the update rule. However, we found in preliminary experiments that using multiple momentum buffers yields negligible value over using a single slow-decaying momentum buffer and setting an appropriate immediate discount -that is, using QHM with high β and appropriate ν.We note that the Aggregated Momentum (AggMo) algorithm (Lucas et al., 2018) precisely performs this linear combination of multiple momentum buffers. While AggMo takes a simple average of the buffers, an extended variant of AggMo allows for other linear combinations. This extended AggMo can be viewed as a many-state generalization of two-state algorithms (including QHM), recovering them when two buffers are used. Appendix H provides a supplemental discussion and empirical comparison of QHM and AggMo, corroborating our preliminary experiments' findings. QHM and QHAdam are computationally cheap, intuitive to interpret, and simple to implement. They can serve as excellent replacements for momentum/NAG and Adam in a variety of settings. In particular, they enable the use of high exponential discount factors (i.e. β) through the use of immediate discounting (i.e. ν). QHM recovers numerous other algorithms in an efficient and accessible manner. Parameter sweep experiments and case studies demonstrate that the QH algorithms can handily outpace their vanilla counterparts. We hope that practitioners and researchers will find these algorithms both practically useful and interesting as a subject of further study. The recommended vanilla Adam setting of β 2 = 0.999 in Kingma & Ba (2015) makes the right-hand side of (19) to be large, and various work has employed Adam with a significantly lower β 2 ; e.g. 0.98 BID12 BID15 . 26 Decreasing β 2 is undesirable, often slowing down training. 27 Moving from Adam to QHAdam, an alternative solution is to decrease ν 2 to be below 1. This decreases the right-hand side of (18), up to a point, and thus imposes a tighter constraint on the magnitudes of updates than the vanilla Adam setting of ν 2 = 1. Fig. 3 shows an example of this phenomenon using a fixed ν 1 , β 1 , and β 2 .Figure 3: Bound from (18), fixing ν 1 = 0.8, β 1 = 0.95, and β 2 = 0.98, and varying ν 2 . 26 We performed experiments on these models indicating that increasing β2 far beyond 0.98 led to training explosion. We suspect that these instability issues are especially prevalent in settings with rare inputs or labels, such as machine translation. 27 In proposing the AdamNC algorithm, Reddi et al. (2018) suggests that β2 should be high to capture a sufficiently long history of past gradients. To recap, we take the optimal AggMo parameterization from an extensive sweep, we convert that parameterization by hand to one for QHM, and we find that the latter outperforms the former on this autoencoder task.These results indicate that using multiple momentum buffers with an arbitrary weighting scheme (i.e. AggMo with K > 2) provides negligible benefit over using a single slow-decaying momentum buffer with an appropriate weight (i.e. QHM with high β and appropriate ν). Lucas et al. (2018) offer an interpretation of AggMo as passive damping for physical systems. In this interpretation, fast-decaying momentum buffers ""dampen"" the oscillations of slow-decaying momentum buffers by providing velocity in an opposite direction.","Momentum-based acceleration stochastic gradient descent SGD is widely used deep learning. propose quasi-hyperbolic momentum algorithm QHM extremely simple alteration momentum SGD averaging plain SGD step momentum step. describe numerous connections identities algorithms characterize set two-state optimization algorithms QHM can recover. Finally propose QH variant Adam called QHAdam empirically demonstrate algorithms lead significantly improved training variety settings including new state-of-the-art result WMT16 EN-DE hope empirical results combined conceptual practical simplicity QHM QHAdam will spur interest practitioners researchers. Code is immediately available. Stochastic gradient descent SGD serves optimizer choice many recent advances deep learning across domains Krizhevskyetal. 2012;etal. 2016a;SGD deep learning is typically augmented either heavy ball momentum technique Polyak 1964 accelerated gradient Nesterov 1983 deterministic setting methods provably yield faster convergence fairly general settings. stochastic setting methods lose many theoretical advantages. However due implicit gradient averaging momentum can confer benefit variance reduction applying less noisy parameter updates plain SGD. Recent work has explicitly shown use momentum variance reducer Rouxetal. 2018.Algorithms Starting gradient variance reduction informal speculative motivation introduce quasi-hyperbolic momentum QHM optimization algorithm Section3. Put simply possible QHM's update rule is a weighted average momentum's plain SGD's update rule. later propose similar variant Adam QHAdam Section 5.Connecting dots QHM is simple yet expressive. Section4 connect QHM plain SGD momentum Nesterov's accelerated gradient PID control algorithms Recht 2018;synthesized Nesterov variants Lessardetal. 2016 noise-robust momentum Cyrusetal. 2018 Triple Momentum Scoyetal. 2018 least-squares acceleration SGD Kidambietal. 2018 connections yield reciprocal benefits -these algorithms aid analyzing QHM conversely QHM recovers many algorithms efficient conceptually simpler manner. characterize set optimization algorithms QHM recovers. Theoretical convergence results note various convergence results follow simply via connections. deterministic full-batch case since QHM recovers Triple Momentum QHM also recovers global linear convergence rate 1−1/√κ strongly convex smooth loss functions.6 first-order methods is the fastest known global convergence rate functions. stochastic minibatch case QHM's recovery AccSGD gives QHM convergence results Kidambietal. 2018 's least-squares regression setting √ κ · log κ · log1 iterations -approximation minimal loss.Unifying two-state optimization algorithms connections demonstrate many two-state optimization algorithms are functionally similar equivalent other. However are often implemented inefficiently parameterizations can be inaccessible practitioners. QHM yields highly accessible efficient version algorithms. Polyak 1964 subfamily better recovered QHM ν 1 NAG Nesterov 1983 subfamily recovered QHM ν β PID Recht 2018 parent worse QHM'sβ restricts PID'skP/k PID bijective worse degenerate;eitherPI PD SNV Lessardetal. 2016 bijective worse used handling multiplicative noise Robust M. Cyrusetal. 2018 subfamily worse SNVw/convergence guarantees Triple M. Scoyetal. 2018 subfamily worse fastest str. convex smoothL · AccSGD Kidambietal. 2018 subfamily worse acceleration least-squares SGD * subfamily means QHM recovers algorithm vice-versa parent means algorithm recovers QHM vice-versa bijective means algorithms recover other. † Efficiency compute/memory vs. QHM.In Appendix characterize set two-state optimization algorithms recoverable QHM. hope is to provide future work routine conversion QHM may leverage accessibility efficiency benefits well many connections algorithms.Many-state optimization algorithms Going beyond single momentum buffer is possible recover many-state algorithms linearly combining many momentum buffers different discount factors update rule. However found preliminary experiments using multiple momentum buffers yields negligible value using single slow-decaying momentum buffer setting appropriate immediate discount -that is,using QHM highβ appropriate ν.We note Aggregated Momentum AggMo algorithm Lucasetal. 2018 precisely performs linear combination multiple momentum buffers. AggMo takes simple average buffers extended variant AggMo allows linear combinations. extended AggMo can be viewed many-state generalization two-state algorithms including QHM recovering when two buffers are used. Appendix H provides supplemental discussion empirical comparison QHM AggMo corroborating preliminary experiments' findings. QHM QHAdam are computationally cheap intuitive interpret simple implement. can serve excellent replacements momentum/NAG Adam variety settings. particular enable use high exponential discount factors.eβ use immediate discounting.eν QHM recovers numerous algorithms efficient accessible manner. Parameter sweep experiments case studies demonstrate QH algorithms can handily outpace vanilla counterparts. hope practitioners researchers will find algorithms practically useful interesting subject study. recommended vanilla Adam setting β2 0.999 Kingma Ba 2015 makes right-hand side 19 large various work has employed Adam significantly lowerβ2;e.g 0.98 BID12 BID15. 26 Decreasingβ2 is undesirable are often slowing training. 27 Moving Adam QHAdam alternative solution is to decreaseν2 1. decreases right-hand side 18 point thus imposes tighter constraint magnitudes updates vanilla Adam setting ν2 1. Fig. 3 shows example phenomenon using fixedν1 β1 β 2.Figure3:Bound 18 fixingν1 0.8 β1 0.95 β2 0.98 varyingν2. 26 performed experiments models indicating increasing β2 far beyond 0.98 led training explosion. suspect instability issues are especially prevalent settings rare inputs labels machine translation. 27 proposing AdamNC algorithm Reddietal. 2018 suggests β2 should be high capture sufficiently long history past gradients. recap take optimal AggMo parameterization extensive sweep convert parameterization hand one QHM find latter outperforms former autoencoder task.These results indicate using multiple momentum buffers arbitrary weighting scheme.e AggMo K 2 provides negligible benefit using single slow-decaying momentum buffer appropriate weight.e QHM highβ appropriateν Lucasetal. 2018 offer interpretation AggMo passive damping physical systems. interpretation fast-decaying momentum buffers dampen oscillations slow-decaying momentum buffers providing velocity opposite direction.",1804,1247,557,0.019,1.447,2025/11/05 17:18:57,0.01,1.286,0.3644859813084112,503.566
"Reinforcement Learning (RL) can model complex behavior policies for goal-directed sequential decision making tasks. A hallmark of RL algorithms is Temporal Difference (TD) learning: value function for the current state is moved towards a bootstrapped target that is estimated using the next state's value function. lambda-returns define the target of the RL agent as a weighted combination of rewards estimated by using multiple many-step look-aheads. Although mathematically tractable, the use of  exponentially decaying weighting of n-step returns based targets in lambda-returns is a rather ad-hoc design choice. Our major contribution  is that we propose a generalization of lambda-returns called Confidence-based Autodidactic Returns (CAR), wherein the RL agent learns the weighting of the n-step returns in an end-to-end manner. In contrast to lambda-returns wherein the RL agent is restricted to use an exponentially decaying weighting scheme, CAR allows the agent to learn to decide how much it wants to weigh the n-step returns based targets. Our experiments, in addition to showing the efficacy of CAR, also empirically demonstrate that using sophisticated weighted mixtures of multi-step returns (like CAR and lambda-returns) considerably outperforms the use of n-step returns. We perform our experiments on the  Asynchronous Advantage Actor Critic (A3C) algorithm in the Atari 2600 domain. Reinforcement Learning (RL) BID21 ) is often used to solve goal-directed sequential decision making tasks wherein conventional Machine Learning methods such as supervised learning are not suitable. Goal-directed sequential decision making tasks are modeled as Markov Decision Process (MDP) BID11 . Traditionally, tabular methods were extensively used for solving MDPs wherein value function or policy estimates were maintained for every state. Such methods become infeasible when the underlying state space of the problem is exponentially large or continuous. Traditional RL methods have also used linear function approximators in conjunction with hand-crafted state spaces for learning policies and value functions. This need for hand-crafted task-specific features has limited the applicability of RL, traditionally.Recent advances in representation learning in the form of deep neural networks provide us with an effective way to achieve generalization BID1 BID6 . Deep neural networks can learn hierarchically compositional representations that enable RL algorithms to generalize over large state spaces. The use of deep neural networks in conjunction with RL objectives has shown remarkable results such as learning to solve the Atari 2600 tasks from raw pixels BID0 BID8 BID16 BID4 , learning to solve complex simulated physics tasks BID24 BID13 BID7 and showing super-human performance on the ancient board game of Go . Building accurate and powerful (in terms of generalization capabilities) state and action value function BID21 estimators is important for successful RL solutions. This is because many practical RL solutions (Q-Learning (Watkins & Dayan, 1992) , SARSA (Rummery & Niranjan, 1994) and Actor-Critic Methods BID5 ) use Temporal Difference (TD) Learning BID20 . In TD learning, a n-step return is used as an estimate of the value function by means of bootstrapping from the n th state's value function estimate. On the other hand, in Monte Carlo learning, the cumulative reward obtained in the entire trajectory following a particular state is used as an estimate for the value function of that state. The ability to build better estimates of the value functions directly results in better policy estimates as well as faster learning. λ-returns (LR) BID21 are very effective in this regard. They are effective for faster propagation of delayed rewards and also result in more reliable learning. LR provide a trade-off between using complete trajectories (Monte Carlo) and bootstrapping from n-step returns (TD learning). They model the TD target using a mixture of n-step returns, wherein the weights of successively longer returns are exponentially decayed. With the advent of deep RL, the use of multi-step returns has gained a lot of popularity BID9 . However, it is to be noted that the use of exponentially decaying weighting for various n-step returns seems to be an ad-hoc design choice made by LR. In this paper, we start off by extensively benchmarking λ-returns (our experiments only use truncated λ-returns due to the nature of the DRL algorithm (A3C) that we work with and we then propose a generalization called the Confidence-based Autodidactic Returns (CAR), In CAR, the DRL agent learns in an end-to-end manner, the weights to assign to the various n-step return based targets. Also in CAR, it's important to note that the weights assigned to various n-step returns change based on the different states from which bootstrapping is done. In this sense, CAR weights are dynamic and using them represents a significant level of sophistication as compared to the usage of λ-returns.In summary, our contributions are:1. To alleviate the need for some ad-hoc choice of weights as in the case of λ-returns, we propose a generalization called Autodidactic Returns and further present a novel derivative of it called Confidence-based Autodidactic Returns (CAR) in the DRL setting.2. We empirically demonstrate that using sophisticated mixtures of multi-step return methods like λ-returns and Confidence-based Autodidactic Returns leads to considerable improvement in the performance of a DRL agent.3. We analyze how the weights learned by CAR are different from that of λ-returns, what the weights signify and how they result in better estimates for the value function. We propose a straightforward way to incorporate λ-returns into the A3C algorithm and carry out a large-scale benchmarking of the resulting algorithm LRA3C. We go on to propose a natural generalization of λ-returns called Confidence-based Autodidactic returns (CAR). In CAR, the agent learns to assign weights dynamically to the various n-step returns from which it can bootstrap. Our experiments demonstrate the efficacy of sophisticated mixture of multi-steps returns with at least one of CARA3C or LRA3C out-performing A3C in 18 out of 22 tasks. In 9 of the tasks CARA3C performs the best whereas in 9 of them LRA3C is the best. CAR gives the agent the freedom to learn and decide how much it wants to weigh each of its n-step returns.The concept of Autodidactic Returns is about the generic idea of giving the DRL agent the ability to model confidence in its own predictions. We demonstrate that this can lead to better Under review as a conference paper at ICLR 2018 TD-targets, in turn leading to improved performances. We have proposed only one way of modeling the autodidactic weights wherein we use the confidence values that are predicted alongside the value function estimates. There are multiple other ways in which these n-step return weights can be modeled. We believe these ways of modeling weighted returns can lead to even better generalization in terms how the agent perceives it's TD-target. Modeling and bootstrapping off TD-targets is fundamental to RL. We believe that our proposed idea of CAR can be combined with any DRL algorithm BID8 BID4 BID16 wherein the TD-target is modeled in terms of n-step returns.",Reinforcement Learning RL can model complex behavior policies goal-directed sequential decision making tasks. hallmark RL algorithms is Temporal Difference TD learning:value function current state is moved towards bootstrapped target is estimated using next state's value function. lambda-returns define target RL agent weighted combination rewards estimated using multiple many-step look-aheads Although mathematically tractable use exponentially decaying weighting n-step returns based targets lambda-returns is a rather ad-hoc design choice. major contribution is that we propose generalization lambda-returns called Confidence-based Autodidactic Returns CAR wherein RL agent learns weighting n-step returns end-to-end manner. contrast lambda-returns wherein RL agent is restricted use exponentially decaying weighting scheme CAR allows agent learn decide how much wants weigh n-step returns based targets. experiments addition showing efficacy CAR also empirically demonstrate using sophisticated weighted mixtures multi-step returns like CAR lambda-returns considerably outperforms use n-step returns. perform experiments Asynchronous Advantage Actor Critic A3C algorithm Atari 2600 domain. Reinforcement Learning RL BID21 is often used solve goal-directed sequential decision making tasks wherein conventional Machine Learning methods supervised learning are not suitable. Goal-directed sequential decision making tasks are modeled Markov Decision Process MDP BID11. Traditionally tabular methods were extensively used solving MDPs wherein value function policy estimates were maintained every state. methods become infeasible when the underlying state space problem is exponentially large continuous. Traditional RL methods have also used linear function approximators conjunction hand-crafted state spaces learning policies value functions. need hand-crafted task-specific features has limited applicability RL traditionally.Recent advances representation learning form deep neural networks provide us effective way achieve generalization BID1 BID6. Deep neural networks can learn hierarchically compositional representations enable RL algorithms generalize large state spaces. use deep neural networks conjunction RL objectives has shown remarkable results learning solve Atari 2600 tasks raw pixels BID0 BID8 BID16 BID4 learning solve complex simulated physics tasks BID24 BID13 BID7 showing super-human performance ancient board game Go. Building accurate powerful terms generalization capabilities state action value function BID21 estimators is important successful RL solutions. is because many practical RL solutions Q-Learning Watkins Dayan 1992 SARSA Rummery Niranjan 1994 Actor-Critic Methods BID5 use Temporal Difference TD Learning BID20. TD learning n-step return is used estimate value function means bootstrapping n th state's value function estimate. hand Monte Carlo learning cumulative reward obtained entire trajectory following particular state is used estimate value function state. ability build better estimates value functions directly results better policy estimates well faster learning. λ-returns LR BID21 are very effective regard. are effective faster propagation delayed rewards also result reliable learning. LR provide trade-off using complete trajectories Monte Carlo bootstrapping n-step returns TD learning can model TD target using mixture n-step returns wherein weights successively longer returns are exponentially decayed. advent deepRL use multi-step returns has gained lot popularity BID9. However isto noted use exponentially decaying weighting various n-step returns seems ad-hoc design choice made LR. paper start extensively benchmarking λ-returns experiments use truncated λ-returns due nature DRL algorithm A3C work propose generalization called Confidence-based Autodidactic Returns CAR CAR DRL agent learns end-to-end manner what the weights assign various n-step return based targets. Also CAR important note weights assigned various n-step returns change based different states which bootstrapping is done. sense CAR weights are dynamic using represents significant level sophistication compared usage λ-returns.In summary contributions are:1 alleviate need ad-hoc choice weights case λ-returns propose generalization called Autodidactic Returns present novel derivative called Confidence-based Autodidactic Returns CAR DRL setting.2 empirically demonstrate using sophisticated mixtures multi-step return methods like λ-returns Confidence-based Autodidactic Returns leads considerable improvement performance DRL agent.3 analyze how the weights learned CAR are different λ-returns what the weights signify how they result better estimates value function. propose straightforward way incorporate λ-returns A3C algorithm carry large-scale benchmarking resulting algorithm LRA3C. go propose natural generalization λ-returns called Confidence-based Autodidactic returns CAR CAR agent learns assign weights dynamically various n-step returns which it can bootstrap. experiments demonstrate efficacy sophisticated mixture multi-steps returns least one CARA3C LRA3C out-performing A3C 18 22 tasks. 9 tasks CARA3C performs best whereas 9 LRA3C is the best. CAR gives agent freedom learn decide how much wants weigh n-step returns.The concept Autodidactic Returns is about the generic idea giving DRL agent ability model confidence predictions. demonstrate can lead better review conference paper ICLR 2018 TD-targets turn leading improved performances. have proposed one way modeling autodidactic weights wherein use confidence values are predicted alongside value function estimates. are multiple ways which these n-step return weights can be modeled. believe ways modeling weighted returns can lead even better generalization terms how the agent perceives TD-target Modeling bootstrapping TD-targets is fundamental RL. believe proposed idea CAR can be combined DRL algorithm BID8 BID4 BID16 wherein TD-target is modeled terms n-step returns.,1469,1044,425,0.014,1.407,2025/11/05 17:18:57,0.01,1.417,0.2398753894080995,450.949
"Current end-to-end deep learning driving models have two problems: (1) Poor
 generalization ability of unobserved driving environment when diversity of train-
 ing driving dataset is limited (2) Lack of accident explanation ability when driving
 models don’t work as expected. To tackle these two problems, rooted on the be-
 lieve that knowledge of associated easy task is benificial for addressing difficult
 task, we proposed a new driving model which is composed of perception module
 for see and think and driving module for behave, and trained it with multi-task
 perception-related basic knowledge and driving knowledge stepwisely.  Specifi-
 cally segmentation map and depth map (pixel level understanding of images) were
 considered as what & where and how far knowledge for tackling easier driving-
 related perception problems before generating final control commands for difficult
 driving task. The results of experiments demonstrated the effectiveness of multi-
 task perception knowledge for better generalization and accident explanation abil-
 ity. With our method the average sucess rate of finishing most difficult navigation
 tasks in untrained city of CoRL test surpassed current benchmark method for 15
 percent in trained weather and 20 percent in untrained weathers. Observing progressive improvement in various fields of pattern recognition with end-to-end deep learning based methods BID13 BID8 , self-driving researchers try to revolutionize autonomous car field with the help of end-to-end deep learning techniques BID3 BID4 . Impressive results have been acquired by mapping camera images directly to driving control commands BID3 with simple structure similar to ones for image classfication task BID19 . Further researches were conducted to improve the performance of deep learning based autonomous driving system, for example, Conditional Imitation Learning approach has been proposed to solve the ambigious action problem.However, two crutial problems failed to be spotted: (1) Poor generalization ability of unobserved driving environment given limited diversity of training scenerios. For example, though addressed the driving direction selection problem, it showed poor generalization ability in unseen test town which has different map and building structure than training town's. This generalization problem is extremely important since collected driving dataset always has limitation of diversity (2) Current end-to-end autonomous approaches lack of accident explanation ability when these models behave unexpectedly. Although saliency map based visualization methods BID20 BID23 BID21 BID2 have been proposed to dig into the 'black box', the only information these methods could bring is the possible attention of the model instead of the perception process of the model.We proposed a new driving approach to solve the two aforementioned problems by using multi-task basic perception knowledge. We argue that when end-to-end model is trained to address a specific difficult task, it's better to train the model with some basic knowledge to solve relevant easier tasks before BID17 ). An analogy for this can be observed when human beings learn a difficult knowledge. For example, to solve a complex integration problem, compared with students without basic math knowledge, students who know about basic knowledge of math are able to learn the core of intergration more quickly and solve other similar integration problems instead of memorizing the solution of the specific problem.Our proposed model consists of two modules: perception module and driving module as in FIG0 . The perception module is used for learning easier driving-related perception knowledge, which we refer as ability of pixel level understanding of input including what & where and how far knowledge. We trained perception module with segmentation map and depth map first, while the former serves as what & where knowledge and the latter serves as how far knowledge. By visualizing inferenced segmentation and depth results whether perception process works well or not could be inferred. After the perception module was trained to have ability of pixel level understanding of its image input, we freezed the perception module weights and trained driving module with driving dataset. This decomposition of end-to-end driving network strucuture is considered to be mediated perception approach BID25 . With our proposed driving structure and stepwise training strategy, the generalization and accident explanation problems were addressed to a certain extent. In this paper we propose a new driving system for better generalization and accident explanation ability by enabling it to do simpler driving-related perception task before generating commands for diffult driving task. Through multiple experiments we empirically proved the effectiveness of the multi basic perception knowledge for better generalization ability of unobserved town when diversity of training dataset is limited. Besides our proposed model has self-explanation ability by visualizing the predicted segmentation and depth maps from the perception module to determine the cause of driving problems when they happen. One interesting result we acquired by comparing different train strategies is that the generalization ability of driving origins from basic knowledge and lies in weights of the perception module which should not be modified during training with driving dataset. We hope our work could movitivate other researches to use multi-task target related perception knowledge for better performance in robot learning. In future we will investigate more effective network structures.",Current end-to-end deep learning driving models have two problems:1 Poor generalization ability unobserved driving environment when diversity train- ing driving dataset is limited 2 Lack accident explanation ability when driving models dont work expected. tackle two problems rooted be- lieve knowledge associated easy task is benificial addressing difficult task proposed new driving model which is composed perception module see think driving module behave trained multi-task perception-related basic knowledge driving knowledge stepwisely. Specifi- cally segmentation map depth map pixel level understanding images were considered what&where how how far knowledge tackling easier driving- related perception problems generating final control commands difficult driving task. results experiments demonstrated effectiveness multi- task perception knowledge better generalization accident explanation abil- ity. method average sucess rate finishing difficult navigation tasks untrained city CoRL test surpassed current benchmark method 15 percent trained weather 20 percent untrained weathers. Observing progressive improvement various fields pattern recognition end-to-end deep learning based methods BID13 BID8 self-driving researchers try revolutionize autonomous car field help end-to-end deep learning techniques BID3 BID4. Impressive results have been acquired mapping camera images directly driving control commands BID3 simple structure similar ones image classfication task BID19. researches were conducted improve performance deep learning based autonomous driving system example Conditional Imitation Learning approach has been proposed solve ambigious action problem.However two crutial problems failed spotted:1 Poor generalization ability unobserved driving environment given limited diversity training scenerios. example though addressed driving direction selection problem showed poor generalization ability unseen test town which has different map building structure training town's generalization problem is extremely important since collected driving dataset always has limitation diversity 2 Current end-to-end autonomous approaches lack accident explanation ability when these models behave unexpectedly. Although saliency map based visualization methods BID20 BID23 BID21 BID2 have been proposed dig 'black box' information methods could bring is the possible attention model instead perception process model.We proposed new driving approach solve two aforementioned problems using multi-task basic perception knowledge. argue when end-to-end model is trained address specific difficult task better train model basic knowledge solve relevant easier tasks BID17 analogy can be observed when human beings learn difficult knowledge. example solve complex integration problem compared students without basic math knowledge students who know basic knowledge math are able learn core intergration quickly solve similar integration problems instead memorizing solution specific problem.Our proposed model consists two modules:perception module driving module FIG0. perception module is used learning easier driving-related perception knowledge which we refer ability pixel level understanding input including what&where and how far knowledge. trained perception module segmentation map depth map first former serves what&where knowledge latter serves what&where how far knowledge. visualizing inferenced segmentation depth results whether perception process works well could inferred. perception module was trained have ability pixel level understanding image input freezed perception module weights trained driving module driving dataset. decomposition end-to-end driving network strucuture is considered mediated perception approach BID25. proposed driving structure stepwise training strategy generalization accident explanation problems were addressed certain extent. paper propose new driving system better generalization accident explanation ability enabling do simpler driving-related perception task generating commands diffult driving task. multiple experiments empirically proved effectiveness multi basic perception knowledge better generalization ability unobserved town when diversity training dataset is limited. Besides proposed model has self-explanation ability visualizing predicted segmentation depth maps perception module determine cause driving problems when they happen. One interesting result acquired comparing different train strategies is that the generalization ability driving origins basic knowledge lies weights perception module which should not be modified training driving dataset. hope work could movitivate researches use multi-task target related perception knowledge better performance robot learning. future will investigate effective network structures.,987,738,249,0.009,1.337,2025/11/05 17:18:57,0.0,1.55,0.0218068535825541,308.182
"Recently there has been a surge of interest in designing graph embedding methods. Few, if any, can scale to a large-sized graph with millions of nodes due to both computational complexity and memory requirements. In this paper, we relax this limitation by introducing the MultI-Level Embedding (MILE) framework – a generic methodology allowing contemporary graph embedding methods to scale to large graphs. MILE repeatedly coarsens the graph into smaller ones using a hybrid matching technique to maintain the backbone structure of the graph. It then applies existing embedding methods on the coarsest graph and refines the embeddings to the original graph through a novel graph convolution neural network that it learns. The proposed MILE framework is agnostic to the underlying graph embedding techniques and can be applied to many existing graph embedding methods without modifying them. We employ our framework on several popular graph embedding techniques and conduct embedding for real-world graphs. Experimental results on five large-scale datasets demonstrate that MILE significantly boosts the speed (order of magnitude) of graph embedding while also often generating embeddings of better quality for the task of node classification. MILE can comfortably scale to a graph with 9 million nodes and 40 million edges, on which existing methods run out of memory or take too long to compute on a modern workstation. In recent years, graph embedding has attracted much interest due to its broad applicability for various tasks BID17 BID10 . However, such methods rarely scale to large datasets (e.g., graphs with over 1 million nodes) since they are computationally expensive and often memory intensive. For example, random-walkbased embedding techniques require a large amount of CPU time to generate a sufficient number of walks and train the embedding model. As another example, embedding methods based on matrix factorization, including GraRep BID1 and NetMF BID18 , requires constructing an enormous objective matrix (usually much denser than adjacency matrix), on which matrix factorization is performed. Even a medium-size graph with 100K nodes can easily require hundreds of GB of memory using those methods. On the other hand, many graph datasets in the real world tend to be large-scale with millions or even billions of nodes. To the best of our knowledge, none of the existing efforts examines how to scale up graph embedding in a generic way. We make the first attempt to close this gap. We are also interested in the related question of whether the quality of such embeddings can be improved along the way. Specifically, we ask: 1) Can we scale up the existing embedding techniques in an agnostic manner so that they can be directly applied to larger datasets?2 ) Can the quality of such embedding methods be strengthened by incorporating the holistic view of the graph?To tackle these problems, we propose a MultI-Level Embedding (MILE) framework for graph embedding. Our approach relies on a three-step process: first, we repeatedly coarsen the original graph into smaller ones by employing a hybrid matching strategy; second, we compute the embeddings on the coarsest graph using an existing embedding techniquesand third, we propose a novel refinement model based on learning a graph convolution network to refine the embeddings from the coarsest graph to the original graph -learning a graph convolution network allows us to compute a refinement procedure that levers the dependencies inherent to the graph structure and the embedding method of choice. To summarize, we find that:• MILE is generalizable : Our MILE framework is agnostic to the underlying graph embedding techniques and treats them as black boxes.• MILE is scalable : MILE can significantly improve the scalability of the embedding methods (up to 30-fold), by reducing the running time and memory consumption.• MILE generates high-quality embeddings : In many cases, we find that the quality of embeddings improves by levering MILE (in some cases is in excess of 10%). In this work, we propose a novel multi-level embedding (MILE) framework to scale up graph embedding techniques, without modifying them. Our framework incorporates existing embedding techniques as black boxes, and significantly improves the scalability of extant methods by reducing both the running time and memory consumption. Additionally, MILE also provides a lift in the quality of node embeddings in most of the cases. A fundamental contribution of MILE is its ability to learn a refinement strategy that depends on both the underlying graph properties and the embedding method in use. In the future, we plan to generalize MILE for information-rich graphs and employing MILE for more applications.",Recently has been a surge interest designing graph embedding methods. if any can scale large-sized graph millions nodes due computational complexity memory requirements. paper relax limitation introducing MultI-Level Embedding MILE framework– generic methodology allowing contemporary graph embedding methods scale large graphs. MILE repeatedly coarsens graph smaller ones using hybrid matching technique maintain backbone structure graph. applies existing embedding methods coarsest graph refines embeddings original graph novel graph convolution neural network learns. proposed MILE framework is agnostic underlying graph embedding techniques can be applied many existing graph embedding methods without modifying them. employ framework several popular graph embedding techniques conduct embedding real-world graphs. Experimental results five large-scale datasets demonstrate MILE significantly boosts speed order magnitude graph embedding also often generating embeddings better quality task node classification. MILE can comfortably scale graph 9 million nodes 40 million edges which existing methods run memory take long compute modern workstation. recent years graph embedding has attracted much interest due broad applicability various tasks BID17 BID10. However methods rarely scale large datasets e.g graphs 1 million nodes since are computationally expensive often memory intensive. example random-walkbased embedding techniques require large amount CPU time generate sufficient number walks train embedding model. another example embedding methods based matrix factorization including GraRep BID1 NetMF BID18 requires constructing enormous objective matrix usually much denser adjacency matrix which matrix factorization is performed. Even medium-size graph 100K nodes can easily require hundreds GB memory using methods. hand many graph datasets real world tend large-scale millions even billions nodes. best knowledge none existing efforts examines how to scale graph embedding generic way. make first attempt close gap. are also interested related question whether quality embeddings can be improved along way. Specifically ask:1 Can we scale existing embedding techniques agnostic manner can directly applied larger datasets? 2 Can the quality embedding methods strengthened incorporating holistic view graph? tackle problems propose MultI-Level Embedding MILE framework graph embedding. approach relies three-step process:first repeatedly coarsen original graph smaller ones employing hybrid matching strategy;second compute embeddings coarsest graph using existing embedding techniquesand third propose novel refinement model based learning graph convolution network refine embeddings coarsest graph original graph -learning graph convolution network allows us compute refinement procedure levers dependencies inherent graph structure embedding method choice. summarize find that:• MILE is generalizable:MILE framework is agnostic underlying graph embedding techniques treats black boxes.• MILE is scalable:MILE can significantly improve scalability embedding methods 30-fold reducing running time memory consumption.• MILE generates high-quality embeddings:many cases find quality embeddings improves levering MILE cases is in excess 10% work propose novel multi-level embedding MILE framework scale graph embedding techniques without modifying them. framework incorporates existing embedding techniques black boxes significantly improves scalability extant methods reducing running time memory consumption. Additionally MILE also provides lift quality node embeddings cases. fundamental contribution MILE is its ability learn refinement strategy depends underlying graph properties embedding method use. future plan generalize MILE information-rich graphs employing MILE applications.,895,597,298,0.009,1.499,2025/11/05 17:18:57,0.0,1.435,0.5264797507788164,297.487
"Anomaly detection discovers regular patterns in unlabeled data and identifies the non-conforming data points, which in some cases are the result of malicious attacks by adversaries. Learners such as One-Class Support Vector Machines (OCSVMs) have been successfully in anomaly detection, yet their performance may degrade significantly in the presence of sophisticated adversaries, who target the algorithm itself by compromising the integrity of the training data. With the rise in the use of machine learning in mission critical day-to-day activities where errors may have significant consequences, it is imperative that machine learning systems are made secure. To address this, we propose a defense mechanism that is based on a contraction of the data, and we test its effectiveness using OCSVMs. The proposed approach introduces a layer of uncertainty on top of the OCSVM learner, making it infeasible for the adversary to guess the specific configuration of the learner. We theoretically analyze the effects of adversarial perturbations on the separating margin of OCSVMs and provide empirical evidence on several benchmark datasets, which show that by carefully contracting the data in low dimensional spaces, we can successfully identify adversarial samples that would not have been identifiable in the original dimensional space. The numerical results show that the proposed method improves OCSVMs performance significantly (2-7%) Anomaly detection refers to the problem of discovering patterns in data and identifying data points that do not conform to the learned patterns. These non-conforming data points are often referred to as anomalies or outliers. Anomaly detection has numerous applications in a variety of domains such as network intrusion detection, credit card fraud detection, and spam filtering. It is an important problem since the presence of anomalies may indicate malicious attacks that could disrupt mission critical operations. Many machine learning methods, such as One-Class Support Vector Machines (OCSVM) BID14 , have been proven to be effective in anomaly detection applications. Although they are designed to withstand the effects of random noise in data, when adversaries deliberately alter the input data and compromise their integrity, the performance of these learning algorithms may degrade significantly.Anomaly detection systems are often deployed in environments where the data naturally evolves. In such situations, the models need to be retrained periodically, in contrast to many conventional machine learning applications, where the current and future data is assumed to have identical properties. This periodic training may allow adversaries to gradually inject malicious data to diminish the decision making capabilities of the learning algorithms BID8 . The aim of the adversaries may be to avoid the detection of attacks or to decrease the performance of the learning system BID8 . To achieve these aims, adversaries can undermine learning algorithms in several ways. For instance, they may manipulate the training data if it is gathered from the real operation of a system (e.g., spam filtering, firewall, anti-virus, etc.) and force the learning algorithm to learn a distorted representation that is favorable to them.A sophisticated adversary has the capacity to conduct an attack in numerous ways. Hence, it is not feasible to provide a general analysis that covers the whole range of attacks, across different machine learning algorithms. In this work, we explore the following key question: Is it possible to make OCSVMs more resistant against adversarial attacks which target the integrity of the training data through distortions? . If an adversary can maliciously perturb the input data used by a learning algorithm, they can force the learner to learn a model that is favorable to them. It has become imperative to secure machine learning systems against such adversaries due to the recent increase of automation in many day to day applications. In the context of image recognition, the perturbations caused by an adversary are usually imperceptible to humans, but they can force a learned model to mis-classify the perturbed images with high confidence. As BID5 have shown, with the emergence of self driving vehicles, an adversary could alter a ""S-T-O-P"" road sign in such a way that a vehicle (learning system) would reliably classify it as a ""Speed Limit 45"" sign. Such perturbations could be imperceptible to humans and could result in the loss of human lives.Our goal is to utilize a nonlinear data projection based algorithm to increase the attack resistance of OCSVMs against an adversarial opponent under realistic assumptions. The theory of nonlinear random projections facilitates large-scale, data-oriented, multi-agent decisions by reducing the number of optimization parameters and variables. Recent work in the literature shows that nonlinear random projections improve the training and evaluation times of kernel machines, without significantly compromising the accuracy of the trained models BID13 BID4 . In this paper, we show that under adversarial conditions, selective nonlinear random projections can be leveraged to increase the attack resistance of OCSVMs as well.A dataset X ∈ R n×d that is projected using a carefully chosen projection matrix A ∈ R d×r comprised of random elements that are normally distributed, would have its pairwise Euclidean distances preserved with high probability in the projected space XA BID9 . Therefore, the properties of the original data distribution would be present in the projected dataset with only minor perturbations. Note that here r is the dimension to which the data is nonlinearly projected and r < d. Since the elements of A are drawn randomly, the learner obtains an additional layer of security as it becomes virtually impossible for the adversary to guess the projection mechanism used by the learner due to the search space becoming unbounded.More formally, let w * pd 2 be the length of the weight vector of the OCSVM in the transformed space, after solving the corresponding optimization problem that includes the distortion made by the adversary and the nonlinear random projection. Let w * p 2 be the length of the weight vector in the transformed space, where there is no adversary present. Since the learner cannot distinguish between the original data and the distorted data, the learner would not have the ability to explicitly calculate w * p 2 . Therefore, for reasonable values of r and small distortions D, we prove in this paper that w * p 2 is bounded above: DISPLAYFORM0 The main contributions of this work are summarized as follows. We derive analytically an upper bound on the length of the weight vector of a OCSVM trained on an undistorted dataset that has been nonlinearly transformed to a lower dimensional space. In addition, the resistance added by nonlinear data transformations against an adversarial opponent is studied through numerical experiments on several benchmark datasets. We believe that our proposed approach can (i) increase the attack resistance of OCSVMs under adversarial conditions, and (ii) give the learner a significant advantage from a security perspective by adding a layer of unpredictability through the randomness of the data transformation in a selective direction. The experimental evaluation presented in the following section demonstrates the effectiveness of our proposed defense mechanism on three benchmark datasets: MNIST, CIFAR-10, and SVHN. We compare the performance of OCSVMs in conjunction with nonlinear random projections, when an active adversary is conducting a directed attack by maliciously distorting the data. We observe that the f-scores across the dimensions decrease between train C |test D and train D |test D . This indicates that a OCSVM trained on clean data can identify adversarial samples better than a OCSVM trained on distorted data. Consequently this shows that OCSVMs are not immune to integrity attacks by design, and by carefully crafting adversarial data points, adversaries can manipulate OCSVMs to learn models that are favorable to them.A comparison between f-scores of train D |test C and train D |test D shows that, as the dimension is reduced from the original dimension, the f-scores increase, but as we reduce the dimension further, the f-scores begin to decrease. The increase in f-score confirms that by projecting data to a lower dimensional space using a carefully selected direction, we can identify adversarial samples that would not have been identifiable in the original feature space. This is confirmed by the graphs in the second row, which show the false positive rate of the OCSVMs under integrity attacks (i.e., number of anomalies that are undetected). We find that there is a significant improvement in detecting adversarial samples under the proposed approach (e.g., 23% on CIFAR-10 and 31% on MNIST).When the dimensions are reduced below a certain dataset dependent threshold the OCSVM performance starts to decline (e.g., SVHN 1,500 vs 463). We postulate that the explanation of this effect is the reduction in distance between classes (in this case perturbed anomalies and normal data points) with the dimension. As we reduce the dimension of the transformation, we are able to reduce the effects of the adversarial datapoints. But at the same time, there is a significant loss of useful information due to the dimensionality reduction. Due to the interplay between these two factors, the performance of OCSVMs reduces as we decrease the dimension beyond a certain threshold. Finally, TAB2 shows the effectiveness of the bound derived in Theorem 1. The results show the consistency of the upper bound, which becomes tighter under dimension reduction.In summary, the above experiments demonstrate that, (i) OCSVMs are vulnerable to adversarial attacks on integrity, (ii) by projecting a distorted dataset to a lower dimension in an appropriate direction we can increase the robustness of the learned model w.r.t. integrity attacks, (iii) the performance, in terms of f-score, starts to decline when the dimensionality is reduced beyond a certain threshold, and (iv) the performance in the projected spaces, when there are no attacks on integrity, is comparable to that in the original dimensional space, but with less computational burden. This paper presents a theoretical and experimental investigation based on a unique combination of unsupervised anomaly detection, using OCSVMs and random projections for dimensionality reduction in the presence of a sophisticated adversary. Our numerical analysis focuses on two main aspects: the performance of OCSVMs in lower dimensional spaces under adversarial conditions and the impact of nonlinear random projections on the robustness of OCSVMs w.r.t. adversarial perturbations. The results suggest that OCSVMs can be significantly affected if an adversary has access to the data on which they are trained. For each dataset, with very high probability, there is at least one dimensionality and projection direction that results in a OCSVM that is able to identify adversarial samples that would not have been identifiable by a OCSVM in the original dimensional space. Due to the layer of uncertainty added by the randomness of the projection, our approach makes the learning system more secure by making it virtually impossible for an adversary to guess the underlying details of the learner. Therefore, our approach can be utilized to make a learning system secure by, (i) reducing the impact of possible adversarial perturbations by contracting, and moving the normal data cloud away from the origin in the projected space, and (ii) making the search space of the adversary unbounded by adding a layer of randomness.Since data contraction is at the core of our proposed approach, for our future work we would like to investigate whether our approach will still hold if used with other learning algorithms. One major question that arises from this work is how to optimally select the number of dimensions to transform the data to. We are currently exploring the possibility of using the intrinsic dimensionality of datasets to address this problem. Since there is a clear information asymmetry between the adversary and learner (due to the randomness), this problem provides a good foundation to explore game-theoretical formulations of anomaly detection and adversarial learning problems under dimensionality reduction techniques. We also plan to study ""boiling frog"" type of attacks, where the adversary gradually injects malicious data over time.A PROOFS Definition 1. Let X ∈ R n×d be the matrix that contains the training data. Similarly, define D ∈ R n×d as the matrix that contains the distortions made by the Adversary. Let A ∈ R d×r be the projection matrix where each element is an i.i.d. N (0, 1) random variable. Define b as a 1 × r row vector where each element is drawn uniformly from [0, 2π] . Using these variables, we define C ∈ R n×r , where the element at row i column j takes the following form.C i,j = cos DISPLAYFORM0 C i,j = cos DISPLAYFORM1 Similarly, we define the matrices C X , C D , S X , S D as follows, Proof: (of Theorem 1) Letα be the vector achieving the optimal solution in the projected space when adversarial distortions are present. Then, the solution for the primal problem in the projected space with adversarial distortions, defined as wSince the optimization problem is a minimization problem, as shown in (2), the optimal solution for the OCSVM without any distortion (i.e., α * ) would give a value less than or equal to the value given byα. Thus, DISPLAYFORM2 Define w * p as the primal solution optimization in the projected space, if there were no adversarial perturbations present, therefore DISPLAYFORM3 B RESULTS","Anomaly detection discovers regular patterns unlabeled data identifies non-conforming data points which in some cases are the result malicious attacks adversaries. Learners One-Class Support Vector Machines OCSVMs have been successfully anomaly detection yet performance may degrade significantly presence sophisticated adversaries who target algorithm compromising integrity training data. rise use machine learning mission critical day-to-day activities where errors may have significant consequences is imperative machine learning systems are made secure. address propose defense mechanism is based contraction data test effectiveness using OCSVMs. proposed approach introduces layer uncertainty top OCSVM learner making infeasible adversary guess specific configuration learner. theoretically analyze effects adversarial perturbations separating margin OCSVMs provide empirical evidence several benchmark datasets which show carefully contracting data low dimensional spaces can successfully identify adversarial samples would have been identifiable original dimensional space. numerical results show proposed method improves OCSVMs performance significantly 2-7 Anomaly detection refers problem discovering patterns data identifying data points do not conform learned patterns. non-conforming data points are often referred anomalies outliers. Anomaly detection has numerous applications variety domains network intrusion detection credit card fraud detection spam filtering. is an important problem since presence anomalies may indicate malicious attacks could disrupt mission critical operations. Many machine learning methods One-Class Support Vector Machines OCSVM BID14 have been proven effective anomaly detection applications. Although are designed withstand effects random noise data when adversaries deliberately alter input data compromise integrity performance learning algorithms may degrade significantly.Anomaly detection systems are often deployed environments where the data naturally evolves. situations models need retrained periodically contrast many conventional machine learning applications where the current future data is assumed have identical properties. periodic training may allow adversaries gradually inject malicious data diminish decision making capabilities learning algorithms BID8. aim adversaries may avoid detection attacks decrease performance learning system BID8. achieve aims when adversaries can undermine learning algorithms several ways. instance may manipulate training data if it is gathered real operation system e.g spam filtering firewall anti-virus etc. force learning algorithm learn distorted representation is are favorable.A sophisticated adversary has the capacity conduct attack numerous ways. Hence is not feasible provide general analysis covers whole range attacks across different machine learning algorithms. work explore following key question:Is it possible make OCSVMs resistant adversarial attacks which target integrity training data distortions? If an adversary can maliciously perturb input data used learning algorithm can can force learner learn model is are favorable them. has become imperative secure machine learning systems adversaries due recent increase automation many day day applications. context image recognition perturbations caused adversary are usually imperceptible humans can can force learned model mis-classify perturbed images high confidence. BID5 have shown emergence self driving vehicles where there is where the adversary could alter S-T-O-P road sign way vehicle learning system would reliably classify Speed Limit 45 sign. perturbations could imperceptible humans could result loss human lives.Our goal is to utilize nonlinear data projection based algorithm increase attack resistance OCSVMs adversarial opponent realistic assumptions. theory nonlinear random projections facilitates large-scale data-oriented multi-agent decisions reducing number optimization parameters variables. Recent work literature shows nonlinear random projections improve training evaluation times kernel machines without significantly compromising accuracy trained models BID13 BID4. paper which show adversarial conditions selective nonlinear random projections can be leveraged increase attack resistance OCSVMs well.A datasetX ∈ R n×d is projected using carefully chosen projection matrix ∈ R d×r comprised random elements are normally distributed would have its pairwise Euclidean distances preserved high probability projected space XA BID9. Therefore properties original data distribution would present projected dataset minor perturbations. Note r is the dimension which the data is nonlinearly projected r d. Since elements are drawn randomly learner obtains additional layer security becomes virtually impossible adversary guess projection mechanism used learner due search space becoming unbounded.More formally letw*pd 2 length weight vector OCSVM transformed space solving corresponding optimization problem includes distortion made adversary nonlinear random projection. Letw*p 2 length weight vector transformed space where there is where the adversary present. Since learner cannot distinguish original data distorted data learner would have the ability explicitly calculatew* p2. Therefore reasonable values r small distortions prove paper w*p2 is bounded above:DISPLAYFORM0 main contributions work are summarized follows. derive analytically upper bound length weight vector OCSVM trained undistorted dataset has been nonlinearly transformed lower dimensional space. addition resistance added nonlinear data transformations adversarial opponent is studied numerical experiments several benchmark datasets. believe proposed approach can(i)increase attack resistance OCSVMs adversarial conditions ii give learner significant advantage security perspective adding layer unpredictability randomness data transformation selective direction. experimental evaluation presented following section demonstrates effectiveness proposed defense mechanism three benchmark datasets:MNIST CIFAR-10 SVHN. compare performance OCSVMs conjunction nonlinear random projections when an active adversary is conducting directed attack maliciously distorting data. observe f-scores across dimensions decrease train C |test train |test D. indicates OCSVM trained clean data can identify adversarial samples better OCSVM trained distorted data. Consequently shows OCSVMs are not immune integrity attacks design carefully crafting adversarial data points when adversaries can manipulate OCSVMs learn models is are favorable.A comparison f-scores train |testC train |test shows dimension is reduced original dimension f-scores increase reduce dimension f-scores begin decrease. increase f-score confirms projecting data lower dimensional space using carefully selected direction can identify adversarial samples would have been identifiable original feature space. is confirmed graphs second row which show false positive rate OCSVMs integrity attacks.e number anomalies are undetected find is a significant improvement detecting adversarial samples proposed approach e.g 23% CIFAR-10 31% MNIST.When dimensions are reduced certain dataset dependent threshold OCSVM performance starts decline e.g SVHN 1,500 vs 463 postulate explanation effect is the reduction distance classes case perturbed anomalies normal data points dimension. reduce dimension transformation are able reduce effects adversarial datapoints. time is a significant loss useful information due dimensionality reduction. Due interplay two factors performance OCSVMs reduces decrease dimension beyond certain threshold. Finally TAB2 shows effectiveness bound derived Theorem1. results show consistency upper bound which becomes tighter dimension reduction.In summary experiments demonstrate OCSVMs are vulnerable adversarial attacks integrity ii projecting distorted dataset lower dimension appropriate direction can increase robustness learned modelw.r.t integrity attacks iii performance terms f-score starts decline when the dimensionality is reduced beyond certain threshold iv performance projected spaces when there are attacks integrity is comparable original dimensional space less computational burden. paper presents theoretical experimental investigation based unique combination unsupervised anomaly detection using OCSVMs random projections dimensionality reduction presence sophisticated adversary. numerical analysis focuses two main aspects:performance OCSVMs lower dimensional spaces adversarial conditions impact nonlinear random projections robustness OCSVMsw.r.t adversarial perturbations. results suggest OCSVMs can be significantly affected if an adversary has access which the data which they are trained. dataset high probability is at least one dimensionality projection direction results OCSVM is able identify adversarial samples would have been identifiable OCSVM original dimensional space. Due layer uncertainty added randomness projection approach makes learning system secure making virtually impossible adversary guess underlying details learner. Therefore approach can be utilized make learning system secure reducing impact possible adversarial perturbations contracting moving normal data cloud away origin projected space ii making search space adversary unbounded adding layer randomness.Since data contraction is at the core proposed approach future work would like investigate whether approach will still hold if used learning algorithms. One major question arises work is how to optimally select number dimensions transform data to. are currently exploring possibility using intrinsic dimensionality datasets address problem. Since is a clear information asymmetry adversary learner due randomness problem provides good foundation explore game-theoretical formulations anomaly detection adversarial learning problems dimensionality reduction techniques. also plan study boiling frog type attacks where there is where the adversary gradually injects malicious data time.A PROOFS Definition 1. LetX∈R n×d matrix contains training data. Similarly define ∈ R n×d matrix contains distortions made Adversary. Let ∈ R d×r projection matrix where each element isani.i.i.dN 0 1 random variable. Defineb 1 × r row vector where each element is drawn uniformly 0 2π Using variables defineC∈R n×r where the element row column j takes following form.C j cos DISPLAYFORM0C j cos DISPLAYFORM1 Similarly define matricesCX C X follows Proof:Theorem1 Letα vector achieving optimal solution projected space when adversarial distortions are present. solution primal problem projected space adversarial distortions defined wSince optimization problem is a minimization problem shown 2 optimal solution OCSVM without distortion.e α* would give value less equal value given byα. Thus DISPLAYFORM2 Definew* p primal solution optimization projected space if there were adversarial perturbations present therefore DISPLAYFORM3 B RESULTS",2699,1807,892,0.04,1.494,2025/11/05 17:18:57,0.01,1.583,0.5109034267912771,930.21
"In this paper, we present a layer-wise learning of stochastic neural networks (SNNs) in an information-theoretic perspective. In each layer of an SNN, the compression and the relevance are defined to quantify the amount of information that the layer contains about the input space and the target space, respectively. We jointly optimize the compression and the relevance of all parameters in an SNN to better exploit the neural network's representation. Previously, the Information Bottleneck (IB) framework (\cite{Tishby99}) extracts relevant information for a target variable. Here, we propose Parametric Information Bottleneck (PIB) for a neural network by utilizing (only) its model parameters explicitly to approximate the compression and the relevance. We show that, as compared to the maximum likelihood estimate (MLE) principle, PIBs : (i) improve the generalization of neural networks in classification tasks, (ii) push the representation of neural networks closer to the optimal information-theoretical representation in a faster manner.   Deep neural networks (DNNs) have demonstrated competitive performance in several learning tasks including image recognition (e.g., BID14 , ), natural language translation (e.g., , ) and game playing (e.g., BID22 ). Specifically in supervised learning contexts, a common practice to achieve good performance is to train DNNs with the maximum likelihood estimate (MLE) principle along with various techniques such as data-specific design of network architecture (e.g., convolutional neural network architecture), regularizations (e.g., early stopping, weight decay, dropout BID25 ), and batch normalization BID12 )), and optimizations (e.g., BID13 ). The learning principle in DNNs has therefore attributed to the MLE principle as a standard one for guiding the learning toward a beneficial direction. However, the MLE principle is very generic that is not specially tailored for neural networks. Thus, a reasonable question is does the MLE principle effectively and sufficiently exploit a neural network's representative power and is there any better alternative? As an attempt to address this important question, this work investigates the learning of DNNs from the information-theoretic perspective.An alternative principle is the Information Bottleneck (IB) framework BID29 ) which extracts relevant information in an input variable X about a target variable Y . More specifically, the IB framework constructs a bottleneck variable Z = Z(X) that is compressed version of X but preserves as much relevant information in X about Y as possible. In this information-theoretic perspective, I(Z, X) 1 , the mutual information of Z and X, captures the compression of Z about X and I(Z, Y ) represents the relevance of Z to Y . The optimal representation Z is determined via the minimization of the following Lagrangian: DISPLAYFORM0 where β is the positive Lagrangian multiplier that controls the trade-off between the complexity of the representation, I(Z, X), and the amount of relevant information in Z, I(Z, Y ). The exact solution to the minimization problem above is found BID29 ) with the implicit selfconsistent equations: DISPLAYFORM1 p(z) = p(z|x)p(x)dx p(y|z) = p(y|x)p(x|z)dx (2) where Z(x; β) is the normalization function, and D KL [. .] is the Kullback -Leibler (KL) divergence BID15 ). Unfortunately, the self-consistent equations are highly non-linear and still non-analytic for most practical cases of interest. Furthermore, the general IB framework assumes that the joint distribution p(X, Y ) is known and does not specify concrete models.On the other hand, the goal of the MLE principle is to match the model distribution p model as close to the empirical data distributionp D as possible (e.g., see Appendix I.B). The MLE principle treats the neural network model p(x x x; θ θ θ) as a whole without explicitly considering the contribution of its internal structures (e.g., hidden layers and hidden neurons). As a result, a neural network with redundant information in hidden layers may have a good distribution match in a training set but show a poor generalization in test sets. In the MLE principle, we only need empirical samples of the joint distribution to maximize the likelihood function of the model given the data. The MLE principle is proved to be mathematically equivalent to the IB principle for the multinomial mixture model for clustering problem when the input distribution X is uniform or has a large sample size BID24 ). However in general the two principles are not obviously related.In this work, we leverage neural networks and the IB principle by viewing neural networks as a set of encoders that sequentially modify the original data space. We then propose a new generalized IB-based objective that takes into account the compression and relevance of all layers in the network as an explicit goal for guiding the encodings in a beneficial manner. Since the objective is designed to optimize all parameters of neural networks and is mainly motivated by the IB principle for deep learning BID28 ), we name this method the Parametric Information Bottleneck (PIB). Because the generalized IB objective in PIB is intractable, we approximate it using variational methods and Monte Carlo estimation. We propose re-using the existing neural network architecture as variational decoders for each hidden layers. The approximate generalized IB objective in turn presents interesting connections with the MLE principle. We show that our PIBs have a better generalization and better exploit the neural network's representation by pushing it closer to the information-theoretical optimal representation as compared to the MLE principle. In this paper we introduced an information-theoretic learning framework to better exploit a neural network's representation. We have also proposed an approximation that fully utilizes all parameters in a neural network and does not resort to any extra models. Our learning framework offers a principled way of interpreting and learning all layers of neural networks and encourages a more Figure 4 : Samples drawn from the prediction of the lower half of the MNIST test data digits based on the upper half for PIB (left, after 60 epochs) and SFNN (right, after 200 epochs). The leftmost column is the original MNIST test digit followed by the masked out digits and nine samples. The rightmost column is obtained by averaging over all generated samples of bottlenecks drawn from the prediction. The figures illustrate the capability of modeling structured output space using PIB and SFNN. informative yet compressed representation, which is supported by qualitative empirical results. One limitation is that we consider here fully-connected feed-forward architecture with binary hidden layers. Since we used generated samples to estimate mutual information, we can potentially extend the learning framework to larger and more complicated neural network architectures. This work is our first step toward exploiting expressive power of large neural networks using informationtheoretic perspective that is not yet fully utilized.",paper present layer-wise learning stochastic neural networks SNNs information-theoretic perspective. layer SNN compression relevance are defined quantify amount information layer contains input space target space respectively. jointly optimize compression relevance parameters SNN better exploit neural network's representation. Previously Information Bottleneck IB framework \cite Tishby99 extracts relevant information target variable. propose Parametric Information Bottleneck PIB neural network utilizing model parameters explicitly approximate compression relevance. show compared maximum likelihood estimate MLE principle PIBs:improve generalization neural networks classification tasks ii push representation neural networks closer optimal information-theoretical representation faster manner. Deep neural networks DNNs have demonstrated competitive performance several learning tasks including image recognition e.g BID14 natural language translation e.g game playing e.g BID22 Specifically supervised learning contexts common practice achieve good performance is to train DNNs maximum likelihood estimate MLE principle along various techniques data-specific design network architecture e.g convolutional neural network architecture regularizations e.g early stopping weight decay dropout BID25 batch normalization BID12 optimizations e.g BID13 learning principle DNNs has therefore attributed MLE principle standard one guiding learning toward beneficial direction. However MLE principle is very generic is not specially tailored neural networks. Thus reasonable question is does the MLE principle effectively sufficiently exploit neural network's representative power is there any better alternative? attempt address important question work investigates learning DNNs information-theoretic perspective.An alternative principle is the Information Bottleneck IB framework BID29 which extracts relevant information input variableX target variable Y. specifically IB framework constructs bottleneck variableZ Z X is compressed version X preserves much relevant information X possible. information-theoretic perspective Z X 1 mutual information Z X captures compression Z X Z represents relevance Z Y. optimal representationZ is determined via minimization following Lagrangian:DISPLAYFORM0 whereβ is the positive Lagrangian multiplier controls trade-off complexity representation Z X amount relevant information Z Z exact solution minimization problem is found BID29 implicit selfconsistent equations:DISPLAYFORM1p z p z|x p x dxp y|z p y|x p x|z dx 2 whereZ x;β is the normalization function KL is the Kullback -Leibler KL divergence BID15 Unfortunately self-consistent equations are highly non-linear still non-analytic practical cases interest. Furthermore general IB framework assumes joint distributionp X is known does not specify concrete models.On hand goal MLE principle is to match model distribution p model close empirical data distributionp possible e.g see Appendix.B MLE principle treats neural network modelp xxx;θθθ whole without explicitly considering contribution internal structures e.g hidden layers hidden neurons result neural network redundant information hidden layers may have a good distribution match training set show poor generalization test sets. MLE principle need empirical samples joint distribution maximize likelihood function model given data. MLE principle is proved mathematically equivalent IB principle multinomial mixture model clustering problem when the input distributionX is uniform has a large sample size BID24 However general two principles are not obviously related.In work leverage neural networks IB principle viewing neural networks set encoders sequentially modify original data space. propose new generalized IB-based objective takes account compression relevance layers network explicit goal guiding encodings beneficial manner. Since objective is designed optimize parameters neural networks is mainly motivated IB principle deep learning BID28 name method Parametric Information Bottleneck PIB generalized IB objective PIB is intractable approximate using variational methods Monte Carlo estimation. propose re-using existing neural network architecture variational decoders hidden layers. approximate generalized IB objective turn presents interesting connections MLE principle. show PIBs have a better generalization is there any better exploit neural network's representation pushing closer information-theoretical optimal representation compared MLE principle. paper introduced information-theoretic learning framework better exploit neural network's representation. have also proposed approximation fully utilizes parameters neural network does not resort extra models. learning framework offers principled way interpreting learning layers neural networks encourages Figure4:Samples drawn prediction lower half MNIST test data digits based upper half PIB left 60 epochs SFNN right 200 epochs leftmost column is the original MNIST test digit followed masked digits nine samples. rightmost column is obtained averaging generated samples bottlenecks drawn prediction. figures illustrate capability modeling structured output space using PIB SFNN. informative yet compressed representation which is supported qualitative empirical results. One limitation is that we consider fully-connected feed-forward architecture binary hidden layers. Since used generated samples estimate mutual information can potentially extend learning framework larger complicated neural network architectures. work is our first step toward exploiting expressive power large neural networks using informationtheoretic perspective is not yet fully utilized.,1385,919,466,0.018,1.507,2025/11/05 17:18:57,0.01,1.61,0.551401869158878,453.545
"The maximum mean discrepancy (MMD) between two probability measures P
 and Q is a metric that is zero if and only if all moments of the two measures
 are equal, making it an appealing statistic for two-sample tests. Given i.i.d. samples
 from P and Q, Gretton et al. (2012) show that we can construct an unbiased
 estimator for the square of the MMD between the two distributions. If P is a
 distribution of interest and Q is the distribution implied by a generative neural
 network with stochastic inputs, we can use this estimator to train our neural network.
 However, in practice we do not always have i.i.d. samples from our target
 of interest. Data sets often exhibit biases—for example, under-representation of
 certain demographics—and if we ignore this fact our machine learning algorithms
 will propagate these biases. Alternatively, it may be useful to assume our data has
 been gathered via a biased sample selection mechanism in order to manipulate
 properties of the estimating distribution Q.
 In this paper, we construct an estimator for the MMD between P and Q when we
 only have access to P via some biased sample selection mechanism, and suggest
 methods for estimating this sample selection mechanism when it is not already
 known. We show that this estimator can be used to train generative neural networks
 on a biased data sample, to give a simulator that reverses the effect of that
 bias. Neural networks with stochastic input layers can be trained to approximately sample from an arbitrary probability distribution P based on samples from P BID7 . Generating simulations from complex distributions has applications in a large number of fields: We can automatically generate illustrations for text BID21 or streams of video BID20 ; we can simulate novel molecular fingerprints to aid scientific exploration BID11 ; and, we can synthesize medical time-series data that can be shared without violating patient privacy BID6 .In this paper, we consider the setting of a feedforward neural network (referred to as the generator) that maps random noise inputs z ∈ R d to some observation space X . The weights of the neural network are trained to minimize some loss function between the resulting simulations and exemplars of real data. The general form of the resulting distribution Q over simulations G(z) is determined by the architecture of the generator-which governs the form of the mapping G-and by the loss function used to train the generator. Generative adversarial networks BID7 use dynamically varying, adversarially learned loss functions specified in terms of the output of a classifier. Other generative networks use a loss function defined using a distributional distance or divergence between the simulation distribution Q and a target distribution P BID0 BID15 BID22 , requiring the generator to mimic the variance in a collection of data points rather than simply converge to a single mode. In particular, the maximum mean discrepancy BID8 has demonstrated good performance as a loss function in this setting BID18 BID19 , since it reduces to zero if and only if all moments of two distributions are equal, requiring the generator to reproduce the full range of variation found in the data.These approaches, like most machine learning methods, assume our data is a representative sample from the distribution of interest. If this assumption is correct, minimizing the distributional distance between the simulations and the data is equivalent to learning a distribution that is indistinguishable under an appropriate two-sample test from our target distribution. However, we run into problems if our data is not in fact a representative sample from our target distribution-for instance, if our data gathering mechanism is susceptible to sample selection bias. The problem of machine learning algorithms replicating and even magnifying human biases is gathering increasing awareness BID2 BID23 , and if we believe our dataset suffers from such biases-for example, if our audio dataset contains primarily male speakers or our image dataset contains primarily white faces -we will typically want to take steps to correct this bias.Even if our data is representative of the underlying distribution, we might want to generate samples from a modified version of this distribution. For example, we might want to alter the demographics of characters in a scene to fit a story-line. In this setting, we can treat our desired modified distribution as our target distribution, and treat our data as if they were sampled from this distribution subject to an appropriately biased sample selection mechanism.If we know the form of our sample selection bias, we can reformulate our loss function to penalize the generator based on the difference between simulated data and the unbiased distribution of interest, which we will refer to as our target distribution. After a review of relevant background information in Section 2, we show in Section 3 that, given a function that describes how our observed data deviates from this target distribution, we can construct an estimator of the MMD between the generator and the target distribution.In practice, we will not know the function linking the target distribution and the empirical data distribution. However, we can approximate this function based on user-provided examples of data points that are over-and under-represented. In Section 4, we discuss ways to estimate this function, and in Section 5 we discuss related work in survey sampling statistics and bias reduction. We demonstrate the efficacy and applicability of our approach in Section 6. We have presented an asymptotically unbiased estimator for the MMD between two distributions P and Q, for use when we only have access to P via a biased sampling mechanism. This mechanism can be specified by a known or estimated thinning function T (x), where samples are then assumed to come from a distribution T (x)P(x)/Z. We show that this estimator can be used to manipulate the distribution of simulations learned by a generative network, in order to correct for sampling bias or to explicitly change the distribution according to a user-specified function.When the thinning function is unknown, it can be estimated from labeled data. We demonstrate this in an interpretable experiment using partially labeled images, where we jointly estimate the thinning function alongside the generator weights. An obvious next step is to explore the use of more sophisticated thinning functions appropriate for complex, multimodal settings.",maximum mean discrepancy MMD two probability measuresP Q is a metric is zero if and onlyif moments two measures are equal making appealing statistic two-sample tests. Given.i.d samples P Q Grettonetal. 2012 show can construct unbiased estimator square MMD two distributions. IfP is a is the distribution interest Q is a is the distribution implied generative neural network stochastic inputs can use estimator train neural network. However practice do not always have i.i.i.d samples target interest. Data sets often exhibit biases example under-representation certain demographics if we ignore fact machine learning algorithms will propagate biases. Alternatively may useful assume data has been gathered via biased sample selection mechanism order manipulate properties estimating distributionQ. paper can construct estimator MMD P Q when we only have access P via biased sample selection mechanism suggest methods estimating sample selection mechanism when it is not already known. show estimator can be used train generative neural networks biased data sample give simulator reverses effect bias. Neural networks stochastic input layers can be trained approximately sample arbitrary probability distributionP based samples P BID7. Generating simulations complex distributions has applications large number fields:can automatically generate illustrations text BID21 streams video BID20;can simulate novel molecular fingerprints aid scientific exploration BID11;can synthesize medical time-series data can be shared without violating patient privacy BID6.In paper consider setting feedforward neural network referred generator maps random noise inputs z∈R observation spaceX. weights neural network are trained minimize loss function resulting simulations exemplars real data. general form resulting distributionQ simulationsG z is determined architecture generator-which governs form mapping G-and loss function used train generator. Generative adversarial networks BID7 use dynamically varying adversarially learned loss functions specified terms output classifier. generative networks use loss function defined using distributional distance divergence simulation distributionQ target distribution P BID0 BID15 BID22 requiring generator mimic variance collection data points rather simply converge single mode. particular maximum mean discrepancy BID8 has demonstrated good performance loss function setting BID18 BID19 since reduces zero if and onlyif moments two distributions are equal requiring generator reproduce full range variation found data.These approaches like machine learning methods assume data is a is representative sample distribution interest. If this assumption is correct minimizing distributional distance simulations data is equivalent learning distribution is indistinguishable appropriate two-sample test target distribution. However run problems if our data is not in fact representative sample target distribution-for instance if our data gathering mechanism is susceptible sample selection bias. problem machine learning algorithms replicating even magnifying human biases is gathering increasing awareness BID2 BID23 if we believe dataset suffers biases-for example if our audio dataset contains primarily male speakers image dataset contains primarily white faces -we will typically want take steps correct bias.Even if our data is a is representative underlying distribution might want generate samples modified version distribution. example might want alter demographics characters scene fit story-line setting can treat desired modified distribution target distribution can treat data if they were sampled distribution subject appropriately biased sample selection mechanism.If know form sample selection bias can reformulate loss function penalize generator based difference simulated data unbiased distribution interest which we will refer target distribution. review relevant background information Section2 show Section3 given function describes how our observed data deviates target distribution can construct estimator MMD generator target distribution.In practice will not know function linking target distribution empirical data distribution. However can approximate function based user-provided examples data points are over-and over-and under-represented Section4 discuss ways estimate function Section5 discuss related work survey sampling statistics bias reduction. demonstrate efficacy applicability approach Section6. have presented asymptotically unbiased estimator MMD two distributionsP Q can use when we only have access P via biased sampling mechanism. mechanism can be specified known estimated thinning function x where samples are then assumed come distribution x P x/Z. show estimator can be used manipulate distribution simulations learned generative network order correct sampling bias explicitly change distribution according user-specified function.When thinning function is unknown can be estimated labeled data. demonstrate interpretable experiment using partially labeled images where we jointly estimate thinning function alongside generator weights. obvious next step is to explore use sophisticated thinning functions appropriate complex multimodal settings.,1230,820,410,0.014,1.5,2025/11/05 17:18:57,0.01,1.702,0.5295950155763238,410.551
"We propose Bayesian Deep Q-Network  (BDQN), a  practical Thompson sampling based Reinforcement Learning (RL) Algorithm. Thompson sampling allows for targeted exploration in high dimensions through posterior sampling but is usually computationally expensive. We address this limitation by introducing uncertainty only at the output layer of the network through a Bayesian Linear Regression (BLR) model, which can be trained with fast closed-form updates and its samples can be drawn efficiently through the Gaussian distribution. We apply our method to a wide range of Atari Arcade Learning Environments. Since BDQN carries out more efficient exploration, it is able to reach higher rewards substantially faster than a key baseline, DDQN. Designing algorithms that achieve an optimal trade-off between exploration and exploitation is one of the primary goal of reinforcement learning (RL). However, targeted exploration in high dimensional spaces is a challenging problem in RL. Recent advances in deep RL mostly deploy simple exploration strategies such as ε-greedy, where the agent chooses the optimistic action, the action with highest promising return, with probability (1 − ε), otherwise, uniformly at random picks one of the available actions. Due to this uniform sampling, the ε-greedy method scales poorly with the dimensionality of state and action spaces. Recent work has considered scaling exploration strategies to large domains BID12 . Several of these papers have focused on employing optimism-under-uncertainty approaches, which essentially rely on computing confidence bounds over different actions, and acting optimistically with respect to that uncertainty.An alternative to optimism-under-uncertainty (Brafman & Tennenholtz, 2003) is Thompson Sampling (TS) BID57 , one of the oldest heuristics for multi arm bandits. TS is a Bayesian approach where one starts with a prior distribution over the belief and compute the posterior beliefs based on the collected data through the interaction with the environment and then maximizes the expected return under the sampled belief. The TS based posterior sampling can provide more targeted exploration since it can trade off uncertainty with the expected return of actions. In contrast, the ε-greedy strategy is indifferent to uncertainty of the actions and the expected rewards of sub-optimistic ones (set of actions excluding the optimistic action).There has been relatively little work on scaling Thompson Sampling to large state spaces. The primary difficulty in implementing Thompson sampling is the difficulty of sampling from general posterior distributions. Prior efforts in this space have generally required extremely expensive computations (e.g. BID21 BID52 )We derive a practical Thompson sampling framework, termed as Bayesian deep Q-networks (BDQN), where we approximate the posterior distribution on the set of Q-functions and sample from this approximated posterior. BDQN is computationally efficient since it incorporates uncertainty only at the output layer, in the form of a Bayesian linear regression model. Due to linearity and by choosing a Gaussian prior, we derive a closed-form analytical update to the approximated posterior distribution over Q functions. We can also draw samples efficiently from the Gaussian distribution. As addressed in BID32 , one of the major benefits of function approximation methods in deep RL is that the estimation of the Q-value, given a state-action pair, can generalize well to other state-action pairs, even if they are visited rarely. We expect this to hold in BDQN as well, but additionally, we also expect the uncertainty of state-action pairs to generalize well.We test BDQN on a wide range of Arcade Learning Environment Atari games BID13 BID15 ) against a strong baseline DDQN BID58 . Aside from simplicity and popularity of DDQN, BDQN and DDQN share the same architecture, and follow same target objective. These are the main reasons we choose DDQN for our comparisons.In table. 1 we see significant gains for BDQN over DDQN. BDQN is able to learn significantly faster and reach higher returns due to more efficient exploration. The evidence of this is further seen from the fact that we are able to train BDQN with much higher learning rates compared to DDQN. This suggests that BDQN is able to learn faster and reach better scores.These promising results suggest that BDQN can further benefit from additional modifications that were done to DQN, e.g. Prioritized Experience Replay , Dueling approach , A3C BID33 , safe exploration BID30 , and etc. This is because BDQN only changes that exploration strategy of DQN, and can easily accommodate additional improvements to DQN.",propose Bayesian Deep Q-Network BDQN practical Thompson sampling based Reinforcement Learning RL Algorithm. Thompson sampling allows targeted exploration high dimensions posterior sampling is usually computationally expensive. address limitation introducing uncertainty output layer network Bayesian Linear Regression BLR model which can be trained fast closed-form updates samples can be drawn efficiently Gaussian distribution. apply method wide range Atari Arcade Learning Environments. Since BDQN carries efficient exploration is able reach higher rewards substantially faster key baseline DDQN. Designing algorithms achieve optimal trade-off exploration exploitation is one primary goal reinforcement learning RL However targeted exploration high dimensional spaces is a challenging problem RL. Recent advances deep RL mostly deploy simple exploration strategies ε-greedy where the agent chooses optimistic action action highest promising return probability 1−ε otherwise uniformly random picks one available actions. Due uniform sampling ε-greedy method scales poorly dimensionality state action spaces. Recent work has considered scaling exploration strategies large domains BID12. Several papers have focused employing optimism-under-uncertainty approaches which essentially rely computing confidence bounds different actions acting optimistically respect uncertainty.An alternative optimism-under-uncertainty Brafman Tennenholtz 2003 is Thompson Sampling TS BID57 one oldest heuristics multi arm bandits. TS is a Bayesian approach where one starts prior distribution belief compute posterior beliefs based collected data interaction environment maximizes expected return sampled belief. TS based posterior sampling can provide targeted exploration since can trade uncertainty expected return actions. contrast ε-greedy strategy is indifferent uncertainty actions expected rewards sub-optimistic ones set actions excluding optimistic action.There has been relatively little work scaling Thompson Sampling large state spaces. primary difficulty implementing Thompson sampling is the difficulty sampling general posterior distributions. Prior efforts space have generally required extremely expensive computations e.g BID21 BID52 derive practical Thompson sampling framework termed Bayesian deep Q-networks BDQN where we approximate posterior distribution set Q-functions sample approximated posterior. BDQN is computationally efficient since incorporates uncertainty output layer form Bayesian linear regression model. Due linearity choosing Gaussian prior derive closed-form analytical update approximated posterior distribution Q functions. can also draw samples efficiently Gaussian distribution. addressed BID32 one major benefits function approximation methods deepRL is that the estimation Q-value given state-action pair can generalize well state-action pairs even if they are visited rarely. expect hold BDQN well additionally also expect uncertainty state-action pairs generalize well.We test BDQN wide range Arcade Learning Environment Atari games BID13 BID15 strong baseline DDQN BID58. Aside simplicity popularity DDQN BDQN DDQN share architecture follow target objective. are the main reasons choose DDQN comparisons.In table. 1 see significant gains BDQN DDQN. BDQN is able learn significantly faster reach higher returns due efficient exploration. evidence is further seen fact are able train BDQN much higher learning rates compared DDQN. suggests BDQN is able learn faster reach better scores.These promising results suggest BDQN can further benefit additional modifications were done DQN e.g Prioritized Experience Replay Dueling approach A3C BID33 safe exploration BID30 etc. is because BDQN changes exploration strategy DQN can easily accommodate additional improvements DQN.,885,616,269,0.008,1.437,2025/11/05 17:18:58,0.0,1.515,0.3333333333333333,294.247
"In this work, we propose the polynomial convolutional neural network (PolyCNN), as a new design of a weight-learning efficient variant of the traditional CNN. The biggest advantage of the PolyCNN is that at each convolutional layer, only one convolutional filter is needed for learning the weights, which we call the seed filter, and all the other convolutional filters are the polynomial transformations of the seed filter, which is termed as an early fan-out. Alternatively, we can also perform late fan-out on the seed filter response to create the number of response maps needed to be input into the next layer. Both early and late fan-out allow the PolyCNN to learn only one convolutional filter at each layer, which can dramatically reduce the model complexity by saving 10x to 50x parameters during learning. While being efficient during both training and testing, the PolyCNN does not suffer performance due to the non-linear polynomial expansion which translates to richer representational power within the convolutional layers. By allowing direct control over model complexity, PolyCNN provides a flexible trade-off between performance and efficiency. We have verified the on-par performance between the proposed PolyCNN and the standard CNN on several visual datasets, such as MNIST, CIFAR-10, SVHN, and ImageNet. Applications of deep convolutional neural networks (CNNs) have been overwhelmingly successful in all aspect of perception tasks, ranging from computer vision to speech recognition and understanding, from biomedical data analysis to quantum physics. In the past couple of years, we have seen the evolution of many successful CNN architectures such as AlexNet BID13 , VGG BID25 , Inception , and ResNet BID8 a) . However, training these networks end-to-end with fully learnable convolutional filters (as is standard practice) is still very computationally expensive and is prone to over-fitting due to the large number of parameters. To alleviate this issue, we have come to think about this question: can we arrive at a more efficient CNN in terms of learnable parameters, without sacrificing the high CNN performance?In this paper, we present an alternative approach to reducing the computational complexity of CNNs while performing as well as standard CNNs. We introduce the polynomial convolutional neural networks (PolyCNN). The core idea behind the PolyCNN is that at each convolutional layer, only one convolutional filter is needed for learning the weights, which we call the seed filter, and all the other convolutional filters are the polynomial transformations of the seed filter, which is termed as an early fan-out. Alternatively , we could also perform late fan-out on the seed filter response to create the number of response maps desired to be input into the next layer. Both early and late fan-out allow the PolyCNN to learn only one convolutional filter at each layer, which can dramatically reduce the model complexity. Parameter savings of at least 10×, 26×, 50×, etc. can be realized during the learning stage depending on the spatial dimensions of the convolutional filters (3 × 3, 5 × 5, 7 × 7 etc. sized filters respectively). While being efficient during both training and testing, the PolyCNN does not suffer performance due to the non-linear polynomial expansion which translates to richer representational power within the convolutional layers. We have verified the on-par performance between the proposed PolyCNN and the standard CNN on several visual datasets, such as MNIST, CIFAR-10, SVHN, and ImageNet. DISPLAYFORM0 PolyCNN Module (Late Fan-Out, Single-Seed) PolyCNN Module (Early Fan-Out, Single-Seed) x l x l+1PolyCNN Module (Early Fan-Out, Multi-Seed) x l x l+1PolyCNN Module (Late Fan-Out, Multi-Seed) (e) ( We have shown the effectiveness of the proposed PolyCNN. Not only can it achieve on-par performance with the state-of-the-art, but also enjoy a significant utility savings. The PyTorch implementation of the PolyCNN will be made publicly available. Inspired by the polynomial correlation filter, in this paper, we have proposed the PolyCNN as an alternative to the standard convolutional neural networks. The PolyCNN module enjoys significant savings in the number of parameters to be learned at training, at least 10× to 50×. PolyCNN have much lower model complexity compared to traditional CNN with standard convolutional layers. The proposed PolyCNN demonstrates performance on par with the state-of-the-art architectures on several image recognition datasets.",work propose polynomial convolutional neural network PolyCNN new design weight-learning efficient variant traditional CNN. biggest advantage PolyCNN is that at each convolutional layer one convolutional filter is needed learning weights which we call seed filter convolutional filters are the polynomial transformations seed filter which is termed early fan-out Alternatively can also perform late fan-out seed filter response create number response maps needed input next layer. early late fan-out allow PolyCNN learn one convolutional filter layer which can dramatically reduce model complexity saving 10x 50x parameters learning. efficient training testing PolyCNN does not suffer performance due non-linear polynomial expansion which translates richer representational power within convolutional layers. allowing direct control model complexity PolyCNN provides flexible trade-off performance efficiency. have verified on-par performance proposed PolyCNN standard CNN several visual datasets MNIST CIFAR-10 SVHN ImageNet. Applications deep convolutional neural networks CNNs have been overwhelmingly successful aspect perception tasks ranging computer vision speech recognition understanding biomedical data analysis quantum physics. past couple years have seen evolution many successful CNN architectures AlexNet BID13 VGG BID25 Inception ResNet BID8 However training networks end-to-end fully learnable convolutional filters is standard practice is still computationally expensive is prone over-fitting due large number parameters. alleviate issue have come think question:can we arrive efficient CNN terms learnable parameters without sacrificing high CNN performance? paper present alternative approach reducing computational complexity CNNs performing well standard CNNs. introduce polynomial convolutional neural networks PolyCNN core idea behind PolyCNN is that at each convolutional layer one convolutional filter is needed learning weights which we call seed filter convolutional filters are the polynomial transformations seed filter which is termed early fan-out Alternatively could also perform late fan-out seed filter response create number response maps desired input next layer. early late fan-out allow PolyCNN learn one convolutional filter layer which can dramatically reduce model complexity. Parameter savings least 10× 26× 50× etc. can be realized learning stage depending spatial dimensions convolutional filters 3×3 5×5 7 × 7 etc. sized filters respectively efficient training testing PolyCNN does not suffer performance due non-linear polynomial expansion which translates richer representational power within convolutional layers. have verified on-par performance proposed PolyCNN standard CNN several visual datasets MNIST CIFAR-10 SVHN ImageNet. DISPLAYFORM0 PolyCNN Module Late Fan-Out Single-Seed PolyCNN Module Early Fan-Out Single-Seed xlxl+1PolyCNN Module Early Fan-Out Multi-Seed xlxl+1PolyCNN Module Late Fan-Out Multi-Seed e have shown effectiveness proposed PolyCNN. can it achieve on-par performance state-of-the-art can also enjoy significant utility savings. PyTorch implementation PolyCNN will be made publicly available. Inspired polynomial correlation filter paper have proposed PolyCNN alternative standard convolutional neural networks. PolyCNN module enjoys significant savings number parameters learned training least 10× 50×. PolyCNN have much lower model complexity compared traditional CNN standard convolutional layers. proposed PolyCNN demonstrates performance par state-of-the-art architectures several image recognition datasets.,910,612,298,0.008,1.487,2025/11/05 17:18:58,0.0,1.565,0.4890965732087229,286.006
"Detecting the emergence of abrupt property changes in time series is a challenging problem. Kernel two-sample test has been studied for this task which makes fewer assumptions on the distributions than traditional parametric approaches. However, selecting kernels is non-trivial in practice. Although kernel selection for the two-sample test has been studied, the insufficient samples in change point detection problem hinder the success of those developed kernel selection algorithms. In this paper, we propose KL-CPD, a novel kernel learning framework for time series CPD that optimizes a lower bound of test power via an auxiliary generative model. With deep kernel parameterization, KL-CPD endows kernel two-sample test with the data-driven kernel to detect different types of change-points in real-world applications. The proposed approach significantly outperformed other state-of-the-art methods in our comparative evaluation of benchmark datasets and simulation studies. Detecting changes in the temporal evolution of a system (biological, physical, mechanical, etc.) in time series analysis has attracted considerable attention in machine learning and data mining for decades BID3 BID7 . This task, commonly referred to as change-point detection (CPD) or anomaly detection in the literature, aims to predict significant changing points in a temporal sequence of observations. CPD has a broad range of real-world applications such as medical diagnostics BID12 , industrial quality control BID4 , financial market analysis BID31 , video anomaly detection ) and more.Figure 1: A sliding window over the time series input with two intervals: the past and the current, where w l , w r are the size of the past and current interval, respectively. X (l) , Xconsists of the data in the past and current interval, respectively.As shown in Fig. 1 , we focus on the retrospective CPD BID36 BID23 , which allows a flexible time window to react on the change-points. Retrospective CPD not only enjoys more robust detection BID9 ) but embraces many applications such as climate change detection BID32 , genetic sequence analysis BID37 , networks intrusion detection BID41 , to name just a few. Various methods have been developed BID17 , and many of them are parametric with strong assumptions on the distributions BID3 BID16 , including auto-regressive models BID40 and state-space models BID20 for tracking changes in the mean, the variance, and the spectrum.Ideally, the detection algorithm should be free of distributional assumptions to have robust performance as neither true data distributions nor anomaly types are known a priori. Thus the parametric assumptions in many works are unavoidably a limiting factor in practice. As an alternative, nonparametric and kernel approaches are free of distributional assumptions and hence enjoy the advantage to produce more robust performance over a broader class of data distributions.Kernel two-sample test has been applied to time series CPD with some success. For example, BID18 presented a test statistic based upon the maximum kernel fisher discriminant ratio for hypothesis testing and BID23 proposed a computational efficient test statistic based on maximum mean discrepancy with block sampling techniques. The performance of kernel methods, nevertheless, relies heavily on the choice of kernels. BID13 BID14 conducted kernel selection for RBF kernel bandwidths via median heuristic. While this is certainly straightforward, it has no guarantees of optimality regarding to the statistical test power of hypothesis testing. BID15 show explicitly optimizing the test power leads to better kernel choice for hypothesis testing under mild conditions. Kernel selection by optimizing the test power, however, is not directly applicable for time series CPD due to insufficient samples, as we discuss in Section 3.In this paper, we propose KL-CPD, a kernel learning framework for time series CPD. Our main contributions are three folds.• In Section 3, we first observe the inaptness of existing kernel learning approaches in a simulated example. We then propose to optimize a lower bound of the test power via an auxiliary generative model, which aims at serving as a surrogate of the abnormal events.• In Section 4, we present a deep kernel parametrization of our framework, which endows a data-driven kernel for the kernel two-sample test. KL-CPD induces composition kernels by combining RNNs and RBF kernels that are suitable for the time series applications.• In Section 5, we conduct extensive benchmark evaluation showing the outstanding performance of KL-CPD in real-world CPD applications. With simulation-based analysis in Section 6, in addition, we can see the proposed method not only boosts the kernel power but also evades the performance degradation as data dimensionality of time series increases.Finally, our experiment code and datasets are available at https://github.com/ OctoberChang/klcpd_code. We propose KL-CPD, a new kernel learning framework for two-sample test by optimizing a lower bound of test power with a auxiliary generator, to resolve the issue of insufficient samples in changepoints detection. The deep kernel parametrization of KL-CPD combines the latent space of RNNs with RBF kernels that effectively detect a variety of change-points from different real-world applications. Extensive evaluation of our new approach along with strong baseline methods on benchmark datasets shows the outstanding performance of the proposed method in retrospective CPD. With simulation analysis in addition we can see that the new method not only boosts the kernel power but also evades the performance degradation as data dimensionality increases.A CONNECTION TO MMD GAN Although our proposed method KL-CPD has a similar objective function as appeared in MMD GAN BID22 , we would like to point out the underlying interpretation and motivations are radically different, as summarized below.The first difference is the interpretation of inner maximization problem max k M k (P, G). MMD GANs BID22 treat whole maximization problem max k M k (P, G) as a new probabilistic distance, which can also be viewed as an extension of integral probability metric (IPM). The properties of the distance is also studied in BID22 ; . A follow-up work by combining BID29 push max k M k (P, G) further to be a scaled distance with gradient norm. However, the maximization problem (4) of this paper defines the lower bound of the test power, which also takes the variance of the empirical estimate into account, instead of the distance.Regarding the goals, MMD GAN aims to learn a generative model that approximates the underlying data distribution P of interests. All the works BID11 BID24 BID34 BID22 use MMD or max k M k (P, G) to define distance, then try to optimize G to be as closed to P as possible. However, that is not the goal of this paper, where G is just an auxiliary generative model which needs to satisfies Eq. (3). Instead, we aim to find the most powerful k for conducting hypothesis test. In practice, we still optimize G toward P because we usually have no prior knowledge (sufficient samples) about Q, and we want to ensure the lower bound still hold for many possible Q (e.g. Q can be also similar to P). However, even with this reason, we still adopt early stopping to prevent the auxiliary G from being exactly the same as P.",Detecting emergence abrupt property changes time series is a challenging problem. Kernel two-sample test has been studied task which makes fewer assumptions distributions traditional parametric approaches. However selecting kernels is non-trivial practice. Although kernel selection two-sample test has been studied insufficient samples change point detection problem hinder success developed kernel selection algorithms. paper propose KL-CPD novel kernel learning framework time series CPD optimizes lower bound test power via auxiliary generative model. deep kernel parameterization KL-CPD endows kernel two-sample test data-driven kernel detect different types change-points real-world applications. proposed approach significantly outperformed state-of-the-art methods comparative evaluation benchmark datasets simulation studies. Detecting changes temporal evolution system biological physical mechanical etc. time series analysis has attracted considerable attention machine learning data mining decades BID3 BID7. task commonly referred change-point detection CPD anomaly detection literature which aims predict significant changing points temporal sequence observations. CPD has a broad range real-world applications medical diagnostics BID12 industrial quality control BID4 financial market analysis BID31 video anomaly detection more.Figure1:sliding window time series input two intervals:past current wherewl wherewr are the size past current interval respectively. X l Xconsists data past current interval respectively.As shown Fig. 1 focus retrospective CPD BID36 BID23 which allows flexible time window react change-points Retrospective CPD enjoys robust detection BID9 embraces many applications climate change detection BID32 genetic sequence analysis BID37 networks intrusion detection BID41 name few. Various methods have been developed BID17 many are parametric strong assumptions distributions BID3 BID16 including auto-regressive models BID40 state-space models BID20 tracking changes mean variance spectrum.Ideally detection algorithm should be free distributional assumptions have robust performance neither true data distributions anomaly types are known priori. Thus parametric assumptions many works are unavoidably limiting factor practice. alternative nonparametric kernel approaches are free distributional assumptions hence enjoy advantage produce robust performance broader class data distributions.Kernel two-sample test has been applied time series CPD success. example BID18 presented test statistic based upon maximum kernel fisher discriminant ratio hypothesis testing BID23 proposed computational efficient test statistic based maximum mean discrepancy block sampling techniques. performance kernel methods nevertheless relies heavily choice kernels. BID13 BID14 conducted kernel selection RBF kernel bandwidths via median heuristic. is certainly straightforward has no guarantees optimality regarding statistical test power hypothesis testing. BID15 show explicitly optimizing test power leads better kernel choice hypothesis testing mild conditions. Kernel selection optimizing test power however is not directly applicable time series CPD due insufficient samples discuss Section 3.In paper propose KL-CPD kernel learning framework time series CPD. main contributions are three folds.• Section3 first observe inaptness existing kernel learning approaches simulated example. propose optimize lower bound test power via auxiliary generative model which aims serving surrogate abnormal events.• Section4 present deep kernel parametrization framework which endows data-driven kernel kernel two-sample test. KL-CPD induces composition kernels combining RNNs RBF kernels are suitable time series applications.• Section5 conduct extensive benchmark evaluation showing outstanding performance KL-CPD real-world CPD applications. simulation-based analysis Section6 addition can see proposed method boosts kernel power also evades performance degradation data dimensionality time series increases.Finally experiment code datasets are available https://github.com/OctoberChang/klcpd_code propose KL-CPD new kernel learning framework two-sample test optimizing lower bound test power auxiliary generator resolve issue insufficient samples changepoints detection. deep kernel parametrization KL-CPD combines latent space RNNs RBF kernels effectively detect variety change-points different real-world applications. Extensive evaluation new approach along strong baseline methods benchmark datasets shows outstanding performance proposed method retrospective CPD. simulation analysis addition can see new method boosts kernel power also evades performance degradation data dimensionality increases.A CONNECTION MMD GAN Although proposed method KL-CPD has a similar objective function appeared MMD GAN BID22 would like point underlying interpretation motivations are radically different summarized below.The first difference is the interpretation inner maximization problem max k k P whereG MMD GANs BID22 treat whole maximization problem max k k P whereG new probabilistic distance which can which also viewed extension integral probability metric IPM properties distance is also studied BID22;follow-up work combining BID29 push max k k P whereG scaled distance gradient norm. However maximization problem 4 paper defines lower bound test power which can which also takes variance empirical estimate account instead distance.Regarding goals MMD GAN aims learn generative model approximates underlying data distributionP interests. works BID11 BID24 BID34 BID22 use MMD maxk k P whereG define distance try optimizeG closed P possible. However is not goal paper whereG is just an auxiliary generative model which needs satisfiesEq. 3 Instead aim find powerfulk conducting hypothesis test. practice still optimize G toward P usually have no prior knowledge sufficient samples Q want ensure lower bound still hold many possibleQ e.gQ can be also similar P However even reason still adopt early stopping prevent auxiliaryG exactly P.,1461,1020,441,0.015,1.432,2025/11/05 17:18:58,0.01,1.436,0.317757009345794,451.335
"Theories in cognitive psychology postulate that humans use similarity as a basis
 for object categorization. However, work in image classification generally as-
 sumes disjoint and equally dissimilar classes to achieve super-human levels of
 performance on certain datasets. In our work, we adapt notions of similarity using
 weak labels over multiple hierarchical levels to boost classification performance.
 Instead of pitting clustering directly against classification, we use a warm-start
 based evaluation to explicitly provide value to a clustering representation by its
 ability to aid classification. We evaluate on CIFAR10 and a fine-grained classifi-
 cation dataset to show improvements in performance with the procedural addition
 of intermediate losses and weak labels based on multiple hierarchy levels. Further-
 more, we show that pretraining AlexNet on hierarchical weak labels in conjunc-
 tion with intermediate losses outperforms a classification baseline by over 17% on
 a subset of Birdsnap dataset. Finally, we show improvement over AlexNet trained
 using ImageNet pre-trained weights as initializations which further supports our 
 claim of the importance of similarity. Similarity is one of the bases of object categorization in humans BID14 . Theories of perceptual categorization in cognitive psychology postulate that humans construct categories by grouping similar stimuli to construct one or several prototypes. New instances are then labeled as the category that they are most similar to. For instance, when one categorizes a specific animal as a dog, they are saying that it is more similar to previously observed dogs than it is to all other objects. This view of categorization better explains the often fuzzy boundaries between real-life classes, where a new object may be equally similar to multiple prototypes. For example, while a dolphin is technically a mammal, its visual appearance is similar to fish, resulting in a lot of people misclassifying it.While research in cognitive psychology on object categorization might indicate that similarity should play a central role in object classification in humans, image classification in computer vision seems to do pretty well without using it. The task is commonly interpreted as one of classifying an image into one of multiple classes that are assumed to be disjoint and equally dissimilar. The use of softmax-based loss functions assumes that the classes are disjoint, while the use of one-hot labels assumes that classes are equally dissimilar. Despite those strong assumptions, which seem to violate human notions of categories, image classification has shown remarkable progress, achieving superhuman performance on multiple datasets BID6 BID3 . Far from being an anomaly, state-of-the-art models across image classification benchmark datasets use losses, such as cross-entropy loss, that make the explicit assumption of disjoint classes. However, BID4 notes that the predictions of ensembles of image classification models produces soft labels that ""define a rich similarity structure over the data"" despite the predictions of individual models not capturing this structure.Can similarity-based metrics improve classification performance in convolutional neural networks? Previous work has tried to answer this question in different problems such as metric learning BID0 , clustering BID16 , and hierarchical classification BID11 . We focus on applications of similarity in the context of convolutional neural networks such as BID5 who use a contrastive loss to perform end-to-end clustering using weak labels. While they show impressive performance on MNIST BID10 and CIFAR-10 (Krizhevsky & Hinton, 2009) , their method does not scale well to more complex datasets. BID13 propose a new loss function, magnet loss, to learn a representational space where distance corresponds to similarity. They show that clustering in this space allows them to achieve state-of-the-art performance on multiple fine-grained classification datasets.1 However, they initialize their model with pre-trained weights on ImageNet BID15 , so it is not clear whether their model is learning a good representation, or if it is finding a good mapping between already learned representations and the labels. BID20 pose the problem as one of hierarchical classification and propose a loss based on an ultra-metric tree representation of a hierarchy over the labels. While their loss has interesting properties, it only outperforms classification losses for datasets with a small number of instances per class. In this work, we use a contrastive loss to improve the classification performance of randomly initialized convolutional neural networks on a fine-grained classification task.What measures of similarity should we teach our model? We represent the relations between our classes in a hierarchy where the labels are all leaf nodes. Therefore, there are two kinds of similarities that we want our model to capture. The first is intra-class similarity-all cats are similar to each other and they are dissimilar to other animals. The second is inter-class similarity-dogs and cats are more similar to each other than they are to non-living objects. For a more complex hierarchy, our model should learn similarity at different levels of the class hierarchy. BID20 use their hierarchical loss function to learn those similarities, however, they observe that reducing the similarity between two classes across all levels of the hierarchy to a single value biases the model towards correct classification at the higher levels of the hierarchy resulting in poor classification performance. BID13 also observe that applying classification losses to the final layer reduces the entire representation of each class to a single scalar value which destroys intra-and inter-class variation. However, these are the same variations that we want our model to capture. We overcome those limitations by explicitly training the model to capture different grains of similarity at different levels of the network through applying an intermediate pairwise contrastive loss at those levels. In this manner, we can use hierarchical information, such as species of birds having the same coarse-grained category of bird while having different fine-grained labels. Despite being able to encode different levels of similarity, a contrastive loss does not require an explicit hierarchy; we only need weak labels for pairs of instances.How can we evaluate the representations learned by a clustering algorithm? Previous work has always tried to compete against classification using metrics biased towards the latter task. While some researchers have used hierarchical metrics BID20 or qualitative measures BID13 to evaluate the quality of their representations, their primary evaluation criteria has consistently been the classification accuracy of their model. We propose another way to evaluate the clustering representations by using the clustering model as a ""warm start"" from which they can train on classification. The intuition is that if the clustering model learned a representations that captures similarity in a space, it would be be at an advantage when it is fine-tuned for classification.We propose the use of a contrastive loss at different layers of a convolutional neural network to learn a notion of similarity across a set of labels. We also propose the use of the accuracy of a model pre-trained for clustering and fine-tuned for classification as an evaluation metric for clustering algorithms. In this work, we argue that similarity-based losses can be applied as a warm start to boost the performance of image classification models. We show that applying a pairwise contrastive loss to intermediate layers of the network results in better clustering performance, as well as better finetuned classification performance. Furthermore, we demonstrate how the pairwise loss can be used to train a model using weak hierarchical labels.We find that training with hierarchical labels results in the highest performance beating models with more parameters and approaches the performance of models pre-trained with ImageNet weights. This is a very significant finding since ImageNet contains multiple bird classes, so a model pretrained with ImageNet has seen many more birds than a model pre-trained with pairwise constraints on Birdsnap34. Nevertheless, it only outperforms a cluster-based warm-start model by just 10%. Regardless, we also show that applying our approach to ImageNet weights still results in a boost of 1.27%. This supports our claim that similarity-based metrics can improve classification performance, but it suggests that the gains we expect decrease if we start of with a good representational space.We hope to expand this in future work in multiple ways. We plan on extending our approach to the entire Birdsnap dataset, as well as to other fine-grained classification datasets. We also hope to perform more extensive analysis of the quality of the embedding spaces learned as it is obvious that the use of the Hungarian algorithm does not accurately reflect the performance of the clustering model.",Theories cognitive psychology postulate humans use similarity basis object categorization. However work image classification generally as- sumes disjoint equally dissimilar classes achieve super-human levels performance certain datasets. work adapt notions similarity using weak labels multiple hierarchical levels boost classification performance. Instead pitting clustering directly classification can use warm-start based evaluation explicitly provide value clustering representation ability aid classification. evaluate CIFAR10 fine-grained classifi- cation dataset show improvements performance procedural addition intermediate losses weak labels based multiple hierarchy levels. Further- show pretraining AlexNet hierarchical weak labels conjunc- tion intermediate losses outperforms classification baseline 17% subset Birdsnap dataset. Finally show improvement AlexNet trained using ImageNet pre-trained weights initializations which further supports claim importance similarity. Similarity is one bases object categorization humans BID14. Theories perceptual categorization cognitive psychology postulate humans construct categories grouping similar stimuli construct one several prototypes. New instances are then labeled category are most is more similar to. instance when one categorizes specific animal dog are saying are most is more similar previously observed dogs isto objects. view categorization better explains often fuzzy boundaries real-life classes where a new object may equally similar multiple prototypes. example dolphin is technically mammal visual appearance is similar fish resulting lot people misclassifying it.While research cognitive psychology object categorization might indicate similarity should play central role object classification humans image classification computer vision seems do pretty well without using it. task is commonly interpreted one classifying image one multiple classes are assumed disjoint equally dissimilar. use softmax-based loss functions assumes classes are disjoint can use one-hot labels assumes classes are equally dissimilar. Despite strong assumptions which seem violate human notions categories image classification has shown remarkable progress achieving superhuman performance multiple datasets BID6 BID3. Far anomaly state-of-the-art models across image classification benchmark datasets use losses cross-entropy loss make explicit assumption disjoint classes. However BID4 notes predictions ensembles image classification models produces soft labels define rich similarity structure data despite predictions individual models capturing structure.Can similarity-based metrics improve classification performance convolutional neural networks? Previous work has tried answer question different problems metric learning BID0 clustering BID16 hierarchical classification BID11. focus applications similarity context convolutional neural networks BID5 who use contrastive loss perform end-to-end clustering using weak labels. show impressive performance MNIST BID10 CIFAR-10 Krizhevsky Hinton 2009 method does not scale well complex datasets. BID13 propose new loss function magnet loss learn representational space where distance corresponds similarity. show clustering space allows achieve state-of-the-art performance multiple fine-grained classification datasets.1 However initialize model pre-trained weights ImageNet BID15 is clear whether model is learning good representation ifit is finding good mapping already learned representations labels. BID20 pose problem one hierarchical classification propose loss based ultra-metric tree representation hierarchy labels. loss has interesting properties outperforms classification losses datasets small number instances per class. work can use contrastive loss improve classification performance randomly initialized convolutional neural networks fine-grained classification task.What measures similarity should we teach model? represent relations classes hierarchy where the labels are all leaf nodes. Therefore are two kinds similarities want model capture. first is intra-class similarity-all cats are are more similar are dissimilar animals. second is inter-class similarity-dogs cats are are more similar areto non-living objects. complex hierarchy model should learn similarity different levels class hierarchy. BID20 use hierarchical loss function learn similarities however observe reducing similarity two classes across levels hierarchy single value biases model towards correct classification higher levels hierarchy resulting poor classification performance. BID13 also observe applying classification losses final layer reduces entire representation class single scalar value which destroys intra-and inter-class variation. However are the variations want model capture. overcome limitations explicitly training model capture different grains similarity different levels network applying intermediate pairwise contrastive loss levels. manner can use hierarchical information species birds coarse-grained category bird different fine-grained labels. Despite able encode different levels similarity contrastive loss does not require explicit hierarchy;need weak labels pairs instances.How can we evaluate representations learned clustering algorithm? Previous work has always tried compete classification using metrics biased towards latter task. researchers have used hierarchical metrics BID20 qualitative measures BID13 evaluate quality representations primary evaluation criteria has consistently classification accuracy model. propose another way evaluate clustering representations using clustering model warm start which they can train classification. intuition is that if the clustering model learned representations captures similarity space would advantage when it is fine-tuned classification.We propose use contrastive loss different layers convolutional neural network learn notion similarity across set labels. also propose use accuracy model pre-trained clustering fine-tuned classification evaluation metric clustering algorithms. work argue similarity-based losses can be applied warm start boost performance image classification models. show applying pairwise contrastive loss intermediate layers network results better clustering performance well better finetuned classification performance. Furthermore demonstrate how the pairwise loss can be used train model using weak hierarchical labels.We find training hierarchical labels results highest performance beating models parameters approaches performance models pre-trained ImageNet weights. is a very significant finding since ImageNet contains multiple bird classes model pretrained ImageNet has seen many birds model pre-trained pairwise constraints Birdsnap34. Nevertheless outperforms cluster-based warm-start model 10%. Regardless also show applying approach ImageNet weights still results boost 1.27%. supports claim similarity-based metrics can improve classification performance suggests gains expect decrease if we start good representational space.We hope expand future work multiple ways. plan extending approach entire Birdsnap dataset well fine-grained classification datasets. also hope perform extensive analysis quality embedding spaces learned is obvious use Hungarian algorithm does not accurately reflect performance clustering model.,1652,1117,535,0.018,1.479,2025/11/05 17:18:58,0.01,1.508,0.4641744548286605,521.274
"Deep reinforcement learning algorithms that estimate state and state-action value functions have been shown to be effective in a variety of challenging domains, including learning control strategies from raw image pixels. However, algorithms that estimate state and state-action value functions typically assume a fully observed state and must compensate for partial or non-Markovian observations by using finite-length frame-history observations or recurrent networks. In this work, we propose a new deep reinforcement learning algorithm based on counterfactual regret minimization that iteratively updates an approximation to a cumulative clipped advantage function and is robust to partially observed state. We demonstrate that on several partially observed reinforcement learning tasks, this new class of algorithms can substantially outperform strong baseline methods: on Pong with single-frame observations, and on the challenging Doom (ViZDoom) and Minecraft (Malmö) first-person navigation benchmarks. Many reinforcement learning problems of practical interest have the property of partial observability, where observations of state are generally non-Markovian. Despite the importance of partial observation in the real world, value function-based methods such as Q-learning (Mnih et al., 2013; BID6 generally assume a Markovian observation space. On the other hand, Monte Carlo policy gradient methods do not assume Markovian observations, but many practical policy gradient methods such as A3C (Mnih et al., 2016) introduce the Markov assumption when using a critic or state-dependent baseline in order to improve sample efficiency.Consider deep reinforcement learning methods that learn a state or state-action value function. One common workaround for the problem of partial observation is to learn value functions on the space of finite-length frame-history observations, under the assumption that frame-histories of sufficient length will give the environment the approximate appearance of full observability. When learning to play Atari 2600 games from images, deep Q-learning algorithms (Mnih et al., 2013; BID6 concatenate the last 4 observed frames of the video screen buffer as input to a state-action value convolutional network. Not all non-Markovian tasks are amenable to finite-length frame-histories; recurrent value functions can incorporate longer and potentially infinite histories BID12 BID8 , but at the cost of solving a harder optimization problem. Can we develop methods that learn a variant of the value function that is more robust to partial observability?Our contribution is a new model-free deep reinforcement learning algorithm based on the principle of regret minimization which does not require access to a Markovian state. Our method learns a policy by estimating a cumulative clipped advantage function, which is an approximation to a type of regret that is central to two partial information game-solving algorithms from which we draw our primary inspiration: counterfactual regret minimization (CFR) BID35 and CFR+ BID28 . Hence we call our algorithm ""advantage-based regret minimization"" (ARM).We evaluate our approach on three visual reinforcement learning domains: Pong with varying framehistory lengths BID2 , and the first-person games Doom BID16 and Minecraft BID15 . Doom and Minecraft exhibit a first-person viewpoint in a 3-dimensional environment and should appear non-Markovian even with frame-history observations. We find that our method offers substantial improvement over prior methods in these partially observ-able environments: on both Doom and Minecraft, our method can learn well-performing policies within about 1 million simulator steps using only visual input frame-history observations. In this paper, we presented a novel deep reinforcement learning algorithm based on counterfactual regret minimization (CFR). We call our method advantage-based regret minimization (ARM). Similarly to prior methods that learn state or state-action value functions, our method learns a cumulative clipped advantage function of observation and action. However, in contrast to these prior methods, ARM is well suited to partially observed or non-Markovian environments, making it an appealing choice in a number of difficult domains. When compared to baseline methods, including deep Q-learning and TRPO, on non-Markovian tasks such as the challenging ViZDoom and Malmö firstperson navigation benchmarks, ARM achieves substantially better results. This illustrates the value of ARM for partially observable problems. In future work, we plan to further explore applications of ARM to more complex tasks, including continuous action spaces.6 APPENDIX 6.1 EXPERIMENTAL DETAILS 6.1.1 PONG (ARCADE LEARNING ENVIRONMENT)We use the preprocessing and convolutional network model of (Mnih et al., 2013) . Specifically, we view every 4th emulator frame, convert the raw frames to grayscale, and perform downsampling to generate a single observed frame. The input observation of the convnet is a concatenation of the most recent frames (either 4 frames or 1 frame). The convnet consists of an 8 × 8 convolution with stride 4 and 16 filters followed by ReLU, a 4 × 4 convolution with stride 2 and 32 filters followed by ReLU, a linear map with 256 filters followed by ReLU, and a linear map with |A| filters where |A| is the action space cardinality (|A| = 6 for Pong).We used Adam with a constant learning rate of α = 10 −4 , a minibatch size of 32, and the moment decay rates set to their defaults β 1 = 0.9 and β 2 = 0.999. Our results on each method are averaged across 3 random seeds.We ran ARM with the hyperparameters: sampling batch size of 12500, 4000/3000 minibatches of Adam for the first/subsequent sampling iterations respectively, and target update step size τ = 0.01. Double DQN uses the tuned hyperparameters . Note that our choice of ARM hyperparameters yields an equivalent number of minibatch gradient updates per sample as used by DQN and double DQN, i.e. 1 minibatch gradient update per 4 simulator steps.",Deep reinforcement learning algorithms estimate state state-action value functions have been shown effective variety challenging domains including learning control strategies raw image pixels. However algorithms estimate state state-action value functions typically assume fully observed state must compensate partial non-Markovian observations using finite-length frame-history observations recurrent networks. work propose new deep reinforcement learning algorithm based counterfactual regret minimization iteratively updates approximation cumulative clipped advantage function is robust partially observed state. demonstrate several partially observed reinforcement learning tasks new class algorithms can substantially outperform strong baseline methods:Pong single-frame observations challenging Doom ViZDoom Minecraft Malmö first-person navigation benchmarks. Many reinforcement learning problems practical interest have the property partial observability where observations state are generally generally non-Markovian Despite importance partial observation real world value function-based methods Q-learning Mnihetal. 2013;BID6 generally assume Markovian observation space. hand Monte Carlo policy gradient methods do not assume Markovian observations many practical policy gradient methods A3C Mnihetal. 2016 introduce Markov assumption when using critic state-dependent baseline order improve sample efficiency.Consider deep reinforcement learning methods learn state state-action value function. One common workaround problem partial observation is to learn value functions space finite-length frame-history observations assumption frame-histories sufficient length will give environment approximate appearance full observability. When learning play Atari 2600 games images deep Q-learning algorithms Mnihetal. 2013;BID6 concatenate last 4 observed frames video screen buffer input state-action value convolutional network. non-Markovian tasks are amenable finite-length frame-histories recurrent value functions can incorporate longer potentially infinite histories BID12 BID8 cost solving harder optimization problem. Can we develop methods learn variant value function is more robust partial observability? contribution is a new model-free deep reinforcement learning algorithm based principle regret minimization which does not require access Markovian state. method learns policy estimating cumulative clipped advantage function which is an approximation type regret is central two partial information game-solving algorithms which we draw primary inspiration:counterfactual regret minimization CFR BID35 CFR+BID28. Hence call algorithm advantage-based regret minimization ARM.We evaluate approach three visual reinforcement learning domains:Pong varying framehistory lengths BID2 first-person games Doom BID16 Minecraft BID15. Doom Minecraft exhibit first-person viewpoint 3-dimensional environment should appear non-Markovian even frame-history observations. find method offers substantial improvement prior methods partially observ-able environments:Doom Minecraft method can learn well-performing policies within 1 million simulator steps using visual input frame-history observations. paper presented novel deep reinforcement learning algorithm based counterfactual regret minimization CFR call method advantage-based regret minimization ARM Similarly prior methods learn state state-action value functions method learns cumulative clipped advantage function observation action. However contrast prior methods ARM is well suited partially observed non-Markovian environments making appealing choice number difficult domains. When compared baseline methods including deep Q-learning TRPO non-Markovian tasks challenging ViZDoom Malmö firstperson navigation benchmarks ARM achieves substantially better results. illustrates value ARM partially observable problems. future work plan explore applications ARM complex tasks including continuous action spaces.6 APPENDIX 6.1 EXPERIMENTAL DETAILS 6.1.1 PONG ARCADE LEARNING ENVIRONMENT use preprocessing convolutional network model Mnihetal. 2013 Specifically view every 4th emulator frame convert raw frames grayscale perform downsampling generate single observed frame. input observation convnet is a concatenation recent frames either 4 frames 1 frame convnet consists 8 × 8 convolution stride4 16 filters followed ReLU 4 × 4 convolution stride2 32 filters followed ReLU linear map 256 filters followed ReLU linear map |A| filters where |A| is the action space cardinality |A| 6 Pong.We used Adam constant learning rate α 10−4 minibatch size 32 moment decay rates set defaultsβ1 0.9 β2 0.999 results method are averaged across 3 random seeds.We ran ARM hyperparameters:sampling batch size 12500 4000/3000 minibatches Adam first/subsequent sampling iterations respectively target update step size τ 0.01 Double DQN uses tuned hyperparameters. Note choice ARM hyperparameters yields equivalent number minibatch gradient updates per sample used DQN double DQN.e 1 minibatch gradient update per 4 simulator steps.,1204,877,327,0.011,1.373,2025/11/05 17:18:58,0.0,1.536,0.1339563862928346,326.19
"Recent deep multi-task learning (MTL) has been witnessed its success in alleviating data scarcity of some task by utilizing domain-specific knowledge from related tasks. Nonetheless, several major issues of deep MTL, including the effectiveness of sharing mechanisms, the efficiency of model complexity and the flexibility of network architectures, still remain largely unaddressed. To this end, we propose a novel generalized latent-subspace based knowledge sharing mechanism for linking task-specific models, namely tensor ring multi-task learning (TRMTL). TRMTL has a highly compact representation, and it is very effective in transferring task-invariant knowledge while being super flexible in learning task-specific features, successfully mitigating the dilemma of both negative-transfer in lower layers and under-transfer in higher layers. Under our TRMTL, it is feasible for each task to have heterogenous input data dimensionality or distinct feature sizes at different hidden layers. Experiments on a variety of datasets demonstrate our model is capable of significantly improving each single task’s performance, particularly favourable in scenarios where some of the tasks have insufficient data. Multi-task learning (MTL) (Caruana, 1997; BID15 is an approach for boosting the overall performance in each individual task by learning multiple related tasks simultaneously. In the deep learning context, jointly fitting sufficiently flexible deep neural networks (DNNs) to data of multiple tasks can be seen as adding an inductive bias to the deep models, which could be beneficial to learn feature representations preferable by all tasks. Recently, the deep MTL has gained much popularity and been successfully explored in an abroad range of applications, such as computer vision BID32 BID16 , natural language processing BID14 , speech recognition BID5 and so on.However, a number of key challenges posed by the issues of ineffectiveness, inefficiency and inflexibility in deep MTL are left largely unaddressed. One major challenge is how to seek effective information sharing mechanisms across related tasks, which is equivalent to designing better parameter sharing patterns in the deep networks. Some previous work BID32 BID30 tried to solve this problem by means of hard parameter sharing BID21 , where the bottom layers are all shared except with one branch per task at the top layers. Although being simple and robust to over-fitting BID0 , this kind of architecture can be harmful when learning high-level task-specific features, since it focuses only on common low-level features of all tasks. Moreover, these common features may be polluted by some noxious tasks, leading to the negative transfer in low-level features among tasks BID31 ). An alternative line of work mitigate this issue to some extent by following the soft parameter sharing strategy BID21 , under which one separate DNN is learned for each task with its own set of parameters, and the individual DNNs are implicitly linked by imposing constraints on the aligned weights. The deep MTL models of this type include using 2 norm regularization BID4 , trace norm regularization BID29 and tensor norm priors BID12 BID13 .The lack of efficiency in model complexity gives rise to another great challenge for current deep MTL. The above soft-sharing based deep models (one set of parameters per task) typically involve enormous number of trainable parameters and require extremely large storage and memory. It is thus usually infeasible to deploy those deep MTL models on resource-constrained devices such as mobile The overall sharing mechanisms of MRN, two variants of DMTRL (for the setting of CNN) and our TRMTL w.r.t. two tasks. The shared portion is depicted in yellow. The circles, squares and thin rectangles represent tensor cores, matrices and vectors, respectively. MRN : original weights are totally shared at the lower layers and the relatedness between tasks at the top layers is modeled by tensor normal priors. DMTRL (TT or Tucker): all layer-wise weights must be equal-sized so as to be stacked and decomposed into factors. For each task, almost all the factors are shard at each layer except the very last 1D vector. Such pattern of sharing is identical at all layers. TRMTL: layer-wise weights are separately encoded into TR-formats for different tasks, and a subset of latent cores are selected to be tied across two tasks. The portions of sharing can be different from layer to layer. phones and wearable computers . BID28 alleviated the issue by integrating tensor factorization with deep MTL and proposed deep multi-task representation learning (DMTRL). Specifically, they first stack up the layer-wise weights from all tasks and then decompose them into low-rank factors, yielding a succinct deep MTL model with fewer parameters. Despite the compactness of the model, DMTRL turns out to be rather restricted on sharing knowledge effectively. This is because, as shown in FIG0 , DMTRL (TT or Tucker) shares almost all fractions of layer-wise weights as common factors, leaving only a tiny portion of weights to encode the task-specific information. Even worse, such pattern of sharing must be identical across all hidden layers, which is vulnerable to the negative transfer of the features. As an effect, the common factors become highly dominant at each layer and greatly suppress model's capability in expressing task-specific variations.The last challenge arises from the flexibility of architecture in deep MTL. Most of deep MTL models force tasks to have the equal-sized layer-wise weights or input dimensionality. This restriction makes little sense for the case of loosely-related tasks, since individual tasks' features (input data) can be quite different and the sizes of layer-wise features (input data) may vary a lot from task to task.In this work, we provide a generalized latent-subspace based solution to addressing aforementioned difficulties of deep MTL, from all aspects of effectiveness, efficiency and flexibility. Regarding the effectiveness, we propose to share different portions of weights as common knowledge at distinct layers, so that each individual task can better convey its private knowledge. As for the efficiency, our proposal shares knowledge in the latent subspace instead of original space by utilizing a general tensor ring (TR) representation with a sequence of latent cores BID21 . One motivation of TR for MTL is it generalizes other chain structured tensor networks , especially tensor train (TT) BID18 , in terms of model expressivity power, as TR can be formulated as a sum of TT networks. On the other hand, TR is able to approximate tensors using lower overall ranks than TT does , thus yielding a more compact and sparselyconnected model with significantly less parameters for deep MTL. Adopting TR-format with much lower ranks could bring more benefits to deep MTL if we tensorize a layer-wise weight of each task into a higher-order weight tensor, since the weight can be decomposed into a relatively larger number but smaller-sized cores. This in turn facilitates the sharing of cores at a finer granularity and further enhances the effectiveness of sharing. Additionally, BID34 In this paper, we have introduced a novel knowledge sharing mechanism for connecting task-specific models in deep MTL, namely TRMTL. The proposed approach models each task separately in the form of TR representation using a sequence latent cores. Next, TRMTL shares the common knowledge by ting any subset of layer-wise TR cores among all tasks, leaving the rest TR cores for private knowledge. TRMTL is highly compact yet super flexible to learn both task-specific and task-invariant features. TRMTL is empirically verified on various datasets and achieves the stateof-the-art results in helping the individual tasks to improve their overall performance. Table 4 : Performance comparison of STL, MRN, DMTRL and our TRMTL on CIFAR-10 with unbalanced training samples, e.g., '5% vs 5% vs 5%' means 5% of training samples are available for the respective task A, task B and task C. TR-ranks R = 10 for TRMTL.","Recent deep multi-task learning MTL has been witnessed success alleviating data scarcity task utilizing domain-specific knowledge related tasks. Nonetheless several major issues deep MTL including effectiveness sharing mechanisms efficiency model complexity flexibility network architectures still remain largely unaddressed. end propose novel generalized latent-subspace based knowledge sharing mechanism linking task-specific models namely tensor ring multi-task learning TRMTL TRMTL has a highly compact representation is effective transferring task-invariant knowledge super flexible learning task-specific features successfully mitigating dilemma negative-transfer lower layers under-transfer higher layers. TRMTL is feasible task have heterogenous input data dimensionality distinct feature sizes different hidden layers. Experiments variety datasets demonstrate model is capable significantly improving single tasks performance particularly favourable scenarios where some of the tasks have insufficient data. Multi-task learning MTL Caruana 1997;BID15 is an approach boosting overall performance individual task learning multiple related tasks simultaneously. deep learning context jointly fitting sufficiently flexible deep neural networks DNNs data multiple tasks can be seen adding inductive bias deep models could beneficial learn feature representations preferable tasks. Recently deep MTL has gained much popularity successfully explored abroad range applications computer vision BID32 BID16 natural language processing BID14 speech recognition BID5 on.However number key challenges posed issues ineffectiveness inefficiency inflexibility deep MTL are left largely unaddressed. One major challenge is how to seek effective information sharing mechanisms across related tasks which is equivalent designing better parameter sharing patterns deep networks. previous work BID32 BID30 tried solve problem means hard parameter sharing BID21 where the bottom layers are all shared except one branch per task top layers. Although simple robust over-fitting BID0 kind architecture can be harmful when learning high-level task-specific features since focuses common low-level features tasks. Moreover common features may polluted noxious tasks leading negative transfer low-level features among tasks BID31 alternative line work mitigate issue extent following soft parameter sharing strategy BID21 which one separate DNN is learned task set parameters individual DNNs are implicitly linked imposing constraints aligned weights. deep MTL models type include using2 norm regularization BID4 trace norm regularization BID29 tensor norm priors BID12 BID13.The lack efficiency model complexity gives rise another great challenge current deep MTL. soft-sharing based deep models one set parameters per task typically involve enormous number trainable parameters require extremely large storage memory. is thus usually infeasible deploy deep MTL models resource-constrained devices mobile overall sharing mechanisms MRN two variants DMTRL setting CNN TRMTLw.r.t two tasks. shared portion is depicted yellow. circles squares thin rectangles represent tensor cores matrices vectors respectively. MRN:original weights are totally shared lower layers relatedness tasks top layers is modeled tensor normal priors. DMTRL TT Tucker layer-wise weights must equal-sized stacked decomposed factors. task almost factors are shard layer except last 1D vector. pattern sharing is identical layers. TRMTL:layer-wise weights are separately encoded TR-formats different tasks subset latent cores are selected tied across two tasks. portions sharing can be different layer layer. phones wearable computers. BID28 alleviated issue integrating tensor factorization deep MTL proposed deep multi-task representation learning DMTRL Specifically first stack layer-wise weights tasks decompose low-rank factors yielding succinct deep MTL model fewer parameters. Despite compactness model DMTRL turns rather restricted sharing knowledge effectively. is because,shown FIG0 DMTRL TT Tucker shares almost fractions layer-wise weights common factors leaving tiny portion weights encode task-specific information. Even worse pattern sharing must identical across hidden layers which is vulnerable negative transfer features. effect common factors become highly dominant layer greatly suppress model's capability expressing task-specific variations.The last challenge arises flexibility architecture deep MTL. deep MTL models force tasks have the equal-sized layer-wise weights input dimensionality. restriction makes little sense case loosely-related tasks since individual tasks' features input data can be quite different sizes layer-wise features input data may vary lot task task.In work provide generalized latent-subspace based solution addressing aforementioned difficulties deep MTL aspects effectiveness efficiency flexibility. Regarding effectiveness propose share different portions weights common knowledge distinct layers individual task can better convey private knowledge. efficiency proposal shares knowledge latent subspace instead original space utilizing general tensor ring TR representation sequence latent cores BID21. One motivation TR MTL is it generalizes chain structured tensor networks especially tensor train TT BID18 terms model expressivity power TR can be formulated sum TT networks. hand TR is able approximate tensors using lower overall ranks TT does,thus yielding compact sparselyconnected model significantly less parameters deep MTL. Adopting TR-format much lower ranks could bring benefits deep MTL if we tensorize layer-wise weight task higher-order weight tensor since weight can be decomposed relatively larger number smaller-sized cores. turn facilitates sharing cores finer granularity enhances effectiveness sharing. Additionally BID34 paper have introduced novel knowledge sharing mechanism connecting task-specific models deep MTL namely TRMTL. proposed approach models task separately form TR representation using sequence latent cores. Next TRMTL shares common knowledge ting subset layer-wise TR cores among tasks leaving rest TR cores private knowledge. TRMTL is highly compact yet super flexible learn task-specific task-invariant features. TRMTL is empirically verified various datasets achieves stateof-the-art results helping individual tasks improve overall performance. Table4:Performance comparison STL MRN DMTRL TRMTL CIFAR-10 unbalanced training samples e.g '5vs5% vs 5%' means 5% training samples are available respective task taskB taskC. TR-ranksR 10 TRMTL.",1587,1106,481,0.016,1.435,2025/11/05 17:18:58,0.01,1.533,0.3271028037383177,502.081
"Neural Processes (NPs) (Garnelo et al., 2018) approach regression by learning to map a context set of observed input-output pairs to a distribution over regression functions. Each function models the distribution of the output given an input, conditioned on the context. NPs have the benefit of fitting observed data efficiently with linear complexity in the number of context input-output pairs, and can learn a wide family of conditional distributions; they learn predictive distributions conditioned on context sets of arbitrary size. Nonetheless, we show that NPs suffer a fundamental drawback of underfitting, giving inaccurate predictions at the inputs of the observed data they condition on. We address this issue by incorporating attention into NPs, allowing each input location to attend to the relevant context points for the prediction. We show that this greatly improves the accuracy of predictions, results in noticeably faster training, and expands the range of functions that can be modelled. Regression tasks are usually cast as modelling the distribution of a vector-valued output y given a vector-valued input x via a deterministic function, such as a neural network, taking x as an input. In this setting, the model is trained on a dataset of input-output pairs, and predictions of the outputs are independent of each other given the inputs. An alternative approach to regression involves using the training data to compute a distribution over functions that map inputs to outputs, and using draws from that distribution to make predictions on test inputs. This approach allows for reasoning about multiple functions consistent with the data, and can capture the co-variability in outputs given inputs. In the Bayesian machine learning literature, non-parametric models such as Gaussian Processes (GPs) are popular choices of this approach.Neural Processes (NPs) BID9 BID12 offer an efficient method to modelling a distribution over regression functions, with prediction complexity linear in the context set size. Once trained, they can predict the distribution of an arbitrary target output conditioned on a set of context inputoutput pairs of an arbitrary size. This flexibility of NPs enables them to model data that can be interpreted as being generated from a stochastic process. It is important to note however that NPs and GPs have different training regimes. NPs are trained on samples from multiple realisations of a stochastic process (i.e. trained on many different functions), whereas GPs are usually trained on observations from one realisation of the stochastic process (a single function). Hence a direct comparison between the two is usually not plausible.Despite their many appealing properties, one substantial weakness of NPs is that they tend to underfit the context set. This manifests in the 1D curve fitting example on the left half of FIG0 as inaccurate predictive means and overestimated variances at the input locations of the context set. The right half of the figure shows this phenomenon when predicting the bottom half of a face image from its top half: although the prediction is globally coherent, the model's reconstruction of the top-half is far from perfect. In an NP, the encoder aggregates the context set to a fixed-length latent summary via a permutation invariant function, and the decoder maps the latent and target input to the target output. We hypothesise that the underfitting behaviour is because the mean-aggregation step in the encoder acts as a bottleneck: since taking the mean across context representations gives the same weight to each context point, it is difficult for the decoder to learn which context points provide relevant information for a given target prediction. In theory, increasing the dimensionality of the representation could address this issue, but we show in Section 4 that in practice, this is not sufficient.To address this issue, we draw inspiration from GPs, which also define a family of conditional distributions for regression. In GPs, the kernel can be interpreted as a measure of similarity among two points in the input domain, and shows which context points (x i , y i ) are relevant for a given query x * . Hence when x * is close to some x i , its y-value prediction y * is necessarily close to y i (assuming small likelihood noise), and there is no risk of underfitting. We implement a similar mechanism in NPs using differentiable attention that learns to attend to the contexts relevant to the given target, while preserving the permutation invariance in the contexts. We evaluate the resulting Attentive Neural Processes (ANPs) on 1D function regression and on 2D image regression. Our results show that ANPs greatly improve upon NPs in terms of reconstruction of contexts as well as speed of training, both against iterations and wall clock time. We also demonstrate that ANPs show enhanced expressiveness relative to the NP and is able to model a wider range of functions. We have proposed ANPs, which augment NPs with attention to resolve the fundamental problem of underfitting. We have shown that this greatly improves the accuracy of predictions in terms of context and target NLL, results in faster training, and expands the range of functions that can be modelled. There is a wide scope of future work for ANPs. Regarding model architecture, one way of incorporating cross-attention into the latent path and modelling the dependencies across the resulting local latents is to also have a global latent, much like the setup of the Neural Statistician but translated to the regression setting. An interesting further application would be to train ANPs on text data, enabling them to fill in the blanks in a stochastic manner. For the image application, the Image Transformer (ImT) BID21 has some interesting connections with ANPs: its local self-attention used to predict consecutive pixel blocks from previous blocks has parallels with how our model attends to context pixels to predict target pixels. Replacing the MLP in the decoder of the ANP with self-attention across the target pixels, we have a model that closely resembles an ImT defined on arbitrary orderings of pixels. This is in contrast to the original ImT, which presumes a fixed ordering and is trained autoregressively. We plan to equip ANPs with self-attention in the decoder, and see how far their expressiveness can be extended. In this setup, however, the targets will affect each other's predictions, so the ordering and grouping of the targets will become important.",Neural Processes NPs Garneloetal. 2018 approach regression learning map context set observed input-output pairs distribution regression functions. function models distribution output given input conditioned context. NPs have the benefit fitting observed data efficiently linear complexity number context input-output pairs can learn wide family conditional distributions;learn predictive distributions conditioned context sets arbitrary size. Nonetheless show NPs suffer fundamental drawback underfitting giving inaccurate predictions inputs observed data condition on. address issue incorporating attention NPs allowing input location attend relevant context points prediction. show greatly improves accuracy predictions results noticeably faster training expands range functions can be modelled. Regression tasks are usually cast modelling distribution vector-valued output given vector-valued input x via deterministic function neural network takingx input. setting have a model is trained dataset input-output pairs predictions outputs are independent given inputs. alternative approach regression involves using training data compute distribution functions map inputs outputs using draws distribution make predictions test inputs. approach allows reasoning multiple functions consistent data can capture co-variability outputs given inputs. Bayesian machine learning literature non-parametric models Gaussian Processes GPs are popular choices approach.Neural Processes NPs BID9 BID12 offer efficient method modelling distribution regression functions prediction complexity linear context set size. trained can predict distribution arbitrary target output conditioned set context inputoutput pairs arbitrary size. flexibility NPs enables model data can be interpreted generated stochastic process. is important note however NPs GPs have different training regimes. NPs are trained samples multiple realisations stochastic process.e trained many different functions whereas GPs are usually trained observations one realisation stochastic process single function Hence direct comparison two is usually plausible.Despite many appealing properties one substantial weakness NPs is that they tend underfit context set. manifests 1D curve fitting example left half FIG0 inaccurate predictive means overestimated variances input locations context set. right half figure shows phenomenon when predicting bottom half face image top half:although prediction is globally coherent model's reconstruction top-half is far perfect. NP encoder aggregates context set fixed-length latent summary via permutation invariant function decoder maps latent target input target output. hypothesise underfitting behaviour is because the mean-aggregation step encoder acts bottleneck:since taking mean across context representations gives weight context point is difficult decoder learn which context points provide relevant information given target prediction. theory increasing dimensionality representation could address issue show Section4 practice is not sufficient.To address issue draw inspiration GPs which also define family conditional distributions regression. GPs kernel can be interpreted measure similarity among two points input domain shows which context points x are relevant given queryx* Hence whenx* is close x y-value prediction * is necessarily close assuming small likelihood noise isno risk underfitting. implement similar mechanism NPs using differentiable attention learns attend contexts relevant given target preserving permutation invariance contexts. evaluate resulting Attentive Neural Processes ANPs 1D function regression 2D image regression. results show ANPs greatly improve upon NPs terms reconstruction contexts well speed training iterations wall clock time. also demonstrate ANPs show enhanced expressiveness relative NP is able model wider range functions. have proposed ANPs which augment NPs attention resolve fundamental problem underfitting. have shown greatly improves accuracy predictions terms context target NLL results faster training expands range functions can be modelled. is a wide scope future work ANPs. Regarding model architecture one way incorporating cross-attention latent path modelling dependencies across resulting local latents is to also have a global latent much like setup Neural Statistician translated regression setting. interesting application would train ANPs text data enabling fill blanks stochastic manner. image application Image Transformer ImT BID21 has some interesting connections ANPs:local self-attention used predict consecutive pixel blocks previous blocks has parallels how our model attends context pixels predict target pixels. Replacing MLP decoder ANP self-attention across target pixels have a model closely resembles ImT defined arbitrary orderings pixels. is in contrast original ImT which presumes fixed ordering is trained autoregressively. plan equip ANPs self-attention decoder see how far expressiveness can be extended. setup however targets will affect other's predictions ordering grouping targets will become important.,1260,815,445,0.014,1.546,2025/11/05 17:18:58,0.01,1.383,0.6728971962616822,437.242
"Deconvolutional layers have been widely used in a variety of deep
 models for up-sampling, including encoder-decoder networks for
 semantic segmentation and deep generative models for unsupervised
 learning. One of the key limitations of deconvolutional operations
 is that they result in the so-called checkerboard problem. This is
 caused by the fact that no direct relationship exists among adjacent
 pixels on the output feature map. To address this problem, we
 propose the pixel deconvolutional layer (PixelDCL) to establish
 direct relationships among adjacent pixels on the up-sampled feature
 map. Our method is based on a fresh interpretation of the regular
 deconvolution operation. The resulting PixelDCL can be used to
 replace any deconvolutional layer in a plug-and-play manner without
 compromising the fully trainable capabilities of original models.
 The proposed PixelDCL may result in slight decrease in efficiency,
 but this can be overcome by an implementation trick. Experimental
 results on semantic segmentation demonstrate that PixelDCL can
 consider spatial features such as edges and shapes and yields more
 accurate segmentation outputs than deconvolutional layers. When used
 in image generation tasks, our PixelDCL can largely overcome the
 checkerboard problem suffered by regular deconvolution operations. Deep learning methods have shown great promise in a variety of artificial intelligence tasks such as image classification BID9 BID26 , semantic segmentation BID16 BID24 BID23 , and natural image generation BID3 BID8 . Some key network layers, such as convolutional layers BID11 , pooling layers, fully connected layers and deconvolutional layers, have been frequently used to create deep models for different tasks. Deconvolutional layers, also known as transposed convolutional layers BID28 , are initially proposed in BID29 . They have been primarily used in deep models that require up-sampling of feature maps, such as generative models BID19 BID15 BID22 and encoder-decoder architectures BID23 BID16 . Although deconvolutional layers are capable of producing larger feature maps from smaller ones, they suffer from the problem of checkerboard artifacts BID17 . This greatly limits deep model's capabilities in generating photo-realistic images and producing smooth outputs on semantic segmentation. To date, very little efforts have been devoted to improving the deconvolution operation.In this work, we propose a simple, efficient, yet effective method, known as the pixel deconvolutional layer (PixelDCL), to address the checkerboard problem suffered by deconvolution operations. Our method is motivated from a fresh interpretation of deconvolution operations, which clearly pinpoints the root of checkerboard artifacts. That is, the up-sampled feature map generated by deconvolution can be considered as the result of periodical shuffling of multiple intermediate feature maps computed from the input feature map by independent convolutions. As a result, adjacent pixels on the output feature map are not directly related, leading to the checkerboard artifacts. To overcome this problem, we propose the pixel deconvolutional operation to be used in PixelDCL. In this new layer, the intermediate feature maps are generated sequentially so that feature maps generated in a later stage are required to depend on previously generated ones. In this way, direct relationships among adjacent pixels on the output feature map have been established. Sequential generation of intermediate feature maps in PixelDCL may result in slight decrease in computational efficiency, but we show Figure 1 : Comparison of semantic segmentation results. The first and second rows are images and ground true labels, respectively. The third and fourth rows are the results of using regular deconvolution and our proposed pixel deconvolution PixelDCL, respectively. that this can be largely overcome by an implementation trick. Experimental results on semantic segmentation (samples in Figure 1) and image generation tasks demonstrate that the proposed PixelDCL can effectively overcome the checkerboard problem and improve predictive and generative performance.Our work is related to the pixel recurrent neural networks (PixelRNNs) and PixelCNNs BID21 , which are generative models that consider the relationship among units on the same feature map. They belong to a more general class of autoregressive methods for probability density estimation BID2 BID10 . By using masked convolutions in training, the training time of PixelRNNs and PixelCNNs is comparable to that of other generative models such as generative adversarial networks (GANs) BID3 BID20 and variational autoencoders (VAEs) BID8 BID6 . However, the prediction time of PixelRNNs or PixelCNNs is very slow since it has to generate images pixel by pixel. In contrast, our PixelDCL can be used to replace any deconvolutional layer in a plug-and-play manner, and the slight decrease in efficiency can be largely overcome by an implementation trick. In this work, we propose pixel deconvolutional layers that can solve the checkerboard problem in deconvolutional layers. The checkerboard problem is caused by the fact that there is no direct relationship among intermediate feature maps generated in deconvolutional layers. PixelDCL proposed here try to add direct dependencies among these generated intermediate feature maps. PixelDCL generates intermediate feature maps sequentially so that the intermediate feature maps generated in a later stage are required to depend on previously generated ones. The establishment of dependencies in PixelDCL can ensure adjacent pixels on output feature maps are directly related. Experimental results on semantic segmentation and image generation tasks show that PixelDCL is effective in overcoming the checkerboard artifacts. Results on semantic segmentation also show that PixelDCL is able to consider local spatial features such as edges and shapes, leading to better segmentation results. In the future, we plan to employ our PixelDCL in a broader class of models, such as the generative adversarial networks (GANs).","Deconvolutional layers have been widely used variety deep models up-sampling including encoder-decoder networks semantic segmentation deep generative models unsupervised learning. One key limitations deconvolutional operations is that they result so-called checkerboard problem. is caused fact is no direct relationship exists among adjacent pixels output feature map. address problem propose pixel deconvolutional layer PixelDCL establish direct relationships among adjacent pixels up-sampled feature map. method is based fresh interpretation regular deconvolution operation. resulting PixelDCL can be used replace deconvolutional layer plug-and-play manner without compromising fully trainable capabilities original models. proposed PixelDCL may result slight decrease efficiency can overcome implementation trick. Experimental results semantic segmentation demonstrate PixelDCL can consider spatial features edges shapes yields accurate segmentation outputs deconvolutional layers. When used image generation tasks PixelDCL can can be largely overcome checkerboard problem suffered regular deconvolution operations. Deep learning methods have shown great promise variety artificial intelligence tasks image classification BID9 BID26 semantic segmentation BID16 BID24 BID23 natural image generation BID3 BID8. key network layers convolutional layers BID11 pooling layers fully connected layers deconvolutional layers have been frequently used create deep models different tasks. Deconvolutional layers also known transposed convolutional layers BID28 are initially proposed BID29. have been primarily used deep models require up-sampling feature maps which are generative models BID19 BID15 BID22 encoder-decoder architectures BID23 BID16. Although deconvolutional layers are capable producing larger feature maps smaller ones suffer problem checkerboard artifacts BID17. greatly limits deep model's capabilities generating photo-realistic images producing smooth outputs semantic segmentation. date little efforts have been devoted improving deconvolution operation.In work propose simple efficient yet effective method known pixel deconvolutional layer PixelDCL address checkerboard problem suffered deconvolution operations. method is motivated fresh interpretation deconvolution operations which clearly pinpoints root checkerboard artifacts. is,the up-sampled feature map generated deconvolution can be considered result periodical shuffling multiple intermediate feature maps computed input feature map independent convolutions. result adjacent pixels output feature map are not are directly related leading checkerboard artifacts. overcome problem propose pixel deconvolutional operation used PixelDCL. new layer intermediate feature maps are generated sequentially feature maps generated later stage are required depend previously generated ones. way direct relationships among adjacent pixels output feature map have been established. Sequential generation intermediate feature maps PixelDCL may result slight decrease computational efficiency show Figure1:Comparison semantic segmentation results. first second rows are images ground true labels respectively. third fourth rows are the results using regular deconvolution proposed pixel deconvolution PixelDCL respectively. can be largely overcome implementation trick. Experimental results semantic segmentation samples Figure1 image generation tasks demonstrate proposed PixelDCL can effectively overcome checkerboard problem improve predictive generative performance.Our work is related pixel recurrent neural networks PixelRNNs PixelCNNs BID21 which are generative models consider relationship among units feature map. belong general class autoregressive methods probability density estimation BID2 BID10. using masked convolutions training training time PixelRNNs PixelCNNs is comparable generative models generative adversarial networks GANs BID3 BID20 variational autoencoders VAEs BID8 BID6. However prediction time PixelRNNs PixelCNNs is very slow since has to generate images pixel pixel. contrast PixelDCL can be used replace deconvolutional layer plug-and-play manner slight decrease efficiency can can be largely overcome implementation trick. work propose pixel deconvolutional layers can solve checkerboard problem deconvolutional layers. checkerboard problem is caused fact is no direct relationship among intermediate feature maps generated deconvolutional layers. PixelDCL proposed try add direct dependencies among generated intermediate feature maps. PixelDCL generates intermediate feature maps sequentially intermediate feature maps generated later stage are required depend previously generated ones. establishment dependencies PixelDCL can ensure adjacent pixels output feature maps are not are directly related. Experimental results semantic segmentation image generation tasks show PixelDCL is effective overcoming checkerboard artifacts. Results semantic segmentation also show PixelDCL is able consider local spatial features edges shapes leading better segmentation results. future plan employ PixelDCL broader class models which are generative adversarial networks GANs",1181,862,319,0.01,1.37,2025/11/05 17:18:58,0.0,1.475,0.1246105919003116,331.728
"In this paper, the preparation of a neural network for pruning and few-bit quantization is formulated as a variational inference problem. To this end, a quantizing prior that leads to a multi-modal, sparse posterior distribution over weights, is introduced and a differentiable Kullback-Leibler divergence approximation for this prior is derived. After training with Variational Network Quantization, weights can be replaced by deterministic quantization values with small to negligible loss of task accuracy (including pruning by setting weights to 0). The method does not require fine-tuning after quantization. Results are shown for ternary quantization on LeNet-5 (MNIST) and DenseNet (CIFAR-10). Parameters of a trained neural network commonly exhibit high degrees of redundancy BID4 which implies an over-parametrization of the network. Network compression methods implicitly or explicitly aim at the systematic reduction of redundancy in neural network models while at the same time retaining a high level of task accuracy. Besides architectural approaches, such as SqueezeNet BID25 or MobileNets (Howard et al., 2017) , many compression methods perform some form of pruning or quantization. Pruning is the removal of irrelevant units (weights, neurons or convolutional filters) BID31 . Relevance of weights is often determined by the absolute value (""magnitude based pruning"" BID15 ), but more sophisticated methods have been known for decades, e.g., based on second-order derivatives (Optimal Brain Damage (LeCun et al., 1990) and Optimal Brain Surgeon BID18 ) or ARD (automatic relevance determination, a Bayesian framework for determining the relevance of weights, BID35 BID39 BID27 ). Quantization is the reduction of the bit-precision of weights, activations or even gradients, which is particularly desirable from a hardware perspective BID46 . Methods range from fixed bit-width computation (e.g., 12-bit fixed point) to aggressive quantization such as binarization of weights and activations BID41 BID52 . Few-bit quantization (2 to 6 bits) is often performed by k-means clustering of trained weights with subsequent fine-tuning of the cluster centers . Pruning and quantization methods have been shown to work well in conjunction . In so-called ""ternary"" networks, weights can have one out of three possible values (negative, zero or positive) which also allows for simultaneous pruning and few-bit quantization BID33 BID53 ).This work is closely related to some recent Bayesian methods for network compression BID34 BID40 that learn a posterior distribution over network weights under a sparsity-inducing prior. The posterior distribution over network parameters allows identifying redundancies through three means: weights with (1) an expected value very close to zero and (2) weights with a large variance can be pruned as they do not contribute much to the overall computation. (3) the posterior variance over non-pruned parameters can be used to determine the required bit-precision (quantization noise can be made as large as implied by the posterior uncertainty). Additionally , Bayesian inference over modelparameters is known to automatically reduce parameter redundancy by penalizing overly complex models BID36 .In this paper we present Variational Network Quantization (VNQ), a Bayesian network compression method for simultaneous pruning and few-bit quantization of weights. We extend previous Bayesian pruning methods by introducing a multi-modal quantizing prior that penalizes weights of low variance unless they lie close to one of the target values for quantization. As a result, weights are either drawn to one of the quantization target values or they are assigned large variance values-see Fig. 1 . After training, our method yields a Bayesian neural network with a multi-modal posterior over weights (typically with one mode fixed at 0), which is the basis for subsequent pruning and quantization. Additionally, posterior uncertainties can also be interesting for network introspection and analysis, as well as for obtaining uncertainty estimates over network predictions BID9 BID8 BID5 . After pruning and hard quantization, and without the need for additional fine-tuning, our method yields a deterministic feed-forward neural network with heavily quantized weights. Our method is applicable to pre-trained networks but can also be used for training from scratch. Target values for quantization can either be manually fixed or they can be learned during training. We demonstrate our method for the case of ternary quantization on LeNet-5 (MNIST) and DenseNet (CIFAR-10). Figure 1: Distribution of weights (means θ and log-variance log σ 2 ) before and after VNQ training of LeNet-5 on MNIST (validation accuracy before: 99.2% vs. after 195 epochs: 99.3%). Top row: scatter plot of weights (blue dots) per layer. Means were initialized from pre-trained deterministic network, variances with log σ 2 = −8. Bottom row: corresponding density 1 . Red shaded areas show the funnel-shaped "" basins of attraction"" induced by the quantizing prior. Positive and negative target values for ternary quantization have been learned per layer. After training, weights with small expected absolute value or large variance (log α ij ≥ log T α = 2 corresponding to the funnel marked by the red dotted line) are pruned and remaining weights are quantized without loss in accuracy. A potential shortcoming of our method is the KL divergence approximation (Sec. 3.3) . While the approximation is reasonably good on the relevant range of θ-and σ-values, there is still room for improvement which could have the benefit that weights are drawn even more tightly onto the quantization levels, resulting in lower accuracy loss after quantization and pruning. Since our functional approximation to the KL divergence only needs to be computed once and an arbitrary amount of ground-truth data can be produced, it should be possible to improve upon the approximation presented here at least by some brute-force function approximation, e.g., a neural network, polynomial or kernel regression. The main difficulty is that the resulting approximation must be differentiable and must not introduce significant computational overhead since the approximation is evaluated once for each network parameter in each gradient step. We have also experimented with a naive Monte-Carlo approximation of the KL divergence term. This has the disadvantage that local reparameterization (where pre-activations are sampled directly) can no longer be used, since weight samples are required for the MC approximation. To keep computational complexity comparable, we used a single sample for the MC approximation. In our LeNet-5 on MNIST experiment the MC approximation achieves comparable accuracy with higher pruning rates compared to our functional KL approximation. However, with DenseNet on CIFAR-10 and the MC approximation validation accuracy plunges catastrophically after pruning and quantization. See Sec. A.3 in the Appendix for more details. Compared to similar methods that only consider network pruning, our pruning rates are significantly lower. This does not seem to be a particular problem of our method since other papers on network ternarization report similar or even lower sparsity levels BID53 roughly achieve between 30% and 50% sparsity). The reason for this might be that heavily quantized networks have a much lower capacity compared to full-precision networks. This limited capacity might require that the network compensates by effectively using more weights such that the pruning rates become significantly lower. Similar trends have also been observed with binary networks, where drops in accuracy could be prevented by increasing the number of neurons (with binary weights) per layer. Principled experiments to test the trade-off between low bit-precision and sparsity rates would be an interesting direction for future work. One starting point could be to test our method with more quantization levels (e.g., 5, 7 or 9) and investigate how this affects the pruning rate.",paper preparation neural network pruning few-bit quantization is formulated variational inference problem. end quantizing prior leads multi-modal sparse posterior distribution weights is introduced differentiable Kullback-Leibler divergence approximation prior is derived. training Variational Network Quantization weights can be replaced deterministic quantization values small negligible loss task accuracy including pruning setting weights 0 method does not require fine-tuning quantization. Results are shown ternary quantization LeNet-5 MNIST DenseNet CIFAR-10 Parameters trained neural network commonly exhibit high degrees redundancy BID4 which implies over-parametrization network. Network compression methods implicitly explicitly aim systematic reduction redundancy neural network models time retaining high level task accuracy. Besides architectural approaches SqueezeNet BID25 MobileNets Howardetal. 2017 many compression methods perform form pruning quantization. Pruning is the removal irrelevant units weights neurons convolutional filters BID31. Relevance weights is often determined absolute value magnitude based pruning BID15 sophisticated methods have been known decades e.g based second-order derivatives Optimal Brain Damage LeCunetal. 1990 Optimal Brain Surgeon BID18 ARD automatic relevance determination Bayesian framework determining relevance weights BID35 BID39 BID27 Quantization is the reduction bit-precision weights activations even gradients which is particularly desirable hardware perspective BID46. Methods range fixed bit-width computation e.g 12-bit fixed point aggressive quantization binarization weights activations BID41 BID52. Few-bit quantization 2 6 bits is often performed k-means clustering trained weights subsequent fine-tuning cluster centers. Pruning quantization methods have been shown work well conjunction. so-called ternary networks weights can have one three possible values negative zero positive which also allows simultaneous pruning few-bit quantization BID33 BID53.This work is closely related recent Bayesian methods network compression BID34 BID40 learn posterior distribution network weights sparsity-inducing prior. posterior distribution network parameters allows identifying redundancies three means:weights 1 expected value close zero 2 weights large variance can be pruned do not contribute much overall computation. 3 posterior variance non-pruned parameters can be used determine required bit-precision quantization noise can be made large implied posterior uncertainty Additionally Bayesian inference modelparameters is known automatically reduce parameter redundancy penalizing overly complex models BID36.In paper present Variational Network Quantization VNQ Bayesian network compression method simultaneous pruning few-bit quantization weights. extend previous Bayesian pruning methods introducing multi-modal quantizing prior penalizes weights low variance unless lie close one target values quantization. result weights are either drawn one quantization target values are assigned large variance values-see Fig. 1. training method yields Bayesian neural network multi-modal posterior weights typically one mode fixed 0 whichis basis subsequent pruning quantization. Additionally posterior uncertainties can also interesting network introspection analysis well obtaining uncertainty estimates network predictions BID9 BID8 BID5. pruning hard quantization without need additional fine-tuning method yields deterministic feed-forward neural network heavily quantized weights. method is applicable pre-trained networks can also used training scratch. Target values quantization can either manually fixed can be learned training. demonstrate method case ternary quantization LeNet-5 MNIST DenseNet CIFAR-10 Figure1:Distribution weights meansθ log-variance logσ2 VNQ training LeNet-5 MNIST validation accuracy before:99.2vs. 195 epochs:99.3 Top row:scatter plot weights blue dots per layer. Means were initialized pre-trained deterministic network variances logσ2 −8 Bottom row:corresponding density1. Red shaded areas show funnel-shaped basins attraction induced quantizing prior. Positive negative target values ternary quantization have been learned per layer. training weights small expected absolute value large variance logαij≥ log α 2 corresponding funnel marked red dotted line are pruned remaining weights are quantized without loss accuracy. potential shortcoming method is the KL divergence approximation Sec. 3.3 approximation is reasonably good relevant range θ-and σ-values is still room improvement could have the benefit weights are drawn even tightly onto quantization levels resulting lower accuracy loss quantization pruning. Since functional approximation KL divergence needs computed arbitrary amount ground-truth data can be produced should be possible improve upon approximation presented least brute-force function approximation e.g neural network polynomial kernel regression. main difficulty is that the resulting approximation must differentiable must introduce significant computational overhead since approximation is evaluated network parameter gradient step. have also experimented naive Monte-Carlo approximation KL divergence term. has the disadvantage local reparameterization where pre-activations are sampled directly can no longer used since weight samples are required MC approximation. keep computational complexity comparable used single sample MC approximation. LeNet-5 MNIST experiment MC approximation achieves comparable accuracy higher pruning rates compared functional KL approximation. However DenseNet CIFAR-10 MC approximation validation accuracy plunges catastrophically pruning quantization. See Sec. A.3 Appendix details. Compared similar methods consider network pruning pruning rates are significantly lower. does not seem particular problem method since papers network ternarization report similar even lower sparsity levels BID53 roughly achieve 30% 50% sparsity reason might heavily quantized networks have a much lower capacity compared full-precision networks. limited capacity might require network compensates effectively using weights pruning rates become significantly lower. Similar trends have also observed binary networks where drops accuracy could prevented increasing number neurons binary weights per layer. Principled experiments test trade-off low bit-precision sparsity rates would interesting direction future work. One starting point could test method quantization levels e.g 5 7 9 investigate how this affects pruning rate.,1579,1111,468,0.017,1.421,2025/11/05 17:18:58,0.01,1.473,0.2834890965732086,485.831
"Deep neural networks (DNNs) although achieving human-level performance in many domains, have very large model size that hinders their broader applications on edge computing devices. Extensive research work have been conducted on DNN model compression or pruning. However, most of the previous work took heuristic approaches. This work proposes a progressive weight pruning approach based on ADMM (Alternating Direction Method of Multipliers), a powerful technique to deal with non-convex optimization problems with potentially combinatorial constraints. Motivated by dynamic programming, the proposed method reaches extremely high pruning rate by using partial prunings with moderate pruning rates. Therefore, it resolves the accuracy degradation and long convergence time problems when pursuing extremely high pruning ratios. It achieves up to 34× pruning rate for ImageNet dataset and 167× pruning rate for MNIST dataset, significantly higher than those reached by the literature work. Under the same number of epochs, the proposed method also achieves faster convergence and higher compression rates. The codes and pruned DNN models are released in the anonymous link bit.ly/2zxdlss. Deep neural networks (DNNs) have achieved human-level performance in many application domains such as image classification BID17 , object recognition BID18 BID9 , natural language processing , etc. At the same time, the networks are growing deeper and bigger for higher classification/recognition performance (i.e., accuracy) BID25 . However, the very large DNN model size increases the computation time of the inference phase. To make matters worse, the large model size hinders DNN' deployments on edge computing, which provides the ubiquitous application scenarios of DNNs besides cloud computing applications.As a result, extensive research efforts have been devoted to DNN model compression, in which DNN weight pruning is a representative technique. BID7 is the first work to present the DNN weight pruning method, which prunes the weights with small magnitudes and retrains the network model, heuristically and iteratively. After that, more sophisticated heuristics have been proposed for DNN weight pruning, e.g., incorporating both weight pruning and growing BID6 , L 1 regularization BID27 , and genetic algorithms BID3 . Other improvement directions of weight pruning include trading-off between accuracy and compression rate, e.g., energy-aware pruning BID29 , incorporating regularity, e.g., channel pruning BID10 , and structured sparsity learning BID27 .While the weight pruning technique explores the redundancy in the number of weights of a network model, there are other sources of redundancy in a DNN model. For example , the weight quantization BID19 BID22 BID34 BID20 BID23 BID13 BID1 and clustering BID8 techniques explore the redundancy in the number of bits for weight representation. The activation pruning technique BID15 BID24 leverages the redundancy in the intermediate results. While our work focuses on weight pruning as the major DNN model compression technique, it is orthogonal to the other model compression techniques and might be integrated under a single ADMM-based framework for achieving more compact network models.The majority of prior work on DNN weight pruning take heuristic approaches to reduce the number of weights as much as possible, while preserving the expressive power of the DNN model. Then one may ask , how can we push for the utmost sparsity of the DNN model without hurting accuracy? and what is the maximum compression rate we can achieve by weight pruning? Towards this end , BID32 took a tentative step by proposing an optimization-based approach that leverages ADMM (Alternating Direction Method of Multipliers), a powerful technique to deal with nonconvex optimization problems with potentially combinatorial constraints. This direct ADMM-based weight pruning technique can be perceived as a smart DNN regularization where the regularization target is dynamically changed in each ADMM iteration. As a result it achieves higher compression (pruning) rate than heuristic methods.Inspired by BID32 , in this paper we propose a progressive weight pruning approach that incorporates both an ADMM-based algorithm and masked retraining, and takes a progressive means targeting at extremely high compression (pruning) rates with negligible accuracy loss. The contributions of this work are summarized as follows:• We make a key observation that when pursuing extremely high compression rates (say 150× for LeNet-5 or 30× for AlexNet), the direct ADMM-based weight pruning approach BID32 cannot produce exactly sparse models upon convergence, in that many weights to be pruned are close to zero but not exactly zero. Certain accuracy degradation will result from this phenomenon if we simply set these weights to zero.• We propose and implement the progressive weight pruning paradigm that reaches an extremely high compression rate through multiple partial prunings with progressive pruning rates. This progressive approach, motivated by dynamic programming, helps to mitigate the long convergence time by direct ADMM pruning.• Extensive experiments are performed by comparing with many state-of-the-art weight pruning approaches and the highest compression rates in the literature are achieved by our progressive weight pruning framework, while the loss of accuracy is kept negligible. Our method achieves up to 34× pruning rate for the ImageNet data set and 167× pruning rate for the MNIST data set, with virtually no accuracy loss. Under the same number of epochs, the proposed method achieves notably better convergence and higher compression rates than prior iterative pruning and direct ADMM pruning methods.We provide codes (both Caffe and TensorFlow versions) and pruned DNN models (both for the ImageNet and MNIST data sets) in the link: bit.ly/2zxdlss. For other types of DNN models, we have tested the proposed method on the facial recognition application on two representative DNN models BID16 BID12 . We demonstrate over 10× weight pruning rate with 0.2% and 0.4% accuracy loss, respectively, compared with the original DNN models.In summary, the experimental results demonstrate that our framework applies to a broad set of representative DNN models and consistently outperforms the prior work. It also applies to the DNN models that consist of mainly convolutional layers, which are different with weight pruning using prior methods. These promising results will significantly contribute to the energy-efficient implementation of DNNs in mobile and embedded systems, and on various hardware platforms.Finally, some recent work have focused on the simultaneous weight pruning and weight quantization, as both will contribute to the model storage compression of DNNs. Weight pruning and quantization can be unified under the ADMM framework, and we demonstrate the comparison results in TAB8 using the LeNet-5 model as illustrative example. As can be observed in the table, we can simultaneously achieve 167× weight reduction and use 2-bit for fully-connected layer weight quantization and 3-bit for convolutional layer weight quantization. The overall accuracy is 99.0%. When we focus on the weight data storage, the compression rate is unprecendented 1,910× compared with the original DNN model with floating point representation. When indices (required in weight pruning) are accounted for, the overall compression rate is 623×, which is still much higher than the prior work. It is interesting to observe that the amount of storage for indices is even higher than that for actual weight data. This work proposes a progressive weight pruning approach based on ADMM, a powerful technique to deal with non-convex optimization problems with potentially combinatorial constraints. Motivated by dynamic programming, the proposed method reaches extremely high pruning rates by using partial prunings, with moderate pruning rates in each partial pruning step. Therefore, it resolves the accuracy degradation and long convergence time problems when pursuing extremely high pruning ratios. It achieves up to 34× pruning rate for the ImageNet data set and 167× pruning rate for the MNIST data set, significantly higher than those reached by work in the existing literature. Under the same number of epochs, the proposed method also achieves better convergence and higher compression rates.","Deep neural networks DNNs although achieving human-level performance many domains have very large model size hinders broader applications edge computing devices. Extensive research work have been conducted DNN model compression pruning. However previous work took heuristic approaches. work proposes progressive weight pruning approach based ADMM Alternating Direction Method Multipliers powerful technique deal non-convex optimization problems potentially combinatorial constraints. Motivated dynamic programming proposed method reaches extremely high pruning rate using partial prunings moderate pruning rates. Therefore resolves accuracy degradation long convergence time problems when pursuing extremely high pruning ratios. achieves 34× pruning rate ImageNet dataset 167× pruning rate MNIST dataset significantly higher reached literature work. number epochs proposed method also achieves faster convergence higher compression rates. codes pruned DNN models are released anonymous link bit.ly/2zxdlss. Deep neural networks DNNs have achieved human-level performance many application domains image classification BID17 object recognition BID18 BID9 natural language processing etc. time networks are growing deeper bigger higher classification/recognition performance.e accuracy BID25. However have very large DNN model size increases computation time inference phase. make matters worse have very large model size hinders DNN' deployments edge computing which provides ubiquitous application scenarios DNNs besides cloud computing applications.As result extensive research efforts have been devoted DNN model compression which DNN weight pruning is a representative technique. BID7 is the first work present DNN weight pruning method which prunes weights small magnitudes retrains network model heuristically iteratively. sophisticated heuristics have been proposed DNN weight pruning e.g incorporating weight pruning growing BID6 L 1 regularization BID27 genetic algorithms BID3. improvement directions weight pruning include trading-off accuracy compression rate e.g energy-aware pruning BID29 incorporating regularity e.g channel pruning BID10 structured sparsity learning BID27.While weight pruning technique explores redundancy number weights network model are other sources redundancy DNN model. example weight quantization BID19 BID22 BID34 BID20 BID23 BID13 BID1 clustering BID8 techniques explore redundancy number bits weight representation. activation pruning technique BID15 BID24 leverages redundancy intermediate results. work focuses weight pruning major DNN model compression technique is orthogonal model compression techniques might integrated single ADMM-based framework achieving compact network models.The majority prior work DNN weight pruning take heuristic approaches reduce number weights much possible preserving expressive power DNN model. one may ask how can we push utmost sparsity DNN model without hurting accuracy? what is the maximum compression rate can achieve weight pruning? Towards end BID32 took tentative step proposing optimization-based approach leverages ADMM Alternating Direction Method Multipliers powerful technique deal nonconvex optimization problems potentially combinatorial constraints. direct ADMM-based weight pruning technique can be perceived smart DNN regularization where the regularization target is dynamically changed ADMM iteration. result achieves higher compression pruning rate heuristic methods.Inspired BID32 paper propose progressive weight pruning approach incorporates ADMM-based algorithm masked retraining takes progressive means targeting extremely high compression pruning rates negligible accuracy loss. contributions work are summarized follows:• make key observation when pursuing extremely high compression rates say 150× LeNet-5 30× AlexNet direct ADMM-based weight pruning approach BID32 cannot produce exactly sparse models upon convergence many weights pruned are close zero exactly zero. Certain accuracy degradation will result phenomenon if we simply set weights zero.• propose implement progressive weight pruning paradigm reaches extremely high compression rate multiple partial prunings progressive pruning rates. progressive approach motivated dynamic programming helps mitigate long convergence time direct ADMM pruning.• Extensive experiments are performed comparing many state-of-the-art weight pruning approaches highest compression rates literature are achieved progressive weight pruning framework loss accuracy is kept negligible. method achieves 34× pruning rate ImageNet data set 167× pruning rate MNIST data set virtually accuracy loss. number epochs proposed method achieves notably better convergence higher compression rates prior iterative pruning direct ADMM pruning methods.We provide codes Caffe TensorFlow versions pruned DNN models ImageNet MNIST data sets link:bit.ly/2zxdlss. types DNN models have tested proposed method facial recognition application two representative DNN models BID16 BID12. demonstrate 10× weight pruning rate 0.2 0.4 accuracy loss respectively compared original DNN models.In summary experimental results demonstrate framework applies broad set representative DNN models consistently outperforms prior work. also applies DNN models consist mainly convolutional layers which are different weight pruning using prior methods. promising results will significantly contribute energy-efficient implementation DNNs mobile embedded systems various hardware platforms.Finally recent work have focused simultaneous weight pruning weight quantization will contribute model storage compression DNNs. Weight pruning quantization can be unified ADMM framework demonstrate comparison results TAB8 using LeNet-5 model illustrative example. can be observed table can simultaneously achieve 167× weight reduction use 2-bit fully-connected layer weight quantization 3-bit convolutional layer weight quantization. overall accuracy is 99.0%. When we focus weight data storage compression rate is unprecendented 1,910× compared original DNN model floating point representation. When indices required weight pruning are accounted overall compression rate is 623× which is still much higher prior work. is interesting observe amount storage indices is even higher actual weight data. work proposes progressive weight pruning approach based ADMM powerful technique deal non-convex optimization problems potentially combinatorial constraints. Motivated dynamic programming proposed method reaches extremely high pruning rates using partial prunings moderate pruning rates partial pruning step. Therefore resolves accuracy degradation long convergence time problems when pursuing extremely high pruning ratios. achieves 34× pruning rate ImageNet data set 167× pruning rate MNIST data set significantly higher reached work existing literature. number epochs proposed method also achieves better convergence higher compression rates.",1600,1151,449,0.016,1.39,2025/11/05 17:18:58,0.01,1.413,0.1869158878504667,467.291
"In this paper, we present a new deep learning architecture for addressing the problem of supervised learning with sparse and irregularly sampled multivariate time series. The architecture is based on the use of a semi-parametric interpolation network followed by the application of a prediction network. The interpolation network allows for information to be shared across multiple dimensions of a multivariate time series during the interpolation stage, while any standard deep learning model can be used for the prediction network. This work is motivated by the analysis of physiological time series data in electronic health records, which are sparse, irregularly sampled, and multivariate. We investigate the performance of this architecture on both classification and regression tasks, showing that our approach outperforms a range of baseline and recently proposed models.
 Over the last several years, there has been significant progress in developing specialized models and architectures that can accommodate sparse and irregularly sampled time series as input BID25 BID20 BID21 BID12 BID4 ). An irregularly sampled time series is a sequence of samples with irregular intervals between their observation times. Irregularly sampled data are considered to be sparse when the intervals between successive observations are often large. Of particular interest in the supervised learning setting are methods that perform end-to-end learning directly using multivariate sparse and irregularly sampled time series as input without the need for a separate interpolation or imputation step.In this work, we present a new model architecture for supervised learning with multivariate sparse and irregularly sampled data: Interpolation-Prediction Networks. The architecture is based on the use of several semi-parametric interpolation layers organized into an interpolation network, followed by the application of a prediction network that can leverage any standard deep learning model. In this work, we use GRU networks BID6 as the prediction network.The interpolation network allows for information contained in each input time series to contribute to the interpolation of all other time series in the model. The parameters of the interpolation and prediction networks are learned end-to-end via a composite objective function consisting of supervised and unsupervised components. The interpolation network serves the same purpose as the multivariate Gaussian process used in the work of BID12 , but remove the restrictions associated with the need for a positive definite covariance matrix.Our approach also allows us to compute an explicit multi-timescale representation of the input time series, which we use to isolate information about transients (short duration events) from broader trends. Similar to the work of BID21 and BID4 , our architecture also explicitly leverages a separate information channel related to patterns of observation times. However, our representation uses a semi-parametric intensity function representation of this information that is more closely related to the work of Lasko (2014) on modeling medical event point processes.Our architecture thus produces three output time series for each input time series: a smooth interpolation modeling broad trends in the input, a short time-scale interpolation modeling transients, and an intensity function modeling local observation frequencies.This work is motivated by problems in the analysis of electronic health records (EHRs) BID25 BID21 BID12 BID4 ). It remains rare for hospital systems to capture dense physiological data streams. Instead, it is common for the physiological time series data in electronic health records to be both sparse and irregularly sampled. The additional issue of the lack of alignment in the observation times across physiological variables is also very common.We evaluate the proposed architecture on two datasets for both classification and regression tasks. Our approach outperforms a variety of simple baseline models as well as the basic and advanced GRU models introduced by BID4 across several metrics. We also compare our model with to the Gaussian process adapter BID19 and multi-task Gaussian process RNN classifier BID12 . Further, we perform full ablation testing of the information channels our architecture can produce to assess their impact on classification and regression performance. In this paper, we have presented a new framework for dealing with the problem of supervised learning in the presence of sparse and irregularly sampled time series. The proposed framework is fully modular. It uses an interpolation network to accommodate the complexity that results from using sparse and irregularly sampled data as supervised learning inputs, followed by the application of a prediction network that operates over the regularly spaced and fully observed, multi-channel output provided by the interpolation network. The proposed approach also addresses some difficulties with prior approaches including the complexity of the Gaussian process interpolation layers used in BID19 BID12 , and the lack of modularity in the approach of BID4 . Our framework also introduces novel elements including the use of semi-parametric, feed-forward interpolation layers, and the decomposition of an irregularly sampled input time series into multi-ple distinct information channels. Our results show statistically significant improvements for both classification and regression tasks over a range of baseline and state-of-the-art methods.Ruslan This data set contains sparse and irregularly sampled physiological signals, medications, diagnostic codes, inhospital mortality, length of stay and more. We focus on predicting in-hospital mortality and length of stay using the first 48 hours of data. We extracted 12 standard physiological variables from each of the 53,211 records obtained after removing hospital admission records with length of stay less than 48 hours. TAB2 shows the features, sampling rates (per hour) and their missingness information computed using the union of all time stamps that exist in any dimension of the input time series. In our experiments, each admission record corresponds to one data case (s n , y n ). Each data case n consists of a sparse and irregularly sampled time series s n with D = 12 dimensions. Each dimension d of s n corresponds to one of the 12 vital sign time series mentioned above. In the case of classification, y n is a binary indicator where y n = 1 indicates that the patient died at any point within the hospital stay following the first 48 hours and y n = 0 indicates that the patient was discharged at any point after the first 48 hours. There are 4310 (8.1%) patients with a y n = 1 mortality label. The complete data set is D = {(s n , y n )|n = 1, ..., N }, and there are N = 53, 211 data cases. The goal in the classification task is to learn a classification function g of the form y n ← g(s n ) whereŷ n is a discrete value.In the case of regression, y n is a real-valued regression target corresponding to the length of stay. Since the data set includes some very long stay durations, we let y n represent the log of the length of stay in days for all models. We convert back from the log number of days to the number of days when reporting results. The complete data set is again D = {(s n , y n )|n = 1, ..., N } with N = 53, 211 data cases (we again require 48 hours worth of data). The goal in the regression task is to learn a regression function g of the formŷ n ← g(s n ) whereŷ n is a continuous value.","paper present new deep learning architecture addressing problem supervised learning sparse irregularly sampled multivariate time series. architecture is based use semi-parametric interpolation network followed application prediction network. interpolation network allows information shared across multiple dimensions multivariate time series interpolation stage standard deep learning model can be used prediction network. work is motivated analysis physiological time series data electronic health records which are sparse irregularly sampled multivariate. investigate performance architecture classification regression tasks showing approach outperforms range baseline recently proposed models. last several years has been significant progress developing specialized models architectures can accommodate sparse irregularly sampled time series input BID25 BID20 BID21 BID12 BID4 irregularly sampled time series is a sequence samples irregular intervals observation times. Irregularly sampled data are considered sparse when the intervals successive observations are often large. particular interest supervised learning setting are methods perform end-to-end learning directly using multivariate sparse irregularly sampled time series input without need separate interpolation imputation step.In work present new model architecture supervised learning multivariate sparse irregularly sampled data:Interpolation-Prediction Networks. architecture is based use several semi-parametric interpolation layers organized interpolation network followed application prediction network can leverage standard deep learning model. work which we use GRU networks BID6 prediction network.The interpolation network allows information contained input time series contribute interpolation time series model. parameters interpolation prediction networks are learned end-to-end via composite objective function consisting supervised unsupervised components. interpolation network serves purpose multivariate Gaussian process used work BID12 remove restrictions associated need positive definite covariance matrix.Our approach also allowsus compute explicit multi-timescale representation input time series which we use isolate information transients short duration events broader trends. Similar work BID21 BID4 architecture also explicitly leverages separate information channel related patterns observation times. However representation uses semi-parametric intensity function representation information is more closely related work Lasko 2014 modeling medical event point processes.Our architecture thus produces three output time series input time series:smooth interpolation modeling broad trends input short time-scale interpolation modeling transients intensity function modeling local observation frequencies.This work is motivated problems analysis electronic health records EHRs BID25 BID21 BID12 BID4 remains rare hospital systems capture dense physiological data streams. Instead is common physiological time series data electronic health records sparse irregularly sampled. additional issue lack alignment observation times across physiological variables is also common.We evaluate proposed architecture two datasets classification regression tasks. approach outperforms variety simple baseline models well basic advanced GRU models introduced BID4 across several metrics. also compare model Gaussian process adapter BID19 multi-task Gaussian process RNN classifier BID12. perform full ablation testing information channels architecture can produce assess impact classification regression performance. paper have presented new framework dealing problem supervised learning presence sparse irregularly sampled time series. proposed framework is fully modular. uses interpolation network accommodate complexity results using sparse irregularly sampled data supervised learning inputs followed application prediction network operates regularly spaced fully observed multi-channel output provided interpolation network. proposed approach also addresses difficulties prior approaches including complexity Gaussian process interpolation layers used BID19 BID12 lack modularity approach BID4. framework also introduces novel elements including use semi-parametric feed-forward interpolation layers decomposition irregularly sampled input time series multi-ple distinct information channels. results show statistically significant improvements classification regression tasks range baseline state-of-the-art methods.Ruslan data set contains sparse irregularly sampled physiological signals medications diagnostic codes inhospital mortality length stay more. focus predicting in-hospital mortality length stay using first 48 hours data. extracted 12 standard physiological variables 53,211 records obtained removing hospital admission records length stay less 48 hours. TAB2 shows features sampling rates per hour missingness information computed using union time stamps exist dimension input time series. experiments admission record corresponds one data case n n data case n consists sparse irregularly sampled time series n 12 dimensions. dimension n corresponds one 12 vital sign time series mentioned above. case classification n is a binary indicator whereyn 1 indicates patient died point within hospital stay following first 48 hours n 0 indicates patient was discharged point first 48 hours. are 4310 8.1 patients n 1 mortality label. complete data set is D ={is againD= n n |n 1... N are N 53 211 data cases. goal classification task is to learn classification functiong form n←g n whereŷn is a discrete value.In case regression n is a real-valued regression target corresponding length stay. Since data set includes long stay durations let n represent log length stay days models. convert back log number days number days when reporting results. complete data set is D ={is againD= n n |n 1... N N 53 211 data cases require 48 hours worth data goal regression task is to learn regression functiong formŷn←g n whereŷn is a continuous value.",1415,957,458,0.015,1.479,2025/11/05 17:18:58,0.01,1.594,0.4641744548286605,454.214
"We introduce an analytic distance function for moderately sized point sets of known cardinality that is shown to have very desirable properties, both as a loss function as well as a regularizer for machine learning applications. We compare our novel construction to other point set distance functions and show proof of concept experiments for training neural networks end-to-end on point set prediction tasks such as object detection. Parametric machine learning models, like artificial neural networks, are routinely trained by empirical risk minimization. If we aim to predict an output y ∈ Y from an input x ∈ X , we collect a training set D of (x, y) pairs and train a parametrized prediction function h θ : X → Y by minimizing DISPLAYFORM0 Here, L : Y × Y → R is a loss function that assigns a scalar loss value to the predictionŷ = h θ (x) for the true value y. Classical machine learning problems allow for standard choices for the loss function. E.g., for regression problems, where y,ŷ ∈ R, it is common to use the squared loss L(ŷ, y) = (ŷ − y) 2 .Assume , however, that we want to train a machine learning system which-given some inputpredicts a set of points. In particular , the ordering of the points is neither semantically meaningful nor in any way consistent across data instances. As an example , one may consider an object detection task such as finding the positions of the black stones on an image of a real-world game of Nine Men's Morris. What should the loss function be in such a case?Naively, we might just impose an arbitrary ordering to the sets and treat them as ordered tuples. However, this conceals an important property of the task, the permutation invariance, from our machine learning system. This property might in fact be crucial to learn such a task efficiently. Instead, we would like our loss function to define a meaningful distance between two sets, which requires such a loss to be permutation-invariant. We discussed a novel point set loss function, which is analytic everywhere, vis-a-vis two other simple alternatives with matching computational complexity for point set prediction tasks as alternatives to more involved approaches BID3 BID2 . Proof of concept experiments showed that end-to-end training with such simple loss functions is a viable approach for point set prediction tasks, such as object detection. We expect that simple constructions such as the ""holographic"" point set distance introduced here may turn out useful not only for point set predictions, but also as a regularizer, for example to encourage (unsupervised) clustering to align its clusters with the clusters found by an earlier version of the model. We will need the following Lemma, which states that the roots of a complex polynomial continuously depend on its coefficients. DISPLAYFORM0 k=0 c k u k be a monic complex polynomial and factor it as F (u) = (u − a 1 )(u − a 2 ) · · · (u − a N ) with a k ∈ C some ordering of the roots. Then, for every ε > 0 there exists δ > 0 such that every polynomial DISPLAYFORM1 Proof. This is a reformulation of the well-known continuity result, a proof of which can be found, for example, inĆurgus & Mascioni (2006) . One notes that, to first order in a small shift in the coefficients of a polynomial, the shift of the zeros can be found by a single step of Newton-Raphson iteration, except at higher-degree zeros (where the derivative of the polynomial in the denominator also has a zero).We can now prove the Proposition. DISPLAYFORM2 We already observed that L(Ẑ, Z) 2 = 0 if and only ifẐ = σ(Z) for some σ ∈ S N . Now assume L(Ẑ , Z) 2 = 0. To see thatẐ can not be a local minimum, we need to show that for any ε > 0 there DISPLAYFORM3 To construct such a Z , we define the polynomial Q λ : C → C, DISPLAYFORM4 which linearly interpolates between PẐ and P Z . Note that Q λ is monic for λ ∈ [0, 1] and Q 0 = PẐ. Let Z λ be some ordering of the roots of Q λ . Then DISPLAYFORM5 Since we assumed L(Ẑ, Z) > 0, this means that L(Z λ , Z) < L(Ẑ, Z) for any λ > 0. It remains to show that for any ε > 0 there is λ ε > 0 and a permutation σ such that d(Ẑ, σ(Z λε )) < ε. However, since the coefficients of Q λ continuously depend on λ, this follows as a simple consequence of Lemma 1.","introduce analytic distance function moderately sized point sets known cardinality is shown have very desirable properties loss function well regularizer machine learning applications. compare novel construction point set distance functions show proof concept experiments training neural networks end-to-end point set prediction tasks object detection. Parametric machine learning models like artificial neural networks are routinely trained empirical risk minimization. If we aim predict output ∈ inputx∈X collect training set x pairs train parametrized prediction functionh θ:X→ minimizing DISPLAYFORM0 L:× →R is a loss function assigns scalar loss value predictionŷ hθ x true value y. Classical machine learning problems allow standard choices loss function. E.g regression problems wherey,ŷ∈R is common use squared lossL ŷ wherey,ŷ− 2.Assume however want train machine learning system which-given inputpredicts set points. particular ordering points is neither semantically meaningful way consistent across data instances. example one may consider object detection task finding positions black stones image real-world game Nine Men's Morris. What should the loss function case? Naively might impose arbitrary ordering sets treat ordered tuples. However conceals important property task permutation invariance machine learning system. property might fact crucial learn task efficiently. Instead would like loss function define meaningful distance two sets which requires loss permutation-invariant discussed novel point set loss function which is analytic everywhere vis-a-vis two simple alternatives matching computational complexity point set prediction tasks alternatives involved approaches BID3 BID2. Proof concept experiments showed end-to-end training simple loss functions is a viable approach point set prediction tasks object detection. expect simple constructions holographic point set distance introduced may turn useful point set predictions also regularizer example encourage unsupervised clustering align clusters clusters found earlier version model. will need following Lemma which states roots complex polynomial continuously depend coefficients. DISPLAYFORM0 k=0ck uk monic complex polynomial factor F u u− 1 u− 2 ··· u− N k∈C ordering roots. everyε 0 existsδ 0 every polynomial DISPLAYFORM1 Proof. is a reformulation well-known continuity result proof which can be found example inĆurgus Mascioni 2006 One notes first order small shift coefficients polynomial shift zeros can be found single step Newton-Raphson iteration except higher-degree zeros where the derivative polynomial denominator also has a zero.We can now prove Proposition. DISPLAYFORM2 already observed L Ẑ Z 2 0 if and only ifẐ σ Z σ∈ N. assumeL Ẑ Z 2 0. see thatẐ can not be a local minimum need show ε 0 DISPLAYFORM3 construct Z define polynomialQλ:C→C DISPLAYFORM4 which linearly interpolates PẐ PZ. Note Qλ is monic λ∈ 0 1 Q0 PẐ. LetZλ ordering roots Qλ. DISPLAYFORM5 Since assumedL Ẑ Z 0 means L Zλ Z L Ẑ Z λ 0. remains show ε 0 isλε 0 permutationσ Ẑ σ Zλε ε. However since coefficients Q λ continuously depend λ follows simple consequence Lemma1.",998,638,360,0.01,1.564,2025/11/05 17:18:58,0.01,1.84,0.7289719626168225,313.273
"We introduce a hierarchical model for efficient placement of computational graphs onto hardware devices, especially in heterogeneous environments with a mixture of CPUs, GPUs, and other computational devices. Our method learns to assign graph operations to groups and to allocate those groups to available devices. The grouping and device allocations are learned jointly. The proposed method is trained with policy gradient and requires no human intervention. Experiments with widely-used
 computer vision and natural language models show that our algorithm can find optimized, non-trivial placements for TensorFlow computational graphs with over 80,000 operations. In addition, our approach outperforms placements by human
 experts as well as a previous state-of-the-art placement method based on deep reinforcement learning. Our method achieves runtime reductions of up to 60.6% per training step when applied to models such as Neural Machine Translation. Deep neural networks have been successfully applied to many practical problems, such as image classification BID20 BID19 BID32 BID29 , speech recognition BID9 , and machine translation BID28 BID1 BID36 . These successes have lead to a surge in demand for the computational resources needed to train and infer with neural networks. A common approach to addressing this demand is to use a distributed environment with a combination of CPUs and GPUs. In this environment, it is typical for a machine learning practitioner to explicitly place the operations of their neural network onto particular computing devices for model parallelism and data parallelism. For example, one might distribute the computation of the first layer in a translation network onto the first GPU and the computation of the second layer onto the second GPU BID28 BID36 . Although these decisions can be made by a human practitioner, such an approach does not scale well or produce optimal results, especially in the case of more complicated networks BID31 a) . Given the growing diversity of hardware devices (e.g., Google TPUs, Intel Nervana, etc.) and recent trends toward automated neural architecture search BID38 BID27 BID2 , where new models are generated, trained and evaluated in an entirely end-to-end fashion, it seems natural to move toward more automated solutions for efficiently distributing computation.Device placement can be framed as the problem of learning to partition a graph across available devices. Given that graph partitioning is a well-studied subject in computer science BID8 BID16 BID26 , traditional graph partitioning methods represent a natural baseline for automated device placement. We ran experiments using Scotch BID26 , a well-established open source library for graph partitioning, which includes optimizations such as k-way Fiduccia-Mattheyses BID8 , Multilevel methods BID3 BID11 BID15 , the Band Method BID5 , the Diffusion Method BID23 , and Dual Recursive Bipartitioning Mapping BID25 . The objective was to balance the computational load across a set of connected processing nodes, while colocating neighboring nodes to minimize communication cost. Despite its promise, this approach yielded disappointing results, likely due to the non-stationarity of the cost function. We target a distributed environment where we use a shared cluster of CPUs and GPUs, and our CPUs may also serve other jobs at the same time. Thus, while cost-based models such as BID21 provide a strong baseline for memory optimizations, since memory usage is deterministic, they cannot be directly applied to environments with dynamic costs.Using deep networks and reinforcement learning for combinatorial optimization has already been proposed BID33 BID4 BID22 . Recent work BID22 ) uses a recurrent neural network (RNN) policy network to predict the placement of operations in a computational graph, optimizing for speed of computation using policy gradient methods. While this approach outperforms traditional graph partitioning heuristics and human expert placements, it is prohibitively expensive for the RNN policy to learn when the number of operations is large. This method is therefore limited to small graphs (with fewer than 1000 nodes) and requires human experts to manually partition the graph into collocation groups as a pre-processing step in order to scale to larger graphs. We refer to the method in BID22 as ColocRL.In this paper, we propose a more flexible approach which learns to optimize device placement for training neural networks that have tens of thousands of operations with no need for manual grouping. Our method consists of a two-level hierarchical network, in which the first model groups the operations of the graph (the Grouper) and the second model places those groups onto devices (the Placer). The Grouper is a feed forward network which reads in information about each operation and its context within the graph, in order to predict the group to which that operation should be assigned. The Placer is a sequence-to-sequence model BID28 that reads in the embedding of the group and predicts the device placement for that group. The entire two-level network is trained jointly using reinforcement learning to optimize for speed of computation and for feasibility (e.g., having sufficient memory available on each device for the computation assigned). Unlike the previous work, our method is end-to-end and does not require human experts to manually group operations as a pre-processing step, making it a fully automated solution to optimizing device placement.Our main result is that our model effectively handles very large graphs and finds non-trivial placements on multiple devices for models such as Inception-V3 BID31 , ResNet BID10 , Language Modeling BID14 , and Neural Machine Translation BID36 . The placements found by our model outperform TensorFlow's default placements BID0 , the Scotch algorithm's placements, and human expert placements, as well as those of ColocRL BID22 ). Our results demonstrate that the proposed approach learns the properties of the environment, including the complex tradeoff between computation and communication in hardware. For example, on a Neural Machine Translation model, our method achieves a 60.6% reduction in training time per iteration. In this paper, we present a hierarchical method for efficiently placing the operations of a computational graph onto devices. Our approach consists of a hierarchical model that first assigns the operations to groups and then places those groups onto devices. We use a policy gradient method to optimize the parameters of the planner. The proposed method enables us to scale to computational graphs containing over 80,000 operations. Unlike previous work, our method is end-to-end and requires no manual effort. On a range of tasks including image classification, language modeling, and machine translation, our method surpasses placements designed by human experts as well as those of previous state-of-the-art deep RL methods. Our approach finds highly granular parallelism within the graph, enabling us to outperform prior methods by up to 60.6%.","introduce hierarchical model efficient placement computational graphs onto hardware devices especially heterogeneous environments mixture CPUs GPUs computational devices. method learns assign graph operations groups allocate groups available devices. grouping device allocations are learned jointly. proposed method is trained policy gradient requires human intervention. Experiments widely-used computer vision natural language models show algorithm can find optimized non-trivial placements TensorFlow computational graphs 80,000 operations. addition approach outperforms placements human experts well previous state-of-the-art placement method based deep reinforcement learning. method achieves runtime reductions 60.6 per training step when applied models Neural Machine Translation. Deep neural networks have been successfully applied many practical problems image classification BID20 BID19 BID32 BID29 speech recognition BID9 machine translation BID28 BID1 BID36. successes have lead surge demand computational resources needed train infer neural networks. common approach addressing demand is to use distributed environment combination CPUs GPUs. environment is typical machine learning practitioner explicitly place operations neural network onto particular computing devices model parallelism data parallelism. example one might distribute computation first layer translation network onto first GPU computation second layer onto second GPU BID28 BID36. Although decisions can be made human practitioner approach does not scale well produce optimal results especially case complicated networks BID31 Given growing diversity hardware devices e.g Google TPUs Intel Nervana etc. recent trends toward automated neural architecture search BID38 BID27 BID2 where new models are generated trained evaluated entirely end-to-end fashion seems natural move toward automated solutions efficiently distributing computation.Device placement can be framed problem learning partition graph across available devices. Given graph partitioning is a well-studied subject computer science BID8 BID16 BID26 traditional graph partitioning methods represent natural baseline automated device placement. ran experiments using Scotch BID26 well-established open source library graph partitioning which includes optimizations k-way Fiduccia-Mattheyses BID8 Multilevel methods BID3 BID11 BID15 Band Method BID5 Diffusion Method BID23 Dual Recursive Bipartitioning Mapping BID25. objective was to balance computational load across set connected processing nodes colocating neighboring nodes minimize communication cost. Despite promise approach yielded disappointing results likely due non-stationarity cost function. target distributed environment where we use shared cluster CPUs GPUs CPUs may also serve jobs time. Thus cost-based models BID21 provide strong baseline memory optimizations since memory usage is deterministic cannot directly applied environments dynamic costs.Using deep networks reinforcement learning combinatorial optimization has already proposed BID33 BID4 BID22. Recent work BID22 uses recurrent neural network RNN policy network predict placement operations computational graph optimizing speed computation using policy gradient methods. approach outperforms traditional graph partitioning heuristics human expert placements is prohibitively expensive RNN policy learn when the number operations is large. method is therefore limited small graphs fewer 1000 nodes requires human experts manually partition graph collocation groups pre-processing step order scale larger graphs. refer method BID22 ColocRL.In paper propose flexible approach which learns optimize device placement training neural networks have tens thousands operations need manual grouping. method consists two-level hierarchical network which the first model groups operations graph Grouper second model places groups onto devices Placer Grouper is a feed forward network which reads information operation context within graph order predict group which that operation should be assigned. Placer is a sequence-to-sequence model BID28 reads embedding group predicts device placement group. entire two-level network is trained jointly using reinforcement learning optimize speed computation feasibility e.g sufficient memory available device computation assigned Unlike previous work method is end-to-end does not require human experts manually group operations pre-processing step making fully automated solution optimizing device placement.Our main result is that our model effectively handles large graphs finds non-trivial placements multiple devices models Inception-V3 BID31 ResNet BID10 Language Modeling BID14 Neural Machine Translation BID36. placements found model outperform TensorFlow's default placements BID0 Scotch algorithm's placements human expert placements well ColocRL BID22 results demonstrate proposed approach learns properties environment including complex tradeoff computation communication hardware. example Neural Machine Translation model method achieves 60.6 reduction training time per iteration. paper present hierarchical method efficiently placing operations computational graph onto devices. approach consists hierarchical model first assigns operations groups places groups onto devices. use policy gradient method optimize parameters planner. proposed method enablesus scale computational graphs containing 80,000 operations. Unlike previous work method is end-to-end requires manual effort. range tasks including image classification language modeling machine translation method surpasses placements designed human experts well previous state-of-the-art deepRL methods. approach finds highly granular parallelism within graph enablingus outperform prior methods 60.6",1316,904,412,0.014,1.456,2025/11/05 17:18:58,0.01,1.5,0.392523364485981,415.686
"Motion is an important signal for agents in dynamic environments, but learning to represent motion from unlabeled video is a difficult and underconstrained problem. We propose a model of motion based on elementary group properties of transformations and use it to train a representation of image motion. While most methods of estimating motion are based on pixel-level constraints, we use these group properties to constrain the abstract representation of motion itself. We demonstrate that a deep neural network trained using this method captures motion in both synthetic 2D sequences and real-world sequences of vehicle motion, without requiring any labels. Networks trained to respect these constraints implicitly identify the image characteristic of motion in different sequence types. In the context of vehicle motion, this method extracts information useful for localization, tracking, and odometry. Our results demonstrate that this representation is useful for learning motion in the general setting where explicit labels are difficult to obtain. Motion perception is a key component of biological and computer vision. By understanding how a stream of images reflects the motion of the world around it, an agent can better judge how to act. For example, a fly can use visual motion cues to dodge an approaching hand and to distinguish this threat from a looming landing surface BID21 ). Motion is an important cue for understanding actions and predicting 3D scene structure, and it has been extensively studied from computational, ethological, and biological perspectives BID10 ).In computer vision, the problem of motion representation has typically been approached from either a local or global perspective. Local representations of motion are exemplified by optical flow. Flow represents image motion as the 2D displacement of individual pixels of an image, giving rich low-level detail while foregoing a compact representation of the underlying scene motion. In contrast , global representations such as those used in visual odometry attempt to compactly explain the movement of the whole scene. Such representations typically rely on a rigid world assumption, thus limiting their applicability to more general settings.Image transformations due to motion form a subspace of all continuous image transformations. Smooth changes in the motion subspace correspond to sequences of images with realistic motion. We wish to characterize this subspace. The motion subspace differs from other image transformation subspaces, such as changes in the space of images of human faces. Smooth changes in this space also form a subspace of image transformations, but one containing transformations that do not occur in natural image sequences, such as the face of one person transforming into the face of another. A representation that characterizes motion should be sensitive to the distinction between image transformations that are realistic (produced by image motion) vs. those that are unrealistic (not produced by image motion).To be useful for understanding and acting on scene motion, a representation should capture the motion of the observer and all relevant scene content. Supervised training of such a representation is challenging: explicit motion labels are difficult to obtain, especially for nonrigid scenes where it can be unclear how the structure and motion of the scene should be decomposed. We propose a framework for learning global, nonrigid motion representations without labels. While most methods of representing motion rely on pixel-level reconstruction or correspondence to guide learning, our method constrains the representation itself by directly addressing the properties of the latent motion space.Motion has several properties that we use to operationalize to what extent a model characterizes it.(1) A model of motion can be read out to estimate metric properties of the motion in the scene, such as the camera translation and rotation. (2) A model of motion should represent the same motion identically regardless of the image content. For example, the motion of an object moving to the right should be represented the same whether the object is a cat or a dog. (3) A model of motion should distinguish sequences produced by natural motion from sequences with image transitions not produced by natural motion, such as cuts.Here, we present a general model of visual motion and describe how the group properties of visual motion can be used to constrain learning in this model (Figure 1) . We enforce the group properties of associativity and invertibility during training using a metric learning approach BID3 ) on recomposed sequences. We describe how this technique can be used to train a deep neural network to represent the motion in image sequences of arbitrary length in a low-dimensional, global fashion. We present evidence that the learned representation captures the global structure of motion in both 2D and 3D settings without labels, hard-coded assumptions about the scene, or explicit feature matching. DISPLAYFORM0 Figure 1: (a) A graphical model describing the relationship between the latent scene structure {S t }, motion {M t }, and the observed images of a sequence. We describe a method for learning a representation M of the motion space M from observed image sequences {I t }. (b) By recomposing sequences of images to satisfy the group properties of associativity and invertibility, we construct pairs of image sequences with equivalent motion. We use these properties to learn an approximate group homomorphism Φ ∈ M between motion in the world and in an embedding. We have presented a new model of motion and a method for learning motion representations. We have shown that enforcing group properties of motion is sufficient to learn a representation of image motion. These results suggest that this representation is able to generalize between scenes with disparate content and motion to learn a motion state representation useful for navigation, prediction, and other behavioral tasks relying on motion. Because of the wide availability of unlabeled video sequences in many settings, we expect our framework to be useful for generating better global motion representations in a variety of real-world tasks.",Motion is an important signal agents dynamic environments learning represent motion unlabeled video is a difficult underconstrained problem. propose model motion based elementary group properties transformations use train representation image motion. methods estimating motion are based pixel-level constraints use group properties constrain abstract representation motion itself. demonstrate deep neural network trained using method captures motion synthetic 2D sequences real-world sequences vehicle motion without requiring labels. Networks trained respect constraints implicitly identify image characteristic motion different sequence types. context vehicle motion method extracts information useful localization tracking odometry. results demonstrate representation is useful learning motion general setting where explicit labels are difficult obtain. Motion perception is a key component biological computer vision. understanding how a stream images reflects motion world around agent can better judge how to act. example fly can use visual motion cues dodge approaching hand distinguish threat looming landing surface BID21 Motion is an important cue understanding actions predicting 3D scene structure has extensively studied computational ethological biological perspectives BID10.In computer vision problem motion representation has typically approached either local global perspective. Local representations motion are exemplified optical flow. Flow represents image motion 2D displacement individual pixels image giving rich low-level detail foregoing compact representation underlying scene motion. contrast global representations used visual odometry attempt compactly explain movement whole scene. representations typically rely rigid world assumption thus limiting applicability general settings.Image transformations due motion form subspace continuous image transformations. Smooth changes motion subspace correspond sequences images realistic motion. wish characterize subspace. motion subspace differs image transformation subspaces changes space images human faces. Smooth changes space also form subspace image transformations one containing transformations do not occur natural image sequences face one person transforming face another. representation characterizes motion should be sensitive distinction image transformations are realistic produced image motion vs. are unrealistic produced image motion.To useful understanding acting scene motion representation should capture motion observer relevant scene content. Supervised training representation is challenging:explicit motion labels are difficult obtain especially nonrigid scenes where it can be unclear how the structure motion scene should be decomposed. propose framework learning global nonrigid motion representations without labels. methods representing motion rely pixel-level reconstruction correspondence guide learning method constrains representation directly addressing properties latent motion space.Motion has several properties use operationalize what extent model characterizes it. 1 model motion can be read estimate metric properties motion scene camera translation rotation. 2 model motion should represent motion identically regardless image content. example motion object moving right should be represented whether object is a cat dog. 3 model motion should distinguish sequences produced natural motion sequences image transitions produced natural motion cuts.Here present general model visual motion describe how the group properties visual motion can be used constrain learning model Figure1 enforce group properties associativity invertibility training using metric learning approach BID3 recomposed sequences. describe how this technique can be used train deep neural network represent motion image sequences arbitrary length low-dimensional global fashion. present evidence learned representation captures global structure motion 2D 3D settings without labels hard-coded assumptions scene explicit feature matching. DISPLAYFORM0 Figure1:graphical model describing relationship latent scene structure motion observed images sequence. describe method learning representation motion space observed image sequences b recomposing sequences images satisfy group properties associativity invertibility construct pairs image sequences equivalent motion. use properties learn approximate group homomorphismΦ ∈ motion world embedding. have presented new model motion method learning motion representations. have shown enforcing group properties motion is sufficient learn representation image motion. results suggest representation is able generalize scenes disparate content motion learn motion state representation useful navigation prediction behavioral tasks relying motion. wide availability unlabeled video sequences many settings expect framework useful generating better global motion representations variety real-world tasks.,1121,715,406,0.014,1.568,2025/11/05 17:18:58,0.01,1.486,0.7414330218068537,380.705
"This paper introduces the concept of continuous convolution to neural networks and deep learning applications in general. Rather than directly using discretized information, input data is first projected into a high-dimensional Reproducing Kernel Hilbert Space (RKHS), where it can be modeled as a continuous function using a series of kernel bases. We then proceed to derive a closed-form solution to the continuous convolution operation between two arbitrary functions operating in different RKHS. Within this framework, convolutional filters also take the form of continuous functions, and the training procedure involves learning the RKHS to which each of these filters is projected, alongside their weight parameters. This results in much more expressive filters, that do not require spatial discretization and benefit from properties such as adaptive support and non-stationarity. Experiments on image classification are performed, using classical datasets, with results indicating that the proposed continuous convolutional neural network is able to achieve competitive accuracy rates with far fewer parameters and a faster convergence rate. In recent years, convolutional neural networks (CNNs) have become widely popular as a deep learning tool for addressing various sorts of problems, most predominantly in computer vision, such as image classification BID22 BID17 , object detection BID30 and semantic segmentation BID8 . The introduction of convolutional filters produces many desirable effects, including: translational invariance, since the same patterns are detected in the entire image; spatial connectivity, as neighboring information is taken into consideration during the convolution process; and shared weights, which results in significantly fewer training parameters and smaller memory footprint.Even though the convolution operation is continuous in nature BID19 , a common assumption in most computational tasks is data discretization, since that is usually how information is obtained and stored: 2D images are divided into pixels, 3D point clouds are divided into voxels, and so forth. Because of that, the exact convolution formulation is often substituted by a discrete approximation BID4 , calculated by sliding the filter over the input data and calculating the dot product of overlapping areas. While much simpler to compute, it requires substantially more computational power, especially for larger datasets and filter sizes BID28 . The fast Fourier transform has been shown to significantly increase performance in convolutional neural network calculations BID18 BID32 , however these improvements are mostly circumstantial, with the added cost of performing such transforms, and do not address memory requirements.To the best of our knowledge, all versions of CNNs currently available in the literature use this discrete approximation to convolution, as a way to simplify calculations at the expense of a potentially more descriptive model. In BID24 a sparse network was used to dramatically decrease computational times by exploiting redundancies, and in BID11 spatial sparseness was exploited to achieve state-of-the-art results in various image classification datasets. Similarly, BID31 used octrees to efficiently partition the space during convolution, thus focusing memory allocation and computation to denser regions. A quantized version was proposed in BID40 to improve performance on mobile devices, with simultaneous computational acceleration and model compression. A lookup-based network is described in BID0 , that encodes convolution as a series of lookups to a dictionary that is trained to cover the observed weight space. This paper takes a different approach and introduces the concept of continuous convolution to neural networks and deep learning applications in general. This is achieved by projecting information into a Reproducing Kernel Hilbert Space (RKHS) BID33 , in which point evaluation takes the form of a continuous linear functional. We employ the Hilbert Maps framework, initially described in BID29 , to reconstruct discrete input data as a continuous function, based on the methodology proposed in BID12 . Within this framework, we derive a closed-form solution to the continuous convolution between two functions that takes place directly in this high-dimensional space, where arbitrarily complex patterns are represented using a series of simple kernels, that can be efficiently convolved to produce a third RKHS modeling activation values. Optimizing this neural network involves learning not only weight parameters, but also the RKHS that defines each convolutional filter, which results is much more descriptive feature maps that can be used for both discriminative and generative tasks. The use of high-dimensional projection, including infinite-layer neural networks BID15 ; BID9 , has been extensively studied in recent times, as a way to combine kernel-based learning with deep learning applications. Note that, while works such as BID26 and BID25 take a similar approach of projecting input data into a RKHS, using the kernel trick, it still relies on discretized image patches, whereas ours operates solely on data already projected to these highdimensional spaces. Also, in these works extra kernel parameters are predetermined and remain fixed during the training process, while ours jointly learns these parameters alongside traditional weight values, thus increasing the degrees of freedom in the resulting feature maps.The proposed technique, entitled Continuous Convolutional Neural Networks (CCNNs), was evaluated in an image classification context, using standard computer vision benchmarks, and achieved competitive accuracy results with substantially smaller network sizes. We also demonstrate its applicability to unsupervised learning, by describing a convolutional auto-encoder that is able to produce latent feature representations in the form of continuous functions, which are then used as initial filters for classification using labeled data. This paper introduced a novel technique for data representation that takes place in a highdimensional Reproducing Kernel Hilbert Space (RKHS), where arbitrarily complex functions can be approximated in a continuous fashion using a series of simple kernels. We show how these kernels can be efficiently convolved to produce approximations of convolution results between two functions in different RKHS, and how this can be applied in an image classification scenario, via the introduction of a novel deep learning architecture entitled Continuous Convolutional Neural Networks (CCNN). Experimental tests using standard benchmark datasets show that this proposed architecture is able to achieve competitive results with much smaller network sizes, by focusing instead on more descriptive individual filters that are used to extract more complex patterns. Although promising, there are still several potential improvements that are left for future work, such as: RKHS sparsification, so only a subset of clusters are used for feature vector calculation, which would greatly improve computational speed and memory requirements; different learning rates and optimization strategies for each class of parameter (cluster location, length-scale and weight), to improve convergence rates; and the use of different kernels for feature vector representation, as a way to encode different properties in the resulting feature maps.",paper introduces concept continuous convolution neural networks deep learning applications general. Rather directly using discretized information input data is first projected high-dimensional Reproducing Kernel Hilbert Space RKHS whereit canbe modeled continuous function using series kernel bases. proceed derive closed-form solution continuous convolution operation two arbitrary functions operating different RKHS. Within framework convolutional filters also take form continuous functions training procedure involves learning RKHS which eachof filters is projected alongside weight parameters. results much expressive filters do not require spatial discretization benefit properties adaptive support non-stationarity Experiments image classification are performed using classical datasets which results indicating proposed continuous convolutional neural network is able achieve competitive accuracy rates far fewer parameters faster convergence rate. recent years convolutional neural networks CNNs have become widely popular deep learning tool addressing various sorts problems predominantly computer vision image classification BID22 BID17 object detection BID30 semantic segmentation BID8. introduction convolutional filters produces many desirable effects including:translational invariance since patterns are detected entire image;spatial connectivity neighboring information is taken consideration convolution process;shared weights which results significantly fewer training parameters smaller memory footprint.Even though convolution operation is continuous nature BID19 common assumption computational tasks is data discretization since is usually how information is obtained stored:2D images are divided pixels 3D point clouds are divided voxels forth. exact convolution formulation is often substituted discrete approximation BID4 calculated sliding filter input data calculating dot product overlapping areas. much simpler compute requires substantially computational power especially larger datasets filter sizes BID28. fast Fourier transform has been shown significantly increase performance convolutional neural network calculations BID18 BID32 however improvements are mostly circumstantial added cost performing transforms do not address memory requirements.To best knowledge versions CNNs currently available literature use discrete approximation convolution way simplify calculations expense potentially descriptive model. BID24 sparse network was used dramatically decrease computational times exploiting redundancies BID11 spatial sparseness was exploited achieve state-of-the-art results various image classification datasets. Similarly BID31 used octrees efficiently partition space convolution thus focusing memory allocation computation denser regions. quantized version was proposed BID40 improve performance mobile devices simultaneous computational acceleration model compression. lookup-based network is described BID0 encodes convolution series lookups dictionary is trained cover observed weight space. paper takes different approach introduces concept continuous convolution neural networks deep learning applications general. is achieved projecting information Reproducing Kernel Hilbert Space RKHS BID33 which point evaluation takes form continuous linear functional. employ Hilbert Maps framework initially described BID29 reconstruct discrete input data continuous function based methodology proposed BID12. Within framework derive closed-form solution continuous convolution two functions takes place directly high-dimensional space where arbitrarily complex patterns are represented using series simple kernels can be efficiently convolved produce third RKHS modeling activation values. Optimizing neural network involves learning weight parameters also RKHS defines convolutional filter which results is much descriptive feature maps can be are used discriminative generative tasks. use high-dimensional projection including infinite-layer neural networks BID15;BID9 has been extensively studied recent times way combine kernel-based learning deep learning applications. Note works BID26 BID25 take similar approach projecting input data RKHS using kernel trick are still relies discretized image patches whereas operates solely data already projected highdimensional spaces. Also works extra kernel parameters are predetermined remain fixed training process jointly learns parameters alongside traditional weight values thus increasing degrees freedom resulting feature maps.The proposed technique entitled Continuous Convolutional Neural Networks CCNNs was evaluated image classification context using standard computer vision benchmarks achieved competitive accuracy results substantially smaller network sizes. also demonstrate applicability unsupervised learning describing convolutional auto-encoder is able produce latent feature representations form continuous functions which are then used initial filters classification using labeled data. paper introduced novel technique data representation takes place highdimensional Reproducing Kernel Hilbert Space RKHS where arbitrarily complex functions can be approximated continuous fashion using series simple kernels. show how these kernels can be efficiently convolved produce approximations convolution results two functions different RKHS how this canbe applied image classification scenario via introduction novel deep learning architecture entitled Continuous Convolutional Neural Networks CCNN Experimental tests using standard benchmark datasets show proposed architecture is able achieve competitive results much smaller network sizes focusing instead descriptive individual filters can be are used extract complex patterns. Although promising are still several potential improvements are left future work as:RKHS sparsification subset clusters are used feature vector calculation would greatly improve computational speed memory requirements;different learning rates optimization strategies class parameter cluster location length-scale weight improve convergence rates;use different kernels feature vector representation way encode different properties resulting feature maps.,1288,899,389,0.013,1.433,2025/11/05 17:18:58,0.01,1.347,0.3208722741433021,421.175
"Convolutional Neural Networks (CNNs) are commonly thought to recognise objects by learning increasingly complex representations of object shapes. Some recent studies suggest a more important role of image textures. We here put these conflicting hypotheses to a quantitative test by evaluating CNNs and human observers on images with a texture-shape cue conflict. We show that ImageNet-trained CNNs are strongly biased towards recognising textures rather than shapes, which is in stark contrast to human behavioural evidence and reveals fundamentally different classification strategies. We then demonstrate that the same standard architecture (ResNet-50) that learns a texture-based representation on ImageNet is able to learn a shape-based representation instead when trained on 'Stylized-ImageNet', a stylized version of ImageNet. This provides a much better fit for human behavioural performance in our well-controlled psychophysical lab setting (nine experiments totalling 48,560 psychophysical trials across 97 observers) and comes with a number of unexpected emergent benefits such as improved object detection performance and previously unseen robustness towards a wide range of image distortions, highlighting advantages of a shape-based representation. How are Convolutional Neural Networks (CNNs) able to reach impressive performance on complex perceptual tasks such as object recognition (Krizhevsky et al., 2012) and semantic segmentation (Long et al., 2015) ? One widely accepted intuition is that CNNs combine low-level features (e.g. edges) to increasingly complex shapes (such as wheels, car windows) until the object (e.g. car) can be readily classified. As Kriegeskorte (2015) puts it, ""the network acquires complex knowledge about the kinds of shapes associated with each category. [...] High-level units appear to learn representations of shapes occurring in natural images"" (p. 429). This notion also appears in other explanations, such as in LeCun et al. (2015) : Intermediate CNN layers recognise ""parts of familiar objects, and subsequent layers [...] detect objects as combinations of these parts"" (p. 436). We term this explanation the shape hypothesis.This hypothesis is supported by a number of empirical findings. Visualisation techniques like Deconvolutional Networks (Zeiler & Fergus, 2014) often highlight object parts in high-level CNN features. 1 Moreover, CNNs have been proposed as computational models of human shape perception by Kubilius et al. (2016) , who conducted an impressive number of experiments comparing human and CNN shape representations and concluded that CNNs ""implicitly learn representations of shape that reflect human shape perception"" (p. 15). Ritter et al. (2017) discovered that CNNs develop a so-called ""shape bias"" just like children, i.e. that object shape is more important than colour for object classification (although see BID15 for contrary evidence). Furthermore, CNNs are currently the most predictive models for human ventral stream object recognition (e.g. BID2 BID2 ; and it is well-known that object shape is the single most important cue for human object recognition (Landau et al., 1988) , much more than other cues like size or texture (which may explain the ease at which humans recognise line drawings or millennia-old cave paintings).On the other hand, some rather disconnected findings point to an important role of object textures for CNN object recognition. CNNs can still classify texturised images perfectly well, even if the global shape structure is completely destroyed BID1 . Conversely , standard CNNs are bad at recognising object sketches where object shapes are preserved yet all texture cues are missing BID0 . Additionally , two studies suggest that local information such as textures may actually be sufficient to ""solve"" ImageNet object recognition: BID6 discovered that a linear classifier on top of a CNN's texture representation (Gram matrix) achieves hardly any classification performance loss compared to original network performance. More recently , BID1 demonstrated that CNNs with explicitly constrained receptive field sizes throughout all layers are able to reach surprisingly high accuracies on ImageNet, even though this effectively limits a model to recognising small local patches rather than integrating object parts for shape recognition. Taken together , it seems that local textures indeed provide sufficient information about object classes-ImageNet object recognition could, in principle, be achieved through texture recognition alone. In the light of these findings, we believe that it is time to consider a second explanation, which we term the texture hypothesis: in contrast to the common assumption, object textures are more important than global object shapes for CNN object recognition.Resolving these two contradictory hypotheses is important both for the deep learning community (to increase our understanding of neural network decisions) as well as for the human vision and neuroscience communities (where CNNs are being used as computational models of human object recognition and shape perception). In this work we aim to shed light on this debate with a number of carefully designed yet relatively straightforward experiments. Utilising style transfer BID7 , we created images with a texture-shape cue conflict such as the cat shape with elephant texture depicted in Figure 1c . This enables us to quantify texture and shape biases in both humans and CNNs. To this end, we perform nine comprehensive and careful psychophysical experiments comparing humans against CNNs on exactly the same images, totalling 48,560 psychophysical trials across 97 observers. These experiments provide behavioural evidence in favour of the texture hypothesis: A cat with an elephant texture is an elephant to CNNs, and still a cat to humans. Beyond quantifying existing biases, we subsequently present results for our two other main contributions: changing biases, and discovering emergent benefits of changed biases. We show that the texture bias in standard CNNs can be overcome and changed towards a shape bias if trained on a suitable data set. Remarkably, networks with a higher shape bias are inherently more robust to many different image distortions (for some even reaching or surpassing human performance, despite never being trained on any of them) and reach higher performance on classification and object recognition tasks. DISPLAYFORM0 As noted in the Introduction, there seems to be a large discrepancy between the common assumption that CNNs use increasingly complex shape features to recognise objects and recent empirical findings which suggest a crucial role of object textures instead. In order to explicitly probe this question, we utilised style transfer BID7 to generate images with conflicting shape and texture information. On the basis of extensive experiments on both CNNs and human observers in a controlled psychophysical lab setting, we provide evidence that unlike humans, ImageNet-trained CNNs tend to classify objects according to local textures instead of global object shapes. In combination with previous work which showed that changing other major object dimensions such as colour BID10 and object size relative to the context (Eckstein et al., 2017) do not have a strong detrimental impact on CNN recognition performance, this highlights the special role that local cues such as textures seem to play in CNN object recognition.Intriguingly, this offers an explanation for a number of rather disconnected findings: CNNs match texture appearance for humans (Wallis et al., 2017) , and their predictive power for neural responses along the human ventral stream appears to be largely due to human-like texture representations, but not human-like contour representations (Laskar et al., 2018; Long & Konkle, 2018) . Furthermore, texture-based generative modelling approaches such as style transfer BID7 , single image super-resolution BID12 as well as static and dynamic texture synthesis BID6 BID5 all produce excellent results using standard CNNs, while CNNbased shape transfer seems to be very difficult BID11 . CNNs can still recognise images with scrambled shapes BID1 ), but they have much more difficulties recognising objects with missing texture information BID0 Yu et al., 2017) . Our hypothesis might also explain why an image segmentation model trained on a database of synthetic texture images transfers to natural images and videos (Ustyuzhaninov et al., 2018) . Beyond that, our results show marked behavioural differences between ImageNet-trained CNNs and human observers. While both human and machine vision systems achieve similarly high accuracies on standard images BID10 , our findings suggest that the underlying classification strategies might actually be very different. This is problematic, since CNNs are being used as computational models for human object recognition (e.g. BID2 BID2 .In order to reduce the texture bias of CNNs we introduced Stylized-ImageNet (SIN), a data set that removes local cues through style transfer and thereby forces networks to go beyond texture recognition. Using this data set, we demonstrated that a ResNet-50 architecture can indeed learn to recognise objects based on object shape, revealing that the texture bias in current CNNs is not by design but induced by ImageNet training data. This indicates that standard ImageNet-trained models may be taking a ""shortcut"" by focusing on local textures, which could be seen as a version of Occam's razor: If textures are sufficient, why should a CNN learn much else? While texture classification may be easier than shape recognition, we found that shape-based features trained on SIN generalise well to natural images.Our results indicate that a more shape-based representation can be beneficial for recognition tasks that rely on pre-trained ImageNet CNNs. Furthermore , while ImageNet-trained CNNs generalise poorly towards a wide range of image distortions (e.g. BID3 BID9 , our ResNet-50 trained on Stylized-ImageNet often reaches or even surpasses human-level robustness (without ever being trained on the specific image degradations). This is exciting because BID10 showed that networks trained on specific distortions in general do not acquire robustness against other unseen image manipulations. This emergent behaviour highlights the usefulness of a shape-based representation: While local textures are easily distorted by all sorts of noise (including those in the real world, such as rain and snow), the object shape remains relatively stable. Furthermore, this finding offers a compellingly simple explanation for the incredible robustness of humans when coping with distortions: a shape-based representation. In summary, we provided evidence that machine recognition today overly relies on object textures rather than global object shapes as commonly assumed. We demonstrated the advantages of a shapebased representation for robust inference (using our Stylized-ImageNet data set 5 to induce such a representation in neural networks). We envision our findings as well as our openly available model weights, code and behavioural data set (49K trials across 97 observers) 6 to achieve three goals: Firstly, an improved understanding of CNN representations and biases. Secondly, a step towards more plausible models of human visual object recognition. Thirdly, a useful starting point for future undertakings where domain knowledge suggests that a shape-based representation may be more beneficial than a texture-based one. We would like to thank Dan Hendrycks for providing the results of We followed the paradigm of Geirhos et al. (2018) for maximal comparability. A trial consisted of 300 ms presentation of a fixation square and a 200 ms presentation of the stimulus image, which was followed by a full-contrast pink noise mask (1/f spectral shape) of the same size lasting for 200 ms. Participants had to choose one of 16 entry-level categories by clicking on a response screen shown for 1500 ms. On this screen, icons of all 16 categories were arranged in a 4 × 4 grid. The experiments were not self-paced and therefore one trial always lasted 2200 ms (300 ms + 200 ms + 200 ms + 1500 ms = 2200 ms). The necessary time to complete an experiment with 1280 stimuli was 47 minutes, for 160 stimuli six minutes, and for 48 stimuli two minutes. In the experiments with 1280 trials, observers were given the possibility of taking a brief break after every block of 256 trials (five blocks in total).As preparation, participants were shown the response screen prior to an experiment and were asked to name all 16 categories in order to get an overview over the possible stimuli categories and to make sure that all categories were clear from the beginning. They were instructed to click on the category they believed was presented. Responses through clicking on a response screen could be changed within the 1500 ms response interval, only the last entered response was counted as the answer. Prior to the real experiment a practice session was performed for the participants to get used to the time course of the experiment and the position of category items on the response screen. This screen was shown for an additional 300 ms in order to provide feedback and indicate whether the entered answer was incorrect. In that case , a short low beep sound occurred and the correct category was highlighted by setting its background to white. The practice session consisted of 320 trials. After 160 trials the participants had the chance to take a short break. In the break, their performance of the first block was shown on the screen along the percentage of trials where no answer was entered. After the practice blocks, observers were shown an example image of the manipulation (not used in the experiment) to minimise surprise. Images used in the practice session were natural images from 16-class-ImageNet BID10 , hence there was no overlap with images or manipulations used in the experiments.","Convolutional Neural Networks where CNNs are commonly thought recognise objects learning increasingly complex representations object shapes. recent studies suggest important role image textures. put conflicting hypotheses quantitative test evaluating CNNs human observers images texture-shape cue conflict. show ImageNet-trained CNNs are strongly biased towards recognising textures rather shapes which is in stark contrast human behavioural evidence reveals fundamentally different classification strategies. demonstrate standard architecture ResNet-50 learns texture-based representation ImageNet is able learn shape-based representation instead when trained 'Stylized-ImageNet' stylized version ImageNet. provides much better fit human behavioural performance well-controlled psychophysical lab setting nine experiments totalling 48,560 psychophysical trials across97 observers comes number unexpected emergent benefits improved object detection performance previously unseen robustness towards wide range image distortions highlighting advantages shape-based representation. How are Convolutional Neural Networks where CNNs able reach impressive performance complex perceptual tasks object recognition Krizhevskyetal. 2012 semantic segmentation Longetal. 2015 One widely accepted intuition is that CNNs combine low-level features e.g edges increasingly complex shapes wheels car windows object e.g car can be readily classified. Kriegeskorte 2015 puts network acquires complex knowledge kinds shapes associated category....High-level units appear learn representations shapes occurring natural images p. 429 notion also appears explanations LeCunetal. 2015 Intermediate CNN layers recognise parts familiar objects subsequent layers... detect objects combinations parts p. 436 term explanation shape hypothesis.This hypothesis is supported number empirical findings. Visualisation techniques like Deconvolutional Networks Zeiler Fergus 2014 often highlight object parts high-level CNN features. 1 Moreover CNNs have been proposed computational models human shape perception Kubiliusetal. 2016 who conducted impressive number experiments comparing human CNN shape representations concluded CNNs implicitly learn representations shape reflect human shape perception p. 15 Ritteretal. 2017 discovered CNNs develop so-called shape bias like children.e object shape is more is important colour object classification although see BID15 contrary evidence Furthermore CNNs are currently predictive models human ventral stream object recognition e.g BID2 BID2;is well-known object shape is the single important cue human object recognition Landauetal. 1988 much cues like size texture may explain ease which humans recognise line drawings millennia-old cave paintings.On hand rather disconnected findings point important role object textures CNN object recognition. CNNs can still classify texturised images perfectly well even if the global shape structure is completely destroyed BID1. Conversely standard CNNs are bad recognising object sketches where object shapes are preserved yet texture cues are missing BID0. Additionally two studies suggest local information textures may actually sufficient solve ImageNet object recognition:BID6 discovered linear classifier top CNN's texture representation Gram matrix achieves hardly classification performance loss compared original network performance. recently BID1 demonstrated CNNs explicitly constrained receptive field sizes throughout layers are able reach surprisingly high accuracies ImageNet even though effectively limits model recognising small local patches rather integrating object parts shape recognition. Taken together seems local textures indeed provide sufficient information object classes-ImageNet object recognition could principle achieved texture recognition alone. light findings believe is time consider second explanation which we term texture hypothesis:contrast common assumption object textures are more important global object shapes CNN object recognition.Resolving two contradictory hypotheses is more is important deep learning community increase understanding neural network decisions well human vision neuroscience communities where CNNs are being used computational models human object recognition shape perception work aim shed light debate number carefully designed yet relatively straightforward experiments. Utilising style transfer BID7 created images texture-shape cue conflict cat shape elephant texture depicted Figure1c. enablesus quantify texture shape biases humans CNNs. end perform nine comprehensive careful psychophysical experiments comparing humans CNNs exactly images totalling 48,560 psychophysical trials across 97 observers. experiments provide behavioural evidence favour texture hypothesis:cat elephant texture is an elephant CNNs still cat humans. Beyond quantifying existing biases subsequently present results two main contributions:changing biases discovering emergent benefits changed biases. show texture bias standard CNNs can be overcome changed towards shape bias if trained suitable data set. Remarkably networks higher shape bias are inherently robust many different image distortions even reaching surpassing human performance despite never trained reach higher performance classification object recognition tasks. DISPLAYFORM0 noted Introduction seems large discrepancy common assumption CNNs use increasingly complex shape features recognise objects recent empirical findings which suggest crucial role object textures instead. order explicitly probe question utilised style transfer BID7 generate images conflicting shape texture information. basis extensive experiments CNNs human observers controlled psychophysical lab setting provide evidence unlike humans ImageNet-trained CNNs tend classify objects according local textures instead global object shapes. combination previous work which showed changing major object dimensions colour BID10 object size relative context Ecksteinetal. 2017 do not have strong detrimental impact CNN recognition performance highlights special role local cues textures seem play CNN object recognition.Intriguingly offers explanation number rather disconnected findings:CNNs match texture appearance humans Wallisetal. 2017 predictive power neural responses along human ventral stream appears largely due human-like texture representations human-like contour representations Laskaretal. 2018;Long Konkle 2018 Furthermore texture-based generative modelling approaches style transfer BID7 single image super-resolution BID12 well static dynamic texture synthesis BID6 BID5 produce excellent results using standard CNNs CNNbased shape transfer seems difficult BID11. CNNs can still recognise images scrambled shapes BID1 have much difficulties recognising objects missing texture information BID0 Yuetal. 2017 hypothesis might also explain why an image segmentation model trained database synthetic texture images transfers natural images videos Ustyuzhaninovetal. 2018 Beyond results show marked behavioural differences ImageNet-trained CNNs human observers. human machine vision systems achieve similarly high accuracies standard images BID10 findings suggest underlying classification strategies might actually different. is problematic since CNNs are being used computational models human object recognition e.g BID2 BID2.In order reduce texture bias CNNs introduced Stylized-ImageNet SIN data set removes local cues style transfer thereby forces networks go beyond texture recognition. Using data set demonstrated ResNet-50 architecture can indeed learn recognise objects based object shape revealing texture bias current CNNs is not by design induced ImageNet training data. indicates standard ImageNet-trained models may taking shortcut focusing local textures could seen version Occam's razor:If textures are sufficient why should a CNN learn much else? texture classification may easier shape recognition found shape-based features trained SIN generalise well natural images.Our results indicate shape-based representation can be beneficial recognition tasks rely pre-trained ImageNet CNNs. Furthermore ImageNet-trained CNNs generalise poorly towards wide range image distortions e.g BID3 BID9 ResNet-50 trained Stylized-ImageNet often reaches even surpasses human-level robustness without ever trained specific image degradations is exciting BID10 showed networks trained specific distortions general do not acquire robustness unseen image manipulations. emergent behaviour highlights usefulness shape-based representation:local textures are easily distorted sorts noise including real world rain snow object shape remains relatively stable. Furthermore finding offers compellingly simple explanation incredible robustness humans when coping distortions:shape-based representation. summary provided evidence machine recognition today overly relies object textures rather global object shapes commonly assumed. demonstrated advantages shapebased representation robust inference using Stylized-ImageNet data set5 induce representation neural networks envision findings well openly available model weights code behavioural data set 49K trials across97 observers 6 achieve three goals:Firstly improved understanding CNN representations biases. Secondly step towards plausible models human visual object recognition. Thirdly useful starting point future undertakings where domain knowledge suggests shape-based representation may beneficial texture-based one. would like thank Dan Hendrycks providing results followed paradigm Geirhosetal. 2018 maximal comparability. trial consisted 300 ms presentation fixation square 200 ms presentation stimulus image which was followed full-contrast pink noise mask 1/f spectral shape size lasting 200ms. Participants had to choose one 16 entry-level categories clicking response screen shown 1500ms. screen icons 16 categories were arranged 4 × 4 grid. experiments were not self-paced therefore one trial always lasted 2200ms 300 ms+200 ms+200ms+1500ms 2200ms necessary time complete experiment 1280 stimuli was 47 minutes 160 stimuli six minutes 48 stimuli two minutes. experiments 1280 trials observers were given possibility taking brief break every block 256 trials five blocks total.As preparation participants were shown response screen prior experiment were asked name 16 categories order get overview possible stimuli categories make sure categories were clear beginning. were instructed click category believed was presented. Responses clicking response screen could changed within 1500 ms response interval last entered response was counted answer. Prior real experiment practice session was performed participants get used time course experiment position category items response screen. screen was shown additional 300ms order provide feedback indicate whether entered answer was incorrect. case short low beep sound occurred correct category was highlighted setting background white. practice session consisted 320 trials. 160 trials participants had the chance take short break. break performance first block was shown screen along percentage trials where no answer was entered. practice blocks observers were shown example image manipulation used experiment minimise surprise. Images used practice session were natural images 16-class-ImageNet BID10 hence was no overlap images manipulations used experiments.",2682,1866,816,0.038,1.437,2025/11/05 17:18:58,0.01,1.403,0.3333333333333333,892.814
"In this work, we exploited different strategies to provide prior knowledge to commonly used generative modeling approaches aiming to obtain speaker-dependent low dimensional representations from short-duration segments of speech data, making use of available information of speaker identities. Namely, convolutional variational autoencoders are employed, and statistics of its learned posterior distribution are used as low dimensional representations of fixed length short-duration utterances. In order to enforce speaker dependency in the latent layer, we introduced a variation of the commonly used prior within the variational autoencoders framework, i.e. the model is simultaneously trained for reconstruction of inputs along with a discriminative task performed on top of latent layers outputs. The effectiveness of both triplet loss minimization and speaker recognition are evaluated as implicit priors on the challenging cross-language NIST SRE 2016 setting and compared against fully supervised and unsupervised baselines.",work exploited different strategies provide prior knowledge commonly used generative modeling approaches aiming obtain speaker-dependent low dimensional representations short-duration segments speech data making use available information speaker identities. Namely convolutional variational autoencoders are employed statistics learned posterior distribution are used low dimensional representations fixed length short-duration utterances. order enforce speaker dependency latent layer introduced variation commonly used prior within variational autoencoders framework.e model is simultaneously trained reconstruction inputs along discriminative task performed top latent layers outputs. effectiveness triplet loss minimization speaker recognition are evaluated implicit priors challenging cross-language NIST SRE 2016 setting compared fully supervised unsupervised baselines.,176,127,49,0.002,1.386,2025/11/05 17:18:58,0.0,1.0,0.1744548286604356,69.619
"The importance-weighted autoencoder (IWAE) approach of Burda et al. defines a sequence of increasingly tighter bounds on the marginal likelihood of latent variable models. Recently, Cremer et al. reinterpreted the IWAE bounds as ordinary variational evidence lower bounds (ELBO) applied to increasingly accurate variational distributions. In this work, we provide yet another perspective on the IWAE bounds. We interpret each IWAE bound as a biased estimator of the true marginal likelihood where for the bound defined on $K$ samples we show the bias to be of order O(1/K). In our theoretical analysis of the IWAE objective we derive asymptotic bias and variance expressions. Based on this analysis we develop jackknife variational inference (JVI),
 a family of bias-reduced estimators reducing the bias to $O(K^{-(m+1)})$ for any given m < K while retaining computational efficiency. Finally, we demonstrate that JVI leads to improved evidence estimates in variational autoencoders. We also report first results on applying JVI to learning variational autoencoders.

 Our implementation is available at https://github.com/Microsoft/jackknife-variational-inference Variational autoencoders (VAE) are a class of expressive probabilistic deep learning models useful for generative modeling, representation learning, and probabilistic regression. Originally proposed in BID8 and BID22 , VAEs consist of a probabilistic model as well as an approximate method for maximum likelihood estimation. In the generative case, the model is defined as DISPLAYFORM0 where z is a latent variable, typically a high dimensional vector; the corresponding prior distribution p(z) is fixed and typically defined as a standard multivariate Normal distribution N (0, I). To achieve an expressive marginal distribution p(x), we define p θ (x|z) through a neural network, making the model (1) a deep probabilistic model.Maximum likelihood estimation of the parameters θ in (1) is intractable, but BID8 and BID22 propose to instead maximize the evidence lower-bound (ELBO), log p(x) ≥ E z∼qω(z|x) log p θ (x|z) p(z) q ω (z|x)=: L E .Here , q ω (z|x) is an auxiliary inference network, parametrized by ω. Simultaneous optimization of (2) over both θ and ω performs approximate maximum likelihood estimation in the model p(x) of FORMULA0 and forms the standard VAE estimation method. 1 The implementation is available at https://github.com/Microsoft/ jackknife-variational-inferenceIn practice L E is estimated using Monte Carlo: we draw K samples z i ∼ q ω (z|x), then use the unbiased estimatorL E of L E ,L DISPLAYFORM1 The VAE approach is empirically very successful but are there fundamental limitations? One limitation is the quality of the model p θ (x|z): this model needs to be expressive enough to model the true distribution over x. Another limitation is that L E is only a lower-bound to the true likelihood. Is this bound tight? It can be shown, BID8 , that when q(z|x) = p(z|x) we have L E = log p(x), hence (2) becomes exact. Therefore, we should attempt to choose an expressive class of distributions q(z|x) and indeed recent work has extensively investigated richer variational families. We discuss these methods in Section 7 but now review the importance weighted autoencoder (IWAE) method we build upon. In summary we proposed to leverage classic higher-order bias removal schemes for evidence estimation. Our approach is simple to implement, computationally efficient, and clearly improves over existing evidence approximations based on variational inference. More generally our jackknife variational inference debiasing formula can also be used to debias log-evidence estimates coming from annealed importance sampling.However, one surprising finding from our work is that using our debiased estimates for training VAE models did not improve over the IWAE training objective and this is surprising because apriori a better evidence estimate should allow for improved model learning.One possible extension to our work is to study the use of other resampling methods for bias reduction; promising candidates are the iterated bootstrap, the Bayesian bootstrap, and the debiasing lemma. These methods could offer further improvements on bias reduction or reduced variance, however, the key challenge is to overcome computational requirements of these methods or, alternatively, to derive key quantities analytically. 6 Application of the debiasing lemma in particular requires the careful construction of a truncation distribution and often produces estimators of high variance.While variance reduction plays a key role in certain areas of machine learning, our hope is that our work shows that bias reduction techniques are also widely applicable. DISPLAYFORM0 Note that only Y K is random in (28), all other quantities are constant. Therefore, by taking the expectation on the left and right side of FORMULA1 we obtain DISPLAYFORM1 The right hand side of FORMULA1 is expressed in terms of the central moments for i ≥ 2, DISPLAYFORM2 of Y K , whereas we are interested in an expression using the central moments i ≥ 2, DISPLAYFORM3 we denote the shared first non-central moment. Because Y K is a sample mean we can use existing results that relate γ i to µ i . In particular (Angelova, 2012, Theorem 1) gives the relations DISPLAYFORM4 DISPLAYFORM5 Expanding FORMULA1 to order five and using the relations FORMULA2 to FORMULA2 gives DISPLAYFORM6 Regrouping the terms by order of K produces the result (8).",importance-weighted autoencoder IWAE approach Burdaetal. defines sequence increasingly tighter bounds marginal likelihood latent variable models. Recently Cremeretal. reinterpreted IWAE bounds ordinary variational evidence lower bounds ELBO applied increasingly accurate variational distributions. work provide yet another perspective IWAE bounds. interpret IWAE bound biased estimator true marginal likelihood where for the bound defined $K samples show bias order 1/K theoretical analysis IWAE objective derive asymptotic bias variance expressions. Based analysis develop jackknife variational inference JVI family bias-reduced estimators reducing bias $O K^ -+1 given K retaining computational efficiency. Finally demonstrate JVI leads improved evidence estimates variational autoencoders. also report first results applying JVI learning variational autoencoders. implementation is available https://github.com/Microsoft/jackknife-variational-inference Variational autoencoders VAE are a class expressive probabilistic deep learning models useful generative modeling representation learning probabilistic regression. Originally proposed BID8 BID22 VAEs consist probabilistic model well approximate method maximum likelihood estimation. generative case model is defined DISPLAYFORM0 wherez is a latent variable typically high dimensional vector;corresponding prior distributionp z is fixed typically defined standard multivariate Normal distribution N 0 achieve expressive marginal distributionp x definepθ x|z neural network making model 1 deep probabilistic model.Maximum likelihood estimation parametersθ 1 is intractable BID8 BID22 propose instead maximize evidence lower-bound ELBO logp x ≥ E z∼qω z|x logpθ x|z p z qω z|x have L E.Here whenqω z|x is an auxiliary inference network parametrized ω. Simultaneous optimization 2 θ ω performs approximate maximum likelihood estimation modelp x FORMULA0 forms standard VAE estimation method. 1 implementation is available https://github.com/Microsoft/jackknife-variational-inferenceIn practiceL E is estimated using Monte Carlo:draw K samplesz ∼qω z|x use unbiased estimatorLE LE L DISPLAYFORM1 VAE approach is empirically successful are there fundamental limitations? One limitation is the quality modelpθ x|z model needs expressive enough model true distribution x. Another limitation is thatLE is only a lower-bound true likelihood. Is this bound tight? can be shown BID8 whenq z|x p z|x haveLE logp x hence 2 becomes exact. Therefore should attempt choose expressive class distributionsq z|x indeed recent work has extensively investigated richer variational families. discuss methods Section7 review importance weighted autoencoder IWAE method build upon. summary proposed leverage classic higher-order bias removal schemes evidence estimation. approach is simple implement computationally efficient clearly improves existing evidence approximations based variational inference. generally jackknife variational inference debiasing formula can also used debias log-evidence estimates coming annealed importance sampling.However one surprising finding work is that using debiased estimates training VAE models did not improve IWAE training objective is surprising apriori better evidence estimate should allow improved model learning.One possible extension work is to study use resampling methods bias reduction;promising candidates are the iterated bootstrap Bayesian bootstrap debiasing lemma. methods could offer improvements bias reduction reduced variance however key challenge is to overcome computational requirements methods alternatively derive key quantities analytically. 6 Application debiasing lemma particular requires careful construction truncation distribution often produces estimators high variance.While variance reduction plays key role certain areas machine learning hope is that our work shows bias reduction techniques are also widely applicable. DISPLAYFORM0 Note K is random 28 quantities are constant. Therefore taking expectation left right side FORMULA1 obtain DISPLAYFORM1 right hand side FORMULA1 is expressed terms central moments ≥2 DISPLAYFORM2 K whereas are interested expression using central moments ≥2 DISPLAYFORM3 denote shared first non-central moment. K is a sample mean can use existing results relateγ µ i. particular Angelova 2012 Theorem1 gives relations DISPLAYFORM4 DISPLAYFORM5 Expanding FORMULA1 order five using relations FORMULA2 FORMULA2 gives DISPLAYFORM6 Regrouping terms order K produces result 8,1168,842,326,0.012,1.387,2025/11/05 17:18:58,0.0,1.526,0.1775700934579437,340.047
"In this paper, we consider the problem of autonomous lane changing for self driving vehicles in a multi-lane, multi-agent setting. We present a framework that demonstrates a more structured and data efficient alternative to end-to-end complete policy learning on problems where the high-level policy is hard to formulate using traditional optimization or rule based methods but well designed low-level controllers are available. Our framework uses deep reinforcement learning solely to obtain a high-level policy for tactical decision making, while still maintaining a tight integration with the low-level controller, thus getting the best of both worlds. We accomplish this with Q-masking, a technique with which we are able to incorporate prior knowledge, constraints, and information from a low-level controller, directly in to the learning process thereby simplifying the reward function and making learning faster and data efficient. We provide preliminary results in a simulator and show our approach to be more efficient than a greedy baseline, and more successful and safer than human driving. In recent years, there has been a growing interest in self driving vehicles. Building such autonomous systems has been an active area of research BID23 BID27 BID3 for its high potential in leading to road networks that are much more safer and efficient. One of the fundamental skills a self driving vehicle must possess is an ability to perform lane change maneuvers, which is especially critical on a multi-lane highway in the presence fast moving traffic (as shown in FIG0 . A bad decision at best leads to congestion and at worst leads to accidents BID8 . Reasoning about interactions with other agents and forming an efficient long term strategy while maintaining safety makes this problem challenging and complex.Prior work on lane changing consists of a diverse set of approaches with early work considering vision based control BID21 . Other methods track trajectories BID14 BID19 , use fuzzy control BID6 , model predictive control BID5 , generate a steering command with adaptive control BID15 , consider planning BID23 BID26 , and mixed logic programming BID4 . However majority of the prior work considers the problem only from a local perspective, i.e. changing between adjacent lanes while avoiding the few neighboring vehicles. There is no notion of a goal, like reaching an exit, which would require reasoning about long term decisions on a strategic level when present on a multi-lane highway among traffic. Formulating a control or optimization based problem to handle such a scenario is not straight forward, would require a lot of hand design and tuning, may work only on a subset of cases, and would generally be intractable. The primary roadblock is that there is no abstraction of what the overall ideal policy should look like, only the ideal outcome is know: reaching the exit safely and efficiently (in least amount of time).Reinforcement learning provides a way to learn arbitrary policies giving specific goals. In recent years learning based methods have been used to address similar or related problems, like learning from human driving BID22 , inverse reinforcement learning BID18 , end-to-end methods that map perception inputs (mainly images) directly to control commands BID13 BID9 BID0 BID25 , and methods that understand the scene via learning to make driving decisions BID2 BID17 . Along these lines deep reinforcement learning has had great success in learning policies from raw sensor information BID12 .In this work, we investigate the use and place of deep reinforcement learning in solving the autonomous lane changing problem. In general learning a full policy than can reason about tactical decisions while at same time address continuous control and collision avoidance can be exceedingly difficult with large notorious to train networks. Thus, an ideal approach would strike the right balance by learning the hard to specify high-level tactical policy while relying on established optimization or rule based method for low-level control.We propose a framework that uses deep Q-learning to learn a high-level tactical decision making policy, and also introduce, Q-masking, a novel technique that forces the agent to explore and learn only a subspace of Q-values. This subspace is directly governed by a low-level module that consists of prior knowledge about the system, constraints of the problem, and information from the lowlevel controller. Not only does Q-masking provide the tight integration between the two paradigms: learning high-level policy and using low-level control, but also heavily simplifies the reward function and makes learning faster and data efficient. By relying on a controller for low-level decisions, we are also able to completely eliminate collisions during training or testing, which makes it a possibility to perform training directly on real systems. We present preliminary benchmarks and show that our framework can outperform a greedy baseline in terms of efficiency and humans driving in the simulator in terms of safety and success, while also generalizing to several unseen scenarios without any extra training. We proposed a framework that leverages the strengths of deep reinforcement learning for high-level tactical decision making, and traditional optimization or rule-based methods for low-level control, by striking the right balance between both domains. At the heart of this framework lies, Q-masking, that provides an interface between the two levels. Using Q-masking we are able to incorporate prior knowledge, constraints about the system and information from the lower-level controller, directly in to the training of the network, simplifying the reward function and making learning faster and more data efficient, while completely eliminating collisions during training or testing. We applied our framework on the problem of autonomous lane changing for self driving cars, where the neural network learned a high-level tactical decision making policy. We presented preliminary results and benchmarked our approach against a greedy baseline and humans driving in the simulator and showed that our approach is able to outperform them both on different metrics with a more efficient and much safer policy. Finally, we demonstrated zero shot generalizations on several unseen scenarios.",paper consider problem autonomous lane changing self driving vehicles multi-lane multi-agent setting. present framework demonstrates structured data efficient alternative end-to-end complete policy learning problems where the high-level policy is hard formulate using traditional optimization rule based methods well designed low-level controllers are available. framework uses deep reinforcement learning solely obtain high-level policy tactical decision making still maintaining tight integration low-level controller thus getting best worlds. accomplish Q-masking technique which we are able incorporate prior knowledge constraints information low-level controller directly learning process thereby simplifying reward function making learning faster data efficient. provide preliminary results simulator show approach efficient greedy baseline successful safer human driving. recent years has been growing interest self driving vehicles. Building autonomous systems has been an active area research BID23 BID27 BID3 high potential leading road networks are much safer efficient. One fundamental skills self driving vehicle must possess is an ability perform lane change maneuvers which is especially critical multi-lane highway presence fast moving traffic shown FIG0. bad decision best leads congestion worst leads accidents BID8. Reasoning interactions agents forming efficient long term strategy maintaining safety makes problem challenging complex.Prior work lane changing consists diverse set approaches early work considering vision based control BID21. methods track trajectories BID14 BID19 use fuzzy control BID6 model predictive control BID5 generate steering command adaptive control BID15 consider planning BID23 BID26 mixed logic programming BID4. However majority prior work considers problem local perspective.e changing adjacent lanes avoiding neighboring vehicles. is no notion goal like reaching exit would require reasoning long term decisions strategic level when present multi-lane highway among traffic. Formulating control optimization based problem handle scenario is not straight forward would require lot hand design tuning may work subset cases would generally intractable. primary roadblock is that thereis abstraction what the overall ideal policy should look like ideal outcome is know:reaching exit safely efficiently least amount time.Reinforcement learning provides way learn arbitrary policies giving specific goals. recent years learning based methods have been used address similar related problems like learning human driving BID22 inverse reinforcement learning BID18 end-to-end methods map perception inputs mainly images directly control commands BID13 BID9 BID0 BID25 methods understand scene via learning make driving decisions BID2 BID17. Along lines deep reinforcement learning has had great success learning policies raw sensor information BID12.In work investigate use place deep reinforcement learning solving autonomous lane changing problem. general learning full policy can reason tactical decisions time address continuous control collision avoidance can be exceedingly difficult large notorious train networks. Thus ideal approach would strike right balance learning hard specify high-level tactical policy relying established optimization rule based method low-level control.We propose framework uses deep Q-learning learn high-level tactical decision making policy are also introduce Q-masking novel technique forces agent explore learn subspace Q-values subspace is directly governed low-level module consists prior knowledge system constraints problem information lowlevel controller. does Q-masking provide tight integration two paradigms:learning high-level policy using low-level control are also heavily simplifies reward function makes learning faster data efficient. relying controller low-level decisions are also able completely eliminate collisions training testing which makes possibility perform training directly real systems. present preliminary benchmarks show framework can outperform greedy baseline terms efficiency humans driving simulator terms safety success are also generalizing several unseen scenarios without extra training. proposed framework leverages strengths deep reinforcement learning high-level tactical decision making traditional optimization rule-based methods low-level control striking right balance domains. heart framework lies Q-masking provides interface two levels. Using Q-masking are able incorporate prior knowledge constraints system information lower-level controller directly training network simplifying reward function making learning faster data efficient completely eliminating collisions training testing. applied framework problem autonomous lane changing self driving cars where the neural network learned high-level tactical decision making policy. presented preliminary results benchmarked approach greedy baseline humans driving simulator showed approach is able outperform different metrics efficient much safer policy. Finally demonstrated zero shot generalizations several unseen scenarios.,1138,764,374,0.011,1.49,2025/11/05 17:18:58,0.01,1.643,0.4984423676012459,349.896
"Despite the recent successes in robotic locomotion control, the design of robot relies heavily on human engineering. Automatic robot design has been a long studied subject, but the recent progress has been slowed due to the large combinatorial search space and the difficulty in evaluating the found candidates. To address the two challenges, we formulate automatic robot design as a graph search problem and perform evolution search in graph space. We propose Neural Graph Evolution (NGE), which performs selection on current candidates and evolves new ones iteratively. Different from previous approaches, NGE uses graph neural networks to parameterize the control policies, which reduces evaluation cost on new candidates with the help of skill transfer from previously evaluated designs. In addition, NGE applies Graph Mutation with Uncertainty (GM-UC) by incorporating model uncertainty, which reduces the search space by balancing exploration and exploitation. We show that NGE significantly outperforms previous methods by an order of magnitude. As shown in experiments, NGE is the first algorithm that can automatically discover kinematically preferred robotic graph structures, such as a fish with two symmetrical flat side-fins and a tail, or a cheetah with athletic front and back legs. Instead of using thousands of cores for weeks, NGE efficiently solves searching problem within a day on a single 64 CPU-core Amazon EC2
 machine.
 The goal of robot design is to find an optimal body structure and its means of locomotion to best achieve a given objective in an environment. Robot design often relies on careful human-engineering and expert knowledge. The field of automatic robot design aims to search for these structures automatically. This has been a long-studied subject, however, with limited success. There are two major challenges: 1) the search space of all possible designs is large and combinatorial, and 2) the evaluation of each design requires learning or testing a separate optimal controller that is often expensive to obtain.In BID28 , the authors evolved creatures with 3D-blocks. Recently, soft robots have been studied in BID13 , which were evolved by adding small cells connected to the old ones. In BID3 , the 3D voxels were treated as the minimum element of the robot. Most evolutionary robots BID8 BID24 require heavy engineering of the initial structures, evolving rules and careful human-guidance. Due to the combinatorial nature of the problem, evolutionary, genetic or random structure search have been the de facto algorithms of automatic robot design in the pioneering works BID28 BID31 BID20 BID16 BID17 BID34 BID2 . In terms of the underlying algorithm, most of these works have a similar population-based optimization loop to the one used in BID28 . None of these algorithms are able to evolve kinematically reasonable structures, as a result of large search space and the inefficient evaluation of candidates.Similar in vein to automatic robot design, automatic neural architecture search also faces a large combinatorial search space and difficulty in evaluation. There have been several approaches to tackle these problems. Bayesian optimization approaches BID29 primarily focus on fine-tuning the number of hidden units and layers from a predefined set. Reinforcement learning BID38 and genetic algorithms BID19 are studied to evolve recurrent neural networks (RNNs) and convolutional neural networks (CNNs) from scratch in order to maximize the validation accuracy. These approaches are computationally expensive because a large number of candidate networks have to be trained from grounds up. BID25 and BID30 propose weight sharing among all possible candidates in the search space to effectively amortize the inner loop training time and thus speed up the architecture search. A typical neural architecture search on ImageNet BID15 ) takes 1.5 days using 200 GPUs BID19 .In this paper, we propose an efficient search method for automatic robot design, Neural Graph Evolution (NGE), that co-evolves both, the robot design and the control policy. Unlike the recent reinforcement learning work, where the control policies are learnt on specific robots carefully designed by human experts BID21 BID0 BID11 , NGE aims to adapt the robot design along with policy learning to maximize the agent's performance. NGE formulates automatic robot design as a graph search problem. It uses a graph as the main backbone of rich design representation and graph neural networks (GNN) as the controller. This is key in order to achieve efficiency of candidate structure evaluation during evolutionary graph search. Similar to previous algorithms like BID28 , NGE iteratively evolves new graphs and removes graphs based on the performance guided by the learnt GNN controller. The specific contributions of this paper are as follows:• We formulate the automatic robot design as a graph search problem.• We utilize graph neural networks (GNNs) to share the weights between the controllers, which greatly reduces the computation time needed to evaluate each new robot design.• To balance exploration and exploitation during the search, we developed a mutation scheme that incorporates model uncertainty of the graphs.We show that NGE automatically discovers robot designs that are comparable to the ones designed by human experts in MuJoCo , while random graph search or naive evolutionary structure search BID28 fail to discover meaningful results on these tasks. In this paper, we introduced NGE, an efficient graph search algorithm for automatic robot design that co-evolves the robot design graph and its controllers. NGE greatly reduces evaluation cost by transferring the learned GNN-based control policy from previous generations, and better explores the search space by incorporating model uncertainties. Our experiments show that the search over the robotic body structures is challenging, where both random graph search and evolutionary strategy fail to discover meaning robot designs. NGE significantly outperforms the naive approaches in both the final performance and computation time by an order of magnitude, and is the first algorithm that can discovers graphs similar to carefully hand-engineered design. We believe this work is an important step towards automated robot design, and may show itself useful to other graph search problems. A DETAILS OF NERVENET++ Similar to NerveNet, we parse the agent into a graph, where each node in the graph corresponds to the physical body part of the agents. For example, the fish in FIG0 can be parsed into a graph of five nodes, namely the torso (0), left-fin (1), right-fin (2), and tail-fin bodies (3, 4). By replacing MLP with NerveNet, the learnt policy has much better performance in terms of robustness and the transfer learning ability. We here propose minor but effective modifications to BID37 , and refer to this model as NerveNet++.In the original NerveNet, at every timestep, several propagation steps need to be performed such that every node is able to receive global information before producing the control signal. This is time and memory consuming, with the minimum number of propagation steps constrained by the depth of the graph.Since the episode of each game usually lasts for several hundred timesteps, it is computationally expensive and ineffective to build the full back-propagation graph. Inspired by BID22 , we employ the truncated graph back-propagation to optimize the policy. NerveNet++ is suitable for an evolutionary search or population-based optimization, as it brings speed-up in wall-clock time, and decreases the amount of memory usage.Therefore in NerveNet++, we propose a propagation model with the memory state, where each node updates its hidden state by absorbing the input feature and a message with time. The number of propagation steps is no longer constrained by the depth of the graph, and in back-propagation, we save memory and time consumption with truncated computation graph. The memory state h t+1,τ u depends on the previous actions, observations, and states. Therefore, the full back-propagation graph will be the same length as the episode length, which is very computationally intensive. The intuition from the authors in BID22 is that, for the RL agents, the dependency of the agents on timesteps that are far-away from the current timestep is limited. Thus, negligible accuracy of the gradient estimator will be lost if we truncate the back-propagation graph. We define a back-propagation length Γ, and optimize the following objective function instead: DISPLAYFORM0 DISPLAYFORM1 Essentially this optimization means that we only back-propagate up to Γ timesteps, namely at the places where κ = 0, we treat the hidden state as input to the network and stop the gradient. To optimize the objective function , we follow same optimization procedure as in BID37 , which is a variant of PPO Schulman et al. (2017) , where a surrogate loss J ppo (θ) is optimized. We refer the readers to these papers for algorithm details.","Despite recent successes robotic locomotion control design robot relies heavily human engineering. Automatic robot design has been a long studied subject recent progress has been slowed due large combinatorial search space difficulty evaluating found candidates. address two challenges formulate automatic robot design graph search problem perform evolution search graph space. propose Neural Graph Evolution NGE which performs selection current candidates evolves new ones iteratively. Different previous approaches NGE uses graph neural networks parameterize control policies which reduces evaluation cost new candidates help skill transfer previously evaluated designs. addition NGE applies Graph Mutation Uncertainty GM-UC incorporating model uncertainty which reduces search space balancing exploration exploitation. show NGE significantly outperforms previous methods order magnitude. shown experiments NGE is the first algorithm can automatically discover kinematically preferred robotic graph structures fish two symmetrical flat side-fins tail cheetah athletic front back legs. Instead using thousands cores weeks NGE efficiently solves searching problem within day single 64 CPU-core Amazon EC2 machine. goal robot design is to find optimal body structure means locomotion best achieve given objective environment. Robot design often relies careful human-engineering expert knowledge. field automatic robot design aims search structures automatically. has been a long-studied subject however limited success. are two major challenges:1 search space possible designs is large combinatorial 2 evaluation design requires learning testing separate optimal controller is often expensive obtain.In BID28 authors evolved creatures 3D-blocks Recently soft robots have been studied BID13 which were evolved adding small cells connected old ones. BID3 3D voxels were treated minimum element robot. evolutionary robots BID8 BID24 require heavy engineering initial structures evolving rules careful human-guidance Due combinatorial nature problem evolutionary genetic random structure search have been the de facto algorithms automatic robot design pioneering works BID28 BID31 BID20 BID16 BID17 BID34 BID2. terms underlying algorithm works have a similar population-based optimization loop one used BID28. None algorithms are able evolve kinematically reasonable structures result large search space inefficient evaluation candidates.Similar vein automatic robot design automatic neural architecture search also faces large combinatorial search space difficulty evaluation. have been several approaches tackle problems. Bayesian optimization approaches BID29 primarily focus fine-tuning number hidden units layers predefined set. Reinforcement learning BID38 genetic algorithms BID19 are studied evolve recurrent neural networks RNNs convolutional neural networks CNNs scratch order maximize validation accuracy. approaches are computationally expensive large number candidate networks have to be trained grounds up. BID25 BID30 propose weight sharing among possible candidates search space effectively amortize inner loop training time thus speed architecture search. typical neural architecture search ImageNet BID15 takes 1.5 days using 200 GPUs BID19.In paper propose efficient search method automatic robot design Neural Graph Evolution NGE co-evolves robot design control policy. Unlike recent reinforcement learning work where the control policies are learnt specific robots carefully designed human experts BID21 BID0 BID11 NGE aims adapt robot design along policy learning maximize agent's performance. NGE formulates automatic robot design graph search problem. uses graph main backbone rich design representation graph neural networks GNN controller. is key order achieve efficiency candidate structure evaluation evolutionary graph search. Similar previous algorithms like BID28 NGE iteratively evolves new graphs removes graphs based performance guided learnt GNN controller. specific contributions paper are as follows:• formulate automatic robot design graph search problem.• utilize graph neural networks GNNs share weights controllers which greatly reduces computation time needed evaluate new robot design.• balance exploration exploitation search developed mutation scheme incorporates model uncertainty graphs.We show NGE automatically discovers robot designs are comparable ones designed human experts MuJoCo where both random graph search naive evolutionary structure search BID28 fail discover meaningful results tasks. paper introduced NGE efficient graph search algorithm automatic robot design co-evolves robot design graph controllers. NGE greatly reduces evaluation cost transferring learned GNN-based control policy previous generations better explores search space incorporating model uncertainties. experiments show search robotic body structures is challenging where both random graph search evolutionary strategy fail discover meaning robot designs. NGE significantly outperforms naive approaches final performance computation time order magnitude is the first algorithm can discovers graphs similar carefully hand-engineered design. believe work is an important step towards automated robot design may show useful graph search problems. DETAILS NERVENET++Similar NerveNet parse agent graph where each node graph corresponds physical body part agents. example fish FIG0 can be parsed graph five nodes namely torso 0 left-fin 1 right-fin 2 tail-fin bodies 3 4 replacing MLP NerveNet learnt policy has much better performance terms robustness transfer learning ability. propose minor effective modifications BID37 refer model NerveNet++.In original NerveNet every timestep several propagation steps need performed every node is able receive global information producing control signal. is time memory consuming minimum number propagation steps constrained depth graph.Since episode game usually lasts several hundred timesteps is which is very computationally expensive ineffective build full back-propagation graph. Inspired BID22 employ truncated graph back-propagation optimize policy. NerveNet++is suitable evolutionary search population-based optimization brings speed-up wall-clock time decreases amount memory usage.Therefore NerveNet++propose propagation model memory state where each node updates hidden state absorbing input feature message time. number propagation steps is no longer constrained depth graph back-propagation save memory time consumption truncated computation graph. memory stateh+1 τ u depends previous actions observations states. Therefore full back-propagation graph will be the same length episode length is which is very computationally intensive. intuition authors BID22 is that,for RL agents dependency agents timesteps are far-away current timestep is limited. Thus negligible accuracy gradient estimator will be lost if we truncate back-propagation graph. define back-propagation lengthΓ optimize following objective function instead:DISPLAYFORM0 DISPLAYFORM1 Essentially optimization means back-propagate Γ timesteps namely places whereκ 0 treat hidden state input network stop gradient. optimize objective function follow optimization procedure BID37 which is a variant PPO Schulmanetal. 2017 where a surrogate loss J ppo θ is optimized. refer readers papers algorithm details.",1745,1216,529,0.022,1.435,2025/11/05 17:18:58,0.01,1.706,0.3271028037383177,541.653
"Deep learning on graphs has become a popular research topic with many applications. However, past work has concentrated on learning graph embedding tasks only, which is in contrast with advances in generative models for images and text. Is it possible to transfer this progress to the domain of graphs? We propose to sidestep hurdles associated with linearization of such discrete structures by having a decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. Our method is formulated as a variational autoencoder. We evaluate on the challenging task of conditional molecule generation. Deep learning on graphs has very recently become a popular research topic, with useful applications across fields such as chemistry BID5 , medicine (Ktena et al.) , or computer vision (Simonovsky & Komodakis, 2017) . Past work has concentrated on learning graph embedding tasks so far, i.e. encoding an input graph into a vector representation. This is in stark contrast with fastpaced advances in generative models for images and text, which have seen massive rise in quality of generated samples. Hence, it is an intriguing question how one can transfer this progress to the domain of graphs, i.e. their decoding from a vector representation. Moreover, the desire for such a method has been mentioned in the past by BID7 .However , learning to generate graphs is a difficult problem for methods based on gradient optimization, as graphs are discrete structures. Incremental construction involves discrete decisions, which are not differentiable. Unlike sequence (text) generation, graphs can have arbitrary connectivity and there is no clear best way how to linearize their construction in a sequence of steps.In this work, we propose to sidestep these hurdles by having the decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. In a probabilistic graph, the existence of nodes and edges, as well as their attributes, are modeled as independent random variables. The method is formulated in the framework of variational autoencoders (VAE) by BID12 .We demonstrate our method , coined GraphVAE, in cheminformatics on the task of molecule generation. Molecular datasets are a challenging but convenient testbed for our generative model, as they easily allow for both qualitative and quantitative tests of decoded samples. While our method is applicable for generating smaller graphs only and its performance leaves space for improvement, we believe our work is an important initial step towards powerful and efficient graph decoders. In this work we addressed the problem of generating graphs from a continuous embedding in the context of variational autoencoders. We evaluated our method on two molecular datasets of different maximum graph size. While we achieved to learn embedding of reasonable quality on small molecules, our decoder had a hard time capturing complex chemical interactions for larger molecules. Nevertheless, we believe our method is an important initial step towards more powerful decoders and will spark interesting in the community.There are many avenues to follow for future work. Besides the obvious desire to improve the current method (for example, by incorporating a more powerful prior distribution or adding a recurrent mechanism for correcting mistakes), we would like to extend it beyond a proof of concept by applying it to real problems in chemistry, such as optimization of certain properties or predicting chemical reactions. An advantage of a graph-based decoder compared to SMILES-based decoder is the possibility to predict detailed attributes of atoms and bonds in addition to the base structure, which might be useful in these tasks. Our autoencoder can also be used to pre-train graph encoders for fine-tuning on small datasets BID6 .",Deep learning graphs has become popular research topic many applications. However past work has concentrated learning graph embedding tasks whichis contrast advances generative models images text. Is it possible transfer progress domain graphs? propose sidestep hurdles associated linearization discrete structures decoder output probabilistic fully-connected graph predefined maximum size directly once. method is formulated variational autoencoder. evaluate challenging task conditional molecule generation. Deep learning graphs has very recently become popular research topic useful applications across fields chemistry BID5 medicine Ktenaetal. computer vision Simonovsky Komodakis 2017 Past work has concentrated learning graph embedding tasks far.e encoding input graph vector representation. is in stark contrast fastpaced advances generative models images text which have seen massive rise quality generated samples. Hence is an intriguing question how one can transfer progress domain graphs.e decoding vector representation. Moreover desire method has been mentioned past BID7.However learning generate graphs is a difficult problem methods based gradient optimization graphs are discrete structures. Incremental construction involves discrete decisions which are not differentiable. Unlike sequence text generation graphs can have arbitrary connectivity is no clear best way how to linearize construction sequence steps.In work propose sidestep hurdles decoder output probabilistic fully-connected graph predefined maximum size directly once. probabilistic graph existence nodes edges well attributes are modeled independent random variables. method is formulated framework variational autoencoders VAE BID12.We demonstrate method coined GraphVAE cheminformatics task molecule generation. Molecular datasets are a challenging convenient testbed generative model easily allow qualitative quantitative tests decoded samples. method is applicable generating smaller graphs performance leaves space improvement believe work is an important initial step towards powerful efficient graph decoders. work addressed problem generating graphs continuous embedding context variational autoencoders. evaluated method two molecular datasets different maximum graph size. achieved learn embedding reasonable quality small molecules decoder had a hard time capturing complex chemical interactions larger molecules. Nevertheless believe method is an important initial step towards powerful decoders will spark interesting community.There are many avenues follow future work. Besides obvious desire improve current method example incorporating powerful prior distribution adding recurrent mechanism correcting mistakes would like extend beyond proof concept applying real problems chemistry optimization certain properties predicting chemical reactions. advantage graph-based decoder compared SMILES-based decoder is the possibility predict detailed attributes atoms bonds addition base structure might useful tasks. autoencoder can also used pre-train graph encoders fine-tuning small datasets BID6.,712,470,242,0.007,1.515,2025/11/05 17:18:58,0.0,1.63,0.5763239875389403,266.409
"Long Short-Term Memory (LSTM) is one of the most widely used recurrent structures in sequence modeling. Its goal is to use gates to control the information flow (e.g., whether to skip some information/transformation or not) in the recurrent computations, although its practical implementation based on soft gates only partially achieves this goal and is easy to overfit. In this paper, we propose a new way for LSTM training, which pushes the values of the gates towards 0 or 1. By doing so, we can (1) better control the information flow: the gates are mostly open or closed, instead of in a middle state; and (2) avoid overfitting to certain extent: the gates operate at their flat regions, which is shown to correspond to better generalization ability. However, learning towards discrete values of the gates is generally difficult. To tackle this challenge, we leverage the recently developed Gumbel-Softmax trick from the field of variational methods, and make the model trainable with standard backpropagation. Experimental results on language modeling and machine translation show that (1) the values of the gates generated by our method are more reasonable and intuitively interpretable, and (2) our proposed method generalizes better and achieves better accuracy on test sets in all tasks. Moreover, the learnt models are not sensitive to low-precision approximation and low-rank approximation of the gate parameters due to the flat loss surface. Recurrent neural networks (RNN) BID10 are widely used in sequence modeling tasks, such as language modeling BID19 BID17 , speech recognition BID44 , time series prediction BID40 , machine translation BID2 , image captioning BID35 BID41 , and image generation BID34 .To address the long-term dependency and gradient vanishing problem of conventional RNN, long short-term memory (LSTM) BID7 BID12 was proposed, which introduces gate functions to control the information in a recurrent unit: a forget gate function to determine how much previous information should be excluded for the current step, an input gate function to find relevant signals to be absorbed into the hidden context, and an output gate function for prediction and decision making. For ease of optimization, in practical implementation, one usually uses element-wise sigmoid function to mimic the gates, whose outputs are soft values between 0 and 1. By using such gates, LSTM usually performs much better than conventional RNN. However , the benefits come with the cost of introducing many more parameters in the gates, which makes the training of a LSTM model inefficient and easy to overfit BID20 BID42 BID30 .In this paper, we explore a new way to train LSTM by pushing the values of the gates to the boundary of their ranges (0, 1)1 . Pushing the values of the gates to 0/1 has certain advantages. First, it well aligns with the original purpose of the development of gates: to get the information in or skip by ""opening"" or ""closing"" the gates during the recurrent computation. Second , training LSTM 1 The output of a gate function is usually a vector. For simplicity , in the paper, we say ""pushing the output of the gate function to 0/1"" when meaning ""pushing each dimension of the output vector of the gate function to either 0 or 1"". We also say that each dimension of the output vector of the gate function is a gate, and say a gate is open/closed if its value is close to 1/0. towards binary-valued gates can make the learnt model generalize better. According to BID11 BID9 BID18 BID4 , a model lying in a flat region of the loss surface is likely to generalize well, since any small perturbation to the model makes little fluctuation to the loss. Training LSTM towards binary-valued gates means seeking a set of parameters to make the values of the gates approaching zero or one, namely residing in the flat region of the sigmoid function. Simple deductions show that this also corresponds to the flat region of the overall loss surface.Technically, pushing the outputs of the gates towards such discrete values is challenging. A straightforward approach is to sharpen the sigmoid function by a smaller temperature. However, this is equivalent to rescaling the input and cannot guarantee the values of the learnt gates to be close to 0 or 1. To tackle this challenge, in this paper, we leverage the Gumbel-Softmax trick that BID15 and BID23 recently develop for variantional methods. The trick aims to generate approximated samples for categorical latent variables in a stochastic computational graph, e.g., variational autoencoder, brings convenience to using reparametrization tricks, and thus leads to efficient learning. Specifically, during training, we apply the Gumbel-Softmax trick to the gates to approximate the values sampled from the Bernoulli distribution given by the parameters, and train the LSTM model with standard backpropagation methods. We call this method Gumbel-Gate LSTM (G 2 -LSTM). We conduct three experiments on two tasks (language modeling and machine translation) to verify our proposed method. We have the following observations from experimental results:• Our model generalizes well: In all tasks, we achieve superior performance to baseline algorithms on the test sets, and the gap between training and test is effectively reduced.• Our model is not sensitive due to its flat loss surface : We apply several model compression algorithms to the parameters in the gates, including low-precision approximation and lowrank approximation, and all results show that our learnt models are better.• The gates in our learnt model are meaningful and intuitively interpretable after visualization. Furthermore, our model can automatically learn the boundaries inside the sentences.The organization of the paper is as follows. We introduce related work in Section 2 and propose our learning algorithm in Section 3. Experiments are reported in Section 4 and future work is discussed in the last section.2 RELATED WORK In this paper, we have designed a new training algorithm for LSTM by leveraging the recently developed Gumbel-Softmax trick. Our training algorithm can push the values of the input and forget gates to 0 or 1, leading to robust LSTM models. Experiments on language modeling and machine translation have demonstrated the effectiveness of the proposed training algorithm.We will explore following directions in the future. First, we have only tested with shallow LSTM models in this paper. We will apply our algorithm to deeper models (e.g., 8+ layers) and test on larger datasets. Second, we have considered the tasks of language modeling and machine translation. We will study more applications such as question answering and text summarization. Third, we are cleaning and refactoring the code and will release the training code to public soon.",Long Short-Term Memory LSTM is one widely used recurrent structures sequence modeling. goal is to use gates control information flow e.g whether skip information/transformation recurrent computations although practical implementation based soft gates partially achieves goal is easy overfit. paper propose new way LSTM training which pushes values gates towards0 1. can(1 better control information flow:gates are mostly open closed instead middle state;2 avoid overfitting certain extent:gates operate flat regions which is shown correspond better generalization ability. However learning towards discrete values gates is generally difficult. tackle challenge leverage recently developed Gumbel-Softmax trick field variational methods make model trainable standard backpropagation. Experimental results language modeling machine translation show 1 values gates generated method are more reasonable intuitively interpretable 2 proposed method generalizes better achieves better accuracy test sets tasks. Moreover learnt models are not sensitive low-precision approximation low-rank approximation gate parameters due flat loss surface. Recurrent neural networks RNN BID10 are widely used sequence modeling tasks language modeling BID19 BID17 speech recognition BID44 time series prediction BID40 machine translation BID2 image captioning BID35 BID41 image generation BID34.To address long-term dependency gradient vanishing problem conventional RNN long short-term memory LSTM BID7 BID12 was proposed which introduces gate functions control information recurrent unit:forget gate function determine how much previous information should be excluded current step input gate function find relevant signals absorbed hidden context output gate function prediction decision making. ease optimization practical implementation one usually uses element-wise sigmoid function mimic gates whose outputs are soft values 0 1. using gates LSTM usually performs much better conventional RNN. However benefits come cost introducing many parameters gates which makes training LSTM model inefficient is easy overfit BID20 BID42 BID30.In paper explore new way train LSTM pushing values gates boundary ranges 0 1 1. Pushing values gates 0/1 has certain advantages. First well aligns original purpose development gates:get information skip opening closing gates recurrent computation. Second training LSTM1 output gate function is usually vector. simplicity paper say pushing output gate function 0/1 when meaning pushing dimension output vector gate function either0 1. also say dimension output vector gate function is a gate say gate is open/closed if its value is close 1/0. towards binary-valued gates can make learnt model generalize better. According BID11 BID9 BID18 BID4 model lying flat region loss surface is likely generalize well since small perturbation model makes little fluctuation loss. Training LSTM towards binary-valued gates means seeking set parameters make values gates approaching zero one namely residing flat region sigmoid function. Simple deductions show also corresponds flat region overall loss surface.Technically pushing outputs gates towards discrete values is challenging. straightforward approach is to sharpen sigmoid function smaller temperature. However is equivalent rescaling input cannot guarantee values learnt gates close 0 1. tackle challenge paper leverage Gumbel-Softmax trick BID15 BID23 recently develop variantional methods. trick aims generate approximated samples categorical latent variables stochastic computational graph e.g variational autoencoder brings convenience using reparametrization tricks thus leads efficient learning. Specifically training apply Gumbel-Softmax trick gates approximate values sampled Bernoulli distribution given parameters train LSTM model standard backpropagation methods. call method Gumbel-Gate LSTM G 2 -LSTM conduct three experiments two tasks language modeling machine translation verify proposed method. have the following observations experimental results:• model generalizes well:tasks achieve superior performance baseline algorithms test sets gap training test is effectively reduced.• model is not sensitive due flat loss surface:will apply several model compression algorithms parameters gates including low-precision approximation lowrank approximation results show learnt models are better.• gates learnt model are meaningful intuitively interpretable visualization. Furthermore model can automatically learn boundaries inside sentences.The organization paper is as follows. introduce related work Section2 propose learning algorithm Section3. Experiments are reported Section4 future work is discussed last section.2 RELATED WORK paper have designed new training algorithm LSTM leveraging recently developed Gumbel-Softmax trick. training algorithm can push values input forget gates 0 1 leading robust LSTM models. Experiments language modeling machine translation have demonstrated effectiveness proposed training algorithm.We will explore following directions future. First have only tested shallow LSTM models paper. will apply algorithm deeper models e.g 8+layers test larger datasets. Second have considered tasks language modeling machine translation. will study applications question answering text summarization. Third are cleaning refactoring code will release training code public soon.,1378,919,459,0.016,1.499,2025/11/05 17:18:58,0.01,1.271,0.5264797507788164,450.064
"We present a personalized recommender system using neural network for recommending
 products, such as eBooks, audio-books, Mobile Apps, Video and Music.
 It produces recommendations based on customer’s implicit feedback history such
 as purchases, listens or watches. Our key contribution is to formulate recommendation
 problem as a model that encodes historical behavior to predict the future
 behavior using soft data split, combining predictor and auto-encoder models. We
 introduce convolutional layer for learning the importance (time decay) of the purchases
 depending on their purchase date and demonstrate that the shape of the time
 decay function can be well approximated by a parametrical function. We present
 offline experimental results showing that neural networks with two hidden layers
 can capture seasonality changes, and at the same time outperform other modeling
 techniques, including our recommender in production. Most importantly, we
 demonstrate that our model can be scaled to all digital categories, and we observe
 significant improvements in an online A/B test. We also discuss key enhancements
 to the neural network model and describe our production pipeline. Finally
 we open-sourced our deep learning library which supports multi-gpu model parallel
 training. This is an important feature in building neural network based recommenders
 with large dimensionality of input and output data. Recently, deep learning based recommender systems gained significant attention by outperforming conventional approaches BID36 . It shows promising results on products like videos BID6 , mobile apps BID5 , music BID31 etc.In the papers mentioned above, we noticed that NN based recommenders are different for each product category (videos, music, mobile apps), requiring unique feature extraction methods and NN topologies. All of these challenges makes it harder to scale over different product categories. In this paper we are exploring effectiveness of a multilayer neural network (NN) for personalized recommendations of products which were never purchased before by a customer. The simplicity of this approach allows us to scale it on various categories of Amazon catalog in production. We focus on improving accuracy of the neural network based personalized recommender.It is noticed in BID6 ) that accuracy of NN depends on how the problem is formulated. They found that NN performs better when it is trained to predict the user's next purchase, rather than a set of randomly held-out purchases. We use the same idea, but on top of this, we propose to train NN model to predict not only future purchase, but all future purchases in the certain time (for example in the next week).Capturing temporal popularity (trendiness) also called seasonal changes of consumption pattern is a challenging and important problem in recommender systems BID33 , which can impact the accuracy of the model over time. In BID33 BID19 authors propose methods to capture seasonality changes using sequence modeling. Another approach BID29 ) models both long-term static and short-term temporal user preferences. In both cases they use different versions of recurrent neural networks. In this paper we propose to combine predictor model (which can captures short term preferences and recommend products which are currently popular) with auto-encoder model (which can capture static customer preferences and recommend products which were popular at any time in the past) using feed forward NN. These models are combined by training them jointly. We re-train NN model every day to learn new popular products and changes in customer preferences. Even though our model is simpler then RNN, we show that it captures seasonality changes well.Improving NN based recommender is important problem, for example in BID6 authors observed that adding features and depth significantly improves precision on holdout data from YouTube catalog. In BID5 authors show that wide and deep NN with multiple features can improve performance of the neural network on mobile apps. So both methods BID5 and BID6 ) require different production pipelines for different data sets: video and mobile apps. In this paper we use only purchase history and focus on improvements of NN accuracy by applying different splits of the training data. It simplifies the production pipeline and allows us to reuse it on all digital categories: video, eBooks, audio-books, mobile apps, and music.Another way of improving recommender system is time decay, which was introduced by BID35 for collaborative filtering. We also apply it on input data for the neural network based recommender and observe positive impact on accuracy metrics. Our contribution is to use convolutional layer BID20 for estimating the shape of time decay function. Convolutional layers are used in existing recommender systems, but it is applied for different purposes, for example in BID15 convolutional layer is used for learning local relation between adjacent songs, in BID37 BID18 it is used for text feature extraction and in BID31 it is used for extracting features from audio signal.There can be millions of products in the catalog and it is a hard problem to run NN based recommender in production with such amount of items BID6 . Both BID6 and BID5 are splitting the problem into candidate generation and ranking. Candidate generation retrieves a small subset of products from a large corpus. These candidates should be relevant to customer interest. Ranking does a fine-level scoring of the candidates and in addition to consumption history it can use more features (context, impression, etc) . Another way of scaling this problem is to learn similarity between products using DSSM approach BID8 which is relying on content features. In this paper we focused on training end-to-end one neural network which is using only purchases events. On one hand it simplifies the production pipeline, because there is no splitting into candidate generation and ranking models and there is no special feature extraction step. But on the other hand we have to deal with large dimensionality of input features and labels. To solve this problem we use multi-GPU model parallelization, implemented by our team in DSSTNE library (10). It allows us to re-train large NN models every day and produce fresh recommendations for our customers.In this paper, we are focused on modeling consumption patterns in digital products (For example, recommending movies to customers based on the movies already purchased). Depending on the domain, we also exclude movies that were already purchased by the customer while computing offline metrics as well as recommending online. We present different methods of splitting the training data and observed that it can improve NN based recommender accuracy metrics. Techniques like the one presented here feed into recommendation technology deployed at Amazon.The rest of the paper is organized as follows. Section 2 introduces offline metrics used for algorithm evaluation . Section 3 details our NN model development procedure, including how different methods are compared. Section 4 provides extensive offline evaluation results, in conjunction with model property exploration. Section 5 presents how to run NN model in production and describes on-line A/B test. Finally, section 6 presents our conclusions. We described a personalized neural network based recommender system which was launched in production on categories like eBooks, Audible, Apps and Video. We are currently working on expand-ing it to non-digital categories. We showed that splitting customer purchases into a history period (input) and a future period (output) in our models led to good results, and some of our production models use this approach (with soft split which combines the auto-encoder model with the future predictor model). We have applied time decay learnt by convolutional layer, or defined by parametrical function to consumption event. It captures the importance of recent activity, and combined with soft split, it leads to significant improvements in offline metrics. We demonstrated that two layer neural networks are outperforming other NN based approaches which are more complicated than our method, both on public dataset (MovieLens) and company's internal datasets. Because of simplicity of the NN model we can scale it on all digital categories. We observed significant KPI improvements during online A/B tests in production. Finally we open sourced our deep learning library which supports multi gpu model parallel training and allows us to train large models in timely manner.There are around 6200 products (movies) purchased (rated) by these customers in the above period of time. Distribution of customers sorted by number of purchases is shown on FIG0 , where H(c) number of purchases made by customer c, c customer index. It shows that 90 percent of the customers have less than 400 purchases. Distribution of products in data X and Y are shown on FIG0 (a), where P X(p), P Y (p) number of purchases of product p in the input (X) and output (Y ) training data accordingly, p product index. Both of these distributions have long tail: 90 percent of purchases are covered by 1000 products. During evaluation we feed XY data to the models and produce output scoresŶ . These scores are sorted and the top K products are returned as recommendations. Before sorting, all previous purchases (products belonging to data XY ) of the selected customer are removed from the recommendations, so that only new products are recommended. These recommendations are compared with future purchases (data Z) for accuracy calculation. We get testing input data XY and testing output data Z by selecting customers who has at least two purchases in period of time dx . . . dyz and at least one purchase in period of time dyz . . . dz. There are 921 customers who satisfy these conditions. Purchases belonging to dates dx . . . dyz assigned to testing input data XY , and belonging to dyz . . . dz assigned to testing output data Z. Accuracy metrics of predictor, soft split and fastXML models are presented on FIG0 . Predictor model has the same PCC@K with soft split and lower precision@K. Both of these models have higher accuracy metrics than fastXML. We observe similar difference in precision between predictor model and fastXML on Figure. 3, but fastXML has higher PCC@K. These results can be used only as an approximation of a performance on real implicit feedbacks (purchase history), because in this section we were using ratings converted to implicit feedbacks.",present personalized recommender system using neural network recommending products eBooks audio-books Mobile Apps Video Music. produces recommendations based customers implicit feedback history purchases listens watches. key contribution is to formulate recommendation problem model encodes historical behavior predict future behavior using soft data split combining predictor auto-encoder models. introduce convolutional layer learning importance time decay purchases depending purchase date demonstrate shape time decay function can be well approximated parametrical function. present offline experimental results showing neural networks two hidden layers can capture seasonality changes time outperform modeling techniques including recommender production. importantly demonstrate model can be scaled digital categories observe significant improvements online/B test. also discuss key enhancements neural network model describe production pipeline. Finally open-sourced deep learning library which supports multi-gpu model parallel training. is an important feature building neural network based recommenders large dimensionality input output data. Recently deep learning based recommender systems gained significant attention outperforming conventional approaches BID36. shows promising results products like videos BID6 mobile apps BID5 music BID31 etc.In papers mentioned noticed NN based recommenders are different product category videos music mobile apps requiring unique feature extraction methods NN topologies. challenges makes harder scale different product categories. paper are exploring effectiveness multilayer neural network NN personalized recommendations products which were never purchased customer. simplicity approach allowsus scale various categories Amazon catalog production. focus improving accuracy neural network based personalized recommender.It is noticed BID6 accuracy NN depends how the problem is formulated. found NN performs better when it is trained predict user's next purchase rather set randomly held-out purchases. use idea top propose train NN model predict future purchase future purchases certain time example next week.Capturing temporal popularity trendiness also called seasonal changes consumption pattern is a challenging important problem recommender systems BID33 which can impact accuracy model time. BID33 BID19 authors propose methods capture seasonality changes using sequence modeling. Another approach BID29 models long-term static short-term temporal user preferences. cases use different versions recurrent neural networks. paper propose combine predictor model which can captures short term preferences recommend products which are currently popular auto-encoder model which can capture static customer preferences recommend products which were popular time past using feed forwardNN. models are combined training jointly. re-train NN model every day learn new popular products changes customer preferences. Even though model is simpler RNN show captures seasonality changes well.Improving NN based recommender is important problem example BID6 authors observed adding features depth significantly improves precision holdout data YouTube catalog. BID5 authors show wide deepNN multiple features can improve performance neural network mobile apps. methods BID5 BID6 require different production pipelines different data sets:video mobile apps. paper use purchase history focus improvements NN accuracy applying different splits training data. simplifies production pipeline allowsus reuse digital categories:video eBooks audio-books mobile apps music.Another way improving recommender system is time decay which was introduced BID35 collaborative filtering. also apply input data neural network based recommender observe positive impact accuracy metrics. contribution is to use convolutional layer BID20 estimating shape time decay function. Convolutional layers are used existing recommender systems is applied different purposes example BID15 convolutional layer is used learning local relation adjacent songs BID37 BID18 is used text feature extraction BID31 is used extracting features audio signal.There can be millions products catalog is a hard problem run NN based recommender production amount items BID6. BID6 BID5 are splitting problem candidate generation ranking. Candidate generation retrieves small subset products large corpus. candidates should be relevant customer interest. Ranking does a fine-level scoring candidates addition consumption history can use features context impression etc Another way scaling problem is to learn similarity products using DSSM approach BID8 which is relying content features. paper focused training end-to-end one neural network which is using purchases events. one hand simplifies production pipeline is splitting candidate generation ranking models is no special feature extraction step. hand have to deal large dimensionality input features labels. solve problem use multi-GPU model parallelization implemented team DSSTNE library 10 allowsus re-train large NN models every day produce fresh recommendations customers.In paper are focused modeling consumption patterns digital products example recommending movies customers based movies already purchased Depending domain also exclude movies were already purchased customer computing offline metrics well recommending online. present different methods splitting training data observed can improve NN based recommender accuracy metrics. Techniques like one presented feed recommendation technology deployed Amazon.The rest paper is organized follows. Section 2 introduces offline metrics used algorithm evaluation. Section 3 details NN model development procedure including how different methods are compared. Section 4 provides extensive offline evaluation results conjunction model property exploration. Section 5 presents how to run NN model production describes on-line/B test. Finally section 6 presents conclusions. described personalized neural network based recommender system which was launched production categories like eBooks Audible Apps Video. are currently working expand-ing non-digital categories. showed splitting customer purchases history period input future period output models led good results production models use approach soft split which combines auto-encoder model future predictor model have applied time decay learnt convolutional layer defined parametrical function consumption event. captures importance recent activity combined soft split leads significant improvements offline metrics. demonstrated two layer neural networks are outperforming NN based approaches which are more complicated method public dataset MovieLens company's internal datasets. simplicity NN model can scale digital categories. observed significant KPI improvements online/B tests production. Finally open sourced deep learning library which supports multi gpu model parallel training allowsus train large models timely manner.There are around 6200 products movies purchased rated customers period time. Distribution customers sorted number purchases is shown FIG0 whereH c number purchases made customerc c customer index. shows 90 percent customers have less 400 purchases. Distribution products dataX are shown FIG0 where PX p P p number purchases productp input X output training data accordingly p product index. distributions have long tail:90 percent purchases are covered 1000 products. evaluation feed XY data models produce output scoresŶ. scores are sorted top K products are returned recommendations. sorting previous purchases products belonging dataXY selected customer are removed recommendations new products are recommended. recommendations are compared future purchases dataZ accuracy calculation. get testing input data XY testing output dataZ selecting customers who has at least two purchases period timedx. dyz least one purchase period time dyz. dz. are 921 customers who satisfy conditions. Purchases belonging datesdx. dyz assigned testing input dataXY belonging dyz. dz assigned testing output dataZ. Accuracy metrics predictor soft split fastXML models are presented FIG0. Predictor model has the same PCC@K soft split lower precision@K models have higher accuracy metrics fastXML. observe similar difference precision predictor model fastXML Figure. 3 fastXML has higher higher PCC@K results can be used approximation performance real implicit feedbacks purchase history section were using ratings converted implicit feedbacks.,1995,1355,640,0.023,1.472,2025/11/05 17:18:58,0.01,1.455,0.4423676012461057,721.761
"Deep Learning (DL) algorithms based on Generative Adversarial Network (GAN) have demonstrated great potentials in computer vision tasks such as image restoration. Despite the rapid development of image restoration algorithms using DL and GANs, image restoration for specific scenarios, such as medical image enhancement and super-resolved identity recognition, are still facing challenges. How to ensure visually realistic restoration while avoiding hallucination or mode- collapse? How to make sure the visually plausible results do not contain hallucinated features jeopardizing downstream tasks such as pathology identification and subject identification?
 Here we propose to resolve these challenges by coupling the GAN based image restoration framework with another task-specific network. With medical imaging restoration as an example, the proposed model conducts additional pathology recognition/classification task to ensure the preservation of detailed structures that are important to this task. Validated on multiple medical datasets, we demonstrate the proposed method leads to improved deep learning based image restoration while preserving the detailed structure and diagnostic features. Additionally, the trained task network show potentials to achieve super-human level performance in identifying pathology and diagnosis.
 Further validation on super-resolved identity recognition tasks also show that the proposed method can be generalized for diverse image restoration tasks. Image restoration is an essential computer vision task and a widely applied technique. Recently there are increasing interests and significant progresses in this area enabling more realistic image super-resolution BID6 ; BID17 ; ; BID2 ; BID43 BID39 , in-painting BID35 ; BID38 ; BID37 ; BID31 and denoising BID35 ; BID41 a) . With the development of image restoration technologies, various applications can be applied in different verticals to reach the unfulfilled needs.Among all the image restoration applications, restoration in medical imaging is one of the most challenging tasks. Image restoration in medical imaging is important and attractive, since it enables imaging in more desirable conditions, e.g. imaging with faster protocols BID29 , cheaper devices and lower radiation BID26 , etc. However, medical image restoration requires a tougher evaluation than restoring natural images. It does not only require sharper and visually realistic restoration, but also requires accurate image completion without altering any pathological features or affecting any diagnostic qualities/properties. Therefore medical image restoration can be a benchmark task for related image restoration techniques.Within this decade, image restoration technique has been rapidly growing by incorporating various prior information into solving the ill-posed inverse imaging task. The prior information evolves from using sparse representation assumption BID23 , enforcing low-rank analysis BID7 to more recently using deep learning based priors BID33 or models BID42 . However there are still several challenges and limitations for existing algorithms: 1) Pixel-wise losses for deep learning do not consider non-local structural information which leads to blurred and not visually plausible restoration BID17 .2) Generative Adversarial Network (GAN) BID11 based methods significantly improve the results to generate visually realistic restoration BID17 . However GANs ensure the consistency to a learned distribution but do not necessarily guarantee the visually plausible solution exactly matches the corresponding ground truth.3) It is still possible that hallucination or mode-collapses may happen while minimizing loss function designed in improved GAN frameworks BID10 , BID0 .4) The discriminator network regularizes on general image distribution and visual quality , but it does not consider what are the key characteristic features such as pathologies, contrasts and image identification that the model needs to preserve for restoring an image.These challenges are critical for vertical applications such as medical imaging and surveillance where not only the visual property but also the fidelity of the recovered details matters for key purposes of pathology or recognizing faces.To solve the problems and challenges for realistic and accurate image restoration, we propose the task-GAN which extends GAN based image restoration framework and includes 3 networks: a Generator, a Discriminator and a Task-specific Network. The new task-specific network predicts the pathology recognition or face identity from both the ground truth images and the restored images. It helps to regularize the training of generator and complement the adversarial loss of GAN to ensure the output images better approximate the ground truth images. Task-GAN both achieves realistic visual quality and preserves the important task-specific features/properties, which are related to the end goal for medical imaging restoration and super-resolution face restoration.The contribution of this work are:• We propose a Task Generative Adversarial Network framework (Task-GAN) to ensure both visually plausible and more accurate (medical/face) image restoration.• A Task Network and a task-driven loss are introduced to ensure the preservation of visual details important to the downstream tasks, and more importantly it regularizes the image restoration to be more accurate both quantitatively and qualitatively.• The method is validated on two in-vivo clinical medical imaging datasets across different modalities, including Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET). Additionally , the generalization of the proposed method is further evaluated on a super-resolution face restoration dataset.• Both quantitative and qualitative evaluations were conducted, including rigorous evaluation by human experts (radiologists) to ensure the image restoration quality and preservation of important visual features.• Results demonstrate the superiority of the proposed method in image restoration and also show the potential of applying the trained task network for super-human level automatic classification/diagnosis.• Theory behind the method is further discussed. More justification on how the proposed method improves GAN to approximate one-to-one mapping.The way of how the proposed Task-GAN improves the image restoration may lead to better model design for other applications. Results on in-vivo medical imaging datasets demonstrate the superior performance of the proposed algorithm on improved image restoration. The proposed task-GAN achieves this by coupling adversarial training with the training of the task-specific network. Detailed contribution of the task-GAN is explained in the figure 4.In comparison, the task of the image restoration is to learn a non-linear mapping from low-quality images in the measurement domain to its corresponding high-quality images in a different highquality domain containing visually realistic images. Shown in figure 4(a ), in addition, the recognition of image is a space separation of features/labels along different dimensions that can be orthogonal to the quality dimensions.In comparison, as is shown in FIG4 ( b), conventional learning strategy learns the image restoration task by regression, which may fail to generate realistic restoration. The learning is usually based on the minimization of an averaged distance penalty which ensures robustness but lead to unrealistic restoration such as blurring. Additionally, the averaged solution is also likely to be away from the distribution of visually plausible solutions that falls out of the high-quality image space as is shown in the figure.GAN-based approach on one hand overcomes this by further enforcing an adversarial loss with a Discriminator network which ensures to generate realistic restoration following the distribution of the target high-quality images. As the figure 4(c ) shows, the solution is no longer an simple average but pushed into the space of visually realistic high-quality images. However , on the other hand, the discriminator only regularizes the output samples to follow the distribution but ignores the inter-sample relationship. For example , it cannot avoid hallucinations or mode-collapse, where the restored images may be over-similar or undesirably add/remove important visual features. As is shown in the figure, the restored image can have a different label as the ground-truth which fails the purpose of image restoration. We can picture the hallucinations or mode-collapse as a ""shrinking"" of solution space.To avoid the possible mode-collapse and ensure a 1-to-1 mapping, various improved GAN models and cost functions have been proposed. For example, Cycle- GAN Zhu et al. (2017) incorporate a cyclic relationship to improve the mapping. However, cyclic relationship does not necessarily lead to exact mappings. The inter-sample relationship as well as the important feature labels can be swapped while still satisfying the cyclic relationship. The illustrating image can be found in the appendix. For example, in the figure, one task label is altered while the cyclic loss is not affected. This may lead to mode-collapse, or specifically a failed image restoration leading to misclassified pathology/normality for medical imaging applications. The consequences of the restoration errors can be huge for medical imaging applications since they can directly lead to mis-diagnosis or overdiagnosis. We can picture the mislabeling or mode-collapse as a ""twisting"" of solution space. This ""twisting"" maintains well within visually-plausible space, however severely changes the positioning around the decision boundary of task-label space. More details of the reasoning and visualization will be place in the appendix.Differently, task-GAN here regularizes both the inter-sample relationship and the sample-label relationship. As is shown in figure 4(d), accurate mapping can be generated with the mixed loss regularization:1 ) pixel-level supervision so the restored image is closer to the ground truth,2) Adversarial loss regularization so that the restored image is within the high-quality space consisting of visually realistic images 3) the task-specific loss that ensure the restored image still preserve the important feature of interests, aka the same labels. In other words, the combination regularization enforce the solution to fall onto the intersection of the manifold preserving pixel-level similarity, distribution consistency and important visual labels. In the view of inter-sample relationship, the task regularization stop the inter-sample relationship to any visual plausible but destructive ""shrinking"" or ""twisting"" around the boundary of task-label space, which ensures more accurate mappings. In this paper, we proposed an improved design of GAN, Task-GAN, which includes a new taskspecific network and corresponding task-specific loss for training GAN based image restoration. Task-GAN is demonstrated to boost the performance of image restoration while preserving important features. Medical imaging applications are used as primary examples, which is one of the most challenging restoration applications since it requires not only realistic restoration, but also high-fidelity as well as accurate classification for subtle diagnostic features. Super-resolution face restoration is used to show the proposed method generalize to natural image applications such as super-resolving face images, where face identity need to be preserved.The proposed method is demonstrated to achieve superior performance compared with GAN on both image quality metrics and task-specific feature preservation (e.g. pathological features, face identity features, etc.). Based on visual inspection from human experts (clinicians/radiologists), anatomical and diagnostic features are preserved better and fewer artifacts are introduced. The trained task network also shows potentials for super-human level diagnosis tasks.Task-GAN further extends the regularization of adversarial training. The mixed loss balances between content similarity, distribution consistency and preserving important features for the given tasks. It results in more accurate image restoration with better visual similarity and avoids modecollapse and hallucinations. Intuitively, task-GAN enforces the solution fall into proper manifold, prevents any alternation (""shrinking"" and ""twisting"") of the restoration from the correct solution space, and preserves both inter-sample relationship and feature-of-interest.In the future, we will explore further improvements in the design of networks and task formulation. The proposed technique is also valuable to other challenging restoration applications that require realistic restoration and preserving distinguishable details for down-stream tasks.","Deep Learning DL algorithms based Generative Adversarial Network GAN have demonstrated great potentials computer vision tasks image restoration. Despite rapid development image restoration algorithms using DL GANs image restoration specific scenarios medical image enhancement super-resolved identity recognition are still facing challenges. How to ensure visually realistic restoration avoiding hallucination mode- collapse? How to make sure visually plausible results do not contain hallucinated features jeopardizing downstream tasks pathology identification subject identification? propose resolve challenges coupling GAN based image restoration framework another task-specific network. medical imaging restoration example proposed model conducts additional pathology recognition/classification task ensure preservation detailed structures are important task. Validated multiple medical datasets demonstrate proposed method leads improved deep learning based image restoration preserving detailed structure diagnostic features. Additionally trained task network show potentials achieve super-human level performance identifying pathology diagnosis. validation super-resolved identity recognition tasks also show proposed method can be generalized diverse image restoration tasks. Image restoration is an essential computer vision task widely applied technique. Recently are increasing interests significant progresses area enabling realistic image super-resolution BID6;BID17;BID2;BID43 BID39 in-painting BID35;BID38;BID37;BID31 denoising BID35;BID41 development image restoration technologies various applications can be applied different verticals reach unfulfilled needs.Among image restoration applications restoration medical imaging is one challenging tasks. Image restoration medical imaging is important attractive since enables imaging desirable conditions e.g imaging faster protocols BID29 cheaper devices lower radiation BID26 etc. However medical image restoration requires tougher evaluation restoring natural images. does not only require sharper visually realistic restoration also requires accurate image completion without altering pathological features affecting diagnostic qualities/properties. Therefore medical image restoration can be a benchmark task related image restoration techniques.Within decade image restoration technique has been rapidly growing incorporating various prior information solving ill-posed inverse imaging task. prior information evolves using sparse representation assumption BID23 enforcing low-rank analysis BID7 recently using deep learning based priors BID33 models BID42. However are still several challenges limitations existing algorithms:1 Pixel-wise losses deep learning do not consider non-local structural information which leads blurred visually plausible restoration BID17 .2 Generative Adversarial Network GAN BID11 based methods significantly improve results generate visually realistic restoration BID17. However GANs ensure consistency learned distribution do not necessarily guarantee visually plausible solution exactly matches corresponding ground truth.3 is still possible hallucination mode-collapses may happen minimizing loss function designed improved GAN frameworks BID10 BID0.4 discriminator network regularizes general image distribution visual quality does consider what are the key characteristic features pathologies contrasts image identification model needs preserve restoring image.These challenges are critical vertical applications medical imaging surveillance where not only the visual property also fidelity recovered details matters key purposes pathology recognizing faces.To solve problems challenges realistic accurate image restoration propose task-GAN which extends GAN based image restoration framework includes 3 networks:Generator Discriminator Task-specific Network. new task-specific network predicts pathology recognition face identity ground truth images restored images. helps regularize training generator complement adversarial loss GAN ensure output images better approximate ground truth images. Task-GAN achieves realistic visual quality preserves important task-specific features/properties which are related end goal medical imaging restoration super-resolution face restoration.The contribution work are:• propose Task Generative Adversarial Network framework Task-GAN ensure visually plausible accurate medical/face image restoration.• Task Network task-driven loss are introduced ensure preservation visual details important downstream tasks importantly regularizes image restoration accurate quantitatively qualitatively.• method is validated two in-vivo clinical medical imaging datasets across different modalities including Magnetic Resonance Imaging MRI Positron Emission Tomography PET Additionally generalization how the proposed method is further evaluated super-resolution face restoration dataset.• quantitative qualitative evaluations were conducted including rigorous evaluation human experts radiologists ensure image restoration quality preservation important visual features.• Results demonstrate superiority how the proposed method image restoration also show potential applying trained task network super-human level automatic classification/diagnosis.• Theory behind method is further discussed. justification how the proposed method improves GAN approximate one-to-one mapping.The way how the proposed Task-GAN improves image restoration may lead better model design applications. Results in-vivo medical imaging datasets demonstrate superior performance how the proposed algorithm improved image restoration. proposed task-GAN achieves coupling adversarial training training task-specific network. Detailed contribution task-GAN is explained figure 4.In comparison task image restoration is to learn non-linear mapping low-quality images measurement domain corresponding high-quality images different highquality domain containing visually realistic images. Shown figure4 addition recognition image is a space separation features/labels along different dimensions can be orthogonal quality dimensions.In comparison is shown FIG4 b conventional learning strategy learns image restoration task regression may fail generate realistic restoration. learning is usually based minimization averaged distance penalty which ensures robustness lead unrealistic restoration blurring. Additionally averaged solution is also likely away distribution visually plausible solutions falls high-quality image space is shown figure.GAN-based approach one hand overcomes enforcing adversarial loss Discriminator network which ensures generate realistic restoration following distribution target high-quality images. figure4 c shows solution is no longer simple average pushed space visually realistic high-quality images. However hand discriminator regularizes output samples follow distribution ignores inter-sample relationship. example cannot avoid hallucinations mode-collapse where the restored images may over-similar undesirably add/remove important visual features. is shown figure where the restored image can have a different label ground-truth which fails purpose image restoration. can picture hallucinations mode-collapse shrinking solution space.To avoid possible mode-collapse ensure 1-to-1 mapping various improved GAN models cost functions have been proposed. example Cycle- GAN Zhuet al. 2017 incorporate cyclic relationship improve mapping. However cyclic relationship does not necessarily lead exact mappings. inter-sample relationship well important feature labels can be swapped still satisfying cyclic relationship. illustrating image can be found appendix. example figure which is one task label is altered cyclic loss is not affected. may lead mode-collapse specifically failed image restoration leading misclassified pathology/normality medical imaging applications. consequences restoration errors can be huge medical imaging applications since can directly lead mis-diagnosis overdiagnosis. can picture mislabeling mode-collapse twisting solution space. twisting maintains well within visually-plausible space however severely changes positioning around decision boundary task-label space. details reasoning visualization will be place appendix.Differently task-GAN regularizes inter-sample relationship sample-label relationship. is shown figure4 accurate mapping can be generated mixed loss regularization:1 pixel-level supervision restored image is closer ground truth,2 Adversarial loss regularization restored image is within high-quality space consisting visually realistic images3 task-specific loss ensure restored image still preserve important feature interests aka labels. words combination regularization enforce solution fall onto intersection manifold preserving pixel-level similarity distribution consistency important visual labels. view inter-sample relationship task regularization stop inter-sample relationship visual plausible destructive shrinking twisting around boundary task-label space which ensures accurate mappings. paper proposed improved design GAN Task-GAN which includes new taskspecific network corresponding task-specific loss training GAN based image restoration. Task-GAN is demonstrated boost performance image restoration preserving important features. Medical imaging applications are used primary examples which is one challenging restoration applications since requires realistic restoration also high-fidelity well accurate classification subtle diagnostic features. Super-resolution face restoration is used show proposed method generalize natural image applications super-resolving face images where face identity need preserved.The proposed method is demonstrated achieve superior performance compared GAN image quality metrics task-specific feature preservation e.g pathological features where face identity features etc. Based visual inspection human experts clinicians/radiologists anatomical diagnostic features are preserved better fewer artifacts are introduced. trained task network also shows potentials super-human level diagnosis tasks.Task-GAN extends regularization adversarial training. mixed loss balances content similarity distribution consistency preserving important features given tasks. results accurate image restoration better visual similarity avoids modecollapse hallucinations. Intuitively task-GAN enforces solution fall proper manifold prevents alternation shrinking twisting restoration correct solution space preserves inter-sample relationship feature-of-interest.In future will explore improvements design networks task formulation. proposed technique is also valuable challenging restoration applications require realistic restoration preserving distinguishable details down-stream tasks.",2247,1612,635,0.025,1.394,2025/11/05 17:18:58,0.01,1.565,0.1993769470404979,747.029
"Unsupervised anomaly detection on multi- or high-dimensional data is of great importance in both fundamental machine learning research and industrial applications, for which density estimation lies at the core. Although previous approaches based on dimensionality reduction followed by density estimation have made fruitful progress, they mainly suffer from decoupled model learning with inconsistent optimization goals and incapability of preserving essential information in the low-dimensional space. In this paper, we present a Deep Autoencoding Gaussian Mixture Model (DAGMM) for unsupervised anomaly detection. Our model utilizes a deep autoencoder to generate a low-dimensional representation and reconstruction error for each input data point, which is further fed into a Gaussian Mixture Model (GMM). Instead of using decoupled two-stage training and the standard Expectation-Maximization (EM) algorithm, DAGMM jointly optimizes the parameters of the deep autoencoder and the mixture model simultaneously in an end-to-end fashion, leveraging a separate estimation network to facilitate the parameter learning of the mixture model. The joint optimization, which well balances autoencoding reconstruction, density estimation of latent representation, and regularization, helps the autoencoder escape from less attractive local optima and further reduce reconstruction errors, avoiding the need of pre-training. Experimental results on several public benchmark datasets show that, DAGMM significantly outperforms state-of-the-art anomaly detection techniques, and achieves up to 14% improvement based on the standard F1 score. Unsupervised anomaly detection is a fundamental problem in machine learning, with critical applications in many areas, such as cybersecurity BID18 ), complex system management BID14 ), medical care BID10 ), and so on. At the core of anomaly detection is density estimation: given a lot of input samples, anomalies are those ones residing in low probability density areas.Although fruitful progress has been made in the last several years, conducting robust anomaly detection on multi-or high-dimensional data without human supervision remains a challenging task. Especially, when the dimensionality of input data becomes higher, it is more difficult to perform density estimation in the original feature space, as any input sample could be a rare event with low probability to observe BID3 ). To address this issue caused by the curse of dimensionality, two-step approaches are widely adopted BID2 ), in which dimensionality reduction is first conducted, and then density estimation is performed in the latent low-dimensional space. However, these approaches could easily lead to suboptimal performance, because dimensionality reduction in the first step is unaware of the subsequent density estimation task, and the key information for anomaly detection could be removed in the first place. Therefore, it is desirable to combine the force of dimensionality reduction and density estimation, although a joint optimization accounting for these two components is usually computationally difficult. Several recent works BID29 ; BID26 ; BID24 ) explored this direction by utilizing the strong modeling capacity of deep networks, but the resulting performance is limited either by a reduced low-dimensional space that is unable to preserve essential information of input samples, an over-simplified density estimation model without enough capacity, or a training strategy that does not fit density estimation tasks.Figure 1: Low-dimensional representations for samples from a private cybersecurity dataset: (1) each sample denotes a network flow that originally has 20 dimensions, (2) red/blue points are abnormal/normal samples, (3) the horizontal axis denotes the reduced 1-dimensional space learned by a deep autoencoder, and (4) the vertical axis denotes the reconstruction error induced by the 1-dimensional representation.In this paper, we propose Deep Autoencoding Gaussian Mixture Model (DAGMM), a deep learning framework that addresses the aforementioned challenges in unsupervised anomaly detection from several aspects.First, DAGMM preserves the key information of an input sample in a low-dimensional space that includes features from both the reduced dimensions discovered by dimensionality reduction and the induced reconstruction error. From the example shown in Figure 1 , we can see that anomalies differ from normal samples in two aspects: (1) anomalies can be significantly deviated in the reduced dimensions where their features are correlated in a different way; and (2) anomalies are harder to reconstruct, compared with normal samples. Unlike existing methods that only involve one of the aspects BID32 ; BID29 ) with sub-optimal performance, DAGMM utilizes a sub-network called compression network to perform dimensionality reduction by an autoencoder, which prepares a low-dimensional representation for an input sample by concatenating reduced low-dimensional features from encoding and the reconstruction error from decoding.Second, DAGMM leverages a Gaussian Mixture Model (GMM) over the learned low-dimensional space to deal with density estimation tasks for input data with complex structures, which are yet rather difficult for simple models used in existing works BID29 ). While GMM has strong capability, it also introduces new challenges in model learning. As GMM is usually learned by alternating algorithms such as Expectation-Maximization (EM) (Huber (2011)), it is hard to perform joint optimization of dimensionality reduction and density estimation favoring GMM learning, which is often degenerated into a conventional two-step approach. To address this training challenge, DAGMM utilizes a sub-network called estimation network that takes the low-dimensional input from the compression network and outputs mixture membership prediction for each sample. With the predicted sample membership, we can directly estimate the parameters of GMM, facilitating the evaluation of the energy/likelihood of input samples. By simultaneously minimizing reconstruction error from compression network and sample energy from estimation network, we can jointly train a dimensionality reduction component that directly helps the targeted density estimation task.Finally, DAGMM is friendly to end-to-end training. Usually, it is hard to learn deep autoencoders by end-to-end training, as they can be easily stuck in less attractive local optima, so pre-training is widely adopted BID22 ; BID26 ; BID24 ). However, pre-training limits the potential to adjust the dimensionality reduction behavior because it is hard to make any significant change to a well-trained autoencoder via fine-tuning. Our empirical study demonstrates that, DAGMM is well-learned by the end-to-end training, as the regularization introduced by the estimation network greatly helps the autoencoder in the compression network escape from less attractive local optima.Experiments on several public benchmark datasets demonstrate that, DAGMM has superior performance over state-of-the-art techniques, with up to 14% improvement of F1 score for anomaly detection. Moreover, we observe that the reconstruction error from the autoencoder in DAGMM by the end-to-end training is as low as the one made by its pre-trained counterpart, while the reconstruction error from an autoencoder without the regularization from the estimation network stays high. In addition, the end-to-end trained DAGMM significantly outperforms all the baseline methods that rely on pre-trained autoencoders. In this paper, we propose the Deep Autoencoding Gaussian Mixture Model (DAGMM) for unsupervised anomaly detection. DAGMM consists of two major components: compression network and estimation network, where the compression network projects samples into a low-dimensional space that preserves the key information for anomaly detection, and the estimation network evaluates sample energy in the low-dimensional space under the framework of Gaussian Mixture Modeling. DAGMM is friendly to end-to-end training: (1) the estimation network predicts sample mixture membership so that the parameters in GMM can be estimated without alternating procedures; and (2) the regularization introduced by the estimation network helps the compression network escape from less attractive local optima and achieve low reconstruction error by end-to-end training. Compared with the pre-training strategy, the end-to-end training could be more beneficial for density estimation tasks, as we can have more freedom to adjust dimensionality reduction processes to favor the subsequent density estimation tasks. In the experimental study, DAGMM demonstrates superior performance over state-of-the-art techniques on public benchmark datasets with up to 14% improvement on the standard F 1 score, and suggests a promising direction for unsupervised anomaly detection on multior high-dimensional data.A BASELINE CONFIGURATION OC-SVM. Unlike other baselines that only need decision thresholds in the testing phase, OC-SVM needs parameter ν be set in the training phase. Although ν intuitively means anomaly ratio in training data, it is non-trivial to set a reasonable ν in the case where training data are all normal samples and anomaly ratio in the testing phase could be arbitrary. In this study, we simply perform exhaustive search to find the optimal ν that renders the highest F 1 score on individual datasets. In particular, ν is set to be 0.1, 0.02, 0.04, and 0.1 for KDDCUP, Thyroid, Arrhythmia, and KDDCUP-Rev, respectively.DSEBM. We use the network structure for the encoding in DAGMM as guidelines to set up DSEBM instances. For KDDCUP and KDDCUP-Rev, it is configured as FC FORMULA0",Unsupervised anomaly detection multi- high-dimensional data is of great importance fundamental machine learning research industrial applications which density estimation lies core. Although previous approaches based dimensionality reduction followed density estimation have made fruitful progress mainly suffer decoupled model learning inconsistent optimization goals incapability preserving essential information low-dimensional space. paper present Deep Autoencoding Gaussian Mixture Model DAGMM unsupervised anomaly detection. model utilizes deep autoencoder generate low-dimensional representation reconstruction error input data point which is further fed Gaussian Mixture Model GMM Instead using decoupled two-stage training standard Expectation-Maximization EM algorithm DAGMM jointly optimizes parameters deep autoencoder mixture model simultaneously end-to-end fashion leveraging separate estimation network facilitate parameter learning mixture model. joint optimization which well balances autoencoding reconstruction which density estimation latent representation regularization helps autoencoder escape less attractive local optima reduce reconstruction errors avoiding need pre-training Experimental results several public benchmark datasets show DAGMM significantly outperforms state-of-the-art anomaly detection techniques achieves 14% improvement based standard F1 score. Unsupervised anomaly detection is a fundamental problem machine learning critical applications many areas cybersecurity BID18 complex system management BID14 medical care BID10 on. core anomaly detection is density estimation:given lot input samples anomalies are those ones residing low probability density areas.Although fruitful progress has been made last several years conducting robust anomaly detection multi-or high-dimensional data without human supervision remains challenging task. Especially when the dimensionality input data becomes higher is more difficult perform density estimation original feature space input sample could rare event low probability observe BID3 address issue caused curse dimensionality two-step approaches are widely adopted BID2 which dimensionality reduction is first conducted which density estimation is performed latent low-dimensional space. However approaches could easily lead suboptimal performance when the dimensionality reduction first step is unaware subsequent density estimation task key information anomaly detection could removed first place. Therefore is desirable combine force dimensionality reduction density estimation although joint optimization accounting two components is usually computationally difficult. Several recent works BID29;BID26;BID24 explored direction utilizing strong modeling capacity deep networks resulting performance is limited either reduced low-dimensional space is unable preserve essential information input samples over-simplified density estimation model without enough capacity training strategy does not fit density estimation tasks.Figure 1:Low-dimensional representations samples private cybersecurity dataset:1 sample denotes network flow originally has 20 dimensions 2 red/blue points are abnormal/normal samples 3 horizontal axis denotes reduced 1-dimensional space learned deep autoencoder 4 vertical axis denotes reconstruction error induced 1-dimensional representation.In paper propose Deep Autoencoding Gaussian Mixture Model DAGMM deep learning framework addresses aforementioned challenges unsupervised anomaly detection several aspects.First DAGMM preserves key information input sample low-dimensional space includes features reduced dimensions discovered dimensionality reduction induced reconstruction error. example shown Figure1 can see anomalies differ normal samples two aspects:1 anomalies can be significantly deviated reduced dimensions where their features are correlated different way;2 anomalies are harder reconstruct compared normal samples. Unlike existing methods involve one aspects BID32;BID29 sub-optimal performance DAGMM utilizes sub-network called compression network perform dimensionality reduction autoencoder which prepares low-dimensional representation input sample concatenating reduced low-dimensional features encoding reconstruction error decoding.Second DAGMM leverages Gaussian Mixture Model GMM learned low-dimensional space deal density estimation tasks input data complex structures which are yet rather difficult simple models used existing works BID29 GMM has strong capability also introduces new challenges model learning. GMM is usually learned alternating algorithms Expectation-Maximization EM Huber 2011 is hard perform joint optimization dimensionality reduction density estimation favoring GMM learning which is often degenerated conventional two-step approach. address training challenge DAGMM utilizes sub-network called estimation network takes low-dimensional input compression network outputs mixture membership prediction sample. predicted sample membership can directly estimate parameters GMM facilitating evaluation energy/likelihood input samples. simultaneously minimizing reconstruction error compression network sample energy estimation network can jointly train dimensionality reduction component directly helps targeted density estimation task.Finally DAGMM is friendly end-to-end training. Usually is hard learn deep autoencoders end-to-end training can easily stuck less attractive local optima pre-training is widely adopted BID22;BID26;BID24 However pre-training limits potential adjust dimensionality reduction behavior is hard make significant change well-trained autoencoder via fine-tuning empirical study demonstrates DAGMM is well-learned end-to-end training regularization introduced estimation network greatly helps autoencoder compression network escape less attractive local optima.Experiments several public benchmark datasets demonstrate DAGMM has superior performance state-of-the-art techniques 14% improvement F1 score anomaly detection. Moreover observe reconstruction error autoencoder DAGMM end-to-end training is as low one made pre-trained counterpart reconstruction error autoencoder without regularization estimation network stays high. addition end-to-end trained DAGMM significantly outperforms baseline methods rely pre-trained autoencoders. paper propose Deep Autoencoding Gaussian Mixture Model DAGMM unsupervised anomaly detection. DAGMM consists two major components:compression network estimation network where the compression network projects samples low-dimensional space preserves key information anomaly detection estimation network evaluates sample energy low-dimensional space framework Gaussian Mixture Modeling. DAGMM is friendly end-to-end training:1 estimation network predicts sample mixture membership parameters GMM can be estimated without alternating procedures;2 regularization introduced estimation network helps compression network escape less attractive local optima achieve low reconstruction error end-to-end training. Compared pre-training strategy end-to-end training could beneficial density estimation tasks can have more freedom adjust dimensionality reduction processes favor subsequent density estimation tasks. experimental study DAGMM demonstrates superior performance state-of-the-art techniques public benchmark datasets 14% improvement standard F 1 score suggests promising direction unsupervised anomaly detection multior high-dimensional data.A BASELINE CONFIGURATION OC-SVM Unlike baselines need decision thresholds testing phase OC-SVM needs parameterν set training phase. Although ν intuitively means anomaly ratio training data is non-trivial set reasonableν case where training data are all normal samples anomaly ratio testing phase could arbitrary. study simply perform exhaustive search find optimalν renders highest F 1 score individual datasets. particular ν is set 0.1 0.02 0.04 0.1 KDDCUP Thyroid Arrhythmia KDDCUP-Rev respectively.DSEBM. use network structure encoding DAGMM guidelines set DSEBM instances. KDDCUP KDDCUP-Rev is configured FC FORMULA0,1815,1287,528,0.019,1.41,2025/11/05 17:18:58,0.01,1.346,0.2492211838006226,517.614
"Generalization from limited examples, usually studied under the umbrella of meta-learning, equips learning techniques with the ability to adapt quickly in dynamical environments and proves to be an essential aspect of lifelong learning. In this paper, we introduce the Projective Subspace Networks (PSN), a deep learning paradigm that learns non-linear embeddings from limited supervision. In contrast to previous studies, the embedding in PSN deems samples of a given class to form an affine subspace. We will show that such modeling leads to robust solutions, yielding competitive results on supervised and semi-supervised few-shot classification. Moreover, our PSN approach has the ability of end-to-end learning. In contrast to previous works, our projective subspace can be thought of as a richer representation capturing higher-order information datapoints for modeling new concepts.",Generalization limited examples usually studied umbrella meta-learning equips learning techniques ability adapt quickly dynamical environments proves essential aspect lifelong learning. paper introduce Projective Subspace Networks PSN deep learning paradigm learns non-linear embeddings limited supervision. contrast previous studies embedding PSN deems samples given class form affine subspace. will show modeling leads robust solutions yielding competitive results supervised semi-supervised few-shot classification. Moreover PSN approach has the ability end-to-end learning. contrast previous works projective subspace can be thought richer representation capturing higher-order information datapoints modeling new concepts.,162,110,52,0.002,1.473,2025/11/05 17:18:58,0.0,1.667,0.4454828660436138,67.825
"This paper investigates whether learning contingency-awareness and controllable aspects of an environment can lead to better exploration in reinforcement learning. To investigate this question, we consider an instantiation of this hypothesis evaluated on the Arcade Learning Element (ALE). In this study, we develop an attentive dynamics model (ADM) that discovers controllable elements of the observations, which are often associated with the location of the character in Atari games. The ADM is trained in a self-supervised fashion to predict the actions taken by the agent. The learned contingency information is used as a part of the state representation for exploration purposes. We demonstrate that combining actor-critic algorithm with count-based exploration using our representation achieves impressive results on a set of notoriously challenging Atari games due to sparse rewards. For example, we report a state-of-the-art score of >11,000 points on Montezuma's Revenge without using expert demonstrations, explicit high-level information (e.g., RAM states), or supervisory data. Our experiments confirm that contingency-awareness is indeed an extremely powerful concept for tackling exploration problems in reinforcement learning and opens up interesting research questions for further investigations. The success of reinforcement learning (RL) algorithms in complex environments hinges on the way they balance exploration and exploitation. There has been a surge of recent interest in developing effective exploration strategies for problems with high-dimensional state spaces and sparse rewards BID8 Oudeyer & Kaplan, 2009; Houthooft et al., 2016; Bellemare et al., 2016; Osband et al., 2016; Pathak et al., 2017; BID5 BID16 . Deep neural networks have seen great success as expressive function approximators within RL and as powerful representation learning methods for many domains. In addition, there have been recent studies on using neural network representations for exploration BID13 Martin et al., 2017; Pathak et al., 2017) . For example, count-based exploration with neural density estimation (Bellemare et al., 2016; BID13 Ostrovski et al., 2017) presents one of the state-of-the-art techniques on the most challenging Atari games with sparse rewards.Despite the success of recent exploration methods, it is still an open question on how to construct an optimal representation for exploration. For example, the concept of visual similarity is used for learning density models as a basis for calculating pseudo-counts (Bellemare et al., 2016; Ostrovski et al., 2017) . However, as BID13 noted, the ideal way to represent states should be based on what is relevant to solving the MDP, rather than only relying on visual similarity. In addition, there remains another question on whether the representations used for recent exploration works are easily interpretable. To address these questions, we investigate whether we can learn a complementary, more intuitive, and interpretable high-level abstraction that can be very effective in exploration by using the ideas of contingency awareness and controllable dynamics.The key idea that we focus on in this work is the notion of contingency awareness BID14 Bellemare et al., 2012) -the agent's understanding of the environmental dynamics and recognizing that some aspects of the dynamics are under the agent's control. Intuitively speaking, this can represent the segmentation mask of the agent operating in the 2D or 3D environments (yet one can think of more abstract and general state spaces). In this study, we investigate the concept of contingency awareness based on self-localization, i.e., the awareness of where the agent is located in the abstract state space. We are interested in discovering parts of the world that are directly dependent on the agent's immediate action, which often reveal the agent's approximate location.For further motivation on the problem, we note that contingency awareness is a very important concept in neuroscience and psychology. In other words, being self-aware of one's location is an important property within many observed intelligent organisms and systems. For example, recent breakthroughs in neuroscience, such as the Nobel Prize winning work on the grid cells (Moser et al., 2015; BID4 , show that organisms that perform very well in spatially-challenging tasks are self-aware of their location. This allows rats to navigate, remember paths to previously visited places and important sub-goals, and find shortcuts. In addition, the notion of contingency awareness has been shown as an important factor in developmental psychology BID14 BID2 . We can think of self-localization (and more broadly self-awareness) as a principled and fundamental direction towards intelligent agents.Based on these discussions, we hypothesize that contingency awareness can be a powerful mechanism for tackling exploration problems in reinforcement learning. We consider an instantiation of this hypothesis evaluated on the Arcade Learning Element (ALE). For example, in the context of 2D Atari games, contingency-awareness roughly corresponds to understanding the notion of controllable entities (e.g., the player's avatar), which Bellemare et al. (2012) refer to as contingent regions. More concretely, as shown in FIG0 , in the game FREEWAY, only the chicken sprite is under the agent's control and not the multiple moving cars; therefore the chicken's location should be an informative element for exploration (Bellemare et al., 2012; Pathak et al., 2017) .In this study, we also investigate whether contingency awareness can be learned without any external annotations or supervision. For this, we provide an instantiation of an algorithm for automatically learning such information and using it for improving exploration on a 2D ALE environment (Bellemare et al., 2013) . Concretely , we employ an attentive dynamics model (ADM) to predict the agent's action chosen between consecutive states. It allows us to approximate the agent's position in 2D environments, but unlike other approaches such as (Bellemare et al., 2012) , it does not require any additional supervision to do so. The ADM learns in an online and self-supervised fashion with pure observations as the agent's policy is updated and does not require hand-crafted features, an environment simulator, or supervision labels for training.In experimental evaluation, our methods significantly improve the performance of A2C on hardexploration Atari games in comparison with competitive methods such as density-based exploration (Bellemare et al., 2016; Ostrovski et al., 2017) and SimHash BID13 . We report very strong results on sparse-reward Atari games, including the state-of-the-art performance on the notoriously difficult MONTEZUMA'S REVENGE, when combining our proposed exploration strategy with PPO , without using expert demonstrations, explicit high-level information (e.g., RAM states), or resetting the environment to an arbitrary state.We summarize our contributions as follows:• We demonstrate the importance of learning contingency awareness for efficient exploration in challenging sparse-reward RL problems.• We develop a novel instance of attentive dynamics model using contingency and controllable dynamics to provide robust localization abilities across the most challenging Atari environments.• We achieve a strong performance on difficult sparse-reward Atari games, including the state-ofthe-art score on the notoriously challenging MONTEZUMA'S REVENGE.Overall, we believe that our experiments confirm the hypothesis that contingency awareness is an extremely powerful concept for tackling exploration problems in reinforcement learning, which opens up interesting research questions for further investigations. This paper investigates whether discovering controllable dynamics via an attentive dynamics model (ADM) can help exploration in challenging sparse-reward environments. We demonstrate the effectiveness of this approach by achieving significant improvements on notoriously difficult video games. That being said, we acknowledge that our approach has certain limitations. Our currently presented instance of state abstraction method mainly focuses on controllable dynamics and employs a simple clustering scheme to abstract away uncontrollable elements of the scene. In more general setting, one can imagine using attentive (forward or inverse) dynamics models to learn an effective and compact abstraction of the controllable and uncontrollable dynamics as well, but we leave this to future work.Key elements of the current ADM method include the use of spatial attention and modelling of the dynamics. These ideas can be generalized by a set of attention-based dynamics models (ADM) operating in forward, inverse, or combined mode. Such models could use attention over a lowerdimensional embedding that corresponds to an intrinsic manifold structure from the environment (i.e., intuitively speaking, this also corresponds to being self-aware of (e.g., locating) where the agent is in the abstract state space). Our experiments with the inverse dynamics model suggest that the mechanism does not have to be perfectly precise, allowing for some error in practice. We speculate that mapping to such subspace could be obtained by techniques of embedding learning.We note that RL environments with different visual characteristics may require different forms of attention-based techniques and properties of the model (e.g., partial observability). Even though this paper focuses on 2D video games, we believe that the presented high-level ideas of learning contingency-awareness (with attention and dynamics models) are more general and could be applicable to more complex 3D environments with some extension. We leave this as future work. We proposed a method of providing contingency-awareness through an attentive dynamics model (ADM). It enables approximate self-localization for an RL agent in 2D environments (as a specific perspective). The agent is able to estimate its position in the space and therefore benefits from a compact and informative representation of the world. This idea combined with a variant of countbased exploration achieves strong results in various sparse-reward Atari games. Furthermore, we report state-of-the-art results of >11,000 points on the infamously challenging MONTEZUMA'S REVENGE without using expert demonstrations or supervision. Though in this work we focus mostly on 2D environments in the form of sparse-reward Atari games, we view our presented high-level concept and approach as a stepping stone towards more universal algorithms capable of similar abilities in various RL environments. DISPLAYFORM0 Perform actor-critic using on-policy samples in E θ A2C ← θ A2C − η∇ θA2C L","paper investigates whether learning contingency-awareness controllable aspects environment can lead better exploration reinforcement learning. investigate question consider instantiation hypothesis evaluated Arcade Learning Element ALE study develop attentive dynamics model ADM discovers controllable elements observations which are which often associated location character Atari games. ADM is trained self-supervised fashion predict actions taken agent. learned contingency information is used part state representation exploration purposes. demonstrate combining actor-critic algorithm count-based exploration using representation achieves impressive results set notoriously challenging Atari games due sparse rewards. example report state-of-the-art score 11,000 points Montezuma's Revenge without using expert demonstrations explicit high-level information e.g RAM states supervisory data. experiments confirm contingency-awareness is indeed extremely powerful concept tackling exploration problems reinforcement learning opens interesting research questions investigations. success reinforcement learning RL algorithms complex environments hinges way balance exploration exploitation. has been a surge recent interest developing effective exploration strategies problems high-dimensional state spaces sparse rewards BID8 Oudeyer Kaplan 2009;Houthooftetal. 2016;Bellemareetal. 2016;Osbandetal. 2016;Pathaketal. 2017;BID5 BID16. Deep neural networks have seen great success expressive function approximators within RL powerful representation learning methods many domains. addition have been recent studies using neural network representations exploration BID13 Martinet al. 2017;Pathaketal. 2017 example count-based exploration neural density estimation Bellemareetal. 2016;BID13 Ostrovskietal. 2017 presents one state-of-the-art techniques challenging Atari games sparse rewards.Despite success recent exploration methods is still open question how to construct optimal representation exploration. example concept visual similarity is used learning density models basis calculating pseudo-counts Bellemareetal. 2016;Ostrovskietal. 2017 However BID13 noted ideal way represent states should be based what is relevant solving MDP rather relying visual similarity. addition remains another question whether representations used recent exploration works are easily interpretable. address questions investigate whether can learn complementary intuitive interpretable high-level abstraction can be very effective exploration using ideas contingency awareness controllable dynamics.The key idea focus work is the notion contingency awareness BID14 Bellemare etal. 2012 -the agent's understanding environmental dynamics recognizing aspects dynamics are under the agent's control. Intuitively speaking can represent segmentation mask where the agent operating 2D 3D environments yet one can think abstract general state spaces study investigate concept contingency awareness based self-localization.e awareness where the agent is located abstract state space. are interested discovering parts world are directly dependent agent's immediate action which are which often reveal agent's approximate location.For motivation problem note contingency awareness is a very is an important concept neuroscience psychology. words self-aware one's location is a very is an important property within many observed intelligent organisms systems. example have been recent breakthroughs neuroscience Nobel Prize winning work grid cells Moseretal. 2015;BID4 show organisms perform well spatially-challenging tasks are self-aware location. allows rats navigate remember paths previously visited places important sub-goals find shortcuts. addition notion contingency awareness has been shown important factor developmental psychology BID14 BID2. can think self-localization broadly self-awareness principled fundamental direction towards intelligent agents.Based discussions hypothesize contingency awareness can be a powerful mechanism tackling exploration problems reinforcement learning. consider instantiation hypothesis evaluated Arcade Learning Element ALE example context 2D Atari games contingency-awareness roughly corresponds understanding notion controllable entities e.g player's avatar which Bellemareetal. 2012 refer contingent regions. concretely shown FIG0 game FREEWAY chicken sprite is under the agent's control multiple moving cars;therefore chicken's location should be an informative element exploration Bellemareetal. 2012;Pathaketal. 2017.In study also investigate whether contingency awareness can be learned without external annotations supervision. provide instantiation algorithm automatically learning information using improving exploration 2D ALE environment Bellemareetal. 2013 Concretely employ attentive dynamics model ADM predict agent's action chosen consecutive states. allowsus approximate agent's position 2D environments unlike approaches Bellemareetal. 2012 does require additional supervision doso. ADM learns online self-supervised fashion pure observations agent's policy is updated does not require hand-crafted features environment simulator supervision labels training.In experimental evaluation methods significantly improve performance A2C hardexploration Atari games comparison competitive methods density-based exploration Bellemareetal. 2016;Ostrovskietal. 2017 SimHash BID13. report strong results sparse-reward Atari games including state-of-the-art performance notoriously difficult MONTEZUMA'S REVENGE when combining proposed exploration strategy PPO without using expert demonstrations explicit high-level information e.g RAM states resetting environment arbitrary state.We summarize contributions follows:• demonstrate importance learning contingency awareness efficient exploration challenging sparse-reward RL problems.• develop novel instance attentive dynamics model using contingency controllable dynamics provide robust localization abilities across challenging Atari environments.• achieve strong performance difficult sparse-reward Atari games including state-ofthe-art score notoriously challenging MONTEZUMA'S REVENGE.Overall believe experiments confirm hypothesis contingency awareness is an extremely powerful concept tackling exploration problems reinforcement learning which opens interesting research questions investigations. paper investigates whether discovering controllable dynamics via attentive dynamics model ADM can help exploration challenging sparse-reward environments. demonstrate effectiveness approach achieving significant improvements notoriously difficult video games. said acknowledge approach has certain limitations. currently presented instance state abstraction method mainly focuses controllable dynamics employs simple clustering scheme abstract away uncontrollable elements scene. general setting one can imagine using attentive forward inverse dynamics models learn effective compact abstraction controllable uncontrollable dynamics well leave future work.Key elements current ADM method include use spatial attention modelling dynamics. ideas can be generalized set attention-based dynamics models ADM operating forward inverse combined mode. models could use attention lowerdimensional embedding corresponds intrinsic manifold structure environment.e intuitively speaking also corresponds self-aware e.g locating where the agent is in the abstract state space experiments inverse dynamics model suggest mechanism does not haveto perfectly precise allowing error practice. speculate mapping subspace could obtained techniques embedding learning.We note RL environments different visual characteristics may require different forms attention-based techniques properties model e.g partial observability Even though paper focuses 2D video games believe presented high-level ideas learning contingency-awareness attention dynamics models are more general could applicable complex 3D environments extension. leave future work. proposed method providing contingency-awareness attentive dynamics model ADM enables approximate self-localization RL agent 2D environments specific perspective where the agent is able estimate position space therefore benefits compact informative representation world. idea combined variant countbased exploration achieves strong results various sparse-reward Atari games. Furthermore report state-of-the-art results 11,000 points infamously challenging MONTEZUMA'S REVENGE without using expert demonstrations supervision. Though work focus mostly 2D environments form sparse-reward Atari games view presented high-level concept approach stepping stone towards universal algorithms capable similar abilities various RL environments. DISPLAYFORM0 Perform actor-critic using on-policy samples E θ A2C← θ A2C−η∇ θA2CL",2025,1405,620,0.025,1.441,2025/11/05 17:18:58,0.01,1.68,0.3457943925233644,698.319
"Disentangling factors of variation has always been a challenging problem in representation learning. Existing algorithms suffer from many limitations, such as unpredictable disentangling factors, bad quality of generated images from encodings, lack of identity information, etc. In this paper, we proposed a supervised algorithm called DNA-GAN trying to disentangle different attributes of images. The latent representations of images are DNA-like, in which each individual piece represents an independent factor of variation. By annihilating the recessive piece and swapping a certain piece of two latent representations, we obtain another two different representations which could be decoded into images. In order to obtain realistic images and also disentangled representations, we introduced the discriminator for adversarial training. Experiments on Multi-PIE and CelebA datasets demonstrate the effectiveness of our method and the advantage of overcoming limitations existing in other methods. The success of machine learning algorithms depends on data representation, because different representations can entangle different explanatory factors of variation behind the data. Although prior knowledge can help us design representations, the vast demand of AI algorithms in various domains cannot be met, since feature engineering is labor-intensive and needs domain expert knowledge. Therefore, algorithms that can automatically learn good representations of data will definitely make it easier for people to extract useful information when building classifiers or predictors.Of all criteria of learning good representations as discussed in BID1 , disentangling factors of variation is an important one that helps separate various explanatory factors. For example, given a human-face image, we can obtain various information about the person, including gender, hair style, facial expression, with/without eyeglasses and so on. All of these information are entangled in a single image, which renders the difficulty of training a single classifier to handle different facial attributes. If we could obtain a disentangled representation of the face image, we may build up only one classifier for multiple attributes.In this paper, we propose a supervised method called DNA-GAN to obtain disentangled representations of images. The idea of DNA-GAN is motivated by the DNA double helix structure, in which different kinds of traits are encoded in different DNA pieces. We make a similar assumption that different visual attributes in an image are controlled by different pieces of encodings in its latent representations. In DNA-GAN, an encoder is used to encode an image to the attribute-relevant part and the attribute-irrelevant part, where different pieces in the attribute-relevant part encode information of different attributes, and the attribute-irrelevant part encodes other information. For example, given a facial image, we are trying to obtain a latent representation that each individual part controls different attributes, such as hairstyles, genders, expressions and so on. Though annihilating recessive pieces and swapping certain pieces, we can obtain novel crossbreeds that can be decoded into new images. By the adversarial discriminator loss and the reconstruction loss, DNA-GAN can reconstruct the input images and generate new images with new attributes. Each attribute is disentangled from others gradually though iterative training. Finally, we are able to obtain disentangled representations in the latent representations.The summary of contributions of our work is as follows:1. We propose a supervised algorithm called DNA-GAN, that is able to disentangle multiple attributes as demonstrated by the experiments of interpolating multiple attributes on Multi-PIE BID5 and CelebA BID12 datasets.2. We introduce the annihilating operation that prevents from trivial solutions: the attributerelevant part encodes information of the whole image instead of a certain attribute.3. We employ iterative training to address the problem of unbalanced multi-attribute image data, which was theoretically proved to be more efficient than random image pairs. In this paper, we propose a supervised algorithm called DNA-GAN that can learn disentangled representations from multi-attribute images. The latent representations of images are DNA-like, consisting of attribute-relevant and attribute-irrelevant parts. By the annihilating operation and attribute hybridization, we are able to create new latent representations which could be decoded into novel images with designed attributes. The iterative training strategy effectively overcomes the difficulty of training on unbalanced datasets and helps disentangle multiple attributes in the latent space.The experimental results not only demonstrate that DNA-GAN is effective in learning disentangled representations and image editing, but also point out its potential in interpretable deep learning, image understanding and transfer learning.There also exist some limitations of our model. Without strong guidance on the attribute-irrelevant parts, some background information is encoded into the attribute-relevant part. As we can see in FIG3 , the background color gets changed when swapping attributes. Besides, our model may fail when several attributes are highly correlated with each other. For example, Male and Mustache are statistically dependent, which are hard to disentangle in the latent representations. These are left as our future work.",Disentangling factors variation has always challenging problem representation learning. Existing algorithms suffer many limitations unpredictable disentangling factors bad quality generated images encodings lack identity information etc. paper proposed supervised algorithm called DNA-GAN trying disentangle different attributes images. latent representations images are DNA-like which each individual piece represents independent factor variation. annihilating recessive piece swapping certain piece two latent representations can obtain another two different representations could decoded images. order obtain realistic images also disentangled representations introduced discriminator adversarial training. Experiments Multi-PIE CelebA datasets demonstrate effectiveness method advantage overcoming limitations existing methods. success machine learning algorithms depends data representation which where different representations can entangle different explanatory factors variation behind data. Although prior knowledge can help us design representations vast demand AI algorithms various domains cannot met since feature engineering is labor-intensive needs domain expert knowledge. Therefore algorithms can automatically learn good representations data will definitely make easier people extract useful information when building classifiers predictors.Of criteria learning good representations discussed BID1 disentangling factors variation is an important one helps separate various explanatory factors. example given human-face image can obtain various information person including gender hair style facial expression/without eyeglasses on. information are entangled single image which renders difficulty training single classifier handle different facial attributes. could obtain disentangled representation face image may build one classifier multiple attributes.In paper propose supervised method called DNA-GAN obtain disentangled representations images. idea DNA-GAN is motivated DNA double helix structure which where different kinds traits are encoded different DNA pieces. make similar assumption different visual attributes image are controlled different pieces encodings latent representations. DNA-GAN encoder is used encode image attribute-relevant part attribute-irrelevant part which where different pieces attribute-relevant part encode information different attributes attribute-irrelevant part encodes information. example given facial image are trying obtain latent representation individual part controls different attributes hairstyles genders expressions on. Though annihilating recessive pieces swapping certain pieces can obtain novel crossbreeds can be decoded new images. adversarial discriminator loss reconstruction loss DNA-GAN can reconstruct input images generate new images new attributes. attribute is disentangled others gradually though iterative training. Finally are is able obtain disentangled representations latent representations.The summary contributions work is as follows:1 follows:1 propose supervised algorithm called DNA-GAN are is able disentangle multiple attributes demonstrated experiments interpolating multiple attributes Multi-PIE BID5 CelebA BID12 datasets.2 introduce annihilating operation prevents trivial solutions:attributerelevant part encodes information whole image instead certain attribute.3 employ iterative training address problem unbalanced multi-attribute image data which was theoretically proved efficient random image pairs. paper propose supervised algorithm called DNA-GAN can learn disentangled representations multi-attribute images. latent representations images are DNA-like consisting attribute-relevant attribute-irrelevant parts. annihilating operation attribute hybridization are is able create new latent representations could decoded novel images designed attributes. iterative training strategy effectively overcomes difficulty training unbalanced datasets helps disentangle multiple attributes latent space.The experimental results demonstrate DNA-GAN is effective learning disentangled representations image editing also point potential interpretable deep learning image understanding transfer learning.There also exist limitations model. Without strong guidance attribute-irrelevant parts background information is encoded attribute-relevant part. can see FIG3 background color gets changed when swapping attributes. Besides model may fail when several attributes are highly correlated other. example Male Mustache are statistically dependent which are hard disentangle latent representations. are left future work.,975,691,284,0.009,1.411,2025/11/05 17:18:58,0.0,1.189,0.2523364485981307,307.51
"Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two separate deep representations: an invariant representation that encodes the information of the class from which the data belongs, and an equivariant representation that encodes the symmetry transformation defining the particular data point within the class manifold (equivariant in the sense that the representation varies naturally with symmetry transformations). This approach to representation learning is conceptually transparent, easy to implement, and in-principle generally applicable to any data comprised of discrete classes of continuous distributions (e.g. objects in images, topics in language, individuals in behavioural data). We demonstrate qualitatively compelling representation learning and competitive quantitative performance, in both supervised and semi-supervised settings, versus comparable modelling approaches in the literature with little fine tuning. Representation learning BID0 is part of the foundation of deep learning; powerful deep neural network models appear to derive their performance from sequentially representing data in more-and-more refined structures, tailored to the training task.However, representation learning has a broader impact than just model performance. Transferable representations are leveraged efficiently for new tasks BID22 , representations are used for human interpretation of machine learning models BID18 , and meaningfully structured (disentangled) representations can be used for model control (e.g. semisupervised learning as in , topic modelling as in BID1 ).Consequently , it is often preferable to have interpretable data representations within a model, in the sense that the information contained in the representation is easily understood and the representation can be used to control the output of the model (e.g. to generate data of a given class or with a particular characteristic). Unfortunately , there is often a tension between optimal model performance and cleanly disentangled or controllable representations.To overcome this, some practitioners have proposed modifying their model's objective functions by inserting parameters in front of particular terms BID2 BID11 , while others have sought to modify the associated generative models BID20 . Further still , attempts have been made to build the symmetries of the data directly into the neural network architecture in order to force the learning of latent variables that transform meaningfully under those symmetries BID27 . The diversity and marginal success of these approaches point to the importance and difficulty of learning meaningful representations in deep generative modelling.In this work we present an approach to probabilistic modelling of data comprised of a finite number of distinct classes, each described by a smooth manifold of instantiations of that class. For convenience , we call our approach EQUIVAE for Equivariant Variational Autoencoder. EQUIVAE is a probabilistic model with 2 latent variables: an invariant latent that represents the global class information, and an equivariant latent that smoothly interpolates between all of the members of that class. The EQUIVAE approach is general in that the symmetry group of the manifold must not be specified (as in for example BID6 ; BID8 ), and it can be used for any number of classes and any dimensionality of both underlying representations. The price that must be paid for this level of model control and flexibility is that some labelled data is needed in order to provide the concept of class invariance versus equivariance to the model. The endeavor to model the content and the style of data separately is certainly not new to this work BID29 . BID25 and BID24 go further, disentangling the continuous sources of variation in their representations using a clamping technique that exposes specific latent components to a single source of variation in the data during training. In the same vein, other approaches have used penalty terms in the objective function that encourage the learning of disentangled representations BID5 BID4 . EQUIVAE does not require any modification to the training algorithm, nor additional penalty terms in the objective function in order to bifurcate the information stored in the two latent variables. This is due to the way in which multiple data points are used to reconstruct a single data point from the same-class manifold, which we consider the primary novel aspect of our approach. In particular, our invariant representation takes as input multiple data points that come from the same class, but are different from the data point to be reconstructed. This invariant representation thus directly learns to encode the information common to the overall class, but not the individual data point, simply due to the information flowing through it.Of further note, we deliberately use a deterministic latent for the invariant representation, and a stochastic latent for the smooth equivariant representation (an idea also employed by BID30 ). This choice is why we do not need to explicitly force the equivariant latent to not contain any class-level information: it is available and easier to access from the deterministic latent.EQUIVAE is also comparable to BID28 , where the authors leverage labelled data explicitly in their generative model in order to force the VAE latent to learn the non-class information BID19 do similarly using adversarial training). The primary difference between those works and ours is that EQUIVAE provides a non-trivial representation of the global information instead of simply using the integer-valued label. Furthermore, this invariant representation can be deterministically evaluated directly on unlabelled data. Practitioners can reuse this embedding on unlabelled data in downstream tasks, along with the equivariant encoder if needed. The invariant representation provides more information than a simple prediction of the class-label distribution.The encoding procedure for the invariant representation in EQUIVAE is partially inspired by BID7 , who use images from various, known coordinates in a scene in order to reconstruct a new image of that scene at new, known coordinates. In contrast, we do not have access to the exact coordinates of the class instance , which in our case corresponds to the unknown, non-trivial manifold structure of the class; we must infer these manifold coordinates in an unsupervised way. BID9 similarly explore the simultaneous usage of multiple data points in generative modelling in order to better capture modelling uncertainty. We have introduced a technique for jointly learning invariant and equivariant representations of data comprised of discrete classes of continuous values. The invariant representation encodes global information about the given class manifold which is ensured by the procedure of reconstructing a data point through complementary samples from the same class. The equivariant representation is a stochastic VAE latent that learns the smooth set of transformations that cover the instances of data on that class manifold. We showed that the invariant latents are so widely separated that a 99.18% accuracy can be achieved on MNIST (87.70% on SVHN) with a simple 0-parameter distance metric based on the invariant embedding. The equivariant latent learns to cover the manifold for each class of data with qualitatively excellent samples and interpolations for each class. Finally, we showed that semi-supervised learning based on such latent variable models is competitive with similar approaches in the literature with essentially no hyperparameter tuning.",Representations learnt deep neural networks tend highly informative opaque terms what information learn encode. introduce approach probabilistic modelling learns represent data two separate deep representations:invariant representation encodes information class which the data belongs equivariant representation encodes symmetry transformation defining particular data point within class manifold equivariant sense representation varies naturally symmetry transformations approach representation learning is conceptually transparent easy implement in-principle generally applicable data comprised discrete classes continuous distributions e.g objects images topics language individuals behavioural data demonstrate qualitatively compelling representation learning competitive quantitative performance supervised semi-supervised settings versus comparable modelling approaches literature little fine tuning. Representation learning BID0 is part foundation deep learning;powerful deep neural network models appear derive performance sequentially representing data more-and-more refined structures tailored training task.However representation learning has a broader impact model performance. Transferable representations are leveraged efficiently new tasks BID22 representations are used human interpretation machine learning models BID18 meaningfully structured disentangled representations can be used model control e.g semisupervised learning topic modelling BID1.Consequently is is often preferable have interpretable data representations within model sense information contained representation is easily understood representation can be used control output model e.g generate data given class particular characteristic Unfortunately is is often tension optimal model performance cleanly disentangled controllable representations.To overcome practitioners have proposed modifying model's objective functions inserting parameters front particular terms BID2 BID11 others have sought modify associated generative models BID20. still attempts have been made build symmetries data directly neural network architecture order force learning latent variables transform meaningfully symmetries BID27. diversity marginal success approaches point importance difficulty learning meaningful representations deep generative modelling.In work present approach probabilistic modelling data comprised finite number distinct classes described smooth manifold instantiations class. convenience call approach EQUIVAE Equivariant Variational Autoencoder. EQUIVAE is a probabilistic model 2 latent variables:invariant latent represents global class information equivariant latent smoothly interpolates members class. EQUIVAE approach is general symmetry group manifold must specified example BID6;BID8 canbe used number classes dimensionality underlying representations. price must paid level model control flexibility is that some labelled data is needed order provide concept class invariance versus equivariance model. endeavor model content style data separately is certainly new work BID29. BID25 BID24go disentangling continuous sources variation representations using clamping technique exposes specific latent components single source variation data training. vein approaches have used penalty terms objective function encourage learning disentangled representations BID5 BID4. EQUIVAE does not require modification training algorithm additional penalty terms objective function order bifurcate information stored two latent variables. is due way which multiple data points are used reconstruct single data point same-class manifold which we consider primary novel aspect approach. particular invariant representation takes input multiple data points come class are different which the data point reconstructed. invariant representation thus directly learns encode information common overall class individual data point simply due information flowing it.Of note deliberately use deterministic latent invariant representation stochastic latent smooth equivariant representation idea also employed BID30 choice is whywedo need explicitly force equivariant latent contain class-level information:is available easier access deterministic latent.EQUIVAE is also comparable BID28 where the authors leverage labelled data explicitly generative model order force VAE latent learn non-class information BID19 do similarly using adversarial training primary difference works is that EQUIVAE provides non-trivial representation global information instead simply using integer-valued label. Furthermore invariant representation can be deterministically evaluated directly unlabelled data. Practitioners can reuse embedding unlabelled data downstream tasks along equivariant encoder if needed. invariant representation provides information simple prediction class-label distribution.The encoding procedure invariant representation EQUIVAE is partially inspired BID7 who use images various known coordinates scene order reconstruct new image scene new known coordinates. contrast do not have access exact coordinates class instance which in our case corresponds unknown non-trivial manifold structure class;must infer manifold coordinates unsupervised way. BID9 similarly explore simultaneous usage multiple data points generative modelling order better capture modelling uncertainty. have introduced technique jointly learning invariant equivariant representations data comprised discrete classes continuous values. invariant representation encodes global information given class manifold which is ensured procedure reconstructing data point complementary samples class. equivariant representation is a stochastic VAE latent learns smooth set transformations cover instances data class manifold. showed invariant latents are so widely separated 99.18 accuracy can be achieved MNIST 87.70 SVHN simple 0-parameter distance metric based invariant embedding. equivariant latent learns cover manifold class data qualitatively excellent samples interpolations class. Finally showed semi-supervised learning based latent variable models is competitive similar approaches literature essentially hyperparameter tuning.,1401,932,469,0.015,1.503,2025/11/05 17:18:58,0.01,1.478,0.5389408099688469,461.838
"Convolutional neural networks (CNNs) have been successfully applied to many recognition and learning tasks using a universal recipe;  training a deep model on a very large dataset of supervised examples. However, this approach is rather restrictive in practice since collecting a large set of labeled images is very expensive. One way to ease this problem is coming up with smart ways for choosing images to be labelled from a  very large collection (i.e. active learning).

 Our empirical study suggests that many of the active learning heuristics in the literature are not effective when applied to CNNs when applied in batch setting. Inspired by these limitations, we define the problem of active learning as core-set selection, i.e. choosing set of points such that a model learned over the selected subset is competitive for the remaining data points. We further present a theoretical result characterizing the performance of any selected subset using the geometry of the datapoints. As an active learning algorithm, we choose the subset which is expected to yield best result according to our characterization. Our experiments show that the proposed method significantly outperforms existing approaches in image classification experiments by a large margin.
 Deep convolutional neural networks (CNNs) have shown unprecedented success in many areas of research in computer vision and pattern recognition, such as image classification, object detection, and scene segmentation. Although CNNs are universally successful in many tasks, they have a major drawback; they need a very large amount of labeled data to be able to learn their large number of parameters. More importantly, it is almost always better to have more data since the accuracy of CNNs is often not saturated with increasing dataset size. Hence, there is a constant desire to collect more and more data. Although this a desired behavior from an algorithmic perspective (higher representative power is typically better), labeling a dataset is a time consuming and an expensive task. These practical considerations raise a critical question: ""what is the optimal way to choose data points to label such that the highest accuracy can be obtained given a fixed labeling budget."" Active learning is one of the common paradigms to address this question.The goal of active learning is to find effective ways to choose data points to label, from a pool of unlabeled data points, in order to maximize the accuracy. Although it is not possible to obtain a universally good active learning strategy BID4 , there exist many heuristics BID38 which have been proven to be effective in practice. Active learning is typically an iterative process in which a model is learned at each iteration and a set of points is chosen to be labelled from a pool of unlabelled points using these aforementioned heuristics. We experiment with many of these heuristics in this paper and find them not effective when applied to CNNs. We argue that the main factor behind this ineffectiveness is the correlation caused via batch acquisition/sampling. In the classical setting, the active learning algorithms typically choose a single point at each iteration; however, this is not feasible for CNNs since i) a single point is likely to have no statistically significant impact on the accuracy due to the local optimization methods, and ii) each iteration requires a full training until convergence which makes it intractable to query labels one-by-one. Hence, it is necessary to query labels for a large subset at each iteration and it results in correlated samples even for moderately small subset sizes.In order to tailor an active learning method for the batch sampling case, we decided to define the active learning as core-set selection problem. Core-set selection problem aims to find a small subset given a large labeled dataset such that a model learned over the small subset is competitive over the whole dataset. Since we have no labels available, we perform the core-set selection without using the labels. In order to attack the unlabeled core-set problem for CNNs, we provide a rigorous bound between an average loss over any given subset of the dataset and the remaining data points via the geometry of the data points. As an active learning algorithm, we try to choose a subset such that this bound is minimized. Moreover, minimization of this bound turns out to be equivalent to the k-Center problem (Wolf, 2011) and we adopt an efficient approximate solution to this combinatorial optimization problem. We further study the behavior of our proposed algorithm empirically for the problem of image classification using three different datasets. Our empirical analysis demonstrates state-of-the-art performance by a large margin. We study the active learning problem for CNNs. Our empirical analysis showed that classical uncertainty based methods have limited applicability to the CNNs due to the correlations caused by batch sampling. We re-formulate the active learning problem as core-set selection and study the core-set problem for CNNs. We further validated our algorithm using an extensive empirical study. Empirical results on three datasets showed state-of-the-art performance by a large margin.A PROOF FOR LEMMA 1Proof. We will start with showing that softmax function defined over C class is , i = 1, 2, ..., C For brevity, we will denote f i (x) as f i . The Jacobian matrix will be, DISPLAYFORM0 Now, Frobenius norm of above matrix will be, DISPLAYFORM1 It is straightforward to show that f i = 1 C is the optimal solution for J * F = max . If we assume, i |w i,j | ≤ α ∀i, j, d, for any convolutional or fully connected layer, we can state: DISPLAYFORM2 On the other hand, using |a − b| ≤ | max(0, a) − max(0, a)| and the fact that max pool layer can be written as a convolutional layer such that only one weight is 1 and others are 0, we can state for ReLU and max-pool layers, DISPLAYFORM3 Combining with the Lipschitz constant of soft-max layer, B PROOF FOR THEOREM 1 DISPLAYFORM4 Before starting our proof, we state the Claim 1 from BID1 . Fix some p, p ∈ [0, 1] and y ∈ {0, 1}. Then, p y∼p (y = y ) ≤ p y∼p (y = y ) + |p − p |","Convolutional neural networks CNNs have been successfully applied many recognition learning tasks using universal recipe;training deep model large dataset supervised examples. However approach is rather restrictive practice since collecting large set labeled images is very expensive. One way ease problem is coming smart ways choosing images labelled large collection.e active learning empirical study suggests many active learning heuristics literature are not effective when applied CNNs when applied batch setting. Inspired limitations define problem active learning core-set selection.e choosing set points model learned selected subset is competitive remaining data points. present theoretical result characterizing performance selected subset using geometry datapoints. active learning algorithm choose subset which is expected yield best result according characterization. experiments show proposed method significantly outperforms existing approaches image classification experiments large margin. Deep convolutional neural networks CNNs have shown unprecedented success many areas research computer vision pattern recognition image classification object detection scene segmentation. Although CNNs are universally successful many tasks have a major drawback;need large amount labeled data able learn large number parameters. importantly is almost always better have more data since accuracy CNNs is often saturated increasing dataset size. Hence is a constant desire collect data. Although desired behavior algorithmic perspective higher representative power is typically better labeling dataset is a time consuming expensive task. practical considerations raise critical question:what is the optimal way choose data points label highest accuracy can be obtained given fixed labeling budget. Active learning is one common paradigms address question.The goal active learning is to find effective ways choose data points label pool unlabeled data points order maximize accuracy. Although is not possible obtain universally good active learning strategy BID4 exist many heuristics BID38 which have been proven effective practice. Active learning is typically iterative process which a model is learned iteration set points is chosen labelled pool unlabelled points using aforementioned heuristics. experiment many heuristics paper find effective when applied CNNs. argue main factor behind ineffectiveness is the correlation caused via batch acquisition/sampling. classical setting active learning algorithms typically choose single point iteration;however is not feasible CNNs since single point is likely have no statistically significant impact accuracy due local optimization methods ii iteration requires full training convergence which makes intractable query labels one-by-one Hence is necessary query labels large subset iteration results correlated samples even moderately small subset sizes.In order tailor active learning method batch sampling case decided define active learning core-set selection problem. Core-set selection problem aims find small subset given large labeled dataset model learned small subset is competitive whole dataset. Since have no labels available perform core-set selection without using labels. order attack unlabeled core-set problem CNNs provide rigorous bound average loss given subset dataset remaining data points via geometry data points. active learning algorithm try choose subset bound is minimized. Moreover minimization bound turns equivalent k-Center problem Wolf 2011 adopt efficient approximate solution combinatorial optimization problem. study behavior proposed algorithm empirically problem image classification using three different datasets. empirical analysis demonstrates state-of-the-art performance large margin. study active learning problem CNNs. empirical analysis showed classical uncertainty based methods have limited applicability CNNs due correlations caused batch sampling. re-formulate active learning problem core-set selection study core-set problem CNNs. validated algorithm using extensive empirical study. Empirical results three datasets showed state-of-the-art performance large margin.A PROOF LEMMA 1Proof. will start showing softmax function defined C class is,i=is1 2... C brevity will denotef x f i. Jacobian matrix will be,DISPLAYFORM0 Frobenius norm matrix will be,DISPLAYFORM1 is straightforward show f 1C is the optimal solution J*F max. If we assume |w j ≤α∀i j convolutional fully connected layer can state:DISPLAYFORM2 hand using|a−b| ≤ max 0 − max 0 fact max pool layer can be written convolutional layer one weight is,i=is1 others are0 can state ReLU max-pool layers DISPLAYFORM3 Combining Lipschitz constant soft-max layer B PROOF THEOREM 1 DISPLAYFORM4 starting proof can state Claim1 BID1. Fix p p∈ 0 1 ∈ 0 1 p y∼p ≤ p y∼p+|p−p",1262,839,423,0.013,1.504,2025/11/05 17:18:58,0.01,1.638,0.542056074766355,397.887
"Recurrent neural networks are known for their notorious exploding and vanishing gradient problem (EVGP). This problem becomes more evident in tasks where the information needed to correctly solve them exist over long time scales, because EVGP prevents important gradient components from being back-propagated adequately over a large number of steps. We introduce a simple stochastic algorithm (\textit{h}-detach) that is specific to LSTM optimization and targeted towards addressing this problem. Specifically, we show that when the LSTM weights are large, the gradient components through the linear path (cell state) in the LSTM computational graph get suppressed. Based on the hypothesis that these components carry information about long term dependencies (which we show empirically), their suppression can prevent LSTMs from capturing them. Our algorithm\footnote{Our code is available at https://github.com/bhargav104/h-detach. } prevents gradients flowing through this path from getting suppressed, thus allowing the LSTM to capture such dependencies better. We show significant improvements over vanilla LSTM gradient based training in terms of convergence speed, robustness to seed and learning rate, and generalization using our modification of LSTM gradient on various benchmark datasets. Recurrent Neural Networks (RNNs) BID25 ; BID4 ) are a class of neural network architectures used for modeling sequential data. Compared to feed-forward networks, the loss landscape of recurrent neural networks are much harder to optimize. Among others, this difficulty may be attributed to the exploding and vanishing gradient problem BID8 BID2 BID24 which is more severe for recurrent networks and arises due to the highly ill-conditioned nature of their loss surface. This problem becomes more evident in tasks where training data has dependencies that exist over long time scales.Due to the aforementioned optimization difficulty, variants of RNN architectures have been proposed that aim at addressing these problems. The most popular among such architectures that are used in a wide number of applications include long short term memory (LSTM, BID9 ) and gated recurrent unit (GRU, Chung et al. (2014) ) networks, which is a variant of LSTM with forget gates BID5 . These architectures mitigate such difficulties by introducing a linear temporal path that allows gradients to flow more freely across time steps. BID0 on the other hand try to address this problem by parameterizing a recurrent neural network to have unitary transition matrices based on the idea that unitary matrices have unit singular values which prevents gradients from exploding/vanishing.Among the aforementioned RNN architectures, LSTMs are arguably most widely used (for instance they have more representational power compared with GRUs BID31 ) and it remains a hard problem to optimize them on tasks that involve long term dependencies. Examples of such tasks are copying problem BID2 BID24 , and sequential MNIST (Le Figure 1 : The computational graph of a typical LSTM. Here we have omitted the inputs x i for convenience. The top horizontal path through the cell state units c t s is the linear temporal path which allows gradients to flow more freely over long durations. The dotted blue crosses along the computational paths denote the stochastic process of blocking the flow of gradients though the h t states (see Eq 2) during the back-propagation phase of LSTM. We call this approach h-detach. et al., 2015) , which are designed in such a way that the only way to produce the correct output is for the model to retain information over long time scales.The goal of this paper is to introduce a simple trick that is specific to LSTM optimization and improves its training on tasks that involve long term dependencies. To achieve this goal, we write out the full back-propagation gradient equation for LSTM parameters and split the composition of this gradient into its components resulting from different paths in the unrolled network. We then show that when LSTM weights are large in magnitude, the gradients through the linear temporal path (cell state) get suppressed (recall that this path was designed to allow smooth gradient flow over many time steps). We show empirical evidence that this path carries information about long term dependencies (see section 3.5) and hence gradients from this path getting suppressed is problematic for such tasks. To fix this problem, we introduce a simple stochastic algorithm that in expectation scales the individual gradient components, which prevents the gradients through the linear temporal path from being suppressed. In essence, the algorithm stochastically prevents gradient from flowing through the h-state of the LSTM (see figure 1) , hence we call it h-detach. Using this method, we show improvements in convergence/generalization over vanilla LSTM optimization on the copying task, transfer copying task, sequential and permuted MNIST, and image captioning. In section 3.5 we showed that LSTMs trained with h-detach are stable even without gradient clipping. We caution that while this is true, in general the gradient magnitude depends on the value of detaching probability used in h-detach. Hence for the general case, we do not recommend removing gradient clipping.When training stacked LSTMs, there are two ways in which h-detach can be used: 1) detaching the hidden state of all LSTMs simultaneously for a given time step t depending on the stochastic variable ξ t ) stochastically detaching the hidden state of each LSTM separately. We leave this for future work.h-detach stochastically blocks the gradient from flowing through the hidden states of LSTM. In corollary 1, we showed that in expectation, this is equivalent to dampening the gradient components from paths other than the cell state path. We especially chose this strategy because of its ease of implementation in current auto-differentiation libraries. Another approach to dampen these gradient components would be to directly multiply these components with a dampening factor. This feature is currently unavailable in these libraries but may be an interesting direction to look into. A downside of using this strategy though is that it will not reduce the amount of computation similar to h-detach (although it will not increase the amount of computation compared with vanilla LSTM either). Regularizing the recurrent weight matrices to have small norm can also potentially prevent the gradient components from the cell state path from being suppressed but it may also restrict the representational power of the model.Given the superficial similarity of h-detach with dropout, we outline the difference between the two methods. Dropout randomly masks the hidden units of a network during the forward pass (and can be seen as a variant of the stochastic delta rule BID6 ). Therefore, a common view of dropout is training an ensemble of networks BID30 . On the other hand, our method does not mask the hidden units during the forward pass. It instead randomly blocks the gradient component through the h-states of the LSTM only during the backward pass and does not change the output of the network during forward pass. More specifically, our theoretical analysis shows the precise behavior of our method: the effect of h-detach is that it changes the update direction used for descent which prevents the gradients through the cell state path from being suppressed.We would also like to point out that even though we show improvements on the image captioning task, it does not fit the profile of a task involving long term dependencies that we focus on. We believe the reason why our method leads to improvements on this task is that the gradient components from the cell state path are important for this task and our theoretical analysis shows that h-detach prevents these components from getting suppressed compared with the gradient components from the other paths. On the same note, we also tried our method on language modeling tasks but did not notice any benefit. We proposed a simple stochastic algorithm called h-detach aimed at improving LSTM performance on tasks that involve long term dependencies. We provided a theoretical understanding of the method using a novel analysis of the back-propagation equations of the LSTM architecture. We note that our method reduces the amount of computation needed during training compared to vanilla LSTM training. Finally, we empirically showed that h-detach is robust to initialization, makes the convergence of LSTM faster, and/or improves generalization compared to vanilla LSTM (and other existing methods) on various benchmark datasets. . The next T − 1 entries are set to a 8 , which constitutes a delay. The next single entry is a 9 , which represents a delimiter, which should indicate to the algorithm that it is now required to reproduce the initial 10 input tokens as output. The remaining 10 input entries are set to a 8 . The target sequence consists of T + 10 repeated entries of a 8 , followed by the first 10 entries of the input sequence in exactly the same order. DISPLAYFORM0 Here denotes the element-wise product, also called the Hadamard product. σ denotes the sigmoid activation function. DISPLAYFORM1 For any ∈ {f, g, o, i}, define E (w) to be a matrix of size dim(h t ) × dim([h t ; x t ]). We set all the elements of this matrix to 0s if if w is not an element of W . Further, if w = (W ) kl , then (E (w)) kl = 1 and (E (w)) k l = 0 for all (k , l ) = (k, l). DISPLAYFORM2 Lemma 1 Let us assume w is an entry of the matrix DISPLAYFORM3 Proof By chain rule of total differentiation, DISPLAYFORM4 We note that, DISPLAYFORM5 DISPLAYFORM6 Recall that h t = o t tanh(c t ), and thus DISPLAYFORM7 Using the previous Lemma as well as the above notation, we get DISPLAYFORM8 DISPLAYFORM9 Then, z t = (A t + B t )z t−1In other words, where all the symbols used to define A t and B t are defined in notation 1.Proof By Corollary 2, we get DISPLAYFORM10 Similarly by Corollary 3, we get DISPLAYFORM11 Thus we have DISPLAYFORM12 Applying this formula recursively proves the claim.Note: Since A t has 0 n 's in the second column of the block matrix representation, it ignores the contribution of z t coming from h t−1 , whereas B t (having non-zero block matrices only in the second column of the block matrix representation) only takes into account the contribution coming from h t−1 . Hence A t captures the contribution of the gradient coming from the cell state c t−1 . T andz t be the analogue of z t when applying h-detach with probability p during back-propagation. Then, z t = (A t + ξ t B t )(A t−1 + ξ t−1 B t−1 ) . . . (A 2 + ξ 2 B 2 )z 1 where ξ t , ξ t−1 , . . . , ξ 2 are i.i.d. Bernoulli random variables with probability p of being 1, A t and B t and are same as defined in theorem 1.Proof Replacing DISPLAYFORM13 Iterating this formula gives, z t = (A t + ξ t B t )(A t−1 + ξ t−1 B t−1 ) . . . (A 3 + ξ 3 B 3 )z 2Corollary 4 E[z t ] = (A t + pB t )(A t−1 + pB t−1 ) . . . (A 3 + pB 3 )z 2It suffices to take the expectation both sides, and use independence of ξ t 's.",Recurrent neural networks are known notorious exploding vanishing gradient problem EVGP problem becomes evident tasks where the information needed correctly solve exist long time scales EVGP prevents important gradient components back-propagated adequately large number steps. introduce simple stochastic algorithm \textit h -detach is specific LSTM optimization targeted towards addressing problem. Specifically show when the when LSTM weights are large gradient components linear path cell state LSTM computational graph get suppressed. Based hypothesis components carry information long term dependencies which we show empirically suppression can prevent LSTMs capturing them. algorithm\footnote code is available https://github.com/bhargav104/h-detach. prevents gradients flowing path getting suppressed thus allowing LSTM capture dependencies better. show significant improvements vanilla LSTM gradient based training terms convergence speed robustness seed learning rate generalization using modification LSTM gradient various benchmark datasets. Recurrent Neural Networks RNNs BID25;BID4 are a class neural network architectures used modeling sequential data. Compared feed-forward networks loss landscape recurrent neural networks are much harder optimize. Among others difficulty may attributed exploding vanishing gradient problem BID8 BID2 BID24 which is more severe recurrent networks arises due highly ill-conditioned nature loss surface. problem becomes evident tasks where training data has dependencies exist long time scales.Due aforementioned optimization difficulty variants RNN architectures have been proposed aim addressing problems. popular among architectures are used wide number applications include long short term memory LSTM BID9 gated recurrent unit GRU Chungetal. 2014 networks which is a variant LSTM forget gates BID5. architectures mitigate difficulties introducing linear temporal path allows gradients flow freely across time steps. BID0 hand try address problem parameterizing recurrent neural network have unitary transition matrices based idea unitary matrices have unit singular values which prevents gradients exploding/vanishing.Among aforementioned RNN architectures LSTMs are arguably widely used instance have more representational power compared GRUs BID31 remains hard problem optimize tasks involve long term dependencies. Examples tasks are copying problem BID2 BID24 sequential MNIST Le Figure1:computational graph typical LSTM. have omitted inputsx convenience. top horizontal path cell state unitsc is the linear temporal path which allows gradients flow freely long durations. dotted blue crosses along computational paths denote stochastic process blocking flow gradients though h states seeEq2 back-propagation phase LSTM. call approach h-detachetal. 2015 which are designed way way produce correct output is for the model retain information long time scales.The goal paper is to introduce simple trick is specific LSTM optimization improves training tasks involve long term dependencies. achieve goal write full back-propagation gradient equation LSTM parameters split composition gradient components resulting different paths unrolled network. show when the when LSTM weights are large magnitude gradients linear temporal path cell state get suppressed recall path was designed allow smooth gradient flow many time steps show empirical evidence path carries information long term dependencies see section 3.5 hence gradients path getting suppressed is problematic tasks. fix problem introduce simple stochastic algorithm expectation scales individual gradient components which prevents gradients linear temporal path suppressed. essence algorithm stochastically prevents gradient flowing h-state LSTM see figure1 hence call h-detach Using method show improvements convergence/generalization vanilla LSTM optimization copying task transfer copying task sequential permuted MNIST image captioning. section 3.5 showed LSTMs trained h-detach are stable even without gradient clipping. caution is true general gradient magnitude depends value detaching probability used which h-detach Hence general case do not recommend removing gradient clipping.When training stacked LSTMs are two ways which h-detach can be used:1 detaching hidden state LSTMs simultaneously given time step depending stochastic variableξ stochastically detaching hidden state LSTM separately. leave future work.h-detach stochastically blocks gradient flowing hidden states LSTM. corollary1 showed expectation is equivalent dampening gradient components paths cell state path. especially chose strategy ease implementation current auto-differentiation libraries. Another approach dampen gradient components would directly multiply components dampening factor. feature is currently unavailable libraries may interesting direction look into. downside using strategy though is that it will reduce amount computation similar h-detach although will not increase amount computation compared vanilla LSTM either Regularizing recurrent weight matrices have small norm can also potentially prevent gradient components cell state path suppressed may also restrict representational power model.Given superficial similarity h-detach dropout outline difference two methods. Dropout randomly masks hidden units network forward pass can be seen variant stochastic delta rule BID6 Therefore common view dropout is training ensemble networks BID30. hand method does not mask hidden units forward pass. instead randomly blocks gradient component h-states LSTM backward pass does not change output network forward pass. specifically theoretical analysis shows precise behavior method:effect h-detach is that it changes update direction used descent which prevents gradients cell state path suppressed.We would also like point even though show improvements image captioning task does not fit profile task involving long term dependencies focus on. believe reason why our method leads improvements task is that the gradient components cell state path are important task theoretical analysis shows h-detach prevents components getting suppressed compared gradient components paths. note also tried method language modeling tasks did not notice benefit. proposed simple stochastic algorithm called h-detach aimed improving LSTM performance tasks involve long term dependencies. provided theoretical understanding method using novel analysis back-propagation equations LSTM architecture. note method reduces amount computation needed training compared vanilla LSTM training. Finally empirically showed h-detach is robust initialization makes convergence LSTM faster/improves generalization compared vanilla LSTM existing methods various benchmark datasets. next − 1 entries are set 8 which constitutes delay. next single entry isa9 which represents delimiter which should indicate algorithm is now required reproduce initial 10 input tokens output. remaining 10 input entries are set 8. target sequence consists+10 repeated entries 8 followed first 10 entries input sequence exactly order. DISPLAYFORM0 denotes element-wise product also called Hadamard product. σ denotes sigmoid activation function. DISPLAYFORM1 ∈ f g defineE w matrix size dim h × dim h t;x set elements matrix 0s ififw is not an element W. ifw W kl E w kl 1 E w kl 0 k l k l DISPLAYFORM2 Lemma 1 Let us assumew is an entry matrix DISPLAYFORM3 Proof chain rule total differentiation DISPLAYFORM4 note DISPLAYFORM5 DISPLAYFORM6 Recall h tanh c thus DISPLAYFORM7 Using previous Lemma well notation get DISPLAYFORM8 DISPLAYFORM9 z+B z t−1In words where all the symbols used define B are are same defined notation 1.Proof Corollary2 get DISPLAYFORM10 Similarly Corollary3 get DISPLAYFORM11 Thus have DISPLAYFORM12 Applying formula recursively proves claim.Note:Since has0n's second column block matrix representation ignores contribution z coming h t−1 whereasB non-zero block matrices second column block matrix representation takes account contribution coming h t−1 Hence captures contribution gradient coming cell state c t−1 andz analogue z when applying h-detach probabilityp back-propagation z+ξ B t−1+ξ t−1 B t−1 2+ξ2 B2 z1 whereξ ξ t−1 ξ2 are i.i.i.d Bernoulli random variables probabilityp 1 B are are same defined theorem 1.Proof Replacing DISPLAYFORM13 Iterating formula gives z+ξ B t−1+ξ t−1 B t−1 3+ξ3 B3 z 2Corollary4E z+pB t−1+pB t−1 3+pB3 z 2It suffices take expectation sides use independence ξ 's,2372,1551,821,0.03,1.529,2025/11/05 17:18:58,0.01,1.581,0.6199376947040495,779.274
"Convolutional Neural Networks (CNNs) significantly improve the state-of-the-art for many applications, especially in computer vision. However, CNNs still suffer from a tendency to confidently classify out-distribution samples from unknown classes into pre-defined known classes. Further, they are also vulnerable to adversarial examples. We are relating these two issues through the tendency of CNNs to over-generalize for areas of the input space not covered well by the training set. We show that a CNN augmented with an extra output class can act as a simple yet effective end-to-end model for controlling over-generalization. As an appropriate training set for the extra class, we introduce two resources that are computationally efficient to obtain: a representative natural out-distribution set and interpolated in-distribution samples. To help select a representative natural out-distribution set among available ones, we propose a simple measurement to assess an out-distribution set's fitness. We also demonstrate that training such an augmented CNN with representative out-distribution natural datasets and some interpolated samples allows it to better handle a wide range of unseen out-distribution samples and black-box adversarial examples without training it on any adversaries. Finally, we show that generation of white-box adversarial attacks using our proposed augmented CNN can become harder, as the attack algorithms have to get around the rejection regions when generating actual adversaries. Convolutional Neural Networks (CNNs) have allowed for significant improvements over the stateof-the-art in the last few years for various applications, and in particular for computer vision. Notwithstanding these successes, challenging issues remain with these models. In the following work, we specifically look at two concerns. First, CNNs are vulnerable to different types of adversarial examples BID26 BID13 BID3 . These adversarial examples are created by deliberately modifying clean samples with imperceptible perturbations, with the aim of misleading CNNs into classifying them to a wrong class with high confidence. Second, CNNs are not able to handle instances coming from outside the task domain on which they are trained -the so-called out-distribution samples BID18 BID15 . In other words, although these examples are semantically and statistically different from the (in-distribution) samples relevant to a given task, the neural network trained on the task assigns such out-of-concept samples with high-confidence to the pre-defined in-distribution classes. Due to the susceptibility of CNNs to both adversaries and out-distribution samples, deploying them for real-world applications, in particular for security-sensitive ones, is a serious concern. These two issues have been treated separately in the past, with two distinct family of approaches. For instance, on the one hand, to handle out-distribution samples, some researchers have proposed threshold-based post-processing approaches with the aim of firstly calibrating the predictive confidence scores provided by either a single pre-trained CNN BID18 BID10 BID17 or an ensemble of CNNs BID15 , and then detecting out-distribution samples according to an optimal threshold. However, it is difficult to define an optimal and stable threshold for rejecting a wide range of out-distribution samples without increasing the false negative rate (i.e., rejecting in-distribution samples). On the other hand, researchers regarded adversarial examples as a distinct issue from the out-distribution problem and attempted to either correctly classify all adversaries through adversarial training of CNNs BID27 BID7 or reject all of them by training a separate detector BID5 BID20 . The performance of these approaches at properly handling adversarial instances mostly depends on having access to a diverse set of training adversaries, which is not only computationally expensive but also handling some possible future adversaries, which have not been discovered yet, most likely is difficult.It is known that deep neural networks (e.g. CNNs) are prone to over-generalization in the input space by partitioning it entirely into a set of pre-defined classes for a given in-distribution set (task), regardless of the fact that in-distribution samples may only be relevant to a small portion of the input space BID18 BID25 BID0 . In this paper, we highlight that the two aforementioned issues of CNNs can be alleviated simultaneously through control of over-generalization. To this end, we propose that an augmented CNN, a regular (naive) CNN with an extra class dubbed as dustbin, can be a simple yet effective solution, if it is trained on appropriate training samples for the dustbin class. Furthermore, we introduce here a computationally-efficient answer to the following key question: how to acquire such an appropriate set to effectively reduced the over-generalized regions induced by naive CNN. We note that our motivation for employing an augmented CNN is different from the threshold-based post-processing approaches that attempt to calibrate the predictive confidence scores of a pre-trained naive CNN without impacting its feature space. Our motivation in fact is to learn a more expressive feature space, where along with learning the sub-manifolds corresponding to in-distribution classes, a distinct extra sub-manifold for the dustbin class can be obtained such that the samples drawn from many over-generalized regions including a wide-range of out-distribution samples and various types of adversaries are mapped to this ""dustbin"" sub-manifold.As a training source for the extra class (dustbin), one can consider using synthetically generated out-distribution samples BID17 BID11 or adversarial examples BID8 . However, using such generated samples is not only computationally expensive but also barely able to effectively reduce over-generalization compared to naive CNNs (see Sec. 3). Instead of such synthetic samples, there are plenty of cost-effective training sources available for the extra dustbin class, namely natural out-distribution datasets. By natural out-distribution sets we mean the sets containing some realistic (not synthetically generated) samples that are semantically and statistically different from those in the in-distribution set. A representative natural out-distribution set for a given in-distribution task should be able to adequately cover the over-generalized regions. To recognize such a representative natural set, we propose a simple measurement to assess its fitness for a given in-distribution set. In addition to the selected set, we generate some artificial out-distribution samples through a straightforward and computationally efficient procedure, namely by interpolating some pair of in-distribution samples. We believe a properly trained augmented CNN can be utilized as a threshold-free baseline for identifying concurrently a broad range of unseen out-distribution samples and different types of strong adversarial attacks.The main contributions of the paper are summarized as:• By limiting the over-generalization regions induced by naive CNNs, we are able to drastically reduce the risk of misclassifying both adversaries and samples from a broad range of (unseen) out-distribution sets. To this end, we demonstrate that an augmented CNN can act as a simple yet effective solution.• We introduce a measurement to select a representative natural out-distribution set among those available for training effective augmented CNNs, instead of synthesizing some dustbin samples using hard-to-train generators.• Based on extensive experiments on a range of different image classification tasks, we demonstrate that properly trained augmented CNNs can significantly reduce the misclassification rates for both 1 ) unseen out-distribution sets, and 2) for various types of strong black-box adversarial examples, even though they are never trained on any specific types of adversaries.• For the generation of white-box adversaries using our proposed augmented CNN, the adversarial attack algorithms frequently encounter dustbin regions rather than regions from other classes when distorting a clean samples, making the adversaries generation process more difficult. In this paper we bridge two issues of CNNs that were previously thought of as unrelated: susceptibility of naive CNNs to various types of adversarial examples and incorrect high confidence prediction for out-distribution samples. We argue these two issues are connected through over-generalization. We propose augmented CNNs as a simple yet effective solution for controlling over-generalization, when they are trained on an appropriate set of dustbin samples. Through empirical evidence, we define an indicator for selecting an ""appropriate"" natural out-distribution set as training samples for dustbin class from among those available and show such selection plays a vital role for training effective augmented CNNs. Through extensive experiments on several augmented CNNs in different settings, we demonstrate that reducing over-generalization can significantly reduce the misclassification error rates of CNNs on adversaries and out-distribution samples, simultaneously, while their accuracy rates on in-distribution samples are maintained. Indeed, reducing over-generalization by such an end-to-end learning model (e.g., augmented CNNs) leads to learning more expressive feature space where these two categories of hostile samples (i.e., adversaries and out-distribution samples) are disentangled from in-distribution samples.",Convolutional Neural Networks CNNs significantly improve state-of-the-art many applications especially computer vision. However CNNs still suffer tendency confidently classify out-distribution samples unknown classes pre-defined known classes. are also vulnerable adversarial examples. are relating two issues tendency CNNs over-generalize areas input space covered well training set. show CNN augmented extra output class can act simple yet effective end-to-end model controlling over-generalization appropriate training set extra class introduce two resources are computationally efficient obtain:representative natural out-distribution set interpolated in-distribution samples. help select representative natural out-distribution set among available ones propose simple measurement assess out-distribution set's fitness. also demonstrate training augmented CNN representative out-distribution natural datasets interpolated samples allows better handle wide range unseen out-distribution samples black-box adversarial examples without training adversaries. Finally show generation white-box adversarial attacks using proposed augmented CNN can become harder attack algorithms have to get around rejection regions when generating actual adversaries. Convolutional Neural Networks CNNs have allowed significant improvements stateof-the-art last years various applications particular computer vision. Notwithstanding successes challenging issues remain models. following work specifically look two concerns. First CNNs are vulnerable different types adversarial examples BID26 BID13 BID3. adversarial examples are created deliberately modifying clean samples imperceptible perturbations aim misleading CNNs classifying wrong class high confidence. Second CNNs are not able handle instances coming outside task domain which they are trained -the so-called out-distribution samples BID18 BID15. words although examples are semantically statistically different in-distribution samples relevant given task neural network trained task assigns out-of-concept samples high-confidence pre-defined in-distribution classes. Due susceptibility CNNs adversaries out-distribution samples deploying real-world applications particular security-sensitive ones is a serious concern. two issues have been treated separately past two distinct family approaches. instance one hand handle out-distribution samples researchers have proposed threshold-based post-processing approaches aim firstly calibrating predictive confidence scores provided either single pre-trained CNN BID18 BID10 BID17 ensemble CNNs BID15 detecting out-distribution samples according optimal threshold. However is difficult define optimal stable threshold rejecting wide range out-distribution samples without increasing false negative rate.e rejecting in-distribution samples hand researchers regarded adversarial examples distinct issue out-distribution problem attempted either correctly classify adversaries adversarial training CNNs BID27 BID7 reject training separate detector BID5 BID20. performance approaches properly handling adversarial instances mostly depends access diverse set training adversaries which is not computationally expensive also handling possible future adversaries which have not discovered yet likely is difficult.It is known deep neural networks e.g CNNs are prone over-generalization input space partitioning entirely set pre-defined classes given in-distribution set task regardless fact in-distribution samples may relevant small portion input space BID18 BID25 BID0. paper highlight two aforementioned issues CNNs can be alleviated simultaneously control over-generalization end propose augmented CNN regular naive CNN extra class dubbed dustbin can be a simple yet effective solution if it is when they are trained appropriate training samples dustbin class. Furthermore introduce computationally-efficient answer following key question:how to acquire appropriate set effectively reduced over-generalized regions induced naive CNN. note motivation employing augmented CNN is different threshold-based post-processing approaches attempt calibrate predictive confidence scores pre-trained naive CNN without impacting feature space. motivation fact is to learn expressive feature space where along learning sub-manifolds corresponding in-distribution classes distinct extra sub-manifold dustbin class can be obtained samples drawn many over-generalized regions including wide-range out-distribution samples various types adversaries are mapped dustbin sub-manifold.As training source extra class dustbin one can consider using synthetically generated out-distribution samples BID17 BID11 adversarial examples BID8. However using generated samples is not only computationally expensive also barely able effectively reduce over-generalization compared naive CNNs see Sec. 3 Instead synthetic samples are plenty cost-effective training sources available extra dustbin class namely natural out-distribution datasets. natural out-distribution sets mean sets containing realistic synthetically generated samples are semantically statistically different in-distribution set. representative natural out-distribution set given in-distribution task should be able adequately cover over-generalized regions. recognize representative natural set propose simple measurement assess fitness given in-distribution set. addition selected set generate artificial out-distribution samples straightforward computationally efficient procedure namely interpolating pair in-distribution samples. believe properly trained augmented CNN can be utilized threshold-free baseline identifying concurrently broad range unseen out-distribution samples different types strong adversarial attacks.The main contributions paper are summarized as:• limiting over-generalization regions induced naive CNNs are able drastically reduce risk misclassifying adversaries samples broad range unseen out-distribution sets. end demonstrate augmented CNN can act simple yet effective solution.• introduce measurement select representative natural out-distribution set among available training effective augmented CNNs instead synthesizing dustbin samples using hard-to-train generators.• Based extensive experiments range different image classification tasks demonstrate properly trained augmented CNNs can significantly reduce misclassification rates 1 unseen out-distribution sets 2 various types strong black-box adversarial examples even though are never trained specific types adversaries.• generation white-box adversaries using proposed augmented CNN adversarial attack algorithms frequently encounter dustbin regions rather regions classes when distorting clean samples making adversaries generation process difficult. paper bridge two issues CNNs were previously thought unrelated:susceptibility naive CNNs various types adversarial examples incorrect high confidence prediction out-distribution samples. argue two issues are connected over-generalization propose augmented CNNs simple yet effective solution controlling over-generalization if it is when they are trained appropriate set dustbin samples. empirical evidence define indicator selecting appropriate natural out-distribution set training samples dustbin class among available show selection plays vital role training effective augmented CNNs. extensive experiments several augmented CNNs different settings demonstrate reducing over-generalization can significantly reduce misclassification error rates CNNs adversaries out-distribution samples simultaneously accuracy rates in-distribution samples are maintained. Indeed reducing over-generalization end-to-end learning model e.g augmented CNNs leads learning expressive feature space where these two categories hostile samples.e adversaries out-distribution samples are disentangled in-distribution samples.,1771,1238,533,0.019,1.431,2025/11/05 17:18:58,0.01,1.521,0.3146417445482866,520.806
"Modern deep artificial neural networks have achieved impressive results through models with very large capacity---compared to the number of training examples---that control overfitting with the help of different forms of regularization. Regularization can be implicit, as is the case of stochastic gradient descent or parameter sharing in convolutional layers, or explicit. Most common explicit regularization techniques, such as dropout and weight decay, reduce the effective capacity of the model and typically require the use of deeper and wider architectures to compensate for the reduced capacity. Although these techniques have been proven successful in terms of results, they seem to waste capacity. In contrast, data augmentation techniques reduce the generalization error by increasing the number of training examples and without reducing the effective capacity. In this paper we systematically analyze the effect of data augmentation on some popular architectures and conclude that data augmentation alone---without any other explicit regularization techniques---can achieve the same performance or higher as regularized models, especially when training with fewer examples. Regularization plays a central role in machine learning. Loosely defined, regularization is any modification applied to a learning algorithm that helps prevent overfitting and improve generalization. Whereas in simple machine learning algorithms the sources of regularization can be easily identified as explicit terms in the objective function, in modern deep neural networks the sources of regularization are multiple and some of them are not explicit, but implicit.Although the terms explicit and implicit regularization have been used recently in the literature (Neyshabur et al., 2014; Zhang et al., 2017) , their distinction is rather subjective. We propose the following definitions:• Explicit regularization techniques are those specifically and solely designed to constrain the effective capacity of a given model in order to reduce overfitting. Furthermore, explicit regularizers are not a structural or essential part of the network architecture, the data or the learning algorithm and can typically be added or removed easily.• Implicit regularization is the reduction of the generalization error or overfitting provided by characteristics of the network architecture, the training data or the learning algorithm, which are not specifically designed to constrain the effective capacity of the given model.Examples of explicit regularizers are weight decay BID14 , which penalizes large parameters; dropout (Srivastava et al., 2014) , which randomly removes a fraction of the neural connections during training; or stochastic depth BID18 , which drops whole layers instead. Implicit regularization effects are provided by the popular stochastic gradient descent (SGD) algorithm, which tends to converge to solutions with small norm (Zhang et al., 2017) ; convolutional layers, which impose parameter sharing based on prior knowledge about the data; batch normalization BID19 , whose main goal is reducing the the internal covariate shift, but also implicitly regularizes the model due to the noise in the batch estimates for mean and variance.Driven by the efficient use and development of GPUs, much research efforts have been devoted to finding ways of training deeper and wider networks of larger capacity (Simonyan & Zisserman, 2014; BID17 Zagoruyko & Komodakis, 2016) , Ironically, their effective capacity is eventually reduced in practice by the use of weight decay and dropout, among other explicit regularizers. It is known , for instance, that the gain in generalization provided by dropout comes at the cost of using larger models and training for longer BID11 . Hence, it seems that with such an approach deep networks are wasting capacity BID4 . As a matter of fact, unlike traditional machine learning models, deep neural networks seem not to need explicit regularizers to generalize well, as recently suggested by Zhang et al. (2017) .One popular technique that also improves generalization is data augmentation. Importantly , it differs from explicit regularizers mainly in that it does not reduce the effective capacity of the model. Data augmentation is a very old practice in machine learning (Simard et al., 1992) and it has been identified as a critical component of many models BID3 BID22 BID24 . However, although some authors have reported the impact of data augmentation on the performance of their models and, in some cases, a comparison of different amount of augmentation BID13 ) the literature lacks, to our knowledge, a systematic analysis of the impact of data augmentation on deep neural networks compared to the most popular regularization techniques. In this work, we have presented a systematic analysis of the role of data augmentation in deep neural networks for object recognition, focusing on the comparison with popular techniques of explicit regularization. We have built upon the work by Zhang et al. (2017) , where the authors concluded that explicit regularization is not necessary, although it improves generalization performance. Here, we have shown that it is not only unnecessary, but also that the generalization gain provided by explicit regularization can be achieved by data augmentation alone.The importance of these results lies in the fact that explicit regularization is the standard tool to enable the generalization of most machine learning methods. However, according to Zhang et al. (2017) , explicit regularization plays a different role in deep learning, not explained by statistical learning theory (Vapnik & Chervonenkis, 1971) . We argue instead that the theory still holds in deep learning, but one has to properly consider the crucial role of implicit regularization. Explicit regularization is no longer necessary because its contribution is already provided by the many elements that implicitly regularize the models: SGD, convolutional layers or data augmentation, among others.Whereas explicit regularizers, such as weight decay and dropout, succeed in mitigating overfitting by blindly reducing the effective capacity of a model, implicit regularization operates more effectively at capturing important characteristics of the data (Neyshabur et al., 2014) . For instance, convolutional layers successfully reduce the capacity of a model by imposing a parameter sharing strategy that incorporates some essential prior domain knowledge, as well as data augmentation by transforming the training examples in a meaningful and plausible way.In this regard it is worth highlighting some of the advantages of data augmentation: Not only does it not reduce the effective capacity of the model, but it increases the number of training examples, which, according to statistical learning theories, reduces the generalization error. Furthermore, if the transformations are such that they reflect plausible variations of the real objects, it increases the robustness of the model and it can be regarded as a data-dependent prior, similarly to unsupervised pre-training BID7 . Besides, unlike explicit regularization techniques, data augmentation does not increase the computational complexity because it can be performed in parallel to the gradient updates on the CPU, making it a computationally free operation. Finally, in Section 2.4 we have shown how data augmentation transparently adapts to architectures of different depth, whereas explicitly regularized models need manual adjustment of the regularization parameters.Deep neural networks can especially benefit from data augmentation because they do not rely on precomputed features and because the large number of parameters allows them to shatter the augmented training set. Actually, if data augmentation is included for training, we might have to reconsider whether deep learning operates in an overparameterization regime, since the model capacity should take into account the amount of training data, which is exponentially increased by augmentation.Some argue that despite these advantages, data augmentation is a highly limited approach because it depends on some prior expert knowledge and it cannot be applied to all domains. However, we argue instead that expert knowledge should not be disregarded but exploited. A single data augmentation scheme can be designed for a broad family of data, e.g. natural images, and effectively applied to a broad set of tasks, e.g. object recognition, segmentation, localization, etc. Besides, some recent works show that it is possible to learn the data augmentation strategies (Lemley et al., 2017; Ratner et al., 2017) and future research will probably yield even better results in different domains.Finally, it is important to note that, due to computational limitations, we have performed a systematic analysis only on CIFAR-10 and CIFAR-100, which consist of very small images. These data sets do not allow performing more agressive data augmentation since the low resolution images can easily show distortions that hinder the recognition of the object. However, some previous works BID13 Springenberg et al., 2014) have shown impressive results by performing heavier data augmentation on higher resolution versions on CIFAR-10. We plan to extend this analysis to higher resolution data sets such as ImageNet and one could expect even more benefits from data augmentation compared to explicit regularization techniques.","Modern deep artificial neural networks have achieved impressive results models large capacity -compared number training examples -that control overfitting help different forms regularization. Regularization can be implicit is the case stochastic gradient descent parameter sharing convolutional layers explicit. common explicit regularization techniques dropout weight decay reduce effective capacity model can typically require use deeper wider architectures compensate reduced capacity. Although techniques have been proven successful terms results seem waste capacity. contrast if data augmentation techniques reduce generalization error increasing number training examples without reducing effective capacity. paper systematically analyze effect data augmentation popular architectures conclude data augmentation alone -without explicit regularization techniques -can achieve performance higher regularized models especially when training fewer examples. Regularization plays central role machine learning. Loosely defined regularization is any modification applied learning algorithm helps prevent overfitting improve generalization. Whereas simple machine learning algorithms sources regularization can be can easily identified explicit terms objective function modern deep neural networks sources regularization are multiple are not explicit implicit.Although terms explicit implicit regularization have been used recently literature Neyshaburetal. 2014;Zhangetal. 2017 distinction is rather subjective. propose following definitions:• Explicit regularization techniques are those specifically solely designed constrain effective capacity given model order reduce overfitting. Furthermore explicit regularizers are not a structural essential part network architecture if data learning algorithm can typically added removed easily.• Implicit regularization is the reduction generalization error overfitting provided characteristics network architecture training data learning algorithm which are not specifically designed constrain effective capacity given model.Examples explicit regularizers are weight decay BID14 which penalizes large parameters;dropout Srivastavaetal. 2014 which randomly removes fraction neural connections training;stochastic depth BID18 which drops whole layers instead. Implicit regularization effects are provided popular stochastic gradient descent SGD algorithm which tends converge solutions small norm Zhangetal. 2017 convolutional layers which impose parameter sharing based prior knowledge data;batch normalization BID19 whose main goal is reducing internal covariate shift also implicitly regularizes model due noise batch estimates mean variance.Driven efficient use development GPUs much research efforts have been devoted finding ways training deeper wider networks larger capacity Simonyan Zisserman 2014;BID17 Zagoruyko Komodakis 2016 Ironically effective capacity is eventually reduced practice use weight decay dropout among explicit regularizers. is known instance gain generalization provided dropout comes cost using larger models training longer BID11. Hence seems approach deep networks are wasting capacity BID4. matter fact unlike traditional machine learning models deep neural networks seem need explicit regularizers generalize well recently suggested Zhangetal. 2017.One popular technique also improves generalization is data augmentation. Importantly differs explicit regularizers mainly does reduce effective capacity model. Data augmentation is a very old practice machine learning Simardetal. 1992 has identified critical component many models BID3 BID22 BID24. However although authors have reported impact data augmentation performance models cases comparison different amount augmentation BID13 literature lacks knowledge systematic analysis impact data augmentation deep neural networks compared popular regularization techniques. work have presented systematic analysis role data augmentation deep neural networks object recognition focusing comparison popular techniques explicit regularization. have built upon work Zhangetal. 2017 where the authors concluded explicit regularization is not necessary although improves generalization performance. have shown is not unnecessary also generalization gain provided explicit regularization can be achieved data augmentation alone.The importance results lies fact explicit regularization is the standard tool enable generalization machine learning methods. However which,according Zhangetal. 2017 explicit regularization plays different role deep learning explained statistical learning theory Vapnik Chervonenkis 1971 argue instead theory still holds deep learning one has to properly consider crucial role implicit regularization. Explicit regularization is no longer necessary contribution is already provided many elements implicitly regularize models:SGD convolutional layers data augmentation among others.Whereas explicit regularizers weight decay dropout succeed mitigating overfitting blindly reducing effective capacity model implicit regularization operates effectively capturing important characteristics data Neyshaburetal. 2014 instance convolutional layers successfully reduce capacity model imposing parameter sharing strategy incorporates essential prior domain knowledge well data augmentation transforming training examples meaningful plausible way.In regard is worth highlighting advantages data augmentation:doesit reduce effective capacity model increases number training examples which,according statistical learning theories reduces generalization error. Furthermore if the transformations are such that they reflect plausible variations real objects increases robustness model can be regarded data-dependent prior similarly unsupervised pre-training BID7. Besides unlike explicit regularization techniques if data augmentation does not increase computational complexity can be performed parallel gradient updates CPU making computationally free operation. Finally Section 2.4 have shown how data augmentation transparently adapts architectures different depth whereas explicitly regularized models need manual adjustment regularization parameters.Deep neural networks can especially benefit data augmentation do not rely precomputed features large number parameters allows shatter augmented training set. Actually if data augmentation is included training might have to reconsider whether deep learning operates overparameterization regime since model capacity should take account amount training data which is exponentially increased augmentation.Some argue despite advantages if data augmentation is a highly limited approach depends prior expert knowledge cannot applied domains. However argue instead expert knowledge should not be disregarded exploited. single data augmentation scheme can be designed broad family data e.g natural images effectively applied broad set tasks e.g object recognition segmentation localization etc. Besides recent works show is possible learn data augmentation strategies Lemleyetal. 2017;Ratneretal. 2017 future research will probably yield even better results different domains.Finally is important note due computational limitations have performed systematic analysis CIFAR-10 CIFAR-100 which consist small images. data sets do not allow performing agressive data augmentation since low resolution images can be can easily show distortions hinder recognition object. However previous works BID13 Springenberg etal. 2014 have shown impressive results performing heavier data augmentation higher resolution versions CIFAR-10 plan extend analysis higher resolution data sets ImageNet one could expect even benefits data augmentation compared explicit regularization techniques.",1755,1207,548,0.022,1.454,2025/11/05 17:18:58,0.01,1.556,0.3862928348909654,553.794
"Text editing on mobile devices can be a tedious process. To perform various editing operations, a user must repeatedly move his or her fingers between the text input area and the keyboard, making multiple round trips and breaking the flow of typing. In this work, we present Gedit, a system of on-keyboard gestures for convenient mobile text editing. Our design includes a ring gesture and flicks for cursor control, bezel gestures for mode switching, and four gesture shortcuts for copy, paste, cut, and undo. Variations of our gestures exist for one and two hands. We conducted an experiment to compare Gedit with the de facto touch+widget based editing interactions. Our results showed that Gedit’s gestures were easy to learn, 24% and 17% faster than the de facto interactions for one- and two-handed use, respectively, and preferred by participants. Text entry is a fundamental input task on almost all computers, including touch-based mobile devices like smartphones and tablets. However, while touch-based text entry has garnered much attention, touch-based text editing has garnered less. Text editing, the process of correcting text, moving and replacing the cursor, selecting character ranges, and performing operations like copy-and-paste, still largely borrows from desktop mouse interactions, leading to certain inefficient editing processes on touch-based mobile devices. Modeless editing operations [18] such as copy, paste, and cut are often handled in a touch+widget [7] manner: to copy text, one must touch exactly on the text to be selected, long-press to trigger ""selection mode,"" drag the selection endpoints to adjust the selection range, and then select ""copy."" However, the cursor is positioned using tap gestures, which are error prone because of the fat finger problem [20] , especially when text characters are small [1] . Also, users must press long enough to exceed a time threshold to trigger selection mode, and later select ""copy"" in a popup menu to complete the operation. These extra steps significantly slow text editing on mobile touch screens. Moreover, if an editing operation must happen during the text entry process, one must lift one's finger from the keyboard area to directly interact with the text input area, introducing unnecessary round-trips [5, 10, 12] and breaking the flow of typing. Previous work has demonstrated the feasibility of gesture shortcuts. Fuccella et al. [7] designed multiple gestures on the keyboard area for different editing operations. For example, one can perform a swipe gesture to move the cursor, or a ""C"" gesture to copy text. They further introduced a gesture to initiate editing mode to avoid conflict with gesture typing [8] . Building upon their work, we improve the cursormoving and edit-initiating gestures and provide a gestureonly system, Gedit, for most text editing operations on mobile devices. For example, one of Gedit's designs, the ring gesture, is shown in Figure 1 . Our work distinguishes itself from Fuccella et al. [7] and other prior work in four important respects: (1) instead of discrete cursor control (e.g., one swipe gesture yields one cursor movement action), we provide a ring gesture for continuous, reversible cursor control. A significant advantage is that a user can move the cursor over a long range without clutching; (2) rather than using a single tap, we use bezel gestures [17] to enter editing mode, which we show is more distinguishable than a key-press [4] ; (3) we added undo functionality to the gesture set, as undo is heavily used in text editing; and (4) we provide text editing gestures in both one-and two-handed modes, a significant design achievement given the constraints of one-handed use. In our design of Gedit, we were careful to ensure that it remains compatible with gesture typing [13, 22] . And because Gedit respects current interaction techniques, it is deployable on today's mobile systems without causing interference. To evaluate Gedit, we conducted a text editing experiment. Our results show that compared to the de facto touch+widget method of text editing described above, Gedit was faster and preferred, especially for one-handed use. Our goal was to evaluate Gedit on its editing efficiency and users' subjective preferences. The results showed that our gesture interactions sped up the text editing process compared to the de facto editing approach of tapping keys and tapping the text input area to position the cursor (touch+widget). Participants especially appreciated the capability that Gedit's gestures offered for one-handed use. Participants generally enjoyed the Gedit gestures. The major reasons were having a feeling of precise control, convenience, and speed. Many participants also mentioned that the editing gestures such as copy and paste were faster than pointing and holding, and also less tedious to perform. Participants had split preferences on the one-vs. two-handed versions of Gedit. Four participants preferred two-handed Gedit because ""it is more intuitive just like the shortcuts"" (P13), and ""the gestures in double-hand mode are easier to perform"" (P14). Four participants preferred one-handed Gedit because ""it is faster, as I don't need to enter the editing mode with another finger"" (P7). As for different gestures, we noticed that participants usually used the ring gesture to fix typos, while using the flick gestures to select whole words. In this paper, we presented Gedit, a system of on-keyboard gestures for text editing: ring and flick gestures for cursor control and text selection, bezel gestures for mode switching, and letter-like gestures for editing commands. The gestures can be performed in both one-and two-handed modes. Through our formal study, we demonstrated that Gedit sped up the editing process and reduced text entry time, was perceived to require less workload, and was preferred to the de facto method of tapping keys and tapping text input areas.",Text editing mobile devices can be a tedious process. perform various editing operations user must repeatedly move fingers text input area keyboard making multiple round trips breaking flow typing. work present Gedit system on-keyboard gestures convenient mobile text editing. design includes ring gesture flicks cursor control bezel gestures mode switching four gesture shortcuts copy paste cut undo. Variations gestures exist one two hands. conducted experiment compare Gedit de facto touch+widget based editing interactions. results showed Gedits gestures were easy learn 24% 17% faster de facto interactions one- two-handed use respectively was preferred participants. Text entry is a fundamental input task almost computers including touch-based mobile devices like smartphones tablets. However touch-based text entry has garnered much attention touch-based text editing has garnered less. Text editing process correcting text moving replacing cursor selecting character ranges performing operations like copy-and-paste still largely borrows desktop mouse interactions leading certain inefficient editing processes touch-based mobile devices. Modeless editing operations 18 copy paste cut are often handled touch+widget 7 manner:copy text one must touch exactly text selected long-press trigger selection mode drag selection endpoints adjust selection range select copy. However cursor is positioned using tap gestures which are error prone fat finger problem 20 especially when text characters are small 1 Also users must press long enough exceed time threshold trigger selection mode later select copy popup menu complete operation. extra steps significantly slow text editing mobile touch screens. Moreover if an editing operation must happen text entry process one must lift one's finger keyboard area directly interact text input area introducing unnecessary round-trips 5 10 12 breaking flow typing. Previous work has demonstrated feasibility gesture shortcuts. Fuccellaetal. 7 designed multiple gestures keyboard area different editing operations. example one can perform swipe gesture move cursor C gesture copy text. introduced gesture initiate editing mode avoid conflict gesture typing 8 Building upon work improve cursormoving edit-initiating gestures provide gestureonly system Gedit text editing operations mobile devices. example one Gedit's designs ring gesture is shown Figure1. work distinguishes Fuccellaetal. 7 prior work four important respects:1 instead discrete cursor control e.g one swipe gesture yields one cursor movement action provide ring gesture continuous reversible cursor control. significant advantage is that a user can move cursor long range without clutching;2 rather using single tap use bezel gestures 17 enter editing mode which we show is more distinguishable key-press 4 3 added undo functionality gesture set undo is heavily used text editing;4 provide text editing gestures one-and two-handed modes significant design achievement given constraints one-handed use. design Gedit were careful ensure remains compatible gesture typing 13 22 Gedit respects current interaction techniques is deployable today's mobile systems without causing interference. evaluate Gedit conducted text editing experiment. results show compared de facto touch+widget method text editing described Gedit was faster preferred especially one-handed use. goal was to evaluate Gedit editing efficiency users' subjective preferences. results showed gesture interactions sped text editing process compared de facto editing approach tapping keys tapping text input area position cursor touch+widget Participants especially appreciated capability Gedit's gestures offered one-handed use. Participants generally enjoyed Gedit gestures. major reasons were having a feeling precise control convenience speed. Many participants also mentioned editing gestures copy paste were faster pointing holding also less tedious perform. Participants had split preferences one-vs two-handed versions Gedit. Four participants preferred two-handed Gedit is more intuitive like shortcuts P13 gestures double-hand mode are easier perform P14 Four participants preferred one-handed Gedit is faster need enter editing mode another finger P7 different gestures noticed participants usually used ring gesture fix typos using flick gestures select whole words. paper presented Gedit system on-keyboard gestures text editing:ring flick gestures cursor control text selection bezel gestures mode switching letter-like gestures editing commands. gestures can be performed one-and two-handed modes. formal study demonstrated Gedit sped editing process reduced text entry time was perceived require less workload was preferred de facto method tapping keys tapping text input areas.,1188,797,391,0.012,1.491,2025/11/05 17:18:58,0.01,1.452,0.5015576323987541,359.65
"Deep learning achieves remarkable generalization capability with overwhelming number of model parameters. Theoretical understanding of deep learning generalization receives recent attention yet remains not fully explored. This paper attempts to provide an alternative understanding from the perspective of maximum entropy. We first derive two feature conditions that softmax regression strictly apply maximum entropy principle. DNN is then regarded as approximating the feature conditions with multilayer feature learning, and proved to be a recursive solution towards maximum entropy principle. The connection between DNN and maximum entropy well explains why typical designs such as shortcut and regularization improves model generalization, and provides instructions for future model development. Deep learning has achieved significant success in various application areas. Its success has been widely ascribed to the remarkable generalization ability. Recent study shows that with very limited training data, a 12-layer fully connected neural network still generalizes well while kernel ridge regression easily overfits with polynomial kernels of more than 6 orders (Wu et al., 2017) . Classical statistical learning theories like Vapnik-Chervonenkis (VC) dimension (Maass, 1994) and Rademacher complexity (Neyshabur et al., 2015) evaluate generalization based on the complexity of the target function class. It is suggested that the models with good generalization capability are expected to have low function complexity. However, most successful deep neural networks already have over 100 hidden layers, e.g., ResNet BID2 and DenseNet BID3 for image recognition. The number of model parameters in these cases is even larger than the number of training samples. Statistical learning theory cannot well explain the generalization capability of deep learning models (Zhang et al., 2017) .Maximum Entropy (ME) is a general principle for designing machine learning models. Models fulfilling the principle of ME make least hypothesis beyond the stated prior data, and thus lead to least biased estimate possible on the given information BID5 . Appropriate feature functions are critical in applying ME principle and largely decide the model generalization capability BID1 . Different selections of feature functions lead to different instantiations of maximum entropy models (Malouf, 2002; Yusuke & Jun'ichi, 2002) . The most simple and wellknown instantiation is that ME principle invents identical formulation of softmax regression by selecting certain feature functions and treating data as conditionally independent (Manning & Klein, 2003) . It is obvious that softmax regression has no guaranty of generalization, indicating that inappropriate feature functions and data hypothesis violates ME principle and undermines the model performance. It remains not fully studied how to select feature functions to maximally fulfill ME principle and guarantee the generalization capability of ME models. Maximum entropy provides a potential but not-ready way to understand deep learning generalization. This paper is motivated to improve the theory behind applying ME principle and use it to understand deep learning generalization. We research on the feature conditions to equivalently apply ME principle, and indicates that deep neural networks (DNN) is essentially a recursive solution to approximate the feature conditions and thus maximally fulfill ME principle.• In Section 2, we first revisit the relation between generalization and ME principle, and conclude that models well fulfilling ME principle requires least data hypothesis so to possess good generalization capability. One general guideline for feature function selection is to transfer the hypothesis on input data to the constrain on model features 1 . This demonstrates the role of feature learning in designing ME models.• Section 3 addresses what features to learn. Specifically, we derive two feature conditions to make softmax regression strictly equivalent to the original ME model (denoted as Maximum Entropy Equivalence Theorem). That is, if the utilized features meet the two conditions, simple softmax regression model can fulfill ME principle and guarantee generalization. These two conditions actually specify the goal of feature learning.• Section 4 resolves how to meet the feature conditions and connects DNN with ME. Based on Maximum Entropy Equivalence Theorem, viewing the output supervision layer as softmax regression, the DNN hidden layers before the output layer can be regarded as learning features to meet the feature conditions. Since the feature conditions are difficult to be directly satisfied, they are optimized and recursively decomposed to a sequence of manageable problems. It is proved that, standard DNN uses the composition of multilayer non-linear functions to realize the recursive decomposition and uses back propagation to solve the corresponding optimization problem.• Section 5 employs the above ME interpretation to explain some generalization-related observations of DNN. Specifically, from the perspective of ME, we provide an alternative way to understand the connection between deep learning and Information Bottleneck (Shwartz-Ziv & Tishby, 2017) . Theoretical explanations on typical generalization design of DNN, e.g., shortcut, regularization , are also provided at last.The contributions are summarized in three-fold:1. We derive the feature conditions that softmax regression strictly apply maximum entropy principle . This helps understanding the relation between generalization and ME models, and provides theoretical guidelines for feature learning in these models.2. We introduce a recursive decomposition solution for applying ME principle. It is proved that DNN maximally fulfills maximum entropy principle by multilayer feature learning and softmax regression, which guarantees the model generalization performance.3. Based on the ME understanding of DNN, we provide explanations to the information bottleneck phenomenon in DNN and typical DNN designs for generalization improvement. This paper regards DNN as a solution to recursively decomposing the original maximum entropy problem. From the perspective of maximum entropy, we ascribe the remarkable generalization capability of DNN to the introduction of least extra data hypothesis. The future work goes in two directions: (1) first efforts will be payed to identifying connections with other generalization theories and explaining more DNN observations like the role of ReLu activation and redundant features; (2) the second direction is to improve and exploit the new theory to provide instructions for future model development of traditional machine learning as well as deep learning methods.",Deep learning achieves remarkable generalization capability overwhelming number model parameters. Theoretical understanding deep learning generalization receives recent attention yet remains fully explored. paper attempts provide alternative understanding perspective maximum entropy. first derive two feature conditions softmax regression strictly apply maximum entropy principle. DNN is then regarded approximating feature conditions multilayer feature learning proved recursive solution towards maximum entropy principle. connection DNN maximum entropy well explains why typical designs shortcut regularization improves model generalization provides instructions future model development. Deep learning has achieved significant success various application areas. success has been widely ascribed remarkable generalization ability. Recent study shows limited training data 12-layer fully connected neural network still generalizes well kernel ridge regression easily overfits polynomial kernels 6 orders Wuetal. 2017 Classical statistical learning theories like Vapnik-Chervonenkis VC dimension Maass 1994 Rademacher complexity Neyshaburetal. 2015 evaluate generalization based complexity target function class. is suggested models good generalization capability are expected have low function complexity. However successful deep neural networks already have over 100 hidden layers e.g ResNet BID2 DenseNet BID3 image recognition. number model parameters cases is even larger number training samples. Statistical learning theory cannot well explain generalization capability deep learning models Zhangetal. 2017.Maximum Entropy is general principle designing machine learning models. Models fulfilling principle make least hypothesis beyond stated prior data thus lead least biased estimate possible given information BID5. Appropriate feature functions are critical applying principle largely decide model generalization capability BID1. Different selections feature functions lead different instantiations maximum entropy models Malouf 2002;Yusuke Jun ichi 2002 simple wellknown instantiation is that ME principle invents identical formulation softmax regression selecting certain feature functions treating data conditionally independent Manning Klein 2003 is obvious softmax regression has no guaranty generalization indicating inappropriate feature functions data hypothesis violates principle undermines model performance. remains fully studied how to select feature functions maximally fulfill principle guarantee generalization capability models. Maximum entropy provides potential not-ready way understand deep learning generalization. paper is motivated improve theory behind applying principle use understand deep learning generalization. research feature conditions equivalently apply principle indicates deep neural networks DNN is essentially recursive solution approximate feature conditions thus maximally fulfill principle.• Section2 first revisit relation generalization principle conclude models well fulfilling principle requires least data hypothesis possess good generalization capability. One general guideline feature function selection is to transfer hypothesis input data constrain model features1. demonstrates role feature learning designing models.• Section3 addresses what features learn. Specifically derive two feature conditions make softmax regression strictly equivalent original model denoted Maximum Entropy Equivalence Theorem is if the utilized features meet two conditions simple softmax regression model can fulfill principle guarantee generalization. two conditions actually specify goal feature learning.• Section 4 resolves how to meet feature conditions connects DNN ME. Based Maximum Entropy Equivalence Theorem viewing output supervision layer softmax regression DNN hidden layers output layer can be regarded learning features meet feature conditions. Since feature conditions are difficult directly satisfied are optimized recursively decomposed sequence manageable problems. is proved standard DNN uses composition multilayer non-linear functions realize recursive decomposition uses back propagation solve corresponding optimization problem.• Section 5 employs interpretation explain generalization-related observations DNN. Specifically perspective provide alternative way understand connection deep learning Information Bottleneck Shwartz-Ziv Tishby 2017 Theoretical explanations typical generalization design DNN e.g shortcut regularization are also provided last.The contributions are summarized three-fold:1 derive feature conditions softmax regression strictly apply maximum entropy principle. helps understanding relation generalization models provides theoretical guidelines feature learning models.2 introduce recursive decomposition solution applying principle. is proved DNN maximally fulfills maximum entropy principle multilayer feature learning softmax regression which guarantees model generalization performance.3 Based understanding DNN provide explanations information bottleneck phenomenon DNN typical DNN designs generalization improvement. paper regards DNN solution recursively decomposing original maximum entropy problem. perspective maximum entropy ascribe remarkable generalization capability DNN introduction least extra data hypothesis. future work goes two directions:1 first efforts will be payed identifying connections generalization theories explaining DNN observations like role ReLu activation redundant features;2 second direction is to improve exploit new theory provide instructions future model development traditional machine learning well deep learning methods.,1219,866,353,0.013,1.408,2025/11/05 17:18:58,0.01,1.406,0.242990654205607,357.504
" As people learn to navigate the world, autonomic nervous system (e.g., ``fight or flight) responses provide intrinsic feedback about the potential consequence of action choices (e.g., becoming nervous when close to a cliff edge or driving fast around a bend.) Physiological changes are correlated with these biological preparations to protect one-self from danger. We present a novel approach to reinforcement learning that leverages a task-independent intrinsic reward function trained on peripheral pulse measurements that are correlated with human autonomic nervous system responses. Our hypothesis is that such reward functions can circumvent the challenges associated with sparse and skewed rewards in reinforcement learning settings and can help improve sample efficiency. We test this in a simulated driving environment and show that it can increase the speed of learning and reduce the number of collisions during the learning stage. The human autonomic nervous system (ANS) is composed of two branches. One of these, the sympathetic nervous system (SNS), is ""hard-wired"" to respond to potentially dangerous situations often reducing, or by-passing, the need for conscious processing. The ability to make rapid decisions and respond to immediate threats is one way of protecting oneself from danger. Whether one is in the African savanna or driving in Boston traffic.The SNS regulates a range of visceral functions from the cardiovascular system to the adrenal system BID9 . The anticipatory response in humans to a threatening situation is for the heart rate to increase, heart rate variability to decrease, blood to be diverted from the extremities and the sweat glands to dilate. This is the body's ""fight or flight"" response.While the primary role of these anticipatory responses is to help one prepare for action, they also play a part in our appraisal of a situation. The combination of sensory inputs, physiological responses and cognitive evaluation form emotions that influence how humans learn, plan and make decisions BID14 . Intrinsic motivation refers to being moved to act based on the way it makes one feel. For example, it is generally undesirable to be in a situation that causes fear and thus we might choose to take actions that help avoid these types of contexts in future. This is contrasted with extrinsic motivation that involves explicit goals BID4 .Driving is an everyday example of a task in which we commonly rely on both intrinsic and extrinsic motivations and experience significant physiological changes. When traveling in a car at highspeed one may experience a heightened state of arousal. This automatic response is correlated with the body's reaction to the greater threats posed by the situation (e.g., the need to adjust steering more rapidly to avoid a pedestrian that might step into the road). Visceral responses are likely to preempt accidents or other events (e.g., a person will become nervous before losing control and hitting someone). Therefore, these signals potentially offer an advantage as a reward mechanism compared to extrinsic rewards based on events that occur in the environment, such as a collision. This paper provides a reinforcement learning (RL) framework that incorporates reward functions for achieving task-specific goals and also minimizes a cost trained on physiological responses to the environment that are correlated with stress. We ask if such a reward function with extrinsic and intrinsic components is useful in a reinforcement learning setting. We test our approach by training a model on real visceral human responses in a driving task.The key challenges of applying RL in the real-world include the amount of training data required and the high-cost associated with failure cases. For example, when using RL in autonomous driving, rewards are often sparse and skewed. Furthermore, bad actions can lead to states that are both catastrophic and expensive to recover from. While much of the work in RL focuses on mechanisms that are task or goal dependent, it is clear that humans also consider the feedback from the body's nervous system for action selection. For example, increased arousal can help signal imminent danger or failure to achieve a goal. Such mechanisms in an RL agent could help reduce the sample complexity as the rewards are continually available and could signal success or failure before the end of the episode. Furthermore, these visceral signals provide a warning mechanism that in turn could lead to safer explorations.Our work is most closely related to that in intrinsically motivated learning BID4 BID26 BID7 BID17 that uses a combination of intrinsic and extrinsic rewards and shows benefits compared to using extrinsic rewards alone. The key distinction in our work is that we specifically aim to build intrinsic reward mechanisms that are visceral and trained on signals correlated with human affective responses. Our approach could also be considered a form of imitation learning BID20 BID19 BID8 BID2 as we use the signal from a human expert for training. However, a difference is that our signal is an implicit response from the driver versus an explicit instruction or action which might commonly be the case in imitation learning.The structural credit assignment problem, or generalization problem, aims to address the challenge posed by large parameter spaces in RL and the need to give the agent the ability to guess, or have some intuition about new situations based on experience BID13 . A significant advantage of our proposed method is the reduced sparsity of the reward signal. This makes learning more practical in a large parameter space. We conduct experiments to provide empirical evidence that this can help reduce the number of epochs required in learning. In a sense, the physiological response could be considered as an informed guess about new scenarios before the explicit outcome is known. The challenge with traditional search-based structured prediction is the assumptions that must be made in the search algorithms that are required BID5 . By training a classifier using a loss based on the human physiological response this problem can potentially be simplified.The core contributions of this paper are to: (1) present a novel approach to learning in which the reward function is augmented with a model learned directly from human nervous system responses, (2) show how this model can be incorporated into a reinforcement learning paradigm and (3) report the results of experiments that show the model can improve both safety (reducing the number of mistakes) and efficiency (reducing the sample complexity) of learning.In summary, we argue that a function trained on physiological responses could be used as an intrinsic reward or value function for artificially intelligent systems, or perhaps more aptly artificially emotionally intelligent systems. We hypothesize that incorporating intrinsic rewards with extrinsic rewards in an RL framework (as shown in FIG0 will both improve learning efficiency as well as reduce catastrophic failure cases that occur during the training. Heightened arousal is an key part of the ""fight or flight"" response we experience when faced with risks to our safety. We have presented a novel reinforcement learning paradigm using an intrinsic reward function trained on peripheral physiological responses and extrinsic rewards based on mission goals. First, we trained a neural architecture to predict a driver's peripheral blood flow modulation based on the first-person video from the vehicle. This architecture acted as the reward in our reinforcement learning step. A major advantage of training a reward on a signal correlated with the sympathetic nervous system responses is that the rewards are non-sparse -the negative reward starts to show up much before the car collides. This leads to efficiency in training and with proper design can lead to policies that are also aligned with the desired mission. While emotions are important for decision-making BID12 , they can also detrimentally effect decisions in certain contexts. Future work will consider how to balance intrinsic and extrinsic rewards and include extensions to representations that include multiple intrinsic drives (such as hunger, fear and pain).We must emphasize that in this work we were not attempting to mimic biological processes or model them explicitly. We were using a prediction of the peripheral blood volume pulse as an indicator of situations that are correlated with high arousal.",people learn navigate world autonomic nervous system e.g fight flight responses provide intrinsic feedback potential consequence action choices e.g becoming nervous when close cliff edge driving fast around bend. Physiological changes are correlated biological preparations protect one-self danger. present novel approach reinforcement learning leverages task-independent intrinsic reward function trained peripheral pulse measurements are correlated human autonomic nervous system responses. hypothesis is that such reward functions can circumvent challenges associated sparse skewed rewards reinforcement learning settings can help improve sample efficiency. test simulated driving environment show can increase speed learning reduce number collisions learning stage. human autonomic nervous system ANS is composed two branches. One sympathetic nervous system SNS is hard-wired respond potentially dangerous situations often reducing by-passing need conscious processing. ability make rapid decisions respond immediate threats is one way protecting oneself danger. Whether one is in the African savanna driving Boston traffic.The SNS regulates range visceral functions cardiovascular system adrenal system BID9. anticipatory response humans threatening situation is for the heart rate increase heart rate variability decrease blood diverted extremities sweat glands dilate. is the body's fight flight response.While primary role anticipatory responses is to help one prepare action can also play part appraisal situation. combination sensory inputs physiological responses cognitive evaluation form emotions influence how humans learn plan make decisions BID14. Intrinsic motivation refers moved act based way makes one feel. example is generally undesirable situation causes fear thus might choose take actions can help avoid types contexts future. is contrasted extrinsic motivation involves explicit goals BID4.Driving is an everyday example task which we commonly rely intrinsic extrinsic motivations experience significant physiological changes. When traveling car highspeed one may experience heightened state arousal. automatic response is correlated body's reaction greater threats posed situation e.g need adjust steering rapidly avoid pedestrian might step road Visceral responses are likely preempt accidents events e.g person will become nervous losing control hitting someone Therefore signals potentially offer advantage reward mechanism compared extrinsic rewards based events occur environment collision. paper provides reinforcement learning RL framework incorporates reward functions achieving task-specific goals also minimizes cost trained physiological responses environment are correlated stress. ask if such a reward function extrinsic intrinsic components is useful reinforcement learning setting. test approach training model real visceral human responses driving task.The key challenges applyingRL real-world include amount training data required high-cost associated failure cases. example when usingRL autonomous driving rewards are often sparse skewed. Furthermore bad actions can lead states are both catastrophic expensive recover from. much work RL focuses mechanisms are task goal dependent is clear humans also consider feedback body's nervous system action selection. example increased arousal can help signal imminent danger failure achieve goal. mechanisms RL agent could help reduce sample complexity rewards are continually available could signal success failure end episode. Furthermore visceral signals provide warning mechanism turn could lead safer explorations.Our work is most closely related intrinsically motivated learning BID4 BID26 BID7 BID17 uses combination intrinsic extrinsic rewards shows benefits compared using extrinsic rewards alone. key distinction work is that we specifically aim build intrinsic reward mechanisms are visceral trained signals correlated human affective responses. approach could also considered form imitation learning BID20 BID19 BID8 BID2 use signal human expert training. However difference is that our signal is an implicit response driver versus explicit instruction action might commonly case imitation learning.The structural credit assignment problem generalization problem aims address challenge posed large parameter spaces RL need give agent ability guess have some intuition new situations based experience BID13. significant advantage proposed method is the reduced sparsity reward signal. makes learning practical large parameter space. conduct experiments provide empirical evidence can help reduce number epochs required learning. sense physiological response could considered informed guess new scenarios explicit outcome is known. challenge traditional search-based structured prediction is the assumptions must made search algorithms are required BID5. training classifier using loss based human physiological response problem can potentially simplified.The core contributions paper to:1 present novel approach learning which the reward function is augmented model learned directly human nervous system responses 2 show how this model can be incorporated reinforcement learning paradigm 3 report results experiments show model can improve safety reducing number mistakes efficiency reducing sample complexity learning.In summary argue function trained physiological responses could used intrinsic reward value function artificially intelligent systems perhaps aptly artificially emotionally intelligent systems. hypothesize incorporating intrinsic rewards extrinsic rewards RL framework shown FIG0 will both improve learning efficiency well reduce catastrophic failure cases occur training. Heightened arousal is an key part fight flight response experience when faced risks safety. have presented novel reinforcement learning paradigm using intrinsic reward function trained peripheral physiological responses extrinsic rewards based mission goals. First trained neural architecture predict driver's peripheral blood flow modulation based first-person video vehicle. architecture acted reward reinforcement learning step. major advantage training reward signal correlated sympathetic nervous system responses is that the rewards are non-sparse -the negative reward starts show much car collides. leads efficiency training proper design can lead policies are also aligned desired mission. emotions are important decision-making BID12 can also detrimentally effect decisions certain contexts. Future work will consider how to balance intrinsic extrinsic rewards include extensions representations include multiple intrinsic drives hunger fear pain.We must emphasize work were not attempting mimic biological processes model explicitly. were using prediction peripheral blood volume pulse indicator situations are correlated high arousal.,1523,1017,506,0.018,1.498,2025/11/05 17:18:59,0.01,1.492,0.5233644859813082,533.149
"Deep convolutional neural networks (CNNs) are known to be robust against label noise on extensive datasets. However, at the same time, CNNs are capable of memorizing all labels even if they are random, which means they can memorize corrupted labels. Are CNNs robust or fragile to label noise? Much of researches focusing on such memorization uses class-independent label noise to simulate label corruption, but this setting is simple and unrealistic. In this paper, we investigate the behavior of CNNs under class-dependently simulated label noise, which is generated based on the conceptual distance between classes of a large dataset (i.e., ImageNet-1k). Contrary to previous knowledge, we reveal CNNs are more robust to such class-dependent label noise than class-independent label noise. We also demonstrate the networks under class-dependent noise situations learn similar representation to the no noise situation, compared to class-independent noise situations. Deep convolutional neural networks (CNNs) excel in supervised image classification tasks BID17 ). Representation learned from such tasks can be transfer to other tasks, including object detection BID31 ; ; BID30 ) and semantic segmentation BID2 ; Badrinarayanan et al.) . Furthermore, if the training dataset is sufficiently larger, CNNs can improve the performance in classification, or learn better transferable representation, even if some labels are corrupted BID20 ; BID36 ; BID22 ).However , recent CNNs have far more parameters than their training samples. Therefore , the networks can memorize all the training data even if all labels are randomly replaced with the wrong ones ; ). This capability may degrade CNNs' performance under the label-corrupted situation, thus learning methods against label noise have been studied.Are CNNs robust or fragile to label noise? To investigate this question, we need to adopt noisy labels in controlled experiments. In previous work , both natural and synthetic noise have been used to research label corrupted situations. Natural noise appears in generally every dataset, and it comes from, for instance, annotators' mislabeling BID3 or their varieties BID6 ). Some researchers have been proposed robust training methods under this type of noise BID19 ; BID15 ; BID38 ). However, natural noise is uncontrollable, in other words, the relationship between the magnitude of noise and CNNs' performance has been unknown.On the other hand, synthetic noise simulates natural one by stochastically replacing ground truth labels with others. Class-independent uniform label permutation is a common setting BID15 ; BID10 ), yet some researchers use class-dependent label permutation, which is considered as more realistic situation BID26 ; BID8 ; BID27 ; BID9 ). Previous research has mainly adopted MNIST (10 classes, 60,000 training samples, BID18 ) or CIFAR-10/100 (10 and 100 classes, 50,000 training samples, BID17 ), and these datasets lack pre-defined conceptual relationships between classes. This limitation results in simplified noise simulation on such datasets, although synthetic noise enables researchers to research the relationship between the noise magnitude and the performance of networks.To investigate whether CNNs are robust or fragile to label corruption, we propose to use simulated noise considering possible mislabeling on ImageNet-1k (Russakovsky et al. (2015) ) to complement the disadvantages. Exploiting ImageNet-1k's conceptual hierarchy , we can divide its 1,000 labels into some clusters. We use these clusters to generate class-conditional label noise. We train several networks on the training dataset with and without corrupted labels. Then we evaluate the performance of the networks on the original validation set, the robustness of the networks against adversarial perturbation BID37 ; BID28 ), and their learned representation using transfer learning, canonical correlation analysis BID29 ; BID25 ).In this paper, we show the performance of CNNs trained on such synthesized noise considering possible mislabeling is better than uniformly synthesized noise, which is contrary to previous research BID8 ; BID27 ). Besides, models trained on class-dependent label noise are more robust to adversarial perturbation than ones trained on class-independent label noise. We also demonstrate CNNs trained under class-conditionally noisy conditions learn similar features to ones trained under the clean condition. As a result, even when 80% of labels are class-dependently corrupted, CNNs can learn useful representation for transfer learning. Meanwhile, we demonstrate class-independent noise leads models to learn different representation from ones trained with data with clean labels or label noise considering conceptual hierarchy. These differences can be attributed to the property of categorical cross entropy loss, which is a well-used loss function for image recognition tasks. We believe using class-independent noise is not a suitable protocol to investigate the CNNs' tolerance in practical situations. Why does class-dependent noise affect less than class-independent noise? We think there are two reasons: class-dependent noise is more informative, and it avoids the loss value getting too large.When class-dependent noise swaps a ground truth label with a wrong one, it is still a similar class to the original. Thus, the network can learn ""which cluster the sample belongs to"". This idea is related to the soft label BID12 ), though in our case, the label is ""hard"". Contrary to this, class-independent noise conveys no information.The other reason results from the property of categorical cross entropy loss. When the label of sample x is i, the loss value can be written as − log[f (x)] i , where f (x) is the corresponding softmax output. Therefore, when a CNN predicts x as i with weaker confidence, the penalty gets larger. Since the wrong label corrupted by class-dependent noise belongs to the same cluster as the ground truth, [f (x)] i is relatively large (c.f. Figure 2 (b) ). However, in the case of classindependent noise, the wrong label has nothing to do with the ground truth, and if the ground truth and the corrupted label are irrelevant, [f (x)] i should be small. Thus, the loss value gets larger, which leads the network to a worse solution.Also, our finding can be applicable to the quality control of annotation of data. Our results show class-dependent noise is more favorable than class-independent noise. Inexperienced but honest annotators will yield class-dependent noise, while lazy and malicious annotators may randomly annotate the labels and will yield class-independent noise. Therefore, according to our results, the administrators of the annotation need to exclude such workers. In this paper, we investigated the relationship between label noise, the performance and representation of CNNs in image classification tasks. We used ImageNet-1k with simulated noise which includes class-independent noise and class-dependent noise considering conceptual similarity. We examined such noise considering possible mislabeling causes less performance decrease and more robustness against adversarial perturbation compared to class-independent noise. Besides, we investigated the internal representation of CNNs trained with and without label corruption. Experiments showed networks trained on class-independently noisy data learn different representation from ones trained on clean or class-conditionally noisy data.Some previous research on label-noise-tolerant learning methods has used class-independent noise. However, as we revealed in this research, this noise setting is so artificial and straightforward that such methods may not be effective against real noise. Meanwhile, our results suggest plain CNNs themselves can be robust against real noise. This property should be good news for practitioners. Nevertheless, it is also shown noise considering possible mislabeling still somewhat degrades the performance of networks. Thus, how to avoid the effect of label noise is still a remaining problem.","Deep convolutional neural networks CNNs are known robust label noise extensive datasets. However time CNNs are capable memorizing labels even if they are random which means can memorize corrupted labels. Are CNNs robust fragile label noise? Much researches focusing memorization uses class-independent label noise simulate label corruption setting is simple unrealistic. paper investigate behavior CNNs class-dependently simulated label noise which is generated based conceptual distance classes large dataset.e ImageNet-1k Contrary previous knowledge reveal CNNs are more are robust class-dependent label noise class-independent label noise. also demonstrate networks class-dependent noise situations learn similar representation noise situation compared class-independent noise situations. Deep convolutional neural networks CNNs excel supervised image classification tasks BID17 Representation learned tasks can be transfer tasks including object detection BID31;BID30 semantic segmentation BID2;Badrinarayananetal. Furthermore if the training dataset is sufficiently larger CNNs can improve performance classification learn better transferable representation even if some if all labels are corrupted BID20;BID36;BID22.However recent CNNs have far parameters training samples. Therefore networks can memorize training data even if some if all labels are randomly replaced wrong ones;capability may degrade CNNs' performance label-corrupted situation thus learning methods label noise have been studied.Are CNNs robust fragile label noise? investigate question need adopt noisy labels controlled experiments. previous work natural synthetic noise have been used research label corrupted situations. Natural noise appears generally every dataset comes instance annotators' mislabeling BID3 varieties BID6 researchers have been proposed robust training methods type noise BID19;BID15;BID38 However natural noise is uncontrollable words relationship magnitude noise CNNs' performance has been unknown.On hand synthetic noise simulates natural one stochastically replacing ground truth labels others. Class-independent uniform label permutation is a common setting BID15;BID10 yet researchers use class-dependent label permutation which is considered realistic situation BID26;BID8;BID27;BID9 Previous research has mainly adopted MNIST 10 classes 60,000 training samples BID18 CIFAR-10/100 10 100 classes 50,000 training samples BID17 datasets lack pre-defined conceptual relationships classes. limitation results simplified noise simulation datasets although synthetic noise enables researchers research relationship noise magnitude performance networks.To investigate whether CNNs are more are robust fragile label corruption propose use simulated noise considering possible mislabeling ImageNet-1k Russakovskyetal. 2015 complement disadvantages. Exploiting ImageNet-1k's conceptual hierarchy can divide 1,000 labels clusters. use clusters generate class-conditional label noise. train several networks training dataset without corrupted labels. evaluate performance networks original validation set robustness networks adversarial perturbation BID37;BID28 learned representation using transfer learning canonical correlation analysis BID29;BID25.In paper show performance CNNs trained synthesized noise considering possible mislabeling is better uniformly synthesized noise which is contrary previous research BID8;BID27 Besides models trained class-dependent label noise are more are robust adversarial perturbation ones trained class-independent label noise. also demonstrate CNNs trained class-conditionally noisy conditions learn similar features ones trained clean condition. result even when80% labels are class-dependently corrupted CNNs can learn useful representation transfer learning. Meanwhile demonstrate class-independent noise leads models learn different representation ones trained data clean labels label noise considering conceptual hierarchy. differences can be attributed property categorical cross entropy loss which is a well-used loss function image recognition tasks. believe using class-independent noise is not a suitable protocol investigate CNNs' tolerance practical situations. Why does class-dependent noise affect less class-independent noise? think are two reasons:class-dependent noise is more informative avoids loss value getting large.When class-dependent noise swaps ground truth label wrong one is still similar class original. Thus network can learn which cluster sample belongs to. idea is related soft label BID12 though case label is hard. Contrary class-independent noise conveys information.The reason results property categorical cross entropy loss. When the label samplex is i,the loss value can be written − log f x where f x is the corresponding softmax output. Therefore when a CNN predictsx weaker confidence penalty gets larger. Since wrong label corrupted class-dependent noise belongs cluster ground truth f x is relatively large c.f Figure2 b However case classindependent noise wrong label has nothing do with the ground truth if the ground truth corrupted label are irrelevant f x should small. Thus loss value gets larger which leads network worse solution.Also finding can be applicable quality control annotation data. results show class-dependent noise is more favorable class-independent noise. Inexperienced honest annotators will yield class-dependent noise lazy malicious annotators may randomly annotate labels will yield class-independent noise. Therefore according results administrators annotation need exclude workers. paper investigated relationship label noise performance representation CNNs image classification tasks. used ImageNet-1k simulated noise which includes class-independent noise class-dependent noise considering conceptual similarity. examined noise considering possible mislabeling causes less performance decrease robustness adversarial perturbation compared class-independent noise. Besides investigated internal representation CNNs trained without label corruption. Experiments showed networks trained class-independently noisy data learn different representation ones trained clean class-conditionally noisy data.Some previous research label-noise-tolerant learning methods has used class-independent noise. However revealed research noise setting is so artificial straightforward methods may effective real noise. Meanwhile results suggest plain CNNs can be robust real noise. property should be good news practitioners. Nevertheless is also shown noise considering possible mislabeling still somewhat degrades performance networks. Thus how to avoid effect label noise is still remaining problem.",1523,1117,406,0.017,1.363,2025/11/05 17:18:59,0.01,1.551,0.1028037383177567,460.346
"Efficient audio synthesis is an inherently difficult machine learning task, as human perception is sensitive to both global structure and fine-scale waveform coherence. Autoregressive models, such as WaveNet, model local structure at the expense of global latent structure and slow iterative sampling, while Generative Adversarial Networks (GANs), have global latent conditioning and efficient parallel sampling, but struggle to generate locally-coherent audio waveforms. Herein, we demonstrate that GANs can in fact generate high-fidelity and locally-coherent audio by modeling log magnitudes and instantaneous frequencies  with sufficient frequency resolution in the spectral domain. Through extensive empirical investigations on the NSynth dataset, we demonstrate that GANs are able to outperform strong WaveNet baselines on automated and human evaluation metrics, and efficiently generate audio several orders of magnitude faster than their autoregressive counterparts.
 Neural audio synthesis, training generative models to efficiently produce audio with both highfidelity and global structure, is a challenging open problem as it requires modeling temporal scales over at least five orders of magnitude (∼0.1ms to ∼100s). Large advances in the state-of-the art have been pioneered almost exclusively by autoregressive models, such as WaveNet, which solve the scale problem by focusing on the finest scale possible (a single audio sample) and rely upon external conditioning signals for global structure BID32 . This comes at the cost of slow sampling speed, since they rely on inefficient ancestral sampling to generate waveforms one audio sample at a time. Due to their high quality, a lot of research has gone into speeding up generation, but the methods introduce significant overhead such as training a secondary student network or writing highly customized low-level kernels BID33 BID25 . Furthermore, since these large models operate at a fine timescale, their autoencoder variants are restricted to only modeling local latent structure due to memory constraints BID9 .On the other end of the spectrum, Generative Adversarial Networks (GANs) BID11 have seen great recent success at generating high resolution images BID2 BID19 BID16 BID22 . Typical GANs achieve both efficient parallel sampling and global latent control by conditioning a stack of transposed convolutions on a latent vector, The potential for audio GANs extends further, as adversarial costs have unlocked intriguing domain transformations for images that could possibly have analogues in audio BID35 BID15 . However , attempts to adapt image GAN architectures to generate waveforms in a straightforward manner ) fail to reach the same level of perceptual fidelity as their image counterparts.Figure 1: Frame-based estimation of audio waveforms. Much of sound is made up of locallycoherent waves with a local periodicity, pictured as the red-yellow sinusoid with black dots at the start of each cycle. Frame-based techniques, whether they be transposed convolutions or STFTs, have a given frame size and stride, here depicted as equal with boundaries at the dotted lines. The alignment between the two (phase, indicated by the solid black line and yellow boxes), precesses in time since the periodicity of the audio and the output stride are not exactly the same. Transposed convolutional filters thus have the difficult task of covering all the necessary frequencies and all possible phase alignments to preserve phase coherence. For an STFT, we can unwrap the phase over the 2π boundary (orange boxes) and take its derivative to get the instantaneous radial frequency (red boxes), which expresses the constant relationship between audio frequency and frame frequency. The spectra are shown for an example trumpet note from the NSynth dataset. By carefully controlling the audio representation used for generative modeling, we have demonstrated high-quality audio generation with GANs on the NSynth dataset, exceeding the fidelity of a strong WaveNet baseline while generating samples tens of thousands of times faster. While this is a major advance for audio generation with GANs, this study focused on a specific controlled dataset, and further work is needed to validate and expand it to a broader class of signals including speech and other types of natural sound. This work also opens up possible avenues for domain transfer and other exciting applications of adversarial losses to audio. Issues of mode collapse and diversity common to GANs exist for audio as well, and we leave it to further work to consider combining adversarial losses with encoders or more straightforward regression losses to better capture the full data distribution.A MEASURING DIVERSITY ACROSS GENERATED EXAMPLES Table 3 , including adding a pitch classifier to the end of the discriminator as in AC-GAN. All models were trained with the ADAM optimizer BID18 . We sweep over learning rates (2e-4, 4e-4, 8e-4) and weights of the auxiliary classifier loss (0.1, 1.0, 10), and find that for all variants (spectral representation, progressive/no progressive, frequency resolution) a learning rate of 8e-4 and classifier loss of 10 perform the best.As in the original progressive GAN paper, both networks use box upscaling/downscaling and the generators use pixel normalization, DISPLAYFORM0 where n, h, w, and c refer to the batch, height, width, and channel dimensions respectively, x is the activations, and C is the total number of channels. The discriminator also appends the standard deviation of the minibatch activations as a scalar channel near the end of the convolutional stack as seen in Table 3 .Since we find it helpful to use a Tanh output nonlinearity for the generator, we normalize real data before passing to the discriminator. We measure the maximum range over 100 examples and independently shift and scale the log-magnitudes and phases to [-0.8, 0 .8] to allow for outliers and use more of the linear regime of the Tanh nonlinearity.We train each GAN variant for 4.5 days on a single V100 GPU, with a batch size of 8. For nonprogressive models, this equates to training on ∼5M examples. For progressive models , we train on 1.6M examples per a stage (7 stages), 800k during alpha blending and 800k after blending. At the last stage we continue training until the 4.5 days completes. Because the earlier stages train faster, the progressive models train on ∼11M examples.For the WaveNet baseline, we also adapt the open source Tensorflow implementation 11 . The decoder is composed of 30 layers of dilated convolution, each of 512 channels and receptive field of 3, and each with a 1x1 convolution skip connection to the output. The layers are divided into 3 stacks of 10, with dilation in each stack increasing from 2 0 to 2 9 , and then repeating. We replace the audio encoder stack with a conditioning stack operating on a one-hot pitch conditioning signal distributed in time (3 seconds on, 1 second off). The conditioning stack is 5 layers of dilated convolution, increasing to 2 5 , and then 3 layers of regular convolution, all with 512 channels. This conditioning signal is then passed through a 1x1 convolution for each layer of the decoder and added to the output of each layer, as in other implementations of WaveNet conditioning. For the 8-bit model we use mulaw encoding of the audio and a categorical loss, while for the 16-bit model we use a quantized mixture of 10 logistics BID29 . WaveNets converged to 150k iterations in 2 days with 32 V100 GPUs trained with synchronous SGD with batch size 1 per GPU, for a total batch size of 32.",Efficient audio synthesis is an inherently difficult machine learning task human perception is sensitive global structure fine-scale waveform coherence. Autoregressive models WaveNet model local structure expense global latent structure slow iterative sampling Generative Adversarial Networks GANs have global latent conditioning efficient parallel sampling struggle generate locally-coherent audio waveforms. Herein demonstrate GANs can in fact generate high-fidelity locally-coherent audio modeling log magnitudes instantaneous frequencies sufficient frequency resolution spectral domain. extensive empirical investigations NSynth dataset demonstrate GANs are able outperform strong WaveNet baselines automated human evaluation metrics efficiently generate audio several orders magnitude faster autoregressive counterparts. Neural audio synthesis training generative models efficiently produce audio highfidelity global structure is a challenging open problem requires modeling temporal scales least five orders magnitude ∼0.1ms ∼100s Large advances state-of-the art have been pioneered almost exclusively autoregressive models WaveNet which solve scale problem focusing finest scale possible single audio sample rely upon external conditioning signals global structure BID32. comes cost slow sampling speed since rely inefficient ancestral sampling generate waveforms one audio sample time. Due high quality lot research has gone speeding generation methods introduce significant overhead training secondary student network writing highly customized low-level kernels BID33 BID25. Furthermore since large models operate fine timescale autoencoder variants are restricted modeling local latent structure due memory constraints BID9.On end spectrum Generative Adversarial Networks GANs BID11 have seen great recent success generating high resolution images BID2 BID19 BID16 BID22. Typical GANs achieve efficient parallel sampling global latent control conditioning stack transposed convolutions latent vector potential audio GANs extends adversarial costs have unlocked intriguing domain transformations images could possibly have analogues audio BID35 BID15. However attempts adapt image GAN architectures generate waveforms straightforward manner fail reach level perceptual fidelity image counterparts.Figure1:Frame-based estimation audio waveforms. Much sound is made locallycoherent waves local periodicity pictured red-yellow sinusoid black dots start cycle. Frame-based techniques whether transposed convolutions STFTs have a given frame size stride depicted equal boundaries dotted lines. alignment two phase indicated solid black line yellow boxes precesses time since periodicity audio output stride are not exactly same. Transposed convolutional filters thus have the difficult task covering necessary frequencies possible phase alignments preserve phase coherence. STFT can unwrap phase 2π boundary orange boxes take derivative get instantaneous radial frequency red boxes which expresses constant relationship audio frequency frame frequency. spectra are shown example trumpet note NSynth dataset. carefully controlling audio representation used generative modeling have demonstrated high-quality audio generation GANs NSynth dataset exceeding fidelity strong WaveNet baseline generating samples tens thousands times faster. is a major advance audio generation GANs study focused specific controlled dataset work is needed validate expand broader class signals including speech types natural sound. work also opens possible avenues domain transfer exciting applications adversarial losses audio. Issues mode collapse diversity common GANs exist audio well leave work consider combining adversarial losses encoders straightforward regression losses better capture full data distribution.A MEASURING DIVERSITY ACROSS GENERATED EXAMPLES Table3 including adding pitch classifier end discriminator AC-GAN models were trained ADAM optimizer BID18. sweep learning rates 2e-4 4e-4 8e-4 weights auxiliary classifier loss 0.1 1.0 10 find variants spectral representation progressive/progressive frequency resolution learning rate 8e-4 classifier loss 10 perform best.As original progressive GAN paper networks use box upscaling/downscaling generators use pixel normalization DISPLAYFORM0 wheren h w c refer batch height width channel dimensions respectively x is the activations C is the total number channels. discriminator also appends standard deviation minibatch activations scalar channel near end convolutional stack seen Table 3.Since find helpful use Tanh output nonlinearity generator normalize real data passing discriminator. measure maximum range 100 examples independently shift scale log-magnitudes phases -0.8 0.8 allow outliers use linear regime Tanh nonlinearity.We train GAN variant 4.5 days single V100 GPU batch size 8. nonprogressive models equates training ∼5M examples. progressive models train 1.6M examples per stage 7 stages 800k alpha blending 800k blending. last stage continue training 4.5 days completes. earlier stages train faster progressive models train ∼11M examples.For WaveNet baseline also adapt open source Tensorflow implementation 11. decoder is composed 30 layers dilated convolution 512 channels receptive field 3 1x1 convolution skip connection output. layers are divided 3 stacks 10 dilation stack increasing 20 29 repeating. replace audio encoder stack conditioning stack operating one-hot pitch conditioning signal distributed time 3 seconds 1 second conditioning stack is 5 layers dilated convolution increasing 25 3 layers regular convolution 512 channels. conditioning signal is then passed 1x1 convolution layer decoder added output layer implementations WaveNet conditioning. 8-bit model use mulaw encoding audio categorical loss 16-bit model use quantized mixture 10 logistics BID29. WaveNets converged 150k iterations 2 days 32 V100 GPUs trained synchronous SGD batch size 1 per GPU total batch size 32.,1558,1052,506,0.017,1.481,2025/11/05 17:18:59,0.01,1.355,0.4704049844236761,479.842
"In this work we propose a novel approach for learning graph representation of the data using gradients obtained via backpropagation. Next we build a neural network architecture compatible with our optimization approach and motivated by graph filtering in the vertex domain. We demonstrate that the learned graph has richer structure than often used nearest neighbors graphs constructed based on features similarity. Our experiments demonstrate that we can improve prediction quality for several convolution on graphs architectures, while others appeared to be insensitive to the input graph. Recently we have seen a rise in deep learning models, which can account for non-linearities and fit a wide range of functions. Multilayer perceptron (MLP), a general purpose neural network, is a powerful predictor, but requires too many parameters to be estimated and often faces the problem of over-fitting, i.e. learns to almost exactly match training data and unable to generalize when it comes to testing.While MLPs treat all features equally, which partially is the cause of excessive number of parameters, Convolutional Neural Networks (CNNs) have significantly fewer parameters and demonstrate groundbreaking results when it comes to object recognition in images BID11 . The parameter reduction is due to utilizing convolutional operation: a window is sliding through the image and applying same linear transformation of the pixels. The number of parameters then is proportional to the size of the window rather than polynomial of the number of data features as in the case of the MLPs.Indeed images posses a specific structure, which can be encoded as a lattice graph, that makes the sliding window procedure meaningful, but inapplicable outside of the image domain. In recent years there have been multiple works (cf. Bronstein et al. (2017) for an overview) on generalizing convolution operation to a general domain, where graph is not a lattice. Citing BID3 -""classification performance critically depends on the quality of the graph"", nonetheless the problem of learning the graph useful for prediction has not been addressed so far and the graph was either known or pre-estimated only based on feature similarity in all of the prior work.There are two major challenges when estimating the graph inside the neural network architecture. First is the architecture itself -majority of the neural networks rely on gradient optimization methods, but the graph is often used in such ways that it is not possible to obtain its gradient. In Section 3 we define a novel neural network architecture which is differentiable with respect to the graph adjacency matrix and built upon graph filtering in the vertex domain, extending the linear polynomial filters of BID20 . Second problem is the series of constraints that are often imposed on the graph and therefore its adjacency. In Section 2 we show how the three common graph properties, undirected sparse edges with positive weights, can be enforced by only utilizing the gradient obtained through backpropagation, therefore allowing us to utilize any of the modern deep learning libraries for graph estimation. In Section 4 we discuss other graph based neural networks and evaluate them from the perspective of graph estimation. In Section 5 we analyze graph estimation and interpretation for text categorization and time series forecasting. We conclude with a discussion in Section 6 2 GRAPH OPTIMIZATION BASED ON BACKPROPAGATION In this section we provide an optimization procedure for learning adjacency matrix of a graph with various properties of interest, assuming that we can obtain its derivative via backpropagation. In a subsequent section we will present novel neural network architecture that will allow us to get the derivative and utilize the graph in meaningful way.Let data X ∈ R N ×D with N observation, D features and response Y ∈ R (or Y ∈ N for classification). Graph G among data features can be encoded as its adjacency matrix A ∈ R D×D . Our goal is to estimate functionŶ := f W (X, A), where W are weight parameters, that minimize some loss L := L(Ŷ , Y ). We assume that we are able to evaluate partial derivative ∂L ∂A . In the most general case, when edges of G can be directed, have negative weights and G can be fully connected, we perform the update A := A − γG ∂L ∂A , where G(·) depends on the optimizer (e.g., identity function for vanilla gradient descent) and γ is the step size. Nonetheless, in the majority of the applications, G is desired to have some (or all) of the following properties:• Undirected graph, in which case A is restricted to be symmetric.• Have Positive edge weights, in which case A ∈ R D×D + .• Be Sparsely connected, in which case A should contain small proportion of non-zero entries.First two properties are necessary for the existence of the graph Laplacian, crucial for the vast amount of neural networks on graphs architectures (e.g., BID2 ; BID8 ; BID3 ). Third property greatly reduces computational complexity, helps to avoid overfitting and improves interpretability of the learned graph. We proceed to present the Undirected Positive Sparse UPS optimizer, that can deliver each of the three properties and can be easily implemented as part of modern deep learning libraries.Remark When node classification is of interest, our approach can be applied to graph between observations (e.g. social networks), then A ∈ R N ×N .",work propose novel approach learning graph representation data using gradients obtained via backpropagation. Next build neural network architecture compatible optimization approach motivated graph filtering vertex domain. demonstrate learned graph has richer structure often used nearest neighbors graphs constructed based features similarity. experiments demonstrate can improve prediction quality several convolution graphs architectures others appeared insensitive input graph. Recently have seen rise deep learning models which can account non-linearities fit wide range functions. Multilayer perceptron MLP general purpose neural network is a powerful predictor requires many parameters estimated often faces problem over-fitting.e learns almost exactly match training data unable generalize when it comes testing.While MLPs treat features equally which partially is the cause excessive number parameters Convolutional Neural Networks CNNs have significantly fewer parameters demonstrate groundbreaking results when it comes object recognition images BID11. parameter reduction is due utilizing convolutional operation:window is sliding image applying linear transformation pixels. number parameters is proportional size window rather polynomial number data features case MLPs.Indeed images posses specific structure which can be encoded lattice graph makes sliding window procedure meaningful inapplicable outside image domain. recent years have been multiple works cf. Bronsteinetal. 2017 overview generalizing convolution operation general domain where graph is not a lattice. Citing BID3 -classification performance critically depends quality graph nonetheless problem learning graph useful prediction has not been addressed far graph was either known pre-estimated based feature similarity prior work.There are two major challenges when estimating graph inside neural network architecture. First is the architecture -majority neural networks rely gradient optimization methods where graph is often used ways is not possible obtain gradient. Section3 define novel neural network architecture which is differentiable respect graph adjacency matrix built upon graph filtering vertex domain extending linear polynomial filters BID20. Second problem is the series constraints are often imposed graph therefore adjacency. Section2 show how the three common graph properties undirected sparse edges positive weights can be enforced utilizing gradient obtained backpropagation therefore allowingus utilize modern deep learning libraries graph estimation. Section4 discuss graph based neural networks evaluate perspective graph estimation. Section5 analyze graph estimation interpretation text categorization time series forecasting. conclude discussion Section 6 2 GRAPH OPTIMIZATION BASED BACKPROPAGATION section provide optimization procedure learning adjacency matrix graph various properties interest assuming can obtain derivative via backpropagation. subsequent section will present novel neural network architecture will allowus get derivative utilize graph meaningful way.Let dataX ∈RN×D N observation features response ∈R ∈N classification Graph G among data features can be encoded adjacency matrix ∈ R D×D goal is to estimate functionŶ:fW X where W are weight parameters minimize lossL:L Ŷ assume are able evaluate partial derivative∂L ∂A general case when edges G can be directed have negative weights G can be fully connected perform update A:−γG∂L∂A whereG · depends optimizer e.g identity function vanilla gradient descent γ is the step size. Nonetheless majority applications whereG is desired have some(following properties:• Undirected graph which case is restricted symmetric.• Have Positive edge weights which case ∈ R D×D+.• Sparsely connected which case should contain small proportion non-zero entries.First two properties are necessary existence graph Laplacian crucial vast amount neural networks graphs architectures e.g BID2;BID8;BID3 Third property greatly reduces computational complexity helps avoid overfitting improves interpretability learned graph. proceed present Undirected Positive Sparse UPS optimizer can deliver three properties can be easily implemented part modern deep learning libraries.Remark When node classification is of interest approach can be applied graph observations e.g social networks ∈RN×N,1071,730,341,0.011,1.467,2025/11/05 17:18:59,0.01,1.5,0.4267912772585671,341.053
"The use of AR in an industrial context could help for the training of new operators. To be able to use an AR guidance system, we need a tool to quickly create a 3D representation of the assembly line and of its AR annotations. This tool should be very easy to use by an operator who is not an AR or VR specialist: typically the manager of the assembly line. This is why we proposed WAAT, a 3D authoring tool allowing user to quickly create 3D models of the workstations, and also test the AR guidance placement. WAAT makes on-site authoring possible, which should really help to have an accurate 3D representation of the assembly line. The verification of AR guidance should also be very useful to make sure everything is visible and doesn't interfere with technical tasks. In addition to these features, our future work will be directed in the deployment of WAAT into a real boiler assembly line to assess the usability of this solution. In a context of constant industrial evolution and a need of more industrial agility to answer the increasingly unpredictable customer requests, having well trained assembly line operators is extremely important. This operator training problematic is well known by the XXX company, a boiler manufacturer for which this training problem is very important during each winter, when boiler orders rise a lot, as many new operators must be hired for a few months. After meetings and interviews with the XXX company, it appears that the training of these operators requires time and human resources. Currently, the training is done in 3 days with one experienced operator showing three trainees how to perform the technical gestures at their workstation. During these training days, none of the workers actually works on the assembly line and no boiler is built. After that, it takes 2 weeks for the operator in training to perform the technical tasks in the required time. Furthermore, only 1/3 of the new operators accept the job at the end of the training. To improve the training of these new operators, we want to propose an AR-based operator training system, allowing the operators to train directly on the assembly line without the need of an experimented operator. This tool could also be used by experimented operator to train on a new position of the assembly line or on a different assembly line. AR can be used in many different ways in the industrial context. It can be use to make expert remote guidance, create new products in collaborative engineering, or realize digital inspection of new prototypes [3] . AR is also used to test the ergonomics of the workstations and the reachability of some equipment. Testing new layout for the plant is also one of the AR use [1] . These different use are interesting, but the most interesting feature of AR and the most used is the assembly assistance, for training use or not [12, 15] . To use our AR-based operator training system we need to be able to create quickly and easily a 3D representation of the assembly line, and to be able to place anchors and markers (the details will be given in section 3.2.1) for the AR guidance elements. Furthermore, this tool must be very easy to use because the operators are not used to this technology. Indeed, the final users of the authoring tool will be the line managers, who are not used to use AR devices, or don't even know what AR is. That is why we need to adapt the interactions to the line manager, to ease the use of the tool. The remaining of this paper is organized as follows: in section 2 we explain the industrial constraints for the use of this authoring tool. Section 3 contains the related work, justifying the choices made in section 4 which describes WAAT, our authoring tool. Finally, section 5 concludes this paper and discusses about future developments. So we created WAAT, a 3D authoring tool allowing untrained users to create 3D models of the assembly line in a boiler factory. WAAT allow fast creation and AR comparison of the 3D and the real model. In case of a mismatch, the user can move the 3D components to match the real workstation. He can test the AR guidance used to train assembly line operators to make sure everything is fully visible and doesn't interfere in the realization of the technical tasks. Every modification made in desktop and AR is saved in a file on a server so there is no need to change on multiple platform. WAAT needs to be tested with 3D elements corresponding to the factory's workstations to find the most suitable level of details the 3D objects need to have, and the level of fidelity in the positioning of the 3D objects. We also have to test this tool with real operators from the factory to test the usability and the intuitiveness of WAAT. To adapt the interactions used to move/rotate/resize the 3D objects to our users, adding accessories such as a controller will be explored. We will also test new AR systems to test their usability and native interactions to see if we can use them, or if we can adapt them to our users. The immersive mode of WAAT will allow us to visualize the augmented environment and test the placement of the operator guidance, even if it's not the focus right now. We will be able to simulate the AR test of the scenes without the need to be in the plant all the time.","use AR industrial context could help which this training new operators. able use AR guidance system need tool quickly create 3D representation assembly line AR annotations. tool should be very easy use operator who is notanAR VR specialist:typically manager assembly line. is why we proposed WAAT 3D authoring tool allowing user quickly create 3D models workstations also test AR guidance placement. WAAT makes on-site authoring possible which should really help have an accurate 3D representation assembly line. verification AR guidance should also useful make sure everything is visible interfere technical tasks. addition features future work will be directed deployment WAAT real boiler assembly line assess usability solution. context constant industrial evolution need industrial agility answer increasingly unpredictable customer requests well trained assembly line operators is extremely important. operator training problematic is well known XXX company when boiler manufacturer which this training problem is very important winter when boiler orders rise lot many new operators must hired months. meetings interviews XXX company appears training operators requires time human resources. Currently training is done 3 days one experienced operator showing three trainees how to perform technical gestures workstation. training days none workers actually works assembly line boiler is built. takes 2 weeks operator training perform technical tasks required time. Furthermore 1/3 new operators accept job end training. improve training new operators want propose AR-based operator training system allowing operators train directly assembly line without need experimented operator. tool could also used experimented operator train new position assembly line different assembly line. AR can be used many different ways industrial context. can be use make expert remote guidance create new products collaborative engineering realize digital inspection new prototypes 3 AR is also used test ergonomics workstations reachability equipment. Testing new layout plant is also one AR use 1 different use are interesting interesting feature AR used is the assembly assistance training use 12 15 use AR-based operator training system need able create quickly easily 3D representation assembly line able place anchors markers details will be given section 3.2.1 AR guidance elements. Furthermore tool must easy use operators are not used technology. Indeed final users authoring tool will be the line managers who are not used use AR devices even know whatAR is. is why we need adapt interactions line manager ease use tool. remaining paper is organized follows:section2 explain industrial constraints use authoring tool. Section 3 contains related work justifying choices made section4 which describes WAAT authoring tool. Finally section 5 concludes paper discusses future developments. created WAAT 3D authoring tool allowing untrained users create 3D models assembly line boiler factory. WAAT allow fast creation AR comparison 3D real model. case mismatch user can move 3D components match real workstation. can test AR guidance used train assembly line operators make sure everything is fully visible interfere realization technical tasks. Every modification made desktop AR is saved file server is no need change multiple platform. WAAT needs tested 3D elements corresponding factory's workstations find suitable level details 3D objects need have,and level fidelity positioning 3D objects. will also have to test tool real operators factory test usability intuitiveness WAAT. adapt interactions used move/rotate/resize 3D objects users adding accessories controller will be explored. will also test newAR systems test usability native interactions see if we can use if can adapt users. immersive mode WAAT will allowus visualize augmented environment test placement operator guidance even if it's not the focus right now. will be able simulate AR test scenes without need plant time.",1087,698,389,0.012,1.557,2025/11/05 17:18:59,0.01,1.795,0.7071651090342675,354.693
"Generative adversarial network (GAN) is one of the best known unsupervised learning techniques these days due to its superior ability to learn data distributions. In spite of its great success in applications, GAN is known to be notoriously hard to train. The tremendous amount of time it takes to run the training algorithm and its sensitivity to hyper-parameter tuning have been haunting researchers in this area. To resolve these issues, we need to first understand how GANs work. Herein, we take a step toward this direction by examining the dynamics of GANs. We relate a large class of GANs including the Wasserstein GANs to max-min optimization problems with the coupling term being linear over the discriminator. By developing new primal-dual optimization tools, we show that, with a proper stepsize choice, the widely used first-order iterative algorithm in training GANs would in fact converge to a stationary solution with a sublinear rate. The same framework also applies to multi-task learning and distributional robust learning problems. We verify our analysis on numerical examples with both synthetic and real data sets. We hope our analysis shed light on future studies on the theoretical properties of relevant machine learning problems. Since it was first invented by Ian Goodfellow in his seminal work BID8 , generative adversarial networks (GANs) have been considered as one of the greatest discoveries in machine learning community. It is an extremely powerful tool to estimate data distributions and generate realistic samples. To train its implicit generative model, GAN uses a discriminator since traditional Bayesian methods that require analytic density functions are no longer applicable. This novel approach inspired by zero sum game theory leads to a significant performance boost; GANs are able to generate samples in a fidelity level that is way beyond traditional Bayesian methods. During the last few years, there have been numerous research articles in this area aiming at improving its performance (Radford et al., 2015; Zhao et al., 2016; Nowozin et al., 2016; Mao et al., 2017) . GANs have now become one of most recognized unsupervised learning techniques and have been widely used in a variety of domains such as image generation (Nguyen et al., 2017) , image super resolution BID16 , imitation learning BID12 .Despite the great progress of GANs, many essential problems remain unsolved. Why is GAN so hard to train? How to tune the hyper-parameters to reduce instability in GAN training? How to eliminate mode collapse and fake images that show up frequently in training ? Comparing with many other machine learning techniques, the properties of GANs are far from being well understood. It is quite likely that the theoretical foundation of GANs will become a longstanding problem. The theoretical difficulty of GANs mainly lies in the following several aspects. First, it is a non-convex optimization problem with a complicated landscape. It is unclear how to solve such optimization problems efficiently. The first-order method widely used in the literature via updating the generator and discriminator along descent/ascent direction does not seem to converge all the time. Although some techniques were proposed to stabilize the training performance of the network, e.g., spectral normalization Miyato et al. (2018) , in fact, there is no evidence that these algorithms guarantee even local optimality. Second, even if there were an efficient algorithm to solve this optimization problem, we do not know how well they generalize. After all, the optimization formulation is based only on the samples generated by the underlying distribution but our goal is to recover this underlying distribution. Of course, this is a problem faced by all machine learning techniques. Last, there are no reliable ways to evaluate the quality of trained models. There are a number of works in this topic (Salimans et al., 2016; BID11 , but human eyes inspection remains the primary approach to judge a GAN model.In the present work, we focus on the first problem and analyze the dynamics of GANs from an optimization point of view. More precisely, we study the convergence properties of the first-order method in GAN training. Our contributions can be summarized as follows. 1) We formulate a large class of GAN problems as a primal-dual optimization problem with a coupling term that is linear over discriminator (see Section 2 for the exact formulation); 2) We prove that the simple primal-dual first-order algorithm converges to a stationary solution with a sublinear convergent rate O(1/t).There have been a number of papers that study the dynamics of GANs from an optimization viewpoint. These works can be roughly divided into three categories. In the first category, the authors focus on high level idea using nonparametric models. This includes the original GAN paper BID8 , the Wasserstein GAN papers ; and many other works proposing new GAN structures. In the second category, the authors consider the unrolled dynamics (Metz et al., 2016) , that is, the discriminator remains optimal or almost optimal during the optimization processes. This is considerably different to the first-order iterative algorithm widely used in GAN training. Recent works BID11 ; BID17 Sanjabi et al. (2018) provide global convergence analysis for this algorithm.The last category is on the first-order primal-dual algorithm, in which both the discriminator and the generator update via (stochastic) gradient descent. However, most of the convergence analysis are local BID4 Mescheder et al., 2017; Nagarajan & Kolter, 2017; BID18 . Other related work including the following: In Qian et al. (2018) the authors consider a gradient descent/ascent algorithm for a special min-max problem arising from robust learning (min problem is unconstrained, max problem has simplex constraints); In Yadav et al. (2018) the GANs are treated as convex-concave primal-dual optimization problems. This formulation is considerably different to our setup where GANs, as they should be, are formulated as nonconvex saddle point problems. In BID5 , the authors investigated the properties of the optimal solutions, which is also different from our work focusing on convergence analysis of the first-order primal-dual algorithm. In Zhao et al. (2018) , some unified framework covering several generative models, e.g., VAE, infoGAN, were proposed in the Lagrangian framework. However, the dual variable in their problem is a Lagrangian multiplier, while in our problem, it is the discriminator of GAN. Besides, the focus of their paper is not the optimization algorithm . In BID2 , the authors related a class of GANs to constrained convex optimization problems. More specifically, such GANs can be viewed as Lagrangian forms of these convex optimization problems. The optimization variables in their formulation are the probability density of the generator and the function values of the discriminator. Many issues like nonconvexity do not show up. This is essentially a nonparametric model, which doesn't apply to cases when the discriminator and the generator are represented by parametric models. On the other hand, our analysis is carried out on the parametric models directly and we have to deal with the nonconvexity of neural networks. In BID9 a primal-dual algorithm has been studied for a non-convex linearly constrained problem (which can be reformulated into a min-max problem, with the max problem being linear and unconstrained, and with linear coupling between variables); In BID10 , BID3 and the references therein, first-order methods have been developed for convex-concave saddle point problems. Compared to these works, our considered problem is more general, allowing non-convexity and non-smoothness in the objective, non-convex coupling between variables, and can further include constraints. Moreover, we provide global convergence rate analysis, which is much stronger than the local analysis mentioned above.It turns out that the primal-dual framework we study in this paper can also be applied to the distributional robust machine learning problems (Namkoong & Duchi, 2016 ) and the multi-task learning problems (Qian et al., 2018) . In multi-task learning, the goal is to train a single neural network that would work for several different machine learning tasks. Similarly, in distributional robust learning, the purpose is to have a single model that would work for a set of data distributions. In both problems, an adversarial layer is utilized to improve the worst case performance , which leads to a primal-dual optimization structure that falls into the scope of problems we consider.The rest of the paper is structured as follows. In Section 2 we introduce GAN and its primal-dual formulation. We provide details of the algorithms with proof sketches in Section 3. The full proofs are relegated to the appendix. We highlight our theoretical results in Section 4 via several numerical examples, with both synthetic and real datasets. In this work, we presented a convergence result for a first-order algorithm on a class of non-convex max-min optimization problems that arise in many machine learning applications such as generative adversarial networks and multi-task learning. To the best of our knowledge, this is the first convergence result for this type of primal-dual algorithms.Our results allow us to analyze GANs with neural network generator as well as general multi-task non-convex supervised learning problems. A critical assumption we made is that the inner maximization loop is a strictly convex problem. For applications in GANs, our assumptions require the discriminator to be a linear combination of predefined basis functions. Extending this to the most general cases where the discriminator is a neural network requires further investigations and will be a future research topic.",Generative adversarial network GAN is one best known unsupervised learning techniques days due superior ability learn data distributions. spite great success applications GAN is known notoriously hard train. tremendous amount time takes run training algorithm sensitivity hyper-parameter tuning have been haunting researchers area. resolve issues need first understand how GANs work. Herein take step toward direction examining dynamics GANs. relate large class GANs including Wasserstein GANs max-min optimization problems coupling term linear discriminator. developing new primal-dual optimization tools show proper stepsize choice widely used first-order iterative algorithm training GANs would fact converge stationary solution sublinear rate. framework also applies multi-task learning distributional robust learning problems. verify analysis numerical examples synthetic real data sets. hope analysis shed light future studies theoretical properties relevant machine learning problems. Since was first invented Ian Goodfellow seminal work BID8 generative adversarial networks GANs have been considered one greatest discoveries machine learning community. is an extremely powerful tool estimate data distributions generate realistic samples. train implicit generative model GAN uses discriminator since traditional Bayesian methods require analytic density functions are no longer applicable. novel approach inspired zero sum game theory leads significant performance boost;GANs are able generate samples fidelity level is way beyond traditional Bayesian methods. last years have been numerous research articles area aiming improving performance Radfordetal. 2015;Zhaoetal. 2016;Nowozinetal. 2016;Maoetal. 2017 GANs have now become one recognized unsupervised learning techniques have been widely used variety domains image generation Nguyenetal. 2017 image super resolution BID16 imitation learning BID12.Despite great progress GANs many essential problems remain unsolved. Why is GAN hard train? How to tune hyper-parameters reduce instability GAN training? How to eliminate mode collapse fake images show frequently training? Comparing many machine learning techniques properties GANs are far well understood. is quite likely theoretical foundation GANs will become longstanding problem. theoretical difficulty GANs mainly lies following several aspects. First is a non-convex optimization problem complicated landscape. is unclear how to solve optimization problems efficiently. first-order method widely used literature via updating generator discriminator along descent/ascent direction does not seem converge time. Although techniques were proposed stabilize training performance network e.g spectral normalization Miyatoet al. 2018 fact is no evidence algorithms guarantee even local optimality. Second even if there were an efficient algorithm solve optimization problem do not know how well generalize. optimization formulation is based samples generated underlying distribution goal is to recover underlying distribution. course is a problem faced machine learning techniques. Last are no reliable ways evaluate quality trained models. are a number works topic Salimansetal. 2016;BID11 human eyes inspection remains primary approach judge GAN model.In present work focus first problem analyze dynamics GANs optimization point view. precisely study convergence properties first-order method GAN training. contributions can be summarized follows. 1 formulate large class GAN problems primal-dual optimization problem coupling term is linear discriminator see Section2 exact formulation 2 prove simple primal-dual first-order algorithm converges stationary solution sublinear convergent rate 1/.There have been a number papers study dynamics GANs optimization viewpoint. works can be roughly divided three categories. first category authors focus high level idea using nonparametric models. includes original GAN paper BID8 Wasserstein GAN papers;many works proposing new GAN structures. second category authors consider unrolled dynamics Metzetal. 2016 is which both is the discriminator remains optimal almost optimal optimization processes. is considerably different first-order iterative algorithm widely used GAN training. Recent works BID11;BID17 Sanjabietal. 2018 provide global convergence analysis algorithm.The last category is on the first-order primal-dual algorithm which both is the discriminator generator update via stochastic gradient descent. However convergence analysis are local BID4 Meschederet al. 2017;Nagarajan Kolter 2017;BID18. related work including following:Qianetal. 2018 authors consider gradient descent/ascent algorithm special min-max problem arising robust learning min problem is unconstrained max problem has simplex constraints Yadavetal. 2018 GANs are treated convex-concave primal-dual optimization problems. formulation is considerably different setup where GANs should are formulated nonconvex saddle point problems. BID5 authors investigated properties optimal solutions which is also different work focusing convergence analysis first-order primal-dual algorithm. Zhaoetal. 2018 unified framework covering several generative models e.g VAE infoGAN were proposed Lagrangian framework. However dual variable problem is a Lagrangian multiplier is a problem which both is the discriminator GAN. Besides focus paper is not the optimization algorithm. BID2 authors related class GANs constrained convex optimization problems. specifically GANs can be viewed Lagrangian forms convex optimization problems. optimization variables formulation are the probability density generator function values discriminator. Many issues like nonconvexity do not show up. is essentially nonparametric model which doesn't apply cases when the discriminator generator are represented parametric models. hand analysis is carried parametric models directly have to deal nonconvexity neural networks. BID9 primal-dual algorithm has been studied non-convex linearly constrained problem which can be reformulated min-max problem max problem linear unconstrained linear coupling variables BID10 BID3 references therein first-order methods have been developed convex-concave saddle point problems. Compared works considered problem is more general allowing non-convexity non-smoothness objective is a non-convex coupling variables can further include constraints. Moreover provide global convergence rate analysis which is much stronger local analysis mentioned above.It turns primal-dual framework study paper can also applied distributional robust machine learning problems Namkoong Duchi 2016 multi-task learning problems Qianetal. 2018 multi-task learning goal is to train single neural network would work several different machine learning tasks. Similarly distributional robust learning purpose is to have a single model would work set data distributions. problems adversarial layer is utilized improve worst case performance which leads primal-dual optimization structure falls scope problems consider.The rest paper is structured follows. Section2 introduce GAN primal-dual formulation. provide details algorithms proof sketches Section3. full proofs are relegated appendix. highlight theoretical results Section 4 via several numerical examples synthetic real datasets. work presented convergence result first-order algorithm class non-convex max-min optimization problems arise many machine learning applications generative adversarial networks multi-task learning. best knowledge is the first convergence result type primal-dual algorithms.Our results allow us analyze GANs neural network generator well general multi-task non-convex supervised learning problems. critical assumption made is that the inner maximization loop is a strictly convex problem. applications GANs assumptions require discriminator linear combination predefined basis functions. Extending general cases where the discriminator is a neural network requires investigations will be a future research topic.,1955,1379,576,0.023,1.418,2025/11/05 17:18:59,0.01,1.72,0.2741433021806849,678.511
"Social dilemmas, where mutual cooperation can lead to high payoffs but participants face incentives to cheat, are ubiquitous in multi-agent interaction. We wish to construct agents that cooperate with pure cooperators, avoid exploitation by pure defectors, and incentivize cooperation from the rest. However, often the actions taken by a partner are (partially) unobserved or the consequences of individual actions are hard to predict. We show that in a large class of games good strategies can be constructed by conditioning one's behavior solely on outcomes (ie. one's past rewards). We call this consequentialist conditional cooperation. We show how to construct such strategies using deep reinforcement learning techniques and demonstrate, both analytically and experimentally, that they are effective in social dilemmas beyond simple matrix games. We also show the limitations of relying purely on consequences and discuss the need for understanding both the consequences of and the intentions behind an action. Deep reinforcement learning (RL) is concerned with constructing agents that start as blank slates and can learn to behave in optimal ways in complex environments.1 A recent stream of research has taken a particular interest in social dilemmas, situations where individuals have incentives to act in ways that undermine socially optimal outcomes (Leibo et al., 2017; Perolat et al., 2017; Lerer & Peysakhovich, 2017; Kleiman-Weiner et al., 2016) . In this paper we consider RL-based strategies for social dilemmas in which information about a partner's actions or the underlying environment is only partially observed.The simplest social dilemma is the Prisoner's Dilemma (PD) in which two players choose between one of two actions: cooperate or defect. Mutual cooperation yields the highest payoffs, but no matter what one's partner is doing, one can get a higher reward by defecting. A well studied strategy for maintaining cooperation when the PD is repeated is tit-for-tat (TFT, Axelrod (2006) ). TFT behaves by copying the prior behavior of their partner, rewarding cooperation today with cooperation tomorrow. Thus, if an agent commits to TFT it makes cooperation the best strategy for the agent's partner. TFT has proven to be a heavily studied strategy because it has intuitive appeal: 1) it is easily explainable, 2) it begins cooperating, 3) it rewards a cooperative partner, 4) it avoids being exploited, 5) it is forgiving.In Markov games cooperation and defection are not single actions, but rather temporally extended policies. Recent work has considered expanding TFT to more complex Markov games either as a heuristic, by learning cooperative and selfish policies and switching between them as needed (Lerer & Peysakhovich, 2017) , or as an outcome of an end-to-end procedure (Foerster et al., 2017c) . TFT is * Both authors contributed equally to this paper. Author ordering was determined at random. 1 This approach has been applied to domains including: single agent decision problems (Mnih et al., 2015) , board and card-based zero-sum games BID15 BID13 Heinrich & Silver, 2016) , video games (Kempka et al., 2016; BID17 Ontanón et al., 2013; BID16 Foerster et al., 2017a) , multi-agent coordination problems (Lowe et al., 2017; Foerster et al., 2017b; BID7 BID14 Peysakhovich & Lerer, 2017) , and the emergence of language (Lazaridou et al., 2017; Das et al., 2017; Evtimova et al., 2017; Havrylov & Titov, 2017; Jorge et al., 2016) .an example of a conditionally cooperative strategy -that is, it cooperates when a certain condition is fulfilled (ie. the partner's last period action was cooperative). TFT , however, has a weakness -it requires perfect observability of a partner's behavior and perfect understanding of each action's future consequences.Our main contribution is to use RL methods to construct conditionally cooperative strategies for games with imperfect information. When information is imperfect, the agent must use what they can observe to try to estimate whether a partner is acting cooperatively (or not) and determine how to respond. We show that when the game is ergodic, observed rewards can be used as a summary statistic -if the current total (or time averaged) reward is above a time-dependent threshold (where the threshold values are computed using RL and a form of self play) the agent cooperates, otherwise the agent does not 2 . We call this consequentialist conditional cooperation (CCC). We show analytically that this strategy cooperates with cooperators, avoids exploitation, and guarantees a good payoff to the CCC agent in the long run.We study CCC agents in a partially observed Markov game which we call Fishery. In Fishery two agents live on different sides of a lake in which fish appear. The game has partial information because agents cannot observe what happens across the lake. Fish spawn randomly , starting young and swim to the other side and become mature. Agents can catch fish on their side of the lake. Catching any fish yields payoff but mature fish are worth more. Therefore, cooperative strategies are those which leave young fish for one's partner. However, there is always a temptation to defect and catch both young and mature fish. We show that CCC agents cooperate with cooperators, avoid exploitation, and get high payoffs when matched with themselves.Second, we show that CCC is an efficient strategy for more complex games where implementing conditional cooperation by fully modeling the effect of an action on future rewards (eg. amTFT (Lerer & Peysakhovich, 2017) ) is computationally demanding. We compare the performance of CCC to amTFT in the Pong Player's Dilemma (PPD). This game is a modification of standard Atari pong such that when an agent scores they gain a reward of 1 but the partner receives a reward of −2. Cooperative payoffs are achieved when both agents try hard not to score but selfish agents are again tempted to defect and try to score points even though this decreases total social reward. We see that CCC is a successful, robust, and simple strategy in this game.However, this does not mean CCC completely dominates forward looking strategies like amTFT. We consider a version of the Pong Players' Dilemma where when a player scores, instead of their partner losing 2 points deterministically they lose 2/p points with probability p. Here the expected rewards of non-cooperation are the same as in the PPD and so expected-future-reward based methods (eg. amTFT) will act identically. However, when p is low it may take a long time for consequentialist agents to detect a defector. Empirically we see that in short risky PPD games CCC agents can be exploited by defectors but that amTFT agents cannot. We close by discussing limitations and progress towards agents that can effectively use both intention and outcome information effectively in navigating the world. In this work we have introduced consequentialist conditionally cooperative strategies and shown that they are useful heuristics in social dilemmas, even in those where information is imperfect either due to the structure of the game or due to the fact that we cannot perfectly forecast a partner's future actions. We have shown that using one's own reward stream as a summary statistic for whether to cooperate (or not) in a given period is guaranteed to work in the limit as long as the underlying game is ergodic. Note that this sometimes (but not always) gives good finite time guarantees. In particular, 4 For simplicity for this experiment we use theπ C andπ D strategies trained in the standard PPD for the risky PPD, this is because the risky PPD is the same (in expectation) as the PPD. the time scale for a CCC agent to detect exploitation is related to the mixing time of the POMG and the stochasticity of rewards; if these are large, then correspondingly long games are required for CCC to perform well.We have also compared consequentialist and forward-looking models. As another simple example of the difference between the two we can consider the random Dictator Game (rDG) introduced by Cushman et al. (2009) . In the rDG, individuals are paired, one (the Dictator) is given an amount of money to split with a Partner, and chooses between one of two dice, a 'fair' die which yields a 50 − 50 split with a high probability and an unfair split with a low probability and an 'unfair' die which yields a 50 − 50 split with low probability. Consequentialist conditional cooperators would label a partner a defector if an unfair outcome came up (regardless of die choice) whereas intention-based cooperators would look at the choice of die, not the actual outcome.For RL trained agents, conditioning purely on intentions (eg. amTFT) has advantages in that it is forward looking and doesn't require ergodicity assumptions but it is an expensive strategy that is complex (or impossible) to implement for POMDPs and requires very precise estimates of potential outcomes. CCC is simple, works in POMDPs and requires only information about payoff rates (rather than actual policies), however it may take a long time to converge. Each has unique advantages and disadvantages. Therefore constructing agents that can solve social dilemmas will require combining consequentialist and intention-based signals.Interestingly, experimental evidence shows that while humans combine both intentions and outcomes, we often rely much more heavily on consequences than 'optimal' behavior would demand. For example, experimental subjects rely heavily on the outcome of the die throw rather than die choice in the rDG (Cushman et al., 2009) . This is evidence for the notion that rather than acting optimally in each situation, humans have social heuristics which are tuned to work across many environments BID6 Hauser et al., 2014; Ouss & Peysakhovich, 2015; BID1 Mao et al., 2017; Niella et al., 2016) . There is much discussion of hybrid environments that include both artificial agents and humans (eg. BID11 Crandall et al. (2017) ). Constructing artificial agents that can do well in such environments will require going beyond the kinds of optimality theorems and experiments highlighted in this and related work.In addition, we have defined cooperative policies as those which maximize the sum of the rewards. This seems like a natural focal point in symmetric games like the ones we have studied but it is well known that human social preferences take into account factors such as inequity (Fehr & Schmidt, 1999) and social norms BID8 . To be successful, AI researchers will have to understand human social heuristics and construct agents that are in tune with human moral and social intuitions BID4 BID6 6 TECHNICAL APPENDIX 6.1 PROOF OF MAIN THEOREM We will use this basic property of almost sure convergence. If a sequence of random variables X n converges to X almost surely then DISPLAYFORM0 The intuition behind the proof is as follows: first, we show that if the CCC agent's partner plays π C then for any R s > 0 there exists a time t s at which the CCC agent's total payoff exceeds the threshold t s T by at least R s with high probability. Intuitively this is because the rate T is lower than ρ CC which is weakly lower than the rate guaranteed to a CCC agent whose partner behaves according to π C always.Second, we will show that for sufficiently large R s , if the CCC agent's total payoff exceeds the threshold by R s then the CCC agent also only plays π C from that point on with high probability.Together this implies that if the partner plays according to π C then with high probability the CCC agent behaves according to π D only a finite amount of times and thus the rates of payoffs for both agents converge to ρ CC .","Social dilemmas where mutual cooperation can lead high payoffs participants face incentives cheat are ubiquitous multi-agent interaction. wish construct agents cooperate pure cooperators avoid exploitation pure defectors incentivize cooperation rest. However often actions taken partner are(partially unobserved consequences individual actions are hard predict. show large class games good strategies can be constructed conditioning one's behavior solely outcomes ie. one's past rewards call consequentialist conditional cooperation. show how to construct strategies using deep reinforcement learning techniques demonstrate analytically experimentally are effective social dilemmas beyond simple matrix games. also show limitations relying purely consequences discuss need understanding consequences intentions behind action. Deep reinforcement learning RL is concerned constructing agents start blank slates can learn behave optimal ways complex environments.1 recent stream research has taken particular interest social dilemmas situations where individuals have incentives act ways undermine socially optimal outcomes Leiboetal. 2017;Perolatetal. 2017;Lerer Peysakhovich 2017;Kleiman-Weineretal. 2016 paper can consider RL-based strategies social dilemmas which where information partner's actions underlying environment is only partially observed.The simplest social dilemma is the Prisoner's Dilemma PD which two players choose one two actions:cooperate defect. Mutual cooperation yields highest payoffs matter what one's partner is doing,one can get higher reward defecting. well studied strategy maintaining cooperation when thePD is repeated is tit-for-tat TFT Axelrod 2006 TFT behaves copying prior behavior partner rewarding cooperation today cooperation tomorrow. Thus if an agent commits TFT makes cooperation best strategy agent's partner. TFT has proven heavily studied strategy has intuitive appeal:1 is easily explainable 2 begins cooperating 3 rewards cooperative partner 4 avoids exploited 5 is forgiving.In Markov games cooperation defection are not single actions rather temporally extended policies. Recent work has considered expanding TFT complex Markov games either heuristic learning cooperative selfish policies switching needed Lerer Peysakhovich 2017 outcome end-to-end procedure Foersteretal. 2017c TFT is* authors contributed equally paper. Author ordering was determined random. 1 approach has been applied domains including:single agent decision problems Mnihetal. 2015 board card-based zero-sum games BID15 BID13 Heinrich Silver 2016 video games Kempkaetal. 2016;BID17 Ontanónetal. 2013;BID16 Foersteretal. 2017a multi-agent coordination problems Loweetal. 2017;Foersteretal. 2017b;BID7 BID14 Peysakhovich Lerer 2017 emergence language Lazaridouetal. 2017;Dasetal. 2017;Evtimovaetal. 2017;Havrylov Titov 2017;Jorgeetal. 2016.an example conditionally cooperative strategy -that is,it cooperates when a certain condition is fulfilled ie. partner's last period action was cooperative TFT however has a weakness -it requires perfect observability partner's behavior perfect understanding action's future consequences.Our main contribution is to use RL methods construct conditionally cooperative strategies games imperfect information. When information is imperfect if an agent must use what they can observe try estimate whether partner is acting cooperatively determine how to respond. show when the game is ergodic observed rewards can be used summary statistic -if current total time averaged reward is above a time-dependent threshold where the threshold values are computed usingRL form self play agent cooperates otherwise agent does not2. call consequentialist conditional cooperation CCC show analytically strategy cooperates cooperators avoids exploitation guarantees good payoff CCC agent long run.We study CCC agents partially observed Markov game which we call Fishery. Fishery two agents live different sides lake which fish appear. game has partial information agents cannot observe what happens across lake. Fish spawn randomly starting young swim side become mature. Agents can catch fish side lake. Catching fish yields payoff mature fish are worth more. Therefore cooperative strategies are those which leave young fish one's partner. However is always temptation defect catch young mature fish. show if the CCC agents cooperate cooperators avoid exploitation get high payoffs when matched themselves.Second will show if the CCC is an efficient strategy complex games where implementing conditional cooperation fully modeling effect action future rewards eg. amTFT Lerer Peysakhovich 2017 is computationally demanding. compare performance CCC amTFT Pong Player's Dilemma PPD game is a modification standard Atari pong when an agent scores gain reward 1 partner receives reward −2 Cooperative payoffs are achieved when both agents try hard score selfish agents are again tempted defect try score points even though decreases total social reward. see if the CCC is a successful robust simple strategy game.However does not mean CCC completely dominates forward looking strategies like amTFT. consider version Pong Players' Dilemma where when a player scores instead partner losing 2 points deterministically lose2/p points probabilityp. expected rewards non-cooperation are the sameas PPD expected-future-reward based methods eg. amTFT will act identically. However whenp is low may take long time consequentialist agents detect defector. Empirically see short risky PPD games CCC agents can be exploited defectors amTFT agents cannot. close discussing limitations progress towards agents can effectively use intention outcome information effectively navigating world. work have introduced consequentialist conditionally cooperative strategies shown are useful heuristics social dilemmas even which where information is imperfect either due structure game due fact cannot perfectly forecast partner's future actions. have shown using one's reward stream summary statistic whether cooperate given period is guaranteed work limit long underlying game is ergodic. Note sometimes always gives good finite time guarantees. particular 4 simplicity experiment use theπ C andπ strategies trained standard PPD risky PPD is because risky PPD is the same(expectation PPD. time scale CCC agent detect exploitation is related mixing time POMG stochasticity rewards;if these are large correspondingly long games are required CCC perform well.We have also compared consequentialist forward-looking models. another simple example difference two can consider random Dictator Game rDG introduced Cushmanetal. 2009 rDG individuals are paired one Dictator is given amount money split Partner chooses one two dice 'fair' die which yields 50 − 50 split high probability unfair split low probability 'unfair' die which yields 50 − 50 split low probability. Consequentialist conditional cooperators would label partner defector if an unfair outcome came regardless die choice whereas intention-based cooperators would look choice die actual outcome.For RL trained agents conditioning purely intentions eg. amTFT has advantages is forward looking require ergodicity assumptions is an expensive strategy is complex impossible implement POMDPs requires precise estimates potential outcomes. CCC is simple works POMDPs requires information payoff rates rather actual policies however may take long time converge. has unique advantages disadvantages. Therefore constructing agents can solve social dilemmas will require combining consequentialist intention-based signals.Interestingly experimental evidence shows humans combine intentions outcomes often rely much heavily consequences 'optimal' behavior would demand. example experimental subjects rely heavily outcome die throw rather die choice rDG Cushmanetal. 2009 is evidence notion rather acting optimally situation humans have social heuristics which are tuned work across many environments BID6 Hauseretal. 2014;Ouss Peysakhovich 2015;BID1 Maoetal. 2017;Niellaetal. 2016 is much discussion hybrid environments include artificial agents humans eg. BID11 Crandalletal. 2017 Constructing artificial agents can do well environments will require going beyond kinds optimality theorems experiments highlighted related work.In addition have defined cooperative policies which maximize sum rewards. seems like natural focal point symmetric games like ones have studied is well known human social preferences take account factors inequity Fehr Schmidt 1999 social norms BID8. successful AI researchers will have to understand human social heuristics construct agents are in tune human moral social intuitions BID4 BID6 6 TECHNICAL APPENDIX 6.1 PROOF MAIN THEOREM will use basic property almost sure convergence. If a sequence random variablesXn converges X almost surely DISPLAYFORM0 intuition behind proof is as follows:first will show if the CCC agent's partner plays πC R 0 exists time which CCC agent's total payoff exceeds threshold leastR high probability. Intuitively is because the rate is lower ρCC which is weakly lower rate guaranteed CCC agent whose partner behaves according π C always.Second will show sufficiently largeR if the CCC agent's total payoff exceeds threshold R if the CCC agent also playsπC point high probability.Together implies if the partner plays according πC high probability CCC agent behaves according π finite amount times thus rates payoffs agents converge ρCC.",2484,1770,714,0.035,1.403,2025/11/05 17:18:59,0.01,1.504,0.2274143302180684,819.079
"In distributed training, the communication cost due to the transmission of gradients
 or the parameters of the deep model is a major bottleneck in scaling up the number
 of processing nodes. To address this issue, we propose dithered quantization for
 the transmission of the stochastic gradients and show that training with Dithered
 Quantized Stochastic Gradients (DQSG) is similar to the training with unquantized
 SGs perturbed by an independent bounded uniform noise, in contrast to the other
 quantization methods where the perturbation depends on the gradients and hence,
 complicating the convergence analysis. We study the convergence of training
 algorithms using DQSG and the trade off between the number of quantization
 levels and the training time. Next, we observe that there is a correlation among the
 SGs computed by workers that can be utilized to further reduce the communication
 overhead without any performance loss. Hence, we develop a simple yet effective
 quantization scheme, nested dithered quantized SG (NDQSG), that can reduce the
 communication significantly without requiring the workers communicating extra
 information to each other. We prove that although NDQSG requires significantly
 less bits, it can achieve the same quantization variance bound as DQSG. Our
 simulation results confirm the effectiveness of training using DQSG and NDQSG
 in reducing the communication bits or the convergence time compared to the
 existing methods without sacrificing the accuracy of the trained model. In recent years, the size of deep learning problems has increased significantly both in terms of the number of available training samples as well as the complexity of the model. Hence, training deep models on a single processing node is unappealing or nearly impossible. As such, large-scale distributed machine learning in which the training samples are distributed among different repository or processing units (referred to as workers) has started to be a viable approach for tackling the memory, storage and computational constraints.The requirement to exchange the gradients or the parameters of the model incurs significant communication overhead which is a major bottleneck in distributed training algorithms. In recent years, there has been a great amount of effort on reducing the communication overhead. The majority of existing methods can be categorized into two groups: The first group mitigates the communication bottleneck by reducing the overall transmission rate via sparsification, quantization and/or compression of the gradients. For example, BID15 reduces the communication overhead significantly by one-bit quantization of the stochastic gradients (SG). However, the reduced accuracy of gradient may impair the convergence rate. Using different quantization levels or adaptive quantizers, one can alleviate such issues by decreasing the error in the quantized gradients in the expense of increased communication bits BID4 . Moreover, applying entropy coding algorithms such as Huffman coding on the quantized values can further reduce the communication bit-rate BID13 ; BID17 . BID0 introduced QSGD which uses probabilistic (stochastic) quantization of SGs instead of ordinary fixed (deterministic) quantization methods. They investigated its convergence guarantee and the trade-off between the quantization precision and variance of QSG. Terngrad BID18 probabilistically quantizes the gradients into {−1, 0, +1} and it is shown that the convergence rate can be improved by layer-wise quantization and gradient clipping.The second group of works attempts to attenuate the communication bottleneck by relaxing the synchronization between workers. Each worker may continue its own computations while some others are still communicating and exchanging parameters. Carefully scheduling and managing the asynchronous parameter exchange can lead to a better utilization of both the communication bandwidth and the computational power of the distributed system. Examples of such approaches include DownpourSGD BID3 , Hogwild! Niu et al. (2011 ), Hogwild++ Zhang et al. (2016 and Stale Synchronous Parallel model of computation BID7 .Our Contributions. Our work in this paper falls within the first line of research, i.e. reducing the communication overhead by quantizing and compressing the gradients. We first introduce using dithered quantization in the distributed computations of the stochastic gradient and show that stochastic quantizer of BID0 and ternarization of BID18 can be considered as special cases of our proposed method, although the reconstruction algorithms are slightly different. The convergence of dithered quantized stochastic gradient descent algorithm is analyzed and its convergence speed w.r.t. the number of workers and quantization precision is investigated. Next , we observe that in a typical distributed system, the stochastic gradients computed by the workers are correlated. However , the existing communication methods ignore that correlation. We tap into the question of how that correlation can be exploited to further reduce the communication without sacrificing the precision or convergence of the learning algorithm. We model the correlation between the stochastic gradients computed by each worker and propose a nested quantization scheme to reduce the communication bits without increasing the variance of the quantization error or reducing the convergence speed of the distributed training algorithm.",distributed training communication cost due transmission gradients parameters deep model is a major bottleneck scaling number processing nodes. address issue propose dithered quantization transmission stochastic gradients show training Dithered Quantized Stochastic Gradients DQSG is similar training unquantized SGs perturbed independent bounded uniform noise contrast quantization methods where the perturbation depends gradients hence complicating convergence analysis. study convergence training algorithms using DQSG trade number quantization levels training time. Next observe is a correlation among SGs computed workers can be utilized reduce communication overhead without performance loss. Hence develop simple yet effective quantization scheme nested dithered quantizedSG NDQSG can reduce communication significantly without requiring workers communicating extra information other. prove although NDQSG requires significantly less bits can achieve quantization variance bound DQSG. simulation results confirm effectiveness training using DQSG NDQSG reducing communication bits convergence time compared existing methods without sacrificing accuracy trained model. recent years size deep learning problems has increased significantly terms number available training samples well complexity model. Hence training deep models single processing node is unappealing nearly impossible. large-scale distributed machine learning which the training samples are distributed among different repository processing units referred workers has started viable approach tackling memory storage computational constraints.The requirement exchange gradients parameters model incurs significant communication overhead which is a major bottleneck distributed training algorithms. recent years has been great amount effort reducing communication overhead. majority existing methods can be categorized two groups:first group mitigates communication bottleneck reducing overall transmission rate via sparsification quantization/compression gradients. example BID15 reduces communication overhead significantly one-bit quantization stochastic gradients SG However reduced accuracy gradient may impair convergence rate. Using different quantization levels adaptive quantizers one can alleviate issues decreasing error quantized gradients expense increased communication bits BID4. Moreover applying entropy coding algorithms Huffman coding quantized values can further reduce communication bit-rate BID13;BID17. BID0 introduced QSGD which uses probabilistic stochastic quantization SGs instead ordinary fixed deterministic quantization methods. investigated convergence guarantee trade-off quantization precision variance QSG. Terngrad BID18 probabilistically quantizes gradients −1 0+1 is shown convergence rate can be improved layer-wise quantization gradient clipping.The second group works attempts attenuate communication bottleneck relaxing synchronization workers. worker may continue computations others are still communicating exchanging parameters. Carefully scheduling managing asynchronous parameter exchange can lead better utilization communication bandwidth computational power distributed system. Examples approaches include DownpourSGD BID3 Hogwild! Niuetal. 2011 Hogwild++Zhang etal. 2016 Stale Synchronous Parallel model computation BID7.Our Contributions. work paper falls within first line research.e reducing communication overhead quantizing compressing gradients. first introduce using dithered quantization distributed computations stochastic gradient show stochastic quantizer BID0 ternarization BID18 can be considered special cases proposed method although reconstruction algorithms are slightly different. convergence dithered quantized stochastic gradient descent algorithm is analyzed convergence speedw.r.t number workers quantization precision is investigated. Next observe typical distributed system stochastic gradients computed workers are correlated. However existing communication methods ignore is a correlation. tap question how that correlation can be exploited reduce communication without sacrificing precision convergence learning algorithm. model correlation stochastic gradients computed worker propose nested quantization scheme reduce communication bits without increasing variance quantization error reducing convergence speed distributed training algorithm.,998,667,331,0.01,1.496,2025/11/05 17:18:59,0.0,1.483,0.5171339563862927,314.839
"Deep neural networks have been shown to perform well in many classical machine learning problems, especially in image classification tasks. However, researchers have found that neural networks can be easily fooled, and they are surprisingly sensitive to small perturbations imperceptible to humans.   Carefully crafted input images (adversarial examples) can force a well-trained neural network to provide arbitrary outputs.   Including adversarial examples during training is a popular defense mechanism against adversarial attacks. In this paper we propose a new defensive mechanism under the generative adversarial network~(GAN) framework. We model the adversarial noise using a generative network, trained jointly with a classification discriminative network as a minimax game. We show empirically that our adversarial network approach works well against black box attacks, with performance on par with state-of-art methods such as ensemble adversarial training and adversarial training with projected gradient descent.
 Deep neural networks have been successfully applied to a variety of tasks, including image classification BID12 , speech recognition BID8 , and human-level playing of video games through deep reinforcement learning BID20 . However, BID29 showed that convolutional neural networks (CNN) are extremely sensitive to carefully crafted small perturbations added to the input images. Since then, many adversarial examples generating methods have been proposed, including Jacobian based saliency map attack (JSMA) BID23 , projected gradient descent (PGD) attack , and C&W's attack BID3 . In general, there are two types of attack models: white box attack and black box attack. Attackers in white box attack model have complete knowledge of the target network, including network's architecture and parameters. Whereas in black box attacks, attackers only have partial or no information on the target network BID25 .Various defensive methods have been proposed to mitigate the effect of the adversarial examples. Adversarial training which augments the training set with adversarial examples shows good defensive performance in terms of white box attacks BID13 . Apart from adversarial training, there are many other defensive approaches including defensive distillation BID24 , using randomization at inference time BID33 , and thermometer encoding BID2 , etc.In this paper, we propose a defensive method based on generative adversarial network (GAN) BID6 . Instead of using the generative network to generate samples that can fool the discriminative network as real data, we train the generative network to generate (additive) adversarial noise that can fool the discriminative network into misclassifying the input image. This allows flexible modeling of the adversarial noise by the generative network, which can take in the original image or a random vector or even the class label to create different types of noise. The discriminative networks used in our approach are just the usual neural networks designed for their specific classification tasks. The purpose of the discriminative network is to classify both clean and adversarial example with correct label, while the generative network aims to generate powerful perturbations to fool the discriminative network. This approach is simple and it directly uses the minimax game concept employed by GAN. Our main contributions include:• We show that our adversarial network approach can produce neural networks that are robust towards black box attacks. In the experiments they show similar, and in some cases better, performance when compared to state-of-art defense methods such as ensemble adversarial training BID30 and adversarial training with projected gradient descent . To our best knowledge we are also the first to study the joint training of a generative attack network and a discriminative network.• We study the effectiveness of different generative networks in attacking a trained discriminative network, and show that a variety of generative networks, including those taking in random noise or labels as inputs, can be effective in attacks. We also show that training against these generative networks can provide robustness against different attacks.The rest of the paper is organized as follows. In Section 2, related works including multiple attack and defense methods are discussed. Section 3 presents our defensive method in details. Experimental results are shown in Section 4, with conclusions of the paper in Section 5. In the experiments above we see that adversarial PGD training usually works best on white box attacks, but there is a tradeoff between accuracies on clean data against accuracies on adversarial examples due to finite model capacity. We can try to use models with larger capacity, but there is always a tradeoff between the two, especially for larger perturbations . There are some recent works that indicate training for standard accuracy and training for adversarial accuracy (e.g., with PGD) are two fairly different problems . Examples generated from PGD are particularly difficult to train against. This makes adversarial PGD training disadvantaged in many black box attack situations, when compared with models trained with weaker adversaries, e.g., ensemble adversarial training and our adversarial networks method.We have also observed in the experiments that for black box attacks, the most effective adversarial examples are usually those constructed from models trained using the same method but with different random seed. This suggests hiding the knowledge of the training method from the attacker could be an important factor in defending against black box attacks. Defending against black box attacks is closely related to the question of the transferability of adversarial examples. Although there are some previous works exploring this question BID15 , the underlying factors affecting transferability are still not well understood.In our experimentation with the architectures of the discriminative and generative networks, the choice of architectures of G φ does not seem to have a big effect on the quality of solution. The dynamics of training, such as the step size used and the number of iterations to run for each network during gradient descent/ascent, seem to have a bigger effect on the saddle point solution quality than the network architecture. It would be interesting to find classes of generative network architectures that lead to substantially different saddle points when trained against a particular discriminative network architecture. Also, recent works have shown that there are connected flat regions in the minima of neural network loss landscapes BID5 BID4 . We believe that the same might hold true for GANs, and it would be interesting to explore how the training dynamics can lead to different GAN solutions that might have different robustness properties.Our approach can be extended with multiple discriminative networks playing against multiple generative networks. It can also be combined with ensemble adversarial training, where some adversarial examples come from static pre-trained models, while some other come from dynamically adjusting generative networks. We have proposed an adversarial network approach to learning discriminative neural networks that are robust to adversarial noise, especially under black box attacks. For future work we are interested in extending the experiments to ImageNet, and exploring the choice of architectures of the discriminative and generative networks and their interaction. generative networks used in this paper. G0 and G1 are encoder-decoder networks, while G2 and G3 are decoder networks using a random vector and a one-hot encoding of the label respectively. The generative networks are parameterized by a factor k determining the number of filters used (width of network). As default we use k = 64, and k = 16 for networks using labels as inputs.EXTRA RESULTS ON CIFAR100 AND WIDE RESNET ON CIFAR10The discriminative and generative networks in our CIFAR100 experiment have the same network architecture as the CIFAR10 experiment, except that the output layer dimension of the D network is 100 other than 10 in CIFAR10. We use learning rate of 0.1 for the first 100k iterations, and 0.01 for another 100k iterations. The batch size is 64 and weight decay is 1E-5. TAB8 gives the results on CIFAR10 using a wider version of Resnet (Model D2), by multiplying the number of filters in each convolutional layer by a factor of 10. Some of the previous works in the literature use models of larger capacity for training adversarially robust models, so we perform experiments on these large capacity models here. First the accuracies increase across the board with larger capacity models. The accuracy gap on clean data between adversarial PGD and standard training still exists, but now there is also a small accuracy gap between our adversarial network approach and standard training. For the rest of the white box and black accuracies the story is similar, the models are weakest against attacks trained with the same method but with a different random seed. Our adversarial network approach has very good performance across different attacks, even as it is not always the winner for each individual attack. TAB10 gives the results of Wide ResNet on CIFAR100, and the results are qualitatively similar.",Deep neural networks have been have shown perform well many classical machine learning problems especially image classification tasks. However researchers have found neural networks can be easily fooled are surprisingly sensitive small perturbations imperceptible humans. Carefully crafted input images adversarial examples can force well-trained neural network provide arbitrary outputs. Including adversarial examples training is a popular defense mechanism adversarial attacks. paper propose new defensive mechanism generative adversarial network~ GAN framework. model adversarial noise using generative network trained jointly classification discriminative network minimax game. show empirically adversarial network approach works well black box attacks performance par state-of-art methods ensemble adversarial training adversarial training projected gradient descent. Deep neural networks have been successfully applied variety tasks including image classification BID12 speech recognition BID8 human-level playing video games deep reinforcement learning BID20. However BID29 showed convolutional neural networks CNN are extremely sensitive carefully crafted small perturbations added input images. Since many adversarial examples generating methods have been proposed including Jacobian based saliency map attack JSMA BID23 projected gradient descent PGD attack C W's attack BID3. general are two types attack models:white box attack black box attack. Attackers white box attack model have complete knowledge target network including network's architecture parameters. Whereas black box attacks attackers have partial information target network BID25.Various defensive methods have been proposed mitigate effect adversarial examples. Adversarial training which augments training set adversarial examples shows good defensive performance terms white box attacks BID13. Apart adversarial training are many defensive approaches including defensive distillation BID24 using randomization inference time BID33 thermometer encoding BID2 etc.In paper propose defensive method based generative adversarial network GAN BID6. Instead using generative network generate samples can fool discriminative network real data train generative network generate additive adversarial noise can fool discriminative network misclassifying input image. allows flexible modeling adversarial noise generative network which can take original image random vector even class label create different types noise. discriminative networks used approach are just the usual neural networks designed specific classification tasks. purpose discriminative network is to classify clean adversarial example correct label generative network aims generate powerful perturbations fool discriminative network. approach is simple directly uses minimax game concept employed GAN. main contributions include:• show adversarial network approach can produce neural networks are robust towards black box attacks. experiments show similar cases better performance when compared state-of-art defense methods ensemble adversarial training BID30 adversarial training projected gradient descent. best knowledge are also first study joint training generative attack network discriminative network.• study effectiveness different generative networks attacking trained discriminative network show variety generative networks including taking random noise labels inputs can be effective attacks. also show training generative networks can provide robustness different attacks.The rest paper is organized follows. Section2 related works including multiple attack defense methods are discussed. Section 3 presents defensive method details. Experimental results are shown Section4 conclusions paper Section5. experiments see adversarial PGD training usually works best white box attacks is tradeoff accuracies clean data accuracies adversarial examples due finite model capacity. can try use models larger capacity is always tradeoff two especially larger perturbations. are some recent works indicate training standard accuracy training adversarial accuracy e.g PGD are two fairly different problems. Examples generated PGD are particularly difficult train against. makes adversarial PGD training disadvantaged many black box attack situations when compared models trained weaker adversaries e.g ensemble adversarial training adversarial networks method.We have also observed experiments black box attacks can be effective adversarial examples are usually constructed models trained using method different random seed. suggests hiding knowledge training method attacker could important factor defending black box attacks. Defending black box attacks is closely related question transferability adversarial examples. Although are some previous works exploring question BID15 underlying factors affecting transferability are still well understood.In experimentation architectures discriminative generative networks choice architectures Gφ does not seem have a big effect quality solution. dynamics training step size used number iterations run network gradient descent/ascent seem have a bigger effect saddle point solution quality network architecture. would interesting find classes generative network architectures lead substantially different saddle points when trained particular discriminative network architecture. Also recent works have been have shown are connected flat regions minima neural network loss landscapes BID5 BID4. believe might hold true GANs would interesting explore how the training dynamics can lead different GAN solutions might have different robustness properties.Our approach can be extended multiple discriminative networks playing multiple generative networks. can also combined ensemble adversarial training where some adversarial examples come static pre-trained models come dynamically adjusting generative networks. have proposed adversarial network approach learning discriminative neural networks are robust adversarial noise especially black box attacks. future work are interested extending experiments ImageNet exploring choice architectures discriminative generative networks interaction. generative networks used paper. G0 G1 are encoder-decoder networks G2 G3 are decoder networks using random vector one-hot encoding label respectively. generative networks are parameterized factor k determining number filters used width network default usek 64 k 16 networks using labels inputs.EXTRA RESULTS CIFAR100 WIDE RESNET CIFAR10The discriminative generative networks CIFAR100 experiment have the same network architecture CIFAR10 experiment except output layer dimension network is 100 10 CIFAR10. use learning rate 0.1 first 100k iterations 0.01 another 100k iterations. batch size is64 weight decay is 1E-5 1E-5 TAB8 gives results CIFAR10 using wider version Resnet ModelD2 multiplying number filters convolutional layer factor 10. previous works literature use models larger capacity training adversarially robust models perform experiments large capacity models here. First accuracies increase across board larger capacity models. accuracy gap clean data adversarial PGD standard training still exists is also small accuracy gap adversarial network approach standard training. rest white box black accuracies story is similar models are weakest attacks trained method different random seed. adversarial network approach has very good performance across different attacks even is not always winner individual attack. TAB10 gives results Wide ResNet CIFAR100 results are qualitatively similar.,1752,1230,522,0.018,1.424,2025/11/05 17:18:59,0.01,1.343,0.2928348909657317,531.392
"Deep learning has become the state of the art approach in many machine learning problems such as classification. It has recently been shown that deep learning is highly vulnerable to adversarial perturbations. Taking the camera systems of self-driving cars as an example, small adversarial perturbations can cause the system to  make errors in important tasks, such as classifying traffic signs or detecting pedestrians. Hence, in order to use deep learning without safety concerns a proper defense strategy is required. We propose to use ensemble methods as a defense strategy against adversarial perturbations. We find that an attack leading one model to misclassify does not imply the same for other networks performing the same task. This makes ensemble methods an attractive defense strategy against adversarial attacks. We empirically show for the MNIST and the CIFAR-10 data sets that ensemble methods not only improve the accuracy of neural networks on test data but also increase their robustness against adversarial perturbations. In recent years, deep neural networks (DNNs) led to significant improvements in many areas ranging from computer vision BID14 BID17 to speech recognition . Some applications that can be solved with DNNs are sensitive from the security perspective, for example camera systems of self driving cars for detecting traffic signs or pedestrians BID21 BID24 . Recently, it has been shown that DNNs can be highly vulnerable to adversaries BID25 BID5 BID20 . The adversary produces some kind of noise on the input of the system to mislead its output behavior, producing undesirable outcomes or misclassification. Adversarial perturbations are carefully chosen in order to be hard, if not impossible, to be detected by the human eye (see FIG1 ). Attacks occur after the training of the DNN is completed. Furthermore, it has been shown that the exact structure of the DNN does not need to be known in order to mislead the system as one can send inputs to the unknown system in order to record its outputs to train a new DNN that imitates its behavior BID21 . Hence, in this manuscript it is assumed that the DNN and all its parameters are fully known to the adversary.There are many methods on how to attack neural networks appearing in the literature. Some of the most well-known ones are the Fast Gradient Sign Method BID5 and its iterative extension BID15 , DeepFool BID19 , Jacobian-Based Saliency Map Attack BID22 , and the L-BFGS Attack BID25 . This shows the need of building neural networks that are themselves robust against any kind of adversarial perturbations.Novel methods on defending against adversarial attacks are appearing more and more frequently in the literature. Some of those defense methods are to train the network with different kinds of adversarially perturbated training data BID5 BID22 , the use of distillation to reduce the effectiveness of the perturbation BID23 or to apply denoising autoencoders to preprocess the data used by the DNN BID7 . It also has been noted that adversarial attacks can be detected BID18 BID4 , but FIG1 : The first line shows original and correctly classified MNIST test data images. In the second line are the corresponding adversarial BIM attacks on a single classifier ( = 0.2, α = 0.025, n = 8) which predicts (from left to right): 6, 8, 1, 5, 9, 3, 0, 2, 2, and 4. Analogously, the third line corresponds to correctly predicted examples of the CIFAR-10 test data set. In the bottom line are the corresponding adversarial BIM attacks on a single classifier ( = 0.02, α = 0.0025, n = 8) which predicts (from left to right): deer, cat, deer, ship, bird, deer, deer, frog, automobile, and automobile. these detection systems are again vulnerable to adversarial attacks. To our knowledge, there is no method that can reliably defend or detect all kinds of adversarial attacks.In this manuscript, ensemble methods are used to obtain a classification system that is more robust against adversarial perturbations. The term ensemble method refers to constructing a set of classifiers used to classify new data points by the weighted or unweighted average of their predictions. Many ensemble methods have been introduced in the literature such as Bayesian averaging, Bagging BID1 and boosting BID3 . These methods frequently win machine learning competitions, for example the Netflix prize BID12 . Initial results on using ensembles of classifiers in adversarial context can be found in BID0 BID9 . However, to the best of our knowledge this is the first manuscript that empirically evaluates the robustness of ensemble methods to adversarial perturbations.One advantage of using ensemble methods as defense against adversarial perturbations is that they also increase the accuracy on unperturbed test data. This is not the case in general for other defense methods (see TAB4 ). However, in most applications a perturbated input can be considered as exception. Hence, it is desirable to obtain a state of the art result on unperturbed test data while making the model more robust against adversarial attacks. Another advantage is that ensemble methods can easily be combined with other defense mechanisms to improve the robustness against adversarial perturbations further (see TAB4 ). However, the advantages come at a cost of an increase of computational complexity and memory requirements which are proportional to the number of classifiers in the ensemble. This paper is organized as follows: In section 2, some methods for producing adversarial perturbations are briefly introduced. Section 3 describes the defense strategy proposed in this manuscript. In section 4, the previous methods are tested on the MNIST and CIFAR-10 data sets and are compared to other defense strategies appearing in the literature. Finally, in section 5 the conclusions are presented. With the rise of deep learning as the state-of-the-art approach for many classification tasks, researchers noted that neural networks are highly vulnerable to adversarial perturbations. This is particularly problematic when neural networks are used in security sensitive applications such as autonomous driving. Hence, with the development of more efficient attack methods against neural networks it is desirable to obtain neural networks that are themselves robust against adversarial attacks.In this manuscript, it is shown that several ensemble methods such as random initialization or Bagging do not only increase the accuracy on the test data, but also make the classifiers considerably more robust against certain adversarial attacks. We consider ensemble methods as sole defense methods, but more robust classifiers can be obtained by combining ensemble methods with other defense mechanisms such as adversarial training. Although only having tested simple attack scenarios, it can be expected that ensemble methods may improve the robustness against other adversarial attacks.",Deep learning has become state art approach many machine learning problems classification. has recently shown deep learning is highly vulnerable adversarial perturbations. Taking camera systems self-driving cars example small adversarial perturbations can cause system make errors important tasks classifying traffic signs detecting pedestrians. Hence order use deep learning without safety concerns proper defense strategy is required. propose use ensemble methods defense strategy adversarial perturbations. find attack leading one model misclassify does not imply networks performing task. makes ensemble methods attractive defense strategy adversarial attacks. empirically show MNIST CIFAR-10 data sets ensemble methods improve accuracy neural networks test data also increase robustness adversarial perturbations. recent years deep neural networks DNNs led significant improvements many areas ranging computer vision BID14 BID17 speech recognition. applications can be solved DNNs are sensitive security perspective example camera systems self driving cars detecting traffic signs pedestrians BID21 BID24. Recently has been is shown DNNs can be highly vulnerable adversaries BID25 BID5 BID20. adversary produces kind noise input system mislead output behavior producing undesirable outcomes misclassification. Adversarial perturbations are carefully chosen order hard if not impossible detected human eye see FIG1 Attacks occur training DNN is completed. Furthermore has been is shown exact structure DNN does not need known order mislead system one can send inputs unknown system order record outputs train new DNN imitates behavior BID21. Hence manuscript is assumed DNN parameters are fully known adversary.There are many methods how to attack neural networks appearing literature. well-known ones are the Fast Gradient Sign Method BID5 iterative extension BID15 DeepFool BID19 Jacobian-Based Saliency Map Attack BID22 L-BFGS Attack BID25. shows need building neural networks are themselves is more robust kind adversarial perturbations.Novel methods defending adversarial attacks are appearing frequently literature. defense methods are to train network different kinds adversarially perturbated training data BID5 BID22 use distillation reduce effectiveness perturbation BID23 apply denoising autoencoders preprocess data used DNN BID7. also has been noted adversarial attacks can be detected BID18 BID4 FIG1:first line shows original correctly classified MNIST test data images. second line are the corresponding adversarial BIM attacks single classifier 0.2 α 0.025 n 8 which predicts left right 6 8 1 5 9 3 0 2 2 4. Analogously third line corresponds correctly predicted examples CIFAR-10 test data set. bottom line are the corresponding adversarial BIM attacks single classifier 0.02 α 0.0025 n 8 which predicts left right deer cat deer ship bird deer deer frog automobile automobile. detection systems are again vulnerable adversarial attacks. knowledge is no method can reliably defend detect kinds adversarial attacks.In manuscript ensemble methods are used obtain classification system are themselves is more robust adversarial perturbations. term ensemble method refers constructing set classifiers used classify new data points weighted unweighted average predictions. Many ensemble methods have been introduced literature Bayesian averaging Bagging BID1 boosting BID3. methods frequently win machine learning competitions example Netflix prize BID12. Initial results using ensembles classifiers adversarial context can be found BID0 BID9. However best knowledge is the first manuscript empirically evaluates robustness ensemble methods adversarial perturbations.One advantage using ensemble methods defense adversarial perturbations is that they also increase accuracy unperturbed test data. is not the case general defense methods see TAB4 However applications perturbated input can be considered exception. Hence is desirable obtain state art result unperturbed test data making model robust adversarial attacks. Another advantage is that ensemble methods can easily combined defense mechanisms improve robustness adversarial perturbations see TAB4 However advantages come cost increase computational complexity memory requirements which are proportional number classifiers ensemble. paper is organized follows:section2 methods producing adversarial perturbations are briefly introduced. Section 3 describes defense strategy proposed manuscript. section4 previous methods are tested MNIST CIFAR-10 data sets are compared defense strategies appearing literature. Finally section5 conclusions are presented. rise deep learning state-of-the-art approach many classification tasks researchers noted neural networks are highly vulnerable adversarial perturbations. is particularly problematic when neural networks are used security sensitive applications autonomous driving. Hence development efficient attack methods neural networks is desirable obtain neural networks are themselves is more robust adversarial attacks.In manuscript has been is shown several ensemble methods random initialization Bagging do not only increase accuracy test data also make classifiers considerably robust certain adversarial attacks. consider ensemble methods sole defense methods robust classifiers can be obtained combining ensemble methods defense mechanisms adversarial training. Although tested simple attack scenarios can be expected ensemble methods may improve robustness adversarial attacks.,1356,937,419,0.015,1.447,2025/11/05 17:18:59,0.01,1.545,0.3644859813084112,448.133
"In this paper, we propose the Associative Conversation Model that generates visual information from textual information and uses it for generating sentences in order to utilize visual information in a dialogue system without image input. In research on Neural Machine Translation, there are studies that generate translated sentences using both images and sentences, and these studies show that visual information improves translation performance. However, it is not possible to use sentence generation algorithms using images for the dialogue systems since many text-based dialogue systems only accept text input. Our approach generates (associates) visual information from input text and generates response text using context vector  fusing associative visual information and sentence textual information. A comparative experiment between our proposed model and a model without association showed that our proposed model is generating useful sentences by associating visual information related to sentences. Furthermore, analysis experiment of visual association showed that our proposed model generates (associates) visual information effective for sentence generation. As a model that can extract knowledge from conversations, the encoder-decoder model has been proposed BID12 BID14 . It consists of an encoder that encodes the input information into a context vector and a decoder that generates sentences using the context. BID14 showed that it is possible to extract knowledge and to conduct conversation by learning pairs of dialogues with the model. For example, BID14 reported that when asked who is Skywalker, their conversation model (NCM) responded ""he is a hero."" NCM has a problem that it is not possible to respond properly to the input texts that require visual information. For example, BID14 reported that when asked how many legs a spider have, NCM responded ""three, i think."" Further, the image or video may contain more detailed information than texts. Consider, for example, a scene in a news program including a closed caption ""one marathon runner won the marathon competition "" and showing an image with the marathon runner with the gold medal. Here, in the video, more detailed information such as the gold medal that does not exist directly in the text is presented. We thought that if such detailed visual information could be extracted from the image, more specific and useful texts could be generated, including ""gold medals"" which can not be obtained with text alone. In recent years, studies have been reported in which translated sentences are generated by adding image features to the context vector encoded by the encoder-decoder model BID1 BID3 BID7 BID8 BID13 . These studies showed that visual information works effectively for generating translation.Meanwhile, visual information is not considered in many text-based dialogue systems, because what is given to the input is only the utterance text. How can the visual information be used without accepting visual information as the input to the dialogue system? Based on the discussion above, we propose an Associative Conversation Model that associates the input text with the visual information and generates the response using both the text and the asso- Figure 1 : Generating a response by visual association. The textual information is used to estimate the corresponding visual information, and a response text is generated using the vector obtained by fusing the textual and visual information. ciated visual information. In our proposed method, we attempted to generate response texts using visual information without inputting images. The contribution of this research is as follows:• We made it possible to generate visual information related to sentence textual information through end-to-end learning of dialogue.• We made it possible to generate sentences using visual information without directly inputting visual information by association. • Our proposed model can generate response texts including useful information compared with a model without association by associating visual information related to input text. Our method is useful for constructing the text-based dialogue systems that automatically extract information from the text and the video data (e.g., TV news) to generate sentences. In a study applying a sentence generation algorithm of translation sentence to a conversation model, there was a problem that it was not possible to respond well to an input text which requires visual information. However, it is not possible to use sentence generation algorithms using images for the dialogue systems since many text-based dialogue systems only accept text input. Based on the discussion above, we propose an Associative Conversation Model that associates the input text with the visual information and generates the response using both the text and the associated visual infor-mation. Comparative experiments with models that do not use association show that association of visual information related to input texts produces response texts that contain valuable information compared to models without association. Analysis of association also showed that our proposed method can generate visual information related to sentence textual information through end-to-end learning of dialogue. Our method is useful for constructing the text-based dialogue systems that automatically extract information from the text and the video data (e.g., TV news) to generate sentences.","paper propose Associative Conversation Model generates visual information textual information uses generating sentences order utilize visual information dialogue system without image input. research Neural Machine Translation are studies generate translated sentences using images sentences are studies show visual information improves translation performance. However is not possible use sentence generation algorithms using images dialogue systems since many text-based dialogue systems accept text input. approach generates associates visual information input text generates response text using context vector fusing associative visual information sentence textual information. comparative experiment proposed model model without association showed proposed model is generating useful sentences associating visual information related sentences. Furthermore analysis experiment visual association showed proposed model generates associates visual information effective sentence generation. model can extract knowledge conversations encoder-decoder model has been proposed BID12 BID14. consists encoder encodes input information context vector decoder generates sentences using context. BID14 showed is is not was not possible extract knowledge conduct conversation learning pairs dialogues model. example BID14 reported when asked who is Skywalker conversation model NCM responded is a hero. NCM has a problem is is not was not possible respond properly input texts require visual information. example BID14 reported when asked how many legs spider have,NCM responded three think. image video may contain detailed information texts. Consider example scene news program including closed caption one marathon runner marathon competition showing image marathon runner gold medal. video detailed information gold medal does not exist directly text is presented. thought if such detailed visual information could extracted image specific useful texts could generated including gold medals which can not be obtained text alone. recent years are studies have been reported which translated sentences are generated adding image features context vector encoded encoder-decoder model BID1 BID3 BID7 BID8 BID13. studies showed visual information works effectively generating translation.Meanwhile visual information is not considered many text-based dialogue systems what is given input is only the utterance text. How can the visual information used without accepting visual information input dialogue system? Based discussion propose Associative Conversation Model associates input text visual information generates response using text asso- Figure1:Generating response visual association. textual information is used estimate corresponding visual information response text is generated using vector obtained fusing textual visual information. ciated visual information. proposed method attempted generate response texts using visual information without inputting images. contribution research is as follows:• made possible generate visual information related sentence textual information end-to-end learning dialogue.• made possible generate sentences using visual information without directly inputting visual information association. • proposed model can generate response texts including useful information compared model without association associating visual information related input text. method is useful constructing text-based dialogue systems automatically extract information text video data e.g TV news generate sentences. study applying sentence generation algorithm translation sentence conversation model was a problem is is not was not possible respond well input text which requires visual information. However is not possible use sentence generation algorithms using images dialogue systems since many text-based dialogue systems accept text input. Based discussion propose Associative Conversation Model associates input text visual information generates response using text associated visual infor-mation Comparative experiments models do not use association show association visual information related input texts produces response texts contain valuable information compared models without association. Analysis association also showed proposed method can generate visual information related sentence textual information end-to-end learning dialogue. method is useful constructing text-based dialogue systems automatically extract information text video data e.g TV news generate sentences.",950,659,291,0.009,1.442,2025/11/05 17:18:59,0.0,1.697,0.3489096573208719,309.909
"Feedforward convolutional neural network has achieved a great success in many computer vision tasks. While it validly imitates the hierarchical structure of biological visual system, it still lacks one essential architectural feature: contextual recurrent connections with feedback, which widely exists in biological visual system. In this work, we designed a Contextual Recurrent Convolutional Network with this feature embedded in a standard CNN structure. We found that such feedback connections could enable lower layers to ``rethink"" about their representations given the top-down contextual information. We carefully studied the components of this network, and showed its robustness and superiority over feedforward baselines in such tasks as noise image classification, partially occluded object recognition and fine-grained image classification. We believed this work could be an important step to help bridge the gap between computer vision models and real biological visual system. It has been long established that the primate's ventral visual system has a hierarchical structure BID5 including early (V1, V2), intermediate (V4), and higher (IT) visual areas. Modern deep convolutional neural networks (CNNs) for image recognition BID10 BID18 trained on large image data sets like ImageNet (Russakovsky et al., 2015) imitate this hierarchical structure with multiple layers. There is a hierarchical correspondence between internal feature representations of a deep CNN's different layers and neural representations of different visual areas BID3 BID25 ; lower visual areas (V1, V2) are best explained by a deep CNN's internal representations from lower layers (Cadena et al., 2017; Khaligh-Razavi & Kriegeskorte, 2014) and higher areas (IT, V4) are best explained by its higher layers (Khaligh-Razavi & Kriegeskorte, 2014; BID24 . Deep CNNs explain neuron responses in ventral visual system better than any other model class BID25 BID9 , and this success indicates that deep CNNs share some similarities with the ventral visual system, in terms of architecture and internal feature representations BID25 .However , there is one key structural component that is missing in the standard feedforward deep CNNs: contextual feedback recurrent connections between neurons in different areas BID5 . These connections greatly contribute to the complexity of the visual system, and may be essential for the success of the visual systems in reality; for example, there are evidences that recurrent connections are crucial for object recognition under noise, clutter, and occlusion BID14 BID19 BID15 .In this paper, we explored a variety of model with different recurrent architectures, contextual modules, and information flows to understand the computational advantages of feedback circuits. We are interested in understanding what and how top-down and bottom-up contextual information can be combined to improve in performance in visual tasks. We investigated VGG16 BID18 , a standard CNN that coarsely approximate the ventral visual hierarchical stream, and its recurrent variants for comparison. To introduce feedback recurrent connections, we divided VGG16's layers into stages and selectively added feedback connections from the groups' highest layers to their lowest layers. At the end of each feedback connection, there is a contextual module (Section 3.2) that refines the bottom-up input with gated contextual information. We tested and compared several networks with such contextual modules against VGG16 in several standard image classification task, as well as visual tasks in which refinement under feedback guidance is more likely to produce some beneficial effects, such as object recognition under degraded conditions (noise, clutter and occlusion) and fine-grained recognition. We found that our network could outperform all the baseline feedforward networks and surpassed them by a large margin in finegrained and occlusion tasks. We also studied the internal feature representations of our network to illustrate the effectiveness of the structure. While much future work has to be done , our work can still be an important step to bridge the gap between biological visual systems and state-of-the-art computer vision models. In this paper, we proposed a novel Contextual Recurrent Convolutional Network. Based on the recurrent connections between layers in the hierarchy of a feedforward deep convolutional neural network, the new network can show some robust properties in some computer vision tasks compared with its feedforward baseline. Moreover, the network shares many common properties with biological visual system. We hope this work will not only shed light on the effectiveness of recurrent connections in robust learning and general computer vision tasks, but also give people some inspirations to bridge the gap between computer vision models and real biological visual system.",Feedforward convolutional neural network has achieved great success many computer vision tasks. validly imitates hierarchical structure biological visual system still lacks one essential architectural feature:contextual recurrent connections feedback which widely exists biological visual system. work designed Contextual Recurrent Convolutional Network feature embedded standard CNN structure. found feedback connections could enable lower layers rethink representations given top-down contextual information. carefully studied components network showed robustness superiority feedforward baselines tasks noise image classification partially occluded object recognition fine-grained image classification. believed work could important step help bridge gap computer vision models real biological visual system. has been long established primate's ventral visual system has a hierarchical structure BID5 including early V1 V2 intermediate V4 higher visual areas. Modern deep convolutional neural networks CNNs image recognition BID10 BID18 trained large image data sets like ImageNet Russakovskyetal. 2015 imitate hierarchical structure multiple layers. is a hierarchical correspondence internal feature representations deep CNN's different layers neural representations different visual areas BID3 BID25;lower visual areas V1 V2 are best explained deep CNN's internal representations lower layers Cadenaetal. 2017;Khaligh-Razavi Kriegeskorte 2014 higher areas V4 are best explained higher layers Khaligh-Razavi Kriegeskorte 2014;BID24. Deep CNNs explain neuron responses ventral visual system better model class BID25 BID9 success indicates deep CNNs share similarities ventral visual system terms architecture internal feature representations BID25.However is one key structural component is missing standard feedforward deep CNNs:contextual feedback recurrent connections neurons different areas BID5. connections greatly contribute complexity visual system may essential success visual systems reality;example are evidences recurrent connections are crucial object recognition noise clutter occlusion BID14 BID19 BID15.In paper explored variety model different recurrent architectures is a contextual modules information flows understand computational advantages feedback circuits. are interested understanding what and how top-down bottom-up contextual information can be combined improve performance visual tasks. investigated VGG16 BID18 standard CNN coarsely approximate ventral visual hierarchical stream recurrent variants comparison. introduce feedback recurrent connections divided VGG16's layers stages selectively added feedback connections groups' highest layers lowest layers. end feedback connection is a contextual module Section 3.2 refines bottom-up input gated contextual information. tested compared several networks contextual modules VGG16 several standard image classification task well visual tasks which refinement feedback guidance is more likely produce beneficial effects object recognition degraded conditions noise clutter occlusion fine-grained recognition. found network could outperform baseline feedforward networks surpassed large margin finegrained occlusion tasks. also studied internal feature representations network illustrate effectiveness structure. much future work has to be done work can still important step bridge gap biological visual systems state-of-the-art computer vision models. paper proposed novel Contextual Recurrent Convolutional Network. Based recurrent connections layers hierarchy feedforward deep convolutional neural network new network can show robust properties computer vision tasks compared feedforward baseline. Moreover network shares many common properties biological visual system. hope work will not only shed light effectiveness recurrent connections robust learning general computer vision tasks also give people inspirations bridge gap computer vision models real biological visual system.,913,640,273,0.008,1.427,2025/11/05 17:18:59,0.0,1.6,0.3021806853582554,288.554
"Deep neural networks have led to a series of breakthroughs, dramatically improving the state-of-the-art in many domains. The techniques driving these advances, however, lack a formal method to account for model uncertainty. While the Bayesian approach to learning provides a solid theoretical framework to handle uncertainty, inference in Bayesian-inspired deep neural networks is difficult. In this paper, we provide a practical approach to Bayesian learning that relies on a regularization technique found in nearly every modern network, batch normalization. We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. Our approach is thoroughly validated in a series of empirical experiments on different tasks and using various measures, showing it to outperform baselines on a majority of datasets with strong statistical significance. Deep learning has dramatically advanced the state of the art in a number of domains, and now surpasses human-level performance for certain tasks such as recognizing the contents of an image BID10 and playing Go (Silver et al., 2017) . But, despite their unprecedented discriminative power, deep networks are prone to make mistakes. Sometimes, the consequences of mistakes are minor -misidentifying a food dish or a species of flower (Liu et al., 2016) may not be life threatening. But deep networks can already be found in settings where errors carry serious repercussions such as autonomous vehicles BID2 and high frequency trading. In medicine, we can soon expect automated systems to screen for skin cancer BID4 , breast cancer (Shen, 2017) , and to diagnose biopsies BID3 . As autonomous systems based on deep learning are increasingly deployed in settings with the potential to cause physical or economic harm, we need to develop a better understanding of when we can be confident in the estimates produced by deep networks, and when we should be less certain.Standard deep learning techniques used for supervised learning lack methods to account for uncertainty in the model, although sometimes the classification network's output vector is mistakenly understood to represent the model's uncertainty. The lack of a confidence measure can be especially problematic when the network encounters conditions it was not exposed to during training. For example, if a network trained to recognize dog breeds is given an image of a cat, it may predict it to belong to a breed of small dog with high probability. When exposed to data outside of the distribution it was trained on, the network is forced to extrapolate, which can lead to unpredictable behavior. In such cases, if the network can provide information about its uncertainty in addition to its point estimate, disaster may be avoided. This work focuses on estimating such predictive uncertainties in deep networks (Figure 1 ).The Bayesian approach provides a solid theoretical framework for modeling uncertainty BID7 , which has prompted several attempts to extend neural networks (NN) into a Bayesian setting. Most notably, Bayesian neural networks (BNNs) have been studied since the 1990's (Neal, 2012) . Although they are simple to formulate, BNNs require substantially more computational resources than their non-Bayesian counterparts, and inference is difficult. Importantly , BNNs do 2 RELATED WORK Bayesian models provide a natural framework for modeling uncertainty, and several approaches have been developed to adapt NNs to Bayesian reasoning. A common approach is to place a prior distribution (often a Gaussian) over each weight. For infinite weights , the resulting model corresponds to a Gaussian process (Neal, 1995) , and for a finite number of weights it corresponds to a Bayesian neural network (MacKay, 1992) . Although simple to formulate, inference in BNNs is difficult BID5 . Therefore, focus has shifted to techniques to approximate the posterior distribution, leading to approximate BNNs. Methods based on variational inference (VI) typically rely on a fully factorized approximate distribution (Kingma & Welling, 2014; Hinton & Van Camp, 1993) but these methods do not scale easily. To alleviate these difficulties , BID9 proposed a model using sampling methods to estimate a factorized posterior. Another approach, probabilistic backpropagation (PBP), also estimates a factorized posterior based on expectation propagation (Hernández-Lobato & Adams, 2015) .Deep Gaussian Processes (DGPs) formulate GPs as Bayesian models capable of working on large datasets with the aid of a number of strategies to address scaling and complexity requirements BID1 . The authors compare DGP with a number of state-of-the-art approximate BNNs, showing superior performance in terms of RMSE and uncertainty quality 2 . Another recent approach to Bayesian learning , Bayesian hypernetworks, use a neural network to learn a distribution of paramaters over another neural network (Krueger et al., 2017) . Although these recent techniques address some of the difficulties with approximate BNNs, they all require modifications to the architecture or the way networks are trained, as well as specialized knowledge from practitioners.Recently, BID5 showed that a network trained with dropout implicitly performs the VI objective. Therefore any network trained with dropout can be treated as an approx. Bayesian model by making multiple predictions as forward passes through the network while sampling different dropout masks for each prediction. An estimate of the posterior can be obtained by computing the mean and variance of the predictions. This technique, referred to here as MCDO, has been empirically demonstrated to be competitive with other approx. BNN methods and DGPs in terms of RMSE and uncertainty quality (Li & Gal, 2017) . However, as the name implies, MCDO depends on dropout . While once ubiquitous in training deep learning models , dropout has largely been replaced by batch normalization in modern networks, limiting its usefulness. The results presented in TAB2 and Appendix 6.6 indicate that MCBN generates meaningful uncertainty estimates which correlate with actual errors in the model's prediction. We show statistically significant improvements over CUBN in the majority of the datasets, both in terms of CRPS and PLL. The visualizations in FIG0 and in Appendix 6.6 show clear correlations between the estimated model uncertainty and actual errors produced by the network. We perform the same experiments using MCDO, and find that MCBN generally performs on par with MCDO. Looking closer, in terms of CRPS, MCBN performs better than MCDO in more cases than not. However, care must be used when comparing different models. The learned network parameters are different, leading to different predictive means which can confound direct comparison.The results on the Yacht Hydrodynamics dataset seem contradictory. The CRPS score for MCBN is extremely negative, while the PLL score is extremely positive. The opposite trend is observed for MCDO. To add to the puzzle, the visualization in FIG0 depicts an extremely promising uncertainty estimation that models the predictive errors with high fidelity. We hypothesize that this strange behavior is due to the small size of the data set, which only contains 60 test samples, or due to the Gaussian assumption of CRPS. There is also a large variability in the model's accuracy on this dataset, which further confounds the measurements for such limited data.One might criticize the overall quality of the uncertainty estimates of MCBN and MCDO based on the magnitude of the CRPS and PLL scores in TAB2 . The scores rarely exceed 10% improvement over the lower bound. However, we caution that these measures should be taken in context. The upper bound is very difficult to achieve in practice (it is optimized for each test sample individually), and the lower bound is a quite reasonable estimate for uncertainty. We have further compared against the recent work of Louizos & Welling (2017) , and find comparable results to their MNF-based variational technique specifically targeted to increase the flexibility of the approximate posterior.Our approximation of the implied prior in Appendix 6.5 also provides a new interpretation of the empirical evidence that significantly lower λ should be used in batch normalized networks (Ioffe & Szegedy, 2015) . From a VA perspective, too strong a regularization for a given dataset size could be seen as constraining the prior distribution of BN units' means, effectively narrowing the approximate posterior.In this work, we have shown that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. We show evidence that the uncertainty estimates from MCBN correlate with actual errors in the model's prediction, and are useful for practical tasks such as regression or semantic image segmentation. Our experiments show that MCBN yields an improvement over the baseline of optimized constant uncertainty on par with MCDO and MNF. Finally, we make contributions to the evaluation of uncertainty quality by suggesting new evaluation metrics based on useful baselines and upper bounds, and proposing a new visualization tool which gives an intuitive visual explanation of uncertainty quality. Finally, it should be noted that, over the past few years, batch normalization has become an integral part of most-if-not-all cutting edge deep networks which signifies the relevance of our work for estimating model uncertainty.",Deep neural networks have led series breakthroughs dramatically improving state-of-the-art many domains. techniques driving advances however lack formal method account model uncertainty. Bayesian approach learning provides solid theoretical framework handle uncertainty inference Bayesian-inspired deep neural networks is is very difficult. paper provide practical approach Bayesian learning relies regularization technique found nearly every modern network batch normalization. show training deep network using batch normalization is equivalent approximate inference Bayesian models demonstrate how this finding allowsus make useful estimates model uncertainty. Using approach is possible make meaningful uncertainty estimates using conventional architectures without modifying network training procedure. approach is thoroughly validated series empirical experiments different tasks using various measures showing outperform baselines majority datasets strong statistical significance. Deep learning has dramatically advanced state art number domains surpasses human-level performance certain tasks recognizing contents image BID10 playingGo Silveretal. 2017 despite unprecedented discriminative power deep networks are prone make mistakes. Sometimes consequences mistakes are minor -misidentifying food dish species flower Liuetal. 2016 may life threatening. deep networks can already found settings where errors carry serious repercussions autonomous vehicles BID2 high frequency trading. medicine can soon expect automated systems screen skin cancer BID4 breast cancer Shen 2017 diagnose biopsies BID3. autonomous systems based deep learning are increasingly deployed settings potential cause physical economic harm need develop better understanding when we can confident estimates produced deep networks whenwe shouldbe less certain.Standard deep learning techniques used supervised learning lack methods account uncertainty model although sometimes classification network's output vector is mistakenly understood represent model's uncertainty. lack confidence measure can be especially problematic when the network encounters conditions was not exposed training. example if a if the network trained recognize dog breeds is given image cat may predict belong breed small dog high probability. When exposed data outside distribution was trained network is forced extrapolate which can lead unpredictable behavior. cases if a if the network can provide information uncertainty addition point estimate disaster may avoided. work focuses estimating predictive uncertainties deep networks Figure1.The Bayesian approach provides solid theoretical framework modeling uncertainty BID7 which has prompted several attempts extend neural networks NN Bayesian setting. notably Bayesian neural networks BNNs have been studied since 1990's Neal 2012 Although are simple formulate BNNs require substantially computational resources non-Bayesian counterparts inference is is very difficult. Importantly BNNs do 2 RELATED WORK Bayesian models provide natural framework modeling uncertainty several approaches have been developed adapt NNs Bayesian reasoning. common approach is to place prior distribution often Gaussian weight. infinite weights resulting model corresponds Gaussian process Neal 1995 finite number weights corresponds Bayesian neural network MacKay 1992 Although simple formulate inference BNNs is is very difficult BID5. Therefore focus has shifted techniques approximate posterior distribution leading approximate BNNs. Methods based variational inference VI typically rely fully factorized approximate distribution Kingma Welling 2014;Hinton Van Camp 1993 methods do not scale easily. alleviate difficulties BID9 proposed model using sampling methods estimate factorized posterior. Another approach probabilistic backpropagation PBP also estimates factorized posterior based expectation propagation Hernández-Lobato Adams 2015.Deep Gaussian Processes DGPs formulate GPs Bayesian models capable working large datasets aid number strategies address scaling complexity requirements BID1. authors compare DGP number state-of-the-art approximate BNNs showing superior performance terms RMSE uncertainty quality2. Another recent approach Bayesian learning Bayesian hypernetworks use neural network learn distribution paramaters another neural network Kruegeretal. 2017 Although recent techniques address difficulties approximate BNNs require modifications architecture way networks are trained well specialized knowledge practitioners.Recently BID5 showed network trained dropout implicitly performs VI objective. Therefore network trained dropout can be treated approx. Bayesian model making multiple predictions forward passes network sampling different dropout masks prediction. estimate posterior can be obtained computing mean variance predictions. technique referred MCDO has been empirically demonstrated competitive approx. BNN methods DGPs terms RMSE uncertainty quality Li Gal 2017 However name implies MCDO depends dropout. ubiquitous training deep learning models dropout has largely replaced batch normalization modern networks limiting usefulness. results presented TAB2 Appendix 6.6 indicate MCBN generates meaningful uncertainty estimates which correlate actual errors model's prediction. show statistically significant improvements CUBN majority datasets terms CRPS PLL. visualizations FIG0 Appendix 6.6 show clear correlations estimated model uncertainty actual errors produced network. perform experiments using MCDO find MCBN generally performs par MCDO. Looking closer terms CRPS MCBN performs better MCDO cases not. However care must used when comparing different models. learned network parameters are different leading different predictive means which can confound direct comparison.The results Yacht Hydrodynamics dataset seem contradictory. CRPS score MCBN is extremely negative PLL score is extremely positive. opposite trend is observed MCDO. add puzzle visualization FIG0 depicts extremely promising uncertainty estimation models predictive errors high fidelity. hypothesize strange behavior is due small size data set which only contains 60 test samples due Gaussian assumption CRPS. is also large variability model's accuracy dataset which further confounds measurements limited data.One might criticize overall quality uncertainty estimates MCBN MCDO based magnitude CRPS PLL scores TAB2. scores rarely exceed10% improvement lower bound. However caution measures should be taken context. upper bound is is very difficult achieve practice is optimized test sample individually lower bound is a quite reasonable estimate uncertainty. have further compared recent work Louizos Welling 2017 find comparable results MNF-based variational technique specifically targeted increase flexibility approximate posterior.Our approximation implied prior Appendix 6.5 also provides new interpretation empirical evidence significantly lowerλ should be used batch normalized networks Ioffe Szegedy 2015 VA perspective strong regularization given dataset size could seen constraining prior distribution BN units' means effectively narrowing approximate posterior.In work have shown training deep network using batch normalization is equivalent approximate inference Bayesian models. Using approach is possible make meaningful uncertainty estimates using conventional architectures without modifying network training procedure. show evidence uncertainty estimates MCBN correlate actual errors model's prediction are useful practical tasks regression semantic image segmentation. experiments show MCBN yields improvement baseline optimized constant uncertainty par MCDO MNF. Finally make contributions evaluation uncertainty quality suggesting new evaluation metrics based useful baselines upper bounds proposing new visualization tool which gives intuitive visual explanation uncertainty quality. Finally should be noted past years batch normalization has become integral part most-if-not-all cutting edge deep networks which signifies relevance work estimating model uncertainty.,1889,1277,612,0.022,1.479,2025/11/05 17:18:59,0.01,1.444,0.4641744548286605,695.071
"Data-parallel neural network training is network-intensive, so gradient dropping was designed to exchange only large gradients.   However, gradient dropping has been shown to slow convergence.   We propose to improve convergence by having each node combine its locally computed gradient with the sparse global gradient exchanged over the network. We empirically confirm with machine translation tasks that gradient dropping with local gradients approaches convergence 48% faster than non-compressed multi-node training and 28% faster compared to vanilla gradient dropping. We also show that gradient dropping with a local gradient update does not reduce the model's final quality. Training a neural network can be slow, especially with a large model or dataset BID12 BID18 . Distributed training is becoming essential to speed up the process. In data-parallel training, multiple workers optimize the same parameters based on different parts of the training data then exchange parameters.Data-parallel training is network intensive because workers send and fetch gradients that have the same size as the model. Several techniques have been proposed to reduce the traffic in dataparallelism training by using quantization to compress the gradient sent BID13 BID1 or selecting sparse matrices BID17 BID5 BID0 BID10 .Gradient dropping, and its extension Deep Gradient Compression BID10 , is a recent approach that compresses the network by sending a small fraction (about 1%) of the largest gradients (by absolute value). This technique is based on the observation that the gradient values are skewed, as most are close to zero. An issue with gradient compression is that gradients are compressed so much that it slows the model's convergence rate and can reduce the model's final quality BID0 .In vanilla gradient dropping, all nodes update with the same sparse gradient exchanged over the network, while other parameters are unchanged. However, each node has computed a local gradient on its own data. Can we exploit this dense local gradient alongside the sparse global gradient to improve convergence? We propose and evaluate three ways to combine them. We significantly reduce convergence damage caused by compressing the gradient through gradient dropping in data-parallelism training. We utilize a locally-computed gradient to predict and reconstruct the dense gradient. Our experiments show that we can improve the training time up to 45% faster compared to a non-compressed multi-node system and 3x faster compared to a single-node system. Local gradient update is also empirically shown to negate the quality loss caused by gradient dropping.",Data-parallel neural network training is network-intensive gradient dropping was designed exchange large gradients. However gradient dropping has been shown slow convergence. propose improve convergence node combine locally computed gradient sparse global gradient exchanged network. empirically confirm machine translation tasks gradient dropping local gradients approaches convergence 48% faster non-compressed multi-node training 28% faster compared vanilla gradient dropping. also show gradient dropping local gradient update does not reduce model's final quality. Training neural network can be slow especially large model dataset BID12 BID18. Distributed training is becoming essential speed process. data-parallel training multiple workers optimize parameters based different parts training data exchange parameters.Data-parallel training is network intensive workers send fetch gradients have the same size model. Several techniques have been proposed reduce traffic dataparallelism training using quantization compress gradient sent BID13 BID1 selecting sparse matrices BID17 BID5 BID0 BID10.Gradient dropping extension Deep Gradient Compression BID10 is a recent approach compresses network sending small fraction 1% largest gradients absolute value technique is based observation gradient values are skewed are close zero. issue gradient compression is that gradients are compressed much slows model's convergence rate can reduce model's final quality BID0.In vanilla gradient dropping nodes update sparse gradient exchanged network parameters are unchanged. However node has computed local gradient data. Can we exploit dense local gradient alongside sparse global gradient improve convergence? propose evaluate three ways combine them. significantly reduce convergence damage caused compressing gradient gradient dropping data-parallelism training. utilize locally-computed gradient predict reconstruct dense gradient. experiments show can improve training time 45% faster compared non-compressed multi-node system 3x faster compared single-node system. Local gradient update is also empirically shown negate quality loss caused gradient dropping.,481,344,137,0.004,1.398,2025/11/05 17:18:59,0.0,1.429,0.2118380062305291,140.439
"    We establish the relation between Distributional RL and the Upper Confidence Bound (UCB) approach to exploration.
     In this paper we show that the density of the Q function estimated by Distributional RL can be successfully used for the estimation of UCB. This approach does not require counting and, therefore, generalizes well to the Deep RL. We also point to the asymmetry of the empirical densities estimated by the Distributional RL algorithms like QR-DQN. This observation leads to the reexamination of the variance's performance in the UCB type approach to exploration. We introduce truncated variance as an alternative estimator of the UCB and a novel algorithm based on it. We empirically show that newly introduced algorithm achieves better performance in multi-armed bandits setting. Finally, we extend this approach to high-dimensional setting and test it on the Atari 2600 games. New approach achieves better performance compared to QR-DQN in 26 of games, 13 ties out of 49 games. Exploration is a long standing problem in Reinforcement Learning (RL). It's been the main focus of the multi-armed bandits literature. Here the algorithms are easier to design and analyze. However, these solutions are quite unfeasible for high dimensional Deep RL setting, where the complication comes from the presence of the function approximator.The multi-armed bandit can be represented by a slot machine with several arms. Each arms' expected reward is unknown to the gambler. Her/his goal is to maximize cumulative reward by pulling bandit's arms. If the true expected rewards are known, then the best strategy is to pull the arm with the highest value. However, gambler only observes stochastic reward after the arm is pulled. One possible solution described by BID18 is to initialize values of arms' estimated means optimistically and then improve the estimates by pulling the same arm again. Arm with a lower true mean will get its estimate decreased over time. Eventually, the best arm will be discovered. The drawback is that the set of the arms has to be enumerated and every arm has to be pulled infinitely many times. In the RL setting an arm corresponds to a state-action pair, which implies that both assumptions are too strong for the Deep RL.Another line of reasoning is Upper Confidence Bound (UCB) type algorithms, e.g. UCB-1, introduce by BID10 . The essence of the approach is nicely summarized by BID0 : 'optimism in the face of uncertainty principle'. The idea is statistically intuitive: pull the arm which has the highest upper confidence bound, hoping for a better mean. Estimation of the arm's UCB is performed via Hoeffdings Inequality 1 which is entirely based on counting the number of times the arm was pulled. UCB extends to the tree search case in the form of UCT developed by BID10 . Although this idea was successfully applied to the problem when perfect model is accessible, i.e. AlphaGo by BID17 , it does not generalize in a straightforward fashion to the general Deep RL setting without perfect model. The main obstacle is the requirement of counting of the state-action pairs. Another popular variation is UCB-V introduced by BID0 . It estimates UCB via the empirical variance, which again involves counting. Therefore, the requirement of counting prevents UCB ideas from successful generalization to the high dimensional setting of Deep RL.The generalization of exploration ideas from multi-armed bandits to Deep RL is challenging. Therefore, one the most popular exploration approaches in Deep RL is the annealed epsilon greedy approach popularized by BID13 . However, epsilon greedy approach is not very efficient, especially in Deep RL. It does not take into account the underlying structure of the environment. Therefore, researchers have been looking for other more efficient ways of exploration in Deep RL setting. For example the idea of parametric noise was explored by BID4 . Posterior sampling for reinforcement learning BID15 ) in Deep RL setting was developed by BID16 . Uncertainty Bellman Equation proposed by BID14 , generalizes Bellman equation to the uncertainty measure. The closest UCB type approach was developed by BID2 . In order to avoid counting authors estimate UCB based on the empirical distribution of the Q function produced by Bootstrapped DQN BID16 ). The approach reduces to estimating an ensemble of randomly initialized Q functions. According to the averaged human normalized learning curve the performance improvement was insignificant. Currently, there is a much better approach to estimating empirical distributions of Q function, i.e. distributional RL , ). The results in the distributional RL are both theoretically sound and achieve state of the art performance in Deep RL environments, like Atari 2600. However, we should note that Distributional RL does not use the whole distribution, but only the mean.Another important characteristic of Distributional RL is that both C51 ) and Quantile Regression DQN (QR-DQN) ) are non parametric in the sense that the estimated distribution is not assumed to belong to any specific parametric family. Hence, it is not assumed to be symmetric or even unimodal 2 . We argue that in the case of asymmetric distributions, variance might become less sensitive in estimating UCB. This problem seems to be overseen by the existing literature. However, this issue might become more important in a more general setting, when symmetric assumption is not simply relaxed but is a very rare case. We empirically show in the Section 4 that symmetry is in fact rare in Distributional RL.In this paper we build upon generic UCB idea. We generalize it to the asymmetric distributions and high-dimensional setting. In order to extend UCB approach to asymmetric distributions, we introduce truncated variability measure and show empirically that it achieves higher performance than variance in bandits setting. Extension of this measure to rich visual environments provided by Atari 2600 platform is based on recent advances in Distributional RL. Recent advancements in RL, namely Distributional RL, not only established new theoretically sound principles but also achieved state-of-the-art performance in challenging high dimensional environments like Atari 2600. The by-product of the Distributional RL is the empirical PDF for the Q function which is not directly used except for the mean computation. UCB on the other hand is a very attractive exploration algorithm in the multi-armed bandits setting, which does not generalize in a straightforward fashion to Deep RL.In this paper we established the connection between the UCB idea and Distributional RL. We also pointed to the asymmetry of the PDFs estimated by Distributional RL, which is not a rare exception but rather the only case. We introduced truncated variability measure as an alternative to the variance and empirically showed that it can be successfully applied to multi-armed bandits and rich visual environments like Atari 2600. It is highly likely that DQN-QUCB+ might be improved through schedule tuning. DQN-QUCB+ might be combined with other advancements in Deep RL, e.g. Rainbow by BID6 , to yield better results.",establish relation DistributionalRL Upper Confidence Bound UCB approach exploration. paper show density Q function estimated DistributionalRL can be successfully used estimation UCB. approach does not require counting therefore generalizes well DeepRL. also point asymmetry empirical densities estimated Distributional RL algorithms like QR-DQN observation leads reexamination variance's performance UCB type approach exploration. introduce truncated variance alternative estimator UCB novel algorithm based it. empirically show newly introduced algorithm achieves better performance multi-armed bandits setting. Finally extend approach high-dimensional setting test Atari 2600 games. New approach achieves better performance compared QR-DQN 26 games 13 ties 49 games. Exploration is a long standing problem Reinforcement Learning RL main focus multi-armed bandits literature. algorithms are easier design analyze. However solutions are quite unfeasible high dimensional DeepRL setting where the complication comes presence function approximator.The multi-armed bandit can be represented slot machine several arms. arms' expected reward is unknown gambler./goal is to maximize cumulative reward pulling bandit's arms. If the true expected rewards are known best strategy is to pull arm highest value. However gambler observes stochastic reward arm is pulled. One possible solution described BID18 is to initialize values arms' estimated means optimistically improve estimates pulling arm again. Arm lower true mean will get estimate decreased time. Eventually best arm will be discovered. drawback is that the set arms has to be enumerated every arm has to be pulled infinitely many times. RL setting arm corresponds state-action pair which implies assumptions are too strong Deep RL.Another line reasoning is Upper Confidence Bound UCB type algorithms e.g UCB-1 introduce BID10. essence approach is nicely summarized BID0:'optimism face uncertainty principle'. idea is statistically intuitive:pull arm which has the highest upper confidence bound hoping better mean. Estimation arm's UCB is performed via Hoeffdings Inequality 1 which is entirely based counting number times arm was pulled. UCB extends tree search case form UCT developed BID10. Although idea was successfully applied problem when perfect model is accessible.e AlphaGo BID17 does not which does not generalize straightforward fashion general Deep RL setting without perfect model. main obstacle is the requirement counting state-action pairs. Another popular variation is UCB-V introduced BID0. estimates UCB via empirical variance which again involves counting. Therefore requirement counting prevents UCB ideas successful generalization high dimensional setting Deep RL.The generalization exploration ideas multi-armed bandits DeepRL is challenging. Therefore one popular exploration approaches DeepRL is the annealed epsilon greedy approach popularized BID13. However epsilon greedy approach is not very efficient especially DeepRL. does not take account underlying structure environment. Therefore researchers have been looking efficient ways exploration Deep RL setting. example idea parametric noise was explored BID4. Posterior sampling reinforcement learning BID15 Deep RL setting was developed BID16. Uncertainty Bellman Equation proposed BID14 generalizes Bellman equation uncertainty measure. closest UCB type approach was developed BID2. order avoid counting authors estimate UCB based empirical distribution Q function produced Bootstrapped DQN BID16 approach reduces estimating ensemble randomly initialized Q functions. According averaged human normalized learning curve performance improvement was insignificant. Currently is a much better approach estimating empirical distributions Q function.e distributionalRL results distributionalRL are both theoretically sound achieve state art performance Deep RL environments like Atari 2600. However should note DistributionalRL does not use whole distribution mean.Another important characteristic DistributionalRL is that both C51 Quantile Regression DQN QR-DQN are non parametric sense estimated distribution is not assumed belong specific parametric family. Hence is not assumed symmetric even unimodal2. argue case asymmetric distributions variance might become less sensitive estimating UCB. problem seems overseen existing literature. However issue might become important general setting when symmetric assumption is not simply relaxed is a very rare case. empirically show Section4 symmetry is in fact rare Distributional RL.In paper build upon generic UCB idea. generalize asymmetric distributions high-dimensional setting. order extend UCB approach asymmetric distributions introduce truncated variability measure show empirically achieves higher performance variance bandits setting. Extension measure rich visual environments provided Atari 2600 platform is based recent advances DistributionalRL. Recent advancements RL namely DistributionalRL established new theoretically sound principles also achieved state-of-the-art performance challenging high dimensional environments like Atari 2600. by-product DistributionalRL is the empirical PDF Q function which is not directly used except mean computation. UCB hand is a very attractive exploration algorithm multi-armed bandits setting does not which does not generalize straightforward fashion Deep RL.In paper established connection UCB idea DistributionalRL. also pointed asymmetry PDFs estimated DistributionalRL which is not rare exception rather case. introduced truncated variability measure alternative variance empirically showed can be successfully applied multi-armed bandits rich visual environments like Atari 2600. is highly likely DQN-QUCB+might improved schedule tuning. DQN-QUCB+might combined advancements DeepRL e.g Rainbow BID6 yield better results.,1407,1010,397,0.014,1.393,2025/11/05 17:18:59,0.01,1.778,0.1962616822429905,431.764
"Good representations facilitate transfer learning and few-shot learning. Motivated by theories of language and communication that explain why communities with large number of speakers have, on average, simpler languages with more regularity, we cast the representation learning problem in terms of learning to communicate. Our starting  point sees traditional autoencoders as  a single encoder with a fixed decoder partner that must learn to communicate. Generalizing from there, we introduce community-based autoencoders in which multiple encoders and decoders collectively learn representations by being randomly paired up on successive training iterations. Our experiments show that increasing community sizes reduce idiosyncrasies in the learned codes, resulting in more invariant representations with increased reusability and structure. The importance of representation learning lies in two dimensions. First and foremost, representation learning is a crucial building block of a neural model being trained to perform well on a particular task, i.e., representation learning that induces the ""right"" manifold structure can lead to models that generalize better, and even extrapolate. Another property of representation learning, and arguably the most important one, is that it can facilitate transfer of knowledge across different tasks , essential for transfer learning and few-shot learning among others BID0 . With this second point in mind, we can define good representations as the ones that are reusable, induce the abstractions that capture the ""right"" type of invariances and can allow for generalizing very quickly to a new task. Significant efforts have been made to learn representations with these properties; one frequently explored direction involves trying to learn disentangled representations BID12 BID6 BID5 BID17 ), while others focus on general regularization methods BID15 BID18 . In this work, we take a different approach to representation learning, inspired by successful abstraction mechanisms found in nature, to wit human language and communication.Human languages and their properties are greatly affected by the size of their linguistic community BID11 BID19 BID16 BID9 . Small linguistic communities of speakers tend to develop more structurally complex languages, while larger communities give rise to simpler languages (Dryer & Haspelmath, 2013) . Moreover, we even observe structural simplification as the effective number of speakers grows, as in the example of English language BID10 . A similar relation between number of speakers and linguistic complexity can also be observed during linguistic communication. Speakers, aiming at maximizing communication effectiveness, adapt and shape their conceptualizations to account for the needs of their specific partners, a phenomenon often termed in dialogue research as partner specificity BID2 ). As such, speakers form conceptual pacts with their listeners BID1 , and in some extreme cases, these pacts are so ad-hoc and idiosyncratic that overhearers cannot follow the discussion BID13 )! But how are all these linguistic situations related to representation learning? We start by drawing an analogy between language and representations induced by the traditional and extensively used framework of autonencoders (AE). In the traditional AE set-up, there is a fixed pair of a single encoder and a single decoder that are trained to maximize a reconstruction loss. However, encoders and decoders co-adapt to one another, yielding idiosyncratic representations. The encoders spend repre-sentational capacity modeling any kind of information about the data that could allow the decoder to successfully reconstruct the input; as long as the encoder and the decoder agree on a representation protocol, this information need not be abstract or systematic. This has a negative impact on the reusability of the representations, something that afterall is a key objective of representation learning. Evidence of this co-adaption is found in the above-mentioned efforts targeting generalization. The human language analogy of the traditional AE setup would be an extreme version of the conceptual pact experiments from BID13 , where two people never communicate with anybody else: the resulting language would be very hard to understand for any outsider.In this work we test whether removing this co-adaptation between encoders and decoders can yield better generalization, much as dropout removes co-adaptation between activations and thereby yields better generalization in general neural networks. We hypothesize that machines that communicate not with a specific partner but with a multitude of partners, will shape the representations they communicate to be simpler in nature. We introduce a simple framework that we term communitybased autoencoders (CbAEs), in which there exist multiple encoders and decoders, and at every training iteration one of each is randomly sampled to perform a traditional autoencoder (AE) training step. Given that the identity of the decoder is not revealed to the encoder during the encoding of the input, the induced representation should be such that all decoders can use it to successfully reconstruct the input. A similar argument holds for the decoder, which at reconstruction time does not have access to the identity of the encoder. We conjecture that this process will reduce the level of idiosyncrasy, resulting in representations that are invariant to the diverse encoders and decoders.We apply CbAEs to two standard computer vision datasets and probe their representations along two axes; their reusability and their structural properties. We find that in contrast to representations induced within a traditional AE framework 1) the CbAE-induced representations encode abstract information that is more easily extracted and re-used for a different task 2) CbAE representations provide an interface that is easier to learn for new users 3) and the underlying topology of the CbAE representations is more aligned to human perceptual data that are disentangled and structured. We have presented Community-based AutoEncoders, a framework in which multiple encoders and decoders collectively learn representations by being randomly paired up on successive training iterations, encouraging a similar lack of co-adaptation that dropout does at the activation level, at model level. Analogous to the structural simplicity found in languages with many speakers, we find that the latent representations induced in this scheme are easier to use and more structured. This result is philosophically interesting in that it suggests that the community size effects found in human languages are general properties of any representation learning system, opening avenues to potential synergies between representation learning linguistics.The price for obtaining these representations is the increase in computational requirements, which is linear in the community size. Due to the reusability of the resulting representations, this cost may be amortized over a number of applications trained on top of the encoders. Furthermore, the community-based training procedure is highly parallelizable, since only the latents and corresponding backpropagated errors need to be sent between the encoders and decoders.","Good representations facilitate transfer learning few-shot learning. Motivated theories language communication explain why communities large number speakers have,on average simpler languages regularity cast representation learning problem terms learning communicate. starting point sees traditional autoencoders single encoder fixed decoder partner must learn communicate. Generalizing introduce community-based autoencoders which multiple encoders decoders collectively learn representations randomly paired successive training iterations. experiments show increasing community sizes reduce idiosyncrasies learned codes resulting invariant representations increased reusability structure. importance representation learning lies two dimensions. First foremost representation learning is a crucial building block neural model trained perform well particular task.e representation learning induces right manifold structure can lead models generalize better even extrapolate. Another property representation learning arguably important one is thatit can facilitate transfer knowledge across different tasks essential transfer learning few-shot learning among others BID0. second point mind can define good representations ones are reusable induce abstractions capture right type invariances can allow generalizing quickly new task. Significant efforts have been made learn representations properties;one frequently explored direction involves trying learn disentangled representations BID12 BID6 BID5 BID17 others focus general regularization methods BID15 BID18. work take different approach representation learning inspired successful abstraction mechanisms found nature wit human language communication.Human languages properties are greatly affected size linguistic community BID11 BID19 BID16 BID9. Small linguistic communities speakers tend develop structurally complex languages larger communities give rise simpler languages Dryer Haspelmath 2013 Moreover even observe structural simplification effective number speakers grows example English language BID10. similar relation number speakers linguistic complexity can also observed linguistic communication. Speakers aiming maximizing communication effectiveness adapt shape conceptualizations account needs specific partners phenomenon often termed dialogue research partner specificity BID2 speakers form conceptual pacts listeners BID1 extreme cases pacts are so ad-hoc idiosyncratic overhearers cannot follow discussion BID13 how are all these linguistic situations related representation learning? start drawing analogy language representations induced traditional extensively used framework autonencoders AE traditional AE set-up is a fixed pair single encoder single decoder are trained maximize reconstruction loss. However encoders decoders co-adapt one another yielding idiosyncratic representations. encoders spend repre-sentational capacity modeling kind information data could allow decoder successfully reconstruct input;long encoder decoder agree representation protocol information need abstract systematic. has a negative impact reusability representations something afterall is a key objective representation learning. Evidence co-adaption is found above-mentioned efforts targeting generalization. human language analogy traditional AE setup would extreme version conceptual pact experiments BID13 where two people never communicate anybody else:resulting language would hard understand outsider.In work test whether removing co-adaptation encoders decoders can yield better generalization much dropout removes co-adaptation activations thereby yields better generalization general neural networks. hypothesize machines communicate specific partner multitude partners will shape representations communicate simpler nature. introduce simple framework term communitybased autoencoders CbAEs which exist multiple encoders decoders every training iteration one is randomly sampled perform traditional autoencoder AE training step. Given identity decoder is not revealed encoder encoding input induced representation should be such that decoders can use successfully reconstruct input. similar argument holds decoder which at reconstruction time does not have access identity encoder. conjecture process will reduce level idiosyncrasy resulting representations are invariant diverse encoders decoders.We apply CbAEs two standard computer vision datasets probe representations along two axes;reusability structural properties. find contrast representations induced within traditional AE framework1 CbAE-induced representations encode abstract information is more easily extracted re-used different task2 CbAE representations provide interface is easier learn new users3 underlying topology CbAE representations is more aligned human perceptual data are disentangled structured. have presented Community-based AutoEncoders framework which multiple encoders decoders collectively learn representations randomly paired successive training iterations encouraging similar lack co-adaptation dropout does at the activation level model level. Analogous structural simplicity found languages many speakers find latent representations induced scheme are easier use structured. result is philosophically interesting suggests community size effects found human languages are general properties representation learning system opening avenues potential synergies representation learning linguistics.The price obtaining representations is the increase computational requirements which is linear community size. Due reusability resulting representations cost may amortized number applications trained top encoders. Furthermore community-based training procedure is highly parallelizable since latents corresponding backpropagated errors need sent encoders decoders.",1316,878,438,0.014,1.499,2025/11/05 17:18:59,0.01,1.556,0.5264797507788164,422.059
"Humans are experts at high-fidelity imitation -- closely mimicking a demonstration, often in one attempt. Humans use this ability to quickly solve a  task instance, and to bootstrap learning of new tasks. Achieving these abilities in autonomous agents is an open problem. In this paper, we introduce an off-policy RL algorithm (MetaMimic) to narrow this gap. MetaMimic can learn both (i) policies for high-fidelity one-shot imitation of diverse novel skills, and (ii) policies that enable the agent to solve tasks more efficiently than the demonstrators. MetaMimic relies on the principle of storing all experiences in a memory and replaying these to learn massive deep neural network policies by off-policy RL. This paper introduces, to the best of our knowledge, the largest existing neural networks for deep RL and shows that larger networks with normalization are needed to achieve one-shot high-fidelity imitation on a challenging manipulation task.
 The results also show that both types of policy can be learned from vision, in spite of the task rewards being sparse, and without access to demonstrator actions. One-shot imitation is a powerful way to show agents how to solve a task. For instance, one or a few demonstrations are typically enough to teach people how to solve a new manufacturing task. In this paper, we introduce an AI agent that when provided with a novel demonstration is able to (i) mimic the demonstration with high-fidelity, or (ii) forego high-fidelity imitation to solve the intended task more efficiently. Both types of imitation can be useful in different domains.Motor control is a notoriously difficult problem, and we are often deceived by how simple a manipulation task might appear to be. Tying shoe-laces, a behaviour many of us learn by imitation, might appear to be simple. Yet, tying shoe-laces is something most 6 year olds struggle with, long after object recognition, walking, speech, often translation, and sometimes even reading comprehension. This long process of learning that eventually results in our ability to rapidly imitate many behaviours provides inspiration for the work in this paper.We refer to high-fidelity imitation as the act of closely mimicking a demonstration trajectory, even when some actions may be accidental or irrelevant to the task. This is sometimes called over-imitation BID28 . It is known that humans over-imitate more than other primates BID18 and that this may be useful for rapidly acquiring new skills BID24 . For AI agents however, learning to closely imitate even one single demonstration from raw sensory input can be difficult. Many recent works focus on using expensive reinforcement learning (RL) methods to solve this problem BID46 BID27 BID37 BID3 . In contrast, high-fidelity imitation in humans is often cheap: in one-shot we can closely mimic a demonstration. Inspired by this, we introduce a meta-learning approach (MetaMimic - FIG0 ) to learn high-fidelity one-shot imitation policies by off-policy RL. These policies, when deployed, require a single demonstration as input in order to mimic the new skill being demonstrated.AI agents could acquire a large and diverse set of skills by high-fidelity imitation with RL. However, representing many behaviours requires the adoption of a model with very high capacity, such as a very large deep neural network. Unfortunately, showing that RL methods can be used to train massive deep neural networks has been an open question because of the variance inherent to these methods. Indeed, traditional deep RL neural networks tend to be small, to the point that researchers have recently questioned their contribution BID42 . In this paper, we show that it is possible to train massive high-fidelity imitation policy π(ot,gt) with off-policy RL. This policy, represented with a massive deep neural network, enables the robot arm to mimic any demonstration in one-shot. In addition to producing an imitation policy that generalizes well, MetaMimic populates its replay memory with all its rich experiences, including not only the demonstration videos, but also its past observations, actions and rewards. By harnessing these augmented experiences, a task policy π(ot) can be trained to solve difficult sparse-reward control tasks.deep networks by off-policy RL to represent many behaviours. Moreover, we show that bigger networks generalize better. These results therefore provide important evidence that RL is indeed a scalable and viable framework for the design of AI agents. Specifically this paper makes the following contributions 1 :• It introduces the MetaMimic algorithm and shows that it is capable of one-shot high-fidelity imitation from video in a complex manipulation domain.• It shows that MetaMimic can harness video demonstrations and enrich them with actions and rewards so as to learn uncoditional policies capable of solving manipulation tasks more efficiently than teleoperating humans. By retaining and taking advantage of all its experiences, MetaMimic also substantially outperforms the state-of-the-art D4PG RL agent, when D4PG uses only the current task experiences.• The experiments provide ablations showing that larger networks (to the best of our knowledge, the largest networks ever used in deep RL) lead to improved generalization in high-fidelity imitation. The ablations also highlight the important value of instance normalization.• The experiments show that increasing the number of demonstrations during training leads to better generalization on one-shot high-fidelity imitation tasks. In this paper, we introduced MetaMimic, a method to 1) train a high-fidelity one-shot imitation policy, and to 2) efficiently train a task policy. MetaMimic employs the largest neural network trained via RL, and works from vision, without the need of expert actions. The one-shot imitation policy can generalize to unseen trajectories and can mimic them closely. Bootstrapping on imitation experiences, the task policy can quickly outperform the demonstrator, and is competitive with methods that receive privileged information.The framework presented in this paper can be extended in a number of ways. First, it would be exciting to combine this work with existing methods for learning third-person imitation rewards BID45 BID3 . This would bring us a step closer to how humans imitate: By watching other agents act in the environment. Second, it would be exciting to extend MetaMimic to imitate demonstrations of a variety of tasks. This may allow it to generalize to demonstrations of unseen tasks.To improve the ease of application of MetaMimic to robotic tasks, it would be desirable to address the question of how to relax the initialization constraints for high-fidelity imitation; specifically not having to set the initial agent observation to be close to the initial demonstration observation.",Humans are experts high-fidelity imitation closely mimicking demonstration are often one attempt. Humans use ability quickly solve task instance bootstrap learning new tasks. Achieving abilities autonomous agents is an open problem. paper introduce off-policy RL algorithm MetaMimic narrow gap. MetaMimic can learn policies high-fidelity one-shot imitation diverse novel skills ii policies enable agent solve tasks efficiently demonstrators. MetaMimic relies principle storing experiences memory replaying learn massive deep neural network policies off-policyRL. paper introduces best knowledge largest existing neural networks deepRL shows larger networks normalization are needed achieve one-shot high-fidelity imitation challenging manipulation task. results also show types policy can be learned vision spite task rewards sparse without access demonstrator actions. One-shot imitation is a powerful way show agents how to solve task. instance one demonstrations are typically enough teach people how to solve new manufacturing task. paper introduce AI agent when provided novel demonstration is able mimic demonstration high-fidelity ii forego high-fidelity imitation solve intended task efficiently. types imitation can be useful different domains.Motor control is a notoriously difficult problem are often deceived how simple manipulation task might appear be. Tying shoe-laces behaviour many us learn imitation might appear simple. Yet tying shoe-laces is something 6 year olds struggle long object recognition walking speech are often translation sometimes even reading comprehension. long process learning eventually results ability rapidly imitate many behaviours provides inspiration work paper.We refer high-fidelity imitation act closely mimicking demonstration trajectory even when some actions may accidental irrelevant task. is sometimes called over-imitation BID28. is known humans over-imitate primates BID18 may useful rapidly acquiring new skills BID24. AI agents however learning closely imitate even one single demonstration raw sensory input can be difficult. Many recent works focus using expensive reinforcement learning RL methods solve problem BID46 BID27 BID37 BID3. contrast high-fidelity imitation humans is often cheap:one-shot can closely mimic demonstration. Inspired introduce meta-learning approach MetaMimic FIG0 learn high-fidelity one-shot imitation policies off-policyRL. policies when deployed require single demonstration input order mimic new skill demonstrated.AI agents could acquire large diverse set skills high-fidelity imitation RL. However representing many behaviours requires adoption model high capacity large deep neural network. Unfortunately showing RL methods can be used train massive deep neural networks has been an open question variance inherent methods. Indeed traditional deep RL neural networks tend small point researchers have recently questioned contribution BID42. paper show is possible train massive high-fidelity imitation policyπ ot gt off-policyRL. policy represented massive deep neural network enables robot arm mimic demonstration one-shot addition producing imitation policy generalizes well MetaMimic populates replay memory rich experiences including demonstration videos also past observations actions rewards. harnessing augmented experiences task policyπ ot can be trained solve difficult sparse-reward control tasks.deep networks off-policyRL represent many behaviours. Moreover show bigger networks generalize better. results therefore provide important evidence RL is indeed scalable viable framework design AI agents. Specifically paper makes following contributions1:• introduces MetaMimic algorithm shows is capable one-shot high-fidelity imitation video complex manipulation domain.• shows MetaMimic can harness video demonstrations enrich actions rewards learn uncoditional policies capable solving manipulation tasks efficiently teleoperating humans. retaining taking advantage experiences MetaMimic also substantially outperforms state-of-the-art D4PG RL agent when D4PG uses current task experiences.• experiments provide ablations showing larger networks best knowledge largest networks ever used deepRL lead improved generalization high-fidelity imitation. ablations also highlight important value instance normalization.• experiments show increasing number demonstrations training leads better generalization one-shot high-fidelity imitation tasks. paper introduced MetaMimic method 1 train high-fidelity one-shot imitation policy 2 efficiently train task policy. MetaMimic employs largest neural network trained viaRL works vision without need expert actions. one-shot imitation policy can generalize unseen trajectories can mimic closely. Bootstrapping imitation experiences task policy can quickly outperform demonstrator is competitive methods receive privileged information.The framework presented paper can be extended number ways. First would exciting combine work existing methods learning third-person imitation rewards BID45 BID3. would bringus step closer how humans imitate:watching agents act environment. Second would exciting extend MetaMimic imitate demonstrations variety tasks. may allow generalize demonstrations unseen tasks.To improve ease application MetaMimic robotic tasks would desirable address question how to relax initialization constraints high-fidelity imitation;specifically set initial agent observation close initial demonstration observation.,1329,902,427,0.014,1.473,2025/11/05 17:18:59,0.01,1.368,0.4454828660436138,413.513
"Normalization methods are a central building block in the deep learning toolbox. They accelerate and stabilize training, while decreasing the dependence on manually tuned learning rate schedules. When learning from multi-modal distributions, the effectiveness of batch normalization (BN), arguably the most prominent normalization method, is reduced. As a remedy, we propose a more flexible approach: by extending the normalization to more than a single mean and variance, we detect modes of data on-the-fly, jointly normalizing samples that share common features. We demonstrate that our method outperforms BN and other widely used normalization techniques in several experiments, including single and multi-task datasets. A challenge in optimizing deep learning models is the change in input distributions at each layer, complicating the training process. Normalization methods, such as batch normalization (BN, BID15 aim to overcome this issue -often referred to as internal covariate shift BID38 . 1 When applied successfully in practice, BN enables the training of very deep networks, shortens training times by supporting larger learning rates, and reduces sensitivity to parameter initializations. As a result, BN has become an integral element of many state-of-the-art machine learning techniques BID12 BID39 .It can be difficult to standardize the activations in a neural network exposed to heterogeneous or multi-modal data. When training a deep neural network on images that come from a diverse set of visual domains, each with significantly different statistics, BN is not effective at normalizing the activations with a single mean and variance . In this paper we relax the assumption that the entire mini-batch should be normalized with the same mean and variance.Our new normalization method, mode normalization (MN), first assigns samples in a mini-batch to different modes via a gating network, and then normalizes each sample with estimators for its corresponding mode FIG0 ). We further show that MN can be incorporated into other normalization techniques such as group normalization (GN, BID45 ) by learning which filters should be grouped together. The proposed methods can easily be implemented as layers in standard deep learning libraries, and their parameters are learned jointly with the other parameters of the network in an end-to-end manner. We evaluate MN on multiple classification tasks where it achieved a consistent improvement over currently available normalization approaches. Stabilizing the training process of deep neural networks is a challenging problem. Several normalization approaches that aim to tackle this issue have recently emerged, enabling training with higher learning rates, faster model convergence, and allowing for more complex network architectures.Here, we showed that normalization approaches can be extended to allow the network to jointly normalize its features within multiple modes. We further demonstrated that accounting for modality in intermediate feature distributions results in a consistent improvement in classification performance for various deep learning architectures. As part of future work, we plan to explore customized, layer-wise mode numbers in MN, and automatically determining them, e.g. by using concepts from sparse regularization. A ADDITIONAL MULTI-TASK RESULTS TAB5 are additional results for jointly training on MNIST, CIFAR10, SVHN, and Fashion-MNIST. The same network is used as in previous multi-task experiments, for hyperparameters see Section 4. In these additional experiments, we varied the batch size to N = {256, 512}. For larger batch sizes, increasing K to values larger than two increases performance, while for a smaller batch size of N = 128 (c.f. TAB0 , errors incurred by finite estimation prevent this benefit from appearing.",Normalization methods are a central building block deep learning toolbox. accelerate stabilize training decreasing dependence manually tuned learning rate schedules. When learning multi-modal distributions effectiveness batch normalization BN arguably prominent normalization method is reduced. remedy propose flexible approach:extending normalization single mean variance detect modes data on-the-fly jointly normalizing samples share common features. demonstrate method outperformsBN widely used normalization techniques several experiments including single multi-task datasets. challenge optimizing deep learning models is the change input distributions layer complicating training process. Normalization methods batch normalization BN BID15 aim overcome issue -often referred internal covariate shift BID38. 1 When applied successfully practice BN enables training deep networks shortens training times supporting larger learning rates reduces sensitivity parameter initializations. result BN has become integral element many state-of-the-art machine learning techniques BID12 BID39.It can be difficult standardize activations neural network exposed heterogeneous multi-modal data. When training deep neural network images come diverse set visual domains significantly different statistics BN is not effective normalizing activations single mean variance. paper relax assumption entire mini-batch should be normalized mean variance.Our new normalization method mode normalization MN first assigns samples mini-batch different modes via gating network normalizes sample estimators corresponding mode FIG0 show MN can be incorporated normalization techniques group normalization GN BID45 learning which filters should be grouped together. proposed methods can easily implemented layers standard deep learning libraries parameters are learned jointly parameters network end-to-end manner. evaluateMN multiple classification tasks where it achieved consistent improvement currently available normalization approaches. Stabilizing training process deep neural networks is a challenging problem. Several normalization approaches aim tackle issue have recently emerged enabling training higher learning rates faster model convergence allowing complex network architectures.Here showed normalization approaches can be extended allow network jointly normalize features within multiple modes. demonstrated accounting modality intermediate feature distributions results consistent improvement classification performance various deep learning architectures. part future work plan explore customized layer-wise mode numbers MN automatically determining e.g using concepts sparse regularization. ADDITIONAL MULTI-TASK RESULTS TAB5 are additional results jointly training MNIST CIFAR10 SVHN Fashion-MNIST network is used previous multi-task experiments hyperparameters see Section4. additional experiments varied batch size N 256 512 larger batch sizes increasingK values larger two increases performance smaller batch size N 128 c.f TAB0 errors incurred finite estimation prevent benefit appearing.,695,464,231,0.007,1.498,2025/11/05 17:18:59,0.0,1.476,0.5233644859813082,266.8
"Multilingual machine translation, which translates multiple languages with a single model, has attracted much attention due to its efficiency of offline training and online serving. However, traditional multilingual translation usually yields inferior accuracy compared with the counterpart using individual models for each language pair, due to language diversity and model capacity limitations. In this paper, we propose a distillation-based approach to boost the accuracy of multilingual machine translation. Specifically, individual models are first trained and regarded as teachers, and then the multilingual model is trained to fit the training data and match the outputs of individual models simultaneously through knowledge distillation. Experiments on IWSLT, WMT and Ted talk translation datasets demonstrate the effectiveness of our method. Particularly, we show that one model is enough to handle multiple languages (up to 44 languages in our experiment), with comparable or even better accuracy than individual models. Neural Machine Translation (NMT) has witnessed rapid development in recent years BID1 BID26 BID36 BID8 BID34 BID32 BID31 BID12 , including advanced model structures BID8 BID34 and human parity achievements . While conventional NMT can well handle single pair translation, training a separate model for each language pair is resource consuming, considering there are thousands of languages in the world 1 . Therefore, multilingual NMT BID17 BID5 BID13 ) is developed which handles multiple language pairs in one model, greatly reducing the offline training and online serving cost.Previous works on multilingual NMT mainly focus on model architecture design through parameter sharing, e.g., sharing encoder, decoder or attention module BID5 or sharing the entire models BID17 BID13 . They achieve comparable accuracy with individual models (each language pair with a separate model) when the languages are similar to each other and the number of language pairs is small (e.g., two or three). However, when handling more language pairs (dozens or even hundreds), the translation accuracy of multilingual model is usually inferior to individual models, due to language diversity.It is challenging to train a multilingual translation model supporting dozens of language pairs while achieving comparable accuracy as individual models. Observing that individual models are usually of higher accuracy than the multilingual model in conventional model training, we propose to transfer the knowledge from individual models to the multilingual model with knowledge distillation, which has been studied for model compression and knowledge transfer and well matches our setting of multilingual translation. It usually starts by training a big/deep teacher model (or ensemble of multiple models), and then train a small/shallow student model to mimic the behaviors of the teacher model, such as its hidden representation BID39 BID29 , its output probabilities BID16 BID6 or directly training on the sentences generated by the teacher model in neural machine translation BID19 ). The student model can (nearly) match the accuracy of the cumbersome teacher model (or the ensemble of multiple models) with knowledge distillation.In this paper, we propose a new method based on knowledge distillation for multilingual translation to eliminate the accuracy gap between the multilingual model and individual models. In our method, multiple individual models serve as teachers, each handling a separate language pair, while the student handles all the language pairs in a single model, which is different from the conventional knowledge distillation where the teacher and student models usually handle the same task. We first train the individual models for each translation pair and then we train the multilingual model by matching with the outputs of all the individual models and the ground-truth translation simultaneously. After some iterations of training, the multilingual model may get higher translation accuracy than the individual models on some language pairs. Then we remove the distillation loss and keep training the multilingual model on these languages pairs with the original log-likelihood loss of the ground-truth translation.We conduct experiments on three translation datasets: IWSLT with 12 language pairs, WMT with 6 language pairs and Ted talk with 44 language pairs. Our proposed method boosts the translation accuracy of the baseline multilingual model and achieve similar (or even better) accuracy as individual models for most language pairs. Specifically, the multilingual model with only 1/44 parameters can match or surpass the accuracy of individual models on the Ted talk datasets. Selective Distillation Considering that distillation from a bad teacher model is likely to hurt the student model and thus result in inferior accuracy, we selectively use distillation in the training process, as shown in Line 15-19 in Algorithm 1. When the accuracy of multilingual model surpasses the individual model for the accuracy threshold τ on a certain language pair, we remove the distillation loss and just train the model with original negative log-likelihood loss for this pair. Note that in one iteration, one language may not uses the distillation loss; it is very likely in later iterations that this language will be distilled again since the multilingual model may become worse than the teacher model for this language. Therefore, we call this mechanism as selective distillation. We also verify the effectiveness of the selective distillation in experiment part (Section 4.3).Top-K Distillation It is burdensome to load all the teacher models in the GPU memory for distillation considering there are dozens or even hundreds of language pairs in the multilingual setting. Alternatively , we first generate the output probability distribution of each teacher model for the sentence pairs offline, and then just load the top-K probabilities of the distribution into memory and normalize them so that they sum to 1 for distillation. This can reduce the memory cost again from the scale of |V | (the vocabulary size) to K. We also study in Section 4.3 that top-K distribution can result in comparable or better distillation accuracy than the full distribution. In this work, we have proposed a distillation-based approach to boost the accuracy of multilingual NMT, which is usually of lower accuracy than the individual models in previous works. Experiments on three translation datasets with up to 44 languages demonstrate the multilingual model based on our proposed method can nearly match or even outperform the individual models, with just 1/N model parameters (N is up to 44 in our experiments).In the future, we will conduct more deep analyses about how distillation helps the multilingual model training. We will apply our method to larger datasets and more languages pairs (hundreds or even thousands), to study the upper limit of our proposed method.",Multilingual machine translation which translates multiple languages single model has attracted much attention due efficiency offline training online serving. However traditional multilingual translation usually yields inferior accuracy compared counterpart using individual models language pair due language diversity model capacity limitations. paper propose distillation-based approach boost accuracy multilingual machine translation. Specifically individual models are first trained regarded teachers multilingual model is trained fit training data match outputs individual models simultaneously knowledge distillation. Experiments IWSLT WMT Ted talk translation datasets demonstrate effectiveness method. Particularly show one model is enough handle multiple languages 44 languages experiment comparable even better accuracy individual models. Neural Machine Translation NMT has witnessed rapid development recent years BID1 BID26 BID36 BID8 BID34 BID32 BID31 BID12 including advanced model structures BID8 BID34 human parity achievements. conventional NMT can well handle single pair translation training separate model language pair is resource consuming considering are thousands languages world1. Therefore multilingual NMT BID17 BID5 BID13 is developed which handles multiple language pairs one model greatly reducing offline training online serving cost.Previous works multilingual NMT mainly focus model architecture design parameter sharing e.g sharing encoder decoder attention module BID5 sharing entire models BID17 BID13. achieve comparable accuracy individual models language pair separate model when the languages are similar number language pairs is small e.g two three However when handling language pairs dozens even hundreds translation accuracy multilingual model is usually inferior individual models due language diversity.It is challenging train multilingual translation model supporting dozens language pairs achieving comparable accuracy individual models. Observing individual models are usually higher accuracy multilingual model conventional model training propose transfer knowledge individual models multilingual model knowledge distillation which has been studied model compression knowledge transfer well matches setting multilingual translation. usually starts training big/deep teacher model ensemble multiple models train small/shallow student model mimic behaviors teacher model hidden representation BID39 BID29 output probabilities BID16 BID6 directly training sentences generated teacher model neural machine translation BID19 student model can(can nearly match accuracy cumbersome teacher model ensemble multiple models knowledge distillation.In paper propose new method based knowledge distillation multilingual translation eliminate accuracy gap multilingual model individual models. method multiple individual models serve teachers when handling separate language pair student handles language pairs single model which is different conventional knowledge distillation where the teacher student models usually handle task. first train individual models translation pair train multilingual model matching outputs individual models ground-truth translation simultaneously. iterations training multilingual model may get higher translation accuracy individual models language pairs. remove distillation loss keep training multilingual model languages pairs original log-likelihood loss ground-truth translation.We conduct experiments three translation datasets:IWSLT 12 language pairs WMT 6 language pairs Ted talk 44 language pairs. proposed method boosts translation accuracy baseline multilingual model achieve similar even better accuracy individual models language pairs. Specifically multilingual model 1/44 parameters can match surpass accuracy individual models Ted talk datasets. Selective Distillation Considering distillation bad teacher model is likely hurt student model thus result inferior accuracy selectively use distillation training process shown Line 15-19 Algorithm1. When the accuracy multilingual model surpasses individual model accuracy thresholdτ certain language pair remove distillation loss train model original negative log-likelihood loss pair. Note one iteration one language may uses distillation loss;is very likely later iterations language will be distilled since multilingual model may become worse teacher model language. Therefore call mechanism selective distillation. also verify effectiveness selective distillation experiment part Section 4.3.Top-K Distillation is burdensome load teacher models GPU memory distillation considering are dozens even hundreds language pairs multilingual setting. Alternatively first generate output probability distribution teacher model sentence pairs offline load top-K probabilities distribution memory normalize sum 1 distillation. can reduce memory cost scale |V vocabulary size K. also study Section 4.3 top-K distribution can result comparable better distillation accuracy full distribution. work have proposed distillation-based approach boost accuracy multilingual NMT which is usually lower accuracy individual models previous works. Experiments three translation datasets 44 languages demonstrate multilingual model based proposed method can(can nearly match even outperform individual models 1/N model parameters N isupto44 experiments.In future will conduct deep analyses how distillation helps multilingual model training. will apply method larger datasets languages pairs hundreds even thousands study upper limit proposed method.,1261,833,428,0.014,1.514,2025/11/05 17:18:59,0.01,1.316,0.5732087227414329,418.806
"What makes humans so good at solving seemingly complex video games?   Unlike computers, humans bring in a great deal of prior knowledge about the world, enabling efficient decision making. This paper investigates the role of human priors for solving video games. Given a sample game, we conduct a series of ablation studies to quantify the importance of various priors. We do this by modifying the video game environment to systematically mask different types of visual information that could be used by humans as priors. We find that removal of some prior knowledge causes a drastic degradation in the speed with which human players solve the game, e.g. from 2 minutes to over 20 minutes. Furthermore, our results indicate that general priors, such as the importance of objects and visual consistency, are critical for efficient game-play. While deep Reinforcement Learning (RL) methods have shown impressive performance on a variety of video games BID17 , they remain woefully inefficient compared to human players, taking millions of action inputs to solve even the simplest Atari games. Much research is currently focused on improving sample efficiency of RL algorithms BID19 BID9 . However, there is an orthogonal issue that is often overlooked: RL agents attack each problem tabula rasa, whereas humans come in with a wealth of prior knowledge about the world, from physics to semantics to affordances.Consider the following motivating example: you are tasked with playing an unfamiliar computer game shown in FIG0 (a) . No manual or instructions are provided; you don't even know which game sprite is controlled by you. Indeed, the only feedback you are ever given is ""terminal"", i.e. once you successfully finish the game. Would you be able to successfully finish this game? How long would it take? We recruited forty human subjects to play this game and found that subjects finished it quite easily, taking just under 1 minute of game-play or 3000 action inputs. This is not overly surprising as one could easily guess that the game's goal is to move the robot sprite towards the princess by stepping on the brick-like objects and using ladders to reach the higher platforms while avoiding the angry pink and the fire objects. Now consider a second scenario in which this same simple game is re-rendered with new textures, getting rid of semantic and affordance BID8 cues, as shown in FIG0 (b) . How would human performance change? We recruited another forty subjects to play this game and found that, on average, it took the players more than twice the time (2 minutes) and action inputs ( 6500) to complete the game. The second game is clearly much harder for humans, likely because it is now more difficult to guess the game structure and goal, as well as to spot obstacles.For comparison, we can also examine how modern RL algorithms perform on these games. This is not so simple, as most standard RL approaches expect very dense rewards (e.g. continuously updated game-score BID17 ), whereas we provide only a terminal reward, to mimic how most humans play video games. In such sparse reward scenarios, standard methods like A3C BID18 are too sample-inefficient and were too slow to finish the games. Hence, we used a curiosity-based RL algorithm specifically tailored to sparse-reward settings BID20 , which was able to solve both games. Unlike humans, RL did not show much difference between the The same game modified by re-rendering the textures. Despite the two games being structurally the same, human players took twice as long to finish the second game as the first one. In comparison, the performance of an RL agent was approximately the same for the two games. two games, taking about 4 million action inputs to solve each one. This should not be surprising: since RL did not have any prior knowledge about the world, both these games carried roughly the same amount of information from the perspective of the agent.This simple motivating experiment highlights the importance of prior knowledge that humans draw upon to quickly solve tasks given to them BID13 BID24 . Developmental psychologists have begun documenting the prior knowledge that children draw upon in learning about the world BID23 BID4 . However, these studies have not explicitly quantified the relative importance of the various priors for problem-solving.In this work, we systematically quantify the importance of different types of priors humans bring to bear while solving one particular kind of problem -video games. We chose video games as the task for our investigation because it is relatively easy to methodically change the game to include or mask different kinds of knowledge and run large-scale human studies. Furthermore, video games, such as ATARI, are a popular choice in the reinforcement learning community.The paper consists of a series of ablation studies on a specially-designed game environment, systematically masking out various types of visual information that could be used by humans as priors. The full game (unlike the motivating example above) was designed to be sufficiently complex and difficult for humans to easily measure changes in performance between different testing conditions. We find that removal of some prior knowledge causes a drastic degradation in the performance of human players from 1 minute to over 20 minutes. Another key finding of our investigation is that while specific knowledge, such as ""ladders are to be climbed"", ""keys are used to open doors"", ""jumping on spikes is dangerous"", is important for humans to quickly solve games, more general priors about the importance of objects and visual consistency are even more critical. While there is no doubt that the performance of deep RL algorithms is impressive, there is much to be learned from human cognition if our goal is to enable RL agents to solve sparse reward tasks with human-like efficiency. Humans have the amazing ability to use their past knowledge (i.e., priors) to solve new tasks quickly. Success in such scenarios critically depends on the agent's ability to explore its environment and then promptly learn from its successes BID6 BID5 . In this vein, our results demonstrate the importance of prior knowledge in helping humans explore efficiently in these sparse reward environments BID11 BID7 .However , being equipped with strong prior knowledge can sometimes lead to constrained exploration that might not be optimal in all environments BID14 BID3 . For instance , consider the game shown in FIG6 consisting of a robot and a princess object. The game environment also includes rewards in hidden locations (shown as dashed yellow boxes only for illustration). When tasked to play this game, human participants (n=30) immediately assume that princess is the goal and do not explore the free space containing hidden rewards. They directly reach the princess and thereby terminate the game with sub-optimal rewards. In contrast, a random agent (30 seeds) ends up obtaining almost four times more reward than human players as shown in FIG6 . Thus, while incorporating prior knowledge in RL agents has many potential benefits, future work should also consider challenges regarding under-constrained exploration in certain kinds of settings.While our paper primarily investigated object priors (and physics priors to some extent), humans also possess rich prior knowledge about the world in the form of intuitive psychology and also bring in various priors about general video game playing such as that moving up and to the right in games is generally correlated with progress, games have goals, etc. Studying the importance of such priors will be an interesting future direction of research.Building RL algorithms that require fewer interactions to reach the goal (i.e., sample efficient algorithms) is an active area of research, and further progress is inevitable. In addition to developing better optimization methods, we believe that instead of always initializing learning from scratch, either incorporating prior knowledge directly or constructing mechanisms for condensing experience into reusable knowledge (i.e., learning priors through continual learning) might be critical for building RL agents with human-like efficiency. Our work takes first steps toward quantifying the importance of various priors that humans employ in solving video games and in understanding how prior knowledge makes humans good at such complex tasks. We believe that our results will inspire researchers to think about different mechanisms of incorporating prior knowledge in the design of RL agents. We also hope that our experimental platform of video games, available in open-source, will fuel more detailed studies investigating human priors and a benchmark for quantifying the efficacy of different mechanisms of incorporating prior knowledge into RL agents.",What makes humans good solving seemingly complex video games? Unlike computers humans bring great deal prior knowledge world enabling efficient decision making. paper investigates role human priors solving video games. Given sample game conduct series ablation studies quantify importance various priors. do this by modifying video game environment systematically mask different types visual information could used humans priors. find removal prior knowledge causes drastic degradation speed which human players solve game e.g 2 minutes 20 minutes. Furthermore results indicate general priors importance objects visual consistency are critical efficient game-play deep Reinforcement Learning RL methods have shown impressive performance variety video games BID17 remain woefully inefficient compared human players taking millions action inputs solve even simplest Atari games. Much research is currently focused improving sample efficiency RL algorithms BID19 BID9. However is an orthogonal issue is often overlooked:RL agents attack problem tabula rasa whereas humans come wealth prior knowledge world physics semantics affordances.Consider following motivating example:are tasked playing unfamiliar computer game shown FIG0 manual instructions are provided;even know which game sprite is controlled you. Indeed feedback are ever given is terminal.e successfully finish game. Would able successfully finish game? How long would take? recruited forty human subjects play game found subjects finished quite easily taking 1 minute game-play 3000 action inputs. is not overly surprising one could easily guess game's goal is to move robot sprite towards princess stepping brick-like objects using ladders reach higher platforms avoiding angry pink fire objects. consider second scenario which this same simple game is re-rendered new textures getting rid semantic affordance BID8 cues shown FIG0 b would human performance change? recruited another forty subjects play game found average took players twice time 2 minutes action inputs 6500 complete game. second game is clearly much harder humans likely is now difficult guess game structure goal well spot obstacles.For comparison can also examine how modern RL algorithms perform games. is not so simple standard RL approaches expect dense rewards e.g continuously updated game-score BID17 whereas provide terminal reward mimic how most humans play video games. sparse reward scenarios standard methods like A3C BID18 are too sample-inefficient were too slow finish games. Hence used curiosity-based RL algorithm specifically tailored sparse-reward settings BID20 which was able solve games. Unlike humans RL did not show much difference game modified re-rendering textures. Despite two games structurally human players took twice long finish second game first one. comparison performance RL agent was approximately two games. two games taking 4 million action inputs solve one. should not be surprising:sinceRL did not have any prior knowledge world games carried roughly amount information perspective agent.This simple motivating experiment highlights importance prior knowledge humans draw upon quickly solve tasks given BID13 BID24. Developmental psychologists have begun documenting prior knowledge children draw upon learning world BID23 BID4. However studies have not explicitly quantified relative importance various priors problem-solving.In work systematically quantify importance different types priors humans bring bear solving one particular kind problem -video games. chose video games task investigation is relatively easy methodically change game include mask different kinds knowledge run large-scale human studies. Furthermore video games ATARI are a popular choice reinforcement learning community.The paper consists series ablation studies specially-designed game environment systematically masking various types visual information could used humans priors. full game unlike motivating example was designed sufficiently complex difficult humans easily measure changes performance different testing conditions. find removal prior knowledge causes drastic degradation performance human players 1 minute 20 minutes. Another key finding investigation is that while specific knowledge ladders are to be climbed keys are used open doors jumping spikes is dangerous is important humans quickly solve games general priors importance objects visual consistency are even critical. is no doubt performance deep RL algorithms is impressive is much learned human cognition if our goal is to enable RL agents solve sparse reward tasks human-like efficiency. Humans have the amazing ability use past knowledge.e priors solve new tasks quickly. Success scenarios critically depends agent's ability explore environment promptly learn successes BID6 BID5. vein results demonstrate importance prior knowledge helping humans explore efficiently sparse reward environments BID11 BID7.However equipped strong prior knowledge can sometimes lead constrained exploration might optimal environments BID14 BID3. instance consider game shown FIG6 consisting robot princess object. game environment also includes rewards hidden locations shown dashed yellow boxes illustration When tasked play game human participants n=30 immediately assume princess is the goal do not explore free space containing hidden rewards. directly reach princess thereby terminate game sub-optimal rewards. contrast random agent 30 seeds ends obtaining almost four times reward human players shown FIG6. Thus incorporating prior knowledge RL agents has many potential benefits future work should also consider challenges regarding under-constrained exploration certain kinds settings.While paper primarily investigated object priors physics priors extent humans also possess rich prior knowledge world form intuitive psychology also bring various priors general video game playing moving right games is generally correlated progress games have goals etc. Studying importance priors will be an interesting future direction research.Building RL algorithms require fewer interactions reach goal.e sample efficient algorithms is an active area research progress is inevitable. addition developing better optimization methods believe instead always initializing learning scratch either incorporating prior knowledge directly constructing mechanisms condensing experience reusable knowledge.e learning priors continual learning might critical building RL agents human-like efficiency. work takes first steps toward quantifying importance various priors humans employ solving video games understanding how prior knowledge makes humans good complex tasks. believe results will inspire researchers think different mechanisms incorporating prior knowledge design RL agents. also hope experimental platform video games available open-source will fuel detailed studies investigating human priors benchmark quantifying efficacy different mechanisms incorporating prior knowledge RL agents.,1658,1108,550,0.021,1.496,2025/11/05 17:18:59,0.01,1.556,0.5171339563862927,546.441
"Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples include grid search, uniform random search, low discrepancy sequences, and other sampling distributions.
 In particular, we propose the use of $k$-determinantal point processes in  hyperparameter optimization via random search. Compared to conventional uniform random search where hyperparameter settings are sampled independently, a $k$-DPP promotes diversity.   We describe an approach that transforms hyperparameter search spaces for efficient use with a $k$-DPP. In addition, we introduce a novel Metropolis-Hastings algorithm which can sample from $k$-DPPs defined over spaces with a mixture of discrete and continuous dimensions. Our experiments show significant benefits over uniform random search  in realistic scenarios with a limited budget for training supervised learners, whether in serial or parallel. Hyperparameter values-regularization strength, model family choices like depth of a neural network or which nonlinear functions to use, procedural elements like dropout rates, stochastic gradient descent step sizes, and data preprocessing choices-can make the difference between a successful application of machine learning and a wasted effort. To search among many hyperparameter values requires repeated execution of often-expensive learning algorithms, creating a major obstacle for practitioners and researchers alike.In general, on request/iteration k, a hyperparameter searcher suggests a hyperparameter configuration x k , a worker trains a model using x k , and returns a validation loss of y k computed on a hold out set. In this work we say a hyperparameter searcher is open loop if x k depends only on {x i } k−1 i=1 ; examples include choosing x k uniformly at random BID4 , or x k coming from a low-discrepancy sequence (c.f., BID12 ). We say a searcher is closed loop if x k depends on both the past configurations and validation losses {(x i , y i )} k−1 i=1 ; examples include Bayesian optimization BID19 and recent reinforcement learning methods BID25 . Note that open loop methods can draw an infinite sequence of configurations before training a single model, whereas closed loop methods rely on validation loss feedback in order to make suggestions.While sophisticated closed loop selection methods have been shown to empirically identify good hyperparameter configurations faster (i.e., with fewer iterations) than open loop methods like random search, two trends have rekindled interest in embarrassingly parallel open loop methods: 1) modern deep learning models can take days or weeks to train with no signs of efficiency breakthroughs, and 2) the rise of cloud resources available to anyone that charge not by the number of machines, but by the number of CPU-hours used so that 10 machines for 100 hours costs the same as 1000 machines for 1 hour. This paper explores the landscape of open loop methods, identifying tradeoffs that are rarely considered, if at all acknowledged. While random search is arguably the most popular open loop method and chooses each x k independently of {x i } k−1 i=1 , it is by no means the only choice. In many ways uniform random search is the least interesting of the methods we will discuss because we will advocate for methods where x k depends on {x i } k−1 i=1 to promote diversity. In particular, we will focus on drawing {x i } k i=1 from a k-determinantal point process (DPP) BID16 . DPPs support real, integer, and categorical dimensions-any of which may have a tree structure-and have computationally efficient methods of drawing samples.Experimentally, we explore the use of our diversity-promoting open-loop hyperparameter optimization method based on k-DPP random search. We find that it significantly outperforms uniform random search in cases where the hyperparameter values have a large effect on performance.Open source implementations of both our hyperparameter optimization algorithm (as an extension to the hyperopt package BID5 ) and the MCMC algorithm introduced in Algorithm 2 will be released upon publication. We have explored open loop hyperparameter optimization built on sampling from k-DPPs. We described how to construct k-DPPs over hyperparameter search spaces, and showed that sampling from these retains the attractive parallelization capabilities of random search. Our experiments demonstrate that, under a limited computation budget, on a number of realistic hyperparameter optimization problems, these approaches perform better than sampling uniformly at random. As we increase the difficulty of our hyperparameter optimization problem (i.e., as values which lead to good model Average best-found model accuracy by iteration when training a convolutional neural network on the ""Stable"" search space (defined in Section 5.2), averaged across 50 trials of hyperparameter optimization, with k = 20. Discretizing the space reduces the accuracy found for both uniform sampling and k-DPP-RBF, but in both cases k-DPP-RBF finds better optima than uniform sampling.evaluations become more scarce) the improvement over sampling uniformly at random increases. An open-source implementation of our method is available.",Driven need parallelizable hyperparameter optimization methods paper studies \emph open loop search methods:sequences are predetermined can be generated single configuration is evaluated. Examples include grid search uniform random search low discrepancy sequences sampling distributions. particular propose use $k $-determinantal point processes hyperparameter optimization via random search. Compared conventional uniform random search where where the hyperparameter settings are sampled independently $k $-DPP promotes diversity. describe approach transforms hyperparameter search spaces efficient use $k $-DPP addition introduce novel Metropolis-Hastings algorithm which can sample $k $-DPPs defined spaces mixture discrete continuous dimensions. experiments show significant benefits uniform random search realistic scenarios limited budget training supervised learners whether serial parallel. Hyperparameter values-regularization strength model family choices like depth neural network which nonlinear functions use procedural elements like dropout rates stochastic gradient descent step sizes data preprocessing choices-can make difference successful application machine learning wasted effort. search among many hyperparameter values requires repeated execution often-expensive learning algorithms creating major obstacle practitioners researchers alike.In general request/iterationk hyperparameter searcher suggests hyperparameter configurationxk worker trains model usingxk returns validation loss k computed hold set. work say hyperparameter searcher is open loop if x k depends x k−1 i=1 examples include choosing x k uniformly random BID4 x k coming low-discrepancy sequence c.f BID12 say searcher is closed loop if x k depends past configurations validation losses x k−1 i=1 examples include Bayesian optimization BID19 recent reinforcement learning methods BID25. Note open loop methods can draw infinite sequence configurations training single model whereas closed loop methods rely validation loss feedback order make suggestions.While sophisticated closed loop selection methods have been shown empirically identify good hyperparameter configurations faster.e fewer iterations open loop methods like random search two trends have rekindled interest embarrassingly parallel open loop methods:1 modern deep learning models can take days weeks train signs efficiency breakthroughs 2 rise cloud resources available anyone charge number machines number CPU-hours used 10 machines 100 hours costs 1000 machines 1 hour. paper explores landscape open loop methods identifying tradeoffs are rarely considered if at all acknowledged. random search is arguably popular open loop method chooses x k independently x k−1 i=1 isby means choice. many ways uniform random search is the least interesting methods will discuss will advocate methods where x k depends x k−1 i=1 promote diversity. particular will focus drawing x k i=1 k-determinantal point process DPP BID16. DPPs support real integer categorical dimensions-any may have a tree structure-and have computationally efficient methods drawing samples.Experimentally explore use diversity-promoting open-loop hyperparameter optimization method based k-DPP random search. find significantly outperforms uniform random search cases where where the hyperparameter values have a large effect performance.Open source implementations hyperparameter optimization algorithm extension hyperopt package BID5 MCMC algorithm introduced Algorithm2 will be released upon publication. have explored open loop hyperparameter optimization built sampling k-DPPs described how to construct k-DPPs hyperparameter search spaces showed sampling retains attractive parallelization capabilities random search. experiments demonstrate limited computation budget number realistic hyperparameter optimization problems approaches perform better sampling uniformly random. increase difficulty hyperparameter optimization problem.e values which lead good model Average best-found model accuracy iteration when training convolutional neural network Stable search space defined Section 5.2 averaged across 50 trials hyperparameter optimization k 20. Discretizing space reduces accuracy found uniform sampling k-DPP-RBF cases k-DPP-RBF finds better optima uniform sampling.evaluations become scarce improvement sampling uniformly random increases. open-source implementation method is available.,1046,738,308,0.009,1.417,2025/11/05 17:18:59,0.0,1.364,0.2710280373831775,302.23
"In inductive transfer learning, fine-tuning pre-trained convolutional networks substantially outperforms training from scratch.
 When using fine-tuning, the underlying assumption is that the pre-trained model extracts generic features, which are at least partially relevant for solving the target task, but would be difficult to extract from the limited amount of data available on the target task.
 However, besides the initialization with the pre-trained model and the early stopping, there is no mechanism in fine-tuning for retaining the features learned on the source task.
 In this paper, we investigate several regularization schemes that explicitly promote the similarity of the final solution with the initial model.
 We eventually recommend a simple $L^2$ penalty using the pre-trained model as a reference, and we show that this approach behaves much better than the standard scheme using weight decay on a partially frozen network. It is now well known that modern convolutional neural networks (e.g. BID14 BID25 BID11 BID28 ) can achieve remarkable performance on large-scale image databases, e.g. ImageNet BID3 ) and Places 365 BID37 ), but it is really dissatisfying to see the vast amounts of data, computing time and power consumption that are necessary to train deep networks. Fortunately, such convolutional networks, once trained on a large database, can be refined to solve related but different visual tasks by means of transfer learning, using fine-tuning BID34 BID25 .Some form of knowledge is believed to be extracted by learning from the large-scale database of the source task and this knowledge is then transferred to the target task by initializing the network with the pre-trained parameters. However , after fine-tuning, some of the parameters may be quite different from their initial values, resulting in possible losses of general knowledge that may be relevant for the targeted problem. In particular , during fine-tuning, L 2 regularization drives the parameters towards the origin and thereby encourages large deviations between the parameters and their initial values.In order to help preserve the acquired knowledge embedded in the initial network, we consider using other parameter regularization methods during fine-tuning. We argue that the standard L 2 regularization, which drives the parameters towards the origin, is not adequate in the framework of transfer learning where the initial values provide a more sensible reference point than the origin. This simple modification keeps the original control of overfitting, by constraining the effective search space around the initial solution, while encouraging committing to the acquired knowledge. We show that it has noticeable effects in inductive transfer learning scenarios.This paper aims at improving transfer learning by requiring less labeled training data. A form of transfer learning is thus considered, where some pieces of knowledge, acquired when solving a previous learning problem, have to be conveyed to another learning problem. Under this setting, we explore several parameter regularization methods that can explicitly retain the knowledge acquired on the source problem. We investigate variants of L 2 penalties using the pre-trained model as reference, which we name L 2 -SP because the pre-trained parameters represent the starting point (-SP) of the fine-tuning process. In addition, we evaluate other regularizers based on the Lasso and Group-Lasso penalties, which can freeze some individual parameters or groups of parameters to the pre-trained parameters. Fisher information is also taken into account when we test L 2 -SP and Group-Lasso-SP approaches.Our experiments indicate that all tested parameter regularization methods using the pre-trained parameters as a reference get an edge over the standard L 2 weight decay approach. We also analyze the effect of L 2 -SP with theoretical arguments and experimental evidence to recommend using L 2 -SP for transfer learning tasks. Among all -SP methods, L 2 -SP and L 2 -SP-Fisher always reach a better accuracy on the target task. We expected L 2 -SP-Fisher to outperform L 2 -SP, since Fisher information helps in continual learning, but there is no significant difference between the two options. Since L 2 -SP is simpler than L 2 -SP-Fisher, we recommend the former, and we focus on the analysis of L 2 -SP, although most of the analysis and the discussion would also apply to L 2 -SP-Fisher. We proposed simple regularization techniques for inductive transfer learning, to encode an explicit bias towards the solution learned on the source task. Most of the regularizers evaluated here have been already used for other purposes, but we demonstrate their relevance for inductive transfer learning with deep convolutional networks.We show that a simple L 2 penalty using the starting point as a reference, L 2 -SP, is useful, even if early stopping is used. This penalty is much more effective than the standard L 2 penalty that is commonly used in fine-tuning. It is also more effective and simpler to implement than the strategy consisting in freezing the first layers of a network. We provide theoretical hints and strong experimental evidence showing that L 2 -SP retains the memory of the features learned on the source database.Besides, we tested the effect of more elaborate penalties, based on L 1 or Group-L 1 norms, or based on Fisher information. None of the L 1 or Group-L 1 options seem to be valuable in the context of inductive transfer learning that we considered here, and using the Fisher information with L 2 -SP does not improve accuracy on the target task. Different approaches, which implement an implicit bias at the functional level, alike BID16 ), remain to be tested: being based on a different principle, their value should be assessed in the framework of inductive transfer learning.",inductive transfer learning fine-tuning pre-trained convolutional networks substantially outperforms training scratch. When using fine-tuning underlying assumption is that the pre-trained model extracts generic features which are at least partially relevant solving target task would difficult extract limited amount data available target task. However besides initialization pre-trained model early stopping is no mechanism fine-tuning retaining features learned source task. paper investigate several regularization schemes can explicitly promote similarity final solution initial model. eventually recommend simple $L^2 penalty using pre-trained model reference show approach behaves much better standard scheme using weight decay partially frozen network. is now well known modern convolutional neural networks e.g BID14 BID25 BID11 BID28 can achieve remarkable performance large-scale image databases e.g ImageNet BID3 Places 365 BID37 is really dissatisfying see vast amounts data computing time power consumption are necessary train deep networks. Fortunately convolutional networks trained large database can be refined solve related different visual tasks means transfer learning using fine-tuning BID34 BID25.Some form knowledge is believed extracted learning large-scale database source task knowledge is then transferred target task initializing network pre-trained parameters. However fine-tuning parameters may quite different initial values resulting possible losses general knowledge may relevant targeted problem. particular fine-tuning L 2 regularization drives parameters towards origin thereby encourages large deviations parameters initial values.In order help preserve acquired knowledge embedded initial network consider using parameter regularization methods fine-tuning argue standard L 2 regularization which drives parameters towards origin is not adequate framework transfer learning where the initial values provide sensible reference point origin. simple modification keeps original control overfitting constraining effective search space around initial solution encouraging committing acquired knowledge. show has noticeable effects inductive transfer learning scenarios.This paper aims improving transfer learning requiring less labeled training data. form transfer learning is thus considered where some pieces knowledge acquired when solving previous learning problem have to be conveyed another learning problem. setting explore several parameter regularization methods can explicitly retain knowledge acquired source problem. investigate variants L 2 penalties using pre-trained model reference which we name L 2 -SP pre-trained parameters represent starting point -SP fine-tuning process. addition evaluate regularizers based Lasso Group-Lasso penalties which can freeze individual parameters groups parameters pre-trained parameters. Fisher information is also taken account when we test L 2 -SP Group-Lasso-SP approaches.Our experiments indicate tested parameter regularization methods using pre-trained parameters reference get edge standard L 2 weight decay approach. also analyze effect L 2 -SP theoretical arguments experimental evidence recommend usingL2 -SP transfer learning tasks. Among -SP methods L 2 -SP L 2 -SP-Fisher always reach better accuracy target task. expected L 2 -SP-Fisher outperform L 2 -SP since Fisher information helps continual learning is significant difference two options. Since L 2 -SP is simpler L 2 -SP-Fisher recommend former focus analysis L 2 -SP although analysis discussion would also apply L 2 -SP-Fisher proposed simple regularization techniques inductive transfer learning encode explicit bias towards solution learned source task. regularizers evaluated have been already used purposes demonstrate relevance inductive transfer learning deep convolutional networks.We show simple L 2 penalty using starting point reference L 2 -SP is useful even if early stopping is used. penalty is much effective standard L 2 penalty is commonly used fine-tuning is also effective simpler implement strategy consisting freezing first layers network. provide theoretical hints strong experimental evidence showing L 2 -SP retains memory features learned source database.Besides tested effect elaborate penalties based L1 Group-L 1 norms based Fisher information. None L1 Group-L 1 options seem valuable context inductive transfer learning considered using Fisher information L 2 -SP does not improve accuracy target task. Different approaches which implement implicit bias functional level alike BID16 remain tested:based different principle value should be assessed framework inductive transfer learning.,1138,777,361,0.011,1.465,2025/11/05 17:18:59,0.01,1.528,0.4205607476635514,332.271
"Artificial neural networks have opened up a world of possibilities in data science and artificial intelligence, but neural networks are cumbersome tools that grow with the complexity of the learning problem. We make contributions to this issue by considering a modified version of the fully connected layer we call a block diagonal inner product layer. These modified layers have weight matrices that are block diagonal, turning a single fully connected layer into a set of densely connected neuron groups. This idea is a natural extension of group, or depthwise separable, convolutional layers applied to the fully connected layers. Block diagonal inner product layers can be achieved by either initializing a purely block diagonal weight matrix or by iteratively pruning off diagonal block entries. This method condenses network storage and speeds up the run time without significant adverse effect on the testing accuracy, thus offering a new approach to improve network computation efficiency. Today, it is well known that larger neural networks can better represent complex data and hence achieve higher accuracy than smaller networks BID14 BID35 BID34 . While larger networks are more capable than their smaller counterparts, their size consumes significant storage and computational resources and memory bandwidth. Ideally, efforts to reduce memory requirements would also lessen computational demand, but often these competing interests force a trade-off. The fully connected layers are unwieldy, yet they continue to be present in the most successful networks BID21 BID43 BID35 . Our work addresses both memory and computational demand without compromise. Focusing our attention on the inner product layers, we decrease network memory footprint and improve network computational demand.While larger network architectures achieve higher accuracy, there are a variety of methods to condense them without much harm to the network accuracy. One such technique that has gained popularity is pruning BID30 BID7 , but traditional pruning has disadvantages related to network runtime. Most existing pruning processes significantly slow down network training, and the final trained network is usually slower to execute BID7 . Sparse format operations require additional overhead that can greatly slow down performance unless one prunes nearly all weight entries, which can damage network accuracy.Localized memory access patterns can be computed faster than non-localized lookups. By implementing block diagonal inner product layers in place of fully connected layers, we condense neural networks in a structured manner that speeds up the final runtime and does little harm to the final accuracy. Block diagonal inner product layers can be implemented by either initializing a purely block diagonal weight matrix or by initializing a fully connected layer and focusing pruning efforts off the diagonal blocks to coax the dense weight matrix into structured sparsity. The first method also reduces the gradient computation time and hence the overall training time. The latter method can improve accuracy and supports the robustness of networks to shaping. That is, pruning can be used as a mapping between architectures-in particular, a mapping to more convenient architectures. Depending on how many iterations the pruning process takes, this method may also speed up training. We have converted a single fully connected layer into a group of smaller inner product learners whose combined efforts form a stronger learner, in essence boosting the layer. These methods also bring artificial neural networks closer to the architecture of biological mammalian brains, which have more local connectivity BID11 ). We have shown that block diagonal inner product layers can reduce network size, training time and final execution time without significant harm to the network performance.While traditional iterative pruning can reduce storage, the random indices of the surviving weights make sparse computation inefficient, slowing down the training and final execution time of the network. Our block diagonal methods address this inefficiency by confining dense regions to blocks along the diagonal. Without pruning, block diagonal method 1 allows for faster training time. Method 2 preserves the learning with focused, structured pruning that reduces computation for speedup during execution. In our experiments, method 2 saw higher accuracy than the purely block diagonal method for the more complex learning problem, CIFAR10; however, the increase in accuracy came in exchange for slightly more time to train the network. There is great deal of flexibility in our block diagonal methods that can be tuned to an individual problem. These methods may also make larger network architectures more feasible to train and use since they convert a fully connected layer into a collection of smaller inner product learners working jointly to form a stronger learner. In particular, GPU memory constraints become less constricting.There is a lot of room for additional speedup with block diagonal layers. Dependency between layers poses a noteworthy bottleneck in network parallelization. With structured sparsity like ours, one no longer needs a full barrier between layers. Additional speedup would be seen in software optimized to support weight matrices with organized sparse form, such as blocks, rather than being optimized for dense matrices. For example, for many small blocks, one can reach up to 6 fold speedup with specialized batched matrix multiplication BID16 . Hardware has been developing to better support sparse operations. Block format may be especially suitable for training on evolving architectures such as neuromorphic systems. These systems, which are far more efficient than GPUs at simulating mammalian brains, have a pronounced 2-D structure and are ill-suited to large dense matrix calculations BID28 BID0 .","Artificial neural networks have opened world possibilities data science artificial intelligence neural networks are cumbersome tools grow complexity learning problem. make contributions issue considering modified version fully connected layer call block diagonal inner product layer. modified layers have weight matrices are block diagonal turning single fully connected layer set densely connected neuron groups. idea is a natural extension group depthwise separable convolutional layers applied fully connected layers. Block diagonal inner product layers can be achieved either initializing purely block diagonal weight matrix iteratively pruning diagonal block entries. method condenses network storage speeds run time without significant adverse effect testing accuracy thus offering new approach improve network computation efficiency. Today is well known larger neural networks can better represent complex data hence achieve higher accuracy smaller networks BID14 BID35 BID34. larger networks are more capable smaller counterparts size consumes significant storage computational resources memory bandwidth. Ideally efforts reduce memory requirements would also lessen computational demand often competing interests force trade-off fully connected layers are unwieldy yet continue present successful networks BID21 BID43 BID35. work addresses memory computational demand without compromise. Focusing attention inner product layers decrease network memory footprint improve network computational demand.While larger network architectures achieve higher accuracy are a variety methods condense without much harm network accuracy. One technique has gained popularity is pruning BID30 BID7 traditional pruning has disadvantages related network runtime. existing pruning processes significantly slow network training final trained network is usually slower execute BID7. Sparse format operations require additional overhead can greatly slow performance unless one prunes nearly weight entries which can damage network accuracy.Localized memory access patterns can be computed faster non-localized lookups. implementing block diagonal inner product layers place fully connected layers condense neural networks structured manner speeds final runtime does little harm final accuracy. Block diagonal inner product layers can be implemented either initializing purely block diagonal weight matrix initializing fully connected layer focusing pruning efforts diagonal blocks coax dense weight matrix structured sparsity. first method also reduces gradient computation time hence overall training time. latter method can improve accuracy supports robustness networks shaping. is,pruning can be used mapping architectures-in particular mapping convenient architectures. Depending how many iterations pruning process takes method may also speed training. have converted single fully connected layer group smaller inner product learners whose combined efforts form stronger learner essence boosting layer. methods also bring artificial neural networks closer architecture biological mammalian brains which have more local connectivity BID11 have shown are block diagonal inner product layers can reduce network size training time final execution time without significant harm network performance.While traditional iterative pruning can reduce storage random indices surviving weights make sparse computation inefficient slowing training final execution time network. block diagonal methods address inefficiency confining dense regions blocks along diagonal. Without pruning block diagonal method1 allows faster training time. Method 2 preserves learning focused structured pruning reduces computation speedup execution. experiments method 2 saw higher accuracy purely block diagonal method complex learning problem CIFAR10;however increase accuracy came exchange slightly time train network. is great deal flexibility block diagonal methods can be tuned individual problem. methods may also make larger network architectures feasible train use since convert fully connected layer collection smaller inner product learners working jointly form stronger learner. particular GPU memory constraints become less constricting.There is a lot room additional speedup block diagonal layers. Dependency layers poses noteworthy bottleneck network parallelization. structured sparsity like one longer needs full barrier layers. Additional speedup would seen software optimized support weight matrices organized sparse form blocks rather optimized dense matrices. example many small blocks one can reach 6 fold speedup specialized batched matrix multiplication BID16. Hardware has been developing better support sparse operations. Block format may especially suitable training evolving architectures neuromorphic systems. systems which are far efficient GPUs simulating mammalian brains have a pronounced 2-D structure are ill-suited large dense matrix calculations BID28 BID0.",1020,742,278,0.01,1.375,2025/11/05 17:18:59,0.0,1.444,0.1401869158878502,315.568
"One of the challenges in the study of generative adversarial networks is the instability of its training. 
 In this paper, we propose a novel weight normalization technique called spectral normalization to stabilize the training of the discriminator.
 Our new normalization technique is computationally light and easy to incorporate into existing implementations. 
 We tested the efficacy of spectral normalization on CIFAR10, STL-10, and ILSVRC2012 dataset, and we experimentally confirmed that spectrally normalized GANs (SN-GANs) is capable of generating images of better or equal quality relative to the previous training stabilization techniques. Generative adversarial networks (GANs) BID11 have been enjoying considerable success as a framework of generative models in recent years, and it has been applied to numerous types of tasks and datasets BID15 . In a nutshell, GANs are a framework to produce a model distribution that mimics a given target distribution, and it consists of a generator that produces the model distribution and a discriminator that distinguishes the model distribution from the target. The concept is to consecutively train the model distribution and the discriminator in turn, with the goal of reducing the difference between the model distribution and the target distribution measured by the best discriminator possible at each step of the training. GANs have been drawing attention in the machine learning community not only for its ability to learn highly structured probability distribution but also for its theoretically interesting aspects. For example, BID26 BID37 BID24 revealed that the training of the discriminator amounts to the training of a good estimator for the density ratio between the model distribution and the target. This is a perspective that opens the door to the methods of implicit models BID24 BID36 that can be used to carry out variational optimization without the direct knowledge of the density function.A persisting challenge in the training of GANs is the performance control of the discriminator. In high dimensional spaces, the density ratio estimation by the discriminator is often inaccurate and unstable during the training, and generator networks fail to learn the multimodal structure of the target distribution. Even worse, when the support of the model distribution and the support of the target distribution are disjoint, there exists a discriminator that can perfectly distinguish the model distribution from the target . Once such discriminator is produced in this situation, the training of the generator comes to complete stop, because the derivative of the so-produced discriminator with respect to the input turns out to be 0. This motivates us to introduce some form of restriction to the choice of the discriminator.In this paper, we propose a novel weight normalization method called spectral normalization that can stabilize the training of discriminator networks. Our normalization enjoys following favorable properties.• Lipschitz constant is the only hyper-parameter to be tuned, and the algorithm does not require intensive tuning of the only hyper-parameter for satisfactory performance.• Implementation is simple and the additional computational cost is small.In fact, our normalization method also functioned well even without tuning Lipschitz constant, which is the only hyper parameter. In this study, we provide explanations of the effectiveness of spectral normalization for GANs against other regularization techniques, such as weight normalization BID31 , weight clipping , and gradient penalty BID12 . We also show that, in the absence of complimentary regularization techniques (e.g., batch normalization, weight decay and feature matching on the discriminator), spectral normalization can improve the sheer quality of the generated images better than weight normalization and gradient penalty. This paper proposes spectral normalization as a stabilizer of training of GANs. When we apply spectral normalization to the GANs on image generation tasks, the generated examples are more diverse than the conventional weight normalization and achieve better or comparative inception scores relative to previous studies. The method imposes global regularization on the discriminator as opposed to local regularization introduced by WGAN-GP, and can possibly used in combinations. In the future work, we would like to further investigate where our methods stand amongst other methods on more theoretical basis, and experiment our algorithm on larger and more complex datasets.",One challenges study generative adversarial networks is the instability training. paper propose novel weight normalization technique called spectral normalization stabilize training discriminator. new normalization technique is computationally light easy incorporate existing implementations. tested efficacy spectral normalization CIFAR10 STL-10 ILSVRC2012 dataset experimentally confirmed spectrally normalized GANs SN-GANs is capable generating images better equal quality relative previous training stabilization techniques. Generative adversarial networks GANs BID11 have been enjoying considerable success framework generative models recent years has applied numerous types tasks datasets BID15. nutshell GANs are a framework produce model distribution mimics given target distribution consists generator produces model distribution discriminator distinguishes model distribution target. concept is to consecutively train model distribution discriminator turn goal reducing difference model distribution target distribution measured best discriminator possible step training. GANs have been drawing attention machine learning community ability learn highly structured probability distribution also theoretically interesting aspects. example BID26 BID37 BID24 revealed training discriminator amounts training good estimator density ratio model distribution target. is a perspective opens door methods implicit models BID24 BID36 can be used carry variational optimization without direct knowledge density function.A persisting challenge training GANs is the performance control discriminator. high dimensional spaces density ratio estimation discriminator is often inaccurate unstable training generator networks fail learn multimodal structure target distribution. Even worse when the support model distribution support target distribution are disjoint exists discriminator can perfectly distinguish model distribution target. discriminator is produced situation training generator comes complete stop derivative so-produced discriminator respect input turns 0. motivatesus introduce form restriction choice discriminator.In paper propose novel weight normalization method called spectral normalization can stabilize training discriminator networks. normalization enjoys following favorable properties.• Lipschitz constant is the only hyper-parameter tuned algorithm does not require intensive tuning hyper-parameter satisfactory performance.• Implementation is simple additional computational cost is small.In fact normalization method also functioned well even without tuning Lipschitz constant which is the hyper parameter. study provide explanations effectiveness spectral normalization GANs regularization techniques weight normalization BID31 weight clipping gradient penalty BID12. also show absence complimentary regularization techniques e.g batch normalization weight decay feature matching discriminator spectral normalization can improve sheer quality generated images better weight normalization gradient penalty. paper proposes spectral normalization stabilizer training GANs. When we apply spectral normalization GANs image generation tasks generated examples are more diverse conventional weight normalization achieve better comparative inception scores relative previous studies. method imposes global regularization discriminator opposed local regularization introduced WGAN-GP can possibly used combinations. future work would like investigate where our methods stand amongst methods theoretical basis experiment algorithm larger complex datasets.,796,508,288,0.008,1.567,2025/11/05 17:18:59,0.0,1.63,0.7383177570093455,278.402
"Humans acquire complex skills by exploiting previously learned skills and making transitions between them. To empower machines with this ability, we propose a method that can learn transition policies which effectively connect primitive skills to perform sequential tasks without handcrafted rewards. To efficiently train our transition policies, we introduce proximity predictors which induce rewards gauging proximity to suitable initial states for the next skill. The proposed method is evaluated on a set of complex continuous control tasks in bipedal locomotion and robotic arm manipulation which traditional policy gradient methods struggle at. We demonstrate that transition policies enable us to effectively compose complex skills with existing primitive skills. The proposed induced rewards computed using the proximity predictor further improve training efficiency by providing more dense information than the sparse rewards from the environments. We make our environments, primitive skills, and code public for further research at https://youngwoon.github.io/transition .",Humans acquire complex skills exploiting previously learned skills making transitions them. empower machines ability propose method can learn transition policies which effectively connect primitive skills perform sequential tasks without handcrafted rewards. efficiently train transition policies introduce proximity predictors which induce rewards gauging proximity suitable initial states next skill. proposed method is evaluated set complex continuous control tasks bipedal locomotion robotic arm manipulation which traditional policy gradient methods struggle at. demonstrate transition policies enableus effectively compose complex skills existing primitive skills. proposed induced rewards computed using proximity predictor improve training efficiency providing dense information sparse rewards environments. make environments primitive skills code public research https://youngwoon.github.io/transition,169,123,46,0.002,1.374,2025/11/05 17:18:59,0.0,1.0,0.1370716510903428,69.57
"Gated recurrent units (GRUs) were inspired by the common gated recurrent unit, long short-term memory (LSTM), as a means of capturing temporal structure with less complex memory unit architecture. Despite their incredible success in tasks such as natural and artificial language processing, speech, video, and polyphonic music, very little is understood about the specific dynamic features representable in a GRU network. As a result, it is difficult to know a priori how successful a GRU-RNN will perform on a given data set. In this paper, we develop a new theoretical framework to analyze one and two dimensional GRUs as a continuous dynamical system, and classify the dynamical features obtainable with such system.
 We found rich repertoire that includes stable limit cycles over time (nonlinear oscillations), multi-stable state transitions with various topologies, and homoclinic orbits. In addition, we show that any finite dimensional GRU cannot precisely replicate the dynamics of a ring attractor, or more generally, any continuous attractor, and is limited to finitely many isolated fixed points in theory. These findings were then experimentally verified in two dimensions by means of time series prediction. Recurrent neural networks (RNNs) have been widely used to capture and utilize sequential structure in natural and artificial languages, speech, video, and various other forms of time series. The recurrent information flow within RNN implies that the data seen in the past has influence on the current state of the RNN, forming a mechanism for having memory through (nonlinear) temporal traces. Unfortunately, training vanilla RNNs (which allow input data to directly interact with the hidden state) to capture long-range dependences within a sequence is challenging due to the vanishing gradient problem BID8 . Several special RNN architectures have been proposed to mitigate this issue, notably the long short-term memory (LSTM; BID9 ) which explicitly guards against unwanted corruption of the information stored in the hidden state until necessary. Recently, a simplification of the LSTM called the gated recurrent unit (GRU; BID1 ) has become wildly popular in the machine learning community thanks to its performance in machine translation BID0 , speech BID16 , music BID2 , video BID4 , and extracting nonlinear dynamics underlying neural data BID15 . As a variant of the vanilla LSTM, GRUs incorporate the use of forget gates, but lack an output gate BID5 . While this feature reduces the number of required parameters, LSTM has been shown to outperform GRU on neural machine translation BID0 . In addition, certain mechanistic tasks, specifically unbounded counting, come easy to LSTM networks but not to GRU networks BID18 . Despite these empirical findings, we lack systematic understanding of the internal time evolution of GRU's memory structure and its capability to represent nonlinear temporal dynamics.In general, a RNN can be written as h t+1 = f (h t , x t ) where x t is the current input in a sequence indexed by t, f is a point-wise nonlinear function, and h t represents the hidden memory state that carries all information responsible for future output. In the absence of input, the hidden state h t can evolve over time on its own: DISPLAYFORM0 where f (·) := f (·, 0) for notational simplicity. In other words, we can consider the temporal evolution of memory stored within RNN as a trajectory of a dynamical system defined by (1). Then we can use dynamical systems theory to investigate the fundamental limits in the expressive power of RNNs in terms of their temporal features. We develop a novel theoretical framework to study the dynamical features fundamentally attainable, in particular, given the particular form of GRU. We then validate the theory by training GRUs to predict time series with prescribed dynamics. Our analysis shows the rich but limited classes of dynamics the GRU can approximate in one, two, and arbitrary dimensions. We developed a new theoretical framework to analyze GRUs as a continuous dynamical system, and showed that two GRUs can exhibit a variety of expressive dynamic features, such as limit cycles, homoclinic orbits, and a substantial catalog of stability structures and bifurcations. However, we also showed that finitely many GRUs cannot exhibit the dynamics of an arbitrary continuous attractor. These claims were then experimentally verified in two dimensions. We believe these findings also unlock new avenues of research on the trainability of recurrent neural networks. Although we have analyzed GRUs only in 1-and 2-dimensions in near exhaustive, we believe that the insights extends to higher-dimensions. We leave rigorous analysis of higher-dimensional GRUs as future work.A CONTINUOUS TIME SYSTEM DERIVATION We begin with the fully gated GRU as a discrete time system, where the input vector x t has been set equal to zero, as depicted in FORMULA0 - FORMULA0 , where is the Hadamard product, and σ is the sigmoid function. DISPLAYFORM0 We recognize that (15) is a forward Euler discretization of a continuous time dynamical system. This allows us to consider the underlying continuous time dynamics on the basis of the discretization. The following steps are a walk through of the derivation:Since z t is a bounded function on R ∀t, there exists a functionz t , such that z t +z t = 1 at each time step (due to the symmetry of z t ,z t is the result of vertically flipping z t about 0.5, the midpoint of its range). As such, we can rewrite (15) withz t as depicted in FORMULA0 . DISPLAYFORM1 Let h(t) ≡ h t−1 . As a result, we can sayz t ≡z(t) and r t ≡ r(t), as depicted in FORMULA7 . DISPLAYFORM2 Dividing both sides of the equation by ∆t yields (24). DISPLAYFORM3 If we take the limit as ∆t → 0, we get the analogous continuous time system to (13) -(15), DISPLAYFORM4 whereḣ ≡",Gated recurrent units GRUs were inspired common gated recurrent unit long short-term memory LSTM means capturing temporal structure less complex memory unit architecture. Despite incredible success tasks natural artificial language processing speech video polyphonic music little is understood specific dynamic features representable GRU network. result is difficult know priori how successful GRU-RNN will perform given data set. paper develop new theoretical framework analyze one two dimensional GRUs continuous dynamical system classify dynamical features obtainable system. found rich repertoire includes stable limit cycles time nonlinear oscillations multi-stable state transitions various topologies homoclinic orbits. addition show finite dimensional GRU cannot precisely replicate dynamics ring attractor generally continuous attractor is limited finitely many isolated fixed points theory. findings were then experimentally verified two dimensions means time series prediction. Recurrent neural networks RNNs have been widely used capture utilize sequential structure natural artificial languages speech video various forms time series. recurrent information flow within RNN implies data seen past has influence current state RNN forming mechanism memory nonlinear temporal traces. Unfortunately training vanilla RNNs which allow input data directly interact hidden state capture long-range dependences within sequence is challenging due vanishing gradient problem BID8. Several special RNN architectures have been proposed mitigate issue notably long short-term memory LSTM;BID9 which explicitly guards unwanted corruption information stored hidden state necessary. Recently simplification LSTM called gated recurrent unit GRU;BID1 has become wildly popular machine learning community thanks performance machine translation BID0 speech BID16 music BID2 video BID4 extracting nonlinear dynamics underlying neural data BID15. variant vanilla LSTM GRUs incorporate use forget gates lack output gate BID5. feature reduces number required parameters LSTM has been shown outperform GRU neural machine translation BID0. addition certain mechanistic tasks specifically unbounded counting come easy LSTM networks GRU networks BID18. Despite empirical findings lack systematic understanding internal time evolution GRU's memory structure capability represent nonlinear temporal dynamics.In general RNN can be written h+1 f h wherex wherex is the current input sequence indexed f is a point-wise nonlinear function h represents hidden memory state carries information responsible future output. absence input hidden stateh can evolve time own:DISPLAYFORM0 wheref · f · 0 notational simplicity. words can consider temporal evolution memory stored within RNN trajectory dynamical system defined 1 can use dynamical systems theory investigate fundamental limits expressive power RNNs terms temporal features. develop novel theoretical framework study dynamical features fundamentally attainable particular given particular form GRU. validate theory training GRUs predict time series prescribed dynamics. analysis shows rich limited classes dynamics GRU can approximate one two arbitrary dimensions. developed new theoretical framework analyze GRUs continuous dynamical system showed two GRUs can exhibit variety expressive dynamic features limit cycles homoclinic orbits substantial catalog stability structures bifurcations. However also showed finitely many GRUs cannot exhibit dynamics arbitrary continuous attractor. claims were then experimentally verified two dimensions. believe findings also unlock new avenues research trainability recurrent neural networks. Although have analyzed GRUs 1-and 2-dimensions near exhaustive believe insights extends higher-dimensions leave rigorous analysis higher-dimensional GRUs future work.A CONTINUOUS TIME SYSTEM DERIVATION begin fully gated GRU discrete time system where the input vectorx has been set equal zero depicted FORMULA0 FORMULA0 where is the Hadamard product σ is the sigmoid function. DISPLAYFORM0 recognize 15 is a forward Euler discretization continuous time dynamical system. allowsus consider underlying continuous time dynamics basis discretization. following steps are a walk derivation:Sincez is a bounded function R∀t exists functionz z+z 1 time step due symmetry z z is the result vertically flippingz 0.5 midpoint range can rewrite 15 withz depicted FORMULA0. DISPLAYFORM1 Leth ≡ h t−1 result can sayz ≡z r ≡r depicted FORMULA7. DISPLAYFORM2 Dividing sides equation ∆t yields 24 DISPLAYFORM3 If we take limit ∆t→0 get analogous continuous time system 13 - 15 DISPLAYFORM4 whereḣ≡,1243,838,405,0.013,1.483,2025/11/05 17:18:59,0.01,1.459,0.4766355140186917,366.033
"Stacked hourglass network has become an important model for Human pose estimation. The estimation of human body posture depends on the global information of the keypoints type and the local information of the keypoints location. The consistent processing of inputs and constraints makes it difficult to form differentiated and determined collaboration mechanisms for each stacked hourglass network. In this paper, we propose a Multi-Scale Stacked Hourglass (MSSH) network to high-light the differentiation capabilities of each Hourglass network for human pose estimation.   The pre-processing network forms feature maps of different scales,and dispatch them to various locations of the stack hourglass network, where the small-scale features reach the front of stacked hourglass network, and large-scale features reach the rear of stacked hourglass network.    And a new loss function is proposed for multi-scale stacked hourglass network.   Different keypoints have different weight coefficients of loss function at different scales, and the keypoints weight coefficients are dynamically adjusted from the top-level hourglass network to the bottom-level hourglass network.   Experimental results show that the pro-posed method is competitive with respect to the comparison algorithm on MPII and LSP datasets. Human pose estimation need locate the body keypoints (head, shoulder, elbow, wrist, knee, ankle, etc.) from the input image, and it is basic method for some advanced vision task BID4 , such as human motion recognition, human-computer interaction, and human reidentification et al. We focus on single-person pose estimation problems in a single RGB image. Due to the high flexibility of the human body and limbs, diverse viewpoint, camera projection transformation and occlusion, it still is a difficult task to accurately determine body keypoints from a single image.In recent years, the deep convolutional neural network (DCNN) has made significant progress in the human pose estimation; especially the stacked hourglass network BID7 has achieved good results and has attracted much attention. The human pose estimation involves two kinds of information: the type and location of body keypoints. The type of body keypoints needs to be determined in a larger receptive field, and the location of body keypoints needs to be based on the specific pixel position, which are respectively equivalent to global information and local information. The hourglass network uses a convolution layer and a deconvolution layer to form an hourglass structure, and establish crossover channels between convolution and deconvolution layers on different scales. Using the hourglass network for human pose estimation, the hourglass structure extracts global information through information compression, and the crossover channels compensates for local information loss in information compression. The stacked hourglass network continuously improves the human pose estimation by enhancing the context constraints among body keypoints through the stacked structure.The stacked hourglass network theoretically increases the stacked depth to expand the receptive field and form a stronger context constraints among body keypoints. However, in practical applications, simply increasing the stacked depth is difficult to effectively improve the accuracy of human pose estimation. The main reason is that the consistent processing of inputs and constraints makes it difficult to form differentiated and determined collaboration mechanisms for each stacked hourglass network, to make up the information loss caused by the functional consistency of hourglass networks. Inspired by multi-scale information fusion from the single hourglass network, we propose a Multi-Scale Stacked Hourglass (MSSH) network. A pre-processing network consisting primarily of residual networks is designed to generate multi-scale features, and features of each scale are sent to different stacked hourglass networks. Each hourglass network has different inputs: the output of the pre-level hourglass network, and the received feature. Small-scale feature input makes the hourglass network tend to focus on global information, such as the type and context constraints of body keypoints, and large-scale feature input makes the hourglass network more likely to focus on local information, such as the location of body keypoints. The input of entire stacking hourglass network has changed from small-scale feature to large-scale feature, and it is a top-down route of body keypoints estimation. The iterative relationship between the loss functions of different scales of the MSSH network is established, so that the pre-level detection results affect the weight of the next keypoint loss function, and the optimization process of network model training is controlled by adaptive weighted loss function. The iterative relationship of the adjacent network loss function is established on the MSSH network, so that the weight of the loss function on pre-level hourglass network affects the weight of the loss function on the current hourglass network. The optimization process of the model training is controlled by the adaptive weighted loss function.The main contributions of this paper can be summarized as follows:• In a multi-scale stacked hourglass network, the pre-processing network generates features of different scales and dispatchs them to every hourglass network, where the small-scale features reaches the front of stacked hourglass network and the large-scale features reaches the rear of stacked hourglass network. From global information to local information, each hourglass network can form a differentiated function, which is conducive to the formation of collaborative processing.• A new loss function of the MSSH network is proposed. The weighting coefficient of the loss function in hourglass network is defined. The weight coefficient and the loss function of the pre-level hourglass network are used to adjust the weight coefficient of the current hourglass network, and the convergence process of the model training is optimized by the adaptive weighted loss function.The remainder of this paper is organized as follows. Section 2 briefly reviews recent work on human pose estimation. Section 3 details the structure of the MSSH network. Section 4 describes the new loss function for MSSH network networks. Section 5 describes the implementation details and experimental results. Section 6 summarizes our paper.",Stacked hourglass network has become important model Human pose estimation. estimation human body posture depends global information keypoints type local information keypoints location. consistent processing inputs constraints makes difficult form differentiated determined collaboration mechanisms stacked hourglass network. paper propose Multi-Scale Stacked Hourglass MSSH network high-light differentiation capabilities Hourglass network human pose estimation. pre-processing network forms feature maps different scales dispatch various locations stack hourglass network where the small-scale features reach front stacked hourglass network large-scale features reach rear stacked hourglass network. new loss function is proposed multi-scale stacked hourglass network. Different keypoints have different weight coefficients loss function different scales keypoints weight coefficients are dynamically adjusted top-level hourglass network bottom-level hourglass network. Experimental results show pro-posed method is competitive respect comparison algorithm MPII LSP datasets. Human pose estimation need locate body keypoints head shoulder elbow wrist knee ankle etc. input image is basic method advanced vision task BID4 human motion recognition human-computer interaction human reidentificationetal. focus single-person pose estimation problems single RGB image. Due high flexibility human body limbs diverse viewpoint camera projection transformation occlusion still is a is difficult task accurately determine body keypoints single image.In recent years deep convolutional neural network DCNN has made significant progress human pose estimation;especially stacked hourglass network BID7 has achieved good results has attracted much attention. human pose estimation involves two kinds information:type location body keypoints. type body keypoints needs determined larger receptive field location body keypoints needs based specific pixel position which are respectively equivalent global information local information. hourglass network uses convolution layer deconvolution layer form hourglass structure establish crossover channels convolution deconvolution layers different scales. Using hourglass network human pose estimation hourglass structure extracts global information information compression crossover channels compensates local information loss information compression. stacked hourglass network continuously improves human pose estimation enhancing context constraints among body keypoints stacked structure.The stacked hourglass network theoretically increases stacked depth expand receptive field form stronger context constraints among body keypoints. However practical applications simply increasing stacked depth is a is difficult effectively improve accuracy human pose estimation. main reason is that the consistent processing inputs constraints makes difficult form differentiated determined collaboration mechanisms stacked hourglass network make information loss caused functional consistency hourglass networks. Inspired multi-scale information fusion single hourglass network propose Multi-Scale Stacked Hourglass MSSH network. pre-processing network consisting primarily residual networks is designed generate multi-scale features features scale are sent different stacked hourglass networks. hourglass network has different inputs:output pre-level hourglass network received feature. Small-scale feature input makes hourglass network tend focus global information type context constraints body keypoints large-scale feature input makes hourglass network likely focus local information location body keypoints. input entire stacking hourglass network has changed small-scale feature large-scale feature is top-down route body keypoints estimation. iterative relationship loss functions different scales MSSH network is established pre-level detection results affect weight next keypoint loss function optimization process network model training is controlled adaptive weighted loss function. iterative relationship adjacent network loss function is established MSSH network weight loss function pre-level hourglass network affects weight loss function current hourglass network. optimization process model training is controlled adaptive weighted loss function.The main contributions paper can be summarized follows:• multi-scale stacked hourglass network pre-processing network generates features different scales dispatchs every hourglass network where the small-scale features reaches front stacked hourglass network large-scale features reaches rear stacked hourglass network. global information local information hourglass network can form differentiated function which is conducive formation collaborative processing.• new loss function MSSH network is proposed. weighting coefficient loss function hourglass network is defined. weight coefficient loss function pre-level hourglass network are used adjust weight coefficient current hourglass network convergence process model training is optimized adaptive weighted loss function.The remainder paper is organized follows. Section 2 briefly reviews recent work human pose estimation. Section 3 details structure MSSH network. Section 4 describes new loss function MSSH network networks. Section 5 describes implementation details experimental results. Section 6 summarizes paper.,1152,808,344,0.011,1.426,2025/11/05 17:18:59,0.01,1.25,0.2990654205607472,338.526
"We present a new unsupervised method for learning general-purpose sentence embeddings.
 Unlike existing methods which rely on local contexts, such as words
 inside the sentence or immediately neighboring sentences, our method selects, for
 each target sentence, influential sentences in the entire document based on a document
 structure. We identify a dependency structure of sentences using metadata
 or text styles. Furthermore, we propose a novel out-of-vocabulary word handling
 technique to model many domain-specific terms, which were mostly discarded by
 existing sentence embedding methods. We validate our model on several tasks
 showing 30% precision improvement in coreference resolution in a technical domain,
 and 7.5% accuracy increase in paraphrase detection compared to baselines. Distributed representations are ever more leveraged to understand text BID20 b; BID16 BID23 . Recently, BID12 proposed a neural network model, SKIP-THOUGHT, that embeds a sentence without supervision by training the network to predict the next sentence for a given sentence. However, unlike human reading with broader context and structure in mind, the existing approaches focus on a small continuous context of neighboring sentences. These approaches work well on less structured text like movie transcripts, but do not work well on structured documents like encylopedic articles and technical reports.To better support semantic understanding of such technical documents, we propose a new unsupervised sentence embedding framework to learn general-purpose sentence representations by leveraging long-distance dependencies between sentences in a document. We observe that understanding a sentence often requires understanding of not only the immediate context but more comprehensive context, including the document title, previous paragraphs or even related articles as shown in Figure 1. For instance, all the sentences in the document can be related to the title of the document (1(a )). The first sentence of each item in a list structure can be influenced by the sentence introducing the list (1(b)) . Moreover , html documents can contain hyperlinks to provide more information about a certain term (1(c)). With the contexts obtained from document structure, we can connect ransomware with payment (1(a)) and the four hashes with Locky (1(b)). In this paper, we presented a novel sentence embedding technique exploiting diverse types of structural contexts and domain-specific OOV words. Our method is unsupervised and applicationindependent, and it can be applied to various NLP applications. We evaluated the method on several NLP tasks including coreference resolution, paraphrase detection and sentence prediction. The results show that our model consistently outperforms the existing approaches confirming that considering the structural context generates better quality sentence representations.",present new unsupervised method learning general-purpose sentence embeddings. Unlike existing methods which rely local contexts words inside sentence immediately neighboring sentences method selects target sentence influential sentences entire document based document structure. identify dependency structure sentences using metadata text styles. Furthermore propose novel out-of-vocabulary word handling technique model many domain-specific terms which were mostly discarded existing sentence embedding methods. validate model several tasks showing30% precision improvement coreference resolution technical domain 7.5 accuracy increase paraphrase detection compared baselines. Distributed representations are ever leveraged understand text BID20b;BID16 BID23. Recently BID12 proposed neural network model SKIP-THOUGHT embeds sentence without supervision training network predict next sentence given sentence. However unlike human reading broader context structure mind existing approaches focus small continuous context neighboring sentences. approaches work well less structured text like movie transcripts do not work well structured documents like encylopedic articles technical reports.To better support semantic understanding technical documents propose new unsupervised sentence embedding framework learn general-purpose sentence representations leveraging long-distance dependencies sentences document. observe understanding sentence often requires understanding immediate context comprehensive context including document title previous paragraphs even related articles shown Figure1. instance sentences document can be related title document 1 first sentence item list structure can be influenced sentence introducing list 1 b Moreover html documents can contain hyperlinks provide information certain term 1 c contexts obtained document structure can connect ransomware payment 1 four hashes Locky 1 b paper presented novel sentence embedding technique exploiting diverse types structural contexts domain-specific OOV words. method is unsupervised applicationindependent can applied various NLP applications. evaluated method several NLP tasks including coreference resolution paraphrase detection sentence prediction. results show model consistently outperforms existing approaches confirming considering structural context generates better quality sentence representations.,514,346,168,0.005,1.486,2025/11/05 17:18:59,0.0,1.4,0.4859813084112147,172.31
"Neural network training relies on our ability to find ````````""good"" minimizers of highly non-convex loss functions. It is well known that certain network architecture designs (e.g., skip connections) produce loss functions that train easier, and well-chosen training parameters (batch size, learning rate, optimizer) produce minimizers that generalize better. However, the reasons for these differences, and their effect on the underlying loss landscape, is not well understood.

 In this paper, we explore the structure of neural loss functions, and the effect of loss landscapes on generalization, using a range of visualization methods. First, we introduce a simple ``""filter normalization"" method that helps us visualize loss function curvature, and make meaningful side-by-side comparisons between loss functions. Then, using a variety of visualizations, we explore how network architecture effects the loss landscape, and how training parameters affect the shape of minimizers. Training neural networks requires minimizing a high-dimensional non-convex loss function -a task that is hard in theory, but sometimes easy in practice. Despite the NP-hardness of training general neural loss functions BID0 , simple gradient methods often find global minimizers (parameter configurations with zero or near-zero training loss), even when data and labels are randomized before training BID39 . However, this good behavior is not universal; the trainability of neural nets is highly dependent on network architecture design choices, the choice of optimizer, variable initialization, and a variety of other considerations. Unfortunately, the effect of each of these choices on the structure of the underlying loss surface is unclear. Because of the prohibitive cost of loss function evaluations (which requires looping over all the data points in the training set), studies in this field have remained predominantly theoretical.Our goal is to use high-resolution visualizations to provide an empirical characterization of neural loss functions, and to explore how different network architecture choices affect the loss landscape. Furthermore, we explore how the non-convex structure of neural loss functions relates to their trainability, and how the geometry of neural minimizers (i.e., their sharpness/flatness, and their surrounding landscape), affects their generalization properties.To do this in a meaningful way, we propose a simple ""filter normalization"" scheme that enables us to do side-by-side comparisons of different minima found by different methods. We then use visualizations to explore sharpness/flatness of minimizers found by different methods, as well as the effect of network architecture choices (use of skip connections, number of filters, network depth) on the loss landscape. Out goal is to understand how differences in loss function geometry effect the generalization of neural nets. In this paper, we presented a new, more accurate visualization technique that provided insights into the consequences of a variety of choices facing the neural network practitioner, including network architecture, optimizer selection, and batch size.Neural networks have advanced dramatically in recent years, largely on the back of anecdotal knowledge and theoretical results with complex assumptions. For progress to continue to be made, a more general understanding of the structure of neural networks is needed. Our hope is that effective visualization, when coupled with continued advances in theory, can result in faster training, simpler models, and better generalization. Figure 4 , the first row uses zero weight decay and the second row uses 5e-4 weight decay.Generalization error for each plot is shown in TAB2 10 TEST AND TRAINING DATA FOR VARIOUS NETWORKS FIG0 , the first row uses zero weight decay and the second row sets weight decay to 5e-4.",Neural network training relies ability find good minimizers highly non-convex loss functions. is well known certain network architecture designs e.g skip connections produce loss functions train easier well-chosen training parameters batch size learning rate optimizer produce minimizers generalize better. However reasons differences effect underlying loss landscape is not well understood. paper explore structure neural loss functions effect loss landscapes generalization using range visualization methods. First introduce simple filter normalization method helps us visualize loss function curvature make meaningful side-by-side comparisons loss functions. using variety visualizations explore how network architecture effects loss landscape how training parameters affect shape minimizers. Training neural networks requires minimizing high-dimensional non-convex loss function -a task is hard theory sometimes easy practice. Despite NP-hardness training general neural loss functions BID0 simple gradient methods often find global minimizers parameter configurations zero near-zero training loss even when data labels are randomized training BID39. However good behavior is not universal;trainability neural nets is highly dependent network architecture design choices choice optimizer variable initialization variety considerations. Unfortunately effect choices structure underlying loss surface is unclear. prohibitive cost loss function evaluations which requires looping data points training set studies field have remained predominantly theoretical.Our goal is to use high-resolution visualizations provide empirical characterization neural loss functions explore how different network architecture choices affect loss landscape. Furthermore explore how the non-convex structure neural loss functions relates trainability how the geometry neural minimizers.e sharpness/flatness surrounding landscape affects generalization properties.To do this in a meaningful way propose simple filter normalization scheme enablesus do side-by-side comparisons different minima found different methods. use visualizations explore sharpness/flatness minimizers found different methods is not well effect network architecture choices use skip connections number filters network depth loss landscape. goal is to understand how differences loss function geometry effect generalization neural nets. paper presented new accurate visualization technique provided insights consequences variety choices facing neural network practitioner including network architecture optimizer selection batch size.Neural networks have advanced dramatically recent years largely back anecdotal knowledge theoretical results complex assumptions. progress continue made general understanding structure neural networks is needed. hope is that effective visualization when coupled continued advances theory can result faster training simpler models better generalization. Figure4 first row uses zero weight decay second row uses 5e-4 weight decay.Generalization error plot is shown TAB2 10 TEST TRAINING DATA VARIOUS NETWORKS FIG0 first row uses zero weight decay second row sets weight decay 5e-4,719,486,233,0.007,1.479,2025/11/05 17:18:59,0.0,1.385,0.4641744548286605,245.341
"Deep models are state-of-the-art for many computer vision tasks including image classification and object detection. However, it has been shown that deep models are vulnerable to adversarial examples. We highlight how one-hot encoding directly contributes to this vulnerability and propose breaking away from this widely-used, but highly-vulnerable mapping. We demonstrate that by leveraging a different output encoding, multi-way encoding, we can make models more robust. Our approach makes it more difficult for adversaries to find useful gradients for generating adversarial attacks. We present state-of-the-art robustness results for black-box, white-box attacks, and achieve higher clean accuracy on four benchmark datasets: MNIST, CIFAR-10, CIFAR-100, and SVHN when combined with adversarial training. The strength of our approach is also presented in the form of an attack for model watermarking, raising challenges in detecting stolen models. Deep learning models are vulnerable to adversarial examples BID19 ]. Evidence shows that adversarial examples are transferable BID14 ; BID11 ]. This weakness can be exploited even if the adversary does not know the target model under attack, posing severe concerns about the security of the models. This is because an adversary can use a substitute model for generating adversarial examples for the target model, also known as black-box attacks.Black-box attacks such as BID4 rely on perturbing input by adding an amount dependent upon the gradient of the loss function with respect to the input of a substitute model. An example adversarial attack is x adv = x + sign(∇ x Loss(f (x)), where f (x) is the model used to generate the attack. This added ""noise"" can fool a model although it may not be visually evident to a human. The assumption of such gradient-based approaches is that the gradients with respect to the input, of the substitute and target models, are correlated.Our key observation is that the setup of conventional deep classification frameworks aids in the correlation of such gradients. Typically, a cross-entropy loss, a soft-max layer, and a one-hot vector encoding for a target label are used when training deep models. These conventions make a model more vulnerable to black-box attacks. This setting constrains the encoding length, and the number of possible non-zero gradient directions at the encoding layer. This makes it easier for an adversary to pick a harmful gradient direction and perform an attack.We aim to increase the adversarial robustness of deep models. Our multi-way encoding representation relaxes the one-hot encoding to a real number encoding, and embeds the encoding in a space that has dimension higher than the number of classes. These encoding methods lead to an increased number of possible gradient directions, as illustrated in Figure 1 . This makes it more difficult for an adversary to pick a harmful direction that would cause a misclassification of a correctly classified point, generating a targeted or untargeted attack. Untargeted attacks aim to misclassify a point, while targeted attacks aim to misclassify a point to a specific target class. Multi-way encoding also helps improve a model's robustness in cases where the adversary has full knowledge of the target model under attack: a white-box attack. The benefits of multi-way encoding are demonstrated in experiments with four benchmark datasets: MNIST, CIFAR-10, CIFAR-100, and SVHN.We also demonstrate the strength of our approach by introducing an attack for the recent model watermarking algorithm of BID24 , which deliberately trains a model to misclassify (a) (b) (c) Figure 1 : Demonstration of the benefit of relaxing and increasing the encoding dimensionality, for a binary classification problem at the final encoding layer. C i is the codebook encoding for class i, axis s i represents the output activation of neuron i in the output encoding layer, where i = 1, . . . , l and l is the encoding dimensionality. The depicted points are correctly classified points of the green and blue classes. The arrows depict the possible non-zero perturbation directions sign( ∂Loss ∂si ). (a) 2D 1of K softmax-crossentropy setup: Only two non-zero gradient directions exist for a 1of K encoding. Of these two directions, only one is an adversarial direction, depicted in red. (b) 2D multi-way encoding: Four non-zero perturbation directions exist. The fraction of directions that now move a point to the adversarial class (red) drops. (c) 3D multi-way encoding: A higher dimensional encoding results in a significantly lower fraction of gradient perturbations whose direction would move an input from the green ground-truth class to the blue class, or vice versa. certain watermarked images. We interpret such watermarked images as adversarial examples. We demonstrate that the multi-way encoding reduces the transferability of the watermarked images, making it more challenging to detect stolen models.We summarize our contributions as follows:1. We show that the traditional 1of K mapping is a source of vulnerability to adversarial gradients. 2. We propose a novel solution using multi-way encoding to alleviate the vulnerability caused by the 1of K mapping. 3. We empirically show that the proposed approach improves model robustness against both black-box and white-box attacks. 4. We also show how to apply our encoding framework in attacking the recently proposed model watermarking scheme of BID24 .",Deep models are state-of-the-art many computer vision tasks including image classification object detection. However has been shown deep models are vulnerable adversarial examples. highlight how one-hot encoding directly contributes vulnerability propose breaking away widely-used highly-vulnerable mapping. demonstrate leveraging different output encoding multi-way encoding can make models robust. approach makes difficult adversaries find useful gradients generating adversarial attacks. present state-of-the-art robustness results black-box white-box attacks achieve higher clean accuracy four benchmark datasets:MNIST CIFAR-10 CIFAR-100 SVHN when combined adversarial training. strength approach is also presented form attack model watermarking raising challenges detecting stolen models. Deep learning models are vulnerable adversarial examples BID19 Evidence shows adversarial examples are transferable BID14;BID11 weakness can be exploited even if the adversary does not know target model attack posing severe concerns security models. is because an adversary can use substitute model generating adversarial examples target model also known black-box attacks.Black-box attacks BID4 rely perturbing input adding amount dependent upon gradient loss function respect input substitute model. example adversarial attack is x adv x+sign ∇ x Loss f x wheref x is the model used generate attack. added noise can fool model although may visually evident human. assumption gradient-based approaches is that the gradients respect input substitute target models are correlated.Our key observation is that the setup conventional deep classification frameworks aids correlation gradients. Typically cross-entropy loss soft-max layer one-hot vector encoding target label are used when training deep models. conventions make model vulnerable black-box attacks. setting constrains encoding length number possible non-zero gradient directions encoding layer. makes easier adversary pick harmful gradient direction perform attack.We aim increase adversarial robustness deep models. multi-way encoding representation relaxes one-hot encoding real number encoding embeds encoding space has dimension higher number classes. encoding methods lead increased number possible gradient directions illustrated Figure1. makes difficult adversary pick harmful direction would cause misclassification correctly classified point generating targeted untargeted attack. Untargeted attacks aim misclassify point targeted attacks aim misclassify point specific target class. Multi-way encoding also helps improve model's robustness cases where the adversary has full knowledge target model attack:white-box attack. benefits multi-way encoding are demonstrated experiments four benchmark datasets:MNIST CIFAR-10 CIFAR-100 SVHN.We also demonstrate strength approach introducing attack recent model watermarking algorithm BID24 which deliberately trains model misclassify b c Figure1:Demonstration benefit relaxing increasing encoding dimensionality binary classification problem final encoding layer. C is the codebook encoding class axis represents output activation neuron output encoding layer wherei=1 l l is the encoding dimensionality. depicted points are correctly classified points green blue classes. arrows depict possible non-zero perturbation directions sign ∂Loss ∂si 2D 1of K softmax-crossentropy setup:two non-zero gradient directions exist 1of K encoding. two directions one is an adversarial direction depicted red. b 2D multi-way encoding:Four non-zero perturbation directions exist. fraction directions move point adversarial class red drops. c 3D multi-way encoding:higher dimensional encoding results significantly lower fraction gradient perturbations whose direction would move input green ground-truth class blue class vice versa. certain watermarked images. interpret watermarked images adversarial examples. demonstrate multi-way encoding reduces transferability watermarked images making challenging detect stolen models.We summarize contributions follows:1 show traditional 1of K mapping is a source vulnerability adversarial gradients. 2. propose novel solution using multi-way encoding alleviate vulnerability caused 1of K mapping. 3. empirically show proposed approach improves model robustness black-box white-box attacks. 4. also show how to apply encoding framework attacking recently proposed model watermarking scheme BID24.,1090,757,333,0.011,1.44,2025/11/05 17:18:59,0.0,1.559,0.3426791277258563,324.935
"Existing approaches to neural machine translation condition each output word on previously generated outputs. We introduce a model that avoids this autoregressive property and produces its outputs in parallel, allowing an order of magnitude lower latency during inference. Through knowledge distillation, the use of input token fertilities as a latent variable, and policy gradient fine-tuning, we achieve this at a cost of as little as 2.0 BLEU points relative to the autoregressive Transformer network used as a teacher. We demonstrate substantial cumulative improvements associated with each of the three aspects of our training strategy, and validate our approach on IWSLT 2016 English–German and two WMT language pairs. By sampling fertilities in parallel at inference time, our non-autoregressive model achieves near-state-of-the-art performance of 29.8 BLEU on WMT 2016 English–Romanian. Neural network based models outperform traditional statistical models for machine translation (MT) BID0 BID9 . However, state-of-the-art neural models are much slower than statistical MT approaches at inference time BID16 . Both model families use autoregressive decoders that operate one step at a time: they generate each token conditioned on the sequence of tokens previously generated. This process is not parallelizable, and, in the case of neural MT models, it is particularly slow because a computationally intensive neural network is used to generate each token.While several recently proposed models avoid recurrence at train time by leveraging convolutions BID6 BID4 or self-attention BID14 as more-parallelizable alternatives to recurrent neural networks (RNNs), use of autoregressive decoding makes it impossible to take full advantage of parallelism during inference.We introduce a non-autoregressive translation model based on the Transformer network BID14 . We modify the encoder of the original Transformer network by adding a module that predicts fertilities, sequences of numbers that form an important component of many traditional machine translation models BID1 . These fertilities are supervised during training and provide the decoder at inference time with a globally consistent plan on which to condition its simultaneously computed outputs.",Existing approaches neural machine translation condition output word previously generated outputs. introduce model avoids autoregressive property produces outputs parallel allowing order magnitude lower latency inference. knowledge distillation use input token fertilities latent variable policy gradient fine-tuning achieve cost little 2.0 BLEU points relative autoregressive Transformer network used teacher. demonstrate substantial cumulative improvements associated three aspects training strategy validate approach IWSLT 2016 English–German two WMT language pairs. sampling fertilities parallel inference time non-autoregressive model achieves near-state-of-the-art performance 29.8 BLEU WMT 2016 English–Romanian Neural network based models outperform traditional statistical models machine translation MT BID0 BID9. However state-of-the-art neural models are much slower statistical MT approaches inference time BID16. model families use autoregressive decoders operate one step time:generate token conditioned sequence tokens previously generated. process is not parallelizable case neural MT models is particularly slow computationally intensive neural network is used generate token.While several recently proposed models avoid recurrence train time leveraging convolutions BID6 BID4 self-attention BID14 more-parallelizable alternatives recurrent neural networks RNNs use autoregressive decoding makes impossible take full advantage parallelism inference.We introduce non-autoregressive translation model based Transformer network BID14. modify encoder original Transformer network adding module predicts fertilities sequences numbers form important component many traditional machine translation models BID1. fertilities are supervised training provide decoder inference time globally consistent plan which to condition simultaneously computed outputs.,414,296,118,0.004,1.399,2025/11/05 17:18:59,0.0,1.333,0.2149532710280372,130.401
"While neural networks have achieved high accuracy on standard image classification benchmarks, their accuracy drops to nearly zero in the presence of small adversarial perturbations to test inputs. Defenses based on regularization and adversarial training have been proposed, but often followed by new, stronger attacks that defeat these defenses. Can we somehow end this arms race? In this work, we study this problem for neural networks with one hidden layer. We first propose a method based on a semidefinite relaxation that outputs a certificate that for a given network and test input, no attack can force the error to exceed a certain value. Second, as this certificate is differentiable, we jointly optimize it with the network parameters, providing an adaptive regularizer that encourages robustness against all attacks. On MNIST, our approach produces a network and a certificate that no that perturbs each pixel by at most $\epsilon = 0.1$ can cause more than $35\%$ test error.
 Despite the impressive (and sometimes even superhuman) accuracies of machine learning on diverse tasks such as object recognition BID18 , speech recognition BID55 , and playing Go BID46 , classifiers still fail catastrophically in the presence of small imperceptible but adversarial perturbations BID50 BID17 BID25 . In addition to being an intriguing phenonemon, the existence of such ""adversarial examples"" exposes a serious vulnerability in current ML systems BID13 BID45 . While formally defining an ""imperceptible"" perturbation is difficult, a commonly-used proxy is perturbations that are bounded in ∞ -norm BID17 BID31 BID53 ; we focus on this attack model in this paper, as even for this proxy it is not known how to construct high-performing image classifiers that are robust to perturbations.While a proposed defense (classifier) is often empirically shown to be successful against the set of attacks known at the time, new stronger attacks are subsequently discovered that render the defense useless. For example, defensive distillation BID42 and adversarial training against the Fast Gradient Sign Method BID17 were two defenses that were later shown to be ineffective against stronger attacks BID53 . In order to break this arms race between attackers and defenders, we need to come up with defenses that are successful against all attacks within a certain class.However, even computing the worst-case error for a given network against all adversarial perturbations in an ∞ -ball is computationally intractable. One common approximation is to replace the worst-case loss with the loss from a given heuristic attack strategy, such as the Fast Gradient Sign Method BID17 or more powerful iterative methods BID7 BID31 . Adversarial training minimizes the loss with respect to these heuristics. However, this essentially minimizes a lower bound on the worst-case loss, which is problematic since points where the bound is loose have disproportionately lower objective values, which could lure and mislead an optimizer. Indeed, while adversarial training often provides robustness against a specific attack, it often fails to generalize to new attacks, as described above. Another approach is to compute the worst-case perturbation exactly using discrete optimization BID21 (b) Figure 1 : Illustration of the margin function f (x) for a simple two-layer network. (a) Contours of f (x) in an ∞ ball around x. Sharp curvature near x renders a linear approximation highly inaccurate, and f (A fgsm (x)) obtained by maximising this approximation is much smaller than f (A opt (x)).(b ) Vector field for ∇f (x) with length of arrows proportional to ∇f (x) 1 . In our approach, we bound f (A opt (x)) by bounding the maximum of ∇f (x) 1 over the neighborhood (green arrow).In general, this could be very different from ∇f (x) 1 at just the point x (red arrow).et al., 2017) . Currently , these approaches can take up to several hours or longer to compute the loss for a single example even for small networks with a few hundred hidden units. Training a network would require performing this computation in the inner loop, which is infeasible.In this paper, we introduce an approach that avoids both the inaccuracy of lower bounds and the intractability of exact computation, by computing an upper bound on the worst-case loss for neural networks with one hidden layer, based on a semidefinite relaxation that can be computed efficiently. This upper bound serves as a certificate of robustness against all attacks for a given network and input. Minimizing an upper bound is safer than minimizing a lower bound, because points where the bound is loose have disproportionately higher objective values, which the optimizer will tend to avoid. Furthermore , our certificate of robustness, by virtue of being differentiable, is trainable-it can be optimized at training time jointly with the network, acting as a regularizer that encourages robustness against all ∞ attacks.In summary, we are the first (along with the concurrent work of BID24 ) to demonstrate a certifiable, trainable, and scalable method for defending against adversarial examples on two-layer networks. We train a network on MNIST whose test error on clean data is 4.2%, and which comes with a certificate that no attack can misclassify more than 35% of the test examples using ∞ perturbations of size = 0.1.Notation. For a vector z ∈ R n , we use z i to denote the i th coordinate of z. For a matrix Z ∈ R m×n , Z i denotes the i th row. For any activation function σ : R → R (e.g., sigmoid, ReLU) and a vector z ∈ R n , σ(z) is a vector in R n with σ(z) i = σ(z i ) (non-linearity is applied element-wise). We use B (z) to denote the ∞ ball of radius around z ∈ R d : B (z) = {z | |z i − z i | ≤ for i = 1, 2, . . . d}. Finally, we denote the vector of all zeros by 0 and the vector of all ones by 1. In this work, we proposed a method for producing certificates of robustness for neural networks, and for training against these certificates to obtain networks that are provably robust against adversaries.Related work. In parallel and independent work, BID24 also provide provably robust networks against ∞ perturbations by using convex relaxations. While our approach uses a single semidefinite program to compute an upper bound on the adversarial loss, Kolter & Wong (2017) use separate linear programs for every data point, and apply their method to networks of depth up to four. In theory, neither bound is strictly tighter than the other, and our experiments TAB2 suggest that the two bounds are complementary. Combining the approaches seems to be a promising future direction. BID21 and the follow-up BID10 also provide certificates of robustness for neural networks against ∞ perturbations. That work uses SMT solvers, which are a tool from the formal verification literature. The SMT solver can answer the binary question ""Is there an adversarial example within distance of the input x?"", and is correct whenever it terminates. The main drawback of SMT and similar formal verification methods is that they are slow-they have worst-case exponential-time scaling in the size of the network; moreover, to use them during training would require a separate search for each gradient step. BID20 use SMT solvers and are able to analyze state-of-the-art networks on MNIST, but they make various approximations such that their numbers are not true upper bounds. BID2 provide tractable certificates but require to be small enough to ensure that the entire ∞ ball around an input lies within the same linear region. For the networks and values of that we consider in our paper, we found that this condition did not hold. Recently, Hein & Andriushchenko (2017) proposed a bound for guaranteeing robustness to p -norm perturbations, based on the maximum p p−1 -norm of the gradient in the -ball around the inputs. BID19 show how to efficiently compute this bound for p = 2, as opposed to our work which focuses on ∞ and requires different techniques to achieve scalability. BID31 perform adversarial training against PGD on the MNIST and CIFAR-10 datasets, obtaining networks that they suggest are ""secure against first-order adversaries"". However, this is based on an empirical observation that PGD is nearly-optimal among gradient-based attacks, and does not correspond to any formal robustness guarantee.Finally, the notion of a certificate appears in the theory of convex optimization, but means something different in that context; specifically, it corresponds to a proof that a point is near the optimum of a convex function, whereas here our certificates provide upper bounds on non-convex functions. Additionally, while robust optimization BID3 provides a tool for optimizing objectives with robustness constraints, applying it directly would involve the same intractable optimization for A opt that we deal with here.Other approaches to verification. While they have not been explored in the context of neural networks, there are approaches in the control theory literature for verifying robustness of dynamical systems, based on Lyapunov functions (Lyapunov, 1892; BID29 . We can think of the activations in a neural network as the evolution of a time-varying dynamical system, and attempt to prove stability around a trajectory of this system BID51 BID52 . Such methods typically use sum-of-squares verification BID38 BID43 and are restricted to relatively low-dimensional dynamical systems, but could plausibly scale to larger settings. Another approach is to construct families of networks that are provably robust a priori, which would remove the need to verify robustness of the learned model; to our knowledge this has not been done for any expressive model families.Adversarial examples and secure ML. There has been a great deal of recent work on the security of ML systems; we provide only a sampling here, and refer the reader to BID0 , BID4 , BID41 , and BID14 for some recent surveys.Adversarial examples for neural networks were first discovered by BID50 , and since then a number of attacks and defenses have been proposed. We have already discussed gradientbased methods as well as defenses based on adversarial training. There are also other attacks based on, e.g., saliency maps BID40 , KL divergence BID33 , and elastic net optimization BID11 ; many of these attacks are collated in the cleverhans repository . For defense, rather than making networks robust to adversaries, some work has focused on simply detecting adversarial examples. However, BID7 recently showed that essentially all known detection methods can be subverted by strong attacks.As explained in BID0 , there are a number of different attack models beyond the testtime attacks considered here, based on different attacker goals and capabilities. For instance, one can consider data poisoning attacks, where an attacker modifies the training set in an effort to affect test-time performance. BID35 , BID26 , and BID5 have demonstrated poisoning attacks against real-world systems.Other types of certificates. Certificates of performance for machine learning systems are desirable in a number of settings. This includes verifying safety properties of air traffic control systems BID21 and self-driving cars (O' Kelly et al., 2016; , as well as security applications such as robustness to training time attacks BID48 . More broadly, certificates of performance are likely necessary for deploying machine learning systems in critical infrastructure such as internet packet routing BID54 BID47 . In robotics, certificates of stability are routinely used both for safety verification BID30 BID32 and controller synthesis BID1 BID51 .In traditional verification work, Rice's theorem BID44 ) is a strong impossibility result essentially stating that most properties of most programs are undecidable. Similarly, we should expect that verifying robustness for arbitrary neural networks is hard. However, the results in this work suggest that it is possible to learn neural networks that are amenable to verification, in the same way that it is possible to write programs that can be formally verified. Optimistically, given expressive enough certification methods and model families, as well as strong enough specifications of robustness, one could even hope to train vector representations of natural images with strong robustness properties, thus finally closing the chapter on adversarial vulnerabilities in the visual domain.",neural networks have achieved high accuracy standard image classification benchmarks accuracy drops nearly zero presence small adversarial perturbations test inputs. Defenses based regularization adversarial training have been proposed often followed new stronger attacks defeat defenses. Can we somehow end arms race? work study problem neural networks one hidden layer. first propose method based semidefinite relaxation outputs certificate given network test input attack can force error exceed certain value. Second certificate is differentiable jointly optimize network parameters providing adaptive regularizer encourages robustness attacks. MNIST approach produces network certificate perturbs pixel $\epsilon 0.1 can cause $35\ test error. Despite impressive sometimes even superhuman accuracies machine learning diverse tasks object recognition BID18 speech recognition BID55 playing Go BID46 classifiers still fail catastrophically presence small imperceptible adversarial perturbations BID50 BID17 BID25. addition intriguing phenonemon existence adversarial examples exposes serious vulnerability current ML systems BID13 BID45. formally defining imperceptible perturbation is difficult commonly-used proxy is perturbations are bounded ∞ -norm BID17 BID31 BID53;focus attack model paper even proxy is not known how to construct high-performing image classifiers are robust perturbations.While proposed defense classifier is often empirically shown successful set attacks known time new stronger attacks are subsequently discovered render defense useless. example defensive distillation BID42 adversarial training Fast Gradient Sign Method BID17 were two defenses were later shown ineffective stronger attacks BID53. order break arms race attackers defenders need come defenses are successful attacks within certain class.However even computing worst-case error given network adversarial perturbations ∞ -ball is computationally intractable. One common approximation is to replace worst-case loss loss given heuristic attack strategy Fast Gradient Sign Method BID17 powerful iterative methods BID7 BID31. Adversarial training minimizes loss respect heuristics. However essentially minimizes lower bound worst-case loss which is problematic since points where the bound is loose have disproportionately lower objective values could lure mislead optimizer. Indeed adversarial training often provides robustness specific attack often fails generalize new attacks described above. Another approach is to compute worst-case perturbation exactly using discrete optimization BID21 b Figure1:Illustration margin functionf x simple two-layer network. Contours f x ∞ ball aroundx. Sharp curvature nearx renders linear approximation highly inaccurate f fgsm x obtained maximising approximation is much smaller f opt x b Vector field ∇f x length arrows proportional ∇f x 1. approach boundf opt x bounding maximum ∇f x 1 neighborhood green arrow.In general could different ∇f x 1 pointx red arrow.etal. 2017 Currently are approaches can take several hours longer compute loss single example even small networks hundred hidden units. Training network would require performing computation inner loop which is infeasible.In paper introduce approach avoids inaccuracy lower bounds intractability exact computation computing upper bound worst-case loss neural networks one hidden layer is based semidefinite relaxation can be computed efficiently. upper bound serves certificate robustness attacks given network input. Minimizing upper bound is safer minimizing lower bound points where the bound is loose have disproportionately higher objective values which the optimizer will tend avoid. Furthermore certificate robustness virtue differentiable is trainable-it can be optimized training time jointly network acting regularizer encourages robustness ∞ attacks.In summary are the first along concurrent work BID24 demonstrate certifiable trainable scalable method defending adversarial examples two-layer networks. train network MNIST whose test error clean data is 4.2 4.2 which comes certificate attack can misclassify 35% test examples using∞ perturbations size 0. 1.Notation. vectorz∈R n usez denote th coordinate z. matrixZ∈R m×n Z denotes th row. activation functionσ:R→R e.g sigmoid ReLU is a vectorz∈R n σ z is a vector Rn σ z σ z non-linearity is applied element-wise useB z denote ∞ ball radius aroundz∈ R d:B z z |z −z ≤ 1 2 Finally denote vector zeros 0 vector ones 1. work proposed method producing certificates robustness neural networks training certificates obtain networks are provably robust adversaries.Related work. parallel independent work BID24 also provide provably robust networks ∞ perturbations using convex relaxations. approach uses single semidefinite program compute upper bound adversarial loss Kolter Wong 2017 use separate linear programs every data point apply method networks depth four. theory neither bound is strictly tighter experiments TAB2 suggest two bounds are complementary. Combining approaches seems promising future direction. BID21 follow-up BID10 also provide certificates robustness neural networks ∞ perturbations. work uses SMT solvers which are a tool formal verification literature. SMT solver can answer binary question Is there an adversarial example within distance inputx? is correct whenever terminates. main drawback SMT similar formal verification methods is that they are slow-they have worst-case exponential-time scaling size network;moreover use training would require separate search gradient step. BID20 use SMT solvers are able analyze state-of-the-art networks MNIST make various approximations numbers are not true upper bounds. BID2 provide tractable certificates require small enough ensure entire ∞ ball around input lies within linear region. networks values consider paper found condition did not hold. Recently Hein Andriushchenko 2017 proposed bound guaranteeing robustness p -norm perturbations is based maximum p p−1 -norm gradient -ball around inputs. BID19 show how to efficiently compute bound p 2 opposed work which focuses ∞ requires different techniques achieve scalability. BID31 perform adversarial training PGD MNIST CIFAR-10 datasets obtaining networks suggest are secure first-order adversaries. However is based empirical observation PGD is nearly-optimal among gradient-based attacks does not correspond formal robustness guarantee.Finally notion certificate appears theory convex optimization means something different context;specifically corresponds proof point is near optimum convex function whereas certificates provide upper bounds non-convex functions. Additionally robust optimization BID3 provides tool optimizing objectives robustness constraints applying directly would involve intractable optimization opt deal here.Other approaches verification. have not explored context neural networks are approaches control theory literature verifying robustness dynamical systems is based Lyapunov functions Lyapunov 1892;BID29. can think activations neural network evolution time-varying dynamical system attempt prove stability around trajectory system BID51 BID52. methods typically use sum-of-squares verification BID38 BID43 are restricted relatively low-dimensional dynamical systems could plausibly scale larger settings. Another approach is to construct families networks are provably robust priori would remove need verify robustness learned model;knowledge has not been done expressive model families.Adversarial examples secureML. has been a great deal recent work security ML systems;provide sampling refer reader BID0 BID4 BID41 BID14 recent surveys.Adversarial examples neural networks were first discovered BID50 since number attacks defenses have been proposed. have already discussed gradientbased methods well defenses based adversarial training. are also attacks based e.g saliency maps BID40 KL divergence BID33 elastic net optimization BID11;many attacks are collated cleverhans repository. defense rather making networks robust adversaries work has focused simply detecting adversarial examples. However BID7 recently showed essentially known detection methods can be subverted strong attacks.As explained BID0 are a number different attack models beyond testtime attacks considered based different attacker goals capabilities. instance one can consider data poisoning attacks where an attacker modifies training set effort affect test-time performance. BID35 BID26 BID5 have demonstrated poisoning attacks real-world systems.Other types certificates. Certificates performance machine learning systems are desirable number settings. includes verifying safety properties air traffic control systems BID21 self-driving cars O' Kellyetal. 2016;well security applications robustness training time attacks BID48. broadly certificates performance are likely necessary deploying machine learning systems critical infrastructure internet packet routing BID54 BID47. robotics certificates stability are routinely used safety verification BID30 BID32 controller synthesis BID1 BID51.In traditional verification work Rice's theorem BID44 is a strong impossibility result essentially stating properties programs are undecidable. Similarly should expect verifying robustness arbitrary neural networks is hard. However results work suggest is possible learn neural networks are amenable verification way is possible write programs can be formally verified. Optimistically given expressive enough certification methods model families well strong enough specifications robustness one could even hope train vector representations natural images strong robustness properties thus finally closing chapter adversarial vulnerabilities visual domain.,2523,1697,826,0.038,1.487,2025/11/05 17:18:59,0.01,1.435,0.4890965732087229,895.259
"We formulate an information-based optimization problem for supervised classification. For invertible neural networks, the control of these information terms is passed down to the latent features and parameter matrix in the last fully connected layer, given that mutual information is invariant under invertible map.   We propose an objective function and prove that it solves the optimization problem. Our framework allows us to learn latent features in an more interpretable form while improving the classification performance. We perform extensive quantitative and qualitative experiments in comparison with the existing state-of-the-art classification models. Quantities of information are nonlinear measures capable of describing complex relationship between unstructured data and they form the basis of the probabilistic algorithms in the literature of machine learning. Information theoretic methods are also reported to be effective on improving deep generative models BID6 ; Kim & Mnih (2018) ) and deep learning models for classification (Grandvalet & Bengio (2004) ; Pereyra et al. (2017) ). Information Bottleneck (IB) problem BID12 ) is formulated as: DISPLAYFORM0 where the solution random variable T is interpreted as a minimal sufficient representation of signal X for label Y and the mutual information is defined as DISPLAYFORM1 p(x, y) log p(x, y) p(x)p(y ) dydx .The term I(X; T ) has its origins in Lossy Compression and Rate-Distortion Theory (Cover & BID7 , conveying an simple idea of ""keep only what is relevant"".However, Saxe et al. (2018) argued that the mutual information I(X; T ) between signal X and feature T in intermediate layer is infinite, as the transformation from X to continuous random variable T is deterministic. In addition they showed experimentally that layers equipped with ReLU actually do not compress too much information, which is supported by many recent work on the invertibility of the neural network BID8 ; Jacobsen et al. (2018) ). This motivates us to consider a different problem with similar principle idea: we would like to establish a theoretically valid objective that allows the neural network to extract only the relevant information for classification from the data.We focus on the discrete prediction random variable Y inferred by the probabilistic model P( Y |X) and introduce the following information optimization problem for supervised classification:maximize I(Y ; Y ) subject to I(X; Y ) − I(Y ; Y ) < τ , for some τ > 0 .The intuition behind this objective lies in twofold:Information perspective: A good classification model should be robust against irrelevant features of X, and prevent over-fitting in the learning process. In optimization problem (3) we maximize the relevant information I(Y ; Y ), while constraining the irrelevant information I(X; Y ) − I(Y ; Y )that X has about Y . Although I(X; Y ) − I(Y ; Y ) converges to zero as I(Y ; Y ) approaching its maximum (see FIG0 ), in practice it's never attained due to the limited capacity of the models or over-fitting. Our proposed constrain addresses the problem of over-fitting: if two models achieve the similar classification accuracy, this constraint prefers the one that does not overfit to spurious factors of variation in X (e.g., pixel-level artifact/noise in the image that accidentally correlates to the labels in the training data).Prediction confidence perspective : A good classification model should not be certain about its decision which is in fact wrong. However, modern neural networks are too confident in their predictions (Guo et al., 2017; Szegedy et al., 2015; Pereyra et al., 2017) . To be more precise, high capacity neural networks mostly assign labels of data with prediction confidence near 0 or 1. In particular, they assign 0 probability to some correct labels and therefore do not have enough flexibility to correct themselves from making the wrong prediction. We propose to compress the irrelevant information I(X; Y ) − I(Y ; Y ), where minimizing I(X; Y ) decreases the confidence on all predictions but maximizing I(Y ; Y ) increases the confidence on the correct predictions. Therefore the overall effect reduces the certainty on the false prediction of Y (see FIG0 ).To solve this optimization problem, we first present some insights on the dynamics of deep neural network, which can be decomposed into two stages: (i) Transformation stage: samples {X k } k=1:n of the high dimensional unstructured signal X are transformed under the deep invertible (information preserving) feature map F to become (almost) linearly separable; (ii) Classification stage: the weight matrix w in the last fully connected layer together with the Softmax function, takes structured features {F (X k )} k=1:n as input and gives predictions.Invertibility of F allows neural networks to pass the control of I(X; Y ) = I(F (X); Y ) towards F (X) and w in the last layer, where F (X) can be interpreted as transformed signal that preserves information about the original signal X and the inference model becomes conceptually linear with classifier w (see FIG0 ). In Section 2 we derive objective function (7) and prove that it solves the optimization problem (3). We show the classification performance is improved in Section 4.1 and the features F (X) are sculpted into a form with more interpretability entry-wise in Section 4.2. . The optimal solution is obtained when the smaller disks coincide , which is typically not achieved in practice. In particular, the trained model may be extremely confident in its prediction (when H( Y ) lies inside of H(X)), but predicts the wrong label (having large grey area). Our optimization problem explicitly prohibits the growth of grey area throughout the training. (R) Logic chart of our formulation: our proposed optimization problem only involves F (X) and w, allowing us to have control over the latent feature F (X) directly.The invertibility property has been empirically demonstrated for complex non-linear deep neural networks that are widely used in practice. We will discuss the literature in Section 3. In addition, we prove in Proposition C.1 that a lower bound of classification error is minimized if neural network is invertible.Our contribution: Our contribution lies in the following: (i) we formulated a novel information optimization problem for supervised classification; (ii) we propose a simple objective function that improves supervised deep learning with better performance and interpretability; (iii) we formally justify the use of 1 , 2 regularization from an information perspective. Different from the naive regularization on w, our regularization on w T F (X) is novel and effective. We give an interpretation of the deep learning dynamics by decomposing it into an signal transformation stage and feature classification stage, where we emphasis importance of the classifier w in the last fully connected layer given that the feature map F is invertible. Then we take the advantage of the fact that mutual information quantities are invariance under invertible mapping to attack our proposed information optimization problem for supervised classification in deep learning. Our theory justifies the use of direct regularization terms on w, F (X) for neural networks with invertibility property. Our regularization improves the performance of neural networks by a noticeable margin and is capable of encouraging the interpretability of the entries of features learned in the last layer.A PROOF OF PROPOSITION 2.1 Proposition 2.1 establishes a connection between I(X, Y ) and the absolute value of the logits |w T F (X)| for the binary case. Intuitively, decreasing the confidence of the model on its predictions will decrease the mutual information I(X; Y ).Proposition 2.1. I(X; Y ) = I(F (X); Y ) is well estimated by its empirical version (Montecarlo approximation) with high probability, which shares the same unique (global) minimum with DISPLAYFORM0 The mutual information I(X; Y ) is given as DISPLAYFORM1 Apply the assumption (II), the marginal distribution of Y is uniformly distributed: DISPLAYFORM2 Substituting FORMULA16 into FORMULA15 yields DISPLAYFORM3 According to the Hoeffding's inequality for bounded random variables [Proposition 2.2.6, Vershynin FORMULA0 ], let M, m denote upper and lower bounds of the integrand of (10) correspondingly, we have DISPLAYFORM4 Equivalently, with probability at least 1 − δ, DISPLAYFORM5 Here n k=1 y∈C p( y|x k ) log(2p( y|x k ))/n is a Monte carlo estimation of RHS of I(X; Y ). Recall that , for the binary case p( y|x) = p( y|F (x)) can expressed as DISPLAYFORM6 Then we have DISPLAYFORM7 which is bounded by [0, log(2)].Take M = log(2 ), m = 0, we have DISPLAYFORM8 hold with probability at least 1 − δ.The conclusion follows from the fact that n k=1 y∈C p( y|x k ) log(2p( y|x k ))/n has a unique global minimum at w T F (x k ) = 0 for each x k .",formulate information-based optimization problem supervised classification. invertible neural networks control information terms is passed latent features parameter matrix last fully connected layer given mutual information is invariant invertible map. propose objective function prove solves optimization problem. framework allowsus learn latent features interpretable form improving classification performance. perform extensive quantitative qualitative experiments comparison existing state-of-the-art classification models. Quantities information are nonlinear measures capable describing complex relationship unstructured data form basis probabilistic algorithms literature machine learning. Information theoretic methods are also reported effective improving deep generative models BID6;Kim Mnih 2018 deep learning models classification Grandvalet Bengio 2004 Pereyraetal. 2017 Information Bottleneck IB problem BID12 is formulated as:DISPLAYFORM0 where the solution random variable is interpreted minimal sufficient representation signalX label mutual information is defined DISPLAYFORM1p x logp x p x p dydx.The term X;has its origins Lossy Compression Rate-Distortion Theory Cover BID7 conveying simple idea keep what is relevant.However Saxeetal. 2018 argued mutual information X;signalX feature intermediate layer is infinite transformation X continuous random variable is deterministic. addition showed experimentally layers equipped ReLU actually do not compress much information which is supported many recent work invertibility neural network BID8;Jacobsenetal. 2018 motivatesus consider different problem similar principle idea:would like establish theoretically valid objective allows neural network extract relevant information classification data.We focus discrete prediction random variable inferred probabilistic modelP |X introduce following information optimization problem supervised classification:maximize Y;subject X;− Y;τ τ 0.The intuition behind objective lies twofold:Information perspective:good classification model should be robust irrelevant features X prevent over-fitting learning process. optimization problem 3 maximize relevant information Y;constraining irrelevant information X;− Y;X has aboutY. Although X;− Y;converges zero Y;approaching maximum see FIG0 practice never attained due limited capacity models over-fitting proposed constrain addresses problem over-fitting if two models achieve similar classification accuracy constraint prefers one does not overfit spurious factors variation X e.g pixel-level artifact/noise image accidentally correlates labels training data.Prediction confidence perspective:good classification model should not be certain decision which is in fact wrong. However modern neural networks are too confident predictions Guoetal. 2017;Szegedyetal. 2015;Pereyraetal. 2017 precise high capacity neural networks mostly assign labels data prediction confidence near0 1. particular assign 0 probability correct labels therefore do not have enough flexibility correct making wrong prediction. propose compress irrelevant information X;− Y;where minimizing X;decreases confidence predictions maximizing Y;increases confidence correct predictions. Therefore overall effect reduces certainty false prediction see FIG0.To solve optimization problem first present insights dynamics deep neural network which can be decomposed two stages:Transformation stage:samples Xk k=1n high dimensional unstructured signal X are transformed deep invertible information preserving feature mapF become almost linearly separable;ii Classification stage:weight matrixw last fully connected layer together Softmax function takes structured features F Xk k=1n input gives predictions.Invertibility F allows neural networks pass control X;F X towardsF X w last layer whereF X can be interpreted transformed signal preserves information original signalX inference model becomes conceptually linear classifierw see FIG0 Section2 derive objective function 7 prove solves optimization problem 3 show classification performance is improved Section 4.1 featuresF X are sculpted form interpretability entry-wise Section 4.2 optimal solution is obtained when the smaller disks coincide which is typically achieved practice. particular trained model may extremely confident prediction whenH lies inside H X predicts wrong label large grey area optimization problem explicitly prohibits growth grey area throughout training. R Logic chart formulation:proposed optimization problem involvesF X w allowingus have control latent featureF X directly.The invertibility property has been empirically demonstrated complex non-linear deep neural networks are widely used practice. will discuss literature Section3. addition prove Proposition C.1 lower bound classification error is minimized if neural network is invertible.Our contribution:contribution lies following:formulated novel information optimization problem supervised classification;ii propose simple objective function improves supervised deep learning better performance interpretability;iii formally justify use 1 2 regularization information perspective. Different naive regularization w regularization w F X is novel effective. give interpretation deep learning dynamics decomposing signal transformation stage feature classification stage where we emphasis importance classifierw last fully connected layer given feature mapF is invertible. take advantage fact mutual information quantities are invariance invertible mapping attack proposed information optimization problem supervised classification deep learning. theory justifies use direct regularization terms w whereF X neural networks invertibility property. regularization improves performance neural networks noticeable margin is capable encouraging interpretability entries features learned last layer.A PROOF PROPOSITION 2.1 Proposition 2.1 establishes connection X absolute value logits|w F X binary case. Intuitively decreasing confidence model predictions will decrease mutual information X;.Proposition 2.1 X;F X is well estimated empirical version Montecarlo approximation high probability which shares unique global minimum DISPLAYFORM0 mutual information X;is given DISPLAYFORM1 Apply assumption II marginal distribution is uniformly distributed:DISPLAYFORM2 Substituting FORMULA16 FORMULA15 yields DISPLAYFORM3 According Hoeffding's inequality bounded random variables Proposition 2.2.6 Vershynin FORMULA0 let denote upper lower bounds integrand 10 correspondingly have DISPLAYFORM4 Equivalently probability least1−δ DISPLAYFORM5 n k=1 y∈Cp y|xk log 2p y|xk/n is a Monte carlo estimation RHS X;Recall binary casep y|x p y|F x can expressed DISPLAYFORM6 have DISPLAYFORM7 which is bounded 0 log 2.Take log 2 0 have DISPLAYFORM8 hold probability least1−δ.The conclusion follows fact n k=1 y∈Cp y|xk log 2p y|xk/n has a unique global minimum w F xk 0 xk.,1894,1247,647,0.031,1.519,2025/11/05 17:18:59,0.01,1.439,0.5887850467289715,691.967
"Powerful generative models, particularly in Natural Language Modelling, are commonly trained by maximizing a variational lower bound on the data log likelihood. These models often suffer from poor use of their latent variable, with ad-hoc annealing factors used to encourage retention of information in the latent variable. We discuss an alternative and general approach to latent variable modelling, based on an objective that encourages a perfect reconstruction by tying a stochastic autoencoder with a variational autoencoder (VAE). This ensures by design that the latent variable captures information about the observations, whilst retaining the ability to generate well. Interestingly, although our model is fundamentally different to a VAE, the lower bound attained is identical to the standard VAE bound but with the addition of a simple pre-factor; thus, providing a formal interpretation of the commonly used, ad-hoc pre-factors in training VAEs. Generative latent variable models are probabilistic models of observed data x of the form p(x, z) = p(x|z)p(z), where z is the latent variable. These models are widespread in machine learning and statistics. They are useful both because of their ability to generate new data and because the posterior p(z|x) provides insight into the low dimensional representation z corresponding to the high dimensional observation x. These latent z values are then often used in downstream tasks, such as topic modelling BID2 , multi-modal language modeling BID8 , and image captioning BID9 BID10 .Latent variable models, particularly in the form of Variational Autoencoders (VAEs) BID7 BID11 , have been successfully employed in natural language modelling tasks using varied architectures for both the encoder and the decoder BID0 BID2 BID12 BID16 BID13 . However , an architecture that is able to effectively capture meaningful semantic information into its latent variables is yet to be discovered.A VAE approach to language modelling was given by BID0 , the graphical model for which is shown in FIG0 (a). This forms a generative model p(x|z)p(z) of sentence x, based on latent variable z. Since the integral p(x) = p(x|z)p(z)dz is typically intractable, a common approach is to maximize the Evidence Lower Bound (ELBO) on the log likelihood, log p(x) ≥ log p(x|z) q(z|x) − D KL [q(z|x)||p(z)]where · q(z|x) is the expectation with respect to the variational distribution q(z|x), and D KL [·||·] represents the Kullback-Leibler (KL) divergence. Summing over all datapoints x gives a lower bound on the likelihood of the full dataset.In language modelling, typically both the generative model (decoder) p(x|z), and variational distribution (encoder) q(z|x), are parameterised using an LSTM recurrent neural networksee for example BID0 . This autoregressive generative model is so powerful that the maximum ELBO is achieved without making appreciable use of the latent variable in the model. Indeed, if trained using the SGVB algorithm BID7 , the model learns to ignore the latent representation and effectively relies solely on the decoder to generate good sentences. This is evidenced by the KL term in the objective function converging to zero, indicating that the approximate posterior distribution of the latent variable is trivially converging to its prior distribution.The dependency between what is represented by latent variables, and the capacity of the decoding distribution (i.e., its ability to model the data without using the latent) is a general phenomenon. BID16 used a lower capacity dilated CNN decoder to generate sentences, preventing the KL term going to zero. BID3 ; BID4 have discussed this in the context of image processing. A clear explanation of this phenomenon in terms of Bit-Back Coding is given in BID1 .A mechanism to avoid the model ignoring the latent entirely, while allowing a high capacity decoder is discussed in BID0 and uses an alternative training procedure called ""KL annealing"" -slowly turning on the KL term in the ELBO during training. KL annealing allows the model to use its latent variable to some degree by forcing the model into a local maximum of its objective function. Modifying the training procedure in this way to preferentially obtain local maxima suggests that the objective function used in BID0 may not be ideal for modelling language in such a way as to create a model that leverages its latent variables. We have seen that AutoGen successfully improves the fidelity of reconstructions from the latent variable as compared to VAEs. It does so in a principled way, by explicitly modelling both generation of the data and high-fidelity reconstruction. This is especially useful when the generative model is powerful, such as the autoregressive LSTM in BID0 .Other work toward enabling latent variables in VAE models to learn meaningful representations has focused on managing the structure of the representation, such as ensuring disentanglement. A detailed discussion of disentanglement in the context of VAEs is given by BID4 and its references. An example of disentangling representations in the context of image generation is BID3 , where the authors restrict the decoding model to describe only local information in the image (e.g., texture, shading), allowing their latents to describe global information (e.g., object geometry, overall color).Demanding high-fidelity reconstructions from latent variables in a model (e.g., AutoGen) is in tension with demanding specific information to be stored in the latent variables (e.g., disentanglement). This can be seen very clearly by comparing our work to BID4 , where the authors introduce an ad-hoc factor of β in front of the KL-divergence term of the VAE objective function, the ELBO. They find that β > 1 is required to improve the disentanglement of their latent representations.Interestingly, β > 1 corresponds analytically to −1 < m < 0 in Equation 9, since the overall normalization of the objective function does not impact the location of its extrema. That is, Equation 9 is equivalent to the β-VAE objective function with β = (1 + m) −1 .Since m in AutoGen represents the number of times a high-fidelity reconstruction is demanded (in addition to a single generation from the prior), β-VAE with β > 1 is analytically equivalent to demanding a negative number of high-fidelity reconstructions. As an analytic function of m, with larger m corresponding to higher-fidelity reconstructions, negative m would correspond to a deprecation of the reconstruction quality. This is indeed what the authors in BID4 find and discuss. They view β-VAE as a technique to trade off more disentangled representations at the cost of lower-fidelity reconstructions, in contrast to our view of AutoGen as a technique to trade off higher-fidelity reconstructions at the cost of slightly inferior generation from the prior.In connecting to β-VAE, we have considered AutoGen with m as a real number. Practically, m could take positive real values, and can be seen as a hyperparameter that requires taskspecific tuning. From our results, we expect m ≈ 1 to be a useful ballpark value, with smaller m improving generation from the prior, and larger m improving reconstruction fidelity. The advantage of tuning m as described is that it has a principled interpretation at integer values; namely that of demanding m exact reconstructions from the latent, as derived in Section 2.In this light, KL annealing amounts to starting with m = ∞ at the beginning, and smoothly reducing m down to 0 during training. Thus, it is equivalent to optimizing the AutoGen lower bound given in Equation 9 with varying m during training. However, AutoGen should never require KL annealing.Scaling of the ELBO is common in multimodal generation, where the reconstruction terms are typically of different orders of magnitude BID14 BID15 . AutoGen can be adapted to provide a bound on a meaningful objective function in multimodal generation with well-scaled terms, by requiring a larger number of reconstructions for one data modality than the other. Autogen thus has broader applications in generative modelling, which the authors leave to future work. In this paper, we introduced AutoGen: a novel modelling approach to improve the descriptiveness of latent variables in generative models, by combining the log likelihood of m high-fidelity reconstructions via a stochastic autoencoder, with the log likelihood of a VAE. This approach is theoretically principled in that it retains a bound on a meaningful objective, and computationally amounts to a simple factor of (1 + m) in front of the reconstruction term in the standard ELBO. We find that the most natural version of AutoGen (with m = 1) provides significantly better reconstructions than the VAE approach to language modelling, and only minimally deprecates generation from the prior.","Powerful generative models particularly Natural Language Modelling are commonly trained maximizing variational lower bound data log likelihood. models often suffer poor use latent variable ad-hoc annealing factors used encourage retention information latent variable. discuss alternative general approach latent variable modelling based objective encourages perfect reconstruction tying stochastic autoencoder variational autoencoder VAE ensures design latent variable captures information observations whilst retaining ability generate well. Interestingly although model is fundamentally different VAE lower bound attained is identical standard VAE bound addition simple pre-factor thus providing formal interpretation commonly used ad-hoc pre-factors training VAEs. Generative latent variable models are probabilistic models observed datax formp x z p x|z p z wherez is the latent variable. models are widespread machine learning statistics. are useful ability generate new data posteriorp z|x provides insight low dimensional representationz corresponding high dimensional observationx. latent z values are then often used downstream tasks topic modelling BID2 multi-modal language modeling BID8 image captioning BID9 BID10.Latent variable models particularly form Variational Autoencoders VAEs BID7 BID11 have been successfully employed natural language modelling tasks using varied architectures encoder decoder BID0 BID2 BID12 BID16 BID13. However architecture is able effectively capture meaningful semantic information latent variables is yet discovered.A VAE approach language modelling was given BID0 graphical model which is shown FIG0 forms generative modelp x|z p z sentencex based latent variablez. Since integralp x p x|z p z dz is typically intractable common approach is to maximize Evidence Lower Bound ELBO log likelihood logp x ≥ logp x|z q z|x − KL q z|x ||p z where·q z|x is the expectation respect variational distributionq z|x KL ·||· represents Kullback-Leibler KL divergence. Summing datapoints x gives lower bound likelihood full dataset.In language modelling typically generative model decoder p x|z variational distribution encoder q z|x are parameterised using LSTM recurrent neural networksee example BID0. autoregressive generative model is so is powerful maximum ELBO is achieved without making appreciable use latent variable model. Indeed if trained using SGVB algorithm BID7 model learns ignore latent representation effectively relies solely decoder generate good sentences. is evidenced KL term objective function converging zero indicating approximate posterior distribution latent variable is trivially converging prior distribution.The dependency what is represented latent variables capacity decoding distribution.e ability model data without using latent is a general phenomenon. BID16 used lower capacity dilated CNN decoder generate sentences preventing KL term going zero. BID3;BID4 have discussed context image processing. clear explanation phenomenon terms Bit-Back Coding is given BID1.A mechanism avoid model ignoring latent entirely allowing high capacity decoder is discussed BID0 uses alternative training procedure called KL annealing -slowly turning KL term ELBO training. KL annealing allows model use latent variable degree forcing model local maximum objective function. Modifying training procedure way preferentially obtain local maxima suggests objective function used BID0 may ideal modelling language way create model leverages latent variables. have seen AutoGen successfully improves fidelity reconstructions latent variable compared VAEs. doessoin principled way explicitly modelling generation data high-fidelity reconstruction. is especially useful when the generative model is so is powerful autoregressive LSTM BID0.Other work toward enabling latent variables VAE models learn meaningful representations has focused managing structure representation ensuring disentanglement. detailed discussion disentanglement context VAEs is given BID4 references. example disentangling representations context image generation is BID3 where the which the authors restrict decoding model describe local information image e.g texture shading allowing latents describe global information e.g object geometry overall color.Demanding high-fidelity reconstructions latent variables model e.g AutoGen is in tension demanding specific information stored latent variables e.g disentanglement can seen clearly comparing work BID4 where the which the authors introduce ad-hoc factor β front KL-divergence term VAE objective function ELBO. find β 1 is required improve disentanglement latent representations.Interestingly β 1 corresponds analytically −1 0 Equation9 since overall normalization objective function does not impact location extrema. is,Equation9 is equivalent β-VAE objective function β 1+−1.Since AutoGen represents number times high-fidelity reconstruction is demanded addition single generation prior β-VAE β 1 is analytically equivalent demanding negative number high-fidelity reconstructions. analytic function larger corresponding higher-fidelity reconstructions negative would correspond deprecation reconstruction quality. is indeed what the authors BID4 find discuss. view β-VAE technique trade disentangled representations cost lower-fidelity reconstructions contrast view AutoGen technique trade higher-fidelity reconstructions cost slightly inferior generation prior.In connecting β-VAE have considered AutoGen real number. Practically could take positive real values can be seen hyperparameter requires taskspecific tuning. results expect ≈1 useful ballpark value smaller improving generation prior larger improving reconstruction fidelity. advantage tuning described is that it has principled interpretation integer values;namely demanding exact reconstructions latent derived Section 2.In light KL annealing amounts starting ∞ beginning smoothly reducing 0 training. Thus is equivalent optimizing AutoGen lower bound given Equation9 varying training. However AutoGen should never require KL annealing.Scaling ELBO is common multimodal generation where the reconstruction terms are typically different orders magnitude BID14 BID15. AutoGen can be adapted provide bound meaningful objective function multimodal generation well-scaled terms requiring larger number reconstructions one data modality other. Autogen thus has broader applications generative modelling where the which the authors leave future work. paper introduced AutoGen:novel modelling approach improve descriptiveness latent variables generative models combining log likelihood high-fidelity reconstructions via stochastic autoencoder log likelihood VAE. approach is theoretically principled retains bound meaningful objective computationally amounts simple factor 1+front reconstruction term standard ELBO. find natural version AutoGen 1 provides significantly better reconstructions VAE approach language modelling minimally deprecates generation prior.",1811,1213,598,0.024,1.493,2025/11/05 17:18:59,0.01,1.407,0.5077881619937696,566.757
"This paper studies the problem of domain division which aims to segment instances drawn from different probabilistic distributions. This problem exists in many previous recognition tasks, such as Open Set Learning (OSL) and Generalized Zero-Shot Learning (G-ZSL), where the testing instances come from either seen or unseen/novel classes with different probabilistic distributions. Previous works only calibrate the confident prediction of classifiers of seen classes (WSVM Scheirer et al. (2014)) or taking unseen classes as outliers Socher et al. (2013). In contrast, this paper proposes a probabilistic way of directly estimating and fine-tuning the decision boundary between seen and unseen classes. In particular, we propose a domain division algorithm to split the testing instances into known, unknown and uncertain domains, and then conduct recognition tasks in each domain. Two statistical tools, namely, bootstrapping and KolmogorovSmirnov (K-S) Test, for the first time, are introduced to uncover and fine-tune the decision boundary of each domain. Critically, the uncertain domain is newly introduced in our framework to adopt those instances whose domain labels cannot be predicted confidently. Extensive experiments demonstrate that our approach achieved the state-of-the-art performance on OSL and G-ZSL benchmarks. This paper discusses the problem of learning to separate two domains which include the instances sampled from different distributions. This is a typical and general research topic that can be potentially used in various recognition tasks, such as Open Set Learning (OSL) and Generalized Zero-Shot Learning (G-ZSL). Particularly, OSL can break the constraints of the closed set in supervised learning, and aim at recognizing the testing instances from one of the seen classes (i.e., known domain), and the novel class (i.e., unknown domain). The novel classes include the testing instances which have different distributions from that of the seen ones. In contrast, G-ZSL targets at distinguishing the labels of instances from the seen and unseen classes. Only the seen classes have the training instances, but unseen classes do not. Note that OSL does not explicitly give the class labels for those instances categorized as the novel class, but G-ZSL requires predicting the class labels of unseen classes. To address G-ZSL, semantic attributes or vectors are introduced as the intermediate representations; each (seen/unseen) class has one semantic prototype that contains class level information. Specifically, a reasonable solution of OSL and G-ZSL is via dividing the known and unknown domains. For training classes, the predictors are constructed to map visual features to the class label space (OSL), (or semantic space (G-ZSL)). Testing is performed on each separated domain to identify seen classes and the novel class (OSL), or both seen and unseen classes (G-ZSL).The key question of OSL and ZSL is how to deal with the newly introduced novel class/unseen classes efficiently in the testing time. This is different from the conventional Zero-Shot Learning (ZSL) task which assumes that, in the testing stage, seen classes would not be misclassified as unseens, and vice versa; ZSL only uses the unseen classes for testing. Unfortunately , the predictors learned on training classes will inevitably make OSL or G-ZSL approaches tend to be biased towards the seen classes, and thus leading to very poor classification results for the novel class (OSL) or unseen classes (G-ZSL) BID39 ; . We show an example in Fig. 1 . On aPY dataset (described in Sec. 6.1) BID10 ), t-SNE van der Maaten & Hinton (2008 is The initial boundary of the known domain is estimated by bootstrapping. We can further divide an uncertain domain by K-S Test. Then we can recognize instances in each domain. (b) The distribution of pairwise intraclass and interclass distances: We compute the empirical density of the pairwise distance in aPY dataset (described in Sec. 6.1). There is a large overlapping of the distribution of the intraclass and interclass distances.employed to visualize the distributions of the testing instances of the ResNet-101 features in BID39 (Fig. 1 (a) ), and semantic features learned by SAE Kodirov et al. (2017) (Fig. 1 (b) ). We categorize the SAE prediction as known or unknown domain labels and compare with the groundtruth in Fig. 1(c) . We show that a large portion of unseen instances being predicted as one of the known classes.A natural recipe for addressing this problem is to learn to separate domains by the distributions of instances; and different classifiers can be directly applied in each domain. However, there are still two key problems. First , visual features alone are not discriminative enough to help to distinguish the seen and unseen/novel classes. As Fig. 2 (a) , bicycle and motorbike, respectively , are one of the seen and unseen classes 1 in aPY dataset (described in Sec. 6.1). We can observe that there is a large overlapping region between their t-SNE visualized feature distributions. That is, the visual features may not be representative enough to differentiate these two classes; the instances of motorbike (circled as the uncertain domain) may be taken as the bicycle, or vice versa; Second, the predictors trained on seen classes may be not trustworthy. A not well-trained predictor may negatively affect the recognition algorithms. Third and even worse, the performance of classifiers in each domain is still very sensitive to the results of domain separation: should the domain of one testing instance be wrongly divided, it would never be correctly categorized by the classifiers.To tackle the aforementioned issues, our key insight (see Fig. 2(a) ) is to introduce a novel domain -uncertain domain that accounts for the overlapping regions of testing instances from seen or novel/unseen classes. Thus, the visual or semantic space can be learned to be divided into known, unknown and uncertain domains. The recognition algorithms will be directly employed in each domain . Nonetheless, how to divide the domains based on known information is also a non-trivial task. Though the supervised classifiers can learn the patterns of known classes, not all classes encountered during testing are known.Formally, we propose exploiting the distribution information of seen and novel/unseen classes to efficiently learn to divide the domains from a probabilistic perspective. Our domain separation algorithm has two steps: the initial division of domains by bootstrapping, and fine-tuning by the Kolmogorov-Smirnov test. Specifically, according to extreme value theory BID30 , the maximum/minimum confidence scores predicted by the classifier of each class can be taken as an extreme value distribution. Since we do not have the prior knowledge of the underlying data distributions of each class; bootstrapping is introduced here as an asymptotically consistent method in estimating an initial boundary of known classes. Nevertheless, the initial boundary estimated by bootstrapping is too relaxed to include novel testing instances as is illustrated in Fig. 2(b) . To finetune the boundary, we exploit the K-S Test to validate whether the learned predictors are trustworthy in a specific region. The uncertain domain introduced thus accounts for those testing instances whose labels are hard to be judged. Recognition models can be conducted in each domain. This paper learns to divide the instances into known, unknown and uncertain domains for the recognition tasks from a probabilistic perspective. The domain division procedure consists of bootstrapping and K-S Test steps. The bootstrapping is used to set an initial threshold for each class; we further employ the K-S test to fine-tune the boundary. Such a domain division algorithm can be used for OSL and G-ZSL tasks, and achieves remarkable results.","paper studies problem domain division which aims segment instances drawn different probabilistic distributions. problem exists many previous recognition tasks Open Set Learning OSL Generalized Zero-Shot Learning G-ZSL where the testing instances come either seen unseen/novel classes different probabilistic distributions. Previous works calibrate confident prediction classifiers seen classes WSVM Scheireretal. 2014 taking unseen classes outliers Socheretal. 2013 contrast paper proposes probabilistic way directly estimating fine-tuning decision boundary seen unseen classes. particular propose domain division algorithm split testing instances known unknown uncertain domains conduct recognition tasks domain. Two statistical tools namely bootstrapping KolmogorovSmirnov K-S Test first time are introduced uncover fine-tune decision boundary domain. Critically uncertain domain is newly introduced framework adopt instances whose domain labels cannot predicted confidently. Extensive experiments demonstrate approach achieved state-of-the-art performance OSL G-ZSL benchmarks. paper discusses problem learning separate two domains which include instances sampled different distributions. is a typical general research topic can be potentially used various recognition tasks Open Set Learning OSL Generalized Zero-Shot Learning G-ZSL Particularly OSL can break constraints closed set supervised learning aim recognizing testing instances one seen classes.e known domain novel class.e unknown domain novel classes include testing instances which have different distributions seen ones. contrast G-ZSL targets distinguishing labels instances seen unseen classes. seen classes have the training instances unseen classes do not. Note OSL does not explicitly give class labels instances categorized novel class G-ZSL requires predicting class labels unseen classes. address G-ZSL semantic attributes vectors are introduced intermediate representations;seen/unseen class has one semantic prototype contains class level information. Specifically reasonable solution OSL G-ZSL is via dividing known unknown domains. training classes predictors are constructed map visual features class label space OSL semantic space G-ZSL Testing is performed separated domain identify seen classes novel class OSL seen unseen classes G-ZSL.The key question OSL ZSL is how to deal newly introduced novel class/unseen classes efficiently testing time. is different conventional Zero-Shot Learning ZSL task which assumes testing stage seen classes would misclassified unseens vice versa;ZSL uses unseen classes testing. Unfortunately predictors learned training classes will inevitably make OSL G-ZSL approaches tend biased towards seen classes thus leading poor classification results novel class OSL unseen classes G-ZSL BID39;show example Fig. 1. aPY dataset described Sec. 6.1 BID10 t-SNE van der Maaten Hinton 2008 is The initial boundary known domain is estimated bootstrapping. can further divide uncertain domain K-S Test. can recognize instances domain. b distribution pairwise intraclass interclass distances:compute empirical density pairwise distance aPY dataset described Sec. 6.1 is large overlapping distribution intraclass interclass distances.employed visualize distributions testing instances ResNet-101 features BID39 Fig. 1 semantic features learned SAE Kodirovetal. 2017 Fig. 1 b categorize SAE prediction known unknown domain labels compare groundtruth Fig. 1 c show is a large portion unseen instances predicted one known classes.A natural recipe addressing problem is to learn separate domains distributions instances;different classifiers can be directly applied domain. However are still two key problems. First visual features alone are not discriminative enough help distinguish seen unseen/novel classes. Fig. 2 bicycle motorbike respectively are one seen unseen classes1 aPY dataset described Sec. 6.1 can observe is a large overlapping region t-SNE visualized feature distributions. is,the visual features may representative enough differentiate two classes;instances motorbike circled uncertain domain may taken bicycle vice versa;Second predictors trained seen classes may trustworthy. well-trained predictor may negatively affect recognition algorithms. Third even worse performance classifiers domain is still sensitive results domain separation:should the domain one testing instance wrongly divided would never correctly categorized classifiers.To tackle aforementioned issues key insight see Fig. 2 isto introduce novel domain -uncertain domain accounts overlapping regions testing instances seen novel/unseen classes. Thus visual semantic space can be learned divided known unknown uncertain domains. recognition algorithms will be directly employed domain. Nonetheless how to divide domains based known information is also non-trivial task. Though supervised classifiers can learn patterns known classes classes encountered testing are known.Formally propose exploiting distribution information seen novel/unseen classes efficiently learn divide domains probabilistic perspective. domain separation algorithm has two steps:initial division domains bootstrapping fine-tuning Kolmogorov-Smirnov test. Specifically according extreme value theory BID30 maximum/minimum confidence scores predicted classifier class can be taken extreme value distribution. Since do not have prior knowledge underlying data distributions class;bootstrapping is introduced asymptotically consistent method estimating initial boundary known classes. Nevertheless initial boundary estimated bootstrapping is too relaxed include novel testing instances is illustrated Fig. 2 b finetune boundary exploit K-S Test validate whether learned predictors are trustworthy specific region. uncertain domain introduced thus accounts testing instances whose labels are hard judged. Recognition models can be conducted domain. paper learns divide instances known unknown uncertain domains recognition tasks probabilistic perspective. domain division procedure consists bootstrapping K-S Test steps. bootstrapping is used set initial threshold class;employ K-S test fine-tune boundary. domain division algorithm can be used OSL G-ZSL tasks achieves remarkable results.",1592,1078,514,0.019,1.477,2025/11/05 17:18:59,0.01,1.5,0.4579439252336449,494.745
"Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average potential over the posterior distribution of weights along with an entropic regularization term. This potential is however not the original loss function in general. So SGD does perform variational inference, but for a different loss than the one used to compute the gradients. Even more surprisingly, SGD does not even converge in the classical sense: we show that the most likely trajectories of SGD for deep networks do not behave like Brownian motion around critical points. Instead, they resemble closed loops with deterministic components. We prove that such out-of-equilibrium behavior is a consequence of highly non-isotropic gradient noise in SGD; the covariance matrix of mini-batch gradients for deep networks has a rank as small as 1% of its dimension. We provide extensive empirical validation of these claims, proven in the appendix. Our first result is to show precisely in what sense stochastic gradient descent (SGD) implicitly performs variational inference, as is often claimed informally in the literature. For a loss function f (x) with weights x ∈ R d , if ρ ss is the steady-state distribution over the weights estimated by SGD, DISPLAYFORM0 where H(ρ) is the entropy of the distribution ρ and η and b are the learning rate and batch-size, respectively. The potential Φ(x), which we characterize explicitly, is related but not necessarily equal to f (x). It is only a function of the architecture and the dataset. This implies that SGD implicitly performs variational inference with a uniform prior, albeit of a different loss than the one used to compute back-propagation gradients.We next prove that the implicit potential Φ(x) is equal to our chosen loss f (x) if and only if the noise in mini-batch gradients is isotropic. This condition, however, is not satisfied for deep networks. Empirically, we find gradient noise to be highly non-isotropic with the rank of its covariance matrix being about 1% of its dimension. Thus, SGD on deep networks implicitly discovers locations where ∇Φ(x) = 0, these are not the locations where ∇ f (x) = 0. This is our second main result: the most likely locations of SGD are not the local minima, nor the saddle points, of the original loss. The deviation of these critical points, which we compute explicitly scales linearly with η/b and is typically large in practice.When mini-batch noise is non-isotropic, SGD does not even converge in the classical sense. We prove that, instead of undergoing Brownian motion in the vicinity of a critical point, trajectories have a deterministic component that causes SGD to traverse closed loops in the weight space. We detect such loops using a Fourier analysis of SGD trajectories. We also show through an example that SGD with non-isotropic noise can even converge to stable limit cycles around saddle points. The continuous-time point-of-view used in this paper gives access to general principles that govern SGD, such analyses are increasingly becoming popular BID61 BID9 . However, in practice, deep networks are trained for only a few epochs with discrete-time updates. Closing this gap is an important future direction. A promising avenue towards this is that for typical conditions in practice such as small mini-batches or large learning rates, SGD converges to the steady-state distribution quickly BID48 . Let F(ρ) be as defined in (11). In non-equilibrium thermodynamics, it is assumed that the local entropy production is a product of the force −∇ δ F δ ρ from (A8) and the probability current −J(x,t) from (FP). This assumption in this form was first introduced by BID46 based on the works of BID41 BID40 . See Frank (2005, Sec. 4 .5) for a mathematical treatment and Jaynes (1980) for further discussion. The rate of entropy (S i ) increase is given by DISPLAYFORM0 This can now be written using (A8) again as DISPLAYFORM1 The first term in the above expression is non-negative, in order to ensure that DISPLAYFORM2 where the second equality again follows by integration by parts. It can be shown (Frank, 2005, Sec. 4.5.5 ) that the condition in Assumption 4, viz., ∇ · j(x) = 0, is sufficient to make the above integral vanish and therefore for the entropy generation to be non-negative.C SOME PROPERTIES OF THE FORCE jThe Fokker-Planck equation (FP) can be written in terms of the probability current as DISPLAYFORM3 Since we have ρ ss ∝ e −β Φ(x) , from the observation (7), we also have that DISPLAYFORM4 and consequently, DISPLAYFORM5 In other words, the conservative force is non-zero only if detailed balance is broken, i.e., J ss = 0. We also have DISPLAYFORM6 which shows using Assumption 4 and ρ ss (x) > 0 for all x ∈ Ω that j(x) is always orthogonal to the gradient of the potential DISPLAYFORM7 Using the definition of j(x) in (8), we have detailed balance when DISPLAYFORM8",Stochastic gradient descent SGD is widely believed perform implicit regularization when used train deep neural networks precise manner which this occurs has thus far elusive. prove SGD minimizes average potential posterior distribution weights along entropic regularization term. potential is however original loss function general. SGD does perform variational inference different loss one used compute gradients. Even surprisingly SGD does not even converge classical sense:show likely trajectories SGD deep networks do not behave like Brownian motion around critical points. Instead resemble closed loops deterministic components. prove out-of-equilibrium behavior is a consequence highly non-isotropic gradient noise SGD;covariance matrix mini-batch gradients deep networks has a rank small 1% dimension. provide extensive empirical validation claims proven appendix. first result is to show precisely what sense stochastic gradient descent SGD implicitly performs variational inference is often claimed informally literature. loss functionf x weightsx∈R ifρss is the steady-state distribution weights estimated SGD DISPLAYFORM0 whereH ρ is the entropy distributionρ η b are the learning rate batch-size respectively. potentialΦ x which we characterize explicitly is related necessarily equal f x is function architecture dataset. implies SGD implicitly performs variational inference uniform prior albeit different loss one used compute back-propagation gradients.We next prove implicit potentialΦ x is equal chosen lossf x if and only if the noise mini-batch gradients is isotropic. condition however is not satisfied deep networks. Empirically find gradient noise highly non-isotropic rank covariance matrix 1% dimension. Thus SGD deep networks implicitly discovers locations where∇Φ x 0 are not locations where∇f x 0. is our second main result:likely locations SGD are not the local minima saddle points original loss. deviation critical points which we compute explicitly scales linearly η/b is typically large practice.When mini-batch noise is non-isotropic SGD does not even converge classical sense. prove instead undergoing Brownian motion vicinity critical point trajectories have a deterministic component causes SGD traverse closed loops weight space. detect loops using Fourier analysis SGD trajectories. also show example SGD non-isotropic noise can even converge stable limit cycles around saddle points. continuous-time point-of-view used paper gives access general principles govern SGD analyses are increasingly becoming popular BID61 BID9. However practice deep networks are trained epochs discrete-time updates. Closing gap is an important future direction. promising avenue towards is that for typical conditions practice small mini-batches large learning rates SGD converges steady-state distribution quickly BID48. LetF ρ defined 11 non-equilibrium thermodynamics is assumed local entropy production is a product force−∇δF δρ A8 probability current−J x FP assumption form was first introduced BID46 based works BID41 BID40. See Frank 2005 Sec. 4.5 mathematical treatment Jaynes 1980 discussion. rate entropy increase is given DISPLAYFORM0 can now be written using A8 DISPLAYFORM1 first term expression is non-negative order ensure DISPLAYFORM2 where the second equality follows integration parts. can be shown Frank 2005 Sec. 4.5.5 condition Assumption4 viz. ∇·j x 0 is sufficient make integral vanish therefore entropy generation non-negative.C PROPERTIES FORCE jThe Fokker-Planck equation FP can be written terms probability current DISPLAYFORM3 Since haveρss∝e −βΦ x observation 7 also have that DISPLAYFORM4 consequently DISPLAYFORM5 words conservative force is non-zero if detailed balance is broken.e Jss 0. also have DISPLAYFORM6 which shows using Assumption4 ρss x 0 x∈Ω j x is always orthogonal gradient potential DISPLAYFORM7 Using definition j x 8 have detailed balance when DISPLAYFORM8,1093,745,348,0.014,1.467,2025/11/05 17:19:00,0.01,1.5,0.4267912772585671,346.483
"The current dominant paradigm for imitation learning relies on strong supervision of expert actions to learn both 'what' and 'how' to imitate. We pursue an alternative paradigm wherein an agent first explores the world without any expert supervision and then distills its experience into a goal-conditioned skill policy with a novel forward consistency loss. In our framework, the role of the expert is only to communicate the goals (i.e., what to imitate) during inference. The learned policy is then employed to mimic the expert (i.e., how to imitate) after seeing just a sequence of images demonstrating the desired task. Our method is 'zero-shot' in the sense that the agent never has access to expert actions during training or for the task demonstration at inference. We evaluate our zero-shot imitator in two real-world settings: complex rope manipulation with a Baxter robot and navigation in previously unseen office environments with a TurtleBot. Through further experiments in VizDoom simulation, we provide evidence that better mechanisms for exploration lead to learning a more capable policy which in turn improves end task performance. Videos, models, and more details are available at https://pathak22.github.io/zeroshot-imitation/.",current dominant paradigm imitation learning relies strong supervision expert actions learn 'what' 'how' imitate. pursue alternative paradigm wherein agent first explores world without expert supervision distills experience goal-conditioned skill policy novel forward consistency loss. framework role expert is only to communicate goals.e what to how to imitate inference. learned policy is then employed mimic expert.e what to how to imitate seeing sequence images demonstrating desired task. method is 'zero-shot' sense agent never has access expert actions training task demonstration inference. evaluate zero-shot imitator two real-world settings:complex rope manipulation Baxter robot navigation previously unseen office environments TurtleBot. experiments VizDoom simulation provide evidence better mechanisms exploration lead learning capable policy which in turn improves end task performance. Videos models details are available https://pathak22.github.io/zeroshot-imitation/.,235,160,75,0.002,1.469,2025/11/05 17:19:00,0.0,1.75,0.4330218068535826,91.924
"Distributional Semantics Models(DSM) derive word space from linguistic items
 in context. Meaning is obtained by defining a distance measure between vectors
 corresponding to lexical entities. Such vectors present several problems. This
 work concentrates on quality of word embeddings, improvement of word embedding
 vectors, applicability of a novel similarity metric used ‘on top’ of the
 word embeddings. In this paper we provide comparison between two methods
 for post process improvements to the baseline DSM vectors. The counter-fitting
 method which enforces antonymy and synonymy constraints into the Paragram
 vector space representations recently showed improvement in the vectors’ capability
 for judging semantic similarity. The second method is our novel RESM
 method applied to GloVe baseline vectors. By applying the hubness reduction
 method, implementing relational knowledge into the model by retrofitting synonyms
 and providing a new ranking similarity definition RESM that gives maximum
 weight to the top vector component values we equal the results for the ESL
 and TOEFL sets in comparison with our calculations using the Paragram and Paragram
 + Counter-fitting methods. For SIMLEX-999 gold standard since we cannot
 use the RESM the results using GloVe and PPDB are significantly worse compared
 to Paragram. Apparently, counter-fitting corrects hubness. The Paragram
 or our cosine retrofitting method are state-of-the-art results for the SIMLEX-999
 gold standard. They are 0.2 better for SIMLEX-999 than word2vec with sense
 de-conflation (that was announced to be state-of the-art method for less reliable
 gold standards). Apparently relational knowledge and counter-fitting is more important
 for judging semantic similarity than sense determination for words. It is to
 be mentioned, though that Paragram hyperparameters are fitted to SIMLEX-999
 results. The lesson is that many corrections to word embeddings are necessary
 and methods with more parameters and hyperparameters perform better.
 Distributional language models are frequently used to measure word similarity in natural language. This is a basis for many semantic tasks. The DSM often consists of a set of vectors; each vector corresponds to a character string, which represents a word. BID14 and BID19 implemented the most commonly used word embedding (WE) algorithms. Vector components in language models created by these algorithms are latent. Similarity between words is defined as a function of vectors corresponding to given words. The cosine measure is the most frequently used similarity function, although many other functional forms were attempted. BID25 highlights the fact that the cosine can be outperformed by ranking based functions.As pointed out by many works, e.g. , evidence suggests that distributional models are far from perfect.Vector space word representations obtained from purely distributional information of words in large unlabeled corpora are not enough to best the state-of-the-art results in query answering benchmarks, because they suffer from several types of weaknesses: 3. Appearance of hubness that distorts distances between vectors, 4. Inability of distinguishing from antonyms. 5. In case of retrofitting distortion vector space -loss of information contained in the original vectorsIn this paper we use the existing word embedding model but with several post process enhancement techniques. We address three of these problems. In particular, we define a novel similarity measure, dedicated for language models.Similarity is a function, which is monotonically opposite to distance. As the distance between two given entities gets shorter, entities are more similar. This holds for language models. Similarity between words is equal to similarity between their corresponding vectors. There are various definitions of distance. The most common Euclidean distance is defined as follows: DISPLAYFORM0 Similarity based on the Euclidean definition is inverse to the distance: DISPLAYFORM1 Angular definition of distance is defined with cosine function: DISPLAYFORM2 We define angular similarity as: DISPLAYFORM3 Both Euclidean and Cosine definitions of distance could be looked at as the analysis of vector components. Simple operations, like addition and multiplication work really well in low dimensional spaces. We believe, that applying those metrics in spaces of higher order is not ideal, hence we compare cosine similarity to a measure of distance dedicated for high dimensional spaces.In this paper we restrict ourselves to three gold standards: TOEFL, ESL and SIMLEX-999. The first two are small but reliably annotated (and therefore confidence in their performance can be assumed 100%). Other used benchmarks suffer from several drawbacks. Both WS- 353 Finkelstein et al. (2001) and MEN Bruni et al. (2012) do not measure the ability of models to reflect similarity. Moreover, as pointed out by , for WS-353, RG Rubenstein & Goodenough (1965) and MEN, state-of-the-art models have reached the average performance of a human annotator on these evaluations. This work compares the state-of-the-art word embedding methods for three most reliable gold standards: TOEFL, ESL and SIMLEX-999. For TOEFL and ESL the GloVe, PPDB baseline with retrofitting, our novel RESM similarity measure and hubness reduction we are able to equal the Paragram results. For SIMLEX-999 Paragram with Counter-fitting results are clearly better than the Glove based methods using the PPDB 1.0. However, we propose the cosine retrofitting that basically achieves the Paragram with Counter-fitting results. The Paragram with Counter-fitting method contains several hyperparameters which is one source of its success. Its effects can be seen in TAB0 at https://arxiv.org/pdf/1506.03487.pdf. The Spearman ρ values for SIMLEX-999 are 0.667 for Paragram300 fitted to WS353, and 0.685 for Paragram300 fitted to SIMLEX-999. The difference is even larger for WS353. Then the Spearman ρ values for WS-353 are 0. 769 for Paragram300 fitted toWS353, and 0.720 for Paragram300 fitted to SIMLEX-999. Still the best word embedding based methods are not able to achieve the performance of other dedicated methods for TOEFL and ESL. The work of BID13 employed 2 fitting constants (and it is not clear that they were the same for all questions) for answering the TOEFL test where only 50 questions are used. Techniques introduced in the paper are lightweight and easy to implement, yet they provide a significant performance boost to the language model. Since the single word embedding is a basic element of any semantic task one can expect a significant improvement of results for these tasks. In particular, SemEval-2017 International Workshop on Semantic Evaluation run (among others) the following tasks(se2):1. Task 1: Semantic Textual Similarity 2. Task 2: Multilingual and Cross-lingual Semantic Word Similarity 3. Task 3: Community Question Answering in the category Semantic comparison for words and texts. Another immediate application would be information retrieval (IR). Expanding queries by adding potentially relevant terms is a common practice in improving relevance in IR systems. There are many methods of query expansion. Relevance feedback takes the documents on top of a ranking list and adds terms appearing in these document to a new query. In this work we use the idea to add synonyms and other similar terms to query terms before the pseudo-relevance feedback. This type of expansion can be divided into two categories. The first category involves the use of ontologies or lexicons (relational knowledge). The second category is word embedding (WE). Here closed words for expansion have to be very precise, otherwise a query drift may occur, and precision and accuracy of retrieval may deteriorate. There are several avenues to further improve the similarity results.1. Use the multi-language version of the methods (e.g. Recski et al. FORMULA0 2. Use PPDB 2.0 to design the Paragram vectors BID18 3. Apply the multi-sense methods (knowledge graps) with state-of-the-art relational enriched vectors 4. Recalibrate annotation results using state-of-the-art results.",Distributional Semantics Models DSM derive word space linguistic items context. Meaning is obtained defining distance measure vectors corresponding lexical entities. vectors present several problems. work concentrates quality word embeddings improvement word embedding vectors applicability novel similarity metric used top word embeddings. paper provide comparison two methods post process improvements baseline DSM vectors. counter-fitting method which enforces antonymy synonymy constraints Paragram vector space representations recently showed improvement vectors capability judging semantic similarity. second method is our novel RESM method applied GloVe baseline vectors. applying hubness reduction method implementing relational knowledge model retrofitting synonyms providing new ranking similarity definition RESM gives maximum weight top vector component values equal results ESL TOEFL sets comparison calculations using Paragram Paragram+Counter-fitting methods. SIMLEX-999 gold standard since cannot use RESM results using GloVe PPDB are significantly worse compared Paragram. Apparently counter-fitting corrects hubness. Paragram cosine retrofitting method are state-of-the-art results SIMLEX-999 gold standard. are 0.2 better SIMLEX-999 word2vec sense de-conflation was announced state-of the-art method less reliable gold standards Apparently relational knowledge counter-fitting is more important judging semantic similarity sense determination words. is to be mentioned though Paragram hyperparameters are fitted SIMLEX-999 results. lesson is that many corrections word embeddings are necessary methods parameters hyperparameters perform better. Distributional language models are frequently used measure word similarity natural language. is a basis many semantic tasks. DSM often consists set vectors;vector corresponds character string which represents word. BID14 BID19 implemented commonly used word embedding algorithms. Vector components language models created algorithms are latent. Similarity words is defined function vectors corresponding given words. cosine measure is the most frequently used similarity function although many functional forms were attempted. BID25 highlights fact cosine can be outperformed ranking based functions.As pointed many works e.g evidence suggests distributional models are far perfect.Vector space word representations obtained purely distributional information words large unlabeled corpora are not enough best state-of-the-art results query answering benchmarks suffer several types weaknesses:3. Appearance hubness distorts distances vectors 4. Inability distinguishing antonyms. 5. case retrofitting distortion vector space -loss information contained original vectorsIn paper use existing word embedding model several post process enhancement techniques. address three problems. particular define novel similarity measure dedicated language models.Similarity is a function which is monotonically opposite distance. distance two given entities gets shorter entities are more similar. holds language models. Similarity words is equal similarity corresponding vectors. are various definitions distance. common Euclidean distance is defined follows:DISPLAYFORM0 Similarity based Euclidean definition is inverse distance:DISPLAYFORM1 Angular definition distance is defined cosine function:DISPLAYFORM2 define angular similarity as:DISPLAYFORM3 Euclidean Cosine definitions distance could looked analysis vector components. Simple operations like addition multiplication work really well low dimensional spaces. believe applying metrics spaces higher order is not ideal hence compare cosine similarity measure distance dedicated high dimensional spaces.In paper restrict three gold standards:TOEFL ESL SIMLEX-999 first two are small reliably annotated therefore confidence performance can be assumed 100% used benchmarks suffer several drawbacks. WS- 353 Finkelsteinet al. 2001 MEN Brunietal. 2012 do not measure ability models reflect similarity. Moreover pointed WS-353 RG Rubenstein Goodenough 1965 MEN state-of-the-art models have reached average performance human annotator evaluations. work compares state-of-the-art word embedding methods three reliable gold standards:TOEFL ESL SIMLEX-999 TOEFL ESL GloVe PPDB baseline retrofitting novel RESM similarity measure hubness reduction are able equal Paragram results. SIMLEX-999 Paragram Counter-fitting results are clearly better Glove based methods using PPDB 1.0 However propose cosine retrofitting basically achieves Paragram Counter-fitting results. Paragram Counter-fitting method contains several hyperparameters which is one source success. effects can be seen TAB0 https://arxiv.org/pdf/1506.03487.pdf. Spearman ρ values SIMLEX-999 are 0.667 Paragram300 fitted WS353 0.685 Paragram300 fitted SIMLEX-999 difference is even larger WS353. Spearman ρ values WS-353 are0. 769 Paragram300 fitted toWS353 0.720 Paragram300 fitted SIMLEX-999 Still best word embedding based methods are not able achieve performance dedicated methods TOEFL ESL. work BID13 employed 2 fitting constants is clear were the questions answering TOEFL test where only 50 questions are used. Techniques introduced paper are lightweight easy implement yet provide significant performance boost language model. Since single word embedding is a basic element semantic task one can expect significant improvement results tasks. particular SemEval-2017 International Workshop Semantic Evaluation run among others following tasks se2:1 Task1:Semantic Textual Similarity2. Task2:Multilingual Cross-lingual Semantic Word Similarity 3. Task3:Community Question Answering category Semantic comparison words texts. Another immediate application would information retrieval IR Expanding queries adding potentially relevant terms is a common practice improving relevance IR systems. are many methods query expansion. Relevance feedback takes documents top ranking list adds terms appearing document new query. work use idea add synonyms similar terms query terms pseudo-relevance feedback. type expansion can be divided two categories. first category involves use ontologies lexicons relational knowledge second category is word embedding closed words expansion have to be very precise otherwise query drift may occur precision accuracy retrieval may deteriorate. are several avenues improve similarity results.1 Use multi-language version methods e.g Recskiet al. FORMULA02. Use PPDB 2.0 design Paragram vectors BID183. Apply multi-sense methods knowledge graps state-of-the-art relational enriched vectors 4. Recalibrate annotation results using state-of-the-art results.,1653,1189,464,0.015,1.39,2025/11/05 17:19:00,0.01,1.5,0.1869158878504667,475.842
"Recurrent neural networks have achieved excellent performance in many applications. However, on portable devices with limited resources, the models are often too large to deploy. For applications on the server with large scale concurrent requests, the latency during inference can also be very critical for costly computing resources. In this work, we address these problems by quantizing the network, both weights and activations, into multiple binary codes {-1,+1}. We formulate the quantization as an optimization problem. Under the key observation that once the quantization coefficients are fixed the binary codes can be derived efficiently by binary search tree, alternating minimization is then applied.   We test the quantization for two well-known RNNs, i.e., long short term memory (LSTM) and gated recurrent unit (GRU), on the language models. Compared with the full-precision counter part, by 2-bit quantization we can achieve ~16x memory saving and  ~6x real inference acceleration on CPUs, with only a reasonable loss in the accuracy. By 3-bit quantization, we can achieve almost no loss in the accuracy or even surpass the original model, with ~10.5x memory saving and ~3x real inference acceleration. Both results beat the exiting quantization works with large margins.   We extend our alternating quantization to image classification tasks. In both RNNs and feedforward neural networks, the method also achieves  excellent performance. Recurrent neural networks (RNNs) are specific type of neural networks which are designed to model the sequence data. In last decades, various RNN architectures have been proposed, such as LongShort-Term Memory (LSTM) BID9 and Gated Recurrent Units BID0 . They have enabled the RNNs to achieve state-of-art performance in many applications, e.g., language models (Mikolov et al., 2010) , neural machine translation BID21 , automatic speech recognition BID5 , image captions BID23 , etc. However, the models often build on high dimensional input/output,e.g., large vocabulary in language models, or very deep inner recurrent networks, making the models have too many parameters to deploy on portable devices with limited resources. In addition, RNNs can only be executed sequentially with dependence on current hidden states. This causes large latency during inference. For applications in the server with large scale concurrent requests, e.g., on-line machine translation and speech recognition, large latency leads to limited requests processed per machine to meet the stringent response time requirements. Thus much more costly computing resources are in demand for RNN based models.To alleviate the above problems, several techniques can be employed, i.e., low rank approximation (Sainath et al., 2013; BID14 BID16 BID22 , sparsity BID19 BID7 , and quantization. All of them are build on the redundancy of current networks and can be combined. In this work, we mainly focus on quantization based methods. More precisely, we are to quantize all parameters into multiple binary codes {−1, +1}.The idea of quantizing both weights and activations is firstly proposed by BID11 . It has shown that even 1-bit binarization can achieve reasonably good performance in some visual classification tasks. Compared with the full precision counterpart, binary weights reduce the memory by a factor of 32. And the costly arithmetic operations between weights and activations can then be replaced by cheap XNOR and bitcount operations BID11 , which potentially leads to much acceleration. Rastegari et al. (2016) further incorporate a real coefficient to compensate for the binarization error. They apply the method to the challenging ImageNet dataset and achieve better performance than pure binarization in BID11 . However, it is still of large gap compared with the full precision networks. To bridge this gap, some recent works BID12 BID29 further employ quantization with more bits and achieve plausible performance. Meanwhile, quite an amount of works, e.g., BID3 BID30 BID6 , quantize the weights only. Although much memory saving can be achieved, the acceleration is very limited in modern computing devices (Rastegari et al., 2016) .Among all existing quantization works, most of them focus on convolutional neural networks (CNNs) while pay less attention to RNNs. As mentioned earlier, the latter is also very demanding. Recently, BID10 showed that binarized LSTM with preconditioned coefficients can achieve promising performance in some easy tasks such as predicting the next character. However, for RNNs with large input/output , e.g., large vocabulary in language models, it is still very challenging for quantization. Both works of BID12 and BID28 test the effectiveness of their multi-bit quantized RNNs to predict the next word. Although using up to 4-bits, the results with quantization still have noticeable gap with those with full precision. This motivates us to find a better method to quantize RNNs . The main contribution of this work is as follows:(a) We formulate the multi-bit quantization as an optimization problem . The binary codes {−1, +1} are learned instead of rule-based. For the first time, we observe that the codes can be optimally derived by the binary search tree once the coefficients are knowns in advance, see, e.g., Algorithm 1. Thus the whole optimization is eased by removing the discrete unknowns , which are very difficult to handle. (b) We propose to use alternating minimization to tackle the quantization problem. By separating the binary codes and real coefficients into two parts, we can solve the subproblem efficiently when one part is fixed. With proper initialization, we only need two alternating cycles to get high precision approximation, which is effective enough to even quantize the activations on-line. (c) We systematically evaluate the effectiveness of our alternating quantization on language models.Two well-known RNN structures, i.e., LSTM and GRU, are tested with different quantization bits. Compared with the full-precision counterpart, by 2-bit quantization we can achieve ∼16× memory saving and ∼6× real inference acceleration on CPUs, with a reasonable loss on the accuracy. By 3-bit quantization, we can achieve almost no loss in accuracy or even surpass the original model with ∼10.5× memory saving and ∼3× real inference acceleration. Both results beat the exiting quantization works with large margins. To illustrate that our alternating quantization is very general to extend, we apply it to image classification tasks. In both RNNs and feedforward neural networks, the technique still achieves very plausible performance. In this work, we address the limitations of RNNs, i.e., large memory and high latency, by quantization. We formulate the quantization by minimizing the approximation error. Under the key observation that some parameters can be singled out when others fixed, a simple yet effective alternating method is proposed. We apply it to quantize LSTM and GRU on language models. By 2-bit weights and activations, we achieve only a reasonably accuracy loss compared with full precision one, with ∼16× reduction in memory and ∼6× real acceleration on CPUs. By 3-bit quantization, we can attain compatible or even better result than the full precision one, with ∼10.5× reduction in memory and ∼3× real acceleration. Both beat existing works with a large margin. We also apply our alternating quantization to image classification tasks. In both RNNs and feedforward neural networks, the method can still achieve very plausible performance. In this section, we discuss the implementation of the binary multiplication kernel in CPUs. The binary multiplication is divided into two steps: Entry-wise XNOR operation (corresponding to entry-wise product in the full precision multiplication) and bit count operation for accumulation (corresponding to compute the sum of all multiplied entries in the full precision multiplication). We test it on Intel Xeon E5-2682 v4 @ 2.50 GHz CPU. For the XNOR operation, we use the Single instruction, multiple data (SIMD) _mm256 _xor _ps, which can execute 256 bit simultaneously. For the bit count operation, we use the function _popcnt64 (Note that this step can further be accelerated by the up-coming instruction _mm512 _popcnt_epi64 , which can execute 512 bits simultaneously. Similarly, the XNOR operation can also be further accelerated by the up-coming _mm512 _xor _ps instruction to execute 512 bits simultaneously). We compare with the much optimized Intel Math Kernel Library (MKL) on full precision matrix vector multiplication and execute all codes in the single-thread mode. We conduct two scales of experiments: a matrix of size 4096 × 1024 multiplying a vector of size 1024 and a matrix of size 42000 × 1024 multiplying a vector of size 1024, which respectively correspond to the hidden state product W h h t−1 and the softmax layer W s h t for Text8 dataset during inference with batch size of 1 (See Eq. (6)). The results are shown in TAB6 . We can see that our alternating quantization step only accounts for a small portion of the total executing time, especially for the larger scale matrix vector multiplication. Compared with the full precision one, the binary multiplication can roughly achieve 6× acceleration with 2-bit quantization and 3× acceleration with 3-bit quantization. Note that this is only a simple test on CPU. Our alternating quantization method can also be extended to GPU, ASIC, and FPGA.",Recurrent neural networks have achieved excellent performance many applications. However portable devices limited resources models are often large deploy. applications server large scale concurrent requests latency inference can also critical costly computing resources. work address problems quantizing network weights activations multiple binary codes -1+1 formulate quantization optimization problem. key observation quantization coefficients are fixed binary codes can be derived efficiently binary search tree alternating minimization is then applied. test quantization two well-known RNNs.e long short term memory LSTM gated recurrent unit GRU language models. Compared full-precision counter part 2-bit quantization can achieve ~16x memory saving ~6x real inference acceleration CPUs reasonable loss accuracy. 3-bit quantization can achieve almost loss accuracy even surpass original model ~10.5x memory saving ~3x real inference acceleration. results beat exiting quantization works large margins. extend alternating quantization image classification tasks. RNNs feedforward neural networks method also achieves excellent performance. Recurrent neural networks RNNs are specific type neural networks which are designed model sequence data. last decades various RNN architectures have been proposed LongShort-Term Memory LSTM BID9 Gated Recurrent Units BID0. have enabled RNNs achieve state-of-art performance many applications e.g language models Mikolovetal. 2010 neural machine translation BID21 automatic speech recognition BID5 image captions BID23 etc. However models often build high dimensional input/output e.g large vocabulary language models deep inner recurrent networks making models have too many parameters deploy portable devices limited resources. addition RNNs can only be executed sequentially dependence current hidden states. causes large latency inference. applications server large scale concurrent requests e.g on-line machine translation speech recognition large latency leads limited requests processed per machine meet stringent response time requirements. Thus much costly computing resources are in demand RNN based models.To alleviate problems several techniques can be employed.e low rank approximation Sainathetal. 2013;BID14 BID16 BID22 sparsity BID19 BID7 quantization. are build redundancy current networks can be combined. work mainly focus quantization based methods. precisely are to quantize parameters multiple binary codes −1+1.The idea quantizing weights activations is firstly proposed BID11. has shown even 1-bit binarization can achieve reasonably good performance visual classification tasks. Compared full precision counterpart binary weights reduce memory factor 32. costly arithmetic operations weights activations can then be replaced cheap XNOR bitcount operations BID11 which potentially leads much acceleration. Rastegarietal. 2016 incorporate real coefficient compensate binarization error. apply method challenging ImageNet dataset achieve better performance pure binarization BID11. However is still large gap compared full precision networks. bridge gap recent works BID12 BID29 employ quantization bits achieve plausible performance. Meanwhile quite amount works e.g BID3 BID30 BID6 are to quantize weights only. Although much memory saving can be achieved acceleration is very limited modern computing devices Rastegarietal. 2016.Among existing quantization works focus convolutional neural networks CNNs pay less attention RNNs. mentioned earlier latter is also demanding. Recently BID10 showed binarized LSTM preconditioned coefficients can achieve promising performance easy tasks predicting next character. However RNNs large input/output e.g large vocabulary language models is still challenging quantization. works BID12 BID28 test effectiveness multi-bit quantized RNNs predict next word. Although using 4-bits results quantization still have noticeable gap full precision. motivatesus find better method quantize RNNs. main contribution work is as follows:formulate multi-bit quantization optimization problem. binary codes −1+1 are learned instead rule-based first time observe codes can be optimally derived binary search tree coefficients are knowns advance see e.g Algorithm1. Thus whole optimization is eased removing discrete unknowns which are very difficult handle. b propose use alternating minimization tackle quantization problem. separating binary codes real coefficients two parts can solve subproblem efficiently when one part is fixed. proper initialization need two alternating cycles get high precision approximation which is effective enough even quantize activations on-line c systematically evaluate effectiveness alternating quantization language models.Two well-known RNN structures.e LSTM GRU are tested different quantization bits. Compared full-precision counterpart 2-bit quantization can achieve ∼16× memory saving ∼6× real inference acceleration CPUs reasonable loss accuracy. 3-bit quantization can achieve almost loss accuracy even surpass original model ∼10.5× memory saving ∼3× real inference acceleration. results beat exiting quantization works large margins. illustrate alternating quantization is very general extend apply image classification tasks. RNNs feedforward neural networks technique still achieves plausible performance. work address limitations RNNs.e large memory high latency quantization. formulate quantization minimizing approximation error. key observation parameters can be singled when others fixed simple yet effective alternating method is proposed. apply quantize LSTM GRU language models. 2-bit weights activations can achieve reasonably accuracy loss compared full precision one ∼16× reduction memory ∼6× real acceleration CPUs. 3-bit quantization can attain compatible even better result full precision one ∼10.5× reduction memory ∼3× real acceleration. beat existing works large margin. also apply alternating quantization image classification tasks. RNNs feedforward neural networks method can still achieve plausible performance. section discuss implementation binary multiplication kernel CPUs. binary multiplication is divided two steps:Entry-wise XNOR operation corresponding entry-wise product full precision multiplication bit count operation accumulation corresponding compute sum multiplied entries full precision multiplication test Intel Xeon E5-2682v4 2.50 GHz CPU. XNOR operation use Single instruction multiple data SIMD _mm256 _xor _ps which can execute 256 bit simultaneously. bit count operation use function _popcnt64 Note step can further be accelerated up-coming instruction _mm512 _popcnt_epi64 which can execute 512 bits simultaneously. Similarly XNOR operation can also accelerated up-coming _mm512 _xor _ps instruction execute 512 bits simultaneously compare much optimized Intel Math Kernel Library MKL full precision matrix vector multiplication execute codes single-thread mode. conduct two scales experiments:matrix size 4096 × 1024 multiplying vector size 1024 matrix size 42000 × 1024 multiplying vector size 1024 which respectively correspond hidden state productW h h t−1 softmax layerW h Text8 dataset inference batch size 1 SeeEq. 6 results are shown TAB6. can see alternating quantization step accounts small portion total executing time especially larger scale matrix vector multiplication. Compared full precision one binary multiplication can roughly achieve 6× acceleration 2-bit quantization 3× acceleration 3-bit quantization. Note is only simple test CPU. alternating quantization method can also extended GPU ASIC FPGA.,1973,1384,589,0.021,1.426,2025/11/05 17:19:00,0.01,1.481,0.2990654205607472,574.882
"The goal of this paper is to demonstrate a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for linear layers in a neural network and test this implementation on the CIFAR-10 dataset. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA-layers with 3900 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers.
 The curse of dimensionality is a major bottleneck in machine learning, stemming from the exponential growth of variables with the number of modes in a data set BID0 ). Typically state-of-the-art convolutional neural networks have millions or billions of parameters. However, previous work has demonstrated that representations stored in the network parameters can be highly compressed without significant reduction in network performance BID15 , BID3 , BID5 ). Determining the best network architecture for a given task remains an open problem.Descriptions of quantum mechanical systems raise a similar challenge; representing n d-dimensional particles requires a rank-n tensor whose memory cost scales as d n . Indeed, it was the promise of harnessing this that led Richard Feynman BID2 ) to suggest the possibility of quantum computation. In the absence of a quantum computer, however, one must use compressed representations of quantum states.A level of compression can be achieved by factorizing the tensorial description of the quantum wavefunction. Many such factorizations are possible, the optimal structure of the factorization being determined by the structure of correlations in the quantum system being studied. A revolution in quantum mechanics was made by realizing that the best way to characterize the distribution of correlations and information in a state is by a quantity known as entanglement -loosely the mutual quantum information between partitions of a quantum system BID1 ).This has led to many successful applications of tensorial approaches to problems in solid state physics and quantum chemistry over the past 25 years BID16 , BID7 ). Intriguing ideas have also emerged over the past few years attempting to bridge the successes of neural networks in machine learning with those of tensorial methods in quantum physics, both at a fundamental level BID10 , BID13 ), and as a practical tool for network design BID9 ). Recent work has suggested that entanglement itself is a useful quantifier of the performance of neural networks BID9 , BID11 The simplest factorization employed in quantum systems is known as the matrix product state BID16 ). In essence, it expresses the locality of information in certain quantum states. It has already been adopted to replace expensive linear layers in neural networks -in which context it has been independently termed tensor trains BID17 ). This led to substantial compression of neural networks with only a small reduction in the accuracy BID15 , BID3 ).Here we use a different tensor factorization -known as the Multi-scale Entanglement Renormalization Ansatz (MERA) -that encodes information in a hierarchical manner BID24 ). MERA works through a process of coarse graining or renormalization. There have been a number of papers looking at the relationship between renormalization and deep learning. MERA is a concrete realization of such a renormalization procedure BID25 ) and so possesses a multi-scale structure that one might anticipate in complex data. A number of works have utilized tree tensor network models that possess a similar hierarchical structure. However, they do not include the disentangler tensors that are essential if each layer of the MERA is to capture correlations on different length scales BID11 ).In this work we employ MERA as a replacement for linear layers in a neural network used to classify the CIFAR-10 dataset. Our results show that this performs better than the tensor train decomposition of the same linear layer, and gives better accuracy for the same level of compression and better compression for the same level of accuracy. In Section 2 we introduce factorizations of fully connected linear layers, starting with the tensor train factorization followed by a tree-like factorization and finally the MERA factorization. In Section 3 we discuss how this is employed as a replacement for a fully connected linear layer in deep learning networks. Section 4 gives our main results and we note connections with the existing literature in Section 5. Finally, in Section 6 we discuss some potential developments of the work. In this report we have replaced the linear layers of the standard neural network with tensorial MERA layers. The first step in achieving this involves expressing a linear layer as a tensor. This can be accomplished by taking a matrix W and reshaping it to be a higher dimensional array. For example, suppose W is d n by d n dimensional with components W AB . It can be transformed into a rank 2n tensor by mapping A to n elements A → i 1 , i 2 , ..., i n and B to another n elements B → j 1 , j 2 , ..., j n . In this case each of the elements of the new tensor will be of size d. FIG0 gives a graphical representation of this rank 2n tensor W i1,i2,... ,in j1,j2,...,jn . It is important to note that in this representation, the lines represent the indices of the tensors rather than weights. FIG0 We have shown that replacing the fully connected layers of a deep neural network with layers based upon the multi-scale entanglement renormalization ansatz can generate significant efficiency gains with only small reduction in accuracy. When applied to the CIFAR-10 data we found the fully connected layers can be replaced with MERA layers with 3900 times less parameters with a reduction in the accuracy of less than 1%. The model significantly outperformed compact fully connected layers with 70 − 100 times as many parameters. Moreover, it outperformed a similar replacement of the fully connected layers with tensor trains, both in terms of accuracy for a given compression and compression for a given accuracy.An added advantage -not explored here -is that a factorized layer can potentially handle much larger input data sets, thus enabling entirely new types of computation. Correlations across these large inputs can be handled much more efficiently by MERA than by tensor trains. Moreover, a compressed network may provide a convenient way to avoid over-fitting of large data sets. The compression achieved by networks with these factorized layers comes at a cost. They can take longer to train than networks containing the large fully connected layers due to the number of tensor contractions required to apply the factorized layer.Our results suggest several immediate directions for future inquiry. Firstly, there are some questions about how to improve the existing model. For example, before the MERA layer is used the input is reshaped into a rank-12 tensor. There isn't a well defined method for how to perform this reshaping optimally and some experimentation is necessary. The best way to initialize the MERA layers is also still an open question.The results presented here are a promising first step for using MERA in a more fundamental way. Since MERA can be viewed as a coarse graining procedure (as explained in Section 2), and image data is often well represented in a hierarchical manner, one possibility would be to simply train a two-dimensional MERA directly on an image dataset, with no reference to a neural network. In BID22 a similar idea was explored with matrix product states being trained directly on MNIST. An alternative possibility would be the replacement of just the convolutional layers of the network with a two-dimensional MERA. Both of these approaches would be closer in spirit to the fundamental ideas about the relationships between quantum physics and machine learning proposed in BID10 and BID13 .Additionally , there has been some work using entanglement measures to explore how correlations are distributed in deep neural networks, and then utilizing these in order to optimize the design of networks BID11 , BID9 ). It would be intriguing to explore such ideas using MERA, for example by using the concrete MERA model explored in this paper, or one of the more ambitious possibilities mentioned above.We end by noting two facts: any variational approximation to a quantum wavefunction can be used to construct a replacement for linear layers of a network. There are many examples and each may have its sphere of useful application. Moreover, quantum computers of the type being developed currently by several groups are precisely described by a type of tensor network (a finite-depth circuit -and one that may very soon be too large to manipulate classically) and could be used as direct replacement for linear layers in a hybrid quantum/classical neural computation scheme.",goal paper is to demonstrate method tensorizing neural networks based upon efficient way approximating scale invariant quantum states Multi-scale Entanglement Renormalization Ansatz MERA employ MERA replacement linear layers neural network test implementation CIFAR-10 dataset. proposed method outperforms factorization using tensor trains providing greater compression level accuracy greater accuracy level compression. demonstrate MERA-layers 3900 times fewer parameters reduction accuracy less 1% compared equivalent fully connected layers. curse dimensionality is a major bottleneck machine learning stemming exponential growth variables number modes data set BID0 Typically state-of-the-art convolutional neural networks have millions billions parameters. However previous work has demonstrated representations stored network parameters can be highly compressed without significant reduction network performance BID15 BID3 BID5 Determining best network architecture given task remains open problem.Descriptions quantum mechanical systems raise similar challenge;representing n d-dimensional particles requires rank-n tensor whose memory cost scales n. Indeed was the promise harnessing led Richard Feynman BID2 suggest possibility quantum computation. absence quantum computer however one must use compressed representations quantum states.A level compression can be achieved factorizing tensorial description quantum wavefunction. Many factorizations are possible optimal structure factorization determined structure correlations quantum system studied. revolution quantum mechanics was made realizing best way characterize distribution correlations information state is by a quantity known entanglement -loosely mutual quantum information partitions quantum system BID1.This has led many successful applications tensorial approaches problems solid state physics quantum chemistry past 25 years BID16 BID7 Intriguing ideas have also emerged past years attempting bridge successes neural networks machine learning tensorial methods quantum physics fundamental level BID10 BID13 practical tool network design BID9 Recent work has suggested entanglement is a useful quantifier performance neural networks BID9 BID11 simplest factorization employed quantum systems is known matrix product state BID16 essence expresses locality information certain quantum states. has already adopted replace expensive linear layers neural networks -in which context has been independently termed tensor trains BID17 led substantial compression neural networks small reduction accuracy BID15 BID3.Here use different tensor factorization -known Multi-scale Entanglement Renormalization Ansatz MERA -that encodes information hierarchical manner BID24 MERA works process coarse graining renormalization. have been a number papers looking relationship renormalization deep learning. MERA is a concrete realization renormalization procedure BID25 possesses multi-scale structure one might anticipate complex data. number works have utilized tree tensor network models possess similar hierarchical structure. However do not include disentangler tensors are essential if each layer MERA is to capture correlations different length scales BID11.In work employ MERA replacement linear layers neural network used classify CIFAR-10 dataset. results show performs better tensor train decomposition linear layer gives better accuracy level compression better compression level accuracy. Section2 introduce factorizations fully connected linear layers starting tensor train factorization followed tree-like factorization finally MERA factorization. Section3 discuss how this is employed replacement fully connected linear layer deep learning networks. Section 4 gives main results note connections existing literature Section5. Finally Section6 discuss potential developments work. report have replaced linear layers standard neural network tensorial MERA layers. first step achieving involves expressing linear layer tensor. can be accomplished taking matrixW reshaping higher dimensional array. example supposeW isdn n dimensional componentsWAB. can be transformed rank 2n tensor mapping n elements → 1 2... n B another n elementsB →j1 j2... jn. case elements new tensor will be of size d. FIG0 gives graphical representation rank 2n tensorW i1 i2... j1 j2... jn. is important note representation lines represent indices tensors rather weights. FIG0 have shown replacing fully connected layers deep neural network layers based upon multi-scale entanglement renormalization ansatz can generate significant efficiency gains small reduction accuracy. When applied CIFAR-10 data found fully connected layers can be replaced MERA layers 3900 times less parameters reduction accuracy less 1%. model significantly outperformed compact fully connected layers 70 − 100 times many parameters. Moreover outperformed similar replacement fully connected layers tensor trains terms accuracy given compression compression given accuracy.An added advantage -not explored -is factorized layer can potentially handle much larger input data sets thus enabling entirely new types computation. Correlations across large inputs can be handled much efficiently MERA tensor trains. Moreover compressed network may provide convenient way avoid over-fitting large data sets. compression achieved networks factorized layers comes cost. can take longer train networks containing large fully connected layers due number tensor contractions required apply factorized layer.Our results suggest several immediate directions future inquiry. Firstly are some questions how to improve existing model. example MERA layer is used input is reshaped rank-12 tensor. well defined method how to perform reshaping optimally experimentation is necessary. best way initialize MERA layers is also still open question.The results presented are a promising first step using MERA fundamental way. Since MERA can be viewed coarse graining procedure explained Section2 image data is often well represented hierarchical manner one possibility would simply train two-dimensional MERA directly image dataset reference neural network. BID22 similar idea was explored matrix product states trained directly MNIST. alternative possibility would replacement convolutional layers network two-dimensional MERA. approaches would closer spirit fundamental ideas relationships quantum physics machine learning proposed BID10 BID13.Additionally has been work using entanglement measures explore how correlations are distributed deep neural networks utilizing order optimize design networks BID11 BID9 would intriguing explore ideas using MERA example using concrete MERA model explored paper one ambitious possibilities mentioned above.We end noting two facts:variational approximation quantum wavefunction can be used construct replacement linear layers network. are many examples may have its sphere useful application. Moreover quantum computers type developed currently several groups are precisely described type tensor network finite-depth circuit -and one may soon large manipulate classically could used direct replacement linear layers hybrid quantum/classical neural computation scheme.,1755,1189,566,0.022,1.476,2025/11/05 17:19:00,0.01,1.561,0.4548286604361368,542.837
"Deep learning models have outperformed traditional methods in many fields such
 as natural language processing and computer vision. However, despite their
 tremendous success, the methods of designing optimal Convolutional Neural Networks
 (CNNs) are still based on heuristics or grid search. The resulting networks
 obtained using these techniques are often overparametrized with huge computational
 and memory requirements. This paper focuses on a structured, explainable
 approach towards optimal model design that maximizes accuracy while keeping
 computational costs tractable. We propose a single-shot analysis of a trained CNN
 that uses Principal Component Analysis (PCA) to determine the number of filters
 that are doing significant transformations per layer, without the need for retraining.
 It can be interpreted as identifying the dimensionality of the hypothesis space
 under consideration. The proposed technique also helps estimate an optimal number
 of layers by looking at the expansion of dimensions as the model gets deeper.
 This analysis can be used to design an optimal structure of a given network on
 a dataset, or help to adapt a predesigned network on a new dataset. We demonstrate
 these techniques by optimizing VGG and AlexNet networks on CIFAR-10,
 CIFAR-100 and ImageNet datasets. This analysis has only been done on activation outputs for convolutional layers before the application of non-linearities such as ReLU. Non-linearities introduce more dimensions, but those are not a function of the number of filters in a layer. Hence we recommend not to perform ReLU in-place while performing this analysis. The number of samples to be taken into account for PCA are recommended to be around 2 orders of magnitudes more than the number of filters we are trying to find redundancy in. This is particularly of importance in the later layers where the activation map sizes are small. We need to collect these activations over many batches to make sure we have enough data to run PCA analysis on. While the percentage variance one would like to retain depends on the application and acceptable error tolerance, empirically we have found that preserving 99.9% puts us at a sweet spot for most cases with less than half a percentage point in accuracy degradation and a considerable gain in computational cost. This analysis comes in handy in three cases: While designing new network for new data; while adapting given network for new data; and while optimizing current network for faster runtimes or reduced power consumption during training or inference in hardware implementations. Another benefit of this analysis is that not only does it deliver an optimal point, but enables an interpretable, graceful exploration of accuracy-energy trade-off with negligible overhead of compute cost and time. This method is orthogonal to other model compression techniques.",Deep learning models have outperformed traditional methods many fields natural language processing computer vision. However despite tremendous success methods designing optimal Convolutional Neural Networks CNNs are still based heuristics grid search. resulting networks obtained using techniques are often overparametrized huge computational memory requirements. paper focuses structured explainable approach towards optimal model design maximizes accuracy keeping computational costs tractable. propose single-shot analysis trained CNN uses Principal Component Analysis PCA determine number filters are doing significant transformations per layer without need retraining. can be interpreted identifying dimensionality hypothesis space consideration. proposed technique also helps estimate optimal number layers looking expansion dimensions model gets deeper. analysis can be used design optimal structure given network dataset help adapt predesigned network new dataset. demonstrate techniques optimizing VGG AlexNet networks CIFAR-10 CIFAR-100 ImageNet datasets. analysis has only been done activation outputs convolutional layers application non-linearities ReLU. Non-linearities introduce dimensions are function number filters layer. Hence recommend perform ReLU in-place performing analysis. number samples taken account PCA are recommended around 2 orders magnitudes number filters are trying find redundancy in. is particularly importance later layers where the activation map sizes are small. need collect activations many batches make sure have enough data run PCA analysis on. percentage variance one would like retain depends application acceptable error tolerance empirically have found preserving 99.9 putsus sweet spot cases less half percentage point accuracy degradation considerable gain computational cost. analysis comes handy three cases:designing new network new data;adapting given network new data;optimizing current network faster runtimes reduced power consumption training inference hardware implementations. Another benefit analysis is that not only doesit deliver optimal point enables interpretable graceful exploration accuracy-energy trade-off negligible overhead compute cost time. method is orthogonal model compression techniques.,538,357,181,0.005,1.507,2025/11/05 17:19:00,0.0,1.556,0.551401869158878,189.147
"Recent work has introduced attacks that extract the architecture information of deep neural networks (DNN), as this knowledge enhances an adversary’s capability to conduct attacks on black-box networks. This paper presents the first in-depth security analysis of DNN fingerprinting attacks that exploit cache side-channels.   First, we define the threat model for these attacks:  our adversary does not need the ability to query the victim model; instead, she runs a co-located process on the host machine victim ’s deep learning  (DL) system is running and passively monitors the accesses of the target functions in the shared framework.   Second, we introduce DeepRecon, an attack that reconstructs the architecture of the victim network by using the internal information extracted via Flush+Reload, a cache side-channel technique. Once the attacker observes function invocations that map directly to architecture attributes of the victim network, the attacker can reconstruct the victim’s entire network architecture.   In our evaluation, we demonstrate that an attacker can accurately reconstruct two complex networks (VGG19 and ResNet50) having only observed one forward propagation. Based on the extracted architecture attributes, we also demonstrate that an attacker can build a meta-model that accurately fingerprints the architecture and family of the pre-trained model in a transfer learning setting. From this meta-model,  we evaluate the importance of the observed attributes in the fingerprinting process. Third, we propose and evaluate new framework-level defense techniques that obfuscate our attacker’s observations. Our empirical security analysis represents a step toward understanding the DNNs’ vulnerability to cache side-channel attacks. Deep neural networks (DNNs) have become an essential tool in various applications, such as face recognition, speech recognition, malware detection, and autonomous driving or aviation BID18 BID1 BID2 BID3 BID21 . A DNN's performance depends widely on the network architecture-the number and types of layers, how the layers are connected, and the activation functions-and, unfortunately, there is no universal architecture that performs well on all tasks. Consequently, researchers and practitioners have devoted substantial efforts to design various DNN architectures to provide high performance for different learning tasks.Owing to their critical role, DNN architectures represent attractive targets for adversaries who aim to mount DNN fingerprinting attacks. In such an attack, the adversary probes a DNN model, considered confidential, until she infers enough attributes of the network to distinguish it among other candidate architectures. In addition to revealing valuable and secret information to the adversary, DNN fingerprinting can enable further attacks on black-box models. While the prior work on adversarial machine learning often assumes a white-box setting, where the adversary knows the DNN model under attack, these attacks are usually unrealistic in practice BID22 . In consequence, researchers have started focusing on a black-box setting, where model architecture is unknown to the adversary. However, in this setting, the adversary often makes some assumptions about the victim model in order to craft successful adversarial examples . Instead of approxi-mating, the adversary can start by conducting a DNN fingerprinting attack to infer the information required about the model, then use this information to craft adversarial examples that can evade the model. This can also enable model extraction attacks BID25 BID12 BID27 and membership inference or model inversion attacks BID19 BID15 .Because of the large number and types of architectural attributes, and the subtle effect that each attribute has on the model's inferences, DNN fingerprinting is challenging when using the typical methods employed in the adversarial machine learning literature. For example , BID27 propose a hyperparameter stealing attack that requires knowledge of the training dataset, the ML algorithm, and the learned model parameters, yet is unable to extract the model architecture. demonstrate a fingerprinting attack against transfer learning; however, they rely on the assumption that the teacher model and learning parameters are known to the attacker. To overcome these challenges, recent work has started to investigate attacks that utilize information leaked by architectural side-channels on the hardware where the DNN model runs. BID8 extract the network architecture of a model running on a hardware accelerator by monitoring off-chip memory addresses. BID30 reduce the search space from 10 35 to 16 candidates within a given network architecture by exploiting cache side-channels.In this paper, we ask the question: how vulnerable are DNNs to side-channel attacks, and what information do adversaries need for architecture fingerprinting? We perform, to the best of our knowledge, the first security analysis of DNNs operating in the presence of cache side-channel attacks. Specifically , we define the threat model for these attacks, including the adversary's capabilities and limitations. We then introduce DeepRecon, an efficient attack that reconstructs a black-box DNN architecture by exploiting the Flush+Reload BID32 technique, and we further evaluate the importance of specific architectural attributes in the success of fingerprinting. Finally, we propose and evaluate new framework-level defenses against these attacks.Our attack works by targeting lines of code corresponding to the execution of specific network architecture attributes of a deep learning (DL) framework. Specifically, these lines of code correspond to instructions to execute functions that are mapped into the instruction cache when the functions are invoked. Once these lines of code are identified, our attack flushes them from the instruction cache shared by the attacker and the victim. The attacker waits for the victim's process to run and then measures the time it takes to re-access those same lines of code. If the victim's DNN model has accessed any of these particular functions, the corresponding lines of code will be present in the instruction cache when the attacker tries to re-access them. Therefore, the access time to call these functions will be measurably faster than if the victim had not loaded them back into the shared instruction cache. On the other hand, if the victim DNN model did not access these particular functions, the corresponding lines will not be present in the cache when accessed by the attacker, and thus the access time will be measurably slower. We show that from this seemingly small amount of information that is leaked to the attacker, much of the victim's DNN architecture can be extracted with no query access required. To launch this attack, we only assume that: 1) an attacker and a victim are co-located in the same machine, and 2) they use the same shared DL framework.In evaluations, we demonstrate that, by learning whether or not specific functions were invoked during inference, we can extract 8 architecture attributes across 13 neural network architectures with high accuracy. Based on the extracted attributes , we demonstrate how an attacker can reconstruct the architectures of two common networks, VGG16 BID20 and ResNet50 BID6 as proof of concept. We also demonstrate a useful example of DeepRecon through model fingerprinting in a transfer learning attack. Finally, we propose countermeasures to obfuscate an attacker from extracting the correct attributes and sequences using observation attacks like DeepRecon and show that these defenses significantly increase the errors in the extracted attributes and can be implemented in various DL frameworks without hardware or operating system support. This paper conducts the first in-depth security analysis of DNN fingerprinting attacks that exploit cache side-channels. We first define the realistic threat model for these attacks: our attacker does not require the ability to query the victim model; she runs a co-located process on the machine where the victims DL system is running and passively monitors the accesses of target functions in a shared framework. We also present DeepRecon, an attack that reconstructs the architecture of a victim network using the architecture attributes extracted via the Flush+Reload technique. Based on the extracted attributes, we further demonstrate that an attacker can build a meta-model that precisely fingerprints the architecture and family of the pre-trained model in a transfer learning setting. With the meta-model, we identified the essential attributes for these attacks. DISPLAYFORM0 Recon.Steps Details VGG16 Recon.(1 ) Block 1 . Block 2. Block 3. Block 4. Block 5. DISPLAYFORM1 (Note that C,P ,F indicate the Convolutional, P ooling, F ully connected layers, and the subscripts mean the activation functions (R: ReLU, and So: Softmax). ) Table 7 : Reconstruction Process of VGG16 Architecture. We list the computation sequences captured by our attack above and the reconstruction process at the bottom.We describe the reconstruction process of VGG16 in Table 7 . The upper table indicates the sequences that our attacker captured, and the bottom shows the actual reconstruction steps. Our attacker identifies the basic building blocks by splitting the sequence with pooling layers. Then, the attacker counts the number of convolutional layers in each block. In VGG16, we found the first two ConvNet blocks have two convolutional layers, and the next three ConvNet blocks have three convolutional layers in each. Additionally, the attacker estimates the number of fully connected layers attached at the end. Once the attacker recovers all the blocks, our attacker can identify the victim architecture as being VGG16 with the ConvNet configuration 'C' or 'D'.B OBFUSCATED RE SNE T50 ARCHITECTURE In Sec. 5.2, we construct the obfuscated ResNet50 architecture by using the unraveled view of the first three blocks in ResNet50 as shown in FIG3 . The upper architecture depicts the block connections in the original ResNet50. In this network, the blocks are computed sequentially, e.g., Residual Block → Identity Block → Identity Block. However , in our unraveled architecture at the bottom, there are individual 8 paths that can be computed independently. We use this architecture to compute the blocks as follows: Residual Block 1, 2 → Identity Block 1 → Residual Block 3, 4 → Identity Block 2 → Identity Block 3. This makes our attacker have difficulty in estimating the architecture attributes and computation sequences of ResNet50.",Recent work has introduced attacks extract architecture information deep neural networks DNN knowledge enhances adversarys capability conduct attacks black-box networks. paper presents first in-depth security analysis DNN fingerprinting attacks exploit cache side-channels First define threat model attacks:adversary does not need ability query victim model;instead runs co-located process host machine victim deep learning DL system is running passively monitors accesses target functions shared framework. Second introduce DeepRecon attack reconstructs architecture victim network using internal information extracted via Flush+Reload cache side-channel technique. attacker observes function invocations map directly architecture attributes victim network attacker can reconstruct victims entire network architecture. evaluation demonstrate attacker can accurately reconstruct two complex networks VGG19 ResNet50 observed one forward propagation. Based extracted architecture attributes also demonstrate attacker can build meta-model accurately fingerprints architecture family pre-trained model transfer learning setting. meta-model evaluate importance observed attributes fingerprinting process. Third propose evaluate new framework-level defense techniques obfuscate attackers observations. empirical security analysis represents step toward understanding DNNs vulnerability cache side-channel attacks. Deep neural networks DNNs have become essential tool various applications face recognition speech recognition malware detection autonomous driving aviation BID18 BID1 BID2 BID3 BID21. DNN's performance depends widely network architecture-the number types layers how the layers are connected activation functions-and unfortunately is no universal architecture performs well tasks. Consequently researchers practitioners have devoted substantial efforts design various DNN architectures provide high performance different learning tasks.Owing critical role DNN architectures represent attractive targets adversaries who aim mount DNN fingerprinting attacks. attack where the adversary probes DNN model considered confidential infers enough attributes network distinguish among candidate architectures. addition revealing valuable secret information adversary DNN fingerprinting can enable attacks black-box models. prior work adversarial machine learning often assumes white-box setting where the adversary knows DNN model attack attacks are usually unrealistic practice BID22. consequence researchers have started focusing black-box setting where model architecture is unknown adversary. However setting where the adversary often makes assumptions victim model order craft successful adversarial examples. Instead approxi-mating where the adversary can start conducting DNN fingerprinting attack infer information required model use information craft adversarial examples can evade model. can also enable model extraction attacks BID25 BID12 BID27 membership inference model inversion attacks BID19 BID15.Because large number types architectural attributes subtle effect attribute has on the model's inferences DNN fingerprinting is challenging when using typical methods employed adversarial machine learning literature. example BID27 propose hyperparameter stealing attack requires knowledge training dataset ML algorithm learned model parameters yet is unable extract model architecture. demonstrate fingerprinting attack transfer learning;however rely assumption teacher model learning parameters are known attacker. overcome challenges recent work has started investigate attacks utilize information leaked architectural side-channels hardware where the DNN model runs. BID8 extract network architecture model running hardware accelerator monitoring off-chip memory addresses. BID30 reduce search space 1035 16 candidates within given network architecture exploiting cache side-channels.In paper ask question:how vulnerable are DNNs side-channel attacks what information do adversaries need architecture fingerprinting? perform best knowledge first security analysis DNNs operating presence cache side-channel attacks. Specifically define threat model attacks including adversary's capabilities limitations. introduce DeepRecon efficient attack reconstructs black-box DNN architecture exploiting Flush+Reload BID32 technique evaluate importance specific architectural attributes success fingerprinting. Finally propose evaluate new framework-level defenses attacks.Our attack works targeting lines code corresponding execution specific network architecture attributes deep learning DL framework. Specifically lines code correspond instructions execute functions are mapped instruction cache when the functions are invoked. lines code are identified attack flushes instruction cache shared attacker victim. attacker waits victim's process run measures time takes re-access lines code. If the victim's DNN model has accessed particular functions corresponding lines code will be will not be present instruction cache when the attacker tries re-access them. Therefore access time call functions will be measurably faster if the victim had not loaded back shared instruction cache. hand if the victim DNN model did not access particular functions corresponding lines will be will not be present cache when accessed attacker thus access time will be measurably slower. show seemingly small amount information is leaked attacker much victim's DNN architecture can be extracted query access required. launch attack assume that:1 attacker victim are co-located machine 2 use shared DL framework.In evaluations demonstrate learning whether specific functions were invoked inference can extract 8 architecture attributes across 13 neural network architectures high accuracy. Based extracted attributes demonstrate how an attacker can reconstruct architectures two common networks VGG16 BID20 ResNet50 BID6 proof concept. also demonstrate useful example DeepRecon model fingerprinting transfer learning attack. Finally propose countermeasures obfuscate attacker extracting correct attributes sequences using observation attacks like DeepRecon show defenses significantly increase errors extracted attributes can be implemented various DL frameworks without hardware operating system support. paper conducts first in-depth security analysis DNN fingerprinting attacks exploit cache side-channels first define realistic threat model attacks:attacker does not require ability query victim model;runs co-located process machine where the victims DL system is running passively monitors accesses target functions shared framework. also present DeepRecon attack reconstructs architecture victim network using architecture attributes extracted via Flush+Reload technique. Based extracted attributes demonstrate attacker can build meta-model precisely fingerprints architecture family pre-trained model transfer learning setting. meta-model identified essential attributes attacks. DISPLAYFORM0 Recon.Steps Details VGG16 Recon. 1 Block1. Block2. Block3. Block4. Block5. DISPLAYFORM1 Note C P F indicate Convolutional P ooling F ully connected layers subscripts mean activation functions R:ReLU So:Softmax Table7:Reconstruction Process VGG16 Architecture. list computation sequences captured attack reconstruction process bottom.We describe reconstruction process VGG16 Table7. upper table indicates sequences attacker captured bottom shows actual reconstruction steps. attacker identifies basic building blocks splitting sequence pooling layers. attacker counts number convolutional layers block. VGG16 found first two ConvNet blocks have two convolutional layers next three ConvNet blocks have three convolutional layers each. Additionally attacker estimates number fully connected layers attached end. attacker recovers blocks attacker can identify victim architecture VGG16 ConvNet configuration 'C' 'D'.B OBFUSCATED SNE T50 ARCHITECTURE Sec. 5.2 construct obfuscated ResNet50 architecture using unraveled view first three blocks ResNet50 shown FIG3. upper architecture depicts block connections original ResNet50. network blocks are computed sequentially e.g Residual Block → Identity Block → Identity Block. However unraveled architecture bottom are individual 8 paths can be computed independently. use architecture compute blocks follows:Residual Block1 2 → Identity Block 1 → Residual Block 3 4 → Identity Block 2 → Identity Block 3. makes attacker have difficulty estimating architecture attributes computation sequences ResNet50.,2021,1383,638,0.023,1.461,2025/11/05 17:19:00,0.01,1.381,0.4080996884735203,702.782
"Learning with a primary objective, such as softmax cross entropy for classification and sequence generation, has been the norm for training deep neural networks for years. Although being a widely-adopted approach, using cross entropy as the primary objective exploits mostly the information from the ground-truth class for maximizing data likelihood, and largely ignores information from the complement (incorrect) classes. We argue that, in addition to the primary objective, training also using a complement objective that leverages information from the complement classes can be effective in improving model performance. This motivates us to study a new training paradigm that maximizes the likelihood of the ground-truth class while neutralizing the probabilities of the complement classes. We conduct extensive experiments on multiple tasks ranging from computer vision to natural language understanding. The experimental results confirm that, compared to the conventional training with just one primary objective, training also with the complement objective further improves the performance of the state-of-the-art models across all tasks. In addition to the accuracy improvement, we also show that models trained with both primary and complement objectives are more robust to single-step adversarial attacks.
 Statistical learning algorithms work by optimizing towards a training objective. A dominant principle for training is to optimize likelihood BID16 , which measures the probability of data given the model under a specific set of parameters. The popularity of deep neural networks has given rise to the use of cross entropy BID13 as its primary training objective, since minimizing cross entropy is essentially equivalent to maximizing likelihood for disjoint classes. Cross entropy has become the standard training objective for many tasks including classification BID12 and sequence generation .Let y i ∈ {0, 1} K be the label of the i th sample in one-hot encoded representation andŷ i ∈ [0, 1] K be the predicted probabilities, the cross entropy H(y,ŷ) is defined as: DISPLAYFORM0 whereŷ ig represents the predicted probability of the ground-truth class for the i th sample. Training with cross entropy as the primary objective aims at findingθ = arg min θ H(y,ŷ), wherê y = h θ (x), h θ is a neural network and x is a sample. Although training using the cross entropy as The model is ResNet-110, and the ""embedding"" is the vector representation before taking the softmax operation. The embedding representation of each sample is projected to two dimensions using t-SNE for visualization purpose. Compared to ( a), the cluster of each class in (b) is ""narrower "" in terms of intra-cluster distance. Also, the clusters in (b) seem to have clean and separable boundaries, leading to more accurate and robust classification results.the primary objective has achieved tremendous success, we have observed one limitation: it exploits mostly the information from the ground-truth class as Eq(1) shows; the information from complement classes (i.e., incorrect classes) has been largely ignored, since the predicted probabilities other thanŷ ig are zeroed out due to the dot product calculation with the one-hot encoded y i . Therefore, for classes other than the ground truth, the model behavior is not explicitly optimized -their predicted probabilities are indirectly minimized whenŷ ig is maximized since the probabilities sum up to 1. One way to utilize the information from the complement classes is to neutralize their predicted probabilities. To this end, we propose Complement Objective Training (COT), a new training paradigm that achieves this optimization goal without compromising the model's primary objective. FIG1 illustrates the comparison between FIG1 : the predicted probabilityŷ from the model trained with just cross entropy as the primary objective, and FIG1 :ŷ from the model trained with both primary and complement objectives. Training with the complement objective finds the parameters θ that evenly suppress complement classes without compromising the primary objective (i.e., maximizingŷ g ), making the model more confident of the ground-truth class. Complement objective training requires a function that complements the primary objective. In this paper, we propose ""complement entropy"" (defined in Section 2) to complement the softmax cross entropy for neutralizing the effects of complement classes. The neural net parameters θ are then updated by alternating iteratively between (a) minimizing cross entropy to increaseŷ g , and (b) maximizing complement entropy to neutralizeŷ j =g . Experimental results (in Section 3) confirm that COT improves the accuracies of the state-of-the-art methods for both (a) the image classification tasks on ImageNet-2012 , Tiny ImageNet, CIFAR-10, CIFAR-100, and SVHN, and (b) language understanding tasks on machine translation and speech recognition. Furthermore, experimental results also show that models trained by COT are more robust to adversarial attacks. In this paper, we study Complement Objective Training (COT), a new training paradigm that optimizes the complement objective in addition to the primary objective. We propose complement entropy as the complement objective for neutralizing the effects of complement (incorrect) classes.Models trained using COT demonstrate superior performance compared to the baseline models. We also find that COT makes the models robust to single-step adversarial attacks.COT can be extended in several ways: first, in this paper, the complement objective is chosen to be the complement entropy. Non-entropy-based complement objectives should also be considered for future studies, which is left as a straight-line future work. Secondly, the exploration of COT on broader applications remains as an open research question. One example would be applying COT on generative models such as Generative Adversarial Networks . Another example would be using COT on object detection and segmentation. Finally, in this work, we show using complement objective help defend single-step adversarial attacks; the behavior of COT on more advanced adversarial attacks deserves further investigation and is left as another future work.A ITERATIVE FAST GRADIENT SIGN METHOD TAB9 shows the performance of the models on the CIFAR-10 dataset under I-FGSM transfer attacks. Generally, the models trained using COT have lower classification error under I-FGSM transfer attacks. The number of iteration is set to 10 in the experiment.",Learning primary objective softmax cross entropy classification sequence generation has been the norm training deep neural networks years. Although widely-adopted approach using cross entropy primary objective exploits mostly information ground-truth class maximizing data likelihood largely ignores information complement incorrect classes. argue addition primary objective training also using complement objective leverages information complement classes can be effective improving model performance. motivatesus study new training paradigm maximizes likelihood ground-truth class neutralizing probabilities complement classes. conduct extensive experiments multiple tasks ranging computer vision natural language understanding. experimental results confirm compared conventional training one primary objective training also complement objective improves performance state-of-the-art models across tasks. addition accuracy improvement also show models trained primary complement objectives are more robust single-step adversarial attacks. Statistical learning algorithms work optimizing towards training objective. dominant principle training is to optimize likelihood BID16 which measures probability data given model specific set parameters. popularity deep neural networks has given rise use cross entropy BID13 primary training objective since minimizing cross entropy is essentially equivalent maximizing likelihood disjoint classes. Cross entropy has become standard training objective many tasks including classification BID12 sequence generation.Let ∈ 0 1 K label th sample one-hot encoded representation andŷ ∈ 0 1 K predicted probabilities cross entropyH ŷ is defined as:DISPLAYFORM0 whereŷ ig represents predicted probability ground-truth class th sample. Training cross entropy primary objective aims findingθ arg minθH ŷ wherê hθ x hθ is a neural network x is a sample. Although training using cross entropy model is ResNet-110 embedding is the vector representation taking softmax operation. embedding representation sample is projected two dimensions using t-SNE visualization purpose. Compared cluster class b is narrower terms intra-cluster distance. Also clusters b seem have clean separable boundaries leading accurate robust classification results.the primary objective has achieved tremendous success have observed one limitation:exploits mostly information ground-truth class Eq 1 shows;information complement classes.e incorrect classes has been largely ignored since predicted probabilities thanŷig are zeroed due dot product calculation one-hot encoded i. Therefore classes ground truth model behavior is not explicitly optimized -their predicted probabilities are indirectly minimized whenŷig is maximized since probabilities sum 1. One way utilize information complement classes is to neutralize predicted probabilities. end propose Complement Objective Training COT new training paradigm achieves optimization goal without compromising model's primary objective. FIG1 illustrates comparison FIG1:predicted probabilityŷ model trained cross entropy primary objective FIG1:ŷ model trained primary complement objectives. Training complement objective finds parametersθ evenly suppress complement classes without compromising primary objective.e maximizingŷg making model confident ground-truth class. Complement objective training requires function complements primary objective. paper propose complement entropy defined Section2 complement softmax cross entropy neutralizing effects complement classes. neural net parametersθ are then updated alternating iteratively minimizing cross entropy increaseŷg b maximizing complement entropy neutralizeŷ j =g Experimental results Section3 confirm COT improves accuracies state-of-the-art methods image classification tasks ImageNet-2012 Tiny ImageNet CIFAR-10 CIFAR-100 SVHN b language understanding tasks machine translation speech recognition. Furthermore experimental results also show models trained COT are more robust adversarial attacks. paper study Complement Objective Training COT new training paradigm optimizes complement objective addition primary objective. propose complement entropy complement objective neutralizing effects complement incorrect classes.Models trained using COT demonstrate superior performance compared baseline models. also find COT makes models robust single-step adversarial attacks.COT can be extended several ways:first paper complement objective is chosen complement entropy. Non-entropy-based complement objectives should also considered future studies which is left straight-line future work. Secondly exploration COT broader applications remains open research question. One example would applying COT generative models Generative Adversarial Networks. Another example would using COT object detection segmentation. Finally work show using complement objective help defend single-step adversarial attacks;behavior COT advanced adversarial attacks deserves investigation is left another future work.A ITERATIVE FAST GRADIENT SIGN METHOD TAB9 shows performance models CIFAR-10 dataset I-FGSM transfer attacks. Generally models trained using COT have lower classification error I-FGSM transfer attacks. number iteration is set 10 experiment.,1240,844,396,0.012,1.469,2025/11/05 17:19:00,0.01,1.438,0.4330218068535826,362.887
"We present a new method for uncertainty estimation and out-of-distribution detection in neural networks with softmax output. We extend softmax layer with an additional constant input. The corresponding additional output is able to represent the uncertainty of the network. The proposed method requires neither additional parameters nor multiple forward passes nor input preprocessing nor out-of-distribution datasets. We show that our method performs comparably to more computationally expensive methods and outperforms baselines on our experiments from image recognition and sentiment analysis domains. The applications of computational learning systems might cause intrusive effects if we assume that predictions are always as accurate as during the experimental phase. Examples include misclassified traffic signs BID5 and an image tagger that classified two African Americans as gorillas BID3 . This is often caused by overconfidence of models that has been observed in the case of deep neural networks BID8 . Such malfunctions can be prevented if we estimate correctly the uncertainty of the machine learning system. Beside AI safety, uncertainty is useful in the active learning setting in which data collection process is expensive or time consuming BID12 BID32 .While uncertainty estimation in neural networks is an active field of research, the current methods are rarely adopted. It is desirable to develop a method that does not create an additional computational overhead. Such a method could be used in environments that focus on quick training and/or inference. If such a method is simple, the ease of implementation should encourage practitioners to develop danger-aware systems in their work.We suggest a method that measures uncertainty of the neural networks with a softmax output layer. We replace this layer with Inhibited Softmax layer BID33 , and we show that it can be used to express the uncertainty of the model. In our experiments the method outperforms baselines and performs comparably with more computationally expensive methods on the out-of-distribution detection task.We contribute with:• The mathematical explanation why the additional Inhibited Softmax output can be interpreted as an uncertainty measure.• The additions to the Inhibited Softmax that improve its uncertainty approximation properties.• The benchmarks comparing Inhibited Softmax, baseline and contemporary methods for measuring uncertainty in neural networks.The modern Bayesian Neural Networks BID0 BID11 BID25 BID27 BID37 BID9 Zhang et al., 2018; BID15 aim to confront this issue by inferring distribution over the models' weights. This approach has been inspired by Bayesian approaches suggested as early as the nineties BID2 BID29 . A very popular regularisation mean -dropout -also can be a source of approximate Bayesian inference BID7 . Such technique, called Monte Carlo dropout BID6 , belongs to the Bayesian Neural Networks class and has been since used in the real-life scenarios (e.g. Leibig et al., 2017) . In the Bayesian Neural Networks the uncertainty is modelled by computing the predictive entropy or mutual information over the probabilities coming from stochastic predictions BID34 .Other methods to measure uncertainty of neural networks include a non-Bayesian ensemble BID19 , a student network that approximates the Monte Carlo posterior predictive distribution BID16 , modelling Markov chain Monte Carlo samples with a GAN BID38 , Monte Carlo Batch Normalization BID35 and the nearest neighbour analysis of penultimate layer embedding BID28 .The concept of uncertainty is not always considered as a homogeneous whole. Some of the authors distinguish two types of uncertainties that influence predictions of machine learning models BID14 : epistemic uncertainty and aleatoric uncertainty. Epistemic uncertainty represents the lack of knowledge about the source probability distribution of the data. This uncertainty can be reduced by increasing the size of the training data. Aleatoric uncertainty arises from homoscedastic , heteroscedastic and label noises and cannot be reduced by the model. We will follow another source BID27 ) that defines the third type: distributional uncertainty. It appears when the test distribution differs from the training distribution, i.e. when new observations have different nature then the ones the model was trained on.A popular benchmark for assessing the ability of the models to capture the distributional uncertainty is distinguishing the original test set from out-of-distribution dataset BID10 . There are works that focus only on this type of uncertainty BID22 . ODIN BID24 does not require changing already existing network and relies on gradient-based input preprocessing. Another work BID4 ) is close to the functionality of our method , as it only adds a single densely connected layer and uses a single forward pass for a sample.Bayesian neural networks are more computationally demanding as they usually require multiple stochastic passes and/or additional parameters to capture the priors specification.To the best of our knowledge, our method is the first that improves upon the baseline, and meets all the following criteria:• No additional learnable parameters required.• Only single forward pass needed.• No additional out-of-distribution or adversarial observations required.• No input preprocessing.The technique we use, Inhibited Softmax, has been successfully used for the prediction of background class in the task of extraction the objects out of aerial imagery BID33 . The original work does not mention other possible applications of this softmax modification. We presented a new method for uncertainty estimation -Inhibited Softmax. The method can be easily applied to various multilayer neural network architectures and does not require additional parameters, multiple stochastic forward passes or OOD examples.The results show that the method outperforms baseline and performs comparably to the other methods. The method does not deteriorate predictive performance of the classifier.The predictive performance from IMDB/Movie Reviews experiment suggests that even if the observation comes from another probability distribution and the uncertainty measure is able to detect it, the network can still serve as a useful classifier.The improvement of the baseline on the sentiment task after adding suggested regularisation indicates it might be worth to apply such measures to other uncertainty estimation methods.",present new method uncertainty estimation out-of-distribution detection neural networks softmax output. extend softmax layer additional constant input. corresponding additional output is able represent uncertainty network. proposed method requires neither additional parameters multiple forward passes input preprocessing out-of-distribution datasets. show method performs comparably computationally expensive methods outperforms baselines experiments image recognition sentiment analysis domains. applications computational learning systems might cause intrusive effects if we assume predictions are always accurate experimental phase. Examples include misclassified traffic signs BID5 image tagger classified two African Americans gorillas BID3. is often caused overconfidence models has been observed case deep neural networks BID8. malfunctions can be prevented if we estimate correctly uncertainty machine learning system. Beside AI safety uncertainty is useful active learning setting which data collection process is expensive time consuming BID12 BID32.While uncertainty estimation neural networks is an active field research current methods are rarely adopted. is desirable develop method does not create additional computational overhead. method could used environments focus quick training/inference. If such a method is simple ease implementation should encourage practitioners develop danger-aware systems work.We suggest method measures uncertainty neural networks softmax output layer. replace layer Inhibited Softmax layer BID33 show can be used express uncertainty model. experiments method outperforms baselines performs comparably computationally expensive methods out-of-distribution detection task.We contribute with:• mathematical explanation why the additional Inhibited Softmax output can be interpreted uncertainty measure.• additions Inhibited Softmax improve uncertainty approximation properties.• benchmarks comparing Inhibited Softmax baseline contemporary methods measuring uncertainty neural networks.The modern Bayesian Neural Networks BID0 BID11 BID25 BID27 BID37 BID9 Zhangetal. 2018;BID15 aim confront issue inferring distribution models' weights. approach has been inspired Bayesian approaches suggested early nineties BID2 BID29. popular regularisation mean -dropout -also can be a source approximate Bayesian inference BID7. technique called Monte Carlo dropout BID6 belongs Bayesian Neural Networks class has been since used real-life scenarios e.g Leibiget al. 2017 Bayesian Neural Networks uncertainty is modelled computing predictive entropy mutual information probabilities coming stochastic predictions BID34.Other methods measure uncertainty neural networks include non-Bayesian ensemble BID19 student network approximates Monte Carlo posterior predictive distribution BID16 modelling Markov chain Monte Carlo samples GAN BID38 Monte Carlo Batch Normalization BID35 nearest neighbour analysis penultimate layer embedding BID28.The concept uncertainty is not always considered homogeneous whole. authors distinguish two types uncertainties influence predictions machine learning models BID14:epistemic uncertainty aleatoric uncertainty. Epistemic uncertainty represents lack knowledge source probability distribution data. uncertainty can be reduced increasing size training data. Aleatoric uncertainty arises homoscedastic heteroscedastic label noises cannot reduced model. will follow another source BID27 defines third type:distributional uncertainty. appears when the test distribution differs training distribution.e when new observations have different nature ones model was trained.A popular benchmark assessing ability models capture distributional uncertainty is distinguishing original test set out-of-distribution dataset BID10. are works focus type uncertainty BID22. ODIN BID24 does not require changing already existing network relies gradient-based input preprocessing. Another work BID4 is close functionality method adds single densely connected layer uses single forward pass sample.Bayesian neural networks are more computationally demanding usually require multiple stochastic passes/additional parameters capture priors specification.To best knowledge method is the first improves upon baseline meets following criteria:• additional learnable parameters required.• single forward pass needed.• additional out-of-distribution adversarial observations required.• input preprocessing.The technique use Inhibited Softmax has been successfully used prediction background class task extraction objects aerial imagery BID33. original work does not mention possible applications softmax modification. presented new method uncertainty estimation -Inhibited Softmax. method can be easily applied various multilayer neural network architectures does not require additional parameters multiple stochastic forward passes OOD examples.The results show method outperforms baseline performs comparably methods. method does not deteriorate predictive performance classifier.The predictive performance IMDB/Movie Reviews experiment suggests even if the observation comes another probability distribution uncertainty measure is able detect network can still serve useful classifier.The improvement baseline sentiment task adding suggested regularisation indicates might worth apply measures uncertainty estimation methods.,1157,843,314,0.011,1.372,2025/11/05 17:19:00,0.0,1.614,0.1308411214953272,339.083
"When deep learning is applied to sensitive data sets, many privacy-related implementation issues arise. These issues are especially evident in the healthcare, finance, law and government industries. Homomorphic encryption could allow a server to make inferences on inputs encrypted by a client, but to our best knowledge, there has been no complete implementation of common deep learning operations, for arbitrary model depths, using homomorphic encryption. This paper demonstrates a novel approach, efficiently implementing many deep learning functions with bootstrapped homomorphic encryption. As part of our implementation, we demonstrate Single and Multi-Layer Neural Networks, for the Wisconsin Breast Cancer dataset, as well as a Convolutional Neural Network for MNIST. Our results give promising directions for privacy-preserving representation learning, and the return of data control to users.

 The healthcare, finance, law and government industries often require complete privacy and confidentiality between various stakeholders and partners. With the advent of highly effective AI using deep learning, many real-world tasks can be made more effective and efficient in these industries. However deep learning approaches are seldom performed with privacy preservation in mind, let alone with the encryption of information throughout the entire process.As a result, current deep learning implementations often cannot be used for these confidential applications. Homomorphic Encryption (HE) BID28 offers an opportunity to address the privacy preservation gap, for data processing in general and deep learning in particular. HE can be used to perform computation on encrypted information BID26 , without ever having access to the plaintext information.Our work combines the paradigms of deep learning and homomorphic encryption, allowing improved privacy for existing server-side models , and thus enabling many novel, intelligent, privacy-guaranteeing services.Figure 1: General overview of our privacy-preserving method for deep learning. Encrypted inputs are fed into our hybrid model on the server-side, and this produces encrypted outputs. Our work shows that with the proposed Hybrid Homomorphic Encryption system, almost any production deep learning model can be converted, such that it can process encrypted inputs. Our design also makes it feasible to implement new or bespoke functionality, as the deep learning paradigm evolves.Depending on the value of the problem and the size of the model, this system is already viable for production use. New and updated HE libraries appear frequently, and our code should adapt to any library which implements homomorphic logic gates. Therefore our software could potentially receive ""free"" performance gains, as the HE paradigm evolves.",When deep learning is applied sensitive data sets many privacy-related implementation issues arise. issues are especially evident healthcare finance law government industries. Homomorphic encryption could allow server make inferences inputs encrypted client best knowledge has been complete implementation common deep learning operations arbitrary model depths using homomorphic encryption. paper demonstrates novel approach efficiently implementing many deep learning functions bootstrapped homomorphic encryption. part implementation demonstrate Single Multi-Layer Neural Networks Wisconsin Breast Cancer dataset well Convolutional Neural Network MNIST. results give promising directions privacy-preserving representation learning return data control users. healthcare finance law government industries often require complete privacy confidentiality various stakeholders partners. advent highly effective AI using deep learning many real-world tasks can be made effective efficient industries. However deep learning approaches are seldom performed privacy preservation mind let alone encryption information throughout entire process.As result current deep learning implementations often cannot used confidential applications. Homomorphic Encryption BID28 offers opportunity address privacy preservation gap data processing general deep learning particular. can be used perform computation encrypted information BID26 without ever access plaintext information.Our work combines paradigms deep learning homomorphic encryption allowing improved privacy existing server-side models thus enabling many novel intelligent privacy-guaranteeing services.Figure1:General overview privacy-preserving method deep learning. Encrypted inputs are fed hybrid model server-side produces encrypted outputs. work shows proposed Hybrid Homomorphic Encryption system almost production deep learning model can be converted can process encrypted inputs. design also makes feasible implement new bespoke functionality deep learning paradigm evolves.Depending value problem size model system is already viable production use. New updated libraries appear frequently code should adapt library which implements homomorphic logic gates. Therefore software could potentially receive free performance gains paradigm evolves.,483,327,156,0.005,1.477,2025/11/05 17:19:00,0.0,1.308,0.4579439252336449,138.978
"In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct machine-checkable proofs in a step-by-step manner. Hence, they provide an opportunity to explore theorem proving with human supervision. We use GamePad to synthesize proofs for a simple algebraic rewrite problem and train baseline models for a formalization of the Feit-Thompson theorem. We address position evaluation (i.e., predict the number of proof steps left) and tactic prediction (i.e., predict the next proof step) tasks, which arise naturally in tactic-based theorem proving. Theorem proving is a challenging AI task that involves symbolic reasoning (e.g., SMT solvers BID2 ) and intuition guided search. Recent work BID7 Loos et al., 2017; has shown the promise of applying deep learning techniques in this domain, primarily on tasks useful for automated theorem provers (e.g., premise selection) which operate with little to no human supervision. In this work, we aim to move closer to learning on proofs constructed with human supervision.We look at theorem proving in the realm of formal proofs. A formal proof is systematically derived in a formal system, which makes it possible to algorithmically (i.e., with a computer) check these proofs for correctness. Thus, formal proofs provide perfect learning signal-theorem statements and proofs are unambiguous. Human mathematicians usually do not write proofs in this style, and instead, construct and communicate proofs in natural language. Although the form and level of detail involved in each kind of proof differ, the logical content is similar in both contexts.Our work focuses on interactive theorem provers (ITPs), which are software tools that enable human users to construct formal proofs. ITPs have at least two features that make them compelling environments for exploring the application of learning techniques to theorem proving. First and foremost, ITPs provide full-fledged programmable environments. Consequently, any machine learning infrastructure built for an ITP can be reused across any problem domain crafted to study an aspect of learning and theorem proving. Second, the proofs are constructed by humans, and thus, have the constraint that they must be relatively human-understandable. Hence, ITPs provide access to large amounts of supervised data (i.e., expert-constructed proofs of theorems that are mathematically interesting). For example, ITPs have been used to build and check the proofs of large mathematical theorems such as the Feit-Thompson theorem BID6 and provide provable guarantees on complex pieces of software such as the CompCert C compiler BID13 .We introduce a system called GamePad 1 that exposes parts of the Coq ITP to enable machine learning tasks and explore a few use cases. We focus on the Coq proof assistant for two reasons. First , Figure 1 : A proof script in Coq (left) and the resulting proof states, proof steps, and the complete proof tree (right). A proof state consists of a context (pink rectangles) and a goal (white rectangles). The initial proof state has as its goal the statement we are trying to prove and an empty context. The arrows indicate what tactic the prover used. The final states of the proof are indicated by the red circles and can be transitioned to only when the goal in the previous state is trivially true.Coq is a mature system with an active developer community that has been used to formalize nontrivial theorems, including Feit-Thompson and CompCert. Second, Coq supports the extraction of verified software. Consequently , one can prove that a program is correct and then run the verified program. The ease of extraction makes Coq a popular choice for program verification.Our contributions are the following. First, we introduce GamePad, which provides a structured Python representation of Coq proofs (Section 3), including all the proof states encountered in a proof, the steps taken, and expression abstract syntax trees (ASTs). The tool also enables lightweight interaction with Coq so that it can be used to dynamically build proofs (e.g., used as an environment for reinforcement learning). Tasks that can leverage this structured representation (Section 4) include position evaluation (i.e., predict the number of proof steps left) and tactic prediction (i.e., predict the next proof step to take). We also discuss how we can use the structured representation to embed proof states into R D (Section 5) . Second, we demonstrate the synthesis of Coq proof scripts that makes use of a tactic prediction model for a hand-crafted algebraic rewriting problem (Section 6). Third and finally, we apply baseline models for position evaluation and tactic prediction to the FeitThompson formalization using data extracted by GamePad (Section 7).The code for GamePad, as well as the associated data sets, models and results, are open source on GitHub at https://github.com/ml4tp/gamepad. In this work, we look at theorem proving problem through the lens of a system that enables learning with proofs constructed with human supervision. We highlight three key aspects of the problem at this level. The first concerns obtaining inputs to a learning algorithm that approximate the level of abstraction faced by a human prover. For this, we use an ITP, as it retains aspects of human supervision. GamePad preserves the structure of the proofs (e.g., annotations regarding implicit arguments) so they can be used for building models. The second involves building models that employ the game-like structure of ITP proofs. Here, we experiment with tactic prediction for toy and real world data sets. Finally, as a consequence of theorem proving at a higher-level (compared to SMT solvers), we will need to be careful to distinguish the syntax from the semantics of terms. Our current approach is to provide structured representations of terms so that more semantic structure can be exploited. While our results are preliminary, our hope is that GamePad provides an accessible starting point to explore the application of machine learning in the context of interactive theorem proving.",paper introduce system called GamePad can be has been used explore application machine learning methods theorem proving Coq proof assistant. Interactive theorem provers Coq enable users construct machine-checkable proofs step-by-step manner. Hence provide opportunity explore theorem proving human supervision. use GamePad synthesize proofs simple algebraic rewrite problem train baseline models formalization Feit-Thompson theorem. address position evaluation.e predict number proof steps left tactic prediction.e predict next proof step tasks which arise naturally tactic-based theorem proving. Theorem proving is a challenging AI task involves symbolic reasoning e.g SMT solvers BID2 intuition guided search. Recent work BID7 Loos etal. 2017;has shown promise applying deep learning techniques domain primarily tasks useful automated theorem provers e.g premise selection which operate little human supervision. work aim move closer learning proofs constructed human supervision.We look theorem proving realm formal proofs. formal proof is systematically derived formal system which makes possible algorithmically.e computer check proofs correctness. Thus formal proofs provide perfect learning signal-theorem statements proofs are unambiguous. Human mathematicians usually do not write proofs style instead construct communicate proofs natural language. Although form level detail involved kind proof differ logical content is similar contexts.Our work focuses interactive theorem provers ITPs which are software tools enable human users construct formal proofs. ITPs have at least two features make compelling environments exploring application learning techniques theorem proving. First foremost ITPs provide full-fledged programmable environments. Consequently machine learning infrastructure built ITP can be reused across problem domain crafted study aspect learning theorem proving. Second proofs are constructed humans thus have the constraint must relatively human-understandable Hence ITPs provide access large amounts supervised data.e expert-constructed proofs theorems are mathematically interesting example ITPs have been used build check proofs large mathematical theorems Feit-Thompson theorem BID6 provide provable guarantees complex pieces software CompCert C compiler BID13.We introduce system called GamePad1 exposes parts Coq ITP enable machine learning tasks explore use cases. focus Coq proof assistant two reasons. First Figure1:proof script Coq left resulting proof states proof steps complete proof tree right proof state consists context pink rectangles goal white rectangles initial proof state has as its goal statement are trying prove empty context. arrows indicate what tactic prover used. final states proof are indicated red circles can be transitioned when the goal previous state is trivially true.Coq is a mature system active developer community can be has been used formalize nontrivial theorems including Feit-Thompson CompCert. Second Coq supports extraction verified software. Consequently one can prove program is correct run verified program. ease extraction makes Coq popular choice program verification.Our contributions are the following. First introduce GamePad which provides structured Python representation Coq proofs Section3 including proof states encountered proof steps taken expression abstract syntax trees ASTs tool also enables lightweight interaction Coq can used dynamically build proofs e.g used environment reinforcement learning Tasks can leverage structured representation Section4 include position evaluation.e predict number proof steps left tactic prediction.e predict next proof step take also discuss how we can use structured representation embed proof states R Section5 Second demonstrate synthesis Coq proof scripts makes use tactic prediction model hand-crafted algebraic rewriting problem Section6 Third finally apply baseline models position evaluation tactic prediction FeitThompson formalization using data extracted GamePad Section7.The code GamePad well associated data sets models results are open source GitHub https://github.com/ml4tp/gamepad. work look theorem proving problem lens system enables learning proofs constructed human supervision. highlight three key aspects problem level. first concerns obtaining inputs learning algorithm approximate level abstraction faced human prover. use ITP retains aspects human supervision. GamePad preserves structure proofs e.g annotations regarding implicit arguments can used building models. second involves building models employ game-like structure ITP proofs. experiment tactic prediction toy real world data sets. Finally consequence theorem proving higher-level compared SMT solvers will need careful distinguish syntax semantics terms. current approach is to provide structured representations terms semantic structure can be exploited. results are preliminary hope is that GamePad provides accessible starting point explore application machine learning context interactive theorem proving.,1238,825,413,0.014,1.501,2025/11/05 17:19:00,0.01,1.5,0.5327102803738313,409.077
"Deep neural networks are usually huge, which significantly limits the deployment on low-end devices. In recent years, many
 weight-quantized models have  been proposed. They have small storage and fast inference, but training can still be time-consuming. This can be improved with distributed learning. To reduce the high communication cost due to worker-server synchronization, recently gradient quantization has also been proposed to train deep networks with full-precision weights. 
 In this paper, we theoretically study how the combination of both weight and gradient quantization affects convergence.
 We show  that (i) weight-quantized models converge to an error related to the weight quantization resolution and weight dimension; (ii) quantizing gradients slows convergence by a factor related to the gradient quantization resolution and dimension; and (iii) clipping the gradient before quantization renders this factor dimension-free, thus allowing the use of fewer bits for gradient quantization. Empirical experiments confirm the theoretical convergence results, and demonstrate that quantized networks can speed up training and have comparable performance as full-precision networks. Deep neural networks are usually huge. The high demand in time and space can significantly limit deployment on low-end devices. To alleviate this problem, many approaches have been recently proposed to compress deep networks. One direction is network quantization, which represents each network weight with a small number of bits. Besides significantly reducing the model size, it also accelerates network training and inference. Many weight quantization methods aim at approximating the full-precision weights in each iteration BID3 BID20 BID23 BID15 BID19 BID8 . Recently, loss-aware quantization minimizes the loss directly w.r.t. the quantized weights BID11 BID10 BID14 , and often achieves better performance than approximation-based methods.Distributed learning can further speed up training of weight-quantized networks BID6 . A key challenge is on reducing the expensive communication cost incurred during synchronization of the gradients and model parameters BID17 . Recently, algorithms that sparsify BID0 BID28 or quantize the gradients BID26 BID29 BID2 have been proposed.In this paper, we consider quantization of both the weights and gradients in a distributed environment. Quantizing both weights and gradients has been explored in the DoReFa-Net BID32 , QNN BID12 , WAGE BID30 and ZipML . We differ from them in two aspects. First, existing methods mainly consider learning on a single machine, and gradient quantization is used to reduce the computations in backpropagation. On the other hand, we consider a distributed environment, and use gradient quantization to reduce communication cost and accelerate distributed learning of weight-quantized networks. Second, while DoReFa-Net, QNN and WAGE show impressive empirical results on the quantized network, theoretical guarantees are not provided. ZipML provides convergence analysis, but is limited to stochastic weight quantization, square loss with the linear model, and requires the stochastic gradients to be unbiased. This can be restrictive as most state-of-the-art weight quantization methods BID23 BID20 BID15 BID8 BID11 BID10 ) are deterministic, and the resultant stochastic gradients are biased.In this paper, we relax the restrictions on the loss function, and study in an online learning setting how the gradient precision affects convergence of weight-quantized networks in a distributed environment. The main findings are:1. With either full-precision or quantized gradients, the average regret of loss-aware weight quantization does not converge to zero, but to an error related to the weight quantization resolution ∆ w and dimension d. The smaller the ∆ w or d, the smaller is the error (Theorems 1 and 2). 2. With either full-precision or quantized gradients, the average regret converges with a O(1/ √ T ) rate to the error, where T is the number of iterations. However, gradient quantization slows convergence (relative to using full-precision gradients) by a factor related to gradient quantization resolution ∆ g and d. The larger the ∆ g or d, the slower is the convergence FIG0 ). This can be problematic when (i) the weight quantized model has a large d (e.g., deep networks); and (ii) the communication cost is a bottleneck in the distributed setting, which favors a small number of bits for the gradients, and thus a large ∆ g . 3. For gradients following the normal distribution, gradient clipping renders the speed degradation mentioned above dimension-free. However, an additional error is incurred. The convergence speedup and error are related to how aggressive clipping is performed. More aggressive clipping results in faster convergence, but a larger error (Theorem 3). 4. Empirical results show that quantizing gradients significantly reduce communication cost, and gradient clipping makes speed degradation caused by gradient quantization negligible. With quantized clipped gradients, distributed training of weight-quantized networks is much faster, while comparable accuracy with the use of full-precision gradients is maintained (Section 4).Notations . For a vector x, √ x is the element-wise square root, x 2 is the element-wise square, Diag(x) returns a diagonal matrix with x on the diagonal, and x y is the element-wise multiplication of vectors x and y. For a matrix Q, x 2 Q = x Qx. For a matrix X, √ X is the element-wise square root, and diag(X) returns a vector extracted from the diagonal elements of X. In this paper, we studied loss-aware weight-quantized networks with quantized gradient for efficient communication in a distributed environment. Convergence analysis is provided for weight-quantized models with full-precision, quantized and quantized clipped gradients. Empirical experiments confirm the theoretical results, and demonstrate that quantized networks can speed up training and have comparable performance as full-precision networks.",Deep neural networks are usually huge which significantly limits deployment low-end devices. recent years many weight-quantized models have been proposed. have small storage fast inference training can still time-consuming can be improved distributed learning. reduce high communication cost due worker-server synchronization recently gradient quantization has also proposed train deep networks full-precision weights. paper theoretically study how the combination weight gradient quantization affects convergence. show weight-quantized models converge error related weight quantization resolution weight dimension;ii quantizing gradients slows convergence factor related gradient quantization resolution dimension;iii clipping gradient quantization renders factor dimension-free thus allowing use fewer bits gradient quantization. Empirical experiments confirm theoretical convergence results demonstrate quantized networks can can further speed training have comparable performance full-precision networks. Deep neural networks are usually huge. high demand time space can significantly limit deployment low-end devices. alleviate problem many approaches have been recently proposed compress deep networks. One direction is network quantization which represents network weight small number bits. Besides significantly reducing model size also accelerates network training inference. Many weight quantization methods aim approximating full-precision weights iteration BID3 BID20 BID23 BID15 BID19 BID8. Recently loss-aware quantization minimizes loss directlyw.r.t quantized weights BID11 BID10 BID14 often achieves better performance approximation-based methods.Distributed learning can can further speed training weight-quantized networks BID6. key challenge is on reducing expensive communication cost incurred synchronization gradients model parameters BID17. Recently algorithms sparsify BID0 BID28 quantize gradients BID26 BID29 BID2 have been proposed.In paper consider quantization weights gradients distributed environment. Quantizing weights gradients has been explored DoReFa-Net BID32 QNN BID12 WAGE BID30 ZipML. differ two aspects. First existing methods mainly consider learning single machine gradient quantization is used reduce computations backpropagation. hand consider distributed environment use gradient quantization reduce communication cost accelerate distributed learning weight-quantized networks. Second DoReFa-Net QNN WAGE show impressive empirical results quantized network theoretical guarantees are not provided. ZipML provides convergence analysis is limited stochastic weight quantization square loss linear model requires stochastic gradients unbiased. can be restrictive state-of-the-art weight quantization methods BID23 BID20 BID15 BID8 BID11 BID10 are deterministic resultant stochastic gradients are biased.In paper relax restrictions loss function study online learning setting how the gradient precision affects convergence weight-quantized networks distributed environment. main findings are:1 either full-precision quantized gradients average regret loss-aware weight quantization does not converge zero error related weight quantization resolution∆ w dimension d. smaller ∆w smaller is the error Theorems1 2 2. either full-precision quantized gradients average regret converges 1/√ rate error whereTis number iterations. However gradient quantization slows convergence relative using full-precision gradients factor related gradient quantization resolution∆ g d. larger ∆g slower is the convergence FIG0 can problematic when(i)weight quantized model has a large e.g deep networks ii communication cost is a bottleneck distributed setting which favors small number bits gradients thus large∆g. 3. gradients following normal distribution gradient clipping renders speed degradation mentioned dimension-free However additional error is incurred. convergence speedup error are related how aggressive clipping is performed. aggressive clipping results faster convergence larger error Theorem3 4. Empirical results show quantizing gradients significantly reduce communication cost gradient clipping makes speed degradation caused gradient quantization negligible. quantized clipped gradients distributed training weight-quantized networks is much faster comparable accuracy use full-precision gradients is maintained Section4.Notations vectorx √x is the element-wise square root x2 is the element-wise square Diag x returns diagonal matrix x diagonal x is the element-wise multiplication vectorsx y. matrixQ x2Q xQx. matrixX √X is the element-wise square root diag X returns vector extracted diagonal elements X. paper studied loss-aware weight-quantized networks quantized gradient efficient communication distributed environment. Convergence analysis is provided weight-quantized models full-precision quantized quantized clipped gradients. Empirical experiments confirm theoretical results demonstrate quantized networks can can further speed training have comparable performance full-precision networks.,1186,845,341,0.011,1.404,2025/11/05 17:19:00,0.01,1.535,0.2305295950155758,344.834
"Sequential learning, also called lifelong learning, studies the problem of learning tasks in a sequence with access restricted to only the data of the current task. In this paper we look at a scenario with fixed model capacity, and postulate that the learning process should not be selfish, i.e. it should account for future tasks to be added and thus leave enough capacity for them. To achieve Selfless Sequential Learning we study different regularization strategies and activation functions. We find that
 imposing sparsity at the level of the representation (i.e. neuron activations) is more beneficial for sequential learning than encouraging parameter sparsity. In particular, we propose a novel regularizer, that encourages representation sparsity by means of neural inhibition. It results in few active neurons which in turn leaves more free neurons to be utilized by upcoming tasks. As neural inhibition over an entire layer can be too drastic, especially for complex tasks requiring strong representations,
 our regularizer only inhibits other neurons in a local neighbourhood, inspired by lateral inhibition processes in the brain. We combine our novel regularizer with state-of-the-art lifelong learning methods that penalize changes to important previously learned parts of the network. We show that our new regularizer leads to increased sparsity which translates in consistent performance improvement on diverse datasets. Sequential learning, also referred to as continual, incremental, or lifelong learning (LLL), studies the problem of learning a sequence of tasks, one at a time, without access to the training data of previous or future tasks. When learning a new task, a key challenge in this context is how to avoid catastrophic interference with the tasks learned previously BID11 BID25 . Some methods exploit an additional episodic memory to store a small amount of previous tasks data to regularize future task learning (e.g. BID28 ). Others store previous tasks models and at test time, select one model or merge the models BID1 BID23 . In contrast, in this work we are interested in the challenging situation of learning a sequence of tasks without access to any previous or future task data and restricted to a fixed model capacity, as also studied in ; ; BID8 ; BID31 ; BID38 . This scenario not only has many practical benefits, including privacy and scalability, but also resembles more closely how the mammalian brain learns tasks over time.The mammalian brain is composed of billions of neurons. Yet at any given time, information is represented by only a few active neurons resulting in a sparsity of 90-95% BID24 . In neural biology, lateral inhibition describes the process where an activated neuron reduces the activity of its weaker neighbors. This creates a powerful decorrelated and compact representation with minimum interference between different input patterns in the brain BID49 . This is in stark contrast with artificial neural networks, which typically learn dense representations that are highly entangled BID3 . Such an entangled representation is quite sensitive to changes in the case. First layer indicates input patterns. Learning the first task utilizes parts indicated in red. Task 2 has different input patterns and uses parts shown in green. Orange indicates changed neurons activations as a result of the second task. In (a), when an example from the first task is encountered again, the activations of the first layer will not be affected by the changes, however, the second and later layer activations are changed. Such interference is largely reduced when imposing sparsity on the representation (b).input patterns, in that it responds differently to input patterns with only small variations. BID11 suggests that an overlapped internal representation plays a crucial role in catastrophic forgetting and reducing this overlap would result in a reduced interference. BID5 show that when the amount of overfitting in a neural network is reduced, the representation correlation is also reduced. As such , learning a disentangled representation is more powerful and less vulnerable to catastrophic interference. However , if the learned disentangled representation at a given task is not sparse, only little capacity is left for the learning of new tasks. This would in turn result in either an underfitting to the new tasks or again a forgetting of previous tasks. In contrast , a sparse and decorrelated representation would lead to a powerful representation and at the same time enough free neurons that can be changed without interference with the neural activations learned for the previous tasks.In general, sparsity in neural networks can be thought of either in terms of the network parameters or in terms of the representation (i.e., the activations). In this paper we postulate, and confirm experimentally, that a sparse and decorrelated representation is preferable over parameter sparsity in a sequential learning scenario. There are two arguments for this: first, a sparse representation is less sensitive to new and different patterns (such as data from new tasks) and second, the training procedure of the new tasks can use the free neurons leading to less interference with the previous tasks, hence reducing forgetting. In contrast, when the effective parameters are spread among different neurons, changing the ineffective ones would change the function of their corresponding neurons and hence interfere with previous tasks (see also FIG0 ). Based on these observations, we propose a new regularizer that exhibits a behavior similar to the lateral inhibition in biological neurons. The main idea of our regularizer is to penalize neurons that are active at the same time. This leads to more sparsity and a decorrelated representation. However, complex tasks may actually require multiple active neurons in a layer at the same time to learn a strong representation. Therefore, our regularizer , Sparse coding through Local Neural Inhibition and Discounting (SLNID), only penalizes neurons locally. Furthermore, we don't want inhibition to affect previously learned tasks, even if later tasks use neurons from earlier tasks. An important component of SLNID is thus to discount inhibition from/to neurons which have high neuron importance -a new concept that we introduce in analogy to parameter importance BID50 . When combined with a state-of-the-art important parameters preservation method , our proposed regularizer leads to sparse and decorrelated representations which improves the lifelong learning performance.Our contribution is threefold. First, we direct attention to Selfless Sequential Learning and study a diverse set of representation based regularizers, parameter based regularizers, as well as sparsity inducing activation functions to this end. These have not been studied extensively in the lifelong learning literature before. Second, we propose a novel regularizer, SLNID, which is inspired by lateral inhibition in the brain. Third, we show that our proposed regularizer consistently outperforms alternatives on three diverse datasets (Permuted MNIST, CIFAR, Tiny Imagenet) and we compare to and outperform state-of-the-art LLL approaches on an 8-task object classification challenge. SLNID can be applied to different regularization based LLL approaches, and we show experiments with MAS and EWC .In the following, we first discuss related approaches to LLL and different regularization criteria from a LLL perspective (Section 2). We proceed by introducing Selfless Sequential Learning and detailing our novel regularizer (Section 3). Section 4 describes our experimental evaluation, while Section 5 concludes the paper. In this paper we study the problem of sequential learning using a network with fixed capacity -a prerequisite for a scalable and computationally efficient solution. A key insight of our approach is that in the context of sequential learning (as opposed to other contexts where sparsity is imposed, such as network compression or avoiding overfitting), sparsity should be imposed at the level of the representation rather than at the level of the network parameters. Inspired by lateral inhibition in the mammalian brain, we impose sparsity by means of a new regularizer that decorrelates nearby active neurons. We integrate this in a model which learns selflessly a new task by leaving capacity for future tasks and at the same time avoids forgetting previous tasks by taking into account neurons importance.",Sequential learning also called lifelong learning studies problem learning tasks sequence access restricted data current task. paper look scenario fixed model capacity postulate learning process should not be selfish.e should account future tasks added thus leave enough capacity them. achieve Selfless Sequential Learning study different regularization strategies activation functions. find imposing sparsity level representation.e neuron activations is more beneficial sequential learning encouraging parameter sparsity. particular propose novel regularizer encourages representation sparsity means neural inhibition. results active neurons which in turn leaves free neurons utilized upcoming tasks. neural inhibition entire layer can be too drastic especially complex tasks requiring strong representations regularizer inhibits neurons local neighbourhood which is inspired lateral inhibition processes brain. combine novel regularizer state-of-the-art lifelong learning methods penalize changes important previously learned parts network. show new regularizer leads increased sparsity which translates consistent performance improvement diverse datasets. Sequential learning also referred continual incremental lifelong learning LLL studies problem learning sequence tasks one time without access training data previous future tasks. When learning new task key challenge context is how to avoid catastrophic interference tasks learned previously BID11 BID25. methods exploit additional episodic memory store small amount previous tasks data regularize future task learning e.g BID28 Others store previous tasks models test time select one model merge models BID1 BID23. contrast work are interested challenging situation learning sequence tasks without access previous future task data restricted fixed model capacity also studied in;BID8;BID31;BID38. scenario has many practical benefits including privacy scalability also resembles closely how the mammalian brain learns tasks time.The mammalian brain is composed billions neurons. Yet given time information is represented active neurons resulting sparsity 90-95 BID24. neural biology lateral inhibition describes process where an activated neuron reduces activity weaker neighbors. creates powerful decorrelated compact representation minimum interference different input patterns brain BID49. is in stark contrast artificial neural networks which typically learn dense representations are highly entangled BID3. entangled representation is quite sensitive changes case. First layer indicates input patterns. Learning first task utilizes parts indicated red. Task2 has different input patterns uses parts shown green. Orange indicates changed neurons activations result second task. whenan example first task is encountered activations first layer will not be affected changes however second later layer activations are changed. interference is largely reduced when imposing sparsity representation b.input patterns responds differently input patterns small variations. BID11 suggests overlapped internal representation plays crucial role catastrophic forgetting reducing overlap would result reduced interference. BID5 show when the amount overfitting neural network is reduced representation correlation is also reduced. learning disentangled representation is more powerful less vulnerable catastrophic interference. However if the learned disentangled representation given task is not sparse little capacity is left learning new tasks. would turn result either underfitting new tasks forgetting previous tasks. contrast sparse decorrelated representation would lead powerful representation time enough free neurons can be changed without interference neural activations learned previous tasks.In general sparsity neural networks can be thought either terms network parameters terms representation.e activations paper postulate confirm experimentally sparse decorrelated representation is preferable parameter sparsity sequential learning scenario. are two arguments this:first sparse representation is less sensitive new different patterns data new tasks second training procedure new tasks can use free neurons leading less interference previous tasks hence reducing forgetting. contrast when the effective parameters are spread among different neurons changing ineffective ones would change function corresponding neurons hence interfere previous tasks see also FIG0 Based observations propose new regularizer exhibits behavior similar lateral inhibition biological neurons. main idea regularizer is to penalize neurons are active time. leads sparsity decorrelated representation. However complex tasks may actually require multiple active neurons layer time learn strong representation. Therefore regularizer Sparse coding Local Neural Inhibition Discounting SLNID penalizes neurons locally. Furthermore want inhibition affect previously learned tasks even if later tasks use neurons earlier tasks. important component SLNID is thus discount inhibition/neurons which have high neuron importance-a new concept introduce analogy parameter importance BID50. When combined state-of-the-art important parameters preservation method proposed regularizer leads sparse decorrelated representations which improves lifelong learning performance.Our contribution is threefold. First direct attention Selfless Sequential Learning study diverse set representation based regularizers parameter based regularizers well sparsity inducing activation functions end. have not been studied extensively lifelong learning literature before. Second propose novel regularizer SLNID which is inspired lateral inhibition brain. Third show proposed regularizer consistently outperforms alternatives three diverse datasets Permuted MNIST CIFAR Tiny Imagenet compare outperform state-of-the-art LLL approaches 8-task object classification challenge. SLNID can be applied different regularization based LLL approaches show experiments MAS EWC.In following first discuss related approaches LLL different regularization criteria LLL perspective Section2 proceed introducing Selfless Sequential Learning detailing novel regularizer Section3 Section 4 describes experimental evaluation Section 5 concludes paper. paper study problem sequential learning using network fixed capacity -a prerequisite scalable computationally efficient solution. key insight approach is that in the context sequential learning opposed contexts where sparsity is imposed network compression avoiding overfitting sparsity should be imposed level representation rather level network parameters. Inspired lateral inhibition mammalian brain impose sparsity means new regularizer decorrelates nearby active neurons. integrate model which learns selflessly new task leaving capacity future tasks time avoids forgetting previous tasks taking account neurons importance.,1573,1054,519,0.017,1.492,2025/11/05 17:19:00,0.01,1.554,0.5046728971962615,494.625
"A Synaptic Neural Network (SynaNN) consists of synapses and neurons. Inspired by the synapse research of neuroscience, we built a synapse model with a nonlinear synapse function of excitatory and inhibitory channel probabilities. Introduced the concept of surprisal space and constructed a commutative diagram, we proved that the inhibitory probability function -log(1-exp(-x)) in surprisal space is the topologically conjugate function of the inhibitory complementary probability 1-x in probability space. Furthermore, we found that the derivative of the synapse over the parameter in the surprisal space is equal to the negative Bose-Einstein distribution. In addition, we constructed a fully connected synapse graph (tensor) as a synapse block of a synaptic neural network. Moreover, we proved the gradient formula of a cross-entropy loss function over parameters, so synapse learning can work with the gradient descent and backpropagation algorithms. In the proof-of-concept experiment, we performed an MNIST training and testing on the MLP model with synapse network as hidden layers. Synapses play an important role in biological neural networks BID11 ). They are joint points of neurons' connection with the capability of learning and memory in neural networks. Based on the analysis of excitatory and inhibitory channels of synapses BID11 ), we proposed a probability model BID6 for probability introduction) of the synapse together with a non-linear function of excitatory and inhibitory probabilities BID17 (synapse function)). Inspired by the concept of surprisal from (Jones (1979)(self-information), BID15 , BID2 (surprisal analysis), BID16 (surprisal theory in language)) or negative logarithmic space BID21 ), we proposed the concept of surprisal space and represented the synapse function as the addition of the excitatory function and inhibitory function in the surprisal space. By applying a commutative diagram, we figured out the fine structure of inhibitory function and proved that it was the topologically conjugate function of an inhibitory function. Moreover, we discovered (rediscovered) that the derivative of the inhibitory function over parameter was equal to the negative Bose-Einstein distribution BID22 ). Furthermore, we constructed a fully connected synapse graph and figured out its synapse tensor expression. From synapse tensor and a cross-entropy loss function, we found and proved its gradient formula that was the basis for gradient descent learning and using backpropagation algorithm. In surprisal space, the parameter (weight) updating for learning was the addition of the value of the negative Bose-Einstein distribution. Finally, we designed the program to implement a Multiple Layer Perceptrons (MLP) BID20 ) for MNIST BID14 ) and tested it to achieve the near equal accuracy of standard MLP in the same setting. In this paper, we presented and analyzed a Synaptic Neural Network (SynaNN). We found the fine structure of synapse and the construction of synapse network as well as the BE distribution in the gradient descent learning. In surprisal space, the input of a neuron is the addition of the identity function and the sum of topologically conjugate functions of inhibitory synapses which is the sum of bits of information. The formula of surprisal synapse function is defined as LS(u, v; θ, γ) = (θ + u) + (I • F • I −1 )(γ + v))The non-linear synaptic neural network may be implemented by physical or chemical components.Instead of using a simple linear synapse function, more synapse functions maybe found in the researches and applications of neural network.",Synaptic Neural Network SynaNN consists synapses neurons. Inspired synapse research neuroscience built synapse model nonlinear synapse function excitatory inhibitory channel probabilities. Introduced concept surprisal space constructed commutative diagram proved inhibitory probability function -log 1-exp -x surprisal space is the topologically conjugate function inhibitory complementary probability 1-x probability space. Furthermore found derivative synapse parameter surprisal space is equal negative Bose-Einstein distribution. addition constructed fully connected synapse graph tensor synapse block synaptic neural network. Moreover proved gradient formula cross-entropy loss function parameters synapse learning can work gradient descent backpropagation algorithms. proof-of-concept experiment performed MNIST training testing MLP model synapse network hidden layers. Synapses play important role biological neural networks BID11 are joint points neurons' connection capability learning memory neural networks. Based analysis excitatory inhibitory channels synapses BID11 proposed probability model BID6 probability introduction synapse together non-linear function excitatory inhibitory probabilities BID17 synapse function Inspired concept surprisal Jones 1979 self-information BID15 BID2 surprisal analysis BID16 surprisal theory language negative logarithmic space BID21 proposed concept surprisal space represented synapse function addition excitatory function inhibitory function surprisal space. applying commutative diagram figured fine structure inhibitory function proved was the topologically conjugate function inhibitory function. Moreover discovered rediscovered derivative inhibitory function parameter was equal negative Bose-Einstein distribution BID22 Furthermore constructed fully connected synapse graph figured synapse tensor expression. synapse tensor cross-entropy loss function found proved gradient formula was the basis gradient descent learning using backpropagation algorithm. surprisal space parameter weight updating learning was the addition value negative Bose-Einstein distribution. Finally designed program implement Multiple Layer Perceptrons MLP BID20 MNIST BID14 tested achieve near equal accuracy standard MLP setting. paper presented analyzed Synaptic Neural Network SynaNN found fine structure synapse construction synapse network well distribution gradient descent learning. surprisal space input neuron is the addition identity function sum topologically conjugate functions inhibitory synapses which is the sum bits information. formula surprisal synapse function is defined LS u v;θ γ θ+u+•F• −1 γ+v non-linear synaptic neural network may implemented physical chemical components.Instead using simple linear synapse function synapse functions maybe found researches applications neural network.,732,477,255,0.007,1.535,2025/11/05 17:19:00,0.0,1.636,0.6386292834890962,250.99
"Many types of relations in physical, biological, social and information systems can be modeled as homogeneous or heterogeneous concept graphs. Hence, learning from and with graph embeddings has drawn a great deal of research interest recently, but only ad hoc solutions have been obtained this far. In this paper, we conjecture that the one-shot supervised learning mechanism is a bottleneck in improving the performance of the graph embedding learning algorithms, and propose to extend this by introducing a multi-shot unsupervised learning framework. Empirical results on several real-world data set show that the proposed model consistently and significantly outperforms existing state-of-the-art approaches on knowledge base completion and graph based multi-label classification tasks. Recent studies have highlighted the importance of learning distributed representations for symbolic data in a wide variety of artificial intelligence tasks BID2 . Research on word embeddings BID14 has led to breakthroughs in many related areas, such as machine translation BID0 , question answering BID28 , and visual-semantic alignments BID10 . However, learning to predict for large-scale knowledge graphs (KGs) is still a challenging problem left, this is largely due to the diversity of the ontologies, and the semantic richness of the concepts, which makes it really hard to generate proper and universally applicable graph embeddings, simply based on word-level embeddings BID4 .Being able to generate reasonable and accurate distributed representations for large-scale knowledge graphs would be particularly valuable, in that it may help predict unobserved facts from limited concepts, uncover gaps in our knowledge, suggest new downstream applications, which clearly reflects the central concerns of the artificial intelligence BID18 BID9 . Therefore , massive attention has been devoted to the potential of embedding entities and relationships of multi-relational data in low-dimensional vector spaces in recent years BID26 .In this paper , we consider the problem of developing simple and efficient model for learning neural representation of generalized knowledge graphs, including the multi-relational heterogeneous graphs, and more specifically defined homogeneous graphs (such as social and biological networks).Following the pioneer work of BID17 and BID3 , almost all of the stateof-the-art approaches try to model the graph embedding learning problem as supervised binary classification problems, their objective functions are usually one-shot (single purpose) . We argue that prior research in this area might have been affected and biased by "" established priors"", which prevents the formulation of a methodology that is objective enough to cope with the highly sparse knowledge graphs. We propose to handle the embedded learning problem of knowledge graphs with an unsupervised neural network model, called the Graph Embedding Network (GEN). The proposed model consists of three simple multi-layer perceptron (MLP) cells, each cell operates in response to a different ""query"" with regard to the input fact, which will be trained sequentially. The formulation of the model is inspired by the neural sequence-to-sequence (seq2seq) model BID23 , except that we attempt to use the MLP cells to mimic the sequence learning capability of the recurrent neural network (RNN), to model the semantic structure of the knowledge graphs.The major contribution of this paper is that: (1) we propose GEN, a novel and efficient multishot framework for embedding learning in generalized knowledge graphs. (2) We show how GEN is in accordance with established principles in cognitive science, providing flexibility in learning representations that works on graphs conforming to different domains. Representation learning of knowledge graphs is a key concern for artificial intelligence and cognitive science. Many types of relations in physical, biological, social and information systems can be modeled with concept (knowledge) graphs. In this paper, we present an efficient scalable framework for learning conceptual embeddings of entities and relations in generalized knowledge graphs, including the homogeneous and heterogeneous graphs. We give evidence that the proposed model learns good representations of all these graphs for knowledge inference and supervised learning. For future work, we plan to investigate more thoroughly the efficacy of the proposed modeling framework, with respect to the decomposition of the semantic information conveyed by the linked concepts into elementary information, i.e. the four Q&A pairs. Also, we seek to enhance the quality of scientific investigations and theoretical conceptualizations on graph embedding learning in the context of semantic interoperability, for there is usually no possibility to interpret the embedded information meaningfully and accurately in order to produce useful results as defined by existing algorithms.",Many types relations physical biological social information systems can be modeled homogeneous heterogeneous concept graphs. Hence learning graph embeddings has drawn great deal research interest recently ad hoc solutions have been obtained far. paper conjecture one-shot supervised learning mechanism is a bottleneck improving performance graph embedding learning algorithms propose extend introducing multi-shot unsupervised learning framework. Empirical results several real-world data set show proposed model consistently significantly outperforms existing state-of-the-art approaches knowledge base completion graph based multi-label classification tasks. Recent studies have highlighted importance learning distributed representations symbolic data wide variety artificial intelligence tasks BID2. Research word embeddings BID14 has led breakthroughs many related areas machine translation BID0 question answering BID28 visual-semantic alignments BID10. However learning predict large-scale knowledge graphs KGs is still challenging problem left is largely due diversity ontologies semantic richness concepts which makes really hard generate proper universally applicable graph embeddings simply based word-level embeddings BID4.Being able generate reasonable accurate distributed representations large-scale knowledge graphs would particularly valuable may help predict unobserved facts limited concepts uncover gaps knowledge suggest new downstream applications which clearly reflects central concerns artificial intelligence BID18 BID9. Therefore massive attention has been devoted potential embedding entities relationships multi-relational data low-dimensional vector spaces recent years BID26.In paper consider problem developing simple efficient model learning neural representation generalized knowledge graphs including multi-relational heterogeneous graphs specifically defined homogeneous graphs social biological networks.Following pioneer work BID17 BID3 almost stateof-the-art approaches try model graph embedding learning problem supervised binary classification problems objective functions are usually one-shot single purpose argue prior research area might have been affected biased established priors which prevents formulation methodology is objective enough cope highly sparse knowledge graphs. propose handle embedded learning problem knowledge graphs unsupervised neural network model called Graph Embedding Network GEN proposed model consists three simple multi-layer perceptron MLP cells cell operates response different query regard input fact which will be trained sequentially. formulation model is inspired neural sequence-to-sequence seq2seq model BID23 except attempt use MLP cells mimic sequence learning capability recurrent neural network RNN model semantic structure knowledge graphs.The major contribution paper that:1 propose GEN novel efficient multishot framework embedding learning generalized knowledge graphs. 2 show how GEN is in accordance established principles cognitive science providing flexibility learning representations works graphs conforming different domains. Representation learning knowledge graphs is a key concern artificial intelligence cognitive science. Many types relations physical biological social information systems can be modeled concept knowledge graphs. paper present efficient scalable framework learning conceptual embeddings entities relations generalized knowledge graphs including homogeneous heterogeneous graphs. give evidence proposed model learns good representations graphs knowledge inference supervised learning. future work plan investigate thoroughly efficacy proposed modeling framework respect decomposition semantic information conveyed linked concepts elementary information.e fourQ pairs. Also seek enhance quality scientific investigations theoretical conceptualizations graph embedding learning context semantic interoperability is usually possibility interpret embedded information meaningfully accurately order produce useful results defined existing algorithms.,861,571,290,0.009,1.508,2025/11/05 17:19:00,0.0,1.429,0.5545171339563861,297.291
"We introduce and study minimax curriculum learning (MCL), a new method for adaptively selecting a sequence of training subsets for a succession of stages in machine learning. The subsets are encouraged to be small and diverse early on, and then larger, harder, and allowably more homogeneous in later stages. At each stage, model weights and training sets are chosen by solving a joint continuous-discrete minimax optimization, whose objective is composed of a continuous loss (reflecting training set hardness) and a discrete submodular promoter of diversity for the chosen subset. MCL repeatedly solves a sequence of such optimizations with a schedule of increasing training set size and decreasing pressure on diversity encouragement. We reduce MCL to the minimization of a surrogate function handled by submodular maximization and continuous gradient methods. We show that MCL achieves better performance and, with a clustering trick, uses fewer labeled samples for both shallow and deep models while achieving the same performance. Our method involves repeatedly solving constrained submodular maximization of an only slowly varying function on the same ground set. Therefore, we develop a heuristic method that utilizes the previous submodular maximization solution as a warm start for the current submodular maximization process to reduce computation while still yielding a guarantee. Inspired by the human interaction between teacher and student, recent studies BID28 BID2 BID56 ) support that learning algorithms can be improved by updating a model on a designed sequence of training sets, i.e., a curriculum. This problem is addressed in curriculum learning (CL) BID6 , where the sequence is designed by a human expert or heuristic before training begins. Instead of relying on a teacher to provide the curriculum, self-paced learning (SPL) BID31 BID58 BID57 BID59 chooses the curriculum during the training process. It does so by letting the student (i.e., the algorithm) determine which samples to learn from based on their hardness. Given a training set D = {(x 1 , y 1 ), . . . , (x n , y n )} of n samples and loss function L(y i , f (x i , w)), where x i ∈ R m represents the feature vector for the i th sample, y i is its label, and f (x i , w) is the predicted label provided by a model with weight w, SPL performs the following: DISPLAYFORM0 SPL jointly learns the model weights w and sample weights ν, which end up being 0-1 indicators of selected samples, and it does so via alternating minimization. Fixing w, minimization w.r.t. ν selects samples with loss L(y i , f (x i , w)) < λ, where λ is a ""hardness parameter"" as it corresponds to the hardness as measure by the current loss (since with large λ, samples with greater loss are allowed in). Self-paced curriculum learning BID27 introduces a blending of ""teacher mode"" in CL and ""student mode"" in SPL, where the teacher can define a region of ν by attaching a linear constraint a T ν ≤ c to Eq. (1). SPL with diversity (SPLD) BID26 , adds to Eq. (1) a negative group sparse regularization term −γ ν 2,1 −γ b j=1 ν (j) 2 , where the samples are divided into b groups beforehand and ν (j) is the weight vector for the j th group. Samples coming from different groups are thus preferred, to the extent that γ > 0 is large. CL, SPL, and SPLD can be seen as a form of continuation scheme BID1 ) that handles a hard task by solving a sequence of tasks moving from easy to hard; the solution to each task is the warm start for the next slightly harder task. That is, each task, in the present case, is determined by the training data subset and other training hyperparameters, and the resulting parameters at the end of a training round are used as the initial parameters for the next training round. Such continuation schemes can reduce the impact of local minima within neural networks BID7 BID5 . With SPL, after each round of alternating minimization to optimize Eq. (1), λ is increased so that the next round selects samples that have a larger loss, a process BID28 BID59 BID2 ) that can both help avoid local minima and reduce generalization error. In SPLD, γ is also increased between training rounds, increasingly preferring diversity. In each case, each round results in a fully trained model for the currently selected training samples.Selection of training samples has been studied in other settings as well, often with a different motivation. In active learning (AL) BID53 and experimental design BID43 , the learner can actively query labels of samples from an unlabeled pool during the training process, and the goal is to reduce annotation costs. The aim is to achieve the same or better performance using fewer labeled samples by ruling out uninformative ones. Diversity modeling was introduced to AL in BID62 . It uses submodular maximization to select diverse training batches from the most uncertain samples. However, changing the diversity during the learning process has not been investigated as far as we know. In boosting BID51 BID19 , the goal is to learn an ensemble of weak classifiers sequentially; it does this by assigning weights to all samples, with larger weights given to samples having larger loss measured by an aggregation of previously trained models. Both active learning and boosting favor samples that are difficult to predict, since they are the most informative to learn. For example, uncertainty sampling BID13 BID52 BID14 BID15 selects samples that are most uncertain, while query by committee BID54 BID14 BID0 selects the ones that multiple models most disagree on. With machine teaching BID28 BID66 BID49 BID65 , a separate teacher helps the training procedure find a good model.The SPL approach starts with a smaller set of easy samples and gradually increases the difficulty of the chosen samples as measured by the sample loss of the model produced by previous round's training. One of the difficulties of this approach is the following: since for any given value of λ the relatively easiest samples are chosen, there is a good chance that the process can repeatedly select a similar training set over multiple rounds and therefore can learn slowly. This is precisely the problem that SPLD address -by concomitantly increasing the desired diversity over rounds, the sample selection procedure chooses from an increasingly diverse set of different groups, as measured by ν 2,1 . Therefore, in SPLD, early stages train on easier not necessarily diverse samples and later stages train on harder more diverse samples.There are several challenges remaining with SPLD, however. One is that in early stages, it is still possible to repeatedly select a similar training set over multiple rounds since diversity might not increase dramatically between successive rounds. Potentially more problematically, it is not clear that having a large diversity selection weight in late stages is desirable. For example, with a reasonably trained model, it might be best to select primarily the hardest samples in the part of the space near the difficult regions of the decision boundaries. With a high diversity weight, samples in these difficult decision boundary regions might be avoided in favor of other samples perhaps already well learnt and having a large margin only because they are diverse, thereby leading to wasted effort. At such point, it would be beneficial to choose points having small margin from the same region but that might not have the greatest diversity, especially when using only a simple notion of diversity such as the group sparse norm v 2,1 . Also, it is possible that late stages of learning can select outliers only because they are both hard and diverse. Lastly, the SPL/SPLD min-min optimization involves minimizing a lower bound of the loss, while normally one would, if anything, wish to minimize the loss directly or at least an upper bound.Motivated by these issues, we introduce a new form of CL that chooses the hardest diverse samples in early rounds of training and then actually decreases, rather than increases, diversity as training rounds proceed. Our contention is that diversity is more important during the early phases of training when only relatively few samples are selected. Later rounds of training will naturally have more diversity opportunity simply because the size of the selected samples is much larger. Also, to avoid successive rounds selecting similar sets of samples, our approach selects the hardest, rather than the easiest, samples at each round. Hence, if a set of samples is learnt well during one training round, those samples will tend to be ill-favored in the next round because they become easier. We also measure hardness via the loss function, but the selection is always based on the hardest and most diverse samples of a given size k, where the degree of diversity is controlled by a parameter λ, and where diversity is measured by an arbitrary non-monotone submodular function. In fact, for binary variables the group sparse norm is also submodular where ν 2,1 = b j=1|C j ∩ A| = F (A) where A is the set for which ν is the characteristic vector, and C j is the set of samples in the j th group. Our approach allows the full expressive class of submodular functions to be used to measure diversity since the selection phases is based on submodular optimization.Evidence for the naturalness of such hardness and diversity adjustment in a curriculum can also be found in human education. For example, courses in primary school usually cover a broad, small, and relatively easy range of topics, in order to expose the young learner to a diversity of knowledge early on. In college and graduate school, by contrast, students focus on advanced deeper knowledge within their majors. As another example, studies of bilingualism BID8 BID35 BID39 BID29 show that learning multiple languages in childhood is beneficial for future brain development, but early-age multi-lingual learning is usually not advanced or concentrated linguistically for any of the languages involved. Still other studies argue that difficulty can be desired at early human learning stages BID10 BID38 ).","introduce study minimax curriculum learning MCL new method adaptively selecting sequence training subsets succession stages machine learning. subsets are encouraged small diverse early larger harder allowably homogeneous later stages. stage model weights training sets are chosen solving joint continuous-discrete minimax optimization whose objective is composed continuous loss reflecting training set hardness discrete submodular promoter diversity chosen subset. MCL repeatedly solves sequence optimizations schedule increasing training set size decreasing pressure diversity encouragement. reduce MCL minimization surrogate function handled submodular maximization continuous gradient methods. show MCL achieves better performance clustering trick uses fewer labeled samples shallow deep models achieving performance. method involves repeatedly solving constrained submodular maximization slowly varying function ground set. Therefore develop heuristic method utilizes previous submodular maximization solution warm start current submodular maximization process reduce computation still yielding guarantee. Inspired human interaction teacher student recent studies BID28 BID2 BID56 support learning algorithms can be improved updating model designed sequence training sets.e curriculum. problem is addressed curriculum learning CL BID6 where the sequence is designed human expert heuristic training begins. Instead relying teacher provide curriculum self-paced learning SPL BID31 BID58 BID57 BID59 chooses curriculum training process. does so by letting student.e algorithm determine which samples learn based hardness. Given training set x1 1 where xn n n samples loss functionL f x w wherex ∈R represents feature vector th sample is label f x w is the predicted label provided model weightw SPL performs following:DISPLAYFORM0 SPL jointly learns model weightsw sample weightsν which end 0-1 indicators selected samples does via alternating minimization. Fixingw minimizationw.r.t ν selects samples lossL f x w λ whereλ is a hardness parameter corresponds hardness measure current loss since largeλ where the samples greater loss are allowed Self-paced curriculum learning BID27 introduces blending teacher mode CL student mode SPL where the teacher can define region ν attaching linear constraint ν≤c Eq. 1 SPL diversity SPLD BID26 adds Eq. 1 negative group sparse regularization term −γ ν 2,1 −γ b j=1ν j 2 where the samples are divided b groups beforehand ν j is the weight vector j th group. Samples coming different groups are thus preferred extent γ 0 is large. CL SPL SPLD can be seen form continuation scheme BID1 handles hard task solving sequence tasks moving easy hard;solution task is the warm start next slightly harder task. is,each task present case is determined training data subset training hyperparameters resulting parameters end training round are used initial parameters next training round. continuation schemes can reduce impact local minima within neural networks BID7 BID5. SPL round alternating minimization optimizeEq. 1 λ is increased next round selects samples have a larger loss process BID28 BID59 BID2 can both help avoid local minima reduce generalization error. SPLD γ is also increased training rounds increasingly preferring diversity. case round results fully trained model currently selected training samples.Selection training samples has been studied settings well often different motivation. active learning AL BID53 experimental design BID43 learner can actively query labels samples unlabeled pool training process goal is to reduce annotation costs. aim is to achieve better performance using fewer labeled samples ruling uninformative ones. Diversity modeling was introduced AL BID62. uses submodular maximization select diverse training batches uncertain samples. However changing diversity learning process has not been investigated far know. boosting BID51 BID19 goal is to learn ensemble weak classifiers sequentially;does this by assigning weights samples larger weights given samples larger loss measured aggregation previously trained models. active learning boosting favor samples are difficult predict since are the most informative learn. example uncertainty sampling BID13 BID52 BID14 BID15 selects samples are most uncertain query committee BID54 BID14 BID0 selects ones multiple models disagree on. machine teaching BID28 BID66 BID49 BID65 separate teacher helps training procedure find good model.The SPL approach starts smaller set easy samples gradually increases difficulty chosen samples measured sample loss model produced previous round's training. One difficulties approach is the following:since given value λ relatively easiest samples are chosen is a good chance process can repeatedly select similar training set multiple rounds therefore can learn slowly. is precisely problem SPLD address -by concomitantly increasing desired diversity rounds sample selection procedure chooses increasingly diverse set different groups measured ν 2,1 Therefore SPLD early stages train easier necessarily diverse samples later stages train harder diverse samples.There are several challenges remaining SPLD however. One is that in early stages is still possible repeatedly select similar training set multiple rounds since diversity might increase dramatically successive rounds. Potentially problematically is not clear large diversity selection weight late stages is desirable. example reasonably trained model might best select primarily hardest samples part space near difficult regions decision boundaries. high diversity weight where the samples difficult decision boundary regions might avoided favor samples perhaps already well learnt large margin are diverse thereby leading wasted effort. point would beneficial choose points small margin region might have the greatest diversity especially when using simple notion diversity group sparse normv 2,1 Also is possible late stages learning can select outliers are hard diverse. Lastly SPL/SPLD min-min optimization involves minimizing lower bound loss normally one would if anything wish minimize loss directly least upper bound.Motivated issues introduce new form CL chooses hardest diverse samples early rounds training actually decreases rather increases where diversity training rounds proceed. contention is that diversity is more important early phases training when only relatively samples are selected. Later rounds training will naturally have more diversity opportunity simply size selected samples is much larger. Also avoid successive rounds selecting similar sets samples approach selects hardest rather easiest where the samples round. Hence if a set samples is learnt well one training round where the samples will tend ill-favored next round become easier. also measure hardness via loss function selection is always based hardest diverse samples given sizek where the degree diversity is controlled parameterλ where diversity is measured arbitrary non-monotone submodular function. fact binary variables group sparse norm is also submodular where ν 2,1 b j=1|Cj∩ A| F where is the set whichν is the characteristic vector Cj is the set samples j th group. approach allows full expressive class submodular functions used measure diversity since selection phases is based submodular optimization.Evidence naturalness hardness diversity adjustment curriculum can also found human education. example courses primary school usually cover broad small relatively easy range topics order expose young learner diversity knowledge early on. college graduate school contrast students focus advanced deeper knowledge within majors. another example studies bilingualism BID8 BID35 BID39 BID29 show learning multiple languages childhood is beneficial future brain development early-age multi-lingual learning is usually advanced concentrated linguistically languages involved. Still studies argue difficulty can be desired early human learning stages BID10 BID38",2034,1351,683,0.028,1.506,2025/11/05 17:19:00,0.01,1.477,0.5482866043613706,737.397
"Progress in probabilistic generative models has accelerated, developing richer models with neural architectures, implicit densities, and with scalable algorithms for their Bayesian inference. However, there has been limited progress in models that capture causal relationships, for example, how individual genetic factors cause major human diseases. In this work, we focus on two challenges in particular: How do we build richer causal models, which can capture highly nonlinear relationships and interactions between multiple causes? How do we adjust for latent confounders, which are variables influencing both cause and effect and which prevent learning of causal relationships? To address these challenges, we synthesize ideas from causality and modern probabilistic modeling. For the first, we describe implicit causal models, a class of causal models that leverages neural architectures with an implicit density. For the second, we describe an implicit causal model that adjusts for confounders by sharing strength across examples. In experiments, we scale Bayesian inference on up to a billion genetic measurements. We achieve state of the art accuracy for identifying causal factors: we significantly outperform the second best result by an absolute difference of 15-45.3%. Probabilistic models provide a language for specifying rich and flexible generative processes BID5 Murphy, 2012) . Recent advances expand this language with neural architectures, implicit densities, and with scalable algorithms for their Bayesian inference BID9 BID15 . However, there has been limited progress in models that capture high-dimensional causal relationships (Pearl, 2000; BID13 Imbens & Rubin, 2015) . Unlike models which learn statistical relationships, causal models let us manipulate the generative process and make counterfactual statements, that is, what would have happened if the distributions changed.As the running example in this work, consider genome-wide association studies (GWAS) BID19 BID7 Kang et al., 2010) . The goal of GWAS is to understand how genetic factors, i.e., single nucleotide polymorphisms (SNPs), cause traits to appear in individuals. Understanding this causation both lets us predict whether an individual has a genetic predisposition to a disease and also understand how to cure the disease by targeting the individual SNPs that cause it.With this example in mind, we focus on two challenges to combining modern probabilistic models and causality. The first is to develop richer, more expressive causal models. Probabilistic causal models represent variables as deterministic functions of noise and other variables, and existing work usually focuses on additive noise models (Hoyer et al., 2009 ) such as linear mixed models (Kang et al., 2010) . These models apply simple nonlinearities such as polynomials, hand-engineered low order interactions between inputs, and assume additive interaction with, e.g., Gaussian noise. In GWAS, strong evidence suggests that susceptibility to common diseases is influenced by epistasis (the interaction between multiple genes) (Culverhouse et al., 2002; McKinney et al., 2006) . We would like to capture and discover such interactions. This requires models with nonlinear, learnable interactions among the inputs and the noise.The second challenge is how to address latent population-based confounders. In GWAS, both latent population structure, i.e., subgroups in the population with ancestry differences, and relatedness among sample individuals produce spurious correlations among SNPs to the trait of interest. Existing methods correct for this correlation in two stages BID19 BID7 Kang et al., 2010) : first, estimate the confounder given data; then, run standard causal inferences given the estimated confounder. These methods are effective in some settings, but they are difficult to understand as principled causal models, and they cannot easily accommodate complex latent structure.To address these challenges, we synthesize ideas from causality and modern probabilistic modeling. For the first challenge, we develop implicit causal models, a class of causal models that leverages neural architectures with an implicit density. With GWAS, implicit causal models generalize previous methods to capture important nonlinearities, such as gene-gene and gene-population interaction. Building on this, for the second challenge, we describe an implicit causal model that adjusts for population-confounders by sharing strength across examples (genes). We derive conditions that prove the model consistently estimates the causal relationship. This theoretically justifies existing methods and generalizes them to more complex latent variable models of the confounder.In experiments, we scale Bayesian inference on implicit causal models on up to a billion genetic measurements. Validating these results are not possible for observational data (Pearl, 2000) , so we first perform an extensive simulation study of 11 configurations of 100,000 SNPs and 940 to 5,000 individuals. We achieve state of the art accuracy for identifying causal factors: we significantly outperform existing genetics methods by an absolute difference of 15-45.3%. In a real-world GWAS, we also show our model discovers real causal relationships-identifying similar SNPs as previous state of the art-while being more principled as a causal model. We described implicit causal models, a rich class of models that can capture high-dimensional, nonlinear causal relationships. With genome-wide association studies, implicit causal models generalize previous successful methods to capture important nonlinearities, such as gene-gene and gene-population interaction. In addition, we described an implicit causal model that adjusts for confounders by sharing strength across examples. Our model achieves state-of-the-art accuracy, significantly outperforming existing genetics methods by 15-45.3%.There are several limitations to learning true causal associations. For example , alleles at different loci typically exhibit linkage disequilibrium, which is a local non-random association influenced by factors such as the rate of recombination, mutation, and genetic drift. The implicit causal model might be extended with variables shared across subsets of SNPs to model the recombination process. Another limitation involves the data, where granularity of sequenced loci may lose signal or attribute causation to a region involving multiple SNPs. Better technology, and accounting for mishaps in the sequencing process in the model, can help.While we focused on GWAS applications in this paper, we also believe implicit causal models have significant potential in other sciences: for example, to design new dynamical theories in high energy physics; and to accurately model structural equations of discrete choices in economics. We're excited about applications to these new domains, leveraging modern probabilistic modeling and causality to drive new scientific understanding.","Progress probabilistic generative models has accelerated developing richer models neural architectures implicit densities scalable algorithms Bayesian inference. However has been limited progress models can capture causal relationships example how individual genetic factors cause major human diseases. work focus two challenges particular:How do we build richer causal models which can capture highly nonlinear relationships interactions multiple causes? How do we adjust latent confounders which are variables influencing cause effect which prevent learning causal relationships? address challenges synthesize ideas causality modern probabilistic modeling. first describe implicit causal models class causal models leverages neural architectures implicit density. second describe implicit causal model adjusts confounders sharing strength across examples. experiments scale Bayesian inference billion genetic measurements. achieve state art accuracy identifying causal factors:significantly outperform second best result absolute difference 15-45.3%. Probabilistic models provide language specifying rich flexible generative processes BID5 Murphy 2012 Recent advances expand language neural architectures implicit densities scalable algorithms Bayesian inference BID9 BID15. However has been limited progress models can capture high-dimensional causal relationships Pearl 2000;BID13 Imbens Rubin 2015 Unlike models which learn statistical relationships causal models letus manipulate generative process make counterfactual statements would have happened if the distributions changed.As running example work consider genome-wide association studies GWAS BID19 BID7 Kanget al. 2010 goal GWAS is to understand how genetic factors.e single nucleotide polymorphisms SNPs cause traits appear individuals. Understanding causation lets us predict whether individual has a genetic predisposition disease also understand how to cure disease targeting individual SNPs cause it.With example mind focus two challenges combining modern probabilistic models causality. first is to develop richer expressive causal models. Probabilistic causal models represent variables deterministic functions noise variables existing work usually focuses additive noise models Hoyeretal. 2009 linear mixed models Kangetal. 2010 models apply simple nonlinearities polynomials hand-engineered low order interactions inputs assume additive interaction e.g Gaussian noise. GWAS strong evidence suggests susceptibility common diseases is influenced epistasis interaction multiple genes Culverhouseetal. 2002;McKinneyetal. 2006 would like capture discover interactions. requires models nonlinear learnable interactions among inputs noise.The second challenge is how to address latent population-based confounders. GWAS latent population structure.e subgroups population ancestry differences relatedness among sample individuals produce spurious correlations among SNPs trait interest. Existing methods correct correlation two stages BID19 BID7 Kangetal. 2010 first estimate confounder given data;run standard causal inferences given estimated confounder. methods are effective settings are difficult understand principled causal models cannot easily accommodate complex latent structure.To address challenges synthesize ideas causality modern probabilistic modeling. first challenge develop implicit causal models class causal models leverages neural architectures implicit density. GWAS implicit causal models generalize previous methods capture important nonlinearities gene-gene gene-population interaction. Building second challenge describe implicit causal model adjusts population-confounders sharing strength across examples genes derive conditions prove model consistently estimates causal relationship. theoretically justifies existing methods generalizes complex latent variable models confounder.In experiments scale Bayesian inference implicit causal models billion genetic measurements. Validating results are not possible observational data Pearl 2000 first perform extensive simulation study 11 configurations 100,000 SNPs 940 5,000 individuals. achieve state art accuracy identifying causal factors:significantly outperform existing genetics methods absolute difference 15-45.3%. real-world GWAS also show model discovers real causal relationships-identifying similar SNPs previous state art-while principled causal model. described implicit causal models rich class models can capture high-dimensional nonlinear causal relationships. genome-wide association studies implicit causal models generalize previous successful methods capture important nonlinearities gene-gene gene-population interaction. addition described implicit causal model adjusts confounders sharing strength across examples. model achieves state-of-the-art accuracy significantly outperforming existing genetics methods 15-45.3%.There are several limitations learning true causal associations. example alleles different loci typically exhibit linkage disequilibrium which is a local non-random association influenced factors rate recombination mutation genetic drift. implicit causal model might extended variables shared across subsets SNPs model recombination process. Another limitation involves data where granularity sequenced loci may lose signal attribute causation region involving multiple SNPs. Better technology accounting mishaps sequencing process model can help.While focused GWAS applications paper also believe implicit causal models have significant potential sciences:example design new dynamical theories high energy physics;accurately model structural equations discrete choices economics. excited applications new domains leveraging modern probabilistic modeling causality drive new scientific understanding.",1317,929,388,0.012,1.418,2025/11/05 17:19:00,0.01,1.63,0.2741433021806849,361.904
"
Few-shot learning trains image classifiers over datasets with few examples per category. 
 It poses challenges for the optimization algorithms, which typically require many examples to fine-tune the model parameters for new categories. 
 Distance-learning-based approaches avoid the optimization issue by embedding the images into a metric space and applying the nearest neighbor classifier for new categories. In this paper, we propose to exploit the object-level relation to learn the image relation feature, which is converted into a distance directly.
 For a new category, even though its images are not seen by the model, some objects may appear in the training images. Hence, object-level relation is useful for inferring the relation of images from unseen categories. Consequently, our model generalizes well for new categories without fine-tuning.
 Experimental results on benchmark datasets show that our approach outperforms state-of-the-art methods. Real-world data typically follows power-law distributions, where the majority of the data categories have only a small number of examples. For instance, to train an image classifier for food images, one would probably crawl few images for some local dishes. Similarly, there are few images for new products, e.g. new toys. However, state-of-the-art image classifiers, i.e. deep convolutional neural networks (ConvNets) BID7 , are hungry for data. The benchmark datasets for ConvNets, including CIFAR10 and ImageNet BID0 , usually have more than 1000 images per category. Fine-tuning ConvNets BID18 by transferring the knowledge (i.e. parameters) learned from a big dataset could alleviate the gap, but still fails to resolve the issue. This is because the widely used gradient-based optimization algorithms need many iterations over plenty of examples to adapt the ConvNets (with a large number of parameters) for new categories.Two types of approaches have been proposed towards addressing the above issue. They are referred as few-shot image classification, which trains classifiers over datasets with few (e.g. less than 20) examples per category. The first set of approaches BID12 ; ; BID2 are based on meta-learning. They train a meta learner to guide the optimization of the classifier for the new categories. They improve the optimization by providing a good initialization BID2 , an adaptive learning rate or even replacing the gradient-based optimization method BID12 . The second set of approaches ; BID17 ; BID13 ; BID15 ; BID16 are based on embedding learning. They learn an embedding function to project the images into a space and then classify images from new categories through the nearest neighbour search. No fine-tuning is required as the nearest neighbour classifier is non-parametric. The embedding functions are vital to the classification accuracy, which must be general enough to extract good embedding features for evaluating the distance/similarity between images belonging to the unseen categories.In this paper, we propose a new few-short learning approach. It is motivated by the observation that human beings are pretty good at few-shot learning. Take the Segway in FIG0 as an example BID6 ) although the Segway could be new to us, we are familiar with its components, e.g. wheels, which are similar to those of the motors or electric scooters. Hence, we know Segway is a traffic tool for riding. Moreover, we are able to analyze the image by decomposing it. For example, we are aware of the relationship between Segway and rider. This kind of relationship-awareness helps in recognition when we see a different rider with another Segway. However, existing methods take each image as a whole without exploiting the object-level information including relation.Based on the above observation, we design our learning model with two parts, namely the relation extraction network and the distance learning network. We draw inspiration from the relation network BID14 . In particular, we compare the objects from two images instead of a single image as BID14 in order to extract the relation between images. The relation is converted into a similarity score. We expect the object relationship to play a crucial role in determining the image relation for distinguishing images from different categories. The training is conducted in episodes, each of which is constructed in the same way as in the test, i.e. with few examples for each category. After training, we extract the relation feature vectors among the query image (to be classified) and each labelled image from the test dataset. Nearest neighbour classifier is then applied with the similarity score calculated from the relation feature vector. Extensive experiments on benchmark datasets confirm the superiority of our approach in terms of classification accuracy against existing work. In this paper, we exploit the object-level relation to infer the image relation. In particular, we consider each 'pixel' on the feature map as an object in the input image, and use the values across all channels as the object feature. In fact, one 'pixel' corresponds to one patch of the original image. Small patches may not contain any objects, while in big patches, there could be multiple objects. In the extreme case where the feature map size is 1x1, the corresponding patch is the whole image. Our model is then equivalent to LearningToCompare Sung et al. (2017) . In fact, we capture object pairs from different locations, whereas LearningToCompare is restricted to element-wise match at the same spatial location. The effectiveness of our approach from the experimental study confirms that the relation extracted from multiple local patches is useful for determining the image relation. Particularly, we do one more set of comparison against Learning2Compare since it has similar architecture as our model. We change the input image size of Learning2Compare to 224x224, i.e. , the same as our model. The accuracy for 5-way 1-shot and 5-way 5-shot is 50.16% and 65.98% respectively. In addition, we compare effect of the feature map size of our model. We vary the feature map size as 1x1, 3x3, 5x5, 7x7 and 9x9. The corresponding accuracy of 5-way 5-shot classification is 64.55%, 67.78%, 69.68%, 69.82%, 70.90%. The improvement becomes marginal for bigger sizes. We can see that with the increasing of objects number (feature map size), the performance improves. It indicates that the objects-level relation does make a difference.The basic idea behind our model is to aggregate the local information for global reasoning. In this paper, we consider the spatial local information. However, the framework is extensible for other local information. For example, if we treat different feature maps as different aspects (or features) of the image, in Figure 2 , we can compare (combine) these feature maps from two images to get c × c local relation features, each of size w × h + w × h. Similarly, we can compare the features of different attributes of each class with the feature maps to do zero-shot learning. It compares the local text information with local image information. ConvNets have shown great success for image classification with many examples per category. However, few-shot learning is challenging because the training algorithms of ConvNets, i.e. gradient based optimization algorithms, require many iterations to fine-tune the parameters over a lot of examples for new image classes. In this paper, we avoid the fine-tuning step by training a model that is general to learn the relation of images from unseen categories. We observe that the object-level relation persists across training and test images, although the relation of images from test datasets is unseen. Therefore, we propose to exploit object-level relation to infer the image relation. In particular, object features are compared (combined) and transformed to extract the image relation feature, which is applied directly for similarity learning. Using the learned similarity from the relation feature, our approach outperforms existing algorithms for few-shot image classification tasks.",Few-shot learning trains image classifiers datasets examples per category. poses challenges optimization algorithms which typically require many examples fine-tune model parameters new categories. Distance-learning-based approaches avoid optimization issue embedding images metric space applying nearest neighbor classifier new categories. paper propose exploit object-level relation learn image relation feature which is converted distance directly. new category even though images are not seen model objects may appear training images. Hence object-level relation is useful inferring relation images unseen categories. Consequently model generalizes well new categories without fine-tuning Experimental results benchmark datasets show approach outperforms state-of-the-art methods. Real-world data typically follows power-law distributions where the majority data categories have only a small number examples. instance train image classifier food images do one would probably crawl images local dishes. Similarly are few images new products e.g new toys. However state-of-the-art image classifiers.e deep convolutional neural networks ConvNets BID7 are hungry data. benchmark datasets ConvNets including CIFAR10 ImageNet BID0 usually have more than 1000 images per category. Fine-tuning ConvNets BID18 transferring knowledge.e parameters learned big dataset could alleviate gap still fails resolve issue. is because the widely used gradient-based optimization algorithms need many iterations plenty examples adapt ConvNets large number parameters new categories.Two types approaches have been proposed towards addressing issue. are referred few-shot image classification which trains classifiers datasets e.g less 20 examples per category. first set approaches BID12;BID2 are based meta-learning train meta learner guide optimization classifier new categories. improve optimization providing good initialization BID2 adaptive learning rate even replacing gradient-based optimization method BID12. second set approaches;BID17;BID13;BID15;BID16 are based embedding learning. learn embedding function project images space classify images new categories nearest neighbour search. fine-tuning is required nearest neighbour classifier is non-parametric non-parametric embedding functions are vital classification accuracy which must general enough extract good embedding features evaluating distance/similarity images belonging unseen categories.In paper propose new few-short learning approach. is motivated observation human beings are pretty good few-shot learning. Take Segway FIG0 example BID6 although Segway could new us are familiar components e.g wheels which are similar motors electric scooters. Hence know Segway is a traffic tool riding. Moreover are able analyze image decomposing it. example are aware relationship Segway rider. kind relationship-awareness helps recognition when we see different rider another Segway. However existing methods take image whole without exploiting object-level information including relation.Based observation design learning model two parts namely relation extraction network distance learning network. draw inspiration relation network BID14. particular can compare objects two images instead single image BID14 order extract relation images. relation is converted similarity score. expect object relationship play crucial role determining image relation distinguishing images different categories. training is conducted episodes which is constructed way test.e examples category. training extract relation feature vectors among query image classified labelled image test dataset. Nearest neighbour classifier is then applied similarity score calculated relation feature vector. Extensive experiments benchmark datasets confirm superiority approach terms classification accuracy existing work. paper exploit object-level relation infer image relation. particular consider 'pixel' feature map object input image use values across channels object feature. fact do one 'pixel' corresponds one patch original image. Small patches may contain objects big patches could multiple objects. extreme case where the feature map size is 1x1 corresponding patch is the whole image. model is then equivalent LearningToCompare Sungetal. 2017 fact capture object pairs different locations whereas LearningToCompare is restricted element-wise match spatial location. effectiveness approach experimental study confirms relation extracted multiple local patches is useful determining image relation. Particularly do one set comparison Learning2Compare since has similar architecture model. change input image size Learning2Compare 224x224.e model. accuracy 5-way 1-shot 5-way 5-shot is 50.16 50.16 65.98 respectively. addition can compare effect feature map size model. vary feature map size 1x1 3x3 5x5 7x7 9x9. corresponding accuracy 5-way 5-shot classification is 64.55 64.55 67.78 69.68 69.82 70.90%. improvement becomes marginal bigger sizes. can see increasing objects number feature map size performance improves. indicates objects-level relation does make difference.The basic idea behind model is to aggregate local information global reasoning. paper consider spatial local information. However framework is extensible local information. example if we treat different feature maps different aspects features image Figure2 can compare combine feature maps two images getc×c local relation features sizew×h+w×h. Similarly can compare features different attributes class feature maps do zero-shot learning. compares local text information local image information. ConvNets have shown great success image classification many examples per category. However few-shot learning is challenging training algorithms ConvNets.e gradient based optimization algorithms require many iterations fine-tune parameters lot examples new image classes. paper avoid fine-tuning step training model is general learn relation images unseen categories. observe object-level relation persists across training test images although relation images test datasets is unseen. Therefore propose exploit object-level relation infer image relation. particular object features are compared combined transformed extract image relation feature which is applied directly similarity learning. Using learned similarity relation feature approach outperforms existing algorithms few-shot image classification tasks.,1596,1086,510,0.018,1.47,2025/11/05 17:19:00,0.01,1.453,0.4361370716510901,507.987
"Word embeddings are widely used in machine learning based natural language processing systems. It is common to use pre-trained word embeddings which provide benefits such as reduced training time and improved overall performance. There has been a recent interest in applying natural language processing techniques to programming languages. However, none of this recent work uses pre-trained embeddings on code tokens. Using extreme summarization as the downstream task, we show that using pre-trained embeddings on code tokens provides the same benefits as it does to natural languages, achieving: over 1.9x speedup, 5\% improvement in test loss, 4\% improvement in F1 scores, and resistance to over-fitting. We also show that the choice of language used for the embeddings does not have to match that of the task to achieve these benefits and that even embeddings pre-trained on human languages provide these benefits to programming languages.    One of the initial steps in a machine learning natural language processing (NLP) pipeline is converting the one-hot encoded R V tokens into dense R D representations, with V being the size of the vocabulary, D the embedding dimensions and V << D. This conversion is usually done with a single layer neural network, commonly called an embedding layer.The parameters of the embedding layer can either be initialized randomly or initialized via ""pretrained"" parameters obtained from a model such as word2vec BID22 a) , GloVe BID25 or a language model BID17 BID11 BID26 .It is common to use pre-trained parameters (most frequently the GloVe embeddings), which act as a form of transfer learning BID23 similar to that of using pre-trained parameters for the convolutional kernels in a machine learning computer vision task BID12 BID14 . These parameters in the embedding layer are then fine-tuned whilst training on the desired downstream task.The use of these pre-trained embeddings over random initialization allows machine learning models to: train faster, achieve improved overall performance BID13 , increase the stability of their training, and reduce the amount of over-fitting BID23 .Recently there has been an increased interest in applying NLP techniques to programming languages and software engineering applications BID30 BID3 , the most common of which involves predicting the names of methods or variables using surrounding source code BID27 BID0 BID4 BID6 a) .Remarkably , none of this work takes advantage of pre-trained embeddings created on source code. From the example below in table 1, we can see how semantic knowledge (provided by the pre-trained code embeddings) of the method body would help us predict the method name, i.e. knowing how pi and radius are used to calculate an area and how height and width are used to calculate an aspect ratio.float getSurfaceArea (int radius) { return 4 * Math.PI * radius * radius; } float getAspectRatio (int height, int width) { return height / width; } Table 1 : Examples showing how the semantics of the variable names within a method can be used to reason about the name of the method body This semantic knowledge is available to us as even though computers do not need to understand the semantic meaning of a method or variable name, they are mainly chosen to be understood by other human programmers BID10 .In this paper , we detail experiments using pre-trained code embeddings on the downstream task of predicting a method name from a method body. This task is known as extreme summarization BID2 as a method name can be thought of as a summary of the method body. Our experiments are focused on answering the following research questions:1. Do pre-trained code embeddings reduce training time?2. Do pre-trained code embeddings improve performance?3. Do pre-trained code embeddings increase stability of training?4. Do pre-trained code embeddings reduce over-fitting?5. How does the choice of corpora used for the pre-trained code embeddings affect all of the above?To answer RQ5, we gather a corpus of C, Java and Python code and train embeddings for each corpus separately, as well as comparing them with embeddings trained on natural language. We then test each of these on the same downstream task, extreme summarization, which is in Java. We also release the pre-trained code embeddings . We refer back to our research questions.Do pre-trained code embeddings reduce training time? Yes, tables 3 and 4 show we get an average of 1.93x speedup. This is correlated with the amount of overlap between the task vocabulary and the embedding vocabulary, shown in figure 2a.Do pre-trained code embeddings improve performance? Yes, tables 3 and 4 show we get an average of 5% relative validation loss improvement. Again, this is correlated with the amount of overlap between the vocabularies, shown in figure 2b.Do pre-trained code embeddings increase stability of training? Although this is difficult to quantify due to how over-fitting interacts with the variance of the validation loss curves, from figures 1a and 1c we can see a clear increase in the variance of the validation loss curves using random embeddings compared to those using pre-trained embeddings.Do pre-trained code embeddings reduce over-fitting? Yes, tables 6 and 7 show that the random embeddings over-fit more than the pre-trained embeddings on every project. However, this does not seem to have a correlation with the amount of vocabulary overlap and further work is needed to determine the cause of this.How does the choice of corpora used for the pre-trained code embeddings affect all of the above? Intuitively, it would seem the best pre-trained embeddings would be those that are trained on the same language as that of the downstream task, but this is not the case. We hypothesize through the examples shown in tables 1 and 5 that the differing syntax between the languages is not as important as sensible semantic method and variable names within the dataset. This semantic information is also contained in human languages, which explains why the English embeddings also receive comparable performance.",Word embeddings are widely used machine learning based natural language processing systems. is common use pre-trained word embeddings which provide benefits reduced training time improved overall performance. has been a recent interest applying natural language processing techniques programming languages. However none recent work uses pre-trained embeddings code tokens. Using extreme summarization downstream task show using pre-trained embeddings code tokens provides benefits does to natural languages achieving:1.9x speedup 5\ improvement test loss 4\ improvement F1 scores resistance how over-fitting also show choice language used embeddings does not have to match task achieve benefits even embeddings pre-trained human languages provide benefits programming languages. One initial steps machine learning natural language processing NLP pipeline is converting one-hot encodedRV tokens denseR representations V size vocabulary embedding dimensions V D. conversion is usually done single layer neural network commonly called embedding layer.The parameters embedding layer can either initialized randomly initialized via pretrained parameters obtained model word2vec BID22 GloVe BID25 language model BID17 BID11 BID26.It is common use pre-trained parameters frequently GloVe embeddings which act form transfer learning BID23 similar using pre-trained parameters convolutional kernels machine learning computer vision task BID12 BID14. parameters embedding layer are then fine-tuned whilst training desired downstream task.The use pre-trained embeddings random initialization allows machine learning models to:train faster achieve improved overall performance BID13 increase stability training reduce amount over-fitting BID23.Recently has been an increased interest applying NLP techniques programming languages software engineering applications BID30 BID3 common which involves predicting names methods variables using surrounding source code BID27 BID0 BID4 BID6.Remarkably none work takes advantage pre-trained embeddings created source code. example table1 can see how semantic knowledge provided pre-trained code embeddings method body would help us predict method name.e knowing howpi radius are used calculate area how height width are used calculate aspect ratio.float getSurfaceArea int radius return 4 * Math.PI * radius * radius;float getAspectRatio int height int width return height/width;Table1:Examples showing how the semantics variable names within method can be used reason name method body semantic knowledge is available us even though computers do not need understand semantic meaning method variable name are mainly chosen understood human programmers BID10.In paper detail experiments using pre-trained code embeddings downstream task predicting method name method body. task is known extreme summarization BID2 method name can be thought summary method body. experiments are focused answering following research questions:1 Do pre-trained code embeddings reduce training time? 2. Do pre-trained code embeddings improve performance? 3. Do pre-trained code embeddings increase stability training? 4. Do pre-trained code embeddings reduce over-fitting5. How does the choice corpora used pre-trained code embeddings affect above? answer RQ5 gather corpus C which is in Java Python code train embeddings corpus separately well comparing embeddings trained natural language. test downstream task extreme summarization which is in Java. also release pre-trained code embeddings. refer back research questions.Do pre-trained code embeddings reduce training time? Yes tables3 4 show get average 1.93x speedup. is correlated amount overlap task vocabulary embedding vocabulary shown figure 2a.Do pre-trained code embeddings improve performance? Yes tables3 4 show get average 5% relative validation loss improvement. is correlated amount overlap vocabularies shown figure 2b.Do pre-trained code embeddings increase stability training? Although is difficult quantify due how over-fitting interacts variance validation loss curves figures1a 1c can see clear increase variance validation loss curves using random embeddings compared using pre-trained embeddings.Do pre-trained code embeddings reduce over-fitting Yes tables6 7 show random embeddings over-fit pre-trained embeddings every project. However does not seem have a correlation amount vocabulary overlap work is needed determine cause this.How does the choice corpora used pre-trained code embeddings affect above? Intuitively would seem best pre-trained embeddings would are trained language downstream task is case. hypothesize examples shown tables1 5 differing syntax languages is not as important sensible semantic method variable names within dataset. semantic information is also contained human languages which explains why the English embeddings also receive comparable performance.,1189,819,370,0.011,1.452,2025/11/05 17:19:00,0.01,1.511,0.3800623052959498,349.553
"Recently, Approximate Policy Iteration (API) algorithms have achieved super-human proficiency in two-player zero-sum games such as Go, Chess, and Shogi without human data. These API algorithms iterate between two policies: a slow policy (tree search), and a fast policy (a neural network). In these two-player games, a reward is always received at the end of the game. However, the Rubik’s Cube has only a single solved state, and episodes are not guaranteed to terminate. This poses a major problem for these API algorithms since they rely on the reward received at the end of the game. We introduce Autodidactic Iteration: an API algorithm that overcomes the problem of sparse rewards by training on a distribution of states that allows the reward to propagate from the goal state to states farther away. Autodidactic Iteration is able to learn how to solve the Rubik’s Cube and the 15-puzzle without relying on human data. Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves — less than or equal to solvers that employ human domain knowledge. The Rubik's Cube is a classic combination game that poses unique and interesting challenges for AI and machine learning. Although the state space is astronomically large (4.2 × 10 19 different states for the 3x3x3 cube), only a single state is considered solved. Furthermore, unlike the game of Go or Chess, the Rubik's Cube is a single-player game and a sequence of random moves, no matter how long, is unlikely to end in the solved state. Developing reinforcement learning algorithms to deal with this property of the Rubik's Cube might provide insight into other sparse-reward environments. While methods for solving the Rubik's Cube have been developed, only relatively recently have methods been derived that can compute the minimal number of moves required to solve the cube from any given starting configuration BID22 . In addition, the Rubik's Cube and its solutions are deeply rooted in group theory, raising interesting and broader questions about the applicability of machine learning methods to complex symbolic systems, including mathematics. Finally, the classical 3x3x3 Rubik's Cube is only one representative of a much larger family of possible combination puzzles, broadly sharing the characteristics described above and including: (1) Rubik's Cubes with longer edges (e.g. 4x4x4); (2) Rubik's Cubes in higher dimensions (e.g. 2x2x2x2); as well as (3) Rubik's cube on non-cubic geometries (Pyriminix, etc) and their combinations. As the length of the sides and dimensions are increased, the complexity of the underlying combinatorial problems rapidly increases and, for instance, God's numbers for the 4x4x4 cube is not known. In short, for all these reasons, the Rubik's Cube and its variations pose interesting challenges for machine learning. Here we develop deep reinforcement learning methods, in particular a new form of Approximate Policy Iteration (API), for addressing these challenges.Figure 1: An illustration of DeepCube. The training and solving process is split up into ADI and MCTS. First, we iteratively train a DNN by estimating the true value of the input states using breadth-first search. Then, using the DNN to guide exploration, we solve cubes using Monte Carlo Tree Search. See methods section for more details.Approximate Policy Iteration BID5 BID2 BID13 BID25 BID18 ) is a core Reinforcement Learning (RL) algorithm. Recently, a new type of API algorithm, called Dual Policy Iteration BID33 , has achieved success in two player zero-sum games such as Go, Chess, Shogi and Hex BID0 BID28 BID9 . AlphaZero BID30 and ExIt BID0 are examples of Dual Policy Iteration. These algorithms update the policy in a more sophisticated way than traditional API methods by using two policies: a fast policy (usually a neural network) and a slow policy (usually tree search). The fast policy is trained via supervised learning on data generated from gameplay from the slow policy. The slow policy then uses the fast policy to guide the tree search. In this way, the fast policy is used to improve the slow policy, and the slow policy generates better data to train the fast policy.This work is the first to solve the Rubik's Cube with reinforcement learning. Although DPI works for two-player games, our work is the first DPI algorithm to succeed in an environment with a high number of states and a small number of reward states. A number of these ""needle in a haystack"" environments such as generating meaningful sentences or code are seen as long-term goals for the field of AI. There is no clear way to apply current DPI algorithms such as AlphaZero or ExIt to sparse-reward environments such as the Rubik's Cube. This is because a randomly initialized policy will be unlikely to encounter the single reward state. This will cause the value function to be biased or divergent and the fast policy will not converge to the optimal policy. In our work we overcome this problem by training the fast policy on a distribution of states that propagate the reward signal to from the goal state to the further states.Our algorithm, called Autodidactic Iteration (ADI), trains a neural network value and policy function through an iterative process. These neural networks are the ""fast policy"" of DPI described earlier.In each iteration, the inputs to the neural network are created by starting from the goal state and randomly taking actions. The targets seek to estimate the optimal value function by performing a breadth-first search from each input state and using the current network to estimate the value of each of the leaves in the tree. Updated value estimates for the root nodes are obtained by recursively backing up the values for each node using a max operator. The policy network is similarly trained by constructing targets from the move that maximizes the value. After the network is trained, it is combined with MCTS to effectively solve the Rubik's Cube. We call the resulting solver DeepCube. DeepCube is based on similar principles as AlphaZero and ExIt, however, these methods receive their reward when the game reaches a terminal state, which is guaranteed to occur given enough play time. On the other hand, one is not guaranteed to find a terminal state in the Rubik's Cube environment and therefore may only encounter rewards of -1, which does not provide enough information to solve the problem. DeepCube addresses this by selecting a state distribution for the training set that allows the reward to be propagated from the terminal state to other states. In addition, while AlphaZero and ExIt make use advanced tree-search algorithms to update the policy, DeepCube is able to find success using the faster and simpler depth-1 BFS.The depth-1 BFS used to improve the policy can also be viewed as doing on-policy temporal difference learning BID34 , specifically TD(0) with function approximation. In this case, the TD(0) algorithm uses a deterministic greedy policy where each episode is one step long. Off-policy methods are often used to train a deterministic policy by using a stochastic behavior policy to facilitate exploration. An alternative approach, called exploring starts, instead changes the distribution of starting states and can also be used to train a deterministic policy in an on-policy fashion BID35 . We use a similar approach to exploring starts by ensuring exploration through the selection of the starting state distribution. The Rubik's Cube can be thought of as a classical planning problem. While traditional planning algorithms, such as Dijkstra's algorithm, would require an infeasible amount of memory to work on environments a state space as large as the Rubik's Cube, we show that Dual Policy Iteration can find a solution path in such an environment. For future work, we look to apply Autodidactic Iteration to a variety of other problems with similar characteristics such as robotic manipulation, two-player games, and path finding. Léon Bottou defines reasoning as ""algebraically manipulating previously acquired knowledge in order to answer a new question"" BID6 . Many machine learning algorithms do not reason about problems but instead use pattern recognition to perform tasks that are intuitive to humans, such as object recognition. By combining neural networks with symbolic AI, we are able to create algorithms which are able to distill complex environments into knowledge and then reason about that knowledge to solve a problem. DeepCube is able to teach itself how to reason in order to solve a complex environment with only one positive reward state using pure reinforcement learning.A KNOWLEDGE LEARNED DeepCube discovered a notable amount of Rubik's Cube knowledge during its training process, including the knowledge of how to use complex permutation groups and strategies similar to the best human ""speed-cubers"". For example, DeepCube heavily uses one particular pattern that commonly appears when examining normal subgroups of the cube: aba −1 . That is, the sequences of moves that perform some action a, performs a different action b, and then reverses the first action with a −1 . An intelligent agent should use these conjugations often because it is necessary for manipulating specific cubelets while not affecting the position of other cubelets.We examine all of the solutions paths that DeepCube generated for the 640 fully scrambled cubes by moving a sliding window across the solutions strings to gather all triplets. We then compute the frequency of each triplet and separate them into two categories: matching the conjugation pattern aba −1 and not matching it. We find that the top 14 most used triplets were, in fact, the aba −1 conjugation. We also compare the distribution of frequencies for the two types of triplets. In Figure 6 , we plot the distribution of frequencies for each of the categories. We notice that conjugations appear consistently more often than the other types of triplets.We also examine the strategies that DeepCube learned. Often, the solver first prioritizes completing a 2x2x2 corner of the cube. This will occur approximately at the half way point in the solution. Then, it uses these conjugations to match adjacent edge and corner cubelets in the correct orientation, and it returns to either the same 2x2x2 corner or to an adjacent one. Once each pair of corner-edge pieces is complete, the solver then places them into their final positions and completes the cube. An example of this strategy is presented in FIG3 . This mirrors a strategy that advanced human ""speed-cubers"" employ when solving the cube, where they prioritize matching together corner and edge cubelets before placing them in their correct locations. Each layer is fully connected. We use elu activation on all layers except for the outputs. A combined value and policy network results in more efficient training compared to separate networks. (Silver et al., 2017b) .We used a feed forward network as the architecture for f θ as shown in Figure 7 . The outputs of the network are a 1 dimensional scalar v, representing the value, and a 12 dimensional vector p, representing the probability of selecting each of the possible moves. The network was then trained using ADI for 2,000,000 iterations. The network witnessed approximately 8 billion cubes, including repeats, and it trained for a period of 44 hours. Our training machine was a 32-core Intel Xeon E5-2620 server with three NVIDIA Titan XP GPUs.During play, the neural network prediction is the major bottleneck for performance. In order to counteract this, we implemented a parallel version of MCTS that had 32 independent workers that shared a single MCTS search tree. Each of the workers queue their prediction requests, and the neural network batches all requests and processes them simultaneously. This parallelization sped up the solver 20x compared to a single core implementation.","Recently Approximate Policy Iteration API algorithms have achieved super-human proficiency two-player zero-sum games Go Chess Shogi without human data. API algorithms iterate two policies:slow policy tree search fast policy neural network two-player games reward is always received end game. However Rubiks Cube has only a single solved state episodes are not guaranteed terminate. poses major problem API algorithms since rely reward received end game. introduce Autodidactic Iteration:API algorithm overcomes problem sparse rewards training distribution states allows reward propagate goal state states farther away. Autodidactic Iteration is able learn how to solve Rubiks Cube 15-puzzle without relying human data. algorithm is able solve 100% randomly scrambled cubes achieving median solve length 30 moves less equal solvers employ human domain knowledge. Rubik's Cube is a classic combination game poses unique interesting challenges AI machine learning. Although state space is astronomically large 4.2×1019 different states 3x3x3 cube single state is considered solved. Furthermore unlike game Go Chess Rubik's Cube is a single-player game sequence random moves matter how long is unlikely end solved state. Developing reinforcement learning algorithms deal property Rubik's Cube might provide insight sparse-reward environments. methods solving Rubik's Cube have been developed relatively recently have methods derived can compute minimal number moves required solve cube given starting configuration BID22. addition Rubik's Cube solutions are deeply rooted group theory raising interesting broader questions applicability machine learning methods complex symbolic systems including mathematics. Finally classical 3x3x3 Rubik's Cube is only is one representative much larger family possible combination puzzles broadly sharing characteristics described including:1 Rubik's Cubes longer edges e.g 4x4x4 2 Rubik's Cubes higher dimensions e.g 2x2x2x2 well 3 Rubik's cube non-cubic geometries Pyriminix etc combinations. length sides dimensions are increased complexity underlying combinatorial problems rapidly increases instance God's numbers 4x4x4 cube is not known. short reasons Rubik's Cube variations pose interesting challenges machine learning. develop deep reinforcement learning methods particular new form Approximate Policy Iteration API addressing challenges.Figure1:illustration DeepCube. training solving process is split ADI MCTS. First iteratively train DNN estimating true value input states using breadth-first search. using DNN guide exploration solve cubes using Monte Carlo Tree Search. See methods section details.Approximate Policy Iteration BID5 BID2 BID13 BID25 BID18 is a core Reinforcement Learning RL algorithm. Recently new type API algorithm called Dual Policy Iteration BID33 has achieved success two player zero-sum games Go Chess Shogi Hex BID0 BID28 BID9. AlphaZero BID30 ExIt BID0 are examples Dual Policy Iteration. algorithms update policy sophisticated way traditional API methods using two policies:fast policy usually neural network slow policy usually tree search fast policy is trained via supervised learning data generated gameplay slow policy. slow policy uses fast policy guide tree search. way fast policy is used improve slow policy slow policy generates better data train fast policy.This work is the first solve Rubik's Cube reinforcement learning. Although DPI works two-player games work is the first DPI algorithm succeed environment high number states small number reward states. number needle haystack environments generating meaningful sentences code are seen long-term goals field AI. is no clear way apply current DPI algorithms AlphaZero ExIt sparse-reward environments Rubik's Cube. is because a randomly initialized policy will be unlikely encounter single reward state. will cause value function biased divergent fast policy will not converge optimal policy. work overcome problem training fast policy distribution states propagate reward signal goal state states.Our algorithm called Autodidactic Iteration ADI trains neural network value policy function iterative process. neural networks are the fast policy DPI described earlier.In iteration inputs neural network are created starting goal state randomly taking actions. targets seek estimate optimal value function performing breadth-first search input state using current network estimate value leaves tree. Updated value estimates root nodes are obtained recursively backing values node using max operator. policy network is similarly trained constructing targets move maximizes value. network is trained is combined MCTS effectively solve Rubik's Cube. call resulting solver DeepCube. DeepCube is based similar principles AlphaZero ExIt however methods receive reward when the game reaches terminal state which is guaranteed occur given enough play time. hand one is not guaranteed find terminal state Rubik's Cube environment therefore may encounter rewards -1 which does not provide enough information solve problem. DeepCube addresses selecting state distribution training set allows reward propagated terminal state states. addition AlphaZero ExIt make use advanced tree-search algorithms update policy DeepCube is able find success using faster simpler depth-1 BFS.The depth-1 BFS used improve policy can also viewed on-policy temporal difference learning BID34 specificallyTD 0 function approximation. case TD 0 algorithm uses deterministic greedy policy where each episode is only is one step long. Off-policy methods are often used train deterministic policy using stochastic behavior policy facilitate exploration. alternative approach called exploring starts instead changes distribution starting states can also used train deterministic policy on-policy fashion BID35. use similar approach exploring starts ensuring exploration selection starting state distribution. Rubik's Cube can be thought classical planning problem. traditional planning algorithms Dijkstra's algorithm would require infeasible amount memory work environments state space large Rubik's Cube show Dual Policy Iteration can find solution path environment. future work look apply Autodidactic Iteration variety problems similar characteristics robotic manipulation two-player games path finding. Léon Bottou defines reasoning algebraically manipulating previously acquired knowledge order answer new question BID6. Many machine learning algorithms do not reason problems instead use pattern recognition perform tasks are intuitive humans object recognition. combining neural networks symbolicAI are able create algorithms which are able distill complex environments knowledge reason knowledge solve problem. DeepCube is able teach how to reason order solve complex environment one positive reward state using pure reinforcement learning.A KNOWLEDGE LEARNED DeepCube discovered notable amount Rubik's Cube knowledge training process including knowledge how to use complex permutation groups strategies similar best human speed-cubers example DeepCube heavily uses one particular pattern commonly appears when examining normal subgroups cube:aba−1 is,the sequences moves perform action performs different actionb reverses first action −1 intelligent agent should use conjugations often is necessary manipulating specific cubelets affecting position cubelets.We examine solutions paths DeepCube generated 640 fully scrambled cubes moving sliding window across solutions strings gather triplets. compute frequency triplet separate two categories:matching conjugation pattern aba−1 matching it. find top14 used triplets were,in fact aba −1 conjugation. also compare distribution frequencies two types triplets. Figure6 plot distribution frequencies categories. notice conjugations appear consistently often types triplets.We also examine strategies DeepCube learned. Often solver first prioritizes completing 2x2x2 corner cube. will occur approximately half way point solution. uses conjugations match adjacent edge corner cubelets correct orientation returns either 2x2x2 corner adjacent one. pair corner-edge pieces is complete solver places final positions completes cube. example strategy is presented FIG3. mirrors strategy advanced human speed-cubers employ when solving cube where they prioritize matching together corner edge cubelets placing correct locations. layer is fully connected. use elu activation layers except outputs. combined value policy network results efficient training compared separate networks. Silveretal. 2017b.We used feed forward network architecture fθ shown Figure7. outputs network are a 1 dimensional scalarv representing value 12 dimensional vectorp representing probability selecting possible moves. network was then trained using ADI 2,000,000 iterations. network witnessed approximately8 billion cubes including repeats trained period 44 hours. training machine was a 32-core Intel Xeon E5-2620 server three NVIDIA TitanXP GPUs.During play neural network prediction is the major bottleneck performance. order counteract implemented parallel version MCTS had 32 independent workers shared single MCTS search tree. workers queue prediction requests neural network batches requests processes simultaneously. parallelization sped solver 20x compared single core implementation.",2408,1622,786,0.031,1.485,2025/11/05 17:19:00,0.01,1.521,0.4828660436137073,797.271
"Answering compositional questions requiring multi-step reasoning is challenging for current models. We introduce an end-to-end differentiable model for interpreting questions, which is inspired by formal approaches to semantics. Each span of text is represented by a denotation in a knowledge graph, together with a vector that captures ungrounded aspects of meaning. Learned composition modules recursively combine constituents, culminating in a grounding for the complete sentence which is an answer to the question. For example, to interpret ‘not green’, the model will represent ‘green’ as a set of entities, ‘not’ as a trainable ungrounded vector, and then use this vector to parametrize a composition function to perform a complement operation. For each sentence, we build a parse chart subsuming all possible parses, allowing the model to jointly learn both the composition operators and output structure by gradient descent. We show the model can learn to represent a variety of challenging semantic operators, such as quantifiers, negation, disjunctions and composed relations on a synthetic question answering task. The model also generalizes well to longer sentences than seen in its training data, in contrast to LSTM and RelNet baselines. We will release our code. Compositionality is a mechanism by which the meanings of complex expressions are systematically determined from the meanings of their parts, and has been widely assumed in the study of both natural languages BID10 , as well as programming and logical languages, as a means for allowing speakers to generalize to understanding an infinite number of sentences. Popular neural network approaches to question answering use a restricted form of compositionality, typically encoding a sentence word-by-word from left-to-right, and finally executing the complete sentence encoding against a knowledge source BID13 . Such models can fail to generalize from training sentences in surprising ways. Inspired by linguistic theories of compositional semantics, we instead build a latent tree of interpretable expressions over a sentence, recursively combining constituents using a small set of neural modules. When tested on longer questions than are found in the training data, we find that our model achieves higher performance than baselines using LSTMs and RelNets.Our approach resembles Montague semantics, in which a tree of interpretable expressions is built over the sentence, with nodes combined by a small set of composition functions. However, both the structure of the sentence and the neural modules that handle composition are learned by end-to-end gradient descent. To achieve this, we define the parametric form of small set of neural modules, and then build a parse chart over each sentence subsuming all possible trees. Each node in the chart represents a span of text with a distribution over groundings (in terms of booleans and knowledge base nodes and edges), as well as a vector representing aspects of the meaning that have not yet been grounded. The representation for a node is built by taking a weighted sum over different ways of building the node (similarly to BID9 ).Typical neural network approaches to grounded question answering first encode a question from left-to-right with a recurrent neural network (RNNs), and then evaluate the encoding against an encoding of the knowledge source (for example, a knowledge base or image) BID14 . In contrast to classical approaches to compositionality, constituents of complex expressions are not given explicit interpretations in isolation. For example , in Which cubes are large or green?, an RNN encoder will not explicitly build an interpretation for the expression large or green. We show that A correct parse for a question given the knowledge graph on the right, using our model. We show the type for each node, and its denotation in terms of the knowledge graph. The words or and not are represented by vectors, which parameterize composition modules. The denotation for the complete question represents the answer to the question. Nodes here have types E for sets of entities, R for relations, V for ungrounded vectors, EV for a combination of entities and a vector, and φ for semantically vacuous nodes. While we show only one parse tree here, our model builds a parse chart subsuming all trees. such approaches can generalize poorly when tested on more complex sentences than they were trained on. In contrast, our approach imposes strong independence assumptions that give a linguistically motivated inductive bias. In particular, it enforces that phrases are interpreted independently of surrounding words, allowing the model to generalize naturally to interpreting phrases in different contexts. In the previous example, large or green will be represented as a particular set of entities in a knowledge graph, and be intersected with the set of entities represented by the cubes node.Another perspective on our work is as a method for learning the layouts of Neural Module Networks (NMNs) BID1 . Work on NMNs has focused on how to construct the structure of the network, variously using rules, parsers and reinforcement learning BID0 BID3 . Our end-to-end differentiable model jointly learns structures and modules by gradient descent.",Answering compositional questions requiring multi-step reasoning is challenging current models. introduce end-to-end differentiable model interpreting questions which is inspired formal approaches semantics. span text is represented denotation knowledge graph together vector captures ungrounded aspects meaning. Learned composition modules recursively combine constituents culminating grounding complete sentence which is an answer question. example interpret green model will represent green set entities trainable ungrounded vector use vector parametrize composition function perform complement operation. sentence build parse chart subsuming possible parses allowing model jointly learn composition operators output structure gradient descent. show model can learn represent variety challenging semantic operators quantifiers negation disjunctions composed relations synthetic question answering task. model also generalizes well longer sentences seen training data contrast LSTM RelNet baselines. will release code. Compositionality is a mechanism which the meanings complex expressions are systematically determined meanings parts has been widely assumed study natural languages BID10 well programming logical languages means allowing speakers generalize understanding infinite number sentences. Popular neural network approaches question answering use restricted form compositionality typically encoding sentence word-by-word left-to-right finally executing complete sentence encoding knowledge source BID13. models can fail generalize training sentences surprising ways. Inspired linguistic theories compositional semantics instead build latent tree interpretable expressions sentence recursively combining constituents using small set neural modules. When tested longer questions are found training data find model achieves higher performance baselines using LSTMs RelNets.Our approach resembles Montague semantics which a tree interpretable expressions is built sentence nodes combined small set composition functions. However structure sentence neural modules handle composition are learned end-to-end gradient descent. achieve define parametric form small set neural modules build parse chart sentence subsuming possible trees. node chart represents span text distribution groundings terms booleans knowledge base nodes edges well vector representing aspects meaning have not yet grounded. representation node is built taking weighted sum different ways building node similarly BID9.Typical neural network approaches grounded question answering first encode question left-to-right recurrent neural network RNNs evaluate encoding encoding knowledge source example knowledge base image BID14. contrast classical approaches compositionality constituents complex expressions are not given explicit interpretations isolation. example Which cubes are large green? RNN encoder will not explicitly build interpretation expression large green. show correct parse question given knowledge graph right using model. show type node denotation terms knowledge graph. words are represented vectors which parameterize composition modules. denotation complete question represents answer question. Nodes have typesE sets entities R relations V ungrounded vectors EV combination entities vector φ semantically vacuous nodes. show one parse tree model builds parse chart subsuming trees. approaches can generalize poorly when tested complex sentences were trained on. contrast approach imposes strong independence assumptions give linguistically motivated inductive bias. particular enforces phrases are interpreted independently surrounding words allowing model generalize naturally interpreting phrases different contexts. previous example large green will be represented particular set entities knowledge graph intersected set entities represented cubes node.Another perspective work is as a method learning layouts Neural Module Networks NMNs BID1. Work NMNs has focused how to construct structure network variously using rules parsers reinforcement learning BID0 BID3. end-to-end differentiable model jointly learns structures modules gradient descent.,993,635,358,0.011,1.564,2025/11/05 17:19:00,0.01,1.424,0.7289719626168225,327.409
"Deep learning software demands reliability and performance. However, many of the existing deep learning frameworks are software libraries that act as an unsafe DSL in Python and a computation graph interpreter. We present DLVM, a design and implementation of a compiler infrastructure with a linear algebra intermediate representation, algorithmic differentiation by adjoint code generation, domain- specific optimizations and a code generator targeting GPU via LLVM. Designed as a modern compiler infrastructure inspired by LLVM, DLVM is more modular and more generic than existing deep learning compiler frameworks, and supports tensor DSLs with high expressivity. With our prototypical staged DSL embedded in Swift, we argue that the DLVM system enables a form of modular, safe and performant frameworks for deep learning. Within the deep learning community, most current approaches to neural networks make use of high-level frameworks with a tensor domain-specific language (DSL) such as Torch BID3 , TensorFlow BID0 , PyTorch (PyTorch Development Team, 2016) , and MXNet BID1 . Traditionally, developers would build a computation graph (or dynamically generate graph nodes) using a DSL and let the framework interpret the computation graph on parallel architectures such as NVIDIA GPUs. While using hand-tuned GPU subroutines usually yields the best performance for complex operators, advanced compiler techniques can be applied to simplify computation, merge high-level operators based on shaping conditions, and fuse compatible elementwise operators to a single kernel to minimize the latency between kernel launches. Recent projects, the TensorFlow XLA compiler and the NNVM compiler BID13 including TVM BID2 , have begun to apply compiler techniques to deep learning systems, targeting LLVM BID10 and various back-ends to achieve good performance. However, their design and implementation have not entirely followed established best practices in widely-used compiler frameworks in the industry.Moreover, some frameworks use operator-overloading algorithmic differentiation (AD) to compute gradients, leaving the gradient computation unoptimizable. The other approach to AD, source code transformation, can produce more efficient code. While frameworks such as TensorFlow already perform AD as a graph transformation and apply various optimizations, their AD transformation is not designed as a transformation pass in the pipeline of their compiler framework, but as part of the DSL library. Making AD part of the compiler framework would greatly simplify the development of DSLs, achieving separation of concerns. We introduce DLVM, a new compiler infrastructure for deep learning systems that addresses shortcomings of existing deep learning frameworks. Our solution includes (1) a domain-specific intermediate representation specifically designed for tensor computation, (2) principled use of modern compiler optimization techniques to substantially simplify neural network computation, including algebra simplification, AD checkpointing, compute kernel fusion, and various traditional compiler optimizations, (3) code generation through a mature compiler infrastructure that allows for transparent targeting of various hardware, and (4) an embedded DSL that supports static analysis, type safety, and natural expression of tensor computation, and has a just-in-time (JIT) compiler targeting DLVM for AD, optimizations, and code generation. The deep learning research community has a rich variety of available frameworks. While two existing projects have attempted a compilers approach to deep learning frameworks, and have respectively achieved good integration with existing systems (TensorFlow XLA) and good performance (NNVM + TVM), their design philosophies have not entirely followed established best practices in optimizing compiler design. While well intentioned, the remaining vast majority of other frameworks have failed to observe that the problem of front-end DSLs, algorithmic differentiation, and converting a neural network into efficient executable code is, at its core, a compilers problem. As a result, important issues of extensibility and optimization have been addressed in less than optimal fashion in such frameworks. Nevertheless, several such frameworks have achieved wide adoption. We believe that the principled application of optimizing compiler techniques will lead to substantial improvements in the tools available to deep learning researchers. DLVM and its associated front-end DSLs have a major role to play in this future. Our existing implementation supports reverse-mode AD in the core language, and utilizes LLVM to target NVIDIA GPUs. In our ongoing work, we plan to substantially increase the number of supported hardware architectures by utilizing HPVM as an additional back-end, and explore more advanced AD techniques such as mixing forward and reverse modes.","Deep learning software demands reliability performance. However many existing deep learning frameworks are software libraries act unsafe DSL Python computation graph interpreter. present DLVM design implementation compiler infrastructure linear algebra intermediate representation algorithmic differentiation adjoint code generation domain- specific optimizations code generator targeting GPU via LLVM. Designed modern compiler infrastructure inspired LLVM DLVM is more modular generic existing deep learning compiler frameworks supports tensor DSLs high expressivity. prototypical staged DSL embedded Swift argue DLVM system enables form modular safe performant frameworks deep learning. Within deep learning community current approaches neural networks make use high-level frameworks tensor domain-specific language DSL Torch BID3 TensorFlow BID0 PyTorch PyTorch Development Team 2016 MXNet BID1. Traditionally developers would build computation graph dynamically generate graph nodes using DSL let framework interpret computation graph parallel architectures NVIDIA GPUs. using hand-tuned GPU subroutines usually yields best performance complex operators advanced compiler techniques can be applied simplify computation merge high-level operators based shaping conditions fuse compatible elementwise operators single kernel minimize latency kernel launches. Recent projects TensorFlow XLA compiler NNVM compiler BID13 including TVM BID2 have begun apply compiler techniques deep learning systems targeting LLVM BID10 various back-ends achieve good performance. However design implementation have not entirely followed established best practices widely-used compiler frameworks industry.Moreover frameworks use operator-overloading algorithmic differentiation AD compute gradients leaving gradient computation unoptimizable. approach AD source code transformation can produce efficient code. frameworks TensorFlow already performAD graph transformation apply various optimizations AD transformation is not designed transformation pass pipeline compiler framework part DSL library. Making AD part compiler framework would greatly simplify development DSLs achieving separation concerns. introduce DLVM new compiler infrastructure deep learning systems addresses shortcomings existing deep learning frameworks. solution includes 1 domain-specific intermediate representation specifically designed tensor computation 2 principled use modern compiler optimization techniques substantially simplify neural network computation including algebra simplification AD checkpointing compute kernel fusion various traditional compiler optimizations 3 code generation mature compiler infrastructure allows transparent targeting various hardware 4 embedded DSL supports static analysis type safety natural expression tensor computation has a just-in-time JIT compiler targeting DLVM AD optimizations code generation. deep learning research community has a rich variety available frameworks. two existing projects have attempted compilers approach deep learning frameworks have respectively achieved good integration existing systems TensorFlow XLA good performance NNVM+TVM design philosophies have not entirely followed established best practices optimizing compiler design. well intentioned remaining vast majority frameworks have failed observe problem front-end DSLs algorithmic differentiation converting neural network efficient executable code is,at its core compilers problem. result important issues extensibility optimization have been addressed less optimal fashion frameworks. Nevertheless several frameworks have achieved wide adoption. believe principled application optimizing compiler techniques will lead substantial improvements tools available deep learning researchers. DLVM associated front-end DSLs have a major role play future. existing implementation supports reverse-mode AD core language utilizes LLVM target NVIDIA GPUs. ongoing work plan substantially increase number supported hardware architectures utilizing HPVM additional back-end explore advanced AD techniques mixing forward reverse modes.",863,600,263,0.008,1.438,2025/11/05 17:19:00,0.0,1.647,0.3364485981308407,274.55
"In this work, we focus on the problem of grounding language by training an agent
 to follow a set of natural language instructions and navigate to a target object
 in a 2D grid environment. The agent receives visual information through raw
 pixels and a natural language instruction telling what task needs to be achieved.
 Other than these two sources of information, our model does not have any prior
 information of both the visual and textual modalities and is end-to-end trainable.
 We develop an attention mechanism for multi-modal fusion of visual and textual
 modalities that allows the agent to learn to complete the navigation tasks and also
 achieve language grounding. Our experimental results show that our attention
 mechanism outperforms the existing multi-modal fusion mechanisms proposed in
 order to solve the above mentioned navigation task. We demonstrate through the
 visualization of attention weights that our model learns to correlate attributes of
 the object referred in the instruction with visual representations and also show
 that the learnt textual representations are semantically meaningful as they follow
 vector arithmetic and are also consistent enough to induce translation between instructions
 in different natural languages. We also show that our model generalizes
 effectively to unseen scenarios and exhibit zero-shot generalization capabilities.
 In order to simulate the above described challenges, we introduce a new 2D environment
 for an agent to jointly learn visual and textual modalities Figure 1: The agent (blue in color) should learn to read the instruction and navigate to green apple.Understanding of natural language instructions is an important aspect of an Artificial Intelligence (AI) system. In order to successfully accomplish tasks specified by natural language instructions, an agent has to extract representations of language that are semantically meaningful and ground it in perceptual elements and actions in the environment.Humans have the ability to understand the true essence of the words and thus they can easily decipher sentences even if it contains some new combination of words. It is not unreasonable to expect the same from an AI agent. The information extracted by agent from the language should be such that it corresponds to the true meaning of the word so that it enables the agent to generalize to even unseen combinations of words. For instance, when given sufficient information about the words such as 'green' and 'bag', it should automatically figure out as to what 'green bag' essentially means.Consider a task in which an agent has to learn to navigate to a target object in a 2D grid environment as shown in figure 1. The environment consists of many objects with different attributes (in our case: green apple, red apple, blue sofa, green sofa, an orange fruit, red car) and multiple obstacles. The agent receives visual information through raw pixels and an instruction telling what task needs to be achieved. The challenges that the agent has to tackle here are manyfold: a) the agent has to develop the capability to recognize various objects, b) have some memory of objects seen in previous states while exploring the environment as the objects may occlude each other and/or may not be present in the agent's field of view c) ground the instruction in visual elements and actions in the environment and d) learn a policy to navigate to the target object by avoiding the obstacles and other non-target objects.We tackle this problem by proposing an end-to-end trainable architecture that creates a combined representation of the image observed by the agent and the instruction it receives. Our model does not have any prior information of both the visual and textual modalities. We develop an attention mechanism for multimodal fusion of visual and textual modalities. Our experimental results show that our attention mechanism outperforms the existing multimodal fusion mechanisms proposed in order to solve the above mentioned task. We demonstrate through the visualization of attention weights that our model learns to correlate attributes of the object referred in the instruction with visual representations and also show that the learnt textual representations are semantically meaningful as they follow vector arithmetic and are also consistent enough to induce translation between instructions in different natural languages. We also show that our model generalizes effectively to unseen scenarios and exhibit zero-shot (ZS) generalization capabilities. In order to simulate the above described challenges, we introduce a new 2D environment for an agent to jointly learn visual and textual modalities. Our 2D environment is also thread compatible. Finally, in order to enable the reproducibility of our research through participation in BID21 and foster further research in this direction, we open source our environment as well as the code and models that we developed. In the paper we presented an attention based simple architecture to achieve grounding of natural language sentences via reinforcement learning. We show that retaining just the representation obtained after multimodal fusion phase (i.e. multiple attention maps) and discarding the visual features helps the agent achieve its goals. We justify this claim by visualization of the attention maps which reveal that they contain sufficient information needed for the agent to find the optimal policy. Through vector arithmetic, we also show that the embeddings learnt by the agent indeed make sense. In order to encourage the research in this direction we have also open sourced our environment as well as the code and models developed.Our environment is capable of supporting rich set of natural language instructions and it's highly flexible. As a future work, we would like to increase the complexity of both the types of sentences generated as well as the environment dynamics by introducing moving objects. We also plan to take forward our approach to a 3D environment to test how well does it extend there. To test if our attention mechanism could scale to 3D environments, we applied our fusion mechanism to the Vizdoom based environment and compared our results with who have recently open sourced their code Chaplot. We replaced their fusion mechanism with our attention based fusion mechanism and the results for the easy, medium and also hard scenario are shown in FIG11 . We have also compared our accuracy values with the results mentioned by the authors in their paper, in table 3, whereby we show significant performance improvement during the test phase including for the zeros shot instructions. The experiments are still running for the hard difficulty case but the results show that our approach converges much faster than the original fusion mechanism used by them. We see that our mechanism thus scales to both 2D as well as 3D environments outperforming other baselines in both the scenarios. The experiments were conducted on the same set of hardware thus ensuring a fair comparison between the plots.The plot shown here differs from the one shown in the paper ) because of a possible difference in hardwares used. We will update the plots as soon as all the experiments have been completed.",work focus problem grounding language training agent follow set natural language instructions navigate target object 2D grid environment. agent receives visual information raw pixels natural language instruction telling what task needs achieved. two sources information model does not have any prior information visual textual modalities is end-to-end trainable. develop attention mechanism multi-modal fusion visual textual modalities allows agent learn complete navigation tasks are also achieve language grounding. experimental results show attention mechanism outperforms existing multi-modal fusion mechanisms proposed order solve mentioned navigation task. demonstrate visualization attention weights model learns correlate attributes object referred instruction visual representations are also show learnt textual representations are semantically meaningful follow vector arithmetic are also consistent enough induce translation instructions different natural languages. have also show model generalizes effectively unseen scenarios exhibit zero-shot generalization capabilities. order simulate described challenges introduce new 2D environment agent jointly learn visual textual modalities Figure1:agent blue color should learn read instruction navigate green apple.Understanding natural language instructions is an important aspect Artificial Intelligence AI system. order successfully accomplish tasks specified natural language instructions agent has to extract representations language are semantically meaningful ground perceptual elements actions environment.Humans have the ability understand true essence words thus can easily decipher sentences even if it contains new combination words. is not unreasonable expect AI agent. information extracted agent language should be such that corresponds true meaning word enables agent generalize even unseen combinations words. instance when given sufficient information words 'green' 'bag' should automatically figure what 'green bag' essentially means.Consider task which an agent has to learn navigate target object 2D grid environment shown figure1. environment consists many objects different attributes case:green apple red apple blue sofa green sofa orange fruit red car multiple obstacles. agent receives visual information raw pixels instruction telling what task needs achieved. challenges agent has to tackle are manyfold:agent has to develop capability recognize various objects b have some memory objects seen previous states exploring environment objects may occlude/may present agent's field viewc ground instruction visual elements actions environment learn policy navigate target object avoiding obstacles non-target objects.We tackle problem proposing end-to-end trainable architecture creates combined representation image observed agent instruction receives. model does not have any prior information visual textual modalities. develop attention mechanism multimodal fusion visual textual modalities. experimental results show attention mechanism outperforms existing multimodal fusion mechanisms proposed order solve mentioned task. demonstrate visualization attention weights model learns correlate attributes object referred instruction visual representations are also show learnt textual representations are semantically meaningful follow vector arithmetic are also consistent enough induce translation instructions different natural languages. have also show model generalizes effectively unseen scenarios exhibit zero-shot ZS generalization capabilities. order simulate described challenges introduce new 2D environment agent jointly learn visual textual modalities. 2D environment is also thread compatible. Finally order enable reproducibility research participation BID21 foster research direction open source environment well code models developed. paper presented attention based simple architecture achieve grounding natural language sentences via reinforcement learning. show retaining representation obtained multimodal fusion phase.e multiple attention maps discarding visual features helps agent achieve goals. justify claim visualization attention maps which reveal contain sufficient information needed agent find optimal policy. vector arithmetic also show embeddings learnt agent indeed make sense. order encourage research direction have also open sourced environment well code models developed.Our environment is capable supporting rich set natural language instructions highly flexible. future work would like increase complexity types sentences generated well environment dynamics introducing moving objects. have also plan take forward approach 3D environment test how well does it extend there. test if our attention mechanism could scale 3D environments applied fusion mechanism Vizdoom based environment compared results who have recently open sourced code Chaplot. replaced fusion mechanism attention based fusion mechanism results easy medium are also hard scenario are shown FIG11. have also compared accuracy values results mentioned authors paper table3 whereby show significant performance improvement test phase including zeros shot instructions. experiments are still running hard difficulty case results show approach converges much faster original fusion mechanism used them. see mechanism thus scales 2D well 3D environments outperforming baselines scenarios. experiments were conducted set hardware thus ensuring fair comparison plots.The plot shown differs one shown paper possible difference hardwares used. will update plots soon experiments have been completed.,1311,827,484,0.015,1.585,2025/11/05 17:19:00,0.01,1.541,0.7943925233644857,454.52
" Current end-to-end machine reading and question answering (Q\&A) models are primarily based on recurrent neural networks (RNNs) with attention. Despite their success, these models are often slow for both training and inference due to the sequential nature of RNNs. We propose a new Q\&A architecture called QANet, which does not require recurrent networks:  Its encoder consists exclusively of convolution and self-attention, where convolution models local interactions and self-attention models global interactions. On the SQuAD dataset, our model is 3x to 13x faster in training and 4x to 9x faster in inference, while achieving equivalent accuracy to recurrent models. The speed-up gain allows us to train the model with much more data. We hence combine our model with data generated by backtranslation from a neural machine translation model. 
 On the SQuAD dataset, our single model, trained with augmented data, achieves 84.6 F1 score on the test set, which is significantly better than the best published F1 score of 81.8. There is growing interest in the tasks of machine reading comprehension and automated question answering. Over the past few years, significant progress has been made with end-to-end models showing promising results on many challenging datasets. The most successful models generally employ two key ingredients: (1) a recurrent model to process sequential inputs, and (2) an attention component to cope with long term interactions. A successful combination of these two ingredients is the Bidirectional Attention Flow (BiDAF) model by BID33 , which achieve strong results on the SQuAD dataset BID31 . A weakness of these models is that they are often slow for both training and inference due to their recurrent nature, especially for long texts. The expensive training not only leads to high turnaround time for experimentation and limits researchers from rapid iteration but also prevents the models from being used for larger dataset. Meanwhile the slow inference prevents the machine comprehension systems from being deployed in real-time applications.In this paper, aiming to make the machine comprehension fast, we propose to remove the recurrent nature of these models. We instead exclusively use convolutions and self-attentions as the building blocks of encoders that separately encodes the query and context. Then we learn the interactions between context and question by standard attentions BID45 BID33 BID2 . The resulting representation is encoded again with our recurrency-free encoder before finally decoding to the probability of each position being the start or end of the answer span. We call this architecture QANet, which is shown in Figure 1 .The key motivation behind the design of our model is the following: convolution captures the local structure of the text, while the self-attention learns the global interaction between each pair of words. The additional context-query attention is a standard module to construct the query-aware context vector for each position in the context paragraph, which is used in the subsequent modeling layers. The feed-forward nature of our architecture speeds up the model significantly. In our experiments on the SQuAD dataset, our model is 3x to 13x faster in training and 4x to 9x faster in inference. As a simple comparison, our model can achieve the same accuracy (77.0 F1 score) as BiDAF model BID33 within 3 hours training that otherwise should have taken 15 hours. The speed-up gain also allows us to train the model with more iterations to achieve better results than competitive models. For instance, if we allow our model to train for 18 hours, it achieves an F1 score of 82.7 on the dev set, which is much better than BID33 , and is on par with best published results.As our model is fast, we can train it with much more data than other models. To further improve the model, we propose a complementary data augmentation technique to enhance the training data. This technique paraphrases the examples by translating the original sentences from English to another language and then back to English, which not only enhances the number of training instances but also diversifies the phrasing.On the SQuAD dataset, QANet trained with the augmented data achieves 84.6 F1 score on the test set, which is significantly better than the best published result of 81.8 by . 2 We also conduct ablation test to justify the usefulness of each component of our model. In summary , the contribution of this paper are as follows:• We propose an efficient reading comprehension model that exclusively built upon convolutions and self-attentions. To the best of our knowledge, we are the first to do so. This combination maintains good accuracy, while achieving up to 13x speedup in training and 9x per training iteration, compared to the RNN counterparts. The speedup gain makes our model the most promising candidate for scaling up to larger datasets.• To improve our result on SQuAD, we propose a novel data augmentation technique to enrich the training data by paraphrasing. It allows the model to achieve higher accuracy that is better than the state-of-the-art. In this paper, we propose a fast and accurate end-to-end model, QANet, for machine reading comprehension. Our core innovation is to completely remove the recurrent networks in the encoder. The resulting model is fully feedforward, composed entirely of separable convolutions, attention, linear layers, and layer normalization, which is suitable for parallel computation. The resulting model is both fast and accurate: It surpasses the best published results on SQuAD dataset while up to 13/9 times faster than a competitive recurrent models for a training/inference iteration. Additionally, we find that we are able to achieve significant gains by utilizing data augmentation consisting of translating context and passage pairs to and from another language as a way of paraphrasing the questions and contexts.",Current end-to-end machine reading question answering Q\ models are primarily based recurrent neural networks RNNs attention. Despite success models are often slow training inference due sequential nature RNNs. propose newQ\ architecture called QANet which does not require recurrent networks:encoder consists exclusively convolution self-attention where convolution models local interactions self-attention models global interactions. SQuAD dataset model is3x 13x faster training 4x 9x faster inference achieving equivalent accuracy recurrent models. speed-up gain allowsus train model much data. hence combine model data generated backtranslation neural machine translation model. SQuAD dataset single model trained augmented data achieves 84.6 F1 score test set which is significantly better best published F1 score 81.8 is growing interest tasks machine reading comprehension automated question answering. past years significant progress has been made end-to-end models showing promising results many challenging datasets. successful models generally employ two key ingredients:1 recurrent model process sequential inputs 2 attention component cope long term interactions. successful combination two ingredients is the Bidirectional Attention Flow BiDAF model BID33 which achieve strong results SQuAD dataset BID31. weakness models is that they are often slow training inference due recurrent nature especially long texts. expensive training leads high turnaround time experimentation limits researchers rapid iteration also prevents models used larger dataset. Meanwhile slow inference prevents machine comprehension systems deployed real-time applications.In paper aiming make machine comprehension fast propose remove recurrent nature models. instead exclusively use convolutions self-attentions building blocks encoders separately encodes query context. learn interactions context question standard attentions BID45 BID33 BID2. resulting representation is encoded recurrency-free encoder finally decoding probability position start end answer span. call architecture QANet which is shown Figure 1.The key motivation behind design model is the following:convolution captures local structure text self-attention learns global interaction pair words. additional context-query attention is a standard module construct query-aware context vector position context paragraph which is used subsequent modeling layers. feed-forward nature architecture speeds model significantly. experiments SQuAD dataset model is3x 13x faster training 4x 9x faster inference. simple comparison model can achieve accuracy 77.0 F1 score BiDAF model BID33 within 3 hours training otherwise should have taken 15 hours. speed-up gain also allows us train model iterations achieve better results competitive models. instance if we allow model train 18 hours achieves F1 score 82.7 dev set which is much better BID33 is on par best published results.As model is is both fast can train much data models. improve model propose complementary data augmentation technique enhance training data. technique paraphrases examples translating original sentences English another language back English which not only enhances number training instances also diversifies phrasing.On SQuAD dataset QANet trained augmented data achieves 84.6 F1 score test set which is significantly better best published result 81.8 by. 2 also conduct ablation test justify usefulness component model. summary contribution paper are as follows:• propose efficient reading comprehension model exclusively built upon convolutions self-attentions best knowledge are the first doso. combination maintains good accuracy achieving 13x speedup training 9x per training iteration compared RNN counterparts. speedup gain makes model promising candidate scaling larger datasets.• improve result SQuAD propose novel data augmentation technique enrich training data paraphrasing. allows model achieve higher accuracy is better state-of-the-art paper propose fast accurate end-to-end model QANet machine reading comprehension. core innovation is to completely remove recurrent networks encoder. resulting model is fully feedforward composed entirely separable convolutions attention linear layers layer normalization which is suitable parallel computation. resulting model is is both fast accurate:surpasses best published results SQuAD dataset 13/9 times faster competitive recurrent models training/inference iteration. Additionally find are able achieve significant gains utilizing data augmentation consisting translating context passage pairs another language way paraphrasing questions contexts.,1179,794,385,0.012,1.485,2025/11/05 17:19:00,0.01,1.697,0.4828660436137073,356.04
"Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective.

 In this paper we introduce the building blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression. Figure 1: Any planar projection of a spherical signal will result in distortions. Rotation of a spherical signal cannot be emulated by translation of its planar projection.Convolutional networks are able to detect local patterns regardless of their position in the image. Like patterns in a planar image, patterns on the sphere can move around, but in this case the ""move"" is a 3D rotation instead of a translation. In analogy to the planar CNN, we would like to build a network that can detect patterns regardless of how they are rotated over the sphere.As shown in Figure 1 , there is no good way to use translational convolution or cross-correlation 1 to analyze spherical signals. The most obvious approach, then, is to change the definition of crosscorrelation by replacing filter translations by rotations. Doing so, we run into a subtle but important difference between the plane and the sphere: whereas the space of moves for the plane (2D translations) is itself isomorphic to the plane, the space of moves for the sphere (3D rotations) is a different, three-dimensional manifold called SO(3) 2 . It follows that the result of a spherical correlation (the output feature map) is to be considered a signal on SO(3), not a signal on the sphere, S 2 . For this reason, we deploy SO(3) group correlation in the higher layers of a spherical CNN BID4 .The implementation of a spherical CNN (S 2 -CNN) involves two major challenges. Whereas a square grid of pixels has discrete translation symmetries, no perfectly symmetrical grids for the sphere exist. This means that there is no simple way to define the rotation of a spherical filter by one pixel. Instead, in order to rotate a filter we would need to perform some kind of interpolation. The other challenge is computational efficiency; SO(3) is a three-dimensional manifold, so a naive implementation of SO(3) correlation is O(n 6 ).We address both of these problems using techniques from non-commutative harmonic analysis BID3 BID11 . This field presents us with a far-reaching generalization of the Fourier transform, which is applicable to signals on the sphere as well as the rotation group. It is known that the SO(3) correlation satisfies a Fourier theorem with respect to the SO(3) Fourier transform, and the same is true for our definition of S 2 correlation. Hence, the S 2 and SO(3) correlation can be implemented efficiently using generalized FFT algorithms.Because we are the first to use cross-correlation on a continuous group inside a multi-layer neural network, we rigorously evaluate the degree to which the mathematical properties predicted by the continuous theory hold in practice for our discretized implementation.Furthermore, we demonstrate the utility of spherical CNNs for rotation invariant classification and regression problems by experiments on three datasets. First, we show that spherical CNNs are much better at rotation invariant classification of Spherical MNIST images than planar CNNs. Second, we use the CNN for classifying 3D shapes. In a third experiment we use the model for molecular energy regression, an important problem in computational chemistry. In this paper we have presented the theory of Spherical CNNs and evaluated them on two important learning problems. We have defined S 2 and SO(3) cross-correlations, analyzed their properties, and implemented a Generalized FFT-based correlation algorithm. Our numerical results confirm the stability and accuracy of this algorithm, even for deep networks. Furthermore, we have shown that Spherical CNNs can effectively generalize across rotations, and achieve near state-of-the-art results on competitive 3D Model Recognition and Molecular Energy Regression challenges, without excessive feature engineering and task-tuning.For intrinsically volumetric tasks like 3D model recognition, we believe that further improvements can be attained by generalizing further beyond SO(3) to the roto-translation group SE(3). The development of Spherical CNNs is an important first step in this direction. Another interesting generalization is the development of a Steerable CNN for the sphere , which would make it possible to analyze vector fields such as global wind directions, as well as other sections of vector bundles over the sphere.Perhaps the most exciting future application of the Spherical CNN is in omnidirectional vision. Although very little omnidirectional image data is currently available in public repositories, the increasing prevalence of omnidirectional sensors in drones, robots, and autonomous cars makes this a very compelling application of our work. We use the ZYZ Euler parameterization for SO(3). An element R ∈ SO(3) is written as DISPLAYFORM0 where α ∈ [0, 2π], β ∈ [0, π] and γ ∈ [0, 2π], and Z resp. Y are rotations around the Z and Y axes.Using this parameterization, the normalized Haar measure is DISPLAYFORM1 We have SO(3) dR = 1. The Haar measure BID23 BID3 ) is sometimes called the invariant measure because it has the property that SO(3) f (R R)dR = SO FORMULA2 f (R)dR (this is analogous to the more familiar property DISPLAYFORM2 f (x)dx for functions on the line). This invariance property allows us to do many useful substitutions.We have a related parameterization for the sphere. An element x ∈ S 2 is written DISPLAYFORM3 where n is the north pole.This parameterization makes explicit the fact that the sphere is a quotient S 2 = SO(3)/ SO(2), where H = SO(2) is the subgroup of rotations around the Z axis. Elements of this subgroup H leave the north pole invariant, and have the form Z(γ). The point x(α, β) ∈ S 2 is associated with the coset representativex = R(α, β, 0) ∈ SO(3). This element represents the cosetxH = {R(α, β, γ)|γ DISPLAYFORM4 The normalized Haar measure for the sphere is DISPLAYFORM5 The normalized Haar measure for SO(2) is DISPLAYFORM6 So we have dR = dx dh, again reflecting the quotient structure.We can think of a function on S 2 as a γ-invariant function on SO(3). Given a function f : S 2 → C we associate the functionf (α, β, γ) = f (α, β). When using normalized Haar measures, we have: DISPLAYFORM7 This will allow us to define the Fourier transform on S 2 from the Fourier transform on SO(3), by viewing a function on S 2 as a γ-invariant function on SO(3) and taking its SO(3)-Fourier transform.",Convolutional Neural Networks CNNs have become method choice learning problems involving2D planar images. However number problems recent interest have created demand models can analyze spherical images. Examples include omnidirectional vision drones robots autonomous cars molecular regression problems global weather climate modelling. naive application convolutional networks planar projection spherical signal is destined fail space-varying distortions introduced projection will make translational weight sharing ineffective. paper introduce building blocks constructing spherical CNNs. propose definition spherical cross-correlation is both expressive rotation-equivariant spherical correlation satisfies generalized Fourier theorem which allowsus compute efficiently using generalized non-commutative Fast Fourier Transform FFT algorithm. demonstrate computational efficiency numerical accuracy effectiveness spherical CNNs applied 3D model recognition atomization energy regression. Figure1:planar projection spherical signal will result distortions. Rotation spherical signal cannot emulated translation planar projection.Convolutional networks are able detect local patterns regardless position image. Like patterns planar image patterns sphere can move around case move is a 3D rotation instead translation. analogy planar CNN would like build network can detect patterns regardless how they are rotated sphere.As shown Figure1 is no good way use translational convolution cross-correlation1 analyze spherical signals. obvious approach is change definition crosscorrelation replacing filter translations rotations. run subtle important difference plane sphere:whereas space moves plane 2D translations is itself isomorphic plane space moves sphere 3D rotations is a different three-dimensional manifold called 3 2. follows result spherical correlation output feature map is to be considered signal 3 signal sphere 2. reason deploy 3 group correlation higher layers spherical CNN BID4.The implementation spherical CNN 2 -CNN involves two major challenges. Whereas square grid pixels has discrete translation symmetries perfectly symmetrical grids sphere exist. means is no simple way define rotation spherical filter one pixel. Instead order rotate filter would need perform kind interpolation. challenge is computational efficiency;3 is a three-dimensional manifold naive implementation 3 correlation isO(n6.We address problems using techniques non-commutative harmonic analysis BID3 BID11. field presentsus far-reaching generalization Fourier transform which is applicable signals sphere well rotation group. is known 3 correlation satisfies Fourier theorem respect 3 Fourier transform is true definition 2 correlation. Hence 2 3 correlation can be implemented efficiently using generalized FFT algorithms.Because are the first use cross-correlation continuous group inside multi-layer neural network rigorously evaluate degree which the mathematical properties predicted continuous theory hold practice discretized implementation.Furthermore demonstrate utility spherical CNNs rotation invariant classification regression problems experiments three datasets. First show spherical CNNs are much better rotation invariant classification Spherical MNIST images planar CNNs. Second use CNN classifying 3D shapes. third experiment use model molecular energy regression important problem computational chemistry. paper have presented theory Spherical CNNs evaluated two important learning problems. have defined 2 3 cross-correlations analyzed properties implemented Generalized FFT-based correlation algorithm. numerical results confirm stability accuracy algorithm even deep networks. Furthermore have shown Spherical CNNs can effectively generalize across rotations achieve near state-of-the-art results competitive 3D Model Recognition Molecular Energy Regression challenges without excessive feature engineering task-tuning.For intrinsically volumetric tasks like 3D model recognition believe improvements can be attained generalizing beyond 3 roto-translation groupSE 3 development Spherical CNNs is an important first step direction. Another interesting generalization is the development Steerable CNN sphere would make possible analyze vector fields global wind directions well sections vector bundles sphere.Perhaps exciting future application Spherical CNN is in omnidirectional vision. Although little omnidirectional image data is currently available public repositories increasing prevalence omnidirectional sensors drones robots autonomous cars makes compelling application work. use ZYZ Euler parameterization 3 elementR∈ 3 is written DISPLAYFORM0 whereα∈ 0 2π β∈ 0 π γ∈ 0 2π Z resp. are rotations around Z axes.Using parameterization normalized Haar measure is DISPLAYFORM1 haveSO(3 dR 1. Haar measure BID23 BID3 is sometimes called invariant measure has the property 3 f RR dR FORMULA2f R dR is analogous familiar property DISPLAYFORM2f x dx functions line invariance property allowsus do many useful substitutions.We have a related parameterization sphere. elementx∈ 2 is written DISPLAYFORM3 wheren is the north pole.This parameterization makes explicit fact sphere is a quotient 2 3/2 whereH 2 is the subgroup rotations around Z axis. Elements subgroup H leave north pole invariant have the formZ γ pointx α β ∈ 2 is associated coset representativex R α β 0 ∈ 3 element represents cosetxH R α β γ |γ DISPLAYFORM4 normalized Haar measure sphere is DISPLAYFORM5 normalized Haar measure 2 is DISPLAYFORM6 havedR dxdh reflecting quotient structure.We can think function 2 γ-invariant function 3 Given functionf:2→C associate functionf α β γ f α β When using normalized Haar measures have:DISPLAYFORM7 will allowus define Fourier transform 2 Fourier transform 3 viewing function 2 γ-invariant function 3 taking 3 -Fourier transform.,1594,1055,539,0.02,1.511,2025/11/05 17:19:00,0.01,1.46,0.5638629283489092,494.112
"We propose a novel method that makes use of deep neural networks and gradient decent to perform automated design on complex real world engineering tasks. Our approach works by training a neural network to mimic the fitness function of a design optimization task and then, using the differential nature of the neural network, perform gradient decent to maximize the fitness. We demonstrate this methods effectiveness by designing an optimized heat sink and both 2D and 3D airfoils that maximize the lift drag ratio under steady state flow conditions. We highlight that our method has two distinct benefits over other automated design approaches. First, evaluating the neural networks prediction of fitness can be orders of magnitude faster then simulating the system of interest. Second, using gradient decent allows the design space to be searched much more efficiently then other gradient free methods. These two strengths work together to overcome some of the current shortcomings of automated design. Automated Design is the process by which an object is designed by a computer to meet or maximize some measurable objective. This is typically performed by modeling the system and then exploring the space of designs to maximize some desired property whether that be an automotive car styling with low drag or power and cost efficient magnetic bearings BID1 BID4 . A notable historic example of this is the 2006 NASA ST5 spacecraft antenna designed by an evolutionary algorithm to create the best radiation pattern (Hornby et al.) . More recently, an extremely compact broadband on-chip wavelength demultiplexer was design to split electromagnetic waves with different frequencies BID17 . While there have been some significant successes in this field the dream of true automated is still far from realized. The main challenges present are heavy computational requirements for accurately modeling the physical system under investigation and often exponentially large search spaces. These two problems negatively complement each other making the computation requirements intractable for even simple problems.Our approach works to solve the current problems of automated design in two ways. First, we learn a computationally efficient representation of the physical system on a neural network. This trained network can be used to evaluate the quality or fitness of the design several orders of magnitude faster. Second, we use the differentiable nature of the trained network to get a gradient on the parameter space when performing optimization. This allows significantly more efficient optimization requiring far fewer iterations then other gradient free methods such as genetic algorithms or simulated annealing. These two strengths of our method overcome the present difficulties with automated design and greatly accelerate optimization.The first problem tackled in this work is designing a simple heat sink to maximize the cooling of a heat source. The setup of our simulation is meant to mimic the conditions seen with an aluminum heat sink on a computer processor. We keep this optimization problem relatively simple and use this only as a first test and introduction to the method. Our second test is on the significantly more difficult task of designing both 2D and 3D airfoils with high lift drag ratios under steady state flow conditions. This problem is of tremendous importance in many engineering areas such as aeronautical, aerospace and automotive engineering. Because this is a particularly challenging problem and often times unintuitive for designers, there has been considerable work using automated design to produce optimized designs. We center much of the discussion in this paper around this problem because of its difficulty and view this as a true test our method. While we only look at these two problems in this work, we emphasize that the ideas behind our method are applicable to a wide variety of automated design problems and present the method with this in mind.As we will go into more detail in later sections, in order to perform our airfoil optimization we need a network that predicts the steady state flow from an objects geometry. This problem has previously been tackled in BID5 where they use a relatively simple network architecture. We found that better perform could be obtained using some of the modern network architecture developments and so, in addition to presenting our novel method of design optimization, we also present this superior network for predicting steady state fluid flow with a neural network. In this work we have presented a novel method for automated design and shown its effectiveness on a variety of tasks. Our method makes use of neural networks and gradient descent to provide powerful and fast optimization. There are many directions for future work such as applying this method to new domains like structural optimization and problems related to electromagnetism. One area of particular interest is design optimization on airfoils in turbulent time dependent flows. Another interesting area to explore is hybrid approaches where the neural network method is used to generate a rough design and then fine tuned with a high fidelity simulation. DISPLAYFORM0 The parameters present are n 1 , n 2 , A i s, and h. We also add the parameter θ that determines the angle of attack. In this work we fixed n 1 to 0.5 and n 2 to 1.0 as this will produce a rounded head on the airfoil. We also fix h to zero making the tail the same height as the head. Thus the trainable parameters are the 42 values corresponding to the A i s for the upper and lower surface. A illustration showing the parameterization can be found in FIG7 . The 3D airfoil has similar parameterization.S(φ, y) = φ n1 (1 − φ) This tells the height of the airfoil at a point (x, y). The trainable parameters here are n 1 , n 2 , A i s, B j s, h, s, and l. Again, n 1 , n 2 , and h are fixed to the values in the 2D case. We also have 2 parameters for the angle θ and ψ that determine the rotation in the x and y direction. We keep ψ at zero and only vary θ at the desired angles during the optimization. The parameters s and l correspond to the sweep present in the wing. This leaves the A i s and B j s for optimization. We split the remaining 39 parameters equally so that 13 values are used for B i s and the remaining 26 are split between the A i s for the upper and lower surface. For a much more in depth look at this parameterization, see BID13 .",propose novel method makes use deep neural networks gradient decent perform automated design complex real world engineering tasks. approach works training neural network mimic fitness function design optimization task using differential nature neural network perform gradient decent maximize fitness. demonstrate methods effectiveness designing optimized heat sink 2D 3D airfoils maximize lift drag ratio steady state flow conditions. highlight method has two distinct benefits automated design approaches. First evaluating neural networks prediction fitness can be orders magnitude faster simulating system interest. Second using gradient decent allows design space searched much efficiently gradient free methods. two strengths work together overcome current shortcomings automated design. Automated Design is the process which an object is designed computer meet maximize measurable objective. is typically performed modeling system exploring space designs maximize desired property whether automotive car styling low drag power cost efficient magnetic bearings BID1 BID4. notable historic example is the 2006 NASA ST5 spacecraft antenna designed evolutionary algorithm create best radiation pattern Hornbyetal. recently extremely compact broadband on-chip wavelength demultiplexer was design split electromagnetic waves different frequencies BID17. have been significant successes field dream true automated is still far realized. main challenges present are heavy computational requirements accurately modeling physical system investigation often exponentially large search spaces. two problems negatively complement making computation requirements intractable even simple problems.Our approach works solve current problems automated design two ways. First learn computationally efficient representation physical system neural network. trained network can be used evaluate quality fitness design several orders magnitude faster. Second use differentiable nature trained network get gradient parameter space when performing optimization. allows significantly efficient optimization requiring far fewer iterations gradient free methods genetic algorithms simulated annealing. two strengths method overcome present difficulties automated design greatly accelerate optimization.The first problem tackled work is designing simple heat sink maximize cooling heat source. setup simulation is meant mimic conditions seen aluminum heat sink computer processor. keep optimization problem relatively simple use first test introduction method. second test is on the significantly difficult task designing 2D 3D airfoils high lift drag ratios steady state flow conditions. problem is of tremendous importance many engineering areas aeronautical aerospace automotive engineering. is a particularly challenging problem often times unintuitive designers has been considerable work using automated design produce optimized designs. center much discussion paper around problem difficulty view true test method. look two problems work emphasize ideas behind method are applicable wide variety automated design problems present method mind.As willgo detail later sections order perform airfoil optimization need network predicts steady state flow objects geometry. problem has previously tackled BID5 where they use relatively simple network architecture. found better perform could obtained using modern network architecture developments addition presenting novel method design optimization also present superior network predicting steady state fluid flow neural network. work have presented novel method automated design shown effectiveness variety tasks. method makes use neural networks gradient descent provide powerful fast optimization. are many directions future work applying method new domains like structural optimization problems related electromagnetism. One area particular interest is design optimization airfoils turbulent time dependent flows. Another interesting area explore is hybrid approaches where the neural network method is used generate rough design fine tuned high fidelity simulation. DISPLAYFORM0 parameters present aren1 n2 h. also add parameterθ determines angle attack. work fixedn1 0.5 n2 1.0 will produce rounded head airfoil. also fixh zero making tail height head. Thus trainable parameters are the 42 values corresponding upper lower surface. illustration showing parameterization can be found FIG7. 3D airfoil has similar parameterization.S φ φn1 1−φ tells height airfoil point x trainable parameters aren1 n2 Bj h l. n1 n2 h are fixed values 2D case. also have 2 parameters angleθ ψ determine rotation x direction. keepψ zero varyθ desired angles optimization. parameters l correspond sweep present wing. leaves Bj optimization. split remaining 39 parameters equally 13 values are used B remaining26 are split upper lower surface. much depth look parameterization see BID13.,1238,784,454,0.013,1.579,2025/11/05 17:19:00,0.01,1.385,0.775700934579439,417.029
"Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well without careful hyperparameter tuning and proper initialization. We investigate whether turning the adversarial min-max problem into an optimization problem by replacing the maximization part with its dual improves the quality of the resulting alignment and explore its connections to Maximum Mean Discrepancy. Our empirical results suggest that using the dual formulation for the restricted family of linear discriminators results in a more stable convergence to a desirable solution when compared with the performance of a primal min-max GAN-like objective and an MMD objective under the same restrictions. We test our hypothesis on the problem of aligning two synthetic point clouds on a plane and on a real-image domain adaptation problem on digits. In both cases, the dual formulation yields an iterative procedure that gives more stable and monotonic improvement over time. Adversarial methods have recently become a popular choice for learning distributions of highdimensional data. The key idea is to learn a parametric representation of a distribution by aligning it with the empirical distribution of interest according to a distance given by a discriminative model. At the same time, the discriminative model is trained to differentiate between true and artificially obtained samples. Generative Adversarial Networks (GANs) that use neural networks to both discriminate samples and parameterize a learned distribution, have achieved particularly impressive results in many applications such as generative modeling of images BID9 BID4 BID26 , image super-resolution BID15 , and image-to-image translation BID13 . Adversarial matching of empirical distributions has also shown promise for aligning train and test data distributions n scenarios involving domain shift BID6 BID30 .However , GANs and related models have proved to be extremely difficult to optimize. It has been widely reported that training GANs is a tricky process that often diverges and requires very careful parameter initialization and tuning. Arjovsky and Bottou have recently identified several theoretical problems with loss functions used by GANs, and have analyzed how they contribute to instability and saturation during training.In this paper, we focus on one of the major barriers to stable optimization of adversarial methods, namely their min-max nature. Adversarial methods seek to match the generated and real distributions by minimizing some notion of statistical distance between the two, which is often defined as a maximal difference between values of certain test (witness) functions that could differentiate these distributions. More specifically in the case of GANs, the distance is usually considered to be equal to the likelihood of the best neural network classifier that discriminates between the distributions, assigning ""real or generated?"" labels to the input points. This way, in order to align these distributions one has to minimize this maximum likelihood w.r.t. the parameters of the learned or aligned distribution.Unfortunately, solving min-max problems using gradient descent is inherently very difficult. Below we use a simple example to demonstrate that different flavors of gradient descent are very unstable when it comes to solving problems of this kind.To address this issue, we explore the possibility of replacing the maximization part of the adversarial alignment problem with a dual minimization problem for linear and kernelized linear discriminators. The resulting dual problem turns out to be much easier to solve via gradient descent. Moreover, we make connections between our formulation and existing objectives such as the Maximum Mean Discrepancy (MMD) BID11 . We show that it is strongly related to the iteratively reweighted empirical estimator of MMD.We first evaluate how well our dual method can handle a point alignment problem on a lowdimensional synthetic dataset. Then, we compare its performance with the analogous primal method on a real-image domain adaptation problem using the Street View House Numbers (SVHN) and MNIST domain adaptation dataset pair. Here the goal is to align the feature distributions produced by the network on the two datasets so that a classifier trained to label digits on SVHN does not loose accuracy on MNIST due to the domain shift. In both cases, we show that our proposed dual formulation of the adversarial distance often shows improvement over time, whereas using the primal formulation results in drifting objective values and often does not converge to a solution.Our contributions can be summarized as follows:• we explore the dual formulation of the adversarial alignment objective for linear and kernelized linear discriminators and how they relate to the Maximum Mean Discrepancy; • we demonstrate experimentally on both synthetic and real datasets that the resulting objective leads to more stable convergence and better alignment quality; • we apply this idea to a domain adaptation scenario and show that the stability of reaching high target classification accuracy is also positively impacted by the dual formulation. While exact dual exists only in the logistic discriminator case, when one can use the duality and solve the inner problem in closed form, we want to stress that our paper presents a more general framework for alignment that can be extended to other classes of functions. More specifically, one can rewrite the quadratic form in kernel logistic regression (3) as a Frobenius inner product of a kernel matrix Q with a symmetric rank 1 alignment matrix S (outer product of alpha with itself). DISPLAYFORM0 The kernel matrix specifies distances between points and S chooses pairs that minimize the total distance. This way the problem reduces to ""maximizing the maximum agreement between the alignment and similarity matrices"" that in turn might be seen as replacing ""adversity"" in the original problem with ""cooperation"" in the dual maximization problem. In our paper, S is a rank 1 matrix, but we could choose different alignment matrix parameterizations and a corresponding regularizer that would correspond to having a neural network discriminator in the adversarial problem or a Wasserstein distance in Earth Mover's Distance form. The resulting problem is not dual to minimization of any existing adversarial distances, but exploits same underlying principle of ""iteratively-reweighted alignment matrix fitting"" discussed in this paper.We assert that in order to understand the basic properties of the resulting formulation, an in-depth discussion of the well-studied logistic case is no less important than the discussion involving complicated deep models, which deserves a paper of its own. This paper proposes a more stable ""cooperative"" problem reformulation rather than a new adversarial objective as many recent papers do. We presented an adversarial objective that does not lead to a min-max problem. We proposed using the dual of the discriminator objective to improve the stability of distribution alignment, showed its connection to MMD, and presented quantitative results for alignment of toy datasets and unsupervised domain adaptation results on real-image classification datasets. Our results suggest that the proposed dual optimization objective is indeed better suited for learning with gradient descent than the saddle point objective that naturally arises from the original primal formulation of adversarial alignment. Further attempts to use duality to reformulate other notions of statistical distances in adversarial settings as computationally feasible minimization problems may be promising. Bottom row: Evolution of target test accuracy over epochs. Our Dual objective (third column) clearly performs well under the majority of the learning rates. WGAN often performs better than MMD and ADDA, but experiences significant oscillations. Different validation heuristics, such as considering only runs that resulted in a significant drop in distance, did not significantly change these trends (Section 9.3). The proportion of runs that outperformed the source baseline after 40 epochs were: 52.3% for Dual, 21.5% for WGAN, 17.1% for MMD and 6.9% for ADDA.",Methods align distributions minimizing adversarial distance have recently achieved impressive results. However approaches are difficult optimize gradient descent often do not converge well without careful hyperparameter tuning proper initialization. investigate whether turning adversarial min-max problem optimization problem replacing maximization part dual improves quality resulting alignment explore connections Maximum Mean Discrepancy. empirical results suggest using dual formulation restricted family linear discriminators results stable convergence desirable solution when compared performance primal min-max GAN-like objective MMD objective restrictions. test hypothesis problem aligning two synthetic point clouds plane real-image domain adaptation problem digits. cases dual formulation yields iterative procedure gives stable monotonic improvement time. Adversarial methods have recently become popular choice learning distributions highdimensional data. key idea is to learn parametric representation distribution aligning empirical distribution interest according distance given discriminative model. time discriminative model is trained differentiate true artificially obtained samples. Generative Adversarial Networks GANs use neural networks discriminate samples parameterize learned distribution have achieved particularly impressive results many applications generative modeling images BID9 BID4 BID26 image super-resolution BID15 image-to-image translation BID13. Adversarial matching empirical distributions has also shown promise aligning train test data distributionsn scenarios involving domain shift BID6 BID30.However GANs related models have proved extremely difficult optimize. has been widely reported training GANs is a tricky process often diverges requires careful parameter initialization tuning. Arjovsky Bottou have recently identified several theoretical problems loss functions used GANs have analyzed how they contribute instability saturation training.In paper focus one major barriers stable optimization adversarial methods namely min-max nature. Adversarial methods seek match generated real distributions minimizing notion statistical distance two which is often defined maximal difference values certain test witness functions could differentiate distributions. specifically case GANs distance is usually considered equal likelihood best neural network classifier discriminates distributions assigning real generated? labels input points. way order align distributions one has to minimize maximum likelihoodw.r.t parameters learned aligned distribution.Unfortunately solving min-max problems using gradient descent is inherently difficult. use simple example demonstrate different flavors gradient descent are very unstable when it comes solving problems kind.To address issue explore possibility replacing maximization part adversarial alignment problem dual minimization problem linear kernelized linear discriminators. resulting dual problem turns much easier solve via gradient descent. Moreover make connections formulation existing objectives Maximum Mean Discrepancy MMD BID11. show is strongly related iteratively reweighted empirical estimator MMD.We first evaluate how well dual method can handle point alignment problem lowdimensional synthetic dataset. compare performance analogous primal method real-image domain adaptation problem using Street View House Numbers SVHN MNIST domain adaptation dataset pair. goal is to align feature distributions produced network two datasets classifier trained label digits SVHN does not loose accuracy MNIST due domain shift. cases show proposed dual formulation adversarial distance often shows improvement time whereas using primal formulation results drifting objective values often does not converge solution.Our contributions can be summarized follows:• explore dual formulation adversarial alignment objective linear kernelized linear discriminators how they relate Maximum Mean Discrepancy;• demonstrate experimentally synthetic real datasets resulting objective leads stable convergence better alignment quality;• apply idea domain adaptation scenario show stability reaching high target classification accuracy is also positively impacted dual formulation. exact dual exists logistic discriminator case when one can use duality solve inner problem closed form want stress paper presents general framework alignment can be extended classes functions. specifically when one can rewrite quadratic form kernel logistic regression 3 Frobenius inner product kernel matrixQ symmetric rank 1 alignment matrix outer product alpha DISPLAYFORM0 kernel matrix specifies distances points chooses pairs minimize total distance. way problem reduces maximizing maximum agreement alignment similarity matrices turn might seen replacing adversity original problem cooperation dual maximization problem. paper is a rank 1 matrix could choose different alignment matrix parameterizations corresponding regularizer would correspond neural network discriminator adversarial problem Wasserstein distance Earth Mover's Distance form. resulting problem is not dual minimization existing adversarial distances exploits underlying principle iteratively-reweighted alignment matrix fitting discussed paper.We assert order understand basic properties resulting formulation in-depth discussion well-studied logistic case is no less important discussion involving complicated deep models which deserves paper own. paper proposes stable cooperative problem reformulation rather new adversarial objective many recent papers do. presented adversarial objective does not lead min-max problem. proposed using dual discriminator objective improve stability distribution alignment showed connection MMD presented quantitative results alignment toy datasets unsupervised domain adaptation results real-image classification datasets. results suggest proposed dual optimization objective is indeed better suited learning gradient descent saddle point objective naturally arises original primal formulation adversarial alignment. attempts use duality reformulate notions statistical distances adversarial settings computationally feasible minimization problems may promising. Bottom row:Evolution target test accuracy epochs. Dual objective third column clearly performs well majority learning rates. WGAN often performs better MMD ADDA experiences significant oscillations. Different validation heuristics considering runs resulted significant drop distance did not significantly change trends Section 9.3 proportion runs outperformed source baseline 40 epochs were:52.3 Dual 21.5 WGAN 17.1 MMD 6.9 ADDA.,1522,1010,512,0.016,1.507,2025/11/05 17:19:00,0.01,1.5,0.551401869158878,481.069
"  There are many applications scenarios for which the computational
  performance and memory footprint of the prediction phase of Deep
  Neural Networks (DNNs) need to be optimized. Binary Deep Neural
  Networks (BDNNs) have been shown to be an effective way of achieving
  this objective. In this paper, we show how Convolutional Neural
  Networks (CNNs) can be implemented using binary
  representations. Espresso is a compact, yet powerful
  library written in C/CUDA that features all the functionalities
  required for the forward propagation of CNNs, in a binary file less
  than 400KB, without any external dependencies. Although it is mainly
  designed to take advantage of massive GPU parallelism, Espresso also
  provides an equivalent CPU implementation for CNNs. Espresso
  provides special convolutional and dense layers for BCNNs,
  leveraging bit-packing and bit-wise computations
  for efficient execution. These techniques provide a speed-up of
  matrix-multiplication routines, and at the same time, reduce memory
  usage when storing parameters and activations. We experimentally
  show that Espresso is significantly faster than existing
  implementations of optimized binary neural networks (~ 2
  orders of magnitude). Espresso is released under the Apache 2.0
  license and is available at http://github.com/organization/project. Convolutional Neural Networks have revolutionized computer vision, pushing the task of object recognition beyond human capabilities BID18 BID25 BID27 . Deep Neural Networks (DNN), have also been successfully applied in other fields, such as speech recognition BID9 and automated translation BID1 BID26 . Despite achieving impressive classification accuracy results, DNNs require too much memory and power to be used effectively on embedded or low-power devices. Many networks consume a considerable amount of memory. Memory remains a very limited resource on mobile platforms making harder the usage of trained DNNs 1 . Even when memory is not an issue, DNNs remain very computationally intensive, and can quickly drain the battery. Reducing the computational load does not only improve energy efficiency, but can also enable further applications. For example, when processing real-time object classification on mobile, being able to perform faster predictions frees up computational resources that can be spent on tasks such as speech recognition and analysis. Therefore, there is a substantial interest in reducing the computational and memory requirements of DNNs.Efficient deep neural networks One way to achieve this target is to use specialized hardware for DNNs. Another strategy is to reduce the network's memory footprint and associated computation, hence increasing its efficiency. Such solutions are preferable as they can be implemented in software without requiring specialized hardware. In our research we follow the software approach, and focus our attention to quantized networks. In this case, the parameters are stored as ""small"" integers (typically less than 8-bit) instead of single precision floating point numbers (32-bit). In particular, we consider the binary deep neural networks (BDNN) proposed by where parameters and activations are 1-bit integers: {−1, +1}. At the expense of a relatively small decrease in accuracy, BDNNs can considerably reduce memory usage, and result in faster execution time (i.e. forward propagation). Further, note that potential hardware implementation of BDNNs would also be cheaper due to the reduced number of required FPUs. While these results are highly promising, currently only proof-of-concept implementations of BinaryNets have been published . Therefore, the availability of a flexible end-to-end framework, with particular emphasis placed on computational efficiency, can enable further research on BDNNs, as well as its application to practical scenarios.Contributions With Espresso we provide an optimized framework for BDNNs capable of achieving state-of-the-art run-time performance with minimal memory footprint while being numerical equivalent to their non-optimized binary counterpart. Espresso provides a complete optimized framework for BDNNs supporting both the dense and the convolutional layer. Current state-ofthe-art optimized BDNNs implementations are limited to the fully connected layer, with the serious drawback of not being able to run optimized state-of-art convolutional BDNNs (BCNNs). While our work is a necessary stepping stone towards optimization of training routines, in this paper we focus on the optimization of forward-propagation (i.e. testing), rather than back-propagation (i.e. training). Espresso is designed to have no external dependencies. This not only results in a highly optimized implementation of BDNNs, but also substantially simplifies its deployment in practical applications, such as those executing on mobile or embedded devices. In this paper we presented Espresso, a highly optimized forward-propagation framework for both traditional DNNs as well as BCNNs, that supports heterogeneous deployment on CPU and GPU. While BinaryNet and Nervana/neon BDNN implementations are limited to MLP networks, our framework also supports the popular CNN while simultaneously outperforming state-of-the-art implementations of MLP networks. Espresso is highly-efficient, light-weight and self-contained. Computation on the GPU side is done though specifically designed CUDA kernels, which, combined with a more careful handling of memory allocation and bit-packing, allows us to obtain considerable performance improvements. In future work we would like to add training capabilities, and perform additional performance comparisons on larger standard datasets.",are many applications scenarios which the computational performance memory footprint prediction phase Deep Neural Networks DNNs need optimized. Binary Deep Neural Networks BDNNs have been shown effective way achieving objective. paper show how Convolutional Neural Networks CNNs can be implemented using binary representations. Espresso is a compact yet powerful library written C/CUDA features functionalities required forward propagation CNNs binary file less 400KB without external dependencies. Although is mainly designed take advantage massive GPU parallelism Espresso also provides equivalent CPU implementation CNNs. Espresso provides special convolutional dense layers BCNNs leveraging bit-packing bit-wise computations efficient execution. techniques provide speed-up matrix-multiplication routines time reduce memory usage when storing parameters activations. experimentally show Espresso is significantly faster existing implementations optimized binary neural networks 2 orders magnitude Espresso is released Apache 2.0 license is available http://github.com/organization/project. Convolutional Neural Networks have revolutionized computer vision pushing task object recognition beyond human capabilities BID18 BID25 BID27. Deep Neural Networks DNN have also successfully applied fields speech recognition BID9 automated translation BID1 BID26. Despite achieving impressive classification accuracy results DNNs require much memory power used effectively embedded low-power devices. Many networks consume considerable amount memory. Memory remains limited resource mobile platforms making harder usage trained DNNs1. Even when memory is not an issue DNNs remain computationally intensive can quickly drain battery. Reducing computational load does not only improve energy efficiency can also enable applications. example when processing real-time object classification mobile able perform faster predictions frees computational resources can be spent tasks speech recognition analysis. Therefore is a substantial interest reducing computational memory requirements DNNs.Efficient deep neural networks One way achieve target is to use specialized hardware DNNs. Another strategy is to reduce network's memory footprint associated computation hence increasing efficiency. solutions are preferable can be implemented software without requiring specialized hardware. research follow software approach focus attention quantized networks. case parameters are stored small integers typically less 8-bit instead single precision floating point numbers 32-bit particular consider binary deep neural networks BDNN proposed where parameters activations are 1-bit integers:−1+1 expense relatively small decrease accuracy BDNNs can considerably reduce memory usage result faster execution time.e forward propagation note potential hardware implementation BDNNs would also cheaper due reduced number required FPUs. results are highly promising currently proof-of-concept implementations BinaryNets have been published. Therefore availability flexible end-to-end framework particular emphasis placed computational efficiency can enable research BDNNs well application practical scenarios.Contributions Espresso provide optimized framework BDNNs capable achieving state-of-the-art run-time performance minimal memory footprint numerical equivalent non-optimized binary counterpart. Espresso provides complete optimized framework BDNNs supporting dense convolutional layer. Current state-ofthe-art optimized BDNNs implementations are limited fully connected layer serious drawback able run optimized state-of-art convolutional BDNNs BCNNs work is a necessary stepping stone towards optimization training routines paper focus optimization forward-propagation.e testing rather back-propagation.e training Espresso is designed have no external dependencies. results highly optimized implementation BDNNs can also substantially simplifies deployment practical applications executing mobile embedded devices. paper presented Espresso highly optimized forward-propagation framework traditional DNNs well BCNNs supports heterogeneous deployment CPU GPU. BinaryNet Nervana/neon BDNN implementations are limited MLP networks framework also supports popular CNN simultaneously outperforming state-of-the-art implementations MLP networks. Espresso is highly-efficient light-weight self-contained Computation GPU side is done though specifically designed CUDA kernels combined careful handling memory allocation bit-packing allowsus obtain considerable performance improvements. future work would like add training capabilities perform additional performance comparisons larger standard datasets.,1086,736,350,0.011,1.476,2025/11/05 17:19:00,0.01,1.421,0.4548286604361368,314.711
"Optimal selection of a subset of items from a given set is a hard problem that requires combinatorial optimization. In this paper, we propose a subset selection algorithm that is trainable with gradient based methods yet achieves near optimal performance via submodular optimization. We focus on the task of identifying a relevant set of sentences for claim verification in the context of the FEVER task. Conventional methods for this task look at sentences on their individual merit and thus do not optimize the informativeness of sentences as a set. We show that our proposed method which builds on the idea of unfolding a greedy algorithm into a computational graph allows both interpretability and gradient based training. The proposed differentiable greedy network (DGN) outperforms discrete optimization algorithms as well as other baseline methods in terms of precision and recall. In this paper, we develop a subset selection algorithm that is differentiable and discrete, which can be trained on supervised data and can model complex dependencies between elements in a straightforward and comprehensible way. This is of particular interest in natural language processing tasks such as fact extraction, fact verification, and question answering where the proposed optimization scheme can be used for evidence retrieval.Conventional evidence retrieval methods that look at lexical or semantic similarity typically treat sentences or documents independently, potentially missing dependencies between them and therefore select redundant evidence. One way to address this shortcoming is by adding a diversity promoting submodular objective function BID28 BID17 BID18 BID6 BID13 . Submodularity is a property of set functions that can be expressed by the notion of diminishing returns that allows near-optimal solutions to be found in polynomial time for NP-hard problems.A submodular set function is a function that maps sets to scalar values and has the property that the incremental value of the function computed with an additional element to an input set never increases as the input set grows. Submodular functions are defined by this natural diminishing returns property, which makes them well suited for tasks such as claim verification. With respect to a claim, the amount of relevant information in a set of sentences has diminishing returns as the set grows, meaning that the amount of additional information in an additional piece of evidence shrinks as the set of selected evidence grows. Thus, any relevancy-measuring function that is learned from data would potentially benefit from a diminishing returns constraint as it would discount redundancy in favor of diverse but relevant evidence. Claim verification often requires complicated induction from multiple sentences, so promoting diversity among selected sentences is important to capture all facets of the claim. The resulting submodular optimization model can then handle dependencies between sentences and features, and despite making the sentence selection problem more difficult computationally, a near-optimal solution can be found efficiently using a simple forward greedy algorithm.The main contribution of this paper is a new optimization scheme which integrates continuous gradient-based and discrete submodular frameworks derived by unfolding a greedy optimization algorithm: the Differentiable Greedy Network (DGN). By unfolding a greedy algorithm into a computational graph, we can combine the advantages in interpretability and representation learning. Deep unfolding is a technique that transforms inference algorithms into computational graphs, thereby allowing the original model parameters to be trained discriminatively on labeled data while still exactly corresponding to the original model parameters BID9 . We show that making a greedy algorithm differentiable and adding trainable parameters leads to promising improvements in recall@k of 10%-18% and precision@k of 5%-27% for a sentence selection task, where k = 1, 3, 5, 7 is the number of selected evidence sentences, on the Fact Extraction and Verification (FEVER) dataset BID27 and, with fewer parameters, performs very similarly to a conventional deep network. As the DGN is bootstrapping a greedy algorithm, it can be easily extended to work on other information retrieval tasks such as question answering as well as other problems that rely on greedy approaches. While more sophisticated neural architectures can deliver better performance, we focus on showing the power of our new optimization scheme on a simpler model.In Section 2, we discuss related work in the domains of information retrieval, submodularity, and deep unfolding. In Section 3, we define submodularity and present the proposed Differentiable Greedy Network (DGN). Section 4 contains experiments and results for baseline models and DGN applied to sentence selection for the FEVER dataset as well as an ablation study. We draw conclusions in Section 5. Also, the attached Appendix 6 contains an additional example demonstrating the utility of promoting diversity. In this paper, we have shown that unfolding a greedy algorithm into a computational graph, allowing us to retain the interpretability and unsupervised initialization of a conventional greedy sentence selection approach while benefiting from supervised learning techniques. The proposed differentiable greedy network (DGN) outperforms conventional discrete optimization algorithms in terms of both recall and precision. Furthermore, as sentence retrieval is often part of a larger pipeline as in the FEVER shared task, using a differentiable greedy network serves as a step towards an end-end trainable system.",Optimal selection subset items given set is a hard problem requires combinatorial optimization. paper propose subset selection algorithm is trainable gradient based methods yet achieves near optimal performance via submodular optimization. focus task identifying relevant set sentences claim verification context FEVER task. Conventional methods task look sentences individual merit thus do not optimize informativeness sentences set. show proposed method which builds idea unfolding greedy algorithm computational graph allows interpretability gradient based training. proposed differentiable greedy network DGN outperforms discrete optimization algorithms well baseline methods terms precision recall. paper develop subset selection algorithm is differentiable discrete which can be trained supervised data can model complex dependencies elements straightforward comprehensible way. is of particular interest natural language processing tasks fact extraction fact verification question answering where the proposed optimization scheme can be used evidence retrieval.Conventional evidence retrieval methods look lexical semantic similarity typically treat sentences documents independently potentially missing dependencies therefore select redundant evidence. One way address shortcoming is by adding diversity promoting submodular objective function BID28 BID17 BID18 BID6 BID13. Submodularity is a property set functions can be expressed notion diminishing returns allows near-optimal solutions found polynomial time NP-hard problems.A submodular set function is a function maps sets scalar values has the property incremental value function computed additional element input set never increases input set grows. Submodular functions are defined natural diminishing returns property which makes well suited tasks claim verification. respect claim amount relevant information set sentences has diminishing returns set grows meaning amount additional information additional piece evidence shrinks set selected evidence grows. Thus relevancy-measuring function is learned data would potentially benefit diminishing returns constraint would discount redundancy favor diverse relevant evidence. Claim verification often requires complicated induction multiple sentences promoting diversity among selected sentences is important capture facets claim. resulting submodular optimization model can then handle dependencies sentences features despite making sentence selection problem difficult computationally near-optimal solution can be found efficiently using simple forward greedy algorithm.The main contribution paper is a new optimization scheme which integrates continuous gradient-based discrete submodular frameworks derived unfolding greedy optimization algorithm:Differentiable Greedy Network DGN unfolding greedy algorithm computational graph can combine advantages interpretability representation learning. Deep unfolding is a technique transforms inference algorithms computational graphs thereby allowing original model parameters trained discriminatively labeled data still exactly corresponding original model parameters BID9. show making greedy algorithm differentiable adding trainable parameters leads promising improvements recall@k 10%-18 precision@k 5%-27 sentence selection task wherek 1 3 5 7 is the number selected evidence sentences Fact Extraction Verification FEVER dataset BID27 fewer parameters performs similarly conventional deep network. DGN is bootstrapping greedy algorithm can be easily extended work information retrieval tasks question answering well problems rely greedy approaches. sophisticated neural architectures can deliver better performance focus showing power new optimization scheme simpler model.In Section2 discuss related work domains information retrieval submodularity deep unfolding. Section3 define submodularity present proposed Differentiable Greedy Network DGN Section 4 contains experiments results baseline models DGN applied sentence selection FEVER dataset well ablation study. draw conclusions Section5. Also attached Appendix 6 contains additional example demonstrating utility promoting diversity. paper have shown unfolding greedy algorithm computational graph allowingus retain interpretability unsupervised initialization conventional greedy sentence selection approach benefiting supervised learning techniques. proposed differentiable greedy network DGN outperforms conventional discrete optimization algorithms terms recall precision. Furthermore sentence retrieval is often part larger pipeline FEVER shared task using differentiable greedy network serves step towards end-end trainable system.,1011,692,319,0.01,1.461,2025/11/05 17:19:00,0.0,1.545,0.4080996884735203,314.098
"The joint optimization of representation learning and clustering in the embedding space has experienced a breakthrough in recent years. In spite of the advance, clustering with representation learning has been limited to flat-level categories, which oftentimes involves cohesive clustering with a focus on instance relations. To overcome the limitations of flat clustering, we introduce hierarchically clustered representation learning (HCRL), which simultaneously optimizes representation learning and hierarchical clustering in the embedding space. Specifically, we place a nonparametric Bayesian prior on embeddings to handle dynamic mixture hierarchies under the variational autoencoder framework, and to adopt the generative process of a hierarchical-versioned Gaussian mixture model. Compared with a few prior works focusing on unifying representation learning and hierarchical clustering, HCRL is the first model to consider a generation of deep embeddings from every component of the hierarchy, not just leaf components. This generation process enables more meaningful separations and mergers of clusters via branches in a hierarchy. In addition to obtaining hierarchically clustered embeddings, we can reconstruct data by the various abstraction levels, infer the intrinsic hierarchical structure, and learn the level-proportion features. We conducted evaluations with image and text domains, and our quantitative analyses showed competent likelihoods and the best accuracies compared with the baselines. Clustering is one of the most traditional and frequently used machine learning tasks. Clustering models are designed to represent intrinsic data structures, such as latent Dirichlet allocation BID2 . The recent development of representation learning has contributed to generalizing model feature engineering, which also enhances data representation BID1 . Therefore, representation learning has been merged into the clustering models, e.g., variational deep embedding (VaDE) (Jiang et al., 2017) . Besides merging representation learning and clustering, another critical line of research is structuring the clustering result, e.g., hierarchical clustering. This paper introduces a unified model enabling nonparametric Bayesian hierarchical clustering with neural-network-based representation learning.Autoencoder (Rumelhart et al., 1985) is a typical neural network for unsupervised representation learning and achieves a non-linear mapping from a high-dimensional input space to a lowdimensional embedding space by minimizing reconstruction errors. To turn the low-dimensional embeddings into random variables, a variational autoencoder (VAE) (Kingma & Welling, 2014) places a Gaussian prior on the embeddings. The autoencoder, whether it is probabilistic or not, has a limitation in reflecting the intrinsic hierarchical structure of data. For instance, VAE assuming a single Gaussian prior needs to be expanded to suggest an elaborate clustering structure.Due to the limitations of modeling the cluster structure with autoencoders, prior works combine the autoencoder and the clustering algorithm. While some early cases pipeline just two models, e.g., Huang et al. (2014) , a typical merging approach is to model an additional loss, such as a clustering loss, in the autoencoders (Xie et al., 2016; Guo et al., 2017; Yang et al., 2017; Nalisnick et al., 2016; BID4 Jiang et al., 2017) . These suggestions exhibit gains from unifying the encoding and the clustering, yet they remain at the parametric and flat-structured clustering. A more recent development releases the previous constraints by using the nonparametric Bayesian approach. Figure 1: Example of hierarchically clustered embeddings on MNIST with three levels of hierarchy, the reconstructed digits from the hierarchical Gaussian mixture components, and the extracted level proportion features. We marked the mean of a Gaussian mixture component with the colored square, and the digit written inside the square refers to the unique index of the mixture component.For example, the infinite mixture of VAEs (IMVAE) BID0 explores the infinite space for VAE mixtures by looking for an adequate embedding space through sampling, such as the Chinese restaurant process (CRP). Whereas IMVAE remains at the flat-structured clustering, VAEnested CRP (VAE-nCRP) (Goyal et al., 2017) captures a more complex structure, i.e., a hierarchical structure of the data, by adopting the nested Chinese restaurant process (nCRP) prior (Griffiths et al., 2004) into the cluster assignment of the Gaussian mixture model. This paper proposes hierarchically clustered representation learning (HCRL) that is a joint model of 1) nonparametric Bayesian hierarchical clustering, and 2) representation learning with neural networks. HCRL extends a previous work on merging flat clustering and representation learning, i.e., VaDE, by incorporating inter-cluster relation modelings. Unlike a previous work of VAE-nCRP, HCRL learns the full spectrum of hierarchical clusterings, such as the level assignment and the level proportion of generating a component hierarchy. These level assignments and proportions were not modeled in VAE-nCRP, so each data instance cannot be analyzed from the perspective of generalization and specialization in a hierarchy. On the contrary, by adding level assignment and proportion modeling, a data instance can be generated from an internal component of the hierarchy, which is limited to the leaf component in VAE-nCRP. Hierarchical mixture density estimation (Vasconcelos & Lippman, 1999) , where all internal and leaf components are directly modeled to generate data, is a flexible framework for hierarchical mixture modeling, such as hierarchical topic modeling (Mimno et al., 2007; Griffiths et al., 2004) , with regard to the learning of the internal components.Specifically, HCRL jointly optimizes soft-divisive hierarchical clustering in an embedding space from VAE via two mechanisms. First, HCRL includes a hierarchical-versioned Gaussian mixture model (HGMM) with a mixture of hierarchically organized Gaussian distributions. Then, HCRL sets the prior of embeddings by adopting the generative processes of HGMM. Second, to handle a dynamic hierarchy structure dealing with the clusters of unequal sizes, we explore the infinite hierarchy space by exploiting an nCRP prior. These mechanisms are fused as a unified objective function; this is done rather than concatenating the two distinct models of clustering and autoencoding. The quantitative evaluations focus on density estimation quality and hierarchical clustering accuracy, which shows that HCRL has competent likelihoods and the best accuracies compared with the baselines. When we observe our results qualitatively, we visualize 1) the hierarchical clusterings, 2) the embeddings under the hierarchy modeling, and 3) the reconstructed images from each Gaussian mixture component, as shown in FIG3 . These experiments were conducted by crossing the data domains of texts and images, so our benchmark datasets include MNIST, CIFAR-100, RCV1 v2, and 20Newsgroups. In this paper, we have introduced a hierarchically clustered representation learning framework for the hierarchical mixture density estimation on deep embeddings. HCRL aims at encoding the relations among clusters as well as among instances to preserve the internal hierarchical structure of data. The main differentiated features of HCRL are 1) the crucial assumption regarding the internal mixture components for having the ability to generate data directly, and 2) the unbalanced autoencoding neural architecture for the level proportion modeling as the encoding structure, and the probabilistic model as the decoding structure. From the modeling and the evaluation, we found that HCRL enables the improvements due to the high flexibility modeling compared with the baselines.",joint optimization representation learning clustering embedding space has experienced breakthrough recent years. spite advance clustering representation learning has been limited flat-level categories which oftentimes involves cohesive clustering focus instance relations. overcome limitations flat clustering introduce hierarchically clustered representation learning HCRL which simultaneously optimizes representation learning hierarchical clustering embedding space. Specifically place nonparametric Bayesian prior embeddings handle dynamic mixture hierarchies variational autoencoder framework adopt generative process hierarchical-versioned Gaussian mixture model. Compared prior works focusing unifying representation learning hierarchical clustering HCRL is the first model consider generation deep embeddings every component hierarchy leaf components. generation process enables meaningful separations mergers clusters via branches hierarchy. addition obtaining hierarchically clustered embeddings can reconstruct data various abstraction levels infer intrinsic hierarchical structure learn level-proportion features. conducted evaluations image text domains quantitative analyses showed competent likelihoods best accuracies compared baselines. Clustering is one traditional frequently used machine learning tasks. Clustering models are designed represent intrinsic data structures latent Dirichlet allocation BID2. recent development representation learning has contributed generalizing model feature engineering which also enhances data representation BID1. Therefore representation learning has been merged clustering models e.g variational deep embedding VaDE Jiangetal. 2017 Besides merging representation learning clustering another critical line research is structuring clustering result e.g hierarchical clustering. paper introduces unified model enabling nonparametric Bayesian hierarchical clustering neural-network-based representation learning.Autoencoder Rumelhartetal. 1985 is a typical neural network unsupervised representation learning achieves non-linear mapping high-dimensional input space lowdimensional embedding space minimizing reconstruction errors. turn low-dimensional embeddings random variables variational autoencoder VAE Kingma Welling 2014 places Gaussian prior embeddings. autoencoder whether is probabilistic has limitation reflecting intrinsic hierarchical structure data. instance VAE assuming single Gaussian prior needs expanded suggest elaborate clustering structure.Due limitations modeling cluster structure autoencoders prior works combine autoencoder clustering algorithm. early cases pipeline two models e.g Huangetal. 2014 is a typical merging approach is to model additional loss clustering loss autoencoders Xieetal. 2016;Guoetal. 2017;Yangetal. 2017;Nalisnicketal. 2016;BID4 Jiangetal. 2017 suggestions exhibit gains unifying encoding clustering yet remain parametric flat-structured clustering. recent development releases previous constraints using nonparametric Bayesian approach. Figure1:Example hierarchically clustered embeddings MNIST three levels hierarchy reconstructed digits hierarchical Gaussian mixture components extracted level proportion features. marked mean Gaussian mixture component colored square digit written inside square refers unique index mixture component.For example infinite mixture VAEs IMVAE BID0 explores infinite space VAE mixtures looking adequate embedding space sampling Chinese restaurant process CRP Whereas IMVAE remains flat-structured clustering VAEnested CRP VAE-nCRP Goyaletal. 2017 captures complex structure.e hierarchical structure data adopting nested Chinese restaurant process nCRP prior Griffithsetal. 2004 cluster assignment Gaussian mixture model. paper proposes hierarchically clustered representation learning HCRL is a joint model 1 nonparametric Bayesian hierarchical clustering 2 representation learning neural networks. HCRL extends previous work merging flat clustering representation learning.e VaDE incorporating inter-cluster relation modelings. Unlike previous work VAE-nCRP HCRL learns full spectrum hierarchical clusterings level assignment level proportion generating component hierarchy. level assignments proportions were not modeled VAE-nCRP data instance cannot analyzed perspective generalization specialization hierarchy. contrary adding level assignment proportion modeling data instance can be generated internal component hierarchy which is limited leaf component VAE-nCRP Hierarchical mixture density estimation Vasconcelos Lippman 1999 where all internal leaf components are directly modeled generate data is a flexible framework hierarchical mixture modeling hierarchical topic modeling Mimnoetal. 2007;Griffithsetal. 2004 regard learning internal components.Specifically HCRL jointly optimizes soft-divisive hierarchical clustering embedding space VAE via two mechanisms. First HCRL includes hierarchical-versioned Gaussian mixture model HGMM mixture hierarchically organized Gaussian distributions. HCRL sets prior embeddings adopting generative processes HGMM. Second handle dynamic hierarchy structure dealing clusters unequal sizes explore infinite hierarchy space exploiting nCRP prior. mechanisms are fused unified objective function;is done rather concatenating two distinct models clustering autoencoding. quantitative evaluations focus density estimation quality hierarchical clustering accuracy which shows HCRL has competent likelihoods best accuracies compared baselines. When we observe results qualitatively visualize1 hierarchical clusterings 2 embeddings hierarchy modeling 3 reconstructed images Gaussian mixture component shown FIG3. experiments were conducted crossing data domains texts images benchmark datasets include MNIST CIFAR-100 RCV1v2 20Newsgroups. paper have introduced hierarchically clustered representation learning framework hierarchical mixture density estimation deep embeddings. HCRL aims encoding relations among clusters well among instances preserve internal hierarchical structure data. main differentiated features HCRL are1 crucial assumption regarding internal mixture components ability generate data directly 2 unbalanced autoencoding neural architecture level proportion modeling encoding structure probabilistic model decoding structure. modeling evaluation found HCRL enables improvements due high flexibility modeling compared baselines.,1523,1038,485,0.017,1.467,2025/11/05 17:19:00,0.01,1.387,0.4267912772585671,451.021
"We introduce a novel geometric perspective and unsupervised model augmentation framework for transforming traditional deep (convolutional) neural networks into adversarially robust classifiers. Class-conditional probability densities based on Bayesian nonparametric mixtures of factor analyzers (BNP-MFA) over the input space are used to design soft decision labels for feature to label isometry. Classconditional distributions over features are also learned using BNP-MFA to develop plug-in maximum a posterior (MAP) classifiers to replace the traditional multinomial logistic softmax classification layers. This novel unsupervised augmented framework, which we call geometrically robust networks (GRN), is applied to CIFAR-10, CIFAR-100, and to Radio-ML (a time series dataset for radio modulation recognition). We demonstrate the robustness of GRN models to adversarial attacks from fast gradient sign method, Carlini-Wagner, and projected gradient descent. DeepConvNets are already prevalent in speech, vision, self-driving cars, biometrics, and robotics. However, they possess discontinuities that are easy targets for attacks as evidenced in dozens of papers (see BID7 BID15 and references therein). Adversarial images can be made to be robust to translation, scale, and rotation BID0 . Adversarial attacks have also been applied to deep reinforcement learning BID9 BID10 and speech recognition BID3 . In this work we will also consider attacks on automatic modulation recognition using deep convolutional networks BID17 . Previous work in creating adversarially robust deep neural network classifiers includes robust optimization with saddle point formulations BID13 , adversarial training (see e.g., BID11 ), ensemble adversarial training BID24 , defensive distillation BID19 , and use of detector-reformer networks BID14 . Defensive distillation has been found to be an insufficient defense BID1 and MagNet of BID14 was also shown to be defeatable in BID4 . A summary of the attacks and defenses from the NIPS 2017 competition on adversarial attack and defense can be found in .In this paper we propose a statistical geometric model augmentation approach to designing robust neural networks. We argue that signal representations involving projections onto lower-dimensional subspaces lower mean square error distortion. We implement a statistical union of subspaces learned using a mixture of factor analyzers to create the auxiliary signal space structural information that neural networks can use to improve robustness. We use the geometry of the input space to create unsupervised soft probabilistic decision labels to replace traditional hard one-hot encoded label vectors. We also use the geometry of the feature space (after soft-decision supervised training) to create accurate class-conditional probability density estimates for MAP classifiers (to replace neural network classification layers). We call this unsupervised geometric augmentation framework geometrically robust networks (GRN). The main contributions of this paper are:1. Geometric analysis of problems with current neural networks.2. A novel soft decision label coding framework using unsupervised statistical-geometric union of subspace learning.3. Maximum a posteriori classification framework based on class-conditional feature vector density estimation.The rest of this paper is organized as follows. In Section 2 we analyze neural networks from a geometric vantage point and recommend solution pathways for overcoming adversarial brittleness. In Section 3 we describe the full details of the proposed geometrically robust network design framework. We give experimental results on two datasets and three attacks in Section 4 and conclude in Section 5. We have demonstrated that geometrical statistically augmented neural network models can achieve state-of-the-art robustness on CIFAR-10 under three different adversarial attack methods. We hope that this work will be the start of further investigation into the idea of using geometrically centered unsupervised learning methods to assist in making deep learning models robust, not only to adversarial noise but to all types of noise. There is more work that could be done to understand the best way to engineer soft decision labels given auxiliary data models. We need to also understand if the training algorithms themselves can be directly manipulated to incorporate outside structural data models.A main selling point of Bayesian nonparametrics has been that the complexity of the model can grow as more data is observed. However, the current training algorithm for the BNP-MFA model is Gibbs sampling, which fails to scale to massive data sets. Stochastic variational inference BID8 has been introduced as one such way to perform variational inference for massive or streaming data sets. We are currently working to cast the BNP-MFA into a stochastic variational framework so that the GRN model can be extended to very large (or even streaming) datasets. Figure 4: Network specification and performance results for proposed geometrically robust networks applied to the Radio-ML dataset (modulation recognition over 11 modulation formats).",introduce novel geometric perspective unsupervised model augmentation framework transforming traditional deep convolutional neural networks adversarially robust classifiers. Class-conditional probability densities based Bayesian nonparametric mixtures factor analyzers BNP-MFA input space are used design soft decision labels feature label isometry. Classconditional distributions features are also learned using BNP-MFA develop plug-in maximum posterior MAP classifiers replace traditional multinomial logistic softmax classification layers. novel unsupervised augmented framework which we call geometrically robust networks GRN is applied CIFAR-10 CIFAR-100 Radio-ML time series dataset radio modulation recognition demonstrate robustness GRN models adversarial attacks fast gradient sign method Carlini-Wagner projected gradient descent. DeepConvNets are already prevalent speech vision self-driving cars biometrics robotics. However possess discontinuities are easy targets attacks evidenced dozens papers see BID7 BID15 references therein Adversarial images can be made robust translation scale rotation BID0. Adversarial attacks have also applied deep reinforcement learning BID9 BID10 speech recognition BID3. work will also consider attacks automatic modulation recognition using deep convolutional networks BID17. Previous work creating adversarially robust deep neural network classifiers includes robust optimization saddle point formulations BID13 adversarial training seee.g BID11 ensemble adversarial training BID24 defensive distillation BID19 use detector-reformer networks BID14. Defensive distillation has been found insufficient defense BID1 MagNet BID14 was also shown defeatable BID4. summary attacks defenses NIPS 2017 competition adversarial attack defense can be found.In paper propose statistical geometric model augmentation approach designing robust neural networks. argue signal representations involving projections onto lower-dimensional subspaces lower mean square error distortion. implement statistical union subspaces learned using mixture factor analyzers create auxiliary signal space structural information neural networks can use improve robustness. use geometry input space create unsupervised soft probabilistic decision labels replace traditional hard one-hot encoded label vectors. also use geometry feature space soft-decision supervised training create accurate class-conditional probability density estimates MAP classifiers replace neural network classification layers call unsupervised geometric augmentation framework geometrically robust networks GRN main contributions paper are:1 Geometric analysis problems current neural networks.2 novel soft decision label coding framework using unsupervised statistical-geometric union subspace learning.3 Maximum posteriori classification framework based class-conditional feature vector density estimation.The rest paper is organized follows. Section2 analyze neural networks geometric vantage point recommend solution pathways overcoming adversarial brittleness. Section3 describe full details proposed geometrically robust network design framework. give experimental results two datasets three attacks Section4 conclude Section5. have demonstrated geometrical statistically augmented neural network models can achieve state-of-the-art robustness CIFAR-10 three different adversarial attack methods. hope work will be the start investigation idea using geometrically centered unsupervised learning methods assist making deep learning models robust adversarial noise types noise. is more work could done understand best way engineer soft decision labels given auxiliary data models. need also understand if the training algorithms can be directly manipulated incorporate outside structural data models.A main selling point Bayesian nonparametrics has been that the complexity model can grow data is observed. However current training algorithm BNP-MFA model is Gibbs sampling which fails scale massive data sets. Stochastic variational inference BID8 has been introduced one way perform variational inference massive streaming data sets. are currently working cast BNP-MFA stochastic variational framework GRN model can be extended large even streaming datasets. Figure4:Network specification performance results proposed geometrically robust networks applied Radio-ML dataset modulation recognition 11 modulation formats,952,706,246,0.008,1.348,2025/11/05 17:19:00,0.0,1.5,0.0560747663551402,285.624
"Reinforcement learning in environments with large state-action spaces is challenging, as exploration can be highly inefficient. Even if the dynamics are simple, the optimal policy can be combinatorially hard to discover. In this work, we propose a hierarchical approach to structured exploration to improve the sample efficiency of on-policy exploration in large state-action spaces. The key idea is to model a stochastic policy as a hierarchical latent variable model, which can learn low-dimensional structure in the state-action space, and to define exploration by sampling from the low-dimensional latent space. This approach enables lower sample complexity, while preserving policy expressivity. In order to make learning tractable, we derive a joint learning and exploration strategy by combining hierarchical variational inference with actor-critic learning. The benefits of our learning approach are that 1) it is principled, 2) simple to implement, 3) easily scalable to settings with many actions and 4) easily composable with existing deep learning approaches. We demonstrate the effectiveness of our approach on learning a deep centralized multi-agent policy, as multi-agent environments naturally have an exponentially large state-action space. In this setting, the latent hierarchy implements a form of multi-agent coordination during exploration and execution (MACE). We demonstrate empirically that MACE can more efficiently learn optimal policies in challenging multi-agent games with a large number (~20) of agents, compared to conventional baselines. Moreover, we show that our hierarchical structure leads to meaningful agent coordination. Reinforcement learning in environments with large state-action spaces is challenging, as exploration can be highly inefficient in high-dimensional spaces. Hence, even if the environment dynamics are simple, the optimal policy can be combinatorially hard to discover. However, for many large-scale environments, the high-dimensional state-action space has (often hidden or implicit) low-dimensional structure which can be exploited. Many natural examples are in collaborative multi-agent problems, whose state-action space is exponentially large in the number of agents, but have a low-dimensional coordination structure. Consider a simple variant of the Hare-Hunters problem (see FIG0 . In this game, N = 2 identical hunters need to capture M = 2 identical static prey within T time-steps, and exactly H = 1 hunter is needed to capture each prey. T is set such that no hunter can capture both preys. There are two equivalent solutions: hunter 1 captures prey 1 and hunter 2 captures prey 2, or vice versa. There are also two suboptimal choices: both hunters choose the same prey. Hence, the hunters must coordinate over a (large) number of time-steps to maximize their reward. This implies the solution space has low-dimensional structure that can be used to accelerate training.In this work, we propose a principled approach to structured exploration to improve sample complexity in large state-action spaces, by learning deep hierarchical policies with a latent structure. As a highlevel intuition, consider a tabular multi-agent policy, which maps discrete (joint) states to action probabilities. For N agents with S states and A actions each, this policy has O((S · A) N ) weights. However, the low-dimensional coordination structure can be captured by a factorized, low-rank matrix, where the factorization can be learned and, for instance, only has O(N K(S + A)) weights. Similarly, our approach both 1) learns a low-dimensional factorization of the policy distribution and 2) defines exploration by also sampling from the low-dimensional latent space. For instance, in the multi-agent setting, we can learn a centralized multi-agent policy with a latent structure that encodes coordination between agents and biases exploration towards policies that encode ""good"" coordination.The key ideas of our approach are: 1) to utilize a shared stochastic latent variable model that defines the structured exploration policy, and 2) to employ a principled variational method to learn the posterior distribution over the latents jointly with the optimal policy. Our approach has several desirable properties. First we do not incorporate any form of prior domain knowledge, but rather discover the coordination structure purely from empirical experience during learning. Second, our variational learning method enables fully differentiable end-to-end training of the entire policy class. Finally, by utilizing a hierarchical policy class, our approach can easily scale to large action spaces (e.g. a large number of coordinating agents). Our approach can also be seen as a deep hierarchical generalization of Thompson sampling, which is a historically popular way to capture correlations between actions (e.g. in the bandit setting BID2 ).To summarize, our contributions in this work are as follows:• We introduce a structured probabilistic policy class that uses a hierarchy of stochastic latent variables.• We propose an efficient and principled algorithm using variational methods to train the policy end-to-end.• To validate our learning framework, we introduce several synthetic multi-agent environments that explicitly require team coordination, and feature competitive pressures that are characteristic of many coordinated decision problems.• We empirically verify that our approach improves sample complexity on coordination games with a large number (N ∼ 20) of agents.• We show that learned latent structures correlate with meaningful coordination patterns. In a sense, we studied the simplest setting that can benefit from structured exploration, in order to isolate the contribution of our work. Our hierarchical model and variational approach are a simple way to implement multi-agent coordination, and easily combine with existing actor-critic methods. Moving forward, there are many ways to expand on our work. Firstly, for complex (partial-information) environments, instead of using reactive policies with simple priors P ∼ N (0, 1), memoryfull policies with flexible priors ) may be needed. Secondly, our approach is complementary to richer forms of communication between agents. Our hierarchical structure can be interpreted as a broadcast channel, where agents are passive receivers of the message λ. Richer communication protocols could be encoded by policies with more complex inter-agent structure. It would be interesting to investigate how to learn these richer structures. We show details on how to derive a tractable learning method to the multi-agent reinforcement learning problem with a centralized controller: DISPLAYFORM0 Instead of directly optimizing (16), we cast it as a probabilistic inference problem, as in BID17 Vlassis et al. (2009) , and optimize a lower bound.To do so, we assume that the total reward R i for each i to be non-negative and bounded. Hence, we can view the total reward R(τ ) as a random variable, whose unnormalized distribution is defined as DISPLAYFORM1 We can then rewrite (16) as a maximum likelihood problem: DISPLAYFORM2 Hence, the RL objective is equivalent to a maximal likelihood problem: DISPLAYFORM3 where the probability of a rollout τ features a marginalization over the latent variables λ t : DISPLAYFORM4 DISPLAYFORM5 Here, we used the hierarchical decomposition for the policy: DISPLAYFORM6 DISPLAYFORM7 This policy distribution is intractable to learn exactly, as it involves margalization over λ t and an unknown flexible distribution P (a i t |λ t , s t ). Hence the maximization in Equation FORMULA17 is hard. Hence, we follow the variational approach and get a lower bound on the log-likelihood log P (R, τ ; θ) in Equation (19) . For this, we use an approximate variational distribution Q R (λ 0:T |τ ; φ) and Jensen's inequality BID12 : DISPLAYFORM8 DISPLAYFORM9 where in the last line we used (20) . By inspecting the quotient in (26), we see that the optimal Q R is a factorized distribution weighted by the total reward R: DISPLAYFORM10 P (s t+1 |s t , a t )Q(λ t |s t ; φ).We see that (26) simplifies to:dλ 0:T Q R (λ 0:T |τ ; φ) log P (R|τ )P (s 0 ) T t=0 P (s t+1 |s t , a t )P (a t , λ t |s t ; θ) P (R|τ )P (s 0 ) T t=0 P (s t+1 |s t , a t )Q(λ t |s t ; φ) (28) = dλ 0:T Q R (λ 0:T |τ ; φ) log T t=0 P (a t , λ t |s t ; θ) Q(λ t |s t , φ)= dλ 0:T Q R (λ 0:T |τ ; φ) T t=0 log P (a t , λ t |s t ; θ) Q(λ t |s t , φ)= dλ 0:T Q R (λ 0:T |τ ; φ) T t=0 log P (a t |λ t , s t ; θ)P (λ t |s t ) Q(λ t |s t , φ)= dλ 0:T Q R (λ 0:T |τ ; φ) DISPLAYFORM11 log P (a t |λ t , s t ; θ) + log P (λ t |s t ) Q(λ t |s t , φ)ELBO(Q R ,θ,φ).The right-hand side in Equation FORMULA30 is called the evidence lower bound (ELBO), which we can maximize as a proxy for (16). The standard choice is to use maximum-entropy standard-normal priors: P (λ t |s t ) = N (0, 1). We can then optimize (32) using e.g. stochastic gradient ascent.","Reinforcement learning environments large state-action spaces is challenging exploration can be highly inefficient. Even if the dynamics are are a simple optimal policy can be combinatorially hard discover. work propose hierarchical approach structured exploration improve sample efficiency on-policy exploration large state-action spaces. key idea is to model stochastic policy hierarchical latent variable model which can can learn low-dimensional structure state-action space define exploration sampling low-dimensional latent space. approach enables lower sample complexity preserving policy expressivity. order make learning tractable derive joint learning exploration strategy combining hierarchical variational inference actor-critic learning. benefits learning approach are that1 is principled 2 simple implement 3 easily scalable settings many actions 4 easily composable existing deep learning approaches. demonstrate effectiveness approach learning deep centralized multi-agent policy multi-agent environments naturally have an exponentially large state-action space. setting latent hierarchy implements form multi-agent coordination exploration execution MACE demonstrate empirically MACE can more efficiently learn optimal policies challenging multi-agent games large number ~20 agents compared conventional baselines. Moreover show hierarchical structure leads meaningful agent coordination. Reinforcement learning environments large state-action spaces is challenging exploration can be highly inefficient high-dimensional spaces. Hence even if the environment dynamics are are a simple optimal policy can be combinatorially hard discover. However are many large-scale environments high-dimensional state-action space has(often hidden implicit low-dimensional structure which can be exploited. Many natural examples are in collaborative multi-agent problems whose state-action space is exponentially large number agents have a low-dimensional coordination structure. Consider simple variant Hare-Hunters problem see FIG0. game hasON 2 identical hunters need capture 2 identical static prey within time-steps exactlyH 1 hunter is needed capture prey. is set hunter can capture preys. are two equivalent solutions:hunter 1 captures prey 1 hunter 2 captures prey 2 vice versa. are also two suboptimal choices:hunters choose prey. Hence hunters must coordinate large number time-steps maximize reward. implies solution space has low-dimensional structure can be used accelerate training.In work propose principled approach structured exploration improve sample complexity large state-action spaces learning deep hierarchical policies latent structure. highlevel intuition consider tabular multi-agent policy which maps discrete joint states action probabilities. N agents states actions policy hasO((· N weights. However have a low-dimensional coordination structure can be captured factorized low-rank matrix where the factorization can be learned instance hasO NK+weights. Similarly approach 1 learns low-dimensional factorization policy distribution 2 defines exploration also sampling low-dimensional latent space. instance multi-agent setting which can can learn centralized multi-agent policy latent structure encodes coordination agents biases exploration towards policies encode good coordination.The key ideas approach are:1 utilize shared stochastic latent variable model defines structured exploration policy 2 employ principled variational method learn posterior distribution latents jointly optimal policy. approach has several desirable properties. First do not incorporate form prior domain knowledge rather discover coordination structure purely empirical experience learning. Second variational learning method enables fully differentiable end-to-end training entire policy class. Finally utilizing hierarchical policy class approach can easily scale large action spaces e.g large number coordinating agents approach can also seen deep hierarchical generalization Thompson sampling which is a historically popular way capture correlations actions e.g bandit setting BID2.To summarize contributions work are as follows:• introduce structured probabilistic policy class uses hierarchy stochastic latent variables.• propose efficient principled algorithm using variational methods train policy end-to-end.• validate learning framework introduce several synthetic multi-agent environments explicitly require team coordination feature competitive pressures are characteristic many coordinated decision problems.• empirically verify approach improves sample complexity coordination games large number N∼20 agents.• show learned latent structures correlate meaningful coordination patterns. sense studied simplest setting can benefit structured exploration order isolate contribution work. hierarchical model variational approach are are a simple way implement multi-agent coordination easily combine existing actor-critic methods. Moving forward are many ways expand work. Firstly complex partial-information environments instead using reactive policies simple priorsP∼ N 0 1 memoryfull policies flexible priors may needed. Secondly approach is complementary richer forms communication agents. hierarchical structure can be interpreted broadcast channel where agents are passive receivers messageλ. Richer communication protocols could encoded policies complex inter-agent structure. would interesting investigate how to learn richer structures. show details how to derive tractable learning method multi-agent reinforcement learning problem centralized controller:DISPLAYFORM0 Instead directly optimizing 16 cast probabilistic inference problem BID17 Vlassisetal. 2009 can optimize lower bound.To do so,we assume total rewardR non-negative bounded. Hence can view total rewardR τ random variable whose unnormalized distribution is defined DISPLAYFORM1 can then rewrite 16 maximum likelihood problem:DISPLAYFORM2 Hence RL objective is equivalent maximal likelihood problem:DISPLAYFORM3 where the probability rollout τ features marginalization latent variablesλ t:DISPLAYFORM4 DISPLAYFORM5 used hierarchical decomposition policy:DISPLAYFORM6 DISPLAYFORM7 policy distribution is intractable learn exactly involves margalization λ unknown flexible distributionP |λ Hence maximization Equation FORMULA17 is hard. Hence follow variational approach get lower bound log-likelihood logP R τ;θ Equation 19 use approximate variational distributionQ R λ0:|τφ Jensen's inequality BID12:DISPLAYFORM8 DISPLAYFORM9 where in the last line used 20 inspecting quotient 26 see optimalQR is a factorized distribution weighted total rewardR:DISPLAYFORM10P+1|s Q λ |s t;φ.We see 26 simplifies to:dλ0:QR λ0:|τφ logP R|τ P 0 t=0P+1|s P λ |s t;θ P R|τ P 0 t=0P+1|s Q λ |s t;φ 28 dλ0:QR λ0:|τφ log t=0P λ |s t;θ Q λ |s φ dλ0:QR λ0:|τφ t=0 logP λ |s t;θ Q λ |s φ dλ0:QR λ0:|τφ t=0 logP |λ t;θ P λ |s Q λ |s φ dλ0:QR λ0:|τφ DISPLAYFORM11 logP |λ t;θ+logP λ |s Q λ |s φ ELBO QR θ φ.The right-hand side Equation FORMULA30 is called evidence lower bound ELBO whichwe can maximize proxy 16 standard choice is to use maximum-entropy standard-normal priors:P λ |s N 0 1 can optimize 32 using e.g stochastic gradient ascent.",1969,1331,638,0.03,1.479,2025/11/05 17:19:00,0.01,1.645,0.4641744548286605,683.935
"Much attention has been devoted recently to the generalization puzzle in deep learning: large, deep networks can generalize well, but existing theories bounding generalization error are exceedingly loose, and thus cannot explain this striking performance. Furthermore, a major hope is that knowledge may transfer across tasks, so that multi-task learning can improve generalization on individual tasks. However we lack analytic theories that can quantitatively predict how the degree of knowledge transfer depends on the relationship between the tasks. We develop an analytic theory of the nonlinear dynamics of generalization in deep linear networks, both within and across tasks. In particular, our theory provides analytic solutions to the training and testing error of deep networks as a function of training time, number of examples, network size and initialization, and the task structure and SNR. Our theory reveals that deep networks progressively learn the most important task structure first, so that generalization error at the early stopping time primarily depends on task structure and is independent of network size. This suggests any tight bound on generalization error must take into account task structure, and explains observations about real data being learned faster than random data. Intriguingly our theory also reveals the existence of a learning algorithm that proveably out-performs neural network training through gradient descent. Finally, for transfer learning, our theory reveals that knowledge transfer depends sensitively, but computably, on the SNRs and input feature alignments of pairs of tasks. Many deep learning practitioners closely monitor both training and test errors, hoping to achieve both a small training error and a small generalization error, or gap between testing and training errors. Training is usually stopped early, before overfitting sets in and increases the test error. This procedure often results in large networks that generalize well on structured tasks, raising an important generalization puzzle BID23 : many existing theories that upper bound generalization error BID4 BID14 BID7 BID8 BID15 BID3 Arora et al., 2018, e.g ) in terms of various measures of network complexity yield very loose bounds. Therefore they cannot explain the impressive generalization capabilities of deep nets.In the absence of any such tight and computable theory of deep network generalization error, we develop an analytic theory of generalization error for deep linear networks. Such networks exhibit highly nonlinear learning dynamics BID19 b) including many prominent phenomena like learning plateaus, saddle points, and sudden drops in training error. Moreover, theory developed for the learning dynamics of deep linear networks directly inspired better initialization schemes for nonlinear networks BID21 BID16 . Here we show that deep linear networks also provide a good theoretical model for generalization dynamics. In particular we develop an analytic theory for both the training and test error of a deep linear network as a function of training time, number of training examples, network architecture, initialization, and task structure and SNR. Our theory matches simulations and reveals that deep networks with small weight initialization learn the most important aspects of a task first. Thus the optimal test error at the early stopping time depends largely on task structure and SNR, and not on network architecture, as long as the architecture is expressive enough to attain small training error. Thus our exact analysis of generalization dynamics reveals the important lesson that any theory that seeks to upper bound generalization error based only on network architecture, and not on task structure, is likely to yield exceedingly loose upper bounds. Intriguingly our theory also reveals a non-gradient-descent learning algorithm that proveably out-performs neural network training through gradient descent.We also apply our theory to multi-task learning, which enables knowledge transfer from one task to another, thereby further lowering generalization error BID6 Luong et al., 2016, e.g.) . Moreover, knowledge transfer across tasks may be key to human generalization capabilities BID10 . We provide an analytic theory for how much knowledge is transferred between pairs of tasks, and we find that it displays a sensitive but computable dependence on the relationship between pairs of tasks, in particular, their SNRs and feature space alignments.We note that a related prior work BID0 ) studied generalization in shallow and deep linear networks, but that work was limited to networks with a single output, thereby precluding the possibility of addressing the issue of transfer learning. Moreover, analyzing networks with a single output also precludes the possibility of addressing interesting tasks that require higher dimensional outputs, for example in language (Dong et al., 2015, e.g.) , generative models (Goodfellow et al., 2014, e.g ), and reinforcement learning Silver et al., 2016, e.g ).",Much attention has been devoted recently generalization puzzle deep learning:large deep networks can generalize well existing theories bounding generalization error are exceedingly loose thus cannot explain striking performance. Furthermore major hope is that knowledge may transfer across tasks multi-task learning can improve generalization individual tasks. However lack analytic theories can quantitatively predict how the degree knowledge transfer depends relationship tasks. develop analytic theory nonlinear dynamics generalization deep linear networks within across tasks. particular theory provides analytic solutions training testing error deep networks function training time number examples network size initialization task structure SNR. theory reveals deep networks progressively learn important task structure first generalization error early stopping time primarily depends task structure is independent network size. suggests tight bound generalization error must take account task structure explains observations real data learned faster random data. Intriguingly theory also reveals existence learning algorithm proveably out-performs neural network training gradient descent. Finally transfer learning theory reveals knowledge transfer depends sensitively computably SNRs input feature alignments pairs tasks. Many deep learning practitioners closely monitor training test errors hoping achieve small training error small generalization error gap testing training errors. Training is usually stopped early overfitting sets increases test error. procedure often results large networks generalize well structured tasks raising important generalization puzzle BID23:many existing theories upper bound generalization error BID4 BID14 BID7 BID8 BID15 BID3 Aroraet al. 2018 e.g terms various measures network complexity yield loose bounds. Therefore cannot explain impressive generalization capabilities deep nets.In absence tight computable theory deep network generalization error develop analytic theory generalization error deep linear networks. networks exhibit highly nonlinear learning dynamics BID19b including many prominent phenomena like learning plateaus saddle points sudden drops training error. Moreover theory developed learning dynamics deep linear networks directly inspired better initialization schemes nonlinear networks BID21 BID16. show deep linear networks also provide good theoretical model generalization dynamics. particular develop analytic theory training test error deep linear network function training time number training examples network architecture initialization task structure SNR. theory matches simulations reveals deep networks small weight initialization learn important aspects task first. Thus optimal test error early stopping time depends largely task structure SNR network architecture long architecture is expressive enough attain small training error. Thus exact analysis generalization dynamics reveals important lesson theory seeks upper bound generalization error based network architecture task structure is likely yield exceedingly loose upper bounds. Intriguingly theory also reveals non-gradient-descent learning algorithm proveably out-performs neural network training gradient descent.We also apply theory multi-task learning which enables knowledge transfer one task another thereby lowering generalization error BID6 Luongetal. 2016 e.g Moreover knowledge transfer across tasks may key human generalization capabilities BID10. provide analytic theory how much knowledge is transferred pairs tasks find displays sensitive computable dependence relationship pairs tasks particular SNRs feature space alignments.We note related prior work BID0 studied generalization shallow deep linear networks work was limited networks single output thereby precluding possibility addressing issue transfer learning. Moreover analyzing networks single output also precludes possibility addressing interesting tasks require higher dimensional outputs example language Dongetal. 2015 e.g generative models Goodfellowetal. 2014 e.g reinforcement learning Silveret al. 2016 e.g,921,642,279,0.009,1.435,2025/11/05 17:19:00,0.0,1.2,0.3271028037383177,288.172
"We conduct a mathematical analysis on the Batch normalization (BN) effect on gradient backpropagation in residual network training in this work, which is believed to play a critical role in addressing the gradient vanishing/explosion problem. Specifically, by analyzing the mean and variance behavior of the input and the gradient in the forward and backward passes through the BN and residual branches, respectively, we show that they work together to confine the gradient variance to a certain range across residual blocks in backpropagation. As a result, the gradient vanishing/explosion problem is avoided. Furthermore, we use the same analysis to discuss the tradeoff between depth and width of a residual network and demonstrate that shallower yet wider resnets have stronger learning performance than deeper yet thinner resnets. Convolutional neural networks (CNNs) BID10 BID1 BID8 aim at learning a feature hierarchy where higher level features are formed by the composition of lower level features. The deep neural networks act as stacked networks with each layer depending on its previous layer's output. The stochastic gradient descent (SGD) method BID12 has proved to be an effective way in training deep networks. The training proceeds in steps with SGD, where a mini-batch from a given dataset is fed at each training step. However, one factor that slows down the stochastic-gradient-based learning of neural networks is the internal covariate shift. It is defined as the change in the distribution of network activations due to the change in network parameters during the training.To improve training efficiency, BID7 introduced a batch normalization (BN) procedure to reduce the internal covariate shift. The BN changes the distribution of each input element at each layer. Let x = (x 1 , x 2 , · · · , x K ), be a K-dimensional input to a layer. The BN first normalizes each dimension of x as DISPLAYFORM0 and then provide the following new input to the layer DISPLAYFORM1 where k = 1, · · · , K and γ k and β k are parameters to be determined. BID7 offered a complete analysis on the BN effect along the forward pass. However, there was little discussion on the BN effect on the backpropagated gradient along the backward pass. This was stated as an open research problem in BID7 . Here, to address this problem, we conduct a mathematical analysis on gradient propagation in batch normalized networks.The number of layers is an important parameter in the neural network design. The training of deep networks has been largely addressed by normalized initialization BID12 BID3 BID11 and intermediate normalization layers BID7 . These techniques enable networks consisting of tens of layers to converge using the SGD in backpropagation. On the other hand, it is observed that the accuracy of conventional CNNs gets saturated and then degrades rapidly as the network layer increases. Such degradation is not caused by over-fitting since adding more layers to a suitably deep model often results in higher training errors BID13 . To address this issue, BID6 introduced the concept of residual branches. A residual network is a stack of residual blocks, where each residual block fits a residual mapping rather than the direct input-output mapping. A similar network, called the highway network, was introduced by BID13 . Being inspired by the LSTM model BID2 , the highway network has additional gates in the shortcut branches of each block.There are two major contributions in this work. First, we propose a mathematical model to analyze the BN effect on gradient propogation in the training of residual networks. It is shown that residual networks perform better than conventional neural networks because residual branches and BN help maintain the gradient variation within a range throughout the training process, thus stabilizing gradient-based-learning of the network. They act as a check on the gradients passing through the network during backpropagation so as to avoid gradient vanishing or explosion. Second, we provide insights into wide residual networks based on the same mathematical analysis. The wide residual network was recently introduced by BID16 . As the gradient goes through the residual network, the network may not learn anything useful since there is no mechanism to force the gradient flow to go through residual block weights during the training. In other words, it might be possible that there are only a few blocks that learn useful representations while a large number of blocks share very little information with small contributions to the ultimate goal. We will show that residual blocks that stay dormant are the chains of blocks at the end of each scale of the residual network.The rest of this paper is organized as follows. Related previous work is reviewed in Sec. 2. Next, we derive a mathematical model for gradient propagation through a layer defined as a combination of batch normalization, convolution layer and ReLU in Sec. 3. Then, we apply this mathematical model to a resnet block in Sec. 4. Afterwards, we use this model to show that the dormant residual blocks are those at the far-end of a scale in deep residual networks in Sec. 5. Concluding remarks and future research directions are given in Sec. 6. We can draw two major conclusions from the analysis conducted above. First, it is proper to relate the above variance analysis to the gradient vanishing and explosion problem. The gradients go through a BN sub-layer in one residual block before moving to the next residual block. As proved in Sec. 3, the gradient mean is zero when it goes through a BN sub-layer and it still stays at zero after passing through a residual block. Thus, if it is normally distributed, the probability of the gradient values between ± 3 standard deviations is 99.7%. A smaller variance would mean lower gradient values. In contrast, a higher variance implies a higher likelihood of discriminatory gradients. Thus, we take the gradient variance across a batch as a measure for stability of gradient backpropagation.Second, recall that the number of filters in each convolution layer of a scale increases by k times with respect to its previous scale. Typically, k = 1 or 2. Without loss of generality, we can assume the following: the variance of weights is about equal across layers, c 1 /c 2 ≈ 1, and k = 2. Then, Eq. (20) can be simplified to DISPLAYFORM0 We see from above that the change in the gradient variance from one residual block to its next is little. This is especially true when the L value is high. This point will be further discussed in the next section.",conduct mathematical analysis Batch normalization BN effect gradient backpropagation residual network training work which is believed play critical role addressing gradient vanishing/explosion problem. Specifically analyzing mean variance behavior input gradient forward backward passes BN residual branches respectively show work together confine gradient variance certain range across residual blocks backpropagation. result gradient vanishing/explosion problem is avoided. Furthermore use analysis discuss tradeoff depth width residual network demonstrate shallower yet wider resnets have stronger learning performance deeper yet thinner resnets. Convolutional neural networks CNNs BID10 BID1 BID8 aim learning feature hierarchy where higher level features are formed composition lower level features. deep neural networks act stacked networks layer depending previous layer's output. stochastic gradient descent SGD method BID12 has proved effective way training deep networks. training proceeds steps SGD where a mini-batch given dataset is fed training step. However one factor slows stochastic-gradient-based learning neural networks is the internal covariate shift. is defined change distribution network activations due change network parameters training.To improve training efficiency BID7 introduced batch normalization BN procedure reduce internal covariate shift. BN changes distribution input element layer. Letx x1 x2 ··· xK K-dimensional input layer. BN first normalizes dimension x DISPLAYFORM0 provide following new input layer DISPLAYFORM1 wherek 1 ··· K γk βk are parameters determined. BID7 offered complete analysis BN effect along forward pass. However was little discussion BN effect backpropagated gradient along backward pass. was stated open research problem BID7. address problem conduct mathematical analysis gradient propagation batch normalized networks.The number layers is an important parameter neural network design. training deep networks has been largely addressed normalized initialization BID12 BID3 BID11 intermediate normalization layers BID7. techniques enable networks consisting tens layers converge using SGD backpropagation. hand is observed accuracy conventional CNNs gets saturated degrades rapidly network layer increases. degradation is not caused over-fitting since adding layers suitably deep model often results higher training errors BID13. address issue BID6 introduced concept residual branches. residual network is a stack residual blocks where each residual block fits residual mapping rather direct input-output mapping. similar network called highway network was introduced BID13. inspired LSTM model BID2 highway network has additional gates shortcut branches block.There are two major contributions work. First propose mathematical model analyze BN effect gradient propogation training residual networks. is shown residual networks perform better conventional neural networks residual branches BN help maintain gradient variation within range throughout training process thus stabilizing gradient-based-learning network. act check gradients passing network backpropagation avoid gradient vanishing explosion. Second provide insights wide residual networks based mathematical analysis. wide residual network was recently introduced BID16. gradient goes residual network network may learn anything useful since is no mechanism force gradient flow go residual block weights training. words might possible are only blocks learn useful representations large number blocks share little information small contributions ultimate goal. will show residual blocks stay dormant are the chains blocks end scale residual network.The rest paper is organized follows. Related previous work is reviewed Sec. 2. Next derive mathematical model gradient propagation layer defined combination batch normalization convolution layer ReLU Sec. 3. apply mathematical model resnet block Sec. 4. Afterwards use model show dormant residual blocks are those at the far-end scale deep residual networks Sec. 5. Concluding remarks future research directions are given Sec. 6. can draw two major conclusions analysis conducted above. First is proper relate variance analysis gradient vanishing explosion problem. gradientsgo BN sub-layer one residual block moving next residual block. proved Sec. 3 gradient mean is zero when it goes BN sub-layer still stays zero passing residual block. Thus if it is normally distributed probability gradient values ± 3 standard deviations is 99.7%. smaller variance would mean lower gradient values. contrast higher variance implies higher likelihood discriminatory gradients. Thus take gradient variance across batch measure stability gradient backpropagation.Second recall number filters convolution layer scale increases k times respect previous scale. Typically k 1 2. Without loss generality can assume following:variance weights is about equal across layers c1/c 2≈1 k 2. Eq. 20 can be simplified DISPLAYFORM0 see change gradient variance one residual block next is little. is especially true when the L value is high. point will be further discussed next section.,1300,862,438,0.014,1.508,2025/11/05 17:19:00,0.01,1.468,0.5545171339563861,425.323
"To study how mental object representations are related to behavior, we estimated sparse, non-negative representations of objects using human behavioral judgments on images representative of 1,854 object categories. These representations predicted a latent similarity structure between objects, which captured most of the explainable variance in human behavioral judgments. Individual dimensions in the low-dimensional embedding were found to be highly reproducible and interpretable as conveying degrees of taxonomic membership, functionality, and perceptual attributes. We further demonstrated the predictive power of the embeddings for explaining other forms of human behavior, including categorization, typicality judgments, and feature ratings, suggesting that the dimensions reflect human conceptual representations of objects beyond the specific task. A central goal in understanding the human mind is to determine how object concepts are represented and how they relate to human behavior. Given the near-infinite number of tasks or contexts of usage, this might appear to be an impossible prospect. Take the example of picking a tomato in a grocery store. A person may recognize it by its color, shape, size, or texture; they may also know many of the more conceptual dimensions of a tomato, such as it being a fruit, or functional ones such as being a salad item. In most cases, however, only a few of these aspects might matter, depending on task context (e.g. as a grocery item or as a projectile in an audience that is not pleased with a presentation). Thus, to understand how we interact meaningfully with the objects around us, we need to tackle three problems simultaneously: (1) determine the object concept, the cognitive representation of behaviorally-relevant dimensions that distinguish an object from other objects. (2) determine which object concept representations are integrated into our perceptual decisions. (3) characterize the influence of the context -determined by the surrounding objects -on those decisions.There have been many attempts to represent object concepts in terms of semantic features, a vector of variables indicating the presence of different aspects of their meaning. These representations have been used to model phenomena such as judgments of typicality or similarity between concepts, or reaction times in various semantic tasks, with the goal of drawing conclusions about mental representations of those concepts (see BID13 for an extensive review of this literature). These features have usually been binary properties, postulated by researchers. A landmark study BID9 departed from this approach by instead asking hundreds of subjects to name binary properties of 541 objects, yielding 2,526 such semantic features. These corresponded to different types of information, e.g. for the concept ""hammer"" subjects might list taxonomic (""is a tool""), functional (""is used to hammer nails""), perceptual (""heavy""), among others. The results revealed that concepts for objects in the same basic level category shared many features; at the same time, there were also features that distinguished even very similar concepts. This effort was later replicated and extended by BID4 , generating 5,929 semantic features for 638 objects.The main issues with features produced in either study are the lack of degree (they can only be present or absent, albeit with varying naming frequencies), the extreme specificity of some features, and the omission of many features shared by the majority of concepts. A separate concern is the fact that, absent a specific context of use for each object, subjects will not likely think of many valid properties (e.g. that a tomato can be thrown). A different approach is to postulate the existence of certain semantic features and ask subjects to judge the degree to which features are salient for each concept, instead of assuming binary features. BID3 did this for 65 features corresponding to types of information for which there is evidence of brain representation (in their terminology: sensory, motor, spatial, temporal, affective, social, cognitive, etc) . This requires experts to specify the features in advance, and not all features can be judged easily by salience. In all three approaches outlined above, there is also no clear way of determining which features are critical to semantic behavior.Here we introduce an approach that uses only information from behavioral judgments about the grouping of object images in the context of other objects to estimate representations of object concepts. We demonstrate that this approach can predict human behavior in face of new combinations of objects and that it also allows prediction of results in other behavioral tasks. We show that individual dimensions in the low-dimensional embedding represent complex combinations of the information in the binary features in BID4 and, furthermore, are interpretable as conveying taxonomic, functional, or perceptual information. Finally, we will discuss the way in which this representation suggests a simple, effective model of judgments of semantic similarity in context. In this paper, we show that human behavioral judgments are well-explained by a strikingly lowdimensional semantic representation of concrete concepts. This representation, which embeds each object in a 49-dimensional vector, allows prediction of subject behavior in face of new combinations of concepts not encountered before, as well as prediction of other behavioral or human-annotated data, such as typicality ratings or similarity judgments. Moreover, the representation is readily interpretable, as positive, sparse dimensions make it easy to identify which concepts load on each dimension. Further, we demonstrate that the value of each dimension in this space can be explained in terms of elementary features elicited directly from human subjects in publicly available norms. Given this converging evidence, we conclude that dimensions represent distinct types of information, from taxonomic (indicators of category membership) to functional or perceptual.As the representations were estimated solely from behavioral data, this suggests a simple model of decision making in the triplet task. This can be viewed in terms of the distinction discussed in Navarro & Lee (2004) for judging concept similarity from semantic feature vectors. They distinguish a dimensional approach for representing stimuli (each feature is a continuous value, each concept is a point in a high-dimensional space, and similarity corresponds to proximity in the space), and a featural approach (each feature is binary, or discrete, and similarity is a function of the number of features that are common to both concepts, or that distinguish them). More refined schemes use modified distance metrics (dimensional) or combine commonality and distinctiveness (featural).The use of sparsity and positivity in the SPoSE representation, and the vector dot product for computing concept similarity, blends the featural and dimensional approaches when making decisions about a triplet of concepts. First , if any two concepts share a semantic category, and the other one does not, the two concepts will likely be grouped together. Because of sparsity, the dot product between concepts will be driven primarily by the number of features are shared between the two concepts in the same category, versus the different one. Second, if any three concepts share a semantic category, they also share most, if not all of their non-zero features. The decision becomes a function of the values of the features shared between them, and hence dimensional rather than featural. Third, if all concepts belong to different categories, there may be very few features in common between any two of them. The results will likely be determined by which of those few features takes a higher value. Results might be idiosyncratic, e.g. two objects grouped because their pictures are both very red, while the alternative grouping would be because they are both string-like, and the former feature is more salient. This is another reason why our features are unbounded: their scale can reflect their importance in decision making. This is akin to learning a distance metric in dimensional approaches.Our object representations capture the information that is necessary to explain subject behavior in the triplet task. Obviously, subjects have a lot more information about each concept that is not necessary or relevant for task performance. A promising direction for further work is to sample additional triplets so as to obtain more fine-grained, within-category distinctions. Beyond this, we have also considered the possibility of there being information influencing behavior that might be too infrequent to be estimated from this type of data, or elicited from human subjects. Yet another possible extension is to consider different types of similarity judgments BID19 , e.g. resulting from asking subjects to group objects based on a specific attribute (size, color, etc.). One avenue for trying to identify this type of information is to predict synset vectors from SPoSE vectors and/or semantic features elicited from subjects, and represent the residuals in terms of a dictionary of new sparse, positive concept features. These could then be used as a complement to SPoSE dimensions.","study how mental object representations are related behavior estimated sparse non-negative representations objects using human behavioral judgments images representative 1,854 object categories. representations predicted latent similarity structure objects which captured explainable variance human behavioral judgments. Individual dimensions low-dimensional embedding were found highly reproducible interpretable conveying degrees taxonomic membership functionality perceptual attributes. demonstrated predictive power embeddings explaining forms human behavior including categorization typicality judgments feature ratings suggesting dimensions reflect human conceptual representations objects beyond specific task. central goal understanding human mind is to determine how object concepts are represented how they relate human behavior. Given near-infinite number tasks contexts usage might appear impossible prospect. Take example picking tomato grocery store. person may recognize color shape size texture;may also know many conceptual dimensions tomato fruit functional ones salad item. cases however aspects might matter depending task context e.g grocery item projectile audience is not pleased presentation Thus understand how we interact meaningfully objects aroundus need tackle three problems simultaneously:1 determine object concept cognitive representation behaviorally-relevant dimensions distinguish object objects. 2 determine which object concept representations are integrated perceptual decisions. 3 characterize influence context -determined surrounding objects -on decisions.There have been many attempts represent object concepts terms semantic features vector variables indicating presence different aspects meaning. representations have been used model phenomena judgments typicality similarity concepts reaction times various semantic tasks goal drawing conclusions mental representations concepts see BID13 extensive review literature features have usually binary properties postulated researchers. landmark study BID9 departed approach instead asking hundreds subjects name binary properties 541 objects yielding 2,526 semantic features. corresponded different types information e.g concept hammer subjects might list taxonomic is a tool functional is used hammer nails perceptual heavy among others. results revealed concepts objects basic level category shared many features;time were also features distinguished even similar concepts. effort was later replicated extended BID4 generating 5,929 semantic features 638 objects.The main issues features produced either study are the lack degree can only present absent albeit varying naming frequencies extreme specificity features omission many features shared majority concepts. separate concern is the fact absent specific context use object subjects will not will likely think many valid properties e.g tomato can be thrown different approach is to postulate existence certain semantic features ask subjects judge degree which features are salient concept instead assuming binary features. BID3 did this for 65 features corresponding types information which there is evidence brain representation terminology:sensory motor spatial temporal affective social cognitive etc requires experts specify features advance features can be judged easily salience. three approaches outlined is also clear way determining which features are critical semantic behavior.Here introduce approach uses information behavioral judgments grouping object images context objects estimate representations object concepts. demonstrate approach can predict human behavior face new combinations objects also allows prediction results behavioral tasks. show individual dimensions low-dimensional embedding represent complex combinations information binary features BID4 furthermore are interpretable conveying taxonomic functional perceptual information. Finally will discuss way which this representation suggests simple effective model judgments semantic similarity context. paper show human behavioral judgments are well-explained strikingly lowdimensional semantic representation concrete concepts. representation which embeds object 49-dimensional vector allows prediction subject behavior face new combinations concepts encountered well prediction behavioral human-annotated data typicality ratings similarity judgments. Moreover representation is readily interpretable positive sparse dimensions make easy identify which concepts load dimension. demonstrate value dimension space can be explained terms elementary features elicited directly human subjects publicly available norms. Given converging evidence conclude dimensions represent distinct types information taxonomic indicators category membership functional perceptual.As representations were estimated solely behavioral data suggests simple model decision making triplet task. can be viewed terms distinction discussed Navarro Lee 2004 judging concept similarity semantic feature vectors. distinguish dimensional approach representing stimuli feature is a continuous value concept is a point high-dimensional space similarity corresponds proximity space featural approach feature is binary discrete similarity is a function number features are common concepts distinguish refined schemes use modified distance metrics dimensional combine commonality distinctiveness featural.The use sparsity positivity SPoSE representation vector dot product computing concept similarity blends featural dimensional approaches when making decisions triplet concepts. First if any two concepts share semantic category one does not,the two concepts will not will likely grouped together. sparsity dot product concepts will be driven primarily number features are shared two concepts category versus different one. Second if any three concepts share semantic category were also share if not non-zero features. decision becomes function values features shared hence dimensional rather featural. Third if all concepts belong different categories may features common two them. results will not will likely determined which of those features takes higher value. Results might idiosyncratic e.g two objects grouped pictures are both very red alternative grouping would are string-like former feature is more salient. is another reason why our features are unbounded:scale can reflect importance decision making. is akin learning distance metric dimensional approaches.Our object representations capture information is is not necessary explain subject behavior triplet task. Obviously subjects have a lot information concept is is not necessary relevant task performance. promising direction work is to sample additional triplets obtain fine-grained within-category distinctions. Beyond have also considered possibility information influencing behavior might infrequent estimated type data elicited human subjects. Yet another possible extension is to consider different types similarity judgments BID19 e.g resulting asking subjects group objects based specific attribute size color etc. One avenue trying identify type information is to predict synset vectors SPoSE vectors/semantic features elicited subjects represent residuals terms dictionary new sparse positive concept features. could used complement SPoSE dimensions.",1712,1085,627,0.022,1.578,2025/11/05 17:19:00,0.01,1.581,0.7725856697819315,672.844
"We frame Question Answering (QA) as a Reinforcement Learning task, an approach that we call Active Question Answering. 

 We propose an agent that sits between the user and a black box QA system and learns to reformulate questions to elicit the best possible answers. The agent probes the system with, potentially many, natural language reformulations of an initial question and aggregates the returned evidence to yield the best answer. 

 The reformulation system is trained end-to-end to maximize answer quality using policy gradient. We evaluate on SearchQA, a dataset of complex questions extracted from Jeopardy!. The agent outperforms a state-of-the-art base model, playing the role of the environment, and other benchmarks.

We also analyze the language that the agent has learned while interacting with the question answering system. We find that successful question reformulations look quite different from natural language paraphrases. The agent is able to discover non-trivial reformulation strategies that resemble classic information retrieval techniques such as term re-weighting (tf-idf) and stemming. Web and social media have become primary sources of information. Users' expectations and information seeking activities co-evolve with the increasing sophistication of these resources. Beyond navigation, document retrieval, and simple factual question answering, users seek direct answers to complex and compositional questions. Such search sessions may require multiple iterations, critical assessment, and synthesis BID19 .The productivity of natural language yields a myriad of ways to formulate a question BID3 . In the face of complex information needs, humans overcome uncertainty by reformulating questions, issuing multiple searches, and aggregating responses. Inspired by humans' ability to ask the right questions, we present an agent that learns to carry out this process for the user. The agent sits between the user and a backend QA system that we refer to as 'the environment'. We call the agent AQA, as it implements an active question answering strategy. AQA aims to maximize the chance of getting the correct answer by sending a reformulated question to the environment. The agent seeks to find the best answer by asking many questions and aggregating the returned evidence. The internals of the environment are not available to the agent, so it must learn to probe a black-box optimally using only question strings. The key component of the AQA agent is a sequence-to-sequence model trained with reinforcement learning (RL) using a reward based on the answer returned by the environment. The second component to AQA combines the evidence from interacting with the environment using a convolutional neural network to select an answer.We evaluate on a dataset of Jeopardy! questions, SearchQA BID7 . These questions are hard to answer by design because they use convoluted language, e.g., Travel doesn't seem to be an issue for this sorcerer & onetime surgeon; astral projection & teleportation are no prob (answer: Doctor Strange). Thus SearchQA tests the ability of AQA to reformulate questions such that the QA system has the best chance of returning the correct answer. AQA improves over the performance of a deep network built for QA, BiDAF BID28 , which has produced state-of-the-art results on multiple tasks, by 11.4% absolute F1, a 32% relative F1 improvement. Additionally, AQA outperforms other competitive heuristic query reformulation benchmarks.AQA defines an instance of machine-machine communication. One side of the conversation, the AQA agent, is trying to adapt its language to improve the response from the other side, the QA environment. To shed some light on this process we perform a qualitative analysis of the language generated by the AQA agent. By evaluating on MSCOCO , we find that the agent's question reformulations diverge significantly from natural language paraphrases. Remarkably, though, the agent is able to learn non-trivial and transparent policies. In particular, the agent is able to discover classic IR query operations such as term re-weighting, resembling tf-idf, and morphological simplification/stemming. A possible reason being that current machine comprehension tasks involve the ranking of short textual snippets, thus incentivizing relevance, more than deep language understanding.2 RELATED WORK Lin & Pantel (2001) learned patterns of question variants by comparing dependency parsing trees. BID6 showed that MT-based paraphrases can be useful in principle by providing significant headroom in oracle-based estimations of QA performance. Recently, BID1 used paraphrasing to augment the training of a semantic parser by expanding through the paraphrases as a latent representation. Bilingual corpora and MT have been used to generate paraphrases by pivoting through a second language. Recent work uses neural translation models and multiple pivots BID18 . In contrast, our approach does not use pivoting and is, to our knowledge, the first direct neural paraphrasing system. BID27 propose phrase-based paraphrasing for query expansion. In contrast with this line of work, our goal is to generate full question reformulations while optimizing directly the end-to-end target performance metrics.Reinforcement learning is gaining traction in natural language understanding across many problems. For example, BID20 use RL to learn control policies for multi-user dungeon games where the state of the game is summarized by a textual description, and BID14 use RL for dialogue generation. Policy gradient methods have been investigated recently for MT and other sequence-to-sequence problems. They alleviate limitations inherent to the word-level optimization of the cross-entropy loss, allowing the use of sequence-level reward functions, like BLEU. Reward functions based on language models and reconstruction errors are used to bootstrap MT with fewer resources BID33 . RL training can also prevent exposure bias; an inconsistency between training and inference time stemming from the fact that the model never sees its own mistakes during training BID26 . We also use policy gradient to optimize our agent, however, we use end-to-end question answering quality as the reward.Uses of policy gradient for QA include , who train a semantic parser to query a knowledge base, and BID29 who propose query reduction networks that transform a query to answer questions that involve multi-hop common sense reasoning. The work of BID21 is most related to ours. They identify a document containing an answer to a question by following links on a graph. Evaluating on a set of questions from the game Jeopardy!, they learn to walk the Wikipedia graph until they reach the predicted answer. In a follow-up, BID22 improve document retrieval with an approach inspired by relevance feedback in combination with RL. They reformulate a query by adding terms from documents retrieved from a search engine for the original query. Our work differs in that we generate complete sequence reformulations rather than adding single terms, and we target question-answering rather than document retrieval.Active QA is also related to recent research on fact-checking: BID32 propose to perturb database queries in order to estimate the support of quantitative claims. In Active QA questions are perturbed semantically with a similar purpose, although directly at the surface natural language form. Figure 1 shows the Active Question Answering (AQA) agent-environment setup. The AQA model interacts with a black-box environment. AQA queries it with many versions of a question , and finally returns the best of the answers found. An episode starts with an original question q 0 . The agent then Figure 1 : The AQA agent-environment setup. In the downward pass the agent reformulates the question and sends variants to the QA system. In the upward pass the final answer is selected. Recently, BID13 trained chatbots that negotiate via language utterances in order to complete a task. They report that the agent's language diverges from human language if there is no incentive for fluency in the reward function. Our findings seem related. The fact that the questions reformulated by AQA do not resemble natural language is not due to the keyword-like SearchQA input questions, because Base-NMT is capable of producing more fluent questions from the same input. AQA learns to re-weight terms by focusing on informative (lower document frequency), query-specific (high query clarity), terms while increasing term frequency (TF) via duplication. At the same time it learns to modify surface forms in ways akin to stemming and morphological analysis.Some of the techniques seem to adapt to the specific properties of current deep QA architectures such as character-based modeling and attention. Sometimes AQA learns to generate semantically nonsensical, novel, surface term variants; e.g., it might transform the adjective dense to densey. The only justification for this is that such forms can be still exploited by the character-based BiDAF question encoder. Finally, repetitions can directly increase the chances of alignment in the attention components.We hypothesize that, while there is no incentive for the model to use human language due to the nature of the task, AQA learns to ask BiDAF questions by optimizing a language that increases the likelihood of BiDAF ranking better the candidate answers. BID10 argue that reading comprehension systems are not capable of significant language understanding and fail easily in adversarial settings. We speculate that current machine comprehension tasks involve mostly pattern matching and relevance modeling. As a consequence deep QA systems might implement sophisticated ranking systems trained to sort snippets of text from the context. As such, they resemble document retrieval systems which incentivizes the (re-)discovery of IR techniques, such as tf-idf re-weighting and stemming, that have been successful for decades BID0 . We propose a new framework to improve question answering. We call it active question answering (AQA), as it aims to improve answering by systematically perturbing input questions. We investigated a first system of this kind that has three components: a question reformulator, a black box QA system, and a candidate answer aggregator. The reformulator and aggregator form a trainable agent that seeks to elicit the best answers from the QA system. Importantly, the agent may only query the environment with natural language questions. Experimental results prove that the approach is highly effective and that the agent is able to learn non-trivial and somewhat interpretable reformulation policies.For future work, we will continue developing active question answering, investigating the sequential, iterative aspects of information seeking tasks, framed as end-to-end RL problems, thus, closing the loop between the reformulator and the selector.","frame Question Answering QA Reinforcement Learning task approach call Active Question Answering. propose agent sits user black box QA system learns reformulate questions elicit best possible answers. agent probes system potentially many natural language reformulations initial question aggregates returned evidence yield best answer. reformulation system is trained end-to-end maximize answer quality using policy gradient. evaluate SearchQA dataset complex questions extracted Jeopardy! agent outperforms state-of-the-art base model playing role environment benchmarks. also analyze language agent has learned interacting question answering system. find successful question reformulations look quite different natural language paraphrases. agent is able discover non-trivial reformulation strategies resemble classic information retrieval techniques term re-weighting tf-idf stemming. Web social media have become primary sources information. Users' expectations information seeking activities co-evolve increasing sophistication resources. Beyond navigation document retrieval simple factual question answering users seek direct answers complex compositional questions. search sessions may require multiple iterations critical assessment synthesis BID19.The productivity natural language yields myriad ways formulate question BID3. face complex information needs humans overcome uncertainty reformulating questions issuing multiple searches aggregating responses. Inspired humans' ability ask right questions present agent learns carry process user. agent sits user backend QA system refer 'the environment'. call agent AQA implements active question answering strategy. AQA aims maximize chance getting correct answer sending reformulated question environment. agent seeks find best answer asking many questions aggregating returned evidence. internals environment are not available agent must learn probe black-box optimally using question strings. key component AQA agent is a sequence-to-sequence model trained reinforcement learning RL using reward based answer returned environment. second component AQA combines evidence interacting environment using convolutional neural network select answer.We evaluate dataset Jeopardy! questions SearchQA BID7. questions are hard answer design use convoluted language e.g Travel seem issue sorcerer onetime surgeon;astral projection teleportation are no prob answer:Doctor Strange Thus SearchQA tests ability AQA reformulate questions QA system has the best chance returning correct answer. AQA improves performance deep network built QA BiDAF BID28 which has produced state-of-the-art results multiple tasks 11.4 absoluteF1 32% relative F1 improvement. Additionally AQA outperforms competitive heuristic query reformulation benchmarks.AQA defines instance machine-machine communication. One side conversation AQA agent is trying adapt language improve response side QA environment. shed light process perform qualitative analysis language generated AQA agent. evaluating MSCOCO find agent's question reformulations diverge significantly natural language paraphrases. Remarkably though agent is able learn non-trivial transparent policies. particular agent is able discover classic IR query operations term re-weighting resembling tf-idf morphological simplification/stemming. possible reason current machine comprehension tasks involve ranking short textual snippets thus incentivizing relevance deep language understanding.2 RELATED WORK Lin Pantel 2001 learned patterns question variants comparing dependency parsing trees. BID6 showed MT-based paraphrases can be useful principle providing significant headroom oracle-based estimations QA performance. Recently BID1 used paraphrasing augment training semantic parser expanding paraphrases latent representation. Bilingual corpora MT have been used generate paraphrases pivoting second language. Recent work uses neural translation models multiple pivots BID18. contrast approach does not use pivoting is,to knowledge first direct neural paraphrasing system. BID27 propose phrase-based paraphrasing query expansion. contrast line work goal is to generate full question reformulations optimizing directly end-to-end target performance metrics.Reinforcement learning is gaining traction natural language understanding across many problems. example BID20 useRL learn control policies multi-user dungeon games where the state game is summarized textual description BID14 useRL dialogue generation. Policy gradient methods have been investigated recently MT sequence-to-sequence problems. alleviate limitations inherent word-level optimization cross-entropy loss allowing use sequence-level reward functions like BLEU. Reward functions based language models reconstruction errors are used bootstrapMT fewer resources BID33. RL training can also prevent exposure bias;inconsistency training inference time stemming fact model never sees mistakes training BID26. also use policy gradient optimize agent however use end-to-end question answering quality reward.Uses policy gradient QA include who train semantic parser query knowledge base BID29 who propose query reduction networks transform query answer questions involve multi-hop common sense reasoning. work BID21 is most related ours. identify document containing answer question following links graph. Evaluating set questions game Jeopardy! learn walk Wikipedia graph reach predicted answer. follow-up BID22 improve document retrieval approach inspired relevance feedback combination RL. reformulate query adding terms documents retrieved search engine original query. work differs generate complete sequence reformulations rather adding single terms target question-answering rather document retrieval.ActiveQA is also related recent research fact-checking BID32 propose perturb database queries order estimate support quantitative claims. Active QA questions are perturbed semantically similar purpose although directly surface natural language form. Figure 1 shows Active Question Answering AQA agent-environment setup. AQA model interacts black-box environment. AQA queries many versions question finally returns best answers found. episode starts original questionq0. agent Figure1:AQA agent-environment setup. downward pass agent reformulates question sends variants QA system. upward pass final answer is selected. Recently BID13 trained chatbots negotiate via language utterances order complete task. report agent's language diverges human language if there is no incentive fluency reward function. findings seem related. fact questions reformulated AQA do not resemble natural language is not due keyword-like SearchQA input questions Base-NMT is capable producing fluent questions input. AQA learns re-weight terms focusing informative lower document frequency query-specific high query clarity terms increasing term frequency TF via duplication. time learns modify surface forms ways akin stemming morphological analysis.Some techniques seem adapt specific properties current deep QA architectures character-based modeling attention. Sometimes AQA learns generate semantically nonsensical novel surface term variants;e.g might transform adjective dense densey. justification is that forms can be still exploited character-based BiDAF question encoder. Finally repetitions can directly increase chances alignment attention components.We hypothesize isno incentive model use human language due nature task AQA learns ask BiDAF questions optimizing language increases likelihood BiDAF ranking better candidate answers. BID10 argue reading comprehension systems are not capable significant language understanding fail easily adversarial settings. speculate current machine comprehension tasks involve mostly pattern matching relevance modeling. consequence deep QA systems might implement sophisticated ranking systems trained sort snippets text context. resemble document retrieval systems which incentivizes re- discovery IR techniques tf-idf re-weighting stemming have been successful decades BID0. propose new framework improve question answering. call active question answering AQA aims improve answering systematically perturbing input questions. investigated first system kind has three components:question reformulator black box QA system candidate answer aggregator. reformulator aggregator form trainable agent seeks elicit best answers QA system. Importantly agent may query environment natural language questions. Experimental results prove approach is highly effective agent is able learn non-trivial somewhat interpretable reformulation policies.For future work will continue developing active question answering investigating sequential iterative aspects information seeking tasks framed end-to-end RL problems thus closing loop reformulator selector.",2069,1427,642,0.022,1.45,2025/11/05 17:19:01,0.01,1.571,0.3738317757009343,709.003
"Most deep latent factor models choose simple priors for simplicity, tractability
 or not knowing what prior to use. Recent studies show that the choice of
 the prior may have a profound effect on the expressiveness of the model,
 especially when its generative network has limited capacity. In this paper, we propose to learn a proper prior from data for adversarial autoencoders
 (AAEs). We introduce the notion of code generators to transform manually selected
 simple priors into ones that can better characterize the data distribution. Experimental results show that the proposed model can generate better image quality and learn better disentangled representations than
 AAEs in both supervised and unsupervised settings. Lastly, we present its
 ability to do cross-domain translation in a  text-to-image synthesis task. Deep latent factor models, such as variational autoencoders (VAEs) and adversarial autoencoders (AAEs), are becoming increasingly popular in various tasks, such as image generation BID6 , unsupervised clustering BID2 BID7 , and cross-domain translation BID10 . These models involve specifying a prior distribution over latent variables and defining a deep generative network (i.e., the decoder) that maps latent variables to data space in stochastic or deterministic fashion. Training such deep models usually requires learning a recognition network (i.e., the encoder) regularized by the prior.Traditionally, a simple prior, such as the standard normal distribution BID5 , is used for tractability, simplicity, or not knowing what prior to use. It is hoped that this simple prior will be transformed somewhere in the deep generative network into a form suitable for characterizing the data distribution. While this might hold true when the generative network has enough capacity, applying the standard normal prior often results in over-regularized models with only few active latent dimensions BID0 .Some recent works BID4 BID3 BID9 suggest that the choice of the prior may have a profound impact on the expressiveness of the model. As an example, in learning the VAE with a simple encoder and decoder, BID4 conjecture that multimodal priors can achieve a higher variational lower bound on the data loglikelihood than is possible with the standard normal prior. BID9 confirm the truth of this conjecture by showing that their multimodal prior, a mixture of the variational posteriors, consistently outperforms simple priors on a number of datasets in terms of maximizing the data log-likelihood. Taking one step further, BID3 learn a tree-structured nonparametric Bayesian prior for capturing the hierarchy of semantics presented in the data. All these priors are learned under the VAE framework following the principle of maximum likelihood.Along a similar line of thinking, we propose in this paper the notion of code generators for learning a prior from data for AAE. The objective is to learn a code generator network to transform a simple prior into one that, together with the generative network, can better characterize the data distribution. To this end, we generalize the framework of AAE in several significant ways:• We replace the simple prior with a learned prior by training the code generator to output latent variables that will minimize an adversarial loss in data space. • We employ a learned similarity metric BID6 in place of the default squared error in data space for training the autoencoder.• We maximize the mutual information between part of the code generator input and the decoder output for supervised and unsupervised training using a variational technique introduced in InfoGAN BID1 .Extensive experiments confirm its effectiveness of generating better quality images and learning better disentangled representations than AAE in both supervised and unsupervised settings, particularly on complicated datasets. In addition, to the best of our knowledge, this is one of the first few works that attempt to introduce a learned prior for AAE.The remainder of this paper is organized as follows: Section 2 reviews the background and related works. Section 3 presents the implementation details and the training process of the proposed code generator. Section 4 compares its performance with AAE in image generation and disentanglement tasks. Lastly, we conclude this paper with remarks on future work. In this paper, we propose to learn a proper prior from data for AAE. Built on the foundation of AAE, we introduce a code generator to transform the manually selected simple prior into one that can better fit the data distribution. We develop a training process that allows to learn both the autoencoder and the code generator simultaneously. We demonstrate its superior performance over AAE in image generation and learning disentangled representations in supervised and unsupervised settings. We also show its ability to do cross-domain translation. Mode collapse and training instability are two major issues to be further investigated in future work. Figure 14: Generated images in accordance with the varying color attribute in the text description ""The flower is pink in color and has petals that are rounded in shape and ruffled."" From left to right, the color attribute is set to pink, red, yellow, orange, purple, blue, white, green, and black, respectively. Note that there is no green or black flower in the dataset. Input latent code ∈ R code size 3 x 3 conv. 64 RELU stride 2 pad 1 4 x 4 upconv. 512 BN. RELU stride 1 3 x 3 residual blcok 64 4 x 4 up sampling residual block 256 stride 2 3 x 3 down sampling residual blcok 128 stride 2 4 x 4 up sampling residual block 128 stride 2 3 x 3 down sampling residual blcok 256 stride 2 4 x 4 up sampling residual block 64 stride 2 3 x 3 down sampling residual block 512 stride 2 3 x 3 conv. image channels Tanh 4 x 4 avg. pooling stride 1 FC. 2 x code size BN. RELU FC. code size Linear Input feature map FC. 2 x noise size BN. RELU 3 x 3 conv. out channels RELU stride 2 pad 1 FC. latent code size BN. Linear 3 x 3 conv. out channels RELU stride 1 pad 1 skip connection output = input + residual RELU Table 4",deep latent factor models choose simple priors simplicity tractability knowing what prior use. Recent studies show choice prior may have a profound effect expressiveness model especially when its when the generative network has limited capacity. paper propose learn proper prior data adversarial autoencoders AAEs introduce notion code generators transform manually selected simple priors ones can better characterize data distribution. Experimental results show proposed model can generate better image quality learn better disentangled representations AAEs supervised unsupervised settings. Lastly present ability do cross-domain translation text-to-image synthesis task. Deep latent factor models variational autoencoders VAEs adversarial autoencoders AAEs are becoming increasingly popular various tasks image generation BID6 unsupervised clustering BID2 BID7 cross-domain translation BID10. models involve specifying prior distribution latent variables defining deep generative network.e decoder maps latent variables data space stochastic deterministic fashion. Training deep models usually requires learning recognition network.e encoder regularized prior.Traditionally simple prior standard normal distribution BID5 is used tractability simplicity knowing what prior use. is hoped simple prior will be transformed somewhere deep generative network form suitable characterizing data distribution. might hold true when its when the generative network has enough capacity applying standard normal prior often results over-regularized models active latent dimensions BID0.Some recent works BID4 BID3 BID9 suggest choice prior may have a profound impact expressiveness model. example learning VAE simple encoder decoder BID4 conjecture multimodal priors can achieve higher variational lower bound data loglikelihood is possible standard normal prior. BID9 confirm truth conjecture showing multimodal prior mixture variational posteriors consistently outperforms simple priors number datasets terms maximizing data log-likelihood Taking one step BID3 learn tree-structured nonparametric Bayesian prior capturing hierarchy semantics presented data. priors are learned VAE framework following principle maximum likelihood.Along similar line thinking propose paper notion code generators learning prior data AAE. objective is to learn code generator network transform simple prior one together generative network can better characterize data distribution. end generalize framework AAE several significant ways:• replace simple prior learned prior training code generator output latent variables will minimize adversarial loss data space. • employ learned similarity metric BID6 place default squared error data space training autoencoder.• maximize mutual information part code generator input decoder output supervised unsupervised training using variational technique introduced InfoGAN BID1.Extensive experiments confirm effectiveness generating better quality images learning better disentangled representations AAE supervised unsupervised settings particularly complicated datasets. addition best knowledge is one first works attempt introduce learned prior AAE.The remainder paper is organized follows:Section 2 reviews background related works. Section 3 presents implementation details training process proposed code generator. Section 4 compares performance AAE image generation disentanglement tasks. Lastly conclude paper remarks future work. paper propose learn proper prior data AAE. Built foundation AAE introduce code generator transform manually selected simple prior one can better fit data distribution. develop training process allows learn autoencoder code generator simultaneously. demonstrate superior performance AAE image generation learning disentangled representations supervised unsupervised settings. also show ability do cross-domain translation. Mode collapse training instability are two major issues investigated future work. Figure14:Generated images accordance varying color attribute text description flower is pink color has petals are rounded shape ruffled. left right color attribute is set pink red yellow orange purple blue white green black respectively. Note is no green black flower dataset. Input latent code∈ R code size3 x 3 conv. 64 RELU stride2 pad14x 4 upconv. 512BN. RELU stride13 x 3 residual blcok 644x4 sampling residual block 256 stride23x 3 sampling residual blcok 128 stride24x 4 sampling residual block 128 stride23x 3 sampling residual blcok 256 stride24x 4 sampling residual block64 stride23x 3 sampling residual block 512 stride23x 3 conv. image channels Tanh4 x 4 avg. pooling stride1FC. 2 x code size BN. RELUFC. code size Linear Input feature mapFC. 2 x noise size BN. RELU3x3 conv. channels RELU stride2 pad1FC. latent code sizeBN. Linear3x3 conv. channels RELU stride1 pad 1 skip connection output input+residual RELU Table4,1283,884,399,0.011,1.451,2025/11/05 17:19:01,0.01,1.222,0.3769470404984424,378.32
"In the past few years, various advancements have been made in generative models owing to the formulation of Generative Adversarial Networks (GANs). GANs have been shown to perform exceedingly well on a wide variety of tasks pertaining to image generation and style transfer. In the field of Natural Language Processing, word embeddings such as word2vec and GLoVe are state-of-the-art methods for applying neural network models on textual data. Attempts have been made for utilizing GANs with word embeddings for text generation. This work presents an approach to text generation using Skip-Thought sentence embeddings in conjunction with GANs based on gradient penalty functions and f-measures. The results of using sentence embeddings with GANs for generating text conditioned on input information are comparable to the approaches where word embeddings are used. Numerous efforts have been made in the field of natural language text generation for tasks such as sentiment analysis BID35 ) and machine translation BID7 BID24 ). Early techniques for generating text conditioned on some input information were template or rule-based engines, or probabilistic models such as n-gram. In recent times, state-of-the-art results on these tasks have been achieved by recurrent BID23 BID20 ) and convolutional neural network models trained for likelihood maximization. This work proposes an approach for text generation using Generative Adversarial Networks with Skip-Thought vectors.GANs BID9 ) are a class of neural networks that explicitly train a generator to produce high-quality samples by pitting against an adversarial discriminative model. GANs output differentiable values and hence the task of discrete text generation has to use vectors as differentiable inputs. This is achieved by training the GAN with sentence embedding vectors produced by SkipThought ), a neural network model for learning fixed length representations of sentences. 4.1 CONDITIONAL GENERATION OF SENTENCES.GANs can be conditioned on data attributes to generate samples BID21 ; Radford et al.) . In this experiment, both the generator and discriminator are conditioned on Skip-Thought encoded vectors ). The encoder converts 70000 sentences from the BookCorpus dataset collected in with a training/test/validation split of 5/1/1 into vectors used as real samples for discriminator. The decoded sentences are used to evaluate model performance under corpus level BLEU-2, BLEU-3 and BLEU-4 metrics (Papineni et al.) , once using only test set as reference and then entire corpus as reference. TAB0 compares these results for different architectures that have been experimented with in this paper.",past years various advancements have been made generative models owing formulation Generative Adversarial Networks GANs GANs have been shown perform exceedingly well wide variety tasks pertaining image generation style transfer. field Natural Language Processing word embeddings word2vec GLoVe are state-of-the-art methods applying neural network models textual data. Attempts have been made utilizing GANs word embeddings text generation. work presents approach text generation using Skip-Thought sentence embeddings conjunction GANs based gradient penalty functions f-measures results using sentence embeddings GANs generating text conditioned input information are comparable approaches where word embeddings are used. Numerous efforts have been made field natural language text generation tasks sentiment analysis BID35 machine translation BID7 BID24 Early techniques generating text conditioned input information were template rule-based engines probabilistic models n-gram recent times state-of-the-art results tasks have been achieved recurrent BID23 BID20 convolutional neural network models trained likelihood maximization. work proposes approach text generation using Generative Adversarial Networks Skip-Thought vectors.GANs BID9 are a class neural networks explicitly train generator produce high-quality samples pitting adversarial discriminative model. GANs output differentiable values hence task discrete text generation has to use vectors differentiable inputs. is achieved training GAN sentence embedding vectors produced SkipThought neural network model learning fixed length representations sentences. 4.1 CONDITIONAL GENERATION SENTENCES.GANs can be conditioned data attributes generate samples BID21;Radfordetal. experiment generator discriminator are conditioned Skip-Thought encoded vectors encoder converts 70000 sentences BookCorpus dataset collected training/test/validation split 5/1/1 vectors used real samples discriminator. decoded sentences are used evaluate model performance corpus level BLEU-2 BLEU-3 BLEU-4 metrics Papinenietal. using test set reference entire corpus reference. TAB0 compares results different architectures have been experimented paper.,506,369,137,0.004,1.371,2025/11/05 17:19:01,0.0,1.5,0.1277258566978191,143.354
"The novel \emph{Unbiased Online Recurrent Optimization} (UORO) algorithm allows for online learning of general recurrent computational graphs such as recurrent network models. It works in a streaming fashion and avoids backtracking through past activations and inputs. UORO is computationally as costly as \emph{Truncated Backpropagation Through Time} (truncated BPTT), a widespread algorithm for online learning of recurrent networks \cite{jaeger2002tutorial}.  UORO is a modification of \emph{NoBackTrack} \cite{DBLP:journals/corr/OllivierC15} that bypasses the need for model sparsity and makes implementation easy in current deep learning frameworks, even for complex models.   Like NoBackTrack, UORO provides unbiased gradient estimates; unbiasedness is the core hypothesis in stochastic gradient descent theory, without which convergence to a local optimum is not guaranteed. On the contrary, truncated BPTT does not provide this property, leading to possible divergence.   On synthetic tasks where truncated BPTT is shown to diverge, UORO converges. For instance, when a parameter has a positive short-term but negative long-term influence, truncated BPTT diverges unless the truncation span is very significantly longer than the intrinsic temporal range of the interactions, while UORO performs well thanks to the unbiasedness of its gradients.
 We introduced UORO, an algorithm for training recurrent neural networks in a streaming, memoryless fashion. UORO is easy to implement, and requires as little computation time as truncated BPTT, at the cost of noise injection. Importantly, contrary to most other approaches, UORO scalably provides unbiasedness of gradient estimates. Unbiasedness is of paramount importance in the current theory of stochastic gradient descent. Furthermore, UORO is experimentally shown to benefit from its unbiasedness, converging even in cases where truncated BPTT fails to reliably achieve good results or diverges pathologically.",novel \emph Unbiased Online Recurrent Optimization UORO algorithm allows online learning general recurrent computational graphs recurrent network models. works streaming fashion avoids backtracking past activations inputs. UORO is computationally costly \emph Truncated Backpropagation Time truncated BPTT widespread algorithm online learning recurrent networks \cite jaeger2002tutorial UORO is a modification \emph NoBackTrack \cite DBLP:journals/corr/OllivierC15 bypasses need model sparsity makes implementation easy current deep learning frameworks even complex models. Like NoBackTrack UORO provides unbiased gradient estimates;unbiasedness is the core hypothesis stochastic gradient descent theory without which convergence local optimum is not guaranteed. contrary truncated BPTT does not provide property leading possible divergence. synthetic tasks where truncated BPTT is shown diverge UORO converges. instance when a parameter has a positive short-term negative long-term influence truncated BPTT diverges unless truncation span is very significantly longer intrinsic temporal range interactions UORO performs well thanks unbiasedness gradients. introduced UORO algorithm training recurrent neural networks streaming memoryless fashion. UORO is easy implement requires little computation time truncated BPTT cost noise injection. Importantly contrary approaches UORO scalably provides unbiasedness gradient estimates. Unbiasedness is of paramount importance current theory stochastic gradient descent. Furthermore UORO is experimentally shown benefit unbiasedness converging even cases where truncated BPTT fails reliably achieve good results diverges pathologically.,408,305,103,0.003,1.338,2025/11/05 17:19:01,0.0,1.571,0.0249221183800623,128.831
"We present a deep learning-based method for super-resolving coarse (low-resolution) labels assigned to groups of image pixels into pixel-level (high-resolution) labels, given the joint distribution between those low- and high-resolution labels. This method involves a novel loss function that minimizes the distance between a distribution determined by a set of model outputs and the corresponding distribution given by low-resolution labels over the same set of outputs. This setup does not require that the high-resolution classes match the low-resolution classes and can be used in high-resolution semantic segmentation tasks where high-resolution labeled data is not available. Furthermore, our proposed method is able to utilize both data with low-resolution labels and any available high-resolution labels, which we show improves performance compared to a network trained only with the same amount of high-resolution data.
 We test our proposed algorithm in a challenging land cover mapping task to super-resolve labels at a 30m resolution to a separate set of labels at a 1m resolution. We compare our algorithm with models that are trained on high-resolution data and show that 1) we can achieve similar performance using only low-resolution data; and 2) we can achieve better performance when we incorporate a small amount of high-resolution data in our training. We also test our approach on a medical imaging problem, resolving low-resolution probability maps into high-resolution segmentation of lymphocytes with accuracy equal to that of fully supervised models. Semantic image segmentation is the task of labeling each pixel in an input image X = {x ij } as belonging to one of L fine-scale application classes, Y = {y ij }, y ∈ {1, . . . , L}. In weakly supervised segmentation, instances in the training set only contain partial observations of the target ground truth labels, e.g., summary of class labels instead of pixel-level labels. We aim to solve a variant of this problem where coarse-scale, low-resolution accessory classes, Z = {z k }; z ∈ {1, . . . , N }, are defined for sets of pixels in the input images, where we are given the joint distribution P (Y, Z) between the accessory class labels and the application labels. Specifically, a training image X is divided into K sets B k , each with an accessory class label z k , and our models are trained to produce the high-resolution application labels y ij . For example, in Figure 1 , a high-resolution aerial image is shown alongside the low-resolution ground truth land cover map (defined over accessory classes) and the target high-resolution version (defined over application classes). We aim to derive the high-resolution land cover map based on the aerial image and low-resolution ground truth.Compared to other weakly supervised image segmentation techniques, the formulation of the problem we aim to solve is more general: it applies both to existing weakly supervised image segmentation problems, as well as to other problems with different characteristics of weak labels. The more general formulation is necessary for tasks such as land cover mapping from aerial imagery and lymphocyte segmentation from pathology imagery. In these applications, coarse labels do not necessarily match the fine-scale labels, as shown in Figure 1 . The distinction between the fine-scale application and coarse-scale accessory classes is necessary for situations in which the ground-truth information that is known about an image does not match with the application classes that we aim to Figure 1 : An Illustration of land cover data and label super-resolution. Our method takes an input image (x) with low-resolution labels (z) and outputs a set of super-resolved label predictions (y), utilizing the statistical descriptions between low-resolution and high-resolution labels (Appendix B) e.g., one low-resolution class designates areas of low-intensity development, with 20% to 49% of impervious surfaces (such as houses or roads).label the image with, but instead suggests a distribution over the application labels. State-of-the-art methods for weakly supervised semantic segmentation exploit the structure of weak labels in ways that are not applicable in our examples: we cannot create bounding boxes around land cover object instances BID7 ; Papandreou et al. FORMULA0 ) -we consider data that is generally given at scales much larger than the objects being segmented and does not carry foreground-background morphology -nor use coarse approximations of ground-truth segmentation (Krähenbühl & Koltun (2011); BID13 ). Other work attempts to match a class ""density function"" to weak labels (Lempitsky & Zisserman (2010) ), but it mainly targets localization and enumeration of small foreground objects with known sizes. Existing Weak supervision approaches also often involve expensive steps in inference, such as CRFs or iterative evaluation BID3 ), which are impractical on large datasets. At the same time, thorough analyses of training algorithms only exist for models that are not sufficiently expressive for the applications we consider (Yu et al. (2013) ). While our formulation of the problem allows us to specifically address the previously mentioned land cover mapping and lymphocyte segmentation, it can also be applied to more traditional segmentation tasks such as foreground/background segmentation as we explore in Appendix. F.Our proposed method is illustrated in FIG0 . Briefly, a standard segmentation network will output probabilistic estimates of the application labels. Our methodology summarizes these estimates over the sets B k , which results in an estimated distribution of application labels for each set. These distributions can then be compared to the expected distribution from the accessory (low-resolution) labels using standard distribution distance metrics. This extension is fully differentiable and can thus be used to train image segmentation neural networks end-to-end from pairs of images and coarse labels.Land cover mapping from aerial imagery is an important application in need of such methodology. Land cover maps are essential in many sustainability-related applications such as conservation planning, monitoring habitat loss, and informing land management. In Section 3.1 we describe land cover mapping in detail and show how our method creates high-resolution land cover maps solely from high-resolution imagery low-resolution labels, at an accuracy similar to that of models trained on high-resolution labels. We further show how to train models with a combination of low-and highresolution labels that outperform the high-res models in transfer learning tasks. As low-resolution labels are much easier to collect, and indeed exist over a much wider geographic area in our land cover mapping application, the ability to combine low-and high-resolution labels is an important feature of our proposed methods.In a second example (Section 3.2), we segment tumor infiltrating lymphocytes from high-resolution (gigapixel) pathology images. Understanding the spatial distribution of immune cells, such as lymphocytes in pathology images, is fundamental for immunology and the treatment of cancer BID10 ; Thorsson et al. (2018) ). Here, coarse labels are probabilities of lymphocyte infiltration (having two or more lymphocytes) on 100×100 pixel regions, given by an automatic classifier (Saltz FORMULA0 ). Our super-resolution model trained on coarse labels performs the same as a lymphocyte classifier trained with high-resolution (cell-level) supervision (Hou et al. (2018) ).To summarize, as our first contribution, we propose a label super-resolution network which utilizes the distribution of high-resolution labels suggested by given low-resolution labels, based on visual cues in the input images, to derive high-resolution label predictions consistent to the input image. Our second contribution is that we evaluate our method extensively on the application of land cover segmentation and conclude that when there are not enough representative high-resolution training data, our method is much more robust than a model trained on high-resolution training data only, since our method utilizes more training data with weak labels. We show the generality of our method on the lymphocyte segmentation task and the task of segmenting foreground given object bounding boxes (in Appendix F). We proposed a label super-resolution network which is capable of deriving high-resolution labels, given low-resolution labels that do not necessarily match the targeting high-resolution labels in a one-to-one manner -we only assume that the joint distribution between the low-resolution and highresolution classes is known. In particular, we train a network to predict high-resolution labels, minimizing the distance/divergence between two distributions: distribution of predicted high-resolution labels and expected distribution suggested by the low-resolution labels. We applied our method in two real-world applications where high res labels are very expensive to obtain compared to low res labels, and achieved similar or better results compared to the conventional fully supervised methods trained on high-resolution labels. We also show how combining low and high res labels leads to better generalization to out-of-sample test sets.Although the main assumption of the model is that the joint distribution over coarse and fine labels is known, the model is in fact robust to errors in estimates of these distributions, as we discuss in Appendix F. There we show that these joint distributions can be acquired or inferred in a variety of ways, thus making label super-resolution widely applicable, including beyond computer vision.",present deep learning-based method super-resolving coarse low-resolution labels assigned groups image pixels pixel-level high-resolution labels where we are given joint distribution low- high-resolution labels. method involves novel loss function minimizes distance distribution determined set model outputs corresponding distribution given low-resolution labels set outputs. setup does not require high-resolution classes match low-resolution classes can be used high-resolution semantic segmentation tasks where high-resolution labeled data is not available. Furthermore proposed method is able utilize data low-resolution labels available high-resolution labels which we show improves performance compared network trained amount high-resolution data. test proposed algorithm challenging land cover mapping task super-resolve labels 30m resolution separate set labels 1m resolution. compare algorithm models are trained high-resolution data show 1 can achieve similar performance using low-resolution data;2 can achieve better performance when we incorporate small amount high-resolution data training. also test approach medical imaging problem resolving low-resolution probability maps high-resolution segmentation lymphocytes accuracy equal fully supervised models. Semantic image segmentation is the task labeling pixel input imageX xij belonging one L fine-scale application classes ij ∈ 1 L weakly supervised segmentation instances training set contain partial observations target ground truth labels e.g summary class labels instead pixel-level labels. aim solve variant problem where coarse-scale low-resolution accessory classes Z zk z∈ 1 N are defined sets pixels input images where we are given joint distributionP Z accessory class labels application labels. Specifically training imageX is divided K setsBk accessory class labelz k models are trained produce high-resolution application labels ij. example Figure1 high-resolution aerial image is shown alongside low-resolution ground truth land cover map defined accessory classes target high-resolution version defined application classes aim derive high-resolution land cover map based aerial image low-resolution ground truth.Compared weakly supervised image segmentation techniques formulation problem aim solve is more general:applies existing weakly supervised image segmentation problems well problems different characteristics weak labels. general formulation is necessary tasks land cover mapping aerial imagery lymphocyte segmentation pathology imagery. applications coarse labels do not necessarily match fine-scale labels shown Figure1. distinction fine-scale application coarse-scale accessory classes is necessary situations which the ground-truth information is known image does not match application classes aim Figure1:Illustration land cover data label super-resolution method takes input image x low-resolution labels z outputs set super-resolved label predictions utilizing statistical descriptions low-resolution high-resolution labels AppendixB e.g one low-resolution class designates areas low-intensity development 20% 49% impervious surfaces houses roads.label image instead suggests distribution application labels. State-of-the-art methods weakly supervised semantic segmentation exploit structure weak labels ways are not applicable examples:cannot create bounding boxes around land cover object instances BID7;Papandreouetal. FORMULA0 -we consider data is generally given scales much larger objects segmented does not carry foreground-background morphology -nor use coarse approximations ground-truth segmentation Krähenbühl Koltun 2011 BID13 work attempts match class density function weak labels Lempitsky Zisserman 2010 mainly targets localization enumeration small foreground objects known sizes. Existing Weak supervision approaches also often involve expensive steps inference CRFs iterative evaluation BID3 which are impractical large datasets. time thorough analyses training algorithms exist models are not sufficiently expressive applications consider Yuetal. 2013 formulation problem allowsus specifically address previously mentioned land cover mapping lymphocyte segmentation can also applied traditional segmentation tasks foreground/background segmentation explore Appendix. F.Our proposed method is illustrated FIG0. Briefly standard segmentation network will output probabilistic estimates application labels. methodology summarizes estimates setsBk which results estimated distribution application labels set. distributions can then be compared expected distribution accessory low-resolution labels using standard distribution distance metrics. extension is fully differentiable can thus used train image segmentation neural networks end-to-end pairs images coarse labels.Land cover mapping aerial imagery is an important application need methodology. Land cover maps are essential many sustainability-related applications conservation planning monitoring habitat loss informing land management. Section 3.1 describe land cover mapping detail show how our method creates high-resolution land cover maps solely high-resolution imagery low-resolution labels accuracy similar models trained high-resolution labels. show how to train models combination low-and highresolution labels outperform high-res models transfer learning tasks. low-resolution labels are much easier collect indeed exist much wider geographic area land cover mapping application ability combine low-and high-resolution labels is an important feature proposed methods.In second example Section 3.2 segment tumor infiltrating lymphocytes high-resolution gigapixel pathology images. Understanding spatial distribution immune cells lymphocytes pathology images is fundamental immunology treatment cancer BID10;Thorssonetal. 2018 coarse labels are probabilities lymphocyte infiltration two lymphocytes 100×100 pixel regions where we are given automatic classifier Saltz FORMULA0 super-resolution model trained coarse labels performs lymphocyte classifier trained high-resolution cell-level supervision Houetal. 2018.To summarize first contribution propose label super-resolution network which utilizes distribution high-resolution labels suggested given low-resolution labels based visual cues input images derive high-resolution label predictions consistent input image. second contribution is that we evaluate method extensively application land cover segmentation conclude when there are enough representative high-resolution training data method is much robust model trained high-resolution training data since method utilizes training data weak labels. show generality method lymphocyte segmentation task task segmenting foreground given object bounding boxes AppendixF proposed label super-resolution network which is capable deriving high-resolution labels where we are given low-resolution labels do not necessarily match targeting high-resolution labels one-to-one manner -we assume joint distribution low-resolution highresolution classes is known. particular train network predict high-resolution labels minimizing distance/divergence two distributions:distribution predicted high-resolution labels expected distribution suggested low-resolution labels. applied method two real-world applications where high res labels are very expensive obtain compared low res labels achieved similar better results compared conventional fully supervised methods trained high-resolution labels. also show how combining low high res labels leads better generalization out-of-sample test sets.Although main assumption model is that the joint distribution coarse fine labels is known model is in fact robust errors estimates distributions discuss AppendixF. show joint distributions can be acquired inferred variety ways thus making label super-resolution widely applicable including beyond computer vision.,1805,1222,583,0.02,1.477,2025/11/05 17:19:01,0.01,1.593,0.4579439252336449,564.598
"We propose a novel framework for combining datasets via alignment of their associated intrinsic dimensions. Our approach assumes that the two datasets are sampled from a common latent space, i.e., they measure equivalent systems. Thus, we expect there to exist a natural (albeit unknown) alignment of the data manifolds associated with the intrinsic geometry of these datasets, which are perturbed by measurement artifacts in the sampling process. Importantly, we do not assume any individual correspondence (partial or complete) between data points. Instead, we rely on our assumption that a subset of data features have correspondence across datasets. We leverage this assumption to estimate relations between intrinsic manifold dimensions, which are given by diffusion map coordinates over each of the datasets. We compute a correlation matrix between diffusion coordinates of the datasets by considering graph (or manifold) Fourier coefficients of corresponding data features. We then orthogonalize this correlation matrix to form an isometric transformation between the diffusion maps of the datasets. Finally, we apply this transformation to the diffusion coordinates and construct a unified diffusion geometry of the datasets together. We show that this approach successfully corrects misalignment artifacts, and allows for integrated data. In biology and other natural science settings we often have the problem that data are measured from the same system but with different sensors or in different days where sensors are calibrated differently. This is often termed batch effect in biology and can include, for example, drastic variations between subjects, experimental settings, or even times of day when an experiment is conducted. In such settings it is important to globally and locally align the datasets such that they can be combined for effective further analysis. Otherwise, measurement artifacts may dominate downstream analysis. For instance, clustering the data will group samples by measurement time or sensor used rather than by biological or meaningful differences between datapoints.Recent works regard the two datasets as views of the same system and construct a multiview diffusion geometry but all of them require at least partial bijection, if not full one, between views BID11 BID12 BID24 Tuia & Camps-Valls, 2016) . Other work directly attempt to match data points directly in ambient space, or by local data geometry and these can be very sensitive to differences in sampling density rather than data geometry BID10 . Here, we present a principled approach called harmonic alignment to for correct this type of effect based on the manifold assumption.The manifold assumption holds that high dimensional data originates from an intrinsically low dimensional smoothly varying space that is mapped via nonlinear functions to observable high dimensional measurements. Thus, we assume that the datasets are from transformed versions of the same low dimensional manifold. We learn the manifolds separately from the two datasets using diffusion geometric approaches and then find an isometric transformation to map from one manifold to the other. Note that we are not aligning points to points. Indeed there may be sampling differences and density differences in the data. However, our manifold learning approach uses an anisotropic kernel that detects the geometry of the data to align rather than point-by-point matching which is done in other methods.Our method involves first embedding each dataset separately into diffusion components, and then finding an isometric transformation that aligns these diffusion representations. To find such transformation, we utilize the duality between diffusion coordinates and geometric harmonics that act as generalized Fourier harmonics in the graph space. The diffusion components are eigenvectors of a Markov-normalized data diffusion operator, whose eigenvalues indicate frequency of the eigenvector. We attempt to find a transformation from one set of eigenvectors to another, via feature correspondences in the data.While datapoint correspondences may be difficult or impossible to obtain since many biological measurements are destructive, feature correspondences are often available. For instance single-cell measurements of cells from the same device, thus containing counts for the same genes, albeit affected by batch differences. Thus when corresponding features are transformed via the graph Fourier transform (GFT) into diffusion coordinates, the representations should be similar, with potentially small frequency-proximal perturbations. For instance, slowly varying features across the manifold should be load to low-frequency eigenvectors of the Markov matrix. This insight allows us to create a correlation matrix between the eigenvectors of one dataset to another based on correlation between feature loadings to the eigenvectors. However, since we know that eigenvectors represent frequency harmonics, we need not compute the entire correlation matrix but rather only the near-diagonal values. This implies that the two manifolds must be perturbed such that low and high frequency eigenvector space are similar. We then find a linear transformation between that maps the eigenvectors of one space into those of the other that maximizes these correlations by orthogonalizing this matrix. This transformation allows us to align the two datasets with each other. Finally, given an aligned representation, we build a robust unified diffusion geometry that is invariant batch effects and sample-specific artifacts and low-pass filter this geometry to denoise the unified manifold. Thus, in addition to aligning the manifolds our method denoises the manifolds as well.We demonstrate the results of our method on artificial manifolds created from rotated MNIST digits, corrupted MNIST digits, as well as on single-cell biological data measuring peripheral blood cells. In each case our method successfully aligns the manifolds such that they have appropriate neighbors within and across the two datasets. We show an application to transfer learning where a lazy classifier trained on one dataset is applied to the other dataset after alignment. Further, comparisons with recently developed methods such as the MNN-based method of BID10 show significant improvements in performance and denoising ability. We presented a novel method for aligning or batch-normalizing two datasets that involves learning and aligning their intrinsic manifold dimensions. Our method leverages the fact that common or corresponding features in the two datasets should have similar harmonics on the graph of the data. Our harmonic alignment method finds an isometric transformation that maximizes the similarity of frequency harmonics of common features. Results show that our method successfully aligns artifi- cially misaligned as well as biological data containing batch effect. Our method has the advantages that it aligns manifold geometry and not density (and thus is insensitive to sampling differences in data) and further our method denoises the datasets to obtain alignments of significant manifold dimensions rather than noise. Future applications of harmonic alignment can include integration of data from different measurement types performed on the same system, where features have known correlations.",propose novel framework combining datasets via alignment associated intrinsic dimensions. approach assumes two datasets are sampled common latent space.e measure equivalent systems. Thus expect exist natural albeit unknown alignment data manifolds associated intrinsic geometry datasets which are perturbed measurement artifacts sampling process. Importantly do not assume individual correspondence partial complete data points. Instead rely assumption subset data features have correspondence across datasets. leverage assumption estimate relations intrinsic manifold dimensions which are given diffusion map coordinates datasets. compute correlation matrix diffusion coordinates datasets considering graph manifold Fourier coefficients corresponding data features. orthogonalize correlation matrix form isometric transformation diffusion maps datasets. Finally apply transformation diffusion coordinates construct unified diffusion geometry datasets together. show approach successfully corrects misalignment artifacts allows integrated data. biology natural science settings often have the problem data are measured system different sensors different days where sensors are calibrated differently. is often termed batch effect biology can include example drastic variations subjects experimental settings even times day when an experiment is conducted. settings is important globally locally align datasets can combined effective analysis. Otherwise measurement artifacts may dominate downstream analysis. instance clustering data will group samples measurement time sensor used rather biological meaningful differences datapoints.Recent works regard two datasets views system construct multiview diffusion geometry require least partial bijection if not full one views BID11 BID12 BID24 Tuia Camps-Valls 2016 work directly attempt match data points directly ambient space local data geometry canbe sensitive differences sampling density rather data geometry BID10. present principled approach called harmonic alignment correct type effect based manifold assumption.The manifold assumption holds high dimensional data originates intrinsically low dimensional smoothly varying space is mapped via nonlinear functions observable high dimensional measurements. Thus do not assume datasets are from are transformed versions low dimensional manifold. learn manifolds separately two datasets using diffusion geometric approaches find isometric transformation map one manifold other. Note are not aligning points points. Indeed may sampling differences density differences data. However manifold learning approach uses anisotropic kernel detects geometry data align rather point-by-point matching which is done methods.Our method involves first embedding dataset separately diffusion components finding isometric transformation aligns diffusion representations. find transformation utilize duality diffusion coordinates geometric harmonics act generalized Fourier harmonics graph space. diffusion components are eigenvectors Markov-normalized data diffusion operator whose eigenvalues indicate frequency eigenvector. attempt find transformation one set eigenvectors another via feature correspondences data.While datapoint correspondences may difficult impossible obtain since many biological measurements are destructive feature correspondences are often available. instance single-cell measurements cells device thus containing counts genes albeit affected batch differences. Thus when corresponding features are from are transformed via graph Fourier transform GFT diffusion coordinates representations should be should have similar potentially small frequency-proximal perturbations. instance slowly varying features across manifold should be load low-frequency eigenvectors Markov matrix. insight allowsus create correlation matrix eigenvectors one dataset another based correlation feature loadings eigenvectors. However since know eigenvectors represent frequency harmonics need compute entire correlation matrix rather near-diagonal values. implies two manifolds must perturbed low high frequency eigenvector space are similar. find linear transformation maps eigenvectors one space maximizes correlations orthogonalizing matrix. transformation allowsus align two datasets other. Finally which are given aligned representation build robust unified diffusion geometry is invariant batch effects sample-specific artifacts low-pass filter geometry denoise unified manifold. Thus addition aligning manifolds method denoises manifolds well.We demonstrate results method artificial manifolds created rotated MNIST digits corrupted MNIST digits well single-cell biological data measuring peripheral blood cells. case method successfully aligns manifolds have appropriate neighbors within across two datasets. show application transfer learning where a lazy classifier trained one dataset is applied dataset alignment. comparisons recently developed methods MNN-based method BID10 show significant improvements performance denoising ability. presented novel method aligning batch-normalizing two datasets involves learning aligning intrinsic manifold dimensions. method leverages fact common corresponding features two datasets should be should have similar harmonics graph data. harmonic alignment method finds isometric transformation maximizes similarity frequency harmonics common features. Results show method successfully aligns artifi- cially misaligned well biological data containing batch effect. method has the advantages aligns manifold geometry density thus is insensitive sampling differences data method denoises datasets obtain alignments significant manifold dimensions rather noise. Future applications harmonic alignment can include integration data different measurement types performed system where features have known correlations.,1276,853,423,0.013,1.496,2025/11/05 17:19:01,0.01,1.375,0.5171339563862927,423.485
"Reinforcement learning (RL) has proven to be a powerful paradigm for deriving complex behaviors from simple reward signals in a wide range of environments. When applying RL to continuous control agents in simulated physics environments, the body is usually considered to be part of the environment. However, during evolution the physical body of biological organisms and their controlling brains are co-evolved, thus exploring a much larger space of actuator/controller configurations. Put differently, the intelligence does not reside only in the agent's mind, but also in the design of their body. 
 We propose a method for uncovering strong agents, consisting of a good combination of a body and policy, based on combining RL with an evolutionary procedure. Given the resulting agent, we also propose an approach for identifying the body changes that contributed the most to the agent performance. We use the Shapley value from cooperative game theory to find the fair contribution of individual components, taking into account synergies between components. 
 We evaluate our methods in an environment similar to the the recently proposed Robo-Sumo task, where agents in a 3D environment with simulated physics compete in tipping over their opponent or pushing them out of the arena. Our results show that the proposed methods are indeed capable of generating strong agents, significantly outperforming baselines that focus on optimizing the agent policy alone. 

 A video is available at: www.youtube.com/watch?v=eei6Rgom3YY Reinforcement Learning (RL) uses a simple reward signal to derive complex agent policies, with recent progress on representing the policy using deep neural networks leading to strong results in game playing BID29 Silver et al., 2016) , robotics BID22 BID23 and dialog systems BID24 . Such algorithms were designed for stationary environments, but having multiple learning agents interact yields a non-stationary environment (Littman, 1994; BID2 . Various approaches were proposed for continuous control, required for locomotion in an physics simulator environment BID16 BID31 BID0 . Although very successful, such approaches consider the body of the agent to be fixed, simply a part of the environment. However, during evolution the physical body of biological organisms is constantly changing; thus, the controlling brain and physical body are jointly optimized, exploring a larger space of actuator-controller configurations.The interaction of evolution with learning by individual animals over their lifetime can result in superior performance (Simpson, 1953) . Researchers refer to how individual learning can enhance evolution at the species level as the ""Baldwin Effect"" (Weber & Depew, 2003) , where learning guides evolution by smoothing the fitness landscape. In learning agents, the physical shape of the body plays a double role. First, a good body has the capability of effectively exerting many forces in the environment. Second, a well-configured body is easier to learn to control, by making it simpler to identify good policies for exerting the forces. Consider a physical task which requires exerting certain forces at the right time, such as locomotion. Some bodies can exert the required forces, while others cannot. Further, some bodies exert the required forces only under a small set of exactly correct policies, whereas others have a wide range of policies under which they exert the required forces (at least approximately). In other words, some bodies have a wide ""basin of attraction"" where a learner can find a policy that exerts at least a part of the required forces; once discovering a policy in this wide basin, the learner can optimize the policy to exert the required forces.This indicates that the intelligence of agents resides not only in their mind (the controller), but also in the design of their body. Our contribution is proposing a method for uncovering strong agents, consisting of a good combination of a body and policy. This stands in contrast to the traditional paradigm, which takes the body as a given (i.e. a fixed part of the environment), as shown in FIG0 . Our technique combines RL with an evolutionary procedure. We also show how to identify the body changes that contributed the most to agent performance, taking into account synergies between them. We demonstrate our method in an environment similar to the Robo-Sumo task (AlShedivat et al., 2017) , where agents in a 3D environment with simulated physics compete in pushing the opponent out of the arena or tipping it over. This environment is based on the MuJoCo physics simulator (Todorov et al., 2012) , allowing us to easily modify the agent's body. Our results show that the proposed methods are indeed capable of generating superior agents, significantly outperforming baselines that focus on optimizing the agent policy alone.Related Work Evolving virtual creatures (EVCs) work uses genetic algorithms to evolve the structure and controllers of virtual creatures in physically simulated environments, without learning (Sims, 1994) . EVCs have a genetically defined morphology and control system that are co-evolved to perform locomotion tasks (Sims, 1994; BID7 BID4 , with some methods using a voxel-based ""soft-body"" BID4 BID17 BID28 . Most such attempts have yielded relatively simple behaviors and morphologies BID7 BID3 . One approach to enable continually increasing complex behavior is using a curriculum BID6 . Researchers hypothesized that embodied cognition, where a controller expresses its behavior through a body, may cause morphological changes to have an immediate detrimental impact on a behavior BID3 . For example, a mutation generating longer legs may harm performance with a controller optimized for shorter legs. This results in pressure to converge on a body design early in evolution, to give the controller a stable platform to optimize. This interdependence can be mitigated by giving the controller time to adapt to morphological changes, so bodies that are easier to learn to control would have an evolutionary advantage, and learning would smooth the fitness landscape; this may speed up body evolution, with the extent of learning required for new bodies decreasing over time (Simpson, 1953; Weber & Depew, 2003) .Scenarios where learning is used only in the evaluation phase of evolved agents are referred to as Baldwinian evolution (Weber & Depew, 2003) , where the results of learning are discarded when an offspring is generated. This is in contrast to ""Lamarkian evolution"" (Whitley et al., 1994; BID20 , where the result of learning is passed on to offspring. Typically the adaption stage uses a genetic algorithm operating to evolve the controller BID3 BID20 . In contrast , we use an RL algorithm to learn to control an evolving body. RL has achieved complex behaviours in continuous control tasks with fixed morphology BID16 BID31 BID0 , and has the potential to adapt to morphological changes. Our experiments evaluate the potential of evolving the bodies of a population of learning agents. We leverage Population Based Training BID18 (PBT), originally proposed to evolve parameters of the controller. To our knowledge, this is the first attempt at evolving the body of continuously controlled RL agents in a physically simulated environment.Preliminaries We apply multi-agent reinforcement learning in partially-observable Markov games (i.e. partially-observable stochastic games) BID34 Littman, 1994; BID13 . In every state, agents take actions given partial observations of the true world state, and each obtains an individual reward. Agents learn an appropriate behavior policy from past interactions. In our case, given the physics simulator state, agents observe an egocentric view consisting of the positions and velocities of their and their opponent's bodies (end effectors and joints) and distances from the edges of the pitch. Our agents have actuated hinges (one at the ""knee"" and one at the ""hip"" of every limb). The full specification for our environment (observations and actions) are given in the Appendix, and are similar to other simulated physics locomotion tasks BID16 . Every agent has its own experience in the environment, and independently learns a policy, attempting to maximize its long term γ-discounted utility, so learning is decentralized BID2 .Our analysis of the relative importance of the body changes uses cooperative game theory. We view the set of body changes as a ""team "" of players, and quantify the impact of individual components, taking into account synergies between them. Game theory studies players who can form teams, looking for fair ways of estimating the impact of individual players in a team. A cooperative game consists of a set A of n players, and a characteristic function v : 2 A → R which maps any team C ⊆ A of players to a real value, showing the performance of the team as a whole. In our case, A consists of all changes to body components resulting in the final body configuration. The marginal contribution of a player i in a team C that includes it (i.e. i ∈ C) is the change in performance resulting from excluding i: DISPLAYFORM0 We define a similar concept for permutations. Denote by π a permutation of the players ( i.e. π : {1, 2, . . . , n} → {1, 2, . . . , n} where π is a bijection), and by Π the set of all player permutations. We refer to the players occurring before i in the permutation π as the predecessors of i in π, and denote by S π (i) the predecessors of i in π, i.e. S π (i) = {j|π(j) < π(i)}. The marginal contribution of a player i in a permutation is the change in performance between i's predecessors and including i, and the performance of i's predecessors alone: BID35 ) is considered a fair allocation of the overall reward achieved by a team to the individual players in a team, reflecting the contribution of each individual player to the team's success BID12 Straffin, 1988) . It is the unique value exhibiting various fairness axioms BID9 BID11 , taking into account synergies between agents (see Section 8 in the Appendix for a detailed discussion and examples of how the Shapley value captures such synergies between body components). The Shapley value is the marginal contribution of a player , averaged across all player permutations, given by the vector DISPLAYFORM1 DISPLAYFORM2 We proposed a framework for jointly optimizing agent body and policy, combining continuous control RL agents with an evolutionary procedure for modifying agent bodies. Our analysis shows that this technique can achieve stronger agents than obtained by optimizing the controller alone. We also used game theoretic solutions to identify the most influential body changes. Several questions remain open. First, can we augment our procedure to also modify the neural network architecture of the controller, similarly to recent neural architecture optimizers BID27 ? Second, can we use similar game theoretic methods to guide the evolutionary process? Finally, How can we ensure the diversity of agents' bodies so as to improve the final performance? Darrell Whitley, V Scott Gordon, and Keith Mathias. Lamarckian evolution, the baldwin effect and function optimization. In International Conference on Parallel Problem Solving from Nature, pp. 5-15. Springer, 1994.",Reinforcement learning RL has proven powerful paradigm deriving complex behaviors simple reward signals wide range environments. When applyingRL continuous control agents simulated physics environments body is usually considered part environment. However evolution physical body biological organisms controlling brains are co-evolved thus exploring much larger space actuator/controller configurations. Put differently intelligence does not reside agent's mind also design body. propose method uncovering strong agents consisting good combination body policy based combiningRL evolutionary procedure. Given resulting agent also propose approach identifying body changes contributed agent performance. use Shapley value cooperative game theory find fair contribution individual components taking account synergies components. evaluate methods environment similar recently proposed Robo-Sumo task where agents 3D environment simulated physics compete tipping opponent pushing arena. results show proposed methods are indeed capable generating strong agents significantly outperforming baselines focus optimizing agent policy alone. video is available at:www.youtube.com/watch?v=eei6Rgom3YY Reinforcement Learning RL uses simple reward signal derive complex agent policies recent progress representing policy using deep neural networks leading strong results game playing BID29 Silver etal. 2016 robotics BID22 BID23 dialog systems BID24. algorithms were designed stationary environments multiple learning agents interact yields non-stationary environment Littman 1994;BID2. Various approaches were proposed continuous control required locomotion physics simulator environment BID16 BID31 BID0. Although successful approaches consider body agent fixed simply part environment. However evolution physical body biological organisms is constantly changing;thus controlling brain physical body are jointly optimized exploring larger space actuator-controller configurations.The interaction evolution learning individual animals lifetime can result superior performance Simpson 1953 Researchers refer how individual learning can enhance evolution species level Baldwin Effect Weber Depew 2003 where learning guides evolution smoothing fitness landscape. learning agents physical shape body plays double role. First good body has the capability effectively exerting many forces environment. Second well-configured body is easier learn control making simpler identify good policies exerting forces. Consider physical task which requires exerting certain forces right time locomotion. bodies can exert required forces others cannot. bodies exert required forces small set exactly correct policies whereas others have a wide range policies which they exert required forces least approximately words bodies have a wide basin attraction where a learner can find policy exerts least part required forces;discovering policy wide basin learner can optimize policy exert required forces.This indicates intelligence agents resides mind controller also design body. contribution is proposing method uncovering strong agents consisting good combination body policy. stands contrast traditional paradigm which takes body given.e fixed part environment shown FIG0. technique combinesRL evolutionary procedure. also show how to identify body changes contributed agent performance taking account synergies them. demonstrate method environment similar Robo-Sumo task AlShedivatetal. 2017 where agents 3D environment simulated physics compete pushing opponent arena tipping over. environment is based MuJoCo physics simulator Todorovetal. 2012 allowingus easily modify agent's body. results show proposed methods are indeed capable generating superior agents significantly outperforming baselines focus optimizing agent policy alone.Related Work Evolving virtual creatures EVCs work uses genetic algorithms evolve structure controllers virtual creatures physically simulated environments without learning Sims 1994 EVCs have a genetically defined morphology control system are co-evolved perform locomotion tasks Sims 1994;BID7 BID4 methods using voxel-based soft-body BID4 BID17 BID28. attempts have yielded relatively simple behaviors morphologies BID7 BID3. One approach enable continually increasing complex behavior is using curriculum BID6. Researchers hypothesized embodied cognition where a controller expresses behavior body may cause morphological changes have an immediate detrimental impact behavior BID3. example mutation generating longer legs may harm performance controller optimized shorter legs. results pressure converge body design early evolution give controller stable platform optimize. interdependence can be mitigated giving controller time adapt morphological changes bodies are easier learn control would have an evolutionary advantage learning would smooth fitness landscape;may speed body evolution extent learning required new bodies decreasing time Simpson 1953;Weber Depew 2003.Scenarios where learning is used evaluation phase evolved agents are referred Baldwinian evolution Weber Depew 2003 where the results learning are discarded when an offspring is generated. is in contrast Lamarkian evolution Whitleyetal. 1994;BID20 where the result learning is passed offspring. Typically adaption stage uses genetic algorithm operating evolve controller BID3 BID20. contrast can we use RL algorithm learn control evolving body. RL has achieved complex behaviours continuous control tasks fixed morphology BID16 BID31 BID0 has the potential adapt morphological changes. experiments evaluate potential evolving bodies population learning agents. leverage Population Based Training BID18 PBT originally proposed evolve parameters controller. knowledge is the first attempt evolving body continuously controlled RL agents physically simulated environment.Preliminaries apply multi-agent reinforcement learning partially-observable Markov games.e partially-observable stochastic games BID34 Littman 1994;BID13. every state where agents take actions given partial observations true world state obtains individual reward. Agents learn appropriate behavior policy past interactions. case given physics simulator state where agents observe egocentric view consisting positions velocities opponent's bodies end effectors joints distances edges pitch. agents have actuated hinges one knee one hip every limb full specification environment observations actions are given Appendix are similar simulated physics locomotion tasks BID16. Every agent has its own experience environment independently learns policy attempting maximize long term γ-discounted utility learning is decentralized BID2.Our analysis relative importance body changes uses cooperative game theory. view set body changes team players quantify impact individual components taking account synergies them. Game theory studies players who can form teams looking fair ways estimating impact individual players team. cooperative game consists set n players characteristic functionv:2 →R which maps teamC⊆ players real value showing performance team whole. case consists changes body components resulting final body configuration. marginal contribution player teamC includes.e ∈C is the change performance resulting excluding i:DISPLAYFORM0 define similar concept permutations. Denote π permutation players.eπ:1 2 n → 1 2 n whereπ is a bijection Π set player permutations. refer players occurring permutationπ predecessors π denote π predecessors π.e π j|π j π marginal contribution player permutation is the change performance i's predecessors including performance i's predecessors alone:BID35 is considered fair allocation overall reward achieved team how individual players team reflecting contribution individual player team's success BID12 Straffin 1988 is unique value exhibiting various fairness axioms BID9 BID11 taking account synergies agents see Section8 Appendix detailed discussion examples how the Shapley value captures synergies body components Shapley value is the marginal contribution player averaged across player permutations given vector DISPLAYFORM1 DISPLAYFORM2 proposed framework jointly optimizing agent body policy combining continuous controlRL agents evolutionary procedure modifying agent bodies. analysis shows technique can achieve stronger agents obtained optimizing controller alone. also used game theoretic solutions identify influential body changes. Several questions remain open. First can we augment procedure also modify neural network architecture controller similarly recent neural architecture optimizers BID27? Second can we use similar game theoretic methods guide evolutionary process? Finally How can we ensure diversity agents' bodies improve final performance? Darrell Whitley V Scott Gordon Keith Mathias. Lamarckian evolution baldwin effect function optimization. International Conference Parallel Problem Solving Nature pp. 5-15 Springer 1994.,2263,1469,794,0.03,1.541,2025/11/05 17:19:01,0.01,1.408,0.6573208722741429,779.134
"Many practical reinforcement learning problems contain catastrophic states that the optimal policy visits infrequently or never. Even on toy problems, deep reinforcement learners periodically revisit these states, once they are forgotten under a new policy. In this paper, we introduce intrinsic fear, a learned reward shaping that accelerates deep reinforcement learning and guards oscillating policies against periodic catastrophes. Our approach incorporates a second model trained via supervised learning to predict the probability of imminent catastrophe. This score acts as a penalty on the Q-learning objective. Our theoretical analysis demonstrates that the perturbed objective yields the same average return under strong assumptions and an $\epsilon$-close average return under weaker assumptions. Our analysis also shows robustness to classification errors. Equipped with intrinsic fear, our DQNs solve the toy environments and improve on the Atari games Seaquest, Asteroids, and Freeway. Following success on Atari games BID20 and the board game Go BID28 , many researchers have begun exploring practical applications of deep reinforcement learning (DRL). Some investigated applications include robotics BID15 , dialogue systems BID6 BID17 , energy management BID23 , and self-driving cars BID26 . Amid this push to apply DRL, we might ask, can we trust these agents in the wild? Agents acting in real-world environments might possess the ability to cause catastrophic outcomes. Consider a self-driving car that might hit pedestrians or a domestic robot that might injure a child. We might hope to prevent DRL agents from ever making catastrophic mistakes. But doing so requires extensive prior knowledge of the environment in order to constrain the exploration of policy space BID7 .Many conflicting definitions of safety and catastrophe exist, a problem that invites further philosophical consideration. In this paper, we introduce a specific but plausible notion of avoidable catastrophes. These are states that prior knowledge dictates an optimal policy should never visit. For example , we might believe that an optimal self-driving algorithm would never hit a pedestrian. Moreover, we assume that an optimal policy never even comes near an avoidable catastrophe state. We define proximity in trajectory space, and not by the geometry of feature space. We denote states proximal to avoidable catastrophes as danger states. While we don't assume prior knowledge of which states are dangerous, we do assume the existence of a catastrophe detector. After encountering a catastrophic state, an agent can realize this and take action to avoid dangerous states in the future.Given this definition, we address two challenges: First, can we expect DRL agents, after experiencing some number of catastrophic failures, to avoid perpetually making the same mistakes? Second, can we use our prior knowledge that catastrophes should be kept at a distance to accelerate learning of a DRL agent? Our experiments show that even on toy problems, the deep Q-network (DQN), a basic algorithm behind many of today's state-of-the-art DRL systems, struggles on both counts. Even in toy environments , DQNs may encounter thousands of catastrophes before learning to avoid them and are susceptible to repeating old errors. We call this latter problem the Sisyphean curse.This poses a formidable obstacle to using DQNs in the real world. How can we hand over responsibility for consequential actions (control of a car, say) to a DRL agent if it may be doomed to periodically remake every kind of mistake, however grave, so long as it continues to learn? Imagine a self-driving car that had to periodically hit a few pedestrians in order to remember that is undesirable. In the tabular setting, an RL agent never forgets the learned dynamics of its environment, even as its policy evolves. Moreover, if the Markovian assumption holds, eventual convergence to a globally optimal policy is guaranteed. Unfortunately, the tabular approach becomes infeasible in high-dimensional, continuous state spaces.The trouble for DQNs owes to the use of function approximation BID22 . When training a DQN, we successively update a neural network based on experiences. These experiences might be sampled in an online fashion, from a trailing window (experience replay buffer), or uniformly from all past experiences. Regardless of which mode we use to train the network , eventually, states that a learned policy never encounters will come to form an infinitesimally small region of the training distribution. At such times, our networks are subject to the classic problem of catastrophic interference BID19 BID18 . Nothing prevents the DQN's policy from drifting back towards a policy that revisits long-forgotten catastrophic mistakes.More formally, we characterize the problem as unfolding in the following steps: (i) Training under distribution D, our agent produces a safe policy π s that avoids catastrophes (ii) Collecting data generated under π s yields a new distribution of transitions D (iii) Training under D , the agent produces π d , a policy that once again experiences avoidable catastrophes. To illustrate the brittleness of modern DRL algorithms, we introduce a simple pathological problem called Adventure Seeker. This problem consists of a one-dimensional continuous state, two actions , simple dynamics, and a clear analytic solution. Nevertheless, the DQN fails. We then show that similar dynamics exist in the classic RL environment Cart-Pole .In this paper, to combat these problems, we propose intrinsic fear. In this approach, we train a supervised fear model that predicts which states are likely to lead to a catastrophe within k r steps. The output of the fear model (a probability), scaled by a fear factor penalizes the Q-learning target. Our approach draws inspiration from intrinsic motivation BID5 . However, instead of perturbing the reward function to encourage the discovery of novel states, we perturb it to discourage revisiting catastrophic states.We validate the approach both empirically and theoretically. Our experiments address both our Adventure Seeker problem and Cartpole as well as the Atari games Seaquest and Asteroids, and Freeway. For these environments, we label each loss of a life as a catastrophic state. On the toy environments, the intrinsic fear agent learns to avoid death indefinitely , achieving unbounded reward per episode. On Seaquest and Asteroids, the intrinsic fear agent improves markedly and on Freeway the improvement is dramatic. Theoretically, we demonstrate the following: First, we prove that when the reward is bounded and the optimal policy rarely visits the catastrophic states, the policy learned on the altered value function has return similar to the optimal policy on the original value function. Second we prove that the method is robust to noise in the danger model. Our experiments demonstrate that DQNs are susceptible to periodically repeating mistakes, however bad, raising questions about their real-world utility when harm can come of actions. While it's easy to visualize these problems on toy examples, similar dynamics are embedded in more complex domains. Consider a domestic robot acting as a barber. The robot might receive positive feedback for giving a closer shave. This reward encourages closer contact at a steeper angle. Of course, the shape of this reward function belies the catastrophe lurking just past the optimal shave. Similar dynamics might be imagines in a vehicle that is rewarded for traveling faster but could risk an accident with excessive speed. Our results with the intrinsic fear model suggest that with only a small amount of prior knowledge (the ability to recognize catastrophe states after the fact), we can simultaneously accelerate learning and avoid catastrophic states. This work represents a first step towards combating some issues relating to safety in RL stemming from catastrophic forgetting.",Many practical reinforcement learning problems contain catastrophic states optimal policy visits infrequently never. Even toy problems deep reinforcement learners periodically revisit states are forgotten new policy. paper introduce intrinsic fear learned reward shaping accelerates deep reinforcement learning guards oscillating policies periodic catastrophes. approach incorporates second model trained via supervised learning predict probability imminent catastrophe. score acts penalty Q-learning objective. theoretical analysis demonstrates perturbed objective yields average return strong assumptions $\epsilon $-close average return weaker assumptions. analysis also shows robustness classification errors. Equipped intrinsic fear DQNs solve toy environments improve Atari games Seaquest Asteroids Freeway. Following success Atari games BID20 board game Go BID28 many researchers have begun exploring practical applications deep reinforcement learning DRL investigated applications include robotics BID15 dialogue systems BID6 BID17 energy management BID23 self-driving cars BID26. Amid push apply DRL might ask can we trust agents wild? Agents acting real-world environments might possess ability cause catastrophic outcomes. Consider self-driving car might hit pedestrians domestic robot might injure child. might hope prevent DRL agents ever making catastrophic mistakes. requires extensive prior knowledge environment order constrain exploration policy space BID7.Many conflicting definitions safety catastrophe exist problem invites philosophical consideration. paper introduce specific plausible notion avoidable catastrophes. are states prior knowledge dictates optimal policy should never visit. example might believe optimal self-driving algorithm would never hit pedestrian. Moreover do assume optimal policy never even comes near avoidable catastrophe state. define proximity trajectory space geometry feature space. denote states proximal avoidable catastrophes danger states. assume prior knowledge which states are dangerous do assume existence catastrophe detector. encountering catastrophic state agent can realize take action avoid dangerous states future.Given definition address two challenges:First can we expect DRL agents experiencing number catastrophic failures avoid perpetually making mistakes? Second can we use prior knowledge catastrophes should be kept distance accelerate learning DRL agent? experiments show even toy problems deep Q-network DQN basic algorithm behind many today's state-of-the-art DRL systems struggles counts. Even toy environments DQNs may encounter thousands catastrophes learning avoid are susceptible repeating old errors. call latter problem Sisyphean curse.This poses formidable obstacle using DQNs real world. How can we hand responsibility consequential actions control car say DRL agent may doomed periodically remake every kind mistake however grave long continues learn? Imagine self-driving car had to periodically hit pedestrians order remember is undesirable. tabular setting RL agent never forgets learned dynamics environment even policy evolves. Moreover if the Markovian assumption holds eventual convergence globally optimal policy is guaranteed. Unfortunately tabular approach becomes infeasible high-dimensional continuous state spaces.The trouble DQNs owes use function approximation BID22. When training DQN successively update neural network based experiences. experiences might sampled online fashion trailing window experience replay buffer uniformly past experiences. Regardless which mode use train network eventually states learned policy never encounters will come form infinitesimally small region training distribution. times networks are subject classic problem catastrophic interference BID19 BID18. Nothing prevents DQN's policy drifting back towards policy revisits long-forgotten catastrophic mistakes.More formally characterize problem unfolding following steps:Training distribution agent produces safe policyπ avoids catastrophes ii Collecting data generated π yields new distribution transitions iii Training agent producesπ policy experiences avoidable catastrophes. illustrate brittleness modern DRL algorithms introduce simple pathological problem called Adventure Seeker. problem consists one-dimensional continuous state two actions simple dynamics clear analytic solution. Nevertheless DQN fails. show similar dynamics exist classic RL environment Cart-Pole.In paper combat problems propose intrinsic fear. approach train supervised fear model predicts which states are likely lead catastrophe withinkr steps. output fear model probability scaled fear factor penalizes Q-learning target. approach draws inspiration intrinsic motivation BID5. However instead perturbing reward function encourage discovery novel states perturb discourage revisiting catastrophic states.We validate approach empirically theoretically. experiments address Adventure Seeker problem Cartpole well Atari games Seaquest Asteroids Freeway. environments label loss life catastrophic state. toy environments intrinsic fear agent learns avoid death indefinitely achieving unbounded reward per episode. Seaquest Asteroids intrinsic fear agent improves markedly Freeway improvement is dramatic. Theoretically demonstrate following:First prove when the reward is bounded optimal policy rarely visits catastrophic states policy learned altered value function has return similar optimal policy original value function. Second prove method is robust noise danger model. experiments demonstrate DQNs are susceptible periodically repeating mistakes however bad raising questions real-world utility when harm can come actions. easy visualize problems toy examples similar dynamics are embedded complex domains. Consider domestic robot acting barber. robot might receive positive feedback giving closer shave. reward encourages closer contact steeper angle. course shape reward function belies catastrophe lurking past optimal shave. Similar dynamics might imagines vehicle is rewarded traveling faster could risk accident excessive speed. results intrinsic fear model suggest small amount prior knowledge ability recognize catastrophe states fact can simultaneously accelerate learning avoid catastrophic states. work represents first step towards combating issues relating safety RL stemming catastrophic forgetting.,1476,978,498,0.015,1.509,2025/11/05 17:19:01,0.01,1.257,0.5576323987538936,485.332
"Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other topological spaces---such as a sphere S^2 or a unit ball B^3---entails unique challenges. In this work, we propose a novel `""volumetric convolution"" operation that can effectively convolve arbitrary functions in B^3. We develop a theoretical framework for ""volumetric convolution"" based on Zernike polynomials and efficiently implement it as a differentiable and an easily pluggable layer for deep networks. Furthermore, our formulation leads to derivation of a  novel formula to measure the symmetry of a function in B^3 around an arbitrary axis, that is useful in 3D shape analysis tasks. We demonstrate the efficacy of proposed volumetric convolution operation on a possible use-case i.e., 3D object recognition task. Convolution-based deep neural networks have performed exceedingly well on 2D representation learning tasks BID11 BID7 . The convolution layers perform parameter sharing to learn repetitive features across the spatial domain while having lower computational cost by using local neuron connectivity. However, most state-of-the-art convolutional networks can only work on Euclidean geometries and their extension to other topological spaces e.g., spheres, is an open research problem. Remarkably, the adaptation of convolutional networks to spherical domain can advance key application areas such as robotics, geoscience and medical imaging. Some recent efforts have been reported in the literature that aim to extend convolutional networks to spherical signals. Initial progress was made by BID1 , who performed conventional planar convolution with a careful padding on a spherical-polar representation and its cube-sphere transformation BID17 . A recent pioneering contribution by used harmonic analysis to perform efficient convolution on the surface of the sphere (S 2 ) to achieve rotational equivariance. These works, however, do not systematically consider radial information in a 3D shape and the feature representations are learned at specified radii. Specifically, estimated similarity between spherical surface and convolutional filter in S 2 , where the kernel can be translated in S 2 . Furthermore, BID23 recently solved the more general problem of SE(3) equivariance by modeling 3D data as dense vector fields in 3D Euclidean space. In this work however, we focus on B 3 to achieve the equivariance to SO(3).In this paper, we propose a novel approach to perform volumetric convolutions inside unit ball (B 3 ) that explicitly learns representations across the radial axis. Although we derive generic formulas to convolve functions in B 3 , we experiment on one possible use case in this work, i.e., 3D shape recognition. In comparison to closely related spherical convolution approaches, modeling and convolving 3D shapes in B 3 entails two key advantages: 'volumetric convolution' can capture both 2D texture and 3D shape features and can handle non-polar 3D shapes. We develop the theory of volumetric convolution using orthogonal Zernike polynomials BID3 , and use careful approximations to efficiently implement it using low computational-cost matrix multiplications. Our experimental results demonstrate significant boost over spherical convolution and that confirm the high discriminative ability of features learned through volumetric convolution.Furthermore, we derive an explicit formula based on Zernike Polynomials to measure the axial symmetry of a function in B 3 , around an arbitrary axis. While this formula can be useful in many function analysis tasks, here we demonstrate one particular use-case with relevance to 3D shape recognition. Specifically, we use the the derived formula to propose a hand-crafted descriptor that accurately encodes the axial symmetry of a 3D shape. Moreover, we decompose the implementation of both volumetric convolution and axial symmetry measurement into differentiable steps, which enables them to be integrated to any end-to-end architecture.Finally, we propose an experimental architecture to demonstrate the practical usefulness of proposed operations. We use a capsule network after the convolution layer as it allows us to directly compare feature discriminability of spherical convolution and volumetric convolution without any bias. In other words, the optimum deep architecture for spherical convolution may not be the same for volumetric convolution. Capsules, however, do not deteriorate extracted features and the final accuracy only depends on the richness of input shape features. Therefore, a fair comparison between spherical and volumetric convolutions can be done by simply replacing the convolution layer.It is worth pointing out that the proposed experimental architecture is only a one possible example out of many possible architectures, and is primarily focused on three factors: 1) Capture useful features with a relatively shallow network compared to state-of-the-art. 2) Show richness of computed features through clear improvements over spherical convolution. 3) Demonstrate the usefulness of the volumetric convolution and axial symmetry feature layers as fully differentiable and easily pluggable layers, which can be used as building blocks for end-to-end deep architectures.The main contributions of this work include:• Development of the theory for volumetric convolution that can efficiently model functions in B 3 .• Implementation of the proposed volumetric convolution as a fully differentiable module that can be plugged into any end-to-end deep learning framework.• The first approach to perform volumetric convolution on 3D objects that can simultaneously model 2D (appearance) and 3D (shape) features.• A novel formula to measure the axial symmetry of a function defined in B 3 , around an arbitrary axis using Zernike polynomials.• An experimental end-to-end trainable framework that combines hand-crafted feature representation with automatically learned representations to obtain rich 3D shape descriptors.The rest of the paper is structured as follows. In Sec. 2 we introduce the overall problem and our proposed solution . Sec. 3 presents an overview of 3D Zernike polynomials. Then, in Sec. 4 and Sec. 5 we derive the proposed volumetric convolution and axial symmetry measurement formula respectively. Sec. 6.2 presents our experimental architecture, and in Sec. 7 we show the effectiveness of the derived operators through extensive experiments. Finally, we conclude the paper in Sec. 8. In this work, we derive a novel 'volumetric convolution' using 3D Zernike polynomials, which can learn feature representations in B 3 . We develop the underlying theoretical foundations for volumetric convolution and demonstrate how it can be efficiently computed and implemented using low-cost matrix multiplications. Furthermore, we propose a novel, fully differentiable method to measure the axial symmetry of a function in B 3 around an arbitrary axis, using 3D Zernike polynomials. Finally, using these operations as building tools, we propose an experimental architecture, that gives competitive results to state-of-the-art with a relatively shallow network, in 3D object recognition task. An immediate extension to this work would be to explore weight sharing along the radius of the sphere.Let f (θ, φ, r) and g(θ, φ, r) be the object function and kernel function (symmetric around north pole) respectively. Then volumetric convolution is defined as, f * g(θ, φ) =< f, τ (θ,φ) g >Applying the rotation η (α,β,γ) to f , we get, η (α,β,γ) (f ) * g(θ, φ) =< η (α,β,γ) (f ), τ (θ,φ) g >By the result 33, we have, DISPLAYFORM0 However, since η α,β,γ (g) = τ α,β (g) we get, η (α,β,γ) (f ) * g(θ, φ) =< f, τ (θ−α,φ−β,) g >We know that, f * g(θ, φ) =< f, τ (θ,φ) g >= η (α,β,γ) (f ) * g(θ, φ) = (f * g)(θ − α, φ − β)η (α,β,γ) (f ) * g(θ, φ) = τ (α,β) (f * g) (Hence, we achieve equivariance over 3D rotations.",Convolution is an efficient technique obtain abstract feature representations using hierarchical layers deep networks. Although performing convolution Euclidean geometries is fairly straightforward extension topological spaces -such sphere S^2 unit ball B^3 -entails unique challenges. work propose novel volumetric convolution operation can effectively convolve arbitrary functions B^3 develop theoretical framework volumetric convolution based Zernike polynomials efficiently implement differentiable easily pluggable layer deep networks. Furthermore formulation leads derivation novel formula measure symmetry function B^3 around arbitrary axis is useful 3D shape analysis tasks. demonstrate efficacy proposed volumetric convolution operation possible use-case.e 3D object recognition task. Convolution-based deep neural networks have performed exceedingly well 2D representation learning tasks BID11 BID7. convolution layers perform parameter sharing learn repetitive features across spatial domain lower computational cost using local neuron connectivity. However state-of-the-art convolutional networks can only work Euclidean geometries extension topological spacese.g spheres is an open research problem. Remarkably adaptation convolutional networks spherical domain can advance key application areas robotics geoscience medical imaging. recent efforts have been reported literature aim extend convolutional networks spherical signals. Initial progress was made BID1 who performed conventional planar convolution careful padding spherical-polar representation cube-sphere transformation BID17. recent pioneering contribution used harmonic analysis perform efficient convolution surface sphere 2 achieve rotational equivariance. works however do not systematically consider radial information 3D shape feature representations are learned specified radii. Specifically estimated similarity spherical surface convolutional filter 2 where the kernel can be translated 2. Furthermore BID23 recently solved general problem SE 3 equivariance modeling 3D data dense vector fields 3D Euclidean space. work however focus B3 achieve equivariance 3.In paper propose novel approach perform volumetric convolutions inside unit ball B3 explicitly learns representations across radial axis. Although derive generic formulas convolve functions B3 experiment one possible use case work.e 3D shape recognition. comparison closely related spherical convolution approaches modeling convolving 3D shapes B 3 entails two key advantages:'volumetric convolution' can capture 2D texture 3D shape features can handle non-polar 3D shapes. develop theory volumetric convolution using orthogonal Zernike polynomials BID3 use careful approximations efficiently implement using low computational-cost matrix multiplications. experimental results demonstrate significant boost spherical convolution confirm high discriminative ability features learned volumetric convolution.Furthermore derive explicit formula based Zernike Polynomials measure axial symmetry function B3 around arbitrary axis. formula can be useful many function analysis tasks demonstrate one particular use-case relevance 3D shape recognition. Specifically use derived formula propose hand-crafted descriptor accurately encodes axial symmetry 3D shape. Moreover decompose implementation volumetric convolution axial symmetry measurement differentiable steps which enables integrated end-to-end architecture.Finally propose experimental architecture demonstrate practical usefulness proposed operations. use capsule network convolution layer allowsus directly compare feature discriminability spherical convolution volumetric convolution without bias. words optimum deep architecture spherical convolution may volumetric convolution. Capsules however do not deteriorate extracted features final accuracy depends richness input shape features. Therefore fair comparison spherical volumetric convolutions can be done simply replacing convolution layer.It is worth pointing proposed experimental architecture is only a one possible example many possible architectures is primarily focused three factors:1 Capture useful features relatively shallow network compared state-of-the-art2 Show richness computed features clear improvements spherical convolution. 3 Demonstrate usefulness volumetric convolution axial symmetry feature layers fully differentiable easily pluggable layers which can be used building blocks end-to-end deep architectures.The main contributions work include:• Development theory volumetric convolution can efficiently model functions B 3.• Implementation proposed volumetric convolution fully differentiable module can be plugged end-to-end deep learning framework.• first approach perform volumetric convolution 3D objects can simultaneously model2D appearance 3D shape features.• novel formula measure axial symmetry function defined B3 around arbitrary axis using Zernike polynomials.• experimental end-to-end trainable framework combines hand-crafted feature representation automatically learned representations obtain rich 3D shape descriptors.The rest paper is structured follows. Sec. 2 introduce overall problem proposed solution. Sec. 3 presents overview 3D Zernike polynomials. Sec. 4 Sec. 5 derive proposed volumetric convolution axial symmetry measurement formula respectively. Sec. 6.2 presents experimental architecture Sec. 7 show effectiveness derived operators extensive experiments. Finally conclude paper Sec. 8. work derive novel 'volumetric convolution' using 3D Zernike polynomials which can learn feature representations B3. develop underlying theoretical foundations volumetric convolution demonstrate how it can be efficiently computed implemented using low-cost matrix multiplications. Furthermore propose novel fully differentiable method measure axial symmetry function B 3 around arbitrary axis using 3D Zernike polynomials. Finally using operations building tools propose experimental architecture gives competitive results state-of-the-art relatively shallow network 3D object recognition task. immediate extension work would explore weight sharing along radius sphere.Letf θ φ r g θ φ r object function kernel function symmetric around north pole respectively. volumetric convolution is defined f*g θ φ f τ θ φ g Applying rotationη α β γ f get η α β γ f *g θ φ η α β γ f τ θ φ g result33 DISPLAYFORM0 However sinceηα β γ g τα β g get η α β γ f *g θ φ f τ θ−α φ−β g know f*g θ φ f τ θ φ g η α β γ f *g θ φ f*g θ−α φ−β η α β γ f *g θ φ τ α β f*g Hence achieve equivariance 3D rotations.,1705,1150,555,0.024,1.483,2025/11/05 17:19:01,0.01,1.594,0.4766355140186917,503.648
"Learning in environments with large state and action spaces, and sparse rewards, can hinder a Reinforcement Learning (RL) agent’s learning through trial-and-error. For instance, following natural language instructions on the Web (such as booking a flight ticket) leads to RL settings where input vocabulary and number of actionable elements on a page can grow very large. Even though recent approaches improve the success rate on relatively simple environments with the help of human demonstrations to guide the exploration, they still fail in environments where the set of possible instructions can reach millions. We approach the aforementioned problems from a different perspective and propose guided RL approaches that can generate unbounded amount of experience for an agent to learn from. Instead of learning from a complicated instruction with a large vocabulary, we decompose it into multiple sub-instructions and schedule a curriculum in which an agent is tasked with a gradually increasing subset of these relatively easier sub-instructions. In addition, when the expert demonstrations are not available, we propose a novel meta-learning framework that generates new instruction following tasks and trains the agent more effectively. We train DQN, deep reinforcement learning agent, with Q-value function approximated with a novel QWeb neural network architecture on these smaller, synthetic instructions. We evaluate the ability of our agent to generalize to new instructions onWorld of Bits benchmark, on forms with up to 100 elements, supporting 14 million possible instructions. The QWeb agent outperforms the baseline without using any human demonstration achieving 100% success rate on several difficult environments. We study the problem of training reinforcement learning agents to navigate the Web (navigator agent) by following certain instructions, such as book a flight ticket or interact with a social media web site, that require learning through large state and action spaces with sparse and delayed rewards. In a typical web environment, an agent might need to carefully navigate through a large number of web elements to follow highly dynamic instructions formulated from large vocabularies. For example, in the case of an instruction ""Book a flight from WTK to LON on 21-Oct-2016"", the agent needs to fill out the origin and destination drop downs with the correct airport codes, select a date, hit submit button, and select the cheapest flight among all the options. Note the difficulty of the task: The agent can fill-out the first three fields in any order. The options for selection are numerous, among all possible airport / date combination only one is correct. The form can only be submitted once all the three fields are filled in. At that point the web environment / web page changes, and flight selection becomes possible. Then the agent can select and book a flight. Reaching the true objective in these tasks through trial-and-error is cumbersome, and reinforcement learning with the sparse reward results in the majority of the episodes generating no signal at all. The problem is exacerbated when learning from large set of instructions where visiting each option could be infeasible. As an example, in the flight-booking environment the number of possible instructions / tasks can grow to more than 14 millions, with more than 1700 vocabulary words and approximately 100 web elements at each episode.A common remedy for these problems is guiding the exploration towards more valuable states by learning from human demonstrations and using pretrained word embeddings. Previous work BID7 ; BID11 ) has shown that the success rate of an agent on Web navigation tasks (Miniwob BID11 )) can be improved via human demonstrations and pretrained word embeddings; however, they indeed use separate demonstrations for each environment and as the complexity of an environment increases, these methods fail to generate any successful episode (such as flight booking and social media interaction environments). But in environments with large state and action spaces, gathering the human demonstrations does not scale, as the training needs large number of human demonstrations for each environment.In this work, we present two methods for reinforcement learning in large state and action spaces with sparse rewards for the web navigation. First, when expert demonstrations or an instructionfollowing policy (ORACLE) are available, we develop curriculum-DQN, a curriculum learning that guides the exploration by starting with an easier instruction following task and gradually increasing the difficulty over a number of training steps. Curriculum-DQN decomposes an instruction into multiple sub-instructions and assigns the web navigation agent (navigator) with an easier task of solving only a subset of these sub-instructions ( FIG0 ). An expert instruction-following policy (ORACLE) places the agent and goal closer to each other.Second, when demonstrations and ORACLE policies are not available, we present a novel metalearning framework that trains a generative model for expert instruction-following demonstrations using an arbitrary web navigation policy without instructions. The key insight here is that we can treat an arbitrary navigation policy (e. g. random policy) as if it was an expert instruction-following policy for some hidden instruction. If we recover the underlying instruction, we can autonomously generate new expert demonstrations, and use them to improve the training of the navigator. Intuitively, generating an instruction from a policy is easier than following an instruction, as the navigator does not need to interact with a dynamic web page and take complicated actions. Motivated by these observations, we develop an instructor agent, a meta-trainer, that trains the navigator by generating new expert demonstrations.In addition to the two trainers, curriculum-DQN and instructor meta-trainer, the paper introduces two novel neural network architectures for encoding web navigation Q-value functions, QWeb and INET, combining self-attention, LSTMs, and shallow encoding. QWeb serves as Q-value function for the learned instruction-following policy, trained with either curriculum-DQN or instructor agent. The INET is Q-value function for the instructor agent. We test the performance of our approaches on a set of Miniwob and Miniwob++ tasks BID7 ). We show that both approaches improve upon a strong baseline and outperform previous state-of-the-art.While we focus on the Web navigation, the methods presented here, automated curriculum generation with attention-equipped DQN, might be of interest to the larger task planning community working to solve goal-oriented tasks in large discrete state and action Markov Decision Processes. In this work, we presented two approaches for training DQN agents in difficult web navigation environments with sparse rewards and large state and action spaces, one in presence of expert demonstrations and the other without the demonstrations. In both cases, we use dense, potential-based rewards to augment the training. When an expert demonstrations are available, curriculum learning decomposes a difficult instruction into multiple sub-instructions and tasks the agent with incrementally larger subset of these sub-instructions; ultimately uncovering the original instruction. When expert demonstrations are not available, we introduced a meta-trainer that generates goal state and instruction pairs with dense reward signals for the QWeb to train more efficiently. Our models outperform previous state-of-the-art models on challenging environments without using any human demonstration. The evaluations also indicate that having a high-quality expert demonstrations is important, as the policies trained from curriculum over demonstrations outperform policies that generate nonperfect demonstrations. In future work, we plan to apply our models on a broader set of navigation tasks with large discrete state and actions, and will experiment with other signals to utilize in the meta-trainer, such as supervised pre-training using behavioral cloning, scheduling a curriculum from the episodes generated by meta-trainer, using meta-trainer as off-policy learning, etc. ACKNOWLEDGMENTSWe thank Amir Fayazi for his help with integrating the Miniwob benchmarks into our ecosystem. We are grateful to Pranav Khaitan and the Deep Dialogue team at Google Research for discussions, as well as to the anonymous reviewers for their valuable feedback.",Learning environments large state action spaces sparse rewards can hinder Reinforcement Learning RL agents learning trial-and-error instance following natural language instructions Web booking flight ticket leads RL settings where input vocabulary number actionable elements page can grow large. Even though recent approaches improve success rate relatively simple environments help human demonstrations guide exploration still fail environments where the set possible instructions can reach millions. approach aforementioned problems different perspective propose guided RL approaches can generate unbounded amount experience agent learn from. Instead learning complicated instruction large vocabulary decompose multiple sub-instructions schedule curriculum which an agent is tasked gradually increasing subset relatively easier sub-instructions addition when the when expert demonstrations are not are available propose novel meta-learning framework generates new instruction following tasks trains agent effectively. train DQN deep reinforcement learning agent Q-value function approximated novel QWeb neural network architecture smaller synthetic instructions. evaluate ability agent generalize new instructions onWorld Bits benchmark forms 100 elements supporting 14 million possible instructions. QWeb agent outperforms baseline without using human demonstration achieving 100% success rate several difficult environments. study problem training reinforcement learning agents navigate Web navigator agent following certain instructions book flight ticket interact social media web site require learning large state action spaces sparse delayed rewards. typical web environment agent might need carefully navigate large number web elements follow highly dynamic instructions formulated large vocabularies. example case instruction Book flight WTK LON 21-Oct-2016 agent needs fill origin destination drop downs correct airport codes select date hit submit button select cheapest flight among options. Note difficulty task:agent can fill-out first three fields order. options selection are numerous among possible airport/date combination one is correct. form can only be submitted three fields are filled in. point web environment/web page changes flight selection becomes possible. agent can select book flight. Reaching true objective tasks trial-and-error is cumbersome reinforcement learning sparse reward results majority episodes generating signal all. problem is exacerbated when learning large set instructions where visiting option could infeasible. example flight-booking environment number possible instructions/tasks can grow 14 millions 1700 vocabulary words approximately 100 web elements episode.A common remedy problems is guiding exploration towards valuable states learning human demonstrations using pretrained word embeddings. Previous work BID7;BID11 has shown success rate agent Web navigation tasks Miniwob BID11 can be improved via human demonstrations pretrained word embeddings;however indeed use separate demonstrations environment complexity environment increases methods fail generate successful episode flight booking social media interaction environments environments large state action spaces gathering human demonstrations does not scale training needs large number human demonstrations environment.In work present two methods reinforcement learning large state action spaces sparse rewards web navigation. First when the when expert demonstrations instructionfollowing policy ORACLE are available develop curriculum-DQN curriculum learning guides exploration starting easier instruction following task gradually increasing difficulty number training steps. Curriculum-DQN decomposes instruction multiple sub-instructions assigns web navigation agent navigator easier task solving subset sub-instructions FIG0 if it expert instruction-following policy ORACLE places agent goal closer other.Second when demonstrations ORACLE policies are not are available present novel metalearning framework trains generative model expert instruction-following demonstrations using arbitrary web navigation policy without instructions. key insight is thatwe can treat arbitrary navigation policy e. g. random policy ifit wasan expert instruction-following policy hidden instruction. If we recover underlying instruction can autonomously generate new expert demonstrations use improve training navigator. Intuitively generating instruction policy is easier following instruction navigator does not need interact dynamic web page take complicated actions. Motivated observations develop instructor agent meta-trainer trains navigator generating new expert demonstrations.In addition two trainers curriculum-DQN instructor meta-trainer paper introduces two novel neural network architectures encoding web navigation Q-value functions QWeb INET combining self-attention LSTMs shallow encoding. QWeb serves Q-value function learned instruction-following policy trained either curriculum-DQN instructor agent. INET is Q-value function instructor agent. test performance approaches set Miniwob Miniwob++tasks BID7 show approaches improve upon strong baseline outperform previous state-of-the-art.While focus Web navigation methods presented automated curriculum generation attention-equipped DQN might interest larger task planning community working solve goal-oriented tasks large discrete state action Markov Decision Processes. work presented two approaches training DQN agents difficult web navigation environments sparse rewards large state action spaces one presence expert demonstrations without demonstrations. cases use dense potential-based rewards augment training. When an When expert demonstrations are not are available curriculum learning decomposes difficult instruction multiple sub-instructions tasks agent incrementally larger subset sub-instructions ultimately uncovering original instruction. When an When expert demonstrations are not are available introduced meta-trainer generates goal state instruction pairs dense reward signals QWeb train efficiently. models outperform previous state-of-the-art models challenging environments without using human demonstration. evaluations also indicate high-quality expert demonstrations is important policies trained curriculum demonstrations outperform policies can generate nonperfect demonstrations. future work plan apply models broader set navigation tasks large discrete state actions will experiment signals utilize meta-trainer supervised pre-training using behavioral cloning scheduling curriculum episodes generated meta-trainer using meta-trainer off-policy learning etc. ACKNOWLEDGMENTSWe thank Amir Fayazi help integrating Miniwob benchmarks ecosystem. are grateful Pranav Khaitan Deep Dialogue team Google Research discussions well anonymous reviewers valuable feedback.,1541,1031,510,0.017,1.495,2025/11/05 17:19:01,0.01,1.357,0.5140186915887852,497.133
"Labeled text classification datasets are typically only available in a few select languages. In order to train a model for e.g news categorization in a language $L_t$ without a suitable text classification dataset there are two options. The first option is to create a new labeled dataset by hand, and the second option is to transfer label information from an existing labeled dataset in a source language $L_s$ to the target language $L_t$. In this paper we propose a method for sharing label information across languages by means of a language independent text encoder. The encoder will give almost identical representations to multilingual versions of the same text. This means that labeled data in one language can be used to train a classifier that works for the rest of the languages. The encoder is trained independently of any concrete classification task and can therefore subsequently be used for any classification task.   We show that it is possible to obtain good performance even in the case where only a comparable corpus of texts is available. Automatic systems that can classify documents quickly and precisely are useful for a wide range of practical applications. For example, organizations may be interested in using sentiment analysis of opinion posts such as tweets that mention their products and services. By classifying the sentiment of each post (e.g. positive, neutral, or negative), the organization can for example learn which parts of a product should be improved.Creating a suitable, large labeled dataset for training a classification model requires a lot of effort and available public datasets are typically only available in the most common languages. In order to train a classification model for a languages L t without a suitable text classification dataset there are two options: The first option is of course to create a new labeled dataset from scratch, and the second option is to use the label information in existing labeled datasets in a language L s and then transfer this label information to L t . The first option usually requires a great amount of work and is typically not a viable solution. The second option is called cross-language text classification (CLTC) BID20 .In this article we present a method for performing CLTC by means of a universal encoder. The method consists of two steps. In the first step, a universal encoder is trained to give similar representations to texts that describe the same topic, even if the texts are in different languages. In the second step, a classification module uses the language-independent representations from the universal encoder as inputs and is trained to predict which category each document belongs to. Compared to previous work, this method has several advantages: The method presented in this article is conceptually similar in spirit to Google's zero-shot machine translation model BID6 , which is used in the Google translate API. That model also uses a shared vocabulary and a language independent encoder. It does, however , require a large corpus of aligned sentences for training. Additionally, translating a text is a much harder problem than merely extracting discriminative features since it requires encoding of e.g. syntactic information that is not necessary for text classification. Therefore such a model is much more complex than it needs to be, and a more parsimonious model is therefore preferable. We will compare our zero-shot classification model with an equivalent model based on the zero-shot translation model in section 3.The rest of the article is organized as follows: We present our CLTC model in section 2. Experiments, data and results are presented in section 3. In section 4 we review previous approaches to cross-lingual text classification. In section 5 we will take a look at some possible improvements and future directions for the method. Finally, we conclude the article in section 6. In this article we have shown how to create a language independent representation using only a corpus of comparable texts. The language independent representation can subsequently be used for zero-shot classification.We show that it is possible to obtain very good performance even when only a comparable corpus of texts is available.The unsupervised classifier of course does not perform better than a supervised classifier trained on the same number of samples. It is, however, equal in performance to a native language supervised classifier trained on about hundred thousand samples. This means that if the number of native samples is limited and a large comparable corpus is available, the performance of our zero-shot classification can be better than that of a monolingual classifier.Our results show that even though it is possible to obtain good results using several languages at once, the best performance is obtained by using only two languages. Our results furthermore show that it is necessary to use a very large embedding size in order to obtain the best possible performance.","Labeled text classification datasets are typically available select languages. order train model e.g news categorization language $L_t without suitable text classification dataset are two options. first option is to create new labeled dataset hand second option is to transfer label information existing labeled dataset source language $L_s target language $L_t$. paper propose method sharing label information across languages means language independent text encoder. encoder will give almost identical representations multilingual versions text. means labeled data one language can be used train classifier works rest languages. encoder is trained independently concrete classification task can therefore subsequently used classification task. show is possible obtain good performance even case where only a comparable corpus texts is available. Automatic systems can classify documents quickly precisely are useful wide range practical applications. example organizations may interested using sentiment analysis opinion posts tweets mention products services. classifying sentiment post e.g positive neutral negative organization can for example learn which parts product should be improved.Creating suitable large labeled dataset training classification model requires lot effort available public datasets are typically available common languages. order train classification model languagesL without suitable text classification dataset are two options:first option is of course create new labeled dataset scratch second option is to use label information existing labeled datasets languageL transfer label information L t. first option usually requires great amount work is typically viable solution. second option is called cross-language text classification CLTC BID20.In article present method performing CLTC means universal encoder. method consists two steps. first step universal encoder is trained give similar representations texts describe topic even if the texts are in different languages. second step classification module uses language-independent representations universal encoder inputs is trained predict which category document belongs to. Compared previous work method has several advantages:method presented article is conceptually similar spirit Google's zero-shot machine translation model BID6 which is used Google translate API. model also uses shared vocabulary language independent encoder. does,is,however require large corpus aligned sentences training. Additionally translating text is a is much harder problem merely extracting discriminative features since requires encoding e.g syntactic information is not is necessary text classification. Therefore model is a is much complex needs parsimonious model is therefore preferable. will compare zero-shot classification model equivalent model based zero-shot translation model section 3.The rest article is organized follows:present CLTC model section2. Experiments data results are presented section3. section4 review previous approaches cross-lingual text classification. section5 will take look possible improvements future directions method. Finally conclude article section6. article have shown how to create language independent representation using corpus comparable texts. language independent representation can subsequently used zero-shot classification.We show is possible obtain good performance even when only a comparable corpus texts is available.The unsupervised classifier course does not perform better supervised classifier trained number samples. does,is,however equal performance native language supervised classifier trained hundred thousand samples. means if the number native samples is limited large comparable corpus is available performance zero-shot classification can be better monolingual classifier.Our results show even though is possible obtain good results using several languages best performance is obtained using two languages. results furthermore show is not is necessary use large embedding size order obtain best possible performance.",914,619,295,0.009,1.477,2025/11/05 17:19:01,0.0,1.449,0.4579439252336449,317.118
"Syntax is a powerful abstraction for language understanding. Many downstream tasks require segmenting input text into meaningful constituent chunks (e.g., noun phrases or entities); more generally, models for learning semantic representations of text benefit from integrating syntax in the form of parse trees (e.g., tree-LSTMs). Supervised parsers have traditionally been used to obtain these trees, but lately interest has increased in unsupervised methods that induce syntactic representations directly from unlabeled text. To this end, we propose the deep inside-outside recursive autoencoder (DIORA), a fully-unsupervised method for discovering syntax that simultaneously learns representations for constituents within the induced tree. Unlike many prior approaches, DIORA does not rely on supervision from auxiliary downstream tasks and is thus not constrained to particular domains. Furthermore, competing approaches do not learn explicit phrase representations along with tree structures, which limits their applicability to phrase-based tasks. Extensive experiments on unsupervised parsing, segmentation, and phrase clustering demonstrate the efficacy of our method. DIORA achieves the state of the art in unsupervised parsing (46.9 F1) on the benchmark WSJ dataset. Syntax in the form of parse trees is an essential component of many natural language processing tasks. Constituent spans taken from a parse tree are useful for tasks such as relation extraction BID0 and semantic role labeling BID1 , while the full parse itself can be used to build higher-quality systems for machine translation BID2 ) and text classification BID3 . Supervised parsers trained on datasets such as the Penn Treebank BID4 are traditionally used to obtain these trees; however, these datasets are generally small and restricted to the newswire domain. For out-of-domain applications, it is generally infeasible to create new treebanks, as syntactic annotation is expensive and time-consuming.Motivated by these limitations, we propose a method that extracts both shallow parses (i.e., noun phrases or entities) and full syntactic trees from any domain or language automatically without any training data. In addition to just producing the parse, we want our model to build representations for internal constituents that obey syntactic and semantic regularities, as we can then easily inject these representations into downstream tasks. Our model extends existing work on latent tree chart parsers BID5 BID6 BID7 BID8 , which build up representations for all internal nodes in the tree (cells in the chart) generated by a soft weighting over all possible sub-trees (Section 2).In previous work, the representation at the root node is used as a sentence encoding and trained to optimize some downstream task, typically natural language inference. Unfortunately , this method requires sentence level annotations to train the model. Worse still, analysis on the trees learned by these models show that they are actually quite poor at capturing syntax that in any way resembles linguistic theory BID9 . To address these issues, we incorporate the inside-outside algorithm BID10 BID11 ) into a latent tree chart parser. The bottom-up inside step is equivalent to the forward-pass of previous latent tree chart parsers BID7 . However, these inside representations are encoded by looking only within the current subtree, completely ignoring outside context. Thus, we perform an additional top-down outside calculation for each node in the tree incorporating external context into sub-tree representations. Finally, we train This news raised hopes for further interest-rate cuts .This news raised hopes for further interest-rate cuts .Figure 1: Example parse trees. Top PRPN-LM prediction, bottom DIORA prediction. DIORA correctly chunks the span 'raised hopes for further interest-rate cuts'. the outside representations of leaves to reconstruct the initial input, which results in a completely unsupervised autoencoder-like objective.Recently, BID12 proposed Parsing-Reading-Predict Networks (PRPN), an RNN based language model with an additional module for inferring syntactic distance. After training, this syntax module can be decomposed to recover a parse BID13 ) via a complex mechanism that involves modeling a distribution over possible syntactic structures with a stick-breaking process. Like DIORA, this model can be trained in a completely unsupervised manner. However, it has no mechanism of explicitly modeling phrases, and span representations can only be generated by post-hoc heuristics. Additionally, finding the most probable tree in DIORA is much simpler than in PRPN, as we can just run the CKY algorithm.To probe different properties of our model, we run experiments on unsupervised parsing, segmentation, and phrase representations. DIORA sets the state-of-the-art for unsupervised parsing on the WSJ dataset, has a greater recall on a more constituent types than PRPN, and demonstrates strong clustering of phrase representations. Latent tree models have been shown to perform particularly poorly on attachments at the beginning and end of the sequence BID9 . To address this, we incorporate a post-processing heuristic (+PP in Table 2 ). We see that PRPN-UP and DIORA benefit much more than PRPN-LM from this heuristic. This is consistent with qualitative analysis showing that DIORA and PRPN-UP incorrectly attach trailing punctuation much more than PRPN-LM. This heuristic simply attaches trailing punctuation to the root of the tree, regardless of its predicted attachment. We find this to be extremely effective, increasing our state-of-the-art WSJ parsing results by by over 3 absolute F1 points.On the MultiNLI dataset, PRPN-LM is the top performing model without using the PP heuristic and DIORA outperforms PRPN-UP. Afterwards, PRPN-UP surpasses DIORA. However, it is worth noting that this is not actually a gold standard evaluation and instead evaluates the ability to replicate the output of a trained parser . Table 2 : Unsupervised Parsing. † indicates trained to optimize NLI task.We use the max unlabeled binary F1 across runs for PRPN-UP 2 , PRPN-LM, and DIORA. F1 was calculated using the parse trees provided by BID13 and all results in the upper portion of the table were copied from BID13 . +PP refers to post-processing heuristic to remove trailing punctuation explained in Section 3.1. In Table 2 we see the breakdown of constituent recall across the 10 most common types. We see that PRPN-UP has the highest recall for the most common type noun-phrase, but drops in every other category. DIORA achieves the highest recall across the most types and is the only model to perform effectively on verb-phrases. However, DIORA performs poorly relative to PRPN at prepositional phrases. Table 3 : Segment recall from WSJ seperated by phrase type. The 10 most frequent phrase types are shown. Highest value in each row is bolded. In this work we presented DIORA, a completely unsupervised method for inducing syntactic trees and segmentations over text. We showed that an auto encoder language modeling objective on top of inside-outside representations of latent tree chart parsers allows us to effectively learn syntactic Third-quarter shipments slipped 7 % from the year-ago period and 17 % from this year 's second quarter Third-quarter shipments slipped 7 % from the year-ago period and 17 % from this year 's second quarter Mr. Hoelzer did n't return phone calls seeking comment on the judge 's decision Mr. Hoelzer did n't return phone calls seeking comment on the judge 's decisionThe earthquake caused many streets to buckle and crack making them impassibleThe earthquake caused many streets to buckle and crack making them impassible Figure 3 : Pairs of example parses for the same sentence from two different models. For each pair, the top is the output of PRPN-LM and bottom was produced by DIORA. Bolden token pairs or spans indicate a parse error by PRPN that was correctly attached by DIORA. Some punctuation was removed for clarity of printed trees. structure of language. In experiments on unsupervised parsing, chunking, and phrase representations we show our model is comparable to or outperforms current baselines, achieving the state-of-the-art performance on unsupervised parsing for the WSJ dataset. .Future work can improve the current method by training larger models over much larger corpora including other domains and languages. While the current model seems to focus primarily on syntax, extra unsupervised objectives or light supervision could be injected into the learning procedure to encourage a more thorough capturing of semantics.",Syntax is a powerful abstraction language understanding. Many downstream tasks require segmenting input text meaningful constituent chunks e.g noun phrases entities generally models learning semantic representations text benefit integrating syntax form parse trees e.g tree-LSTMs Supervised parsers have traditionally used obtain trees lately interest has increased unsupervised methods induce syntactic representations directly unlabeled text. end propose deep inside-outside recursive autoencoder DIORA fully-unsupervised method discovering syntax simultaneously learns representations constituents within induced tree. Unlike many prior approaches DIORA does not rely supervision auxiliary downstream tasks is thus constrained particular domains. Furthermore competing approaches do not learn explicit phrase representations along tree structures which limits applicability phrase-based tasks. Extensive experiments unsupervised parsing segmentation phrase clustering demonstrate efficacy method. DIORA achieves state art unsupervised parsing 46.9F1 benchmark WSJ dataset. Syntax form parse trees is an essential component many natural language processing tasks. Constituent spans taken parse tree are useful tasks relation extraction BID0 semantic role labeling BID1 full parse can be used build higher-quality systems machine translation BID2 text classification BID3. Supervised parsers trained datasets Penn Treebank BID4 are traditionally used obtain trees;however datasets are generally small restricted newswire domain. out-of-domain applications is generally infeasible create new treebanks syntactic annotation is expensive time-consuming.Motivated limitations propose method extracts shallow parses.e noun phrases entities full syntactic trees domain language automatically without training data. addition producing parse want model build representations internal constituents obey syntactic semantic regularities can easily inject representations downstream tasks. model extends existing work latent tree chart parsers BID5 BID6 BID7 BID8 which build representations internal nodes tree cells chart generated soft weighting possible sub-trees Section2.In previous work representation root node is used sentence encoding trained optimize downstream task typically natural language inference. Unfortunately method requires sentence level annotations train model. Worse still analysis trees learned models show are is not actually quite poor capturing syntax way resembles linguistic theory BID9. address issues incorporate inside-outside algorithm BID10 BID11 latent tree chart parser. bottom-up inside step is equivalent forward-pass previous latent tree chart parsers BID7. However inside representations are encoded looking within current subtree completely ignoring outside context. Thus perform additional top-down outside calculation node tree incorporating external context sub-tree representations. Finally train news raised hopes interest-rate cuts.This news raised hopes interest-rate cuts.Figure1:Example parse trees. Top PRPN-LM prediction bottom DIORA prediction. DIORA correctly chunks span 'raised hopes interest-rate cuts'. outside representations leaves reconstruct initial input which results completely unsupervised autoencoder-like objective.Recently BID12 proposed Parsing-Reading-Predict Networks PRPN RNN based language model additional module inferring syntactic distance. training syntax module can be decomposed recover parse BID13 via complex mechanism involves modeling distribution possible syntactic structures stick-breaking process. Like DIORA model can be trained completely unsupervised manner. However has no mechanism explicitly modeling phrases span representations can only be generated post-hoc heuristics. Additionally finding probable tree DIORA is much simpler PRPN can run CKY algorithm.To probe different properties model can run experiments unsupervised parsing segmentation phrase representations. DIORA sets state-of-the-art unsupervised parsing WSJ dataset has a greater recall constituent types PRPN demonstrates strong clustering phrase representations. Latent tree models have been shown perform particularly poorly attachments beginning end sequence BID9. address incorporate post-processing heuristic+PP Table2 see PRPN-UP DIORA benefit much PRPN-LM heuristic. is consistent qualitative analysis showing DIORA PRPN-UP incorrectly attach trailing punctuation much PRPN-LM heuristic simply attaches trailing punctuation root tree regardless predicted attachment. find extremely effective increasing state-of-the-art WSJ parsing results 3 absolute F1 points.On MultiNLI dataset PRPN-LM is the top performing model without using PP heuristic DIORA outperforms PRPN-UP Afterwards PRPN-UP surpasses DIORA. However is worth noting are is not actually gold standard evaluation instead evaluates ability replicate output trained parser. Table2:Unsupervised Parsing. † indicates trained optimize NLI task.We use max unlabeled binaryF1 across runs PRPN-UP2 PRPN-LM DIORA. F1 was calculated using parse trees provided BID13 results upper portion table were copied BID13.+PP refers post-processing heuristic remove trailing punctuation explained Section 3.1 Table2 see breakdown constituent recall across 10 common types. see PRPN-UP has the highest recall common type noun-phrase drops every category. DIORA achieves highest recall across types is the only model perform effectively verb-phrases However DIORA performs poorly relative PRPN prepositional phrases. Table3:Segment recall WSJ seperated phrase type. 10 frequent phrase types are shown. Highest value row is bolded. work presented DIORA completely unsupervised method inducing syntactic trees segmentations text. showed auto encoder language modeling objective top inside-outside representations latent tree chart parsers allowsus effectively learn syntactic Third-quarter shipments slipped7% year-ago period 17% year 's second quarter Third-quarter shipments slipped7% year-ago period 17% year 's second quarter Mr. Hoelzer did n't return phone calls seeking comment judge 's decisionMr. Hoelzer did n't return phone calls seeking comment judge 's decisionThe earthquake caused many streets buckle crack making impassibleThe earthquake caused many streets buckle crack making impassible Figure3:Pairs example parses sentence two different models. pair top is the output PRPN-LM bottom was produced DIORA. Bolden token pairs spans indicate parse error PRPN was correctly attached DIORA. punctuation was removed clarity printed trees. structure language. experiments unsupervised parsing chunking phrase representations show model is comparable outperforms current baselines achieving state-of-the-art performance unsupervised parsing WSJ dataset. .Future work can improve current method training larger models much larger corpora including domains languages. current model seems focus primarily syntax extra unsupervised objectives light supervision could injected learning procedure encourage thorough capturing semantics.,1699,1211,488,0.016,1.403,2025/11/05 17:19:01,0.01,1.391,0.2274143302180684,495.737
"Careful tuning of the learning rate, or even schedules thereof, can be crucial to effective neural net training. There has been much recent interest in gradient-based meta-optimization, where one tunes hyperparameters, or even learns an optimizer, in order to minimize the expected loss when the training procedure is unrolled. But because the training procedure must be unrolled thousands of times, the meta-objective must be defined with an orders-of-magnitude shorter time horizon than is typical for neural net training. We show that such short-horizon meta-objectives cause a serious bias towards small step sizes, an effect we term short-horizon bias. We introduce a toy problem, a noisy quadratic cost function, on which we analyze short-horizon bias by deriving and comparing the optimal schedules for short and long time horizons. We then run meta-optimization experiments (both offline and online) on standard benchmark datasets, showing that meta-optimization chooses too small a learning rate by multiple orders of magnitude, even when run with a moderately long time horizon (100 steps) typical of work in the area. We believe short-horizon bias is a fundamental problem that needs to be addressed if meta-optimization is to scale to practical neural net training regimes. The learning rate is one of the most important and frustrating hyperparameters to tune in deep learning. Too small a value causes slow progress, while too large a value causes fluctuations or even divergence. While a fixed learning rate often works well for simpler problems, good performance on the ImageNet BID23 benchmark requires a carefully tuned schedule. A variety of decay schedules have been proposed for different architectures, including polynomial, exponential, staircase, etc. Learning rate decay is also required to achieve convergence guarantee for stochastic gradient methods under certain conditions BID2 . Clever learning rate heuristics have resulted in large improvements in training efficiency BID5 BID28 . A related hyperparameter is momentum; typically fixed to a reasonable value such as 0.9, careful tuning can also give significant performance gains BID29 . While optimizers such as Adam BID8 are often described as adapting coordinate-specific learning rates, in fact they also have global learning rate and momentum hyperparameters analogously to SGD, and tuning at least the learning rate can be important to good performance.In light of this, it is not surprising that there have been many attempts to adapt learning rates, either online during optimization BID26 BID25 , or offline by fitting a learning rate schedule BID16 . More ambitiously, others have attempted to learn an optimizer BID1 BID12 BID4 BID14 BID32 BID20 . All of these approaches are forms of meta-optimization, where one defines a meta-objective (typically the expected loss after some number of optimization steps) and tunes the hyperparameters to minimize this meta-objective. But because gradient-based meta-optimization can require thousands of updates, each of which unrolls the entire base-level optimization procedure, the meta-optimization is thousands of times more expensive than the baselevel optimization. Therefore, the meta-objective must be defined with a much smaller time horizon (e.g. hundreds of updates) than we are ordinarily interested in for large-scale optimization. The hope is that the learned hyperparameters or optimizer will generalize well to much longer time horizons. Unfortunately, we show that this is not achieved in this paper. This is because of a strong tradeoff between short-term and long-term performance, which we refer to as short-horizon bias. In this work, we investigate the short-horizon bias both mathematically and empirically. First, we analyze a quadratic cost function with noisy gradients based on BID25 . We consider this a good proxy for neural net training because secondorder optimization algorithms have been shown to train neural networks in orders-of-magnitude fewer iterations BID17 , suggesting that much of the difficulty of SGD training can be explained by quadratic approximations to the cost. In our noisy quadratic problem, the dynamics of SGD with momentum can be analyzed exactly, allowing us to derive the greedy-optimal (i.e. 1-step horizon) learning rate and momentum in closed form, as well as to (locally) minimize the long-horizon loss using gradient descent. We analyze the differences between the short-horizon and long-horizon schedules.Interestingly, when the noisy quadratic problem is either deterministic or spherical, greedy schedules are optimal. However, when the problem is both stochastic and badly conditioned (as is most neural net training), the greedy schedules decay the learning rate far too quickly, leading to slow convergence towards the optimum. This is because reducing the learning rate dampens the fluctuations along high curvature directions, giving it a large immediate reduction in loss. But this comes at the expense of long-run performance, because the optimizer fails to make progress along low curvature directions. This phenomenon is illustrated in FIG0 , a noisy quadratic problem in 2 dimensions, in which two learning rate schedule are compared: a small fixed learning rate (blue), versus a larger fixed learning rate (red) followed by exponential decay (yellow). The latter schedule initially has higher loss, but it makes more progress towards the optimum, such that it achieves an even smaller loss once the learning rate is decayed. Figure 2 shows this effect quantitatively for a noisy quadratic problem in 1000 dimensions (defined in Section 2.3). The solid lines show the loss after various numbers of steps of lookahead with a fixed learning rate; if this is used as the meta-objective, it favors small learning rates. The dashed curves show the loss if the same trajectories are followed by 50 steps with an exponentially decayed learning rate; these curves favor higher learning rates, and bear little obvious relationship to the solid ones. This illustrates the difficulty of selecting learning rates based on short-horizon information. In this paper, we analyzed the problem of short-horizon bias in meta-optimization. We presented a noisy quadratic toy problem which we analyzed mathematically, and observed that the optimal learning rate schedule differs greatly from a greedy schedule that minimizes training loss one step ahead. While the greedy schedule tends to decay the learning rate drastically to reduce the loss on high curvature directions, the optimal schedule keeps a high learning rate in order to make steady progress on low curvature directions, and eventually achieves far lower loss. We showed that this bias stems from the combination of stochasticity and ill-conditioning: when the problem is either deterministic or spherical, the greedy learning rate schedule is globally optimal; however, when the problem is both stochastic and ill-conditioned (as is most neural net training), the greedy schedule performs poorly. We empirially verified the short-horizon bias in the context of neural net training by applying gradient based meta-optimization, both offline and online. We found the same pathological behaviors as in the noisy quadratic problem -a fast learning rate decay and poor long-run performance.While our results suggest that meta-optimization should not be applied blindly, our noisy quadratic analysis also provides grounds for optimism: by removing ill-conditioning (by using a good preconditioner) and/or stochasticity (with large batch sizes or variance reduction techniques), it may be possible to enter the regime where short-horizon meta-optimization works well. It remains to be seen whether this is achievable with existing optimization algorithms.We calculate the mean of the parameter θ (t+1) , DISPLAYFORM0 Let's assume the following initial conditions: DISPLAYFORM1 Then Eq.(10) and Eq.(11) describes how E θ (t) , E v (t) changes over time t.",Careful tuning learning rate even schedules thereof can be crucial effective neural net training. has been much recent interest gradient-based meta-optimization where one tunes hyperparameters even learns optimizer order minimize expected loss when the training procedure is unrolled. training procedure must unrolled thousands times meta-objective must defined orders-of-magnitude shorter time horizon is typical neural net training. show short-horizon meta-objectives cause serious bias towards small step sizes effect term short-horizon bias. introduce toy problem when the noisy quadratic cost function which we analyze short-horizon bias deriving comparing optimal schedules short long time horizons. run meta-optimization experiments offline online standard benchmark datasets showing meta-optimization chooses small learning rate multiple orders magnitude even when run moderately long time horizon 100 steps typical work area. believe short-horizon bias is a fundamental problem needs addressed if meta-optimization is to scale practical neural net training regimes. learning rate is one important frustrating hyperparameters tune deep learning. small value causes slow progress large value causes fluctuations even divergence. fixed learning rate often works well simpler problems good performance ImageNet BID23 benchmark requires carefully tuned schedule. variety decay schedules have been proposed different architectures including polynomial exponential staircase etc. Learning rate decay is also required achieve convergence guarantee stochastic gradient methods certain conditions BID2. Clever learning rate heuristics have resulted large improvements training efficiency BID5 BID28. related hyperparameter is momentum;typically fixed reasonable value 0.9 careful tuning can also give significant performance gains BID29. optimizers Adam BID8 are often described adapting coordinate-specific learning rates fact also have global learning rate momentum hyperparameters analogously SGD tuning least learning rate can be important good performance.In light is not surprising have been many attempts adapt learning rates either online optimization BID26 BID25 offline fitting learning rate schedule BID16. ambitiously others have attempted learn optimizer BID1 BID12 BID4 BID14 BID32 BID20. approaches are forms meta-optimization where one defines meta-objective typically expected loss number optimization steps tunes hyperparameters minimize meta-objective gradient-based meta-optimization can require thousands updates which unrolls entire base-level optimization procedure meta-optimization is thousands times expensive baselevel optimization. Therefore meta-objective must defined much smaller time horizon e.g hundreds updates are ordinarily interested large-scale optimization. hope is that the learned hyperparameters optimizer will generalize well much longer time horizons. Unfortunately show is not achieved paper. is becauseof strong tradeoff short-term long-term performance which we refer short-horizon bias. work investigate short-horizon bias mathematically empirically. First which we analyze quadratic cost function noisy gradients based BID25. consider good proxy neural net training secondorder optimization algorithms have been shown train neural networks orders-of-magnitude fewer iterations BID17 suggesting much difficulty SGD training can be explained quadratic approximations cost. noisy quadratic problem dynamics SGD momentum can be analyzed exactly allowingus derive greedy-optimal.e 1-step horizon learning rate momentum closed form well locally minimize long-horizon loss using gradient descent. analyze differences short-horizon long-horizon schedules.Interestingly when the noisy quadratic problem is either deterministic spherical greedy schedules are optimal. However when the problem is both stochastic badly conditioned is most neural net training greedy schedules decay learning rate far quickly leading slow convergence towards optimum. is because reducing learning rate dampens fluctuations along high curvature directions giving large immediate reduction loss. comes expense long-run performance optimizer fails make progress along low curvature directions. phenomenon is illustrated FIG0 when the noisy quadratic problem 2 dimensions which two learning rate schedule are compared:small fixed learning rate blue versus larger fixed learning rate red followed exponential decay yellow latter schedule initially has higher loss makes progress towards optimum achieves even smaller loss learning rate is decayed. Figure 2 shows effect quantitatively noisy quadratic problem 1000 dimensions defined Section 2.3 solid lines show loss various numbers steps lookahead fixed learning rate;if this is used meta-objective favors small learning rates. dashed curves show loss if the same trajectories are followed 50 steps exponentially decayed learning rate;curves favor higher learning rates bear little obvious relationship solid ones. illustrates difficulty selecting learning rates based short-horizon information. paper analyzed problem short-horizon bias meta-optimization presented noisy quadratic toy problem which we analyzed mathematically observed optimal learning rate schedule differs greatly greedy schedule minimizes training loss one step ahead. greedy schedule tends decay learning rate drastically reduce loss high curvature directions optimal schedule keeps high learning rate order make steady progress low curvature directions eventually achieves far lower loss. showed bias stems combination stochasticity ill-conditioning when the problem is either deterministic spherical greedy learning rate schedule is globally optimal;however when the problem is both stochastic ill-conditioned is most neural net training greedy schedule performs poorly. empirially verified short-horizon bias context neural net training applying gradient based meta-optimization offline online. found pathological behaviors noisy quadratic problem-a fast learning rate decay poor long-run performance.While results suggest meta-optimization should not be applied blindly when the noisy quadratic analysis also provides grounds optimism:removing ill-conditioning using good preconditioner/stochasticity large batch sizes variance reduction techniques may possible enter regime where short-horizon meta-optimization works well. remains seen whether is achievable existing optimization algorithms.We calculate mean parameterθ+1 DISPLAYFORM0 Let's assume following initial conditions:DISPLAYFORM1 Eq. 10 Eq. 11 describes howEθ Ev changes time t.,1505,1059,446,0.015,1.421,2025/11/05 17:19:01,0.01,1.552,0.2834890965732086,477.773
"Mainstream captioning models often follow a sequential structure to generate cap-
 tions, leading to issues such as introduction of irrelevant semantics, lack of diversity
 in the generated captions, and inadequate generalization performance. In this paper,
 we present an alternative paradigm for image captioning, which factorizes the
 captioning procedure into two stages: (1) extracting an explicit semantic represen-
 tation from the given image; and (2) constructing the caption based on a recursive
 compositional procedure in a bottom-up manner. Compared to conventional ones,
 our paradigm better preserves the semantic content through an explicit factorization
 of semantics and syntax. By using the compositional generation procedure, caption
 construction follows a recursive structure, which naturally fits the properties of
 human language. Moreover, the proposed compositional procedure requires less
 data to train, generalizes better, and yields more diverse captions. Image captioning, the task to generate short descriptions for given images, has received increasing attention in recent years. State-of-the-art models BID0 BID1 BID2 BID3 mostly adopt the encoder-decoder paradigm BID2 , where the content of the given image is first encoded via a convolutional network into a feature vector, which is then decoded into a caption via a recurrent network. In particular, the words in the caption are produced in a sequential manner -the choice of each word depends on both the preceding word and the image feature. Despite its simplicity and the effectiveness shown on various benchmarks BID4 BID5 , the sequential model has a fundamental problem. Specifically, it could not reflect the inherent hierarchical structures of natural languages BID6 BID7 in image captioning and other generation tasks, although it could implicitly capture such structures in tasks taking the complete sentences as input, e.g. parsing BID8 , and classification BID9 .As a result, sequential models have several significant drawbacks. First , they rely excessively on n-gram statistics rather than hierarchical dependencies among words in a caption. Second , such models usually favor the frequent n-grams BID10 in the training set, which, as shown in Figure 1 , may lead to captions that are only correct syntactically but not semantically, containing semantic concepts that are irrelevant to the conditioned image. Third , the entanglement of syntactic rules and semantics obscures the dependency structure and makes sequential models difficult to generalize.To tackle these issues, we propose a new paradigm for image captioning, where the extraction of semantics (i.e. what to say) and the construction of syntactically correct captions (i.e. how to say) are decomposed into two stages. Specifically , it derives an explicit representation of the semantic content of the given image, which comprises a set of noun-phrases, e.g. a white cat, a cloudy sky or two men. With these noun-phrases as the basis, it then proceeds to construct the caption through recursive composition until a complete caption is obtained. In particular , at each step of the composition, a higher-level phrase is formed by joining two selected sub-phrases via a connecting phrase. It is Preprint . Work in progress.a large building with a clock tower a building with a clock on the side of it a building with a clock on the side of it Figure 1 : This figure shows three test images in MS-COCO BID4 with captions generated by the neural image captioner BID2 , which contain n-gram building with a clock that appeared frequently in the training set but is not semantically correct for these images.noteworthy that the compositional procedure described above is not a hand-crafted algorithm. Instead, it consists of two parametric modular nets, a connecting module for phrase composition and an evaluation module for deciding the completeness of phrases.The proposed paradigm has several key advantages compared to conventional captioning models: BID0 The factorization of semantics and syntax not only better preserves the semantic content of the given image but also makes caption generation easy to interpret and control. (2) The recursive composition procedure naturally reflects the inherent structures of natural language and allows the hierarchical dependencies among words and phrases to be captured. Through a series of ablative studies, we show that the proposed paradigm can effectively increase the diversity of the generated captions while preserving semantic correctness. It also generalizes better to new data and can maintain reasonably good performance when the number of available training data is small. In this paper, we propose a novel paradigm for image captioning. While the typical existing approaches encode images using feature vectors and generate captions sequentially, the proposed method generates captions in a compositional manner. In particular, our approach factorizes the captioning procedure into two stages. In the first stage, an explicit representation of the input image, consisting of noun-phrases, is extracted. In the second stage, a recursive compositional procedure is applied to assemble extracted noun-phrases into a caption. As a result, caption generation follows a hierarchical structure, which naturally fits the properties of human language. On two datasets, the proposed compositional procedure is shown to preserve semantics more effectively, require less data to train, generalize better across datasets, and yield more diverse captions.","Mainstream captioning models often follow sequential structure generate cap- tions leading issues introduction irrelevant semantics lack diversity generated captions inadequate generalization performance. paper present alternative paradigm image captioning which factorizes captioning procedure two stages:1 extracting explicit semantic represen- tation given image;2 constructing caption based recursive compositional procedure bottom-up manner. Compared conventional ones paradigm better preserves semantic content explicit factorization semantics syntax. using compositional generation procedure caption construction follows recursive structure which naturally fits properties human language. Moreover proposed compositional procedure requires less data train generalizes better yields diverse captions. Image captioning task generate short descriptions given images has received increasing attention recent years. State-of-the-art models BID0 BID1 BID2 BID3 mostly adopt encoder-decoder paradigm BID2 where the content given image is first encoded via convolutional network feature vector which is then decoded caption via recurrent network. particular words caption are produced sequential manner -the choice word depends preceding word image feature. Despite simplicity effectiveness shown various benchmarks BID4 BID5 sequential model has a fundamental problem. Specifically could reflect inherent hierarchical structures natural languages BID6 BID7 image captioning generation tasks although could implicitly capture structures tasks taking complete sentences input e.g parsing BID8 classification BID9.As result sequential models have several significant drawbacks. First rely excessively n-gram statistics rather hierarchical dependencies among words caption. Second models usually favor frequent n-grams BID10 training set which,as shown Figure1 may lead captions are only correct syntactically is not semantically containing semantic concepts are irrelevant conditioned image. Third entanglement syntactic rules semantics obscures dependency structure makes sequential models difficult generalize.To tackle issues propose new paradigm image captioning where the extraction semantics.e what to say construction syntactically correct captions.e how to say are decomposed two stages. Specifically derives explicit representation semantic content given image which comprises set noun-phrases e.g white cat cloudy sky two men. noun-phrases basis proceeds construct caption recursive composition complete caption is obtained. particular step composition higher-level phrase is formed joining two selected sub-phrases via connecting phrase. is Preprint. Work progress.a large building clock tower building clock side building clock side Figure1:figure shows three test images MS-COCO BID4 captions generated neural image captioner BID2 which contain n-gram building clock appeared frequently training set is not semantically correct images.noteworthy compositional procedure described is not a hand-crafted algorithm. Instead consists two parametric modular nets connecting module phrase composition evaluation module deciding completeness phrases.The proposed paradigm has several key advantages compared conventional captioning models:BID0 factorization semantics syntax better preserves semantic content given image also makes caption generation easy interpret control. 2 recursive composition procedure naturally reflects inherent structures natural language allows hierarchical dependencies among words phrases captured. series ablative studies show proposed paradigm can effectively increase diversity generated captions preserving semantic correctness. also generalizes better new data can maintain reasonably good performance when the number available training data is small. paper propose novel paradigm image captioning. typical existing approaches encode images using feature vectors generate captions sequentially proposed method generates captions compositional manner. particular approach factorizes captioning procedure two stages. first stage explicit representation input image consisting noun-phrases is extracted. second stage recursive compositional procedure is applied assemble extracted noun-phrases caption. result caption generation follows hierarchical structure which naturally fits properties human language. two datasets proposed compositional procedure is shown preserve semantics effectively require less data train generalize better across datasets yield diverse captions.",1035,693,342,0.011,1.494,2025/11/05 17:19:01,0.01,1.452,0.5109034267912771,317.667
"While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss. The practical successes of deep learning in various fields such as image processing BID34 BID18 BID21 , biomedicine BID9 BID29 BID28 , and language translation BID2 BID41 still outpace our theoretical understanding. While hyperparameter adjustment strategies exist BID3 , formal measures for assessing the generalization capabilities of deep neural networks have yet to be identified BID44 . Previous approaches for improving theoretical and practical comprehension focus on interrogating networks with input data. These methods include i) feature visualization of deep convolutional neural networks BID43 BID36 , ii) sensitivity and relevance analysis of features BID25 , iii) a descriptive analysis of the training process based on information theory BID39 BID33 BID32 BID1 , and iv) a statistical analysis of interactions of the learned weights BID40 . Additionally, BID27 develop a measure of expressivity of a neural network and use it to explore the empirical success of batch normalization, as well as for the definition of a new regularization method. They note that one key challenge remains, namely to provide meaningful insights while maintaining theoretical generality. This paper presents a method for elucidating neural networks in light of both aspects.We develop neural persistence, a novel measure for characterizing neural network structural complexity. In doing so, we adopt a new perspective that integrates both network weights and connectivity while not relying on interrogating networks through input data. Neural persistence builds on computational techniques from algebraic topology, specifically topological data analysis (TDA), which was already shown to be beneficial for feature extraction in deep learning BID19 and describing the complexity of GAN sample spaces BID23 . More precisely, we rephrase deep networks with fully-connected layers into the language of algebraic topology and develop a measure for assessing the structural complexity of i) individual layers, and ii) the entire network. In this work, we present the following contributions: -We introduce neural persistence, a novel measure for characterizing the structural complexity of neural networks that can be efficiently computed. -We prove its theoretical properties, such as upper and lower bounds, thereby arriving at a normalization for comparing neural networks of varying sizes. -We demonstrate the practical utility of neural persistence in two scenarios: i) it correctly captures the benefits of dropout and batch normalization during the training process, and ii) it can be easily used as a competitive early stopping criterion that does not require validation data. In this work, we presented neural persistence, a novel topological measure of the structural complexity of deep neural networks. We showed that this measure captures topological information that pertains to deep learning performance. Being rooted in a rich body of research, our measure is theoretically well-defined and, in contrast to previous work, generally applicable as well as computationally efficient. We showed that our measure correctly identifies networks that employ best practices such as dropout and batch normalization. Moreover, we developed an early stopping criterion that exhibits competitive performance while not relying on a separate validation data set. Thus, by saving valuable data for training, we managed to boost accuracy, which can be crucial for enabling deep learning in regimes of smaller sample sizes. Following Theorem 2, we also experimented with using the p-norm of all weights of the neural network as a proxy for neural persistence. However, this did not yield an early stopping measure because it was never triggered, thereby suggesting that neural persistence captures salient information that would otherwise be hidden among all the weights of a network. We extended our framework to convolutional neural networks (see Section A.4) by deriving a closed-form approximation, and observed that an early stopping criterion based on neural persistence for convolutional layers will require additional work. Furthermore, we conjecture that assessing dissimilarities of networks by means of persistence diagrams (making use of higher-dimensional topological features), for example, will lead to further insights regarding their generalization and learning abilities. Another interesting avenue for future research would concern the analysis of the 'function space' learned by a neural network. On a more general level, neural persistence demonstrates the great potential of topological data analysis in machine learning.",many approaches make neural networks fathomable have been proposed are restricted interrogating network input data. Measures characterizing monitoring structural properties however have not been developed. work propose neural persistence complexity measure neural network architectures based topological data analysis weighted stratified graphs. demonstrate usefulness approach show neural persistence reflects best practices developed deep learning community dropout batch normalization. Moreover derive neural persistence-based stopping criterion shortens training process achieving comparable accuracies early stopping based validation loss. practical successes deep learning various fields image processing BID34 BID18 BID21 biomedicine BID9 BID29 BID28 language translation BID2 BID41 still outpace theoretical understanding. hyperparameter adjustment strategies exist BID3 formal measures assessing generalization capabilities deep neural networks have yet identified BID44. Previous approaches improving theoretical practical comprehension focus interrogating networks input data. methods include feature visualization deep convolutional neural networks BID43 BID36 ii sensitivity relevance analysis features BID25 iii descriptive analysis training process based information theory BID39 BID33 BID32 BID1 iv statistical analysis interactions learned weights BID40. Additionally BID27 develop measure expressivity neural network use explore empirical success batch normalization well definition new regularization method. note one key challenge remains namely provide meaningful insights maintaining theoretical generality. paper presents method elucidating neural networks light aspects.We develop neural persistence novel measure characterizing neural network structural complexity. adopt new perspective integrates network weights connectivity relying interrogating networks input data. Neural persistence builds computational techniques algebraic topology specifically topological data analysis TDA which was already shown beneficial feature extraction deep learning BID19 describing complexity GAN sample spaces BID23. precisely rephrase deep networks fully-connected layers language algebraic topology develop measure assessing structural complexity individual layers ii entire network. work present following contributions:-We introduce neural persistence novel measure characterizing structural complexity neural networks can be efficiently computed. -We prove theoretical properties upper lower bounds thereby arriving normalization comparing neural networks varying sizes. -We demonstrate practical utility neural persistence two scenarios:correctly captures benefits dropout batch normalization training process ii can be easily used competitive early stopping criterion does not require validation data. work presented neural persistence novel topological measure structural complexity deep neural networks. showed measure captures topological information pertains deep learning performance. rooted rich body research measure is theoretically well-defined contrast previous work generally applicable well computationally efficient. showed measure correctly identifies networks employ best practices dropout batch normalization. Moreover have not been developed early stopping criterion exhibits competitive performance relying separate validation data set. Thus saving valuable data training managed boost accuracy which can be crucial enabling deep learning regimes smaller sample sizes. Following Theorem2 also experimented using p-norm weights neural network proxy neural persistence. However did not yield early stopping measure was never triggered thereby suggesting neural persistence captures salient information would otherwise hidden among weights network. extended framework convolutional neural networks see Section A.4 deriving closed-form approximation observed early stopping criterion based neural persistence convolutional layers will require additional work. Furthermore conjecture assessing dissimilarities networks means persistence diagrams making use higher-dimensional topological features example will lead insights regarding generalization learning abilities. Another interesting avenue future research would concern analysis 'function space' learned neural network. general level neural persistence demonstrates great potential topological data analysis machine learning.,937,627,310,0.009,1.494,2025/11/05 17:19:01,0.0,1.714,0.5109034267912771,297.219
"Deep neural networks (DNNs) are vulnerable to adversarial examples, which are carefully crafted instances aiming to cause prediction errors for DNNs. Recent research on adversarial examples has examined local neighborhoods in the input space of DNN models. However, previous work has limited what regions to consider, focusing either on low-dimensional subspaces or small balls. In this paper, we argue that information from larger neighborhoods, such as from more directions and from greater distances, will better characterize the relationship between adversarial examples and the DNN models. First, we introduce an attack, OPTMARGIN, which generates adversarial examples robust to small perturbations. These examples successfully evade a defense that only considers a small ball around an input instance. Second, we analyze a larger neighborhood around input instances by looking at properties of surrounding decision boundaries, namely the distances to the boundaries and the adjacent classes. We find that the boundaries around these adversarial examples do not resemble the boundaries around benign examples. Finally, we show that, under scrutiny of the surrounding decision boundaries, our OPTMARGIN examples do not convincingly mimic benign examples. Although our experiments are limited to a few specific attacks, we hope these findings will motivate new, more evasive attacks and ultimately, effective defenses. Recent research in adversarial examples in deep learning has examined local neighborhoods in the input space of deep learning models. BID9 and BID15 examine limited regions around benign samples to study why some adversarial examples transfer across different models. BID10 explore regions around benign samples to validate the robustness of an adversarially trained model. BID14 examine regions around adversarial examples to estimate the examples' robustness to random noise. BID0 determine that considering the region around an input instance produces more robust classification than looking at the input instance alone as a single point. In this paper, we argue that information from larger neighborhoods-both in more directions and at greater distances-will better help us understand adversarial examples in high-dimensional datasets.First, we describe a concrete limitation in a system that utilizes information in small neighborhoods. Cao & Gong's region classification defense (2017) takes the majority prediction in a small ball around an input instance. We introduce an attack method, OPTMARGIN, for generating adversarial examples that are robust to small perturbations, which can evade this defense.Second, we provide an example of how to analyze an input instance's surroundings in the model's input space. We introduce a technique that looks at the decision boundaries around an input instance, and we use this technique to characterize our robust OPTMARGIN adversarial examples. Our analysis reveals that, while OPTMARGIN adversarial examples are robust enough to fool region classification, the decision boundaries around them do not resemble the boundaries around benign examples, in terms of distances from the example to the adjacent classes.Third, as an extension to the above observation, we train a classifier to differentiate the decision boundary information that comes from different types of input instances. We show that our classifier can differentiate OPTMARGIN and benign examples with 90.4% accuracy, whereas region classification limits itself to a small region and fails. However, it remains to be seen whether a more sophisticated attack can find adversarial examples surrounded by decision boundaries that more accurately mimic the boundaries around benign examples.To summarize, our contributions are:1. We demonstrate OPTMARGIN, a new attack that evades region classification systems with low-distortion adversarial examples.2. We introduce an analysis of decision boundaries around an input instance that explains the effectiveness of OPTMARGIN adversarial examples and also shows the attack's weaknesses.3. We demonstrate the expressiveness of decision boundary information by using it to classify different kinds of input instances.We have released the code we used at https://github.com/sunblaze-ucb/ decision-boundaries. We considered the benefits of examining large neighborhoods around a given input in input space. We demonstrated an effective OPTMARGIN attack against a region classification defense, which only considered a small ball of the input space around a given instance. We analyzed the neighborhood of examples generated by this new attack by looking at the decision boundaries around them, as well as the boundaries around benign examples and less robust adversarial examples. This analysis incorporated information from many directions in input space and from longer distances than previous work. We found that the comprehensive information about surrounding decision boundaries reveals there are still differences between our robust adversarial examples and benign examples.",Deep neural networks DNNs are vulnerable adversarial examples which are carefully crafted instances aiming cause prediction errors DNNs. Recent research adversarial examples has examined local neighborhoods input space DNN models. However previous work has limited what regions consider focusing either low-dimensional subspaces small balls. paper argue information larger neighborhoods directions greater distances will better characterize relationship adversarial examples DNN models. First introduce attack OPTMARGIN which generates adversarial examples robust small perturbations. examples successfully evade defense considers small ball around input instance. Second analyze larger neighborhood around input instances looking properties surrounding decision boundaries namely distances boundaries adjacent classes. find boundaries around adversarial examples do not resemble boundaries around benign examples. Finally show scrutiny surrounding decision boundaries OPTMARGIN examples do not convincingly mimic benign examples. Although experiments are limited specific attacks hope findings will motivate new evasive attacks ultimately effective defenses. Recent research adversarial examples deep learning has examined local neighborhoods input space deep learning models. BID9 BID15 examine limited regions around benign samples study why some adversarial examples transfer across different models. BID10 explore regions around benign samples validate robustness adversarially trained model. BID14 examine regions around adversarial examples estimate examples' robustness random noise. BID0 determine considering region around input instance produces robust classification looking input instance alone single point. paper argue information larger neighborhoods-both directions greater distances-will better help us understand adversarial examples high-dimensional datasets.First describe concrete limitation system utilizes information small neighborhoods. Cao Gong's region classification defense 2017 takes majority prediction small ball around input instance. introduce attack method OPTMARGIN generating adversarial examples are robust small perturbations which can evade defense.Second provide example how to analyze input instance's surroundings model's input space. introduce technique looks decision boundaries around input instance use technique characterize robust OPTMARGIN adversarial examples. analysis reveals OPTMARGIN adversarial examples are robust enough fool region classification decision boundaries around do not resemble boundaries around benign examples terms distances example adjacent classes.Third extension observation train classifier differentiate decision boundary information comes different types input instances. show classifier can differentiate OPTMARGIN benign examples 90.4 accuracy whereas region classification limits small region fails. However remains seen whether sophisticated attack can find adversarial examples surrounded decision boundaries accurately mimic boundaries around benign examples.To summarize contributions are:1 demonstrate OPTMARGIN new attack evades region classification systems low-distortion adversarial examples.2 introduce analysis decision boundaries around input instance explains effectiveness OPTMARGIN adversarial examples also shows attack's weaknesses.3 demonstrate expressiveness decision boundary information using classify different kinds input instances.We have released code used https://github.com/sunblaze-ucb/decision-boundaries considered benefits examining large neighborhoods around given input input space. demonstrated effective OPTMARGIN attack region classification defense which only considered small ball input space around given instance. analyzed neighborhood examples generated new attack looking decision boundaries around well boundaries around benign examples less robust adversarial examples. analysis incorporated information many directions input space longer distances previous work. found comprehensive information surrounding decision boundaries reveals are still differences robust adversarial examples benign examples.,886,606,280,0.009,1.462,2025/11/05 17:19:01,0.0,1.364,0.4112149532710277,293.056
"Machine learning models are usually tuned by nesting optimization of model weights inside the optimization of hyperparameters.   We give a method to collapse this nested optimization into joint stochastic optimization of both weights and hyperparameters.   Our method trains a neural network to output approximately optimal weights as a function of hyperparameters.   We show that our method converges to locally optimal weights and hyperparameters for sufficiently large hypernets.   We compare this method to standard hyperparameter optimization strategies and demonstrate its effectiveness for tuning thousands of hyperparameters. Hyperparameter λ Training and validation loss of a neural net, estimated by crossvalidation (crosses) or by a hypernet (lines), which outputs 7, 850-dimensional network weights. The training and validation loss can be cheaply evaluated at any hyperparameter value using a hypernet. Standard cross-validation requires training from scratch each time.Model selection and hyperparameter tuning is a major bottleneck in designing predictive models. Hyperparameter optimization can be seen as a nested optimization: The inner optimization finds model parameters w which minimizes the training loss LTrain given hyperparameters λ. The outer optimization chooses λ to minimize a validation loss LValid. : DISPLAYFORM0 Standard practice in machine learning solves (1) by gradient-free optimization of hyperparameters, such as grid search, random search, or Bayesian optimization. Each set of hyperparameters is evaluated by reinitializing weights and training the model to completion. This is wasteful, since it trains the model from scratch each time, even if the hyperparameters change a small amount. Hyperband BID14 and freezethaw Bayesian optimization (Swersky et al., 2014 ) resume model training and do not waste this effort. Furthermore, gradient-free optimization scales poorly beyond 10 or 20 dimensions.How can we avoid re-training from scratch each time?We usually estimate the parameters with stochastic optimization, but the true optimal parameters are a deterministic function of the hyperparameters λ: DISPLAYFORM1 We propose to learn this function. Specifically , we train a neural network with inputs of hyperparameters, and outputs of an approximately optimal set of weights given the hyperparameters.This provides two major benefits: First, we can train the hypernet to convergence using stochastic gradient descent, denoted SGD, without training any particular model to completion. Second, differentiating through the hypernet allows us to optimize hyperparameters with gradient-based stochastic optimization.P a ra m e te r w H y p e r p a r a m e t e r λ Loss L Train (w, In this paper, we:• Presented algorithms that efficiently learn a differentiable approximation to a best-response without nested optimization.• Showed empirically that hypernets can provide a better inductive bias for hyperparameter optimization than Gaussian processes fit directly to the validation loss.• Gave a theoretical justification that sufficiently large networks will learn the best-response for all hyperparameters it is trained against.We hope that this initial exploration of stochastic hyperparameter optimization will inspire further refinements, such as hyper-regularization methods, or uncertainty-aware exploration using Bayesian hypernetworks. A EXTRA EXPERIMENTS A.1 OPTIMIZING 10 HYPERPARAMETERS Here, we optimize a model with 10 hyperparameters, in which a separate L 2 weight decay is applied to the weights for each digit class in a linear regression model to see if we can optimize medium-sized models. The conditional hyperparameter distribution and optimizer for the hypernet and hyperparameters is the same the prior experiments. A linear hypernet is used, resulting in 86, 350 hyper-weights. Algorithm 3 is compared against random search and .Figure 8, right, shows that our method converges more quickly and to a better optimum than either alternative method, demonstrating that medium-sized hyperparameter optimization problems can be solved with Algorithm 3. Figure 8 : Validation and test losses during hyperparameter optimization. A separate L 2 weight decay is applied to the weights of each digit class, resulting in 10 hyperparameters. The weights w φ * are output by the hypernet for current hyperparameterλ, while random losses are for the best result of a random search. Hypernetwork-based optimization converges faster than random search or Bayesian optimization. We also observe significant overfitting of the hyperparameters on the validation set, which may be reduced be introducing hyperhyperparameters (parameters of the hyperparameter prior). The runtime includes the inner optimization for gradient-free approaches so that equal cumulative computational time is compared for each method.Factors affecting this include removing the overhead of constructing tuples of hyperparameters and optimized weights, viewing more hyperparameter samples, or having a better inductive bias from learning weights.",Machine learning models are usually tuned nesting optimization model weights inside optimization hyperparameters. give method collapse nested optimization joint stochastic optimization weights hyperparameters. method trains neural network output approximately optimal weights function hyperparameters. show method converges locally optimal weights hyperparameters sufficiently large hypernets. compare method standard hyperparameter optimization strategies demonstrate effectiveness tuning thousands hyperparameters. Hyperparameter λ Training validation loss neural net estimated crossvalidation crosses hypernet lines which outputs7 850-dimensional network weights. training validation loss can be cheaply evaluated hyperparameter value using hypernet. Standard cross-validation requires training scratch time.Model selection hyperparameter tuning is a major bottleneck designing predictive models. Hyperparameter optimization can be seen nested optimization:inner optimization finds model parametersw which minimizes training loss LTrain given hyperparametersλ. outer optimization choosesλ minimize validation loss LValid. DISPLAYFORM0 Standard practice machine learning solves 1 gradient-free optimization hyperparameters grid search random search Bayesian optimization. set hyperparameters is evaluated reinitializing weights training model completion. is wasteful since trains model scratch time even if the hyperparameters change small amount. Hyperband BID14 freezethaw Bayesian optimization Swerskyetal. 2014 resume model training do not waste effort. Furthermore gradient-free optimization scales poorly beyond10 20 dimensions.How can we avoid re-training scratch time? usually estimate parameters stochastic optimization true optimal parameters are a deterministic function hyperparametersλ:DISPLAYFORM1 propose learn function. Specifically can train neural network inputs hyperparameters outputs approximately optimal set weights given hyperparameters.This provides two major benefits:First can train hypernet convergence using stochastic gradient descent denoted SGD without training particular model completion. Second differentiating hypernet allowsus optimize hyperparameters gradient-based stochastic optimization.P ra eterw H perp r e e r λ Loss L Train w paper we:• Presented algorithms efficiently learn differentiable approximation best-response without nested optimization.• Showed empirically hypernets can provide better inductive bias hyperparameter optimization Gaussian processes fit directly validation loss.• Gave theoretical justification sufficiently large networks will learn best-response hyperparameters is trained against.We hope initial exploration stochastic hyperparameter optimization will inspire refinements hyper-regularization methods uncertainty-aware exploration using Bayesian hypernetworks. EXTRA EXPERIMENTS A.1 OPTIMIZING 10 HYPERPARAMETERS optimize model 10 hyperparameters which a separate L 2 weight decay is applied weights digit class linear regression model see if we can optimize medium-sized models. conditional hyperparameter distribution optimizer hypernet hyperparameters is the same the prior experiments. linear hypernet is used resulting 86 350 hyper-weights Algorithm3 is compared random search.Figure8 right shows method converges quickly better optimum either alternative method demonstrating medium-sized hyperparameter optimization problems can be solved Algorithm3. Figure8:Validation test losses hyperparameter optimization. separate L 2 weight decay is applied weights digit class resulting 10 hyperparameters. weightswφ* are output hypernet current hyperparameterλ random losses are for the best result random search. Hypernetwork-based optimization converges faster random search Bayesian optimization. also observe significant overfitting hyperparameters validation set may reduced introducing hyperhyperparameters parameters hyperparameter prior runtime includes inner optimization gradient-free approaches equal cumulative computational time is compared method.Factors affecting include removing overhead constructing tuples hyperparameters optimized weights viewing hyperparameter samples better inductive bias learning weights.,936,665,271,0.008,1.408,2025/11/05 17:19:01,0.0,1.615,0.242990654205607,294.185
"Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM). Our estimator can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Furthermore, our Bayesian treatment naturally shrinks the sample covariance matrix towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. Finally, we discuss some financial applications of the GP-LVM model. Many financial problems require the estimation of covariance matrices between given assets. This may be useful to optimize one's portfolio, i.e.: maximize the portfolio returns w T r and/or minimize the volatility √ w T Kw. Indeed, Markowitz received a Noble Price in economics for his treatment of modern portfolio theory BID9 . In practice, estimating historical returns and high-dimensional covariance matrices is challenging and often times equally weighted portfolio outperforms the portfolio constructed from sample estimates BID6 . The estimation of covariance matrices is especially hard, when the number of assets is large compared to the number of observations. Sample estimations in those cases are very unstable or can even become singular. To cope with this problem, a wide range of estimators, e.g. factor models such as the single-index model BID16 or shrinkage estimators BID8 , have been developed and employed in portfolio optimization.With todays machine learning techniques we can even further improve those estimates. Machine learning has already arrived in finance. BID10 trained an agent via reinforcement learning to optimally execute trades. BID4 forecast asset prices with neural networks and BID1 with Gaussian Processes. Recently, BID5 made an ansatz to optimally allocate portfolios using deep autoencoders. BID21 used Gaussian Processes to build volatility models and BID20 to estimate time varying covariance matrices. Bayesian machine learning methods are used more and more in this domain. The fact, that in Bayesian framework parameters are not treated as true values, but as random variables, accounts for estimation uncertainties and can even alleviate the unwanted impacts of outliers. Furthermore, one can easily incorporate additional information and/or personal views by selecting suitable priors.In this paper, we propose a Bayesian covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM) BID7 , which can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Our Bayesian treatment naturally shrinks the sample covariance matrix (which maximizes the likelihood function) towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. We evaluated our model on the stocks of S&P500 and found significant improvements in terms of model fit compared to classical linear models. Furthermore we suggest some financial applications, where Gaussian Processes can be used as well. That includes portfolio allocation, price prediction for less frequently traded stocks and non-linear clustering of stocks into their sub-sectors.In section 2 we begin with an introduction to the Bayesian non-parametric Gaussian Processes and discuss the associated requirements for learning. Section 3 introduces the financial background needed for portfolio optimization and how to relate it to Gaussian Processes. In section 4 we conduct experiments on covariance matrix estimations and discuss the results. We conclude in section 5. We applied the Gaussian Process Latent Variable Model (GP-LVM) to estimate the covariance matrix between different assets, given their time series. We then showed how the GP-LVM can be seen as a non-linear extension to the CAPM with latent factors. Based on the R 2 -score and the ELBO, we concluded, that for fixed latent space dimension Q, every non-linear kernel can capture more structure than the linear one.The estimated covariance matrix helps us to build a minimal risk portfolio according to Markowitz Portfolio theory. We evaluated the performance of different models on the S&P500 from year 2008 to 2018. Again, non-linear kernels had lower risk in the suggested portfolio and higher Sharpe ratios than the linear kernel and the baseline measures. Furthermore, we showed how to use the GP-LVM to fill in missing prices of less frequently traded assets and we discussed the role of the latent positions of the assets. In the future, one could also put a Gaussian Process on the latent positions and allow them to vary in time, which would lead to a time-dependent covariance matrix.",Estimating covariances financial assets plays important role risk management. practice when the sample size is small compared number variables empirical estimate is known unstable. propose novel covariance estimator based Gaussian Process Latent Variable Model GP-LVM estimator can be considered non-linear extension standard factor models readily interpretable parameters reminiscent market betas. Furthermore Bayesian treatment naturally shrinks sample covariance matrix towards structured matrix given prior thereby systematically reduces estimation errors. Finally discuss financial applications GP-LVM model. Many financial problems require estimation covariance matrices given assets. may useful optimize one's portfolio.e maximize portfolio returnsw r/minimize volatility√w Kw. Indeed Markowitz received Noble Price economics treatment modern portfolio theory BID9. practice estimating historical returns high-dimensional covariance matrices is challenging often times equally weighted portfolio outperforms portfolio constructed sample estimates BID6. estimation covariance matrices is especially hard when the number assets is large compared number observations. Sample estimations cases are very unstable can even become singular. cope problem wide range estimators e.g factor models single-index model BID16 shrinkage estimators BID8 have been developed employed portfolio optimization.With todays machine learning techniques can even improve estimates. Machine learning has already arrived finance. BID10 trained agent via reinforcement learning optimally execute trades. BID4 forecast asset prices neural networks BID1 Gaussian Processes. Recently BID5 made ansatz optimally allocate portfolios using deep autoencoders. BID21 used Gaussian Processes build volatility models BID20 estimate time varying covariance matrices. Bayesian machine learning methods are used domain. fact Bayesian framework parameters are not treated true values random variables accounts estimation uncertainties can even alleviate unwanted impacts outliers. Furthermore one can easily incorporate additional information/personal views selecting suitable priors.In paper propose Bayesian covariance estimator based Gaussian Process Latent Variable Model GP-LVM BID7 which can be considered non-linear extension standard factor models readily interpretable parameters reminiscent market betas. Bayesian treatment naturally shrinks sample covariance matrix which maximizes likelihood function towards structured matrix given prior thereby systematically reduces estimation errors. evaluated model stocks P500 found significant improvements terms model fit compared classical linear models. Furthermore suggest financial applications where Gaussian Processes can be used well. includes portfolio allocation price prediction less frequently traded stocks non-linear clustering stocks sub-sectors.In section2 begin introduction Bayesian non-parametric Gaussian Processes discuss associated requirements learning. Section 3 introduces financial background needed portfolio optimization how to relate Gaussian Processes. section4 conduct experiments covariance matrix estimations discuss results. conclude section5. applied Gaussian Process Latent Variable Model GP-LVM estimate covariance matrix different assets given time series. showed how the GP-LVM can be seen non-linear extension CAPM latent factors. Based R 2 -score ELBO concluded fixed latent space dimension Q every non-linear kernel can capture structure linear one.The estimated covariance matrix helpsus build minimal risk portfolio according Markowitz Portfolio theory. evaluated performance different models P500 year 2008 2018. non-linear kernels had lower risk suggested portfolio higher Sharpe ratios linear kernel baseline measures. Furthermore showed how to use GP-LVM fill missing prices less frequently traded assets discussed role latent positions assets. future one could also put Gaussian Process latent positions allow vary time would lead time-dependent covariance matrix.,898,627,271,0.008,1.432,2025/11/05 17:19:01,0.0,1.481,0.317757009345794,293.141
"We study how, in generative adversarial networks, variance in the discriminator's output affects the generator's ability to learn the data distribution. In particular, we contrast the results from various well-known techniques for training GANs when the discriminator is near-optimal and updated multiple times per update to the generator. As an alternative, we propose an additional method to train GANs by explicitly modeling the discriminator's output as a bi-modal Gaussian distribution over the real/fake indicator variables. In order to do this, we train the Gaussian classifier to match the target bi-modal distribution implicitly through meta-adversarial training. We observe that our new method, when trained together with a strong discriminator, provides meaningful, non-vanishing gradients. Generative adversarial networks BID7 are a framework for training a generator of some target (i.e., ""real"") distribution without explicitly defining a parametric generating distribution or a tractable likelihood function. Training the generator relies on a learning signal from a discriminator or discriminator, which is optimized on a relatively simple objective to distinguish between (i.e., classify) generated (i.e., ""fake"") and real samples. In order to match the true distribution, the generator parameters are optimized to maximize the loss as defined by the discriminator, which by analogy makes the generator and discriminator adversaries.In recent years, GANs have attained strong recognition as being able to generate high-quality images with sharp edges in comparison to maximum-likelihood estimation-based methods BID4 BID10 BID22 BID2 BID26 . Despite their recent successes, GANs can also be notoriously hard to train, suffering from collapse (i.e., mapping its noise to a very small set of singular outputs), missing modes of the real distribution BID3 , and vanishing and/or unstable gradients . In practice, successful learning is highly reliant on hyperparameter-tuning and model choice, and finding architectures that work with adversarial learning objectives with any / all of the above problems can be challenging BID20 .Many methods have been proposed to address learning difficulties associated with learning instability.• The use of autoencoders or posterior models in the generator or discriminator. These have been shown help to alleviate mode collapse or stabilize learning BID12 BID3 BID5 .• Regularizing the discriminator, such as with input noise , instance noise BID23 , and gradient norm regularization BID21 ).• Alternate difference measures, such as integral probability metrics (IPMs, Sriperumbudur et al., 2009 ) metrics. The most well-known of these use a dual formulation of the Wasserstein distance. These are implemented via either weight clipping or gradient penalty BID8 . These can yeild stable gradients, high-quality samples and work on a variety of architectures.On this last point, it is unclear whether the metric or the associated regularization used to impose Lipschitz is important, as regularization techniques have also been shown to be effective with stabilizing learning in f -divergences BID21 . In this paper, we study the integral role of variance in the discriminator's output in the regime of the generated distribution and how it ultimately affects learning. In the following sections , we describe theoretical motivations, an empirical analysis from multiple variants of GANs, and finally propose a regularization scheme to combat vanishing gradients on part of the discriminator when it is well-trained. In this paper, we have demonstrated the importance of intra-class variance in the discriminator's output. In particular, our results show that methods whose discriminators tend to map inputs of a class to single real values are unable to provide a reliable learning signal for the generator. Furthermore, variance in the discriminator's output is essential to allow the generator to learn in the presence of a well-trained discriminator. We proposed a technique, conceptually in line with LDA, which ensures the discriminator's output distribution follows a specified prior. Taking a broader perspective, we also introduced a new regularization technique called meta-adversarial learning, which can be applied to ensure enforce various desirable properties in GANs.","study how,in generative adversarial networks variance discriminator's output affects generator's ability learn data distribution. particular contrast results various well-known techniques training GANs when the discriminator is near-optimal updated multiple times per update generator. alternative propose additional method do this,train GANs explicitly modeling discriminator's output bi-modal Gaussian distribution real/fake indicator variables. order do this,train Gaussian classifier match target bi-modal distribution implicitly meta-adversarial training. observe new method when trained together strong discriminator provides meaningful non-vanishing gradients. Generative adversarial networks BID7 are a framework training generator target.e real distribution without explicitly defining parametric generating distribution tractable likelihood function. Training generator relies learning signal discriminator discriminator which is optimized relatively simple objective distinguish.e classify generated.e fake real samples. order match true distribution generator parameters are optimized maximize loss defined discriminator which by analogy makes generator discriminator adversaries.In recent years GANs have attained strong recognition able generate high-quality images sharp edges comparison maximum-likelihood estimation-based methods BID4 BID10 BID22 BID2 BID26. Despite recent successes GANs can also notoriously hard do this,train suffering collapse.e mapping noise small set singular outputs missing modes real distribution BID3 vanishing/unstable gradients. practice successful learning is highly reliant hyperparameter-tuning model choice finding architectures work adversarial learning objectives/problems can be challenging BID20.Many methods have been proposed address learning difficulties associated learning instability.• use autoencoders posterior models generator discriminator. have been shown help alleviate mode collapse stabilize learning BID12 BID3 BID5.• Regularizing discriminator input noise instance noise BID23 gradient norm regularization BID21.• Alternate difference measures integral probability metrics IPMs Sriperumbuduretal. 2009 metrics. well-known use dual formulation Wasserstein distance. are implemented via either weight clipping gradient penalty BID8. can yeild stable gradients high-quality samples work variety architectures.On last point is unclear whether metric associated regularization used impose Lipschitz is important regularization techniques have also shown effective stabilizing learning f -divergences BID21. paper study integral role variance discriminator's output regime generated distribution how it ultimately affects learning. following sections describe theoretical motivations empirical analysis multiple variants GANs finally propose regularization scheme combat vanishing gradients part discriminator when it is well-trained well-trained paper have demonstrated importance intra-class variance discriminator's output. particular results show methods whose discriminators tend map inputs class single real values are unable provide reliable learning signal generator. Furthermore variance discriminator's output is essential allow generator learn presence well-trained discriminator. proposed technique conceptually line LDA which ensures discriminator's output distribution follows specified prior. Taking broader perspective also introduced new regularization technique called meta-adversarial learning which can be applied ensure enforce various desirable properties GANs.",799,545,254,0.008,1.466,2025/11/05 17:19:01,0.0,1.63,0.4236760124610589,276.667
"We introduce NoisyNet, a deep reinforcement learning agent with parametric noise added to its weights, and show that the induced stochasticity of the agent’s policy can be used to aid efficient exploration. The parameters of the noise are learned with gradient descent along with the remaining network weights.   NoisyNet is straightforward to implement and adds little computational overhead. We find that replacing the conventional exploration heuristics for A3C, DQN and Dueling agents (entropy reward and epsilon-greedy respectively) with NoisyNet yields substantially higher scores for a wide range of Atari games, in some cases advancing the agent from sub to super-human performance. Despite the wealth of research into efficient methods for exploration in Reinforcement Learning (RL) (Kearns & Singh, 2002; Jaksch et al., 2010) , most exploration heuristics rely on random perturbations of the agent's policy, such as -greedy BID20 or entropy regularisation BID25 , to induce novel behaviours. However such local 'dithering' perturbations are unlikely to lead to the large-scale behavioural patterns needed for efficient exploration in many environments BID1 .Optimism in the face of uncertainty is a common exploration heuristic in reinforcement learning. Various forms of this heuristic often come with theoretical guarantees on agent performance BID1 Lattimore et al., 2013; Jaksch et al., 2010; BID0 Kearns & Singh, 2002) . However , these methods are often limited to small state-action spaces or to linear function approximations and are not easily applied with more complicated function approximators such as neural networks (except from work by BID12 b) but it doesn't come with convergence guarantees). A more structured approach to exploration is to augment the environment's reward signal with an additional intrinsic motivation term BID19 ) that explicitly rewards novel discoveries. Many such terms have been proposed, including learning progress (Oudeyer & Kaplan, 2007) , compression progress BID17 , variational information maximisation (Houthooft et al., 2016) and prediction gain BID3 . One problem is that these methods separate the mechanism of generalisation from that of exploration; the metric for intrinsic reward, and-importantly-its weighting relative to the environment reward, must be chosen by the experimenter, rather than learned from interaction with the environment. Without due care, the optimal policy can be altered or even completely obscured by the intrinsic rewards; furthermore, dithering perturbations are usually needed as well as intrinsic reward to ensure robust exploration (Ostrovski et al., 2017) . Exploration in the policy space itself, for example, with evolutionary or black box algorithms (Moriarty et al., 1999; BID9 BID16 , usually requires many prolonged interactions with the environment. Although these algorithms are quite generic and can apply to any type of parametric policies (including neural networks), they are usually not data efficient and require a simulator to allow many policy evaluations.We propose a simple alternative approach, called NoisyNet, where learned perturbations of the network weights are used to drive exploration. The key insight is that a single change to the weight vector can induce a consistent, and potentially very complex, state-dependent change in policy over multiple time steps -unlike dithering approaches where decorrelated (and, in the case of -greedy, state-independent) noise is added to the policy at every step. The perturbations are sampled from a noise distribution. The variance of the perturbation is a parameter that can be considered as the energy of the injected noise. These variance parameters are learned using gradients from the reinforcement learning loss function, along side the other parameters of the agent. The approach differs from parameter compression schemes such as variational inference (Hinton & Van Camp, 1993; BID7 BID14 BID8 BID11 and flat minima search (Hochreiter & Schmidhuber, 1997) since we do not maintain an explicit distribution over weights during training but simply inject noise in the parameters and tune its intensity automatically. Consequently, it also differs from Thompson sampling BID22 Lipton et al., 2016) as the distribution on the parameters of our agents does not necessarily converge to an approximation of a posterior distribution.At a high level our algorithm is a randomised value function, where the functional form is a neural network. Randomised value functions provide a provably efficient means of exploration (Osband et al., 2014) . Previous attempts to extend this approach to deep neural networks required many duplicates of sections of the network (Osband et al., 2016) . By contrast in our NoisyNet approach while the number of parameters in the linear layers of the network is doubled, as the weights are a simple affine transform of the noise, the computational complexity is typically still dominated by the weight by activation multiplications, rather than the cost of generating the weights. Additionally, it also applies to policy gradient methods such as A3C out of the box (Mnih et al., 2016) . Most recently (and independently of our work) Plappert et al. (2017) presented a similar technique where constant Gaussian noise is added to the parameters of the network. Our method thus differs by the ability of the network to adapt the noise injection with time and it is not restricted to Gaussian noise distributions. We need to emphasise that the idea of injecting noise to improve the optimisation process has been thoroughly studied in the literature of supervised learning and optimisation under different names (e.g., Neural diffusion process (Mobahi, 2016) and graduated optimisation BID15 ). These methods often rely on a noise of vanishing size that is non-trainable, as opposed to NoisyNet which tunes the amount of noise by gradient descent.NoisyNet can also be adapted to any deep RL algorithm and we demonstrate this versatility by providing NoisyNet versions of DQN (Mnih et al., 2015) , Dueling BID24 and A3C (Mnih et al., 2016) algorithms. Experiments on 57 Atari games show that NoisyNet-DQN and NoisyNetDueling achieve striking gains when compared to the baseline algorithms without significant extra computational cost, and with less hyper parameters to tune. Also the noisy version of A3C provides some improvement over the baseline. We have presented a general method for exploration in deep reinforcement learning that shows significant performance improvements across many Atari games in three different agent architectures. In particular, we observe that in games such as Beam rider, Asteroids and Freeway that the standard DQN, Dueling and A3C perform poorly compared with the human player, NoisyNet-DQN, NoisyNet-Dueling and NoisyNet-A3C achieve super human performance, respectively. Although the improvements in performance might also come from the optimisation aspect since the cost functions are modified, the uncertainty in the parameters of the networks introduced by NoisyNet is the only exploration mechanism of the method. Having weights with greater uncertainty introduces more variability into the decisions made by the policy, which has potential for exploratory actions, but further analysis needs to be done in order to disentangle the exploration and optimisation effects.Another advantage of NoisyNet is that the amount of noise injected in the network is tuned automatically by the RL algorithm. This alleviates the need for any hyper parameter tuning (required with standard entropy bonus and -greedy types of exploration). This is also in contrast to many other methods that add intrinsic motivation signals that may destabilise learning or change the optimal policy. Another interesting feature of the NoisyNet approach is that the degree of exploration is contextual and varies from state to state based upon per-weight variances. While more gradients are needed, the gradients on the mean and variance parameters are related to one another by a computationally efficient affine function, thus the computational overhead is marginal. Automatic differentiation makes implementation of our method a straightforward adaptation of many existing methods. A similar randomisation technique can also be applied to LSTM units BID10 and is easily extended to reinforcement learning, we leave this as future work.Note NoisyNet exploration strategy is not restricted to the baselines considered in this paper. In fact, this idea can be applied to any deep RL algorithms that can be trained with gradient descent, including DDPG (Lillicrap et al., 2015) , TRPO BID18 or distributional RL (C51) BID4 . As such we believe this work is a step towards the goal of developing a universal exploration strategy.",introduce NoisyNet deep reinforcement learning agent parametric noise added weights show induced stochasticity agents policy can be used aid efficient exploration. parameters noise are learned gradient descent along remaining network weights. NoisyNet is straightforward implement adds little computational overhead. find replacing conventional exploration heuristics A3C DQN Dueling agents entropy reward epsilon-greedy respectively NoisyNet yields substantially higher scores wide range Atari games cases advancing agent sub super-human performance. Despite wealth research efficient methods exploration Reinforcement Learning RL Kearns Singh 2002;Jakschetal. 2010 exploration heuristics rely random perturbations agent's policy -greedy BID20 entropy regularisation BID25 induce novel behaviours. However local 'dithering' perturbations are unlikely lead large-scale behavioural patterns needed efficient exploration many environments BID1.Optimism face uncertainty is a common exploration heuristic reinforcement learning. Various forms heuristic often come theoretical guarantees agent performance BID1 Lattimore etal. 2013;Jakschetal. 2010;BID0 Kearns Singh 2002 However methods are often limited small state-action spaces linear function approximations are not is easily applied complicated function approximators neural networks except work BID12b come convergence guarantees structured approach exploration is to augment environment's reward signal additional intrinsic motivation term BID19 explicitly rewards novel discoveries. Many terms have been proposed including learning progress Oudeyer Kaplan 2007 compression progress BID17 variational information maximisation Houthooftetal. 2016 prediction gain BID3. One problem is that these methods separate mechanism generalisation exploration;metric intrinsic reward and-importantly-its weighting relative environment reward must chosen experimenter rather learned interaction environment. Without due care optimal policy can be altered even completely obscured intrinsic rewards;furthermore dithering perturbations are usually needed well intrinsic reward ensure robust exploration Ostrovskietal. 2017 Exploration policy space example evolutionary black box algorithms Moriartyetal. 1999;BID9 BID16 usually requires many prolonged interactions environment. Although algorithms are quite generic can apply type parametric policies including neural networks are usually data efficient require simulator allow many policy evaluations.We propose simple alternative approach called NoisyNet where learned perturbations network weights are used drive exploration. key insight is that a single change weight vector can induce consistent potentially complex state-dependent change policy multiple time steps -unlike dithering approaches where decorrelated case -greedy state-independent noise is added policy every step. perturbations are sampled noise distribution. variance perturbation is a parameter can be considered energy injected noise. variance parameters are learned using gradients reinforcement learning loss function along side parameters agent. approach differs parameter compression schemes variational inference Hinton Van Camp 1993;BID7 BID14 BID8 BID11 flat minima search Hochreiter Schmidhuber 1997 since do not maintain explicit distribution weights training simply inject noise parameters tune intensity automatically. Consequently also differs Thompson sampling BID22 Lipton etal. 2016 distribution parameters agents does not necessarily converge approximation posterior distribution.At high level algorithm is a randomised value function where the functional form is a neural network. Randomised value functions provide provably efficient means exploration Osbandetal. 2014 Previous attempts extend approach deep neural networks required many duplicates sections network Osbandetal. 2016 contrast NoisyNet approach number parameters linear layers network is doubled weights are a simple affine transform noise computational complexity is typically still dominated weight activation multiplications rather cost generating weights. Additionally also applies policy gradient methods A3C box Mnihetal. 2016 recently independently work Plappertetal. 2017 presented similar technique where constant Gaussian noise is added parameters network. method thus differs ability network adapt noise injection time is not restricted Gaussian noise distributions. need emphasise idea injecting noise improve optimisation process has been thoroughly studied literature supervised learning optimisation different names e.g Neural diffusion process Mobahi 2016 graduated optimisation BID15 methods often rely noise vanishing size is non-trainable opposed NoisyNet which tunes amount noise gradient descent.NoisyNet can also adapted deep RL algorithm demonstrate versatility providing NoisyNet versions DQN Mnihetal. 2015 Dueling BID24 A3C Mnihetal. 2016 algorithms. Experiments 57 Atari games show NoisyNet-DQN NoisyNetDueling achieve striking gains when compared baseline algorithms without significant extra computational cost less hyper parameters tune. Also noisy version A3C provides improvement baseline. have presented general method exploration deep reinforcement learning shows significant performance improvements across many Atari games three different agent architectures. particular observe games Beam rider Asteroids Freeway standard DQN Dueling A3C perform poorly compared human player NoisyNet-DQN NoisyNet-Dueling NoisyNet-A3C achieve super human performance respectively. Although improvements performance might also come optimisation aspect since cost functions are modified uncertainty parameters networks introduced NoisyNet is the only exploration mechanism method. weights greater uncertainty introduces variability decisions made policy which has potential exploratory actions analysis needs done order disentangle exploration optimisation effects.Another advantage NoisyNet is that the amount noise injected network is tuned automatically RL algorithm. alleviates need hyper parameter tuning required standard entropy bonus -greedy types exploration is also contrast many methods add intrinsic motivation signals may destabilise learning change optimal policy. Another interesting feature NoisyNet approach is that the degree exploration is contextual varies state state based upon per-weight variances. gradients are needed gradients mean variance parameters are related one another computationally efficient affine function thus computational overhead is marginal. Automatic differentiation makes implementation method straightforward adaptation many existing methods. similar randomisation technique can also applied LSTM units BID10 are not is easily extended reinforcement learning leave future work.Note NoisyNet exploration strategy is not restricted baselines considered paper. fact idea can be applied deep RL algorithms can be trained gradient descent including DDPG Lillicrapetal. 2015 TRPO BID18 distributionalRL C51 BID4. believe work is a step towards goal developing universal exploration strategy.,1728,1201,527,0.019,1.439,2025/11/05 17:19:01,0.01,1.554,0.3395638629283489,541.156
"Localization is the problem of estimating the location of an autonomous agent from an observation and a map of the environment. Traditional methods of localization, which filter the belief based on the observations, are sub-optimal in the number of steps required, as they do not decide the actions taken by the agent. We propose ""Active Neural Localizer"", a fully differentiable neural network that learns to localize efficiently. The proposed model incorporates ideas of traditional filtering-based localization methods, by using a structured belief of the state with multiplicative interactions to propagate belief, and combines it with a policy model to minimize the number of steps required for localization. Active Neural Localizer is trained end-to-end with reinforcement learning. We use a variety of simulation environments for our experiments which include random 2D mazes, random mazes in the Doom game engine and a photo-realistic environment in the Unreal game engine. The results on the 2D environments show the effectiveness of the learned policy in an idealistic setting while results on the 3D environments demonstrate the model's capability of learning the policy and perceptual model jointly from raw-pixel based RGB observations. We also show that a model trained on random textures in the Doom environment generalizes well to a photo-realistic office space environment in the Unreal engine. Localization is the problem of estimating the position of an autonomous agent given a map of the environment and agent observations. The ability to localize under uncertainity is required by autonomous agents to perform various downstream tasks such as planning, exploration and targetnavigation. Localization is considered as one of the most fundamental problems in mobile robotics (Cox & Wilfong, 1990; BID1 . Localization is useful in many real-world applications such as autonomous vehicles, factory robots and delivery drones.In this paper we tackle the global localization problem where the initial position of the agent is unknown. Despite the long history of research, global localization is still an open problem, and there are not many methods developed which can be learnt from data in an end-to-end manner, instead typically requiring significant hand-tuning and feature selection by domain experts. Another limitation of majority of localization approaches till date is that they are passive, meaning that they passively estimate the position of the agent from the stream of incoming observations, and do not have the ability to decide the actions taken by the agent. The ability to decide the actions can result in faster as well as more accurate localization as the agent can learn to navigate quickly to unambiguous locations in the environment.We propose ""Active Neural Localizer"", a neural network model capable of active localization using raw pixel-based observations and a map of the environment 12 . Based on the Bayesian filtering algorithm for localization BID13 , the proposed model contains a perceptual model to estimate the likelihood of the agent's observations, a structured component for representing the belief, multiplicative interactions to propagate the belief based on observations and a policy model over the current belief to localize accurately while minimizing the number of steps required for localization. The entire model is fully differentiable and trained using reinforcement learning, allowing the perceptual model and the policy model to be learnt simultaneously in an end-to-end fashion. A variety of 2D and 3D simulation environments are used for testing the proposed model. We show that the Active Neural Localizer is capable of generalizing to not only unseen maps in the same domain but also across domains. In this paper, we proposed a fully-differentiable model for active global localization which uses structured components for Bayes filter-like belief propagation and learns a policy based on the belief to localize accurately and efficiently. This allows the policy and observation models to be trained jointly using reinforcement learning. We showed the effectiveness of the proposed model on a variety of challenging 2D and 3D environments including a realistic map in the Unreal environment. The results show that our model consistently outperforms the baseline models while being order of magnitudes faster. We also show that a model trained on random textures in the Doom simulation environment is able to generalize to photo-realistic Office map in the Unreal simulation environment. While this gives us hope that model can potentially be transferred to real-world environments, we leave that for future work. The limitation of the model to adapt to dynamic lightning can potentially be tackled by training the model with dynamic lightning in random mazes in the Doom environment. There can be several extensions to the proposed model too. The model can be combined with Neural Map BID32 to train an end-to-end model for a SLAM-type system and the architecture can also be utilized for end-to-end planning under uncertainity.",Localization is the problem estimating location autonomous agent observation map environment. Traditional methods localization which filter belief based observations are sub-optimal number steps required do decide actions taken agent. propose Active Neural Localizer fully differentiable neural network learns localize efficiently. proposed model incorporates ideas traditional filtering-based localization methods using structured belief state multiplicative interactions propagate belief combines policy model minimize number steps required localization. Active Neural Localizer is trained end-to-end reinforcement learning. use variety simulation environments experiments which include random 2D mazes random mazes Doom game engine photo-realistic environment Unreal game engine. results 2D environments show effectiveness learned policy idealistic setting results 3D environments demonstrate model's capability learning policy perceptual model jointly raw-pixel based RGB observations. also show model trained random textures Doom environment generalizes well photo-realistic office space environment Unreal engine. Localization is the problem estimating position autonomous agent given map environment agent observations. ability localize uncertainity is required autonomous agents perform various downstream tasks planning exploration targetnavigation. Localization is considered one fundamental problems mobile robotics Cox Wilfong 1990;BID1. Localization is useful many real-world applications autonomous vehicles factory robots delivery drones.In paper tackle global localization problem where the initial position agent is unknown. Despite long history research global localization is still open problem are many methods developed which can be learnt data end-to-end manner instead typically requiring significant hand-tuning feature selection domain experts. Another limitation majority localization approaches till date is that they are passive meaning passively estimate position agent stream incoming observations do not have the ability decide actions taken agent. ability decide actions can result faster well accurate localization agent can learn navigate quickly unambiguous locations environment.We propose Active Neural Localizer neural network model capable active localization using raw pixel-based observations map environment12. Based Bayesian filtering algorithm localization BID13 proposed model contains perceptual model estimate likelihood agent's observations structured component representing belief multiplicative interactions propagate belief based observations policy model current belief localize accurately minimizing number steps required localization. entire model is fully differentiable trained using reinforcement learning allowing perceptual model policy model learnt simultaneously end-to-end fashion. variety 2D 3D simulation environments are used testing proposed model. show Active Neural Localizer is capable generalizing unseen maps domain also across domains. paper proposed fully-differentiable model active global localization which uses structured components Bayes filter-like belief propagation learns policy based belief localize accurately efficiently. allows policy observation models trained jointly using reinforcement learning. showed effectiveness proposed model variety challenging2D 3D environments including realistic map Unreal environment. results show model consistently outperforms baseline models order magnitudes faster. also show model trained random textures Doom simulation environment is able generalize photo-realistic Office map Unreal simulation environment. gives us hope model can potentially transferred real-world environments leave future work. limitation model adapt dynamic lightning can potentially tackled training model dynamic lightning random mazes Doom environment. can be several extensions proposed model too. model can be combined Neural Map BID32 train end-to-end model SLAM-type system architecture can also utilized end-to-end planning uncertainity.,923,611,312,0.009,1.511,2025/11/05 17:19:01,0.0,1.393,0.5638629283489092,307.955
"Machine translation is an important real-world application, and neural network-based AutoRegressive Translation (ART) models have achieved very promising accuracy. Due to the unparallelizable nature of the autoregressive factorization, ART models have to generate tokens one by one during decoding and thus suffer from high inference latency. Recently, Non-AutoRegressive Translation (NART) models were proposed to reduce the inference time. However, they could only achieve inferior accuracy compared with ART models. To improve the accuracy of NART models, in this paper, we propose to leverage the hints from a well-trained ART model to train the NART model. We define two hints for the machine translation task: hints from hidden states and hints from word alignments, and use such hints to regularize the optimization of NART models. Experimental results show that the NART model trained with hints could achieve significantly better translation performance than previous NART models on several tasks. In particular, for the WMT14 En-De and De-En task, we obtain BLEU scores of 25.20 and 29.52 respectively, which largely outperforms the previous non-autoregressive baselines. It is even comparable to a strong LSTM-based ART model (24.60 on WMT14 En-De), but one order of magnitude faster in inference. Neural machine translation has attracted much attention from the research community BID1 BID13 BID5 and has been gradually adopted by industry in the past several years BID22 . Despite the huge variety of model architectures BID1 BID6 BID19 , given a source sentence x = (x 1 , ..., x Tx ) and a target sentence y = (y 1 , ..., y Ty ), most neural machine translation models decompose and estimate the conditional probability P (y|x) in an universal autoregressive manner: P (y|x) = Π Ty t=1 P (y t |y <t , x),where y <t represents the first t − 1 words of y. During inference, given an input sentence, those models generate the translation results sequentially, token by token from left to right. We call all such models AutoRegressive neural machine Translation (ART) models. A state-of-the-art ART model, Transformer BID19 , is shown in the left part of Figure 1 .A well-known limitation of the ART models is that the inference process can hardly be parallelized, and the inference time is linear with respect to the length of the target sequence. As a result, the ART models suffer from long inference time BID22 , which is sometimes unaffordable for industrial applications. Consequently , people start to develop Non-AutoRegressive neural machine Translation (NART) models to speed up the inference process BID7 BID15 . These models use the general encoder-decoder framework: the encoder takes a source sentence x as input and generates a set of contextual embeddings and predicted length T y ; conditioned on the contextual embeddings, the decoder takes a transformed copy of x as input and predicts the target tokens at all the positions independently in parallel according to the following decomposition:P (y|x, T y ) = Π Ty t=1 P (y t |T y , x).While the NART models achieve significant speedup during inference BID7 , their accuracy is considerably lower than their ART counterpart. Most of the previous works attribute the poor performance to this unavoidable conditional independence assumption of the NART model. To tackle this issue , they try to improve the expressiveness and accuracy of the decoder input in different ways: BID7 introduce fertilities from statistical machine translation models into the NART models, BID15 base the decoding process of their proposed model on an iterative refinement process, and take a step further to embed an autoregressive submodule that consists of discrete latent variables into their model. Although such methods provide better expressiveness of decoder inputs and improve the final translation accuracy, the inference speed of these models will be hurt due to the overhead of the introduced modules, which contradicts with the original purpose of introducing the NART models, i.e., to parallelize and speed up neural machine translation models.Different from previous works that develop new submodules for decoder input, we improve the translation model from another perspective. We aim to provide more guided signals during optimization. That is, we do not introduce any new prediction submodule but introduce better regularization. The reason we tackle the problem from this perspective lies in two points: First, the encoder input (source words) contains all semantic information for translation, and the decoder input in the NART model can be considered as a middle layer between input and output. It is not clear how much gain can be achieved by developing a sophisticated submodule for a middle layer in a deep neural network. Second, the encoder-decoder-based NART model is already over-parameterized.We believe that such neural network still has great ability and space to be better optimized if we can provide it with stronger and richer signals, for example, from a much better ART model: Once we have a well-trained ART model, we actually know rich information about the contexts to make the prediction at each time step and the natural word alignments between bilingual sentences. All the information could be invaluable towards the improved training of a NART model.To well leverage an ART model, we use the hint-based training framework BID17 BID3 , in which the information from hidden layers of teacher model (referred as hints) are used to guide the training process of a student model. However, hint-based training was developed for image classification models and it is challenging to define and use hints for translation. First, the translation model is composed of stacked encoder layers, attention layers, and stacked decoder layers. It is not clear how to define hints in such an encoder-decoder framework. Second, the NART and ART models are of different architectures on the decoding stage. It is not obvious how to leverage hints from the teacher to the training of student with a different architecture. We find that directly applying hints used in the classification tasks fails. In this paper, we first investigate the causes of the bad performance of the NART model, and then define hints targeting to solve the problems. According to our empirical study, we find that the hidden states of the NART model differ from the ART model: the positions where the NART model outputs incoherent tokens will have very high hidden states similarity. Also, the attention distributions of the NART model are more ambiguous than those of ART model. Based on these observations, we design two kinds of hints from the hidden states and attention distributions of the ART model, to help the training of the NART model.We have conducted experiments on the widely used WMT14 English-to-German/German-toEnglish (En-De/De-En) task and IWSLT14 German-to-English task. For WMT14 En-De task, our proposed method achieves a BLEU score of 25.20 which significantly outperforms the nonautoregressive baseline models and is even comparable to a strong ART baseline, Google's LSTMbased translation model (24.60 BID22 ). For WMT14 De-En task, we also achieve significant performance gains, reaching 29.52 in terms of BLEU.2 RELATED WORKS 2.1 AUTOREGRESSIVE TRANSLATION Given a sentence x = (x 1 , . . . , x Tx ) from the source language, the straight-forward way for translation is to generate the words in the target language y = (y 1 , . . . , y Ty ) one by one from left to right. This is also known as the autoregressive factorization in which the joint probability is decomposed into a chain of conditional probabilities, as in the Eqn. (1). Deep neural networks are widely used to model such conditional probabilities based on the encoder-decoder framework. The encoder takes the source tokens (x 1 , . . . , x Tx ) as input and encodes x into a set of context states c = (c 1 , . . . , c Tx ). The decoder takes c and subsequence y <t as input and estimates P (y t |y <t , c) according to some parametric function. Non-autoregressive translation (NART) models have suffered from low-quality translation results.In this paper, we proposed to use hints from well-trained autoregressive translation (ART) models to enhance the training of NART models. Our results on WMT14 En-De and De-En significantly outperform previous NART baselines, and achieve comparable accuracy to an LSTM-based ART model, with one order of magnitude faster in inference. In the future, we will focus on designing new architectures and new training methods for NART models to achieve comparable accuracy as the state-of-the-art ART models such as Transformer.","Machine translation is an important real-world application neural network-based AutoRegressive Translation ART models have achieved promising accuracy. Due unparallelizable nature autoregressive factorization ART models have to generate tokens one one decoding thus suffer high inference latency. Recently Non-AutoRegressive Translation NART models were proposed reduce inference time. However could achieve inferior accuracy compared ART models. improve accuracy NART models paper propose leverage hints well-trained ART model train NART model. define two hints machine translation task:hints hidden states hints word alignments use hints regularize optimization NART models. Experimental results show NART model trained hints could achieve significantly better translation performance previous NART models several tasks. particular WMT14 En-De De-En task obtain BLEU scores 25.20 29.52 respectively which largely outperforms previous non-autoregressive baselines. is even comparable strong LSTM-based ART model 24.60 WMT14 En-De one order magnitude faster inference. Neural machine translation has attracted much attention research community BID1 BID13 BID5 has been gradually adopted industry past several years BID22. Despite huge variety model architectures BID1 BID6 BID19 given source sentencex x1... xTx target sentence 1... Ty neural machine translation models decompose estimate conditional probabilityP y|x universal autoregressive manner:P y|x Π Ty t=1P |y x wherey represents first − 1 words y. inference given input sentence models generate translation results sequentially token token left right. call models AutoRegressive neural machine Translation ART models. state-of-the-art ART model Transformer BID19 is shown left part Figure 1.A well-known limitation ART models is that the inference process can hardly parallelized inference time is linear respect length target sequence. result ART models suffer long inference time BID22 which is sometimes unaffordable industrial applications. Consequently people start develop Non-AutoRegressive neural machine Translation NART models speed inference process BID7 BID15. models use general encoder-decoder framework:encoder takes source sentencex input generates set contextual embeddings predicted length y;conditioned contextual embeddings decoder takes transformed copy x input predicts target tokens positions independently parallel according following decomposition:P y|x Π Ty t=1P |T x.While NART models achieve significant speedup inference BID7 accuracy is considerably lower ART counterpart. previous works attribute poor performance unavoidable conditional independence assumption NART model. tackle issue try improve expressiveness accuracy decoder input different ways:BID7 introduce fertilities statistical machine translation models NART models BID15 base decoding process proposed model iterative refinement process take step embed autoregressive submodule consists discrete latent variables model. Although methods provide better expressiveness decoder inputs improve final translation accuracy inference speed models will be hurt due overhead introduced modules which contradicts original purpose introducing NART models.e parallelize speed neural machine translation models.Different previous works develop new submodules decoder input improve translation model another perspective. aim provide guided signals optimization. is,we do not introduce new prediction submodule introduce better regularization. reason tackle problem perspective lies two points:First encoder input source words contains semantic information translation decoder input NART model can be considered middle layer input output. is not clear how much gain can be achieved developing sophisticated submodule middle layer deep neural network. Second encoder-decoder-based NART model is already over-parameterized.We believe neural network still has great ability space better optimized if we can provide stronger richer signals example much better ART model:have a well-trained ART model actually know rich information contexts make prediction time step natural word alignments bilingual sentences. information could invaluable towards improved training NART model.To well leverage ART model use hint-based training framework BID17 BID3 which the information hidden layers teacher model referred hints are used guide training process student model. However hint-based training was developed image classification models is challenging define use hints translation. First translation model is composed stacked encoder layers attention layers stacked decoder layers. is not clear how to define hints encoder-decoder framework. Second NART ART models are of different architectures decoding stage. is not obvious how to leverage hints teacher training student different architecture. find directly applying hints used classification tasks fails. paper first investigate causes bad performance NART model define hints targeting solve problems. According empirical study find hidden states NART model differ ART model:positions where the NART model outputs incoherent tokens will have very high hidden states similarity. Also attention distributions NART model are more ambiguous ART model. Based observations design two kinds hints hidden states attention distributions ART model help training NART model.We have conducted experiments widely used WMT14 English-to-German/German-toEnglish En-De/De-En task IWSLT14 German-to-English task. WMT14 En-De task proposed method achieves BLEU score 25.20 which significantly outperforms nonautoregressive baseline models is even comparable strong ART baseline Google's LSTMbased translation model 24.60 BID22 WMT14 De-En task also achieve significant performance gains reaching 29.52 terms BLEU.2 RELATED WORKS 2.1 AUTOREGRESSIVE TRANSLATION Given sentencex x1 xTx source language straight-forward way translation is to generate words target language 1 Ty one one left right. is also known autoregressive factorization which the joint probability is decomposed chain conditional probabilities Eqn. 1 Deep neural networks are widely used model conditional probabilities based encoder-decoder framework. encoder takes source tokens x1 xTx input encodesx set context statesc c1 cTx decoder takesc subsequence input estimatesP |y c according parametric function. Non-autoregressive translation NART models have suffered low-quality translation results.In paper proposed use hints well-trained autoregressive translation ART models enhance training NART models. results WMT14 En-De De-En significantly outperform previous NART baselines achieve comparable accuracy LSTM-based ART model one order magnitude faster inference. future will focus designing new architectures new training methods NART models achieve comparable accuracy state-of-the-art ART models Transformer.",1782,1194,588,0.02,1.492,2025/11/05 17:19:01,0.01,1.571,0.5046728971962615,518.955
"Artificial neural networks are built on the basic operation of linear combination and non-linear activation function. Theoretically this structure can approximate any continuous function with three layer architecture. But in practice learning  the parameters of such network can be hard. Also the choice of activation function can greatly impact the performance of the network. In this paper we are proposing to replace the basic linear combination operation with non-linear operations that do away with the need of additional non-linear activation function. To this end we are proposing the use of elementary  morphological operations (dilation and erosion) as the basic operation in neurons. We show that these networks (Denoted as Morph-Net) with morphological operations can approximate any smooth function requiring less number of parameters than what is necessary for normal neural networks. The results show that our network perform favorably when compared with similar structured network. We have carried out our experiments on  MNIST, Fashion-MNIST, CIFAR10 and CIFAR100. In artificial neural networks, the basic building block is an artificial neuron or perceptron that simply computes the linear combination of the input BID22 . It is usually followed by a non-linear activation function to model the non-linearity of the output. Although the neurons are simple in nature, when connected together they can approximate any continuous function of the input BID4 . This has been successfully utilized in solving different real world problems like image classification (Krizhevsky et al., 2012) , semantic segmentation BID13 and image generation BID6 . While these models are quite powerful in nature, their efficient training can be hard in general BID12 and they need support of specials techniques, such as batch normalization BID5 and dropout BID24 , in order to achieve better generalization capabilities. Their training time also depends on the choice of activation function BID15 .In this paper we are proposing new building blocks for building networks similar to neural network. Here , instead of the linear combination operation of the artificial neurons, we use a non-linear operation that eliminates the need of additional activation function while requiring a small number of neurons to attain same performance or better. More specifically, We use morphological operations (i.e. dilation and erosion) as the elementary operation of the neurons in the network. Our contribution in this paper is building a network with these operations that has the following properties.1. Networks built with with dilation-erosion neurons followed by linear combination can approximate any continuous function given enough dilation/erosion neurons. 2. As dilation and erosion operation are non-linear by themselves, requirement of separate non-linear activation function is eliminated. 3. The use of dilation-erosion operation greatly increases number of possible decision boundaries. As a result, complex decision boundaries can be learned using small number of parameters.The rest of the paper is organized as follows. Section 2 describes the prior work on morphological neural network. In Section 3, we introduce our proposed network and prove its capabilities theoretically. We further demonstrate its capabilities empirically on a few benchmark datasets in Section 4. Lastly Section 6 concludes the paper. In this paper we have proposed a new class of networks that uses both normal and morphological neurons. These network consists of three layers only: input layer, dilation-erosion layer with dilation and erosion neurons followed by linear combination layer giving the output of the network with normal artificial neurons. We have done our analysis using this three layer network only, but its deeper version can also be explored. We have shown that this three layer architecture can approximate any sufficiently smooth function without requiring any non-linear activation function. These networks are able to learn a large number of hyperplanes with very few neurons in the dilation-erosion layer thereby providing superior results compared to other networks with three layer architecture. The improved results could also be the result of 'feature selection' by the max/min operator in the dilation erosion layer. In this work we have only worked with fully connected layers, i.e. a node in a layer is connected to all the nodes in the previous layer. This type of connectivity is not very efficient for image data where architectures with convolution layers perform better. So, extending this work to the case where a structuring element operates by sliding over the whole image, should be the next logical step.APPENDIX A PROOF OF LEMMA 1 From equation 9 we have DISPLAYFORM0 Now this equation can be rewritten as follows DISPLAYFORM1 where s + ik and s − ik denote the k th component of the i th structuring element of dilation and erosion neurons, respectively. The above equation can be further expressed in the following form, DISPLAYFORM2 Where DISPLAYFORM3 are define in the following way DISPLAYFORM4 Now, without any loss of generality we can write equation 17 as follows DISPLAYFORM5 where DISPLAYFORM6 Finally, we can rewrite equation 18 as DISPLAYFORM7 where l = m + n, α i ∈ {1, −1} and φ i (x)'s are of the following form DISPLAYFORM8 DISPLAYFORM9 In equation 20, v DISPLAYFORM10 represents sum of multi-oder hinge function.However, it may be noted that taking l ≥ d results hinge hyper planes which can span any where in d dimensional input space. We can assume there are l 1 and l 2 number of terms where α = 1 and α = −1 respectively, then DISPLAYFORM11 where l 1 + l 2 = l and φ i (x), φ i (x) is of same form as equation 20. Threfore can write, DISPLAYFORM12 DISPLAYFORM13 where k i ∈ {1, 2, .. , d + 1}∀i. In equation 24 we are taking maximum of (d + 1) l1 terms. Similarly we can derive same expression for Proof From equation 19, without any loss of generality we can assume there are t 1 and t 2 number of terms where α = 1 and α = −1 respectively, then DISPLAYFORM14 where t 1 + t 2 = l and φ i (x), φ i (x) are of same form as equation 20.As sum of PWL functions is also a PWL function, hence each t1 i=1 φ i (x) and t2 i=1 φ i (x) and PWL. Now, if t 1 > 0, from Proposition 3 we can conclude that g(x) is PWL linear function since difference of two continuous PWL function is PWL function . If t 1 = 0 then g(x) becomes PWL concave function.Hence, can say g(x) is PWL function.It may be noted that if l < d then PWL hyperplane will be in parallel to at least one of the axis. Taking l ≥ d results PWL hyperplane which may span anywhere in d dimensional space.Theorem 2 (Universal approximation) Using only a single dilation-erosion layer followed by a linear combination layer any continuous function can be approximated.",Artificial neural networks are built basic operation linear combination non-linear activation function. Theoretically structure can approximate continuous function three layer architecture. practice learning parameters network can be hard. Also choice activation function can greatly impact performance network. paper are proposing replace basic linear combination operation non-linear operations do away need additional non-linear activation function. end are proposing use elementary morphological operations dilation erosion basic operation neurons. show networks Denoted Morph-Net morphological operations can approximate smooth function requiring less number parameters what is necessary normal neural networks. results show network perform favorably when compared similar structured network. have carried experiments MNIST Fashion-MNIST CIFAR10 CIFAR100. artificial neural networks basic building block is an artificial neuron perceptron simply computes linear combination input BID22. is usually followed non-linear activation function model non-linearity output. Although neurons are simple nature when connected together can approximate continuous function input BID4. has been successfully utilized solving different real world problems like image classification Krizhevskyetal. 2012 semantic segmentation BID13 image generation BID6. models are quite powerful nature efficient training can be hard general BID12 need support specials techniques batch normalization BID5 dropout BID24 order achieve better generalization capabilities. training time also depends choice activation function BID15.In paper are proposing new building blocks building networks similar neural network. instead linear combination operation artificial neurons use non-linear operation eliminates need additional activation function requiring small number neurons attain performance better. specifically use morphological operations.e dilation erosion elementary operation neurons network. contribution paper is building network operations has the following following properties.1 Networks built dilation-erosion neurons followed linear combination can approximate continuous function given enough dilation/erosion neurons. 2. dilation erosion operation are non-linear requirement separate non-linear activation function is eliminated. 3. use dilation-erosion operation greatly increases number possible decision boundaries. result complex decision boundaries can be learned using small number parameters.The rest paper is organized follows. Section 2 describes prior work morphological neural network. Section3 introduce proposed network prove capabilities theoretically. demonstrate capabilities empirically benchmark datasets Section4. Lastly Section 6 concludes paper. paper have proposed new class networks uses normal morphological neurons. network consists three layers only:input layer dilation-erosion layer dilation erosion neurons followed linear combination layer giving output network normal artificial neurons. have done analysis using three layer network deeper version can also explored. have shown three layer architecture can approximate sufficiently smooth function without requiring non-linear activation function. networks are able learn large number hyperplanes neurons dilation-erosion layer thereby providing superior results compared networks three layer architecture. improved results could also result 'feature selection' max/min operator dilation erosion layer. work have only worked fully connected layers.e node layer is connected nodes previous layer. type connectivity is not very efficient image data where architectures convolution layers perform better. extending work case where a structuring element operates sliding whole image should be the next logical step.APPENDIX PROOF LEMMA1 equation9 have DISPLAYFORM0 equation can be rewritten follows DISPLAYFORM1 wheres+ik − ik denote k th component th structuring element dilation erosion neurons respectively. equation can be further expressed following form DISPLAYFORM2 Where DISPLAYFORM3 are define following way DISPLAYFORM4 without loss generality can write equation17 follows DISPLAYFORM5 where DISPLAYFORM6 Finally can rewrite equation18 DISPLAYFORM7 wherel+n α ∈ 1 −1 φ x 's are of the following form DISPLAYFORM8 DISPLAYFORM9 equation20 v DISPLAYFORM10 represents sum multi-oder hinge function.However may noted takingl≥ results hinge hyper planes which can span where in d dimensional input space. can assume arel1 l 2 number terms whereα 1 α −1 respectively DISPLAYFORM11 wherel1+l 2 l φ x φ x is of same are of same form equation20. Threfore can write DISPLAYFORM12 DISPLAYFORM13 wherek ∈ 1 2..+1 ∀i equation24 are taking maximum+1 l1 terms. Similarly can derive expression Proof equation19 without loss generality can assume aret1 2 number terms whereα 1 α −1 respectively DISPLAYFORM14 wheret1+2 l φ x φ x is of same are of same form equation 20.As sum PWL functions is also PWL function hence t1 i=1φ x t2 i=1φ x is PWL. ift1 0 Proposition3 can conclude g x is PWL linear function since difference two continuous PWL function is PWL function. Ift1 0 g x becomes PWL concave function.Hence can sayg x is PWL function.It may noted ifl PWL hyperplane will be in parallel least one axis. Takingl≥ results PWL hyperplane may span anywhere dimensional space.Theorem2 Universal approximation Using single dilation-erosion layer followed linear combination layer continuous function can be approximated.,1425,985,440,0.015,1.447,2025/11/05 17:19:01,0.01,1.485,0.3644859813084112,458.372
"With the rapidly scaling up of deep neural networks (DNNs), extensive research studies on network model compression such as weight pruning have been performed for efficient deployment. This work aims to advance the compression beyond the weights to the activations of DNNs. We propose the Integral Pruning (IP) technique which integrates the activation pruning with the weight pruning. Through the learning on the different importance of neuron responses and connections, the generated network, namely IPnet, balances the sparsity between activations and weights and therefore further improves execution efficiency. The feasibility and effectiveness of IPnet are thoroughly evaluated through various network models with different activation functions and on different datasets. With <0.5% disturbance on the testing accuracy, IPnet saves 71.1% ~ 96.35% of computation cost, compared to the original dense models with up to 5.8x and 10x reductions in activation and weight numbers, respectively. Deep neural networks (DNNs) have demonstrated significant advantages in many real-world applications, such as image classification, object detection and speech recognition BID6 BID15 BID16 . On the one hand, DNNs are developed for improving performance in these applications, which leads to intensive demands in data storage, communication and processing. On the other hand, the ubiquitous intelligence promotes the deployment of DNNs in light-weight embedded systems that are equipped with only limited memory and computation resource. To reduce the model size while ensuring the performance quality, DNN pruning is widely explored. Redundant weight parameters are removed by zeroing-out those in small values BID4 BID13 . Utilizing the zero-skipping technique BID5 on sparse weight parameters can further save the computation cost. In addition, many specific DNN accelerator designs BID0 BID14 leveraged the intrinsic zero-activation pattern of the rectified linear unit (ReLU) to realize the activation sparsity. The approach, however, cannot be directly extended to other activation functions, e.g., leaky ReLU.Although these techniques achieved tremendous success, pruning only the weights or activations cannot lead to the best inference speed, which is a crucial metric in DNN deployment, for the following reasons. First, the existing weight pruning methods mainly focus on the model size reduction. However, the most essential challenge of speeding up DNNs is to minimize the computation cost, such as the intensive multiple-and-accumulate operations (MACs). Particularly, the convolution (conv) layers account for most of the computation cost and dominate the inference time in DNNs BID13 . Because weights are shared in convolution, the execution speed of conv layers is usually bounded by computation instead of memory accesses BID7 BID21 . Second, the activation in DNNs is not strictly limited with ReLU. The intrinsic zeroactivation patterns do not exist in non-ReLU activation functions, such as leaky ReLU and sigmoid. Third, the weights and activations of a network together determine the network performance. Our experiment shows that the zero-activation percentage obtained by ReLU decreases after applying the weight pruning BID5 . Such a deterioration in activation sparsity could potentially eliminate the advantage of the aforementioned accelerator designs.In this work, we propose the integral pruning (IP) technique to minimize the computation cost of DNNs by pruning both weights and activations. As the pruning processes for weights and activations are correlated, IP learns dynamic activation masks by attaching activation pruning to weight pruning after static weight masks are well trained. Through the learning on the different importance of neuron responses and connections, the generated network, namely IPnet, balances the sparsity between activations and weights and therefore further improves execution efficiency. Moreover, our method not only stretches the intrinsic activation sparsity of ReLU, but also targets as a general approach for other activation functions, such as leaky ReLU. Our experiments on various network models with different activation functions and on different datasets show substantial reduction in MACs by the proposed IPnet. Compared to the original dense models, IPnet can obtain up to 5.8× activation compression rate, 10× weight compression rate and eliminate 71.1% ∼ 96.35% of MACs. Compared to state-of-the-art weight pruning technique BID4 , IPnet can further reduce the computation cost 1.2× ∼ 2.7×. The static activation pruning approach has been widely adopted in efficient DNN accelerator designs BID0 BID14 . By selecting a proper static threshold θ in Equation (2), more activations can be pruned with little impact on model accuracy. For the activation pruning in IP, the threshold is dynamically set according to the winner rate and activation distribution layer-wise. The comparison between static and dynamic pruning is conducted on ResNet-32 for CIFAR-10 dataset. For the static pruning setup, the θ for leaky ReLU is assigned in the range of [0.07, 0.14], which brings different activation sparsity patterns. To minimize the computation cost in DNNs, IP combining weight pruning and activation pruning is proposed in this paper. The experiment results on various models for MNIST, CIFAR-10 and ImageNet datasets have demonstrated considerable computation cost reduction. In total, a 2.3× -5.8× activation compression rate and a 2.5× -10× weight compression rate are obtained. Only 3.65% -28.9% of MACs are left with marginal effects on model accuracy, which outperforms the weight pruning by 1.2× -2.7×. The IPnets are targeted for the dedicated DNN accelerator designs with efficient sparse matrix storage and computation units on chip. The IPnets featuring compressed model size and reduced computation cost will meet the constraints from memory space and computing resource in embedded systems.",rapidly scaling deep neural networks DNNs extensive research studies network model compression weight pruning have been performed efficient deployment. work aims advance compression beyond weights activations DNNs. propose Integral Pruning IP technique which integrates activation pruning weight pruning. learning different importance neuron responses connections generated network namely IPnet balances sparsity activations weights therefore improves execution efficiency. feasibility effectiveness IPnet are thoroughly evaluated various network models different activation functions different datasets. 0.5 disturbance testing accuracy IPnet saves 71.1 96.35 computation cost compared original dense models 5.8x 10x reductions activation weight numbers respectively. Deep neural networks DNNs have demonstrated significant advantages many real-world applications image classification object detection speech recognition BID6 BID15 BID16. one hand DNNs are developed improving performance applications which leads intensive demands data storage communication processing. hand ubiquitous intelligence promotes deployment DNNs light-weight embedded systems are equipped limited memory computation resource. reduce model size ensuring performance quality DNN pruning is widely explored. Redundant weight parameters are removed zeroing-out small values BID4 BID13. Utilizing zero-skipping technique BID5 sparse weight parameters can further save computation cost. addition many specific DNN accelerator designs BID0 BID14 leveraged intrinsic zero-activation pattern rectified linear unit ReLU realize activation sparsity. approach however cannot directly extended activation functions e.g leaky ReLU.Although techniques achieved tremendous success pruning weights activations cannot lead best inference speed which is a crucial metric DNN deployment following reasons. First existing weight pruning methods mainly focus model size reduction. However essential challenge speeding DNNs is to minimize computation cost intensive multiple-and-accumulate operations MACs Particularly convolution conv layers account computation cost dominate inference time DNNs BID13. weights are shared convolution execution speed conv layers is usually bounded computation instead memory accesses BID7 BID21. Second activation DNNs is not strictly limited ReLU. intrinsic zeroactivation patterns do not exist non-ReLU activation functions leaky ReLU sigmoid. Third weights activations network together determine network performance. experiment shows zero-activation percentage obtained ReLU decreases applying weight pruning BID5. deterioration activation sparsity could potentially eliminate advantage aforementioned accelerator designs.In work propose integral pruning IP technique minimize computation cost DNNs pruning weights activations. pruning processes weights activations are correlated IP learns dynamic activation masks attaching activation pruning weight pruning static weight masks are well trained. learning different importance neuron responses connections generated network namely IPnet balances sparsity activations weights therefore improves execution efficiency. Moreover method stretches intrinsic activation sparsity ReLU also targets general approach activation functions leaky ReLU. experiments various network models different activation functions different datasets show substantial reduction MACs proposed IPnet. Compared original dense models IPnet can obtain 5.8× activation compression rate 10× weight compression rate eliminate 71.1 ∼ 96.35 MACs. Compared state-of-the-art weight pruning technique BID4 IPnet can further reduce computation cost 1.2×∼ 2.7×. static activation pruning approach has been widely adopted efficient DNN accelerator designs BID0 BID14. selecting proper static thresholdθ Equation 2 activations can be pruned little impact model accuracy. activation pruning IP threshold is dynamically set according winner rate activation distribution layer-wise comparison static dynamic pruning is conducted ResNet-32 CIFAR-10 dataset. static pruning setup θ leaky ReLU is assigned range 0.07 0.14 which brings different activation sparsity patterns. minimize computation cost DNNs IP combining weight pruning activation pruning is proposed paper. experiment results various models MNIST CIFAR-10 ImageNet datasets have demonstrated considerable computation cost reduction. total 2.3× -5.8× activation compression rate 2.5× -10× weight compression rate are obtained. 3.65 -28.9 MACs are left marginal effects model accuracy which outperforms weight pruning 1.2× -2.7×. IPnets are targeted dedicated DNN accelerator designs efficient sparse matrix storage computation units chip. IPnets featuring compressed model size reduced computation cost will meet constraints memory space computing resource embedded systems.,1170,831,339,0.011,1.408,2025/11/05 17:19:01,0.01,1.303,0.242990654205607,337.572
"The Variational Auto Encoder (VAE) is a popular generative 
latent variable model that is often 
applied for representation learning.
 Standard VAEs assume continuous valued 
latent variables and are trained by maximization
of the evidence lower bound (ELBO). Conventional methods obtain a 
differentiable estimate of the ELBO with reparametrized sampling and
optimize it with Stochastic Gradient Descend (SGD). However, this is not possible if 
we want to train VAEs with discrete valued latent variables, 
since reparametrized sampling is not possible. Till now, there
exist no simple solutions to circumvent this problem.
 In this paper, we propose an easy method to train VAEs 
with binary or categorically valued latent representations. Therefore, we use a differentiable
estimator for the ELBO which is based on importance sampling. In experiments, we verify the approach and
train two different VAEs architectures with Bernoulli and 
Categorically distributed latent representations on two different benchmark
datasets.	 In this paper, we derived an easy estimator for the ELBO, which does not rely on reparametrized sampling and therefore can be used to obtain differentiable estimates, even if reparametrization is not possible, e.g. if the latent variables z are Bernoulli or Categorically distributed. We have shown theoretically and in experiments, close to the optimal parameter configuration, the variance of the estimator approaches zero. This is a very desirable property for training.",Variational Auto Encoder VAE is a popular generative latent variable model is often applied representation learning. Standard VAEs assume continuous valued latent variables are trained maximization evidence lower bound ELBO Conventional methods obtain differentiable estimate ELBO reparametrized sampling optimize Stochastic Gradient Descend SGD However is not possible if we want train VAEs discrete valued latent variables since reparametrized sampling is not possible. Till exist simple solutions circumvent problem. paper propose easy method train VAEs binary categorically valued latent representations. Therefore use differentiable estimator ELBO which is based importance sampling. experiments verify approach train two different VAEs architectures Bernoulli Categorically distributed latent representations two different benchmark datasets. paper derived easy estimator ELBO which does not rely reparametrized sampling therefore can be used obtain differentiable estimates even if reparametrization is not possible e.g if the latent variablesz are Bernoulli Categorically distributed. have shown theoretically experiments close optimal parameter configuration variance estimator approaches zero. is a very desirable property training.,305,204,101,0.003,1.495,2025/11/05 17:19:01,0.0,1.786,0.5140186915887852,99.273
"Distributed computing can significantly reduce the training time of neural networks. Despite its potential, however, distributed training has not been widely adopted: scaling the training process is difficult, and existing SGD methods require substantial tuning of hyperparameters and learning schedules to achieve sufficient accuracy when increasing the number of workers. In practice, such tuning can be prohibitively expensive given the huge number of potential hyperparameter configurations and the effort required to test each one.
    
 We propose DANA, a novel approach that scales out-of-the-box to large clusters using the same hyperparameters and learning schedule optimized for training on a single worker, while maintaining similar final accuracy without additional overhead. DANA estimates the future value of model parameters by adapting Nesterov Accelerated Gradient to a distributed setting, and so mitigates the effect of gradient staleness, one of the main difficulties in scaling SGD to more workers.

 Evaluation on three state-of-the-art network architectures and three datasets shows that DANA scales as well as or better than existing work without having to tune any hyperparameters or tweak the learning schedule. For example, DANA achieves 75.73% accuracy on ImageNet when training ResNet-50 with 16 workers, similar to the non-distributed baseline. Modern deep neural networks are comprised of millions of parameters, which require massive amounts of data and time to learn. Steady growth of these networks over the years has made it impractical to train them from scratch on a single GPU. Distributing the computations over several GPUs can drastically reduce this training time. Unfortunately, stochastic gradient descent (SGD), typically used to train these networks, is an inherently sequential algorithm. As a result, training deep neural networks on multiple workers (computational devices) is difficult, especially when trying to maintain high efficiency, scalability and final accuracy.Data Parallelism is a common practice for distributing computation: data is split across multiple workers and each worker computes over its own data. Synchronous SGD (SSGD) is the most straightforward method to distribute the training process of neural networks: each worker computes the gradients over its own separate mini-batches, which are then aggregated to update a single model. The result is identical to multiplying the batch size B by the number of workers N , so the effective batch size is B · N . This severely limits scalability and reduces the model accuracy if not handled carefully BID25 BID6 BID8 . Furthermore, synchronization limits SSGD progress to the slowest worker: all workers must finish their current mini-batch and update the parameter server before any can proceed to the next mini-batch.Asynchronous SGD (ASGD) addresses these drawbacks by removing synchronization between the workers BID5 . Unfortunately, it suffers from gradient staleness: gradients sent by workers are often based on parameters that are older than the master's (parameter server) current parameters. Hence, distributed ASGD suffers from slow convergence and reduced final accuracy, and may not converge at all if the number of workers is high BID34 . Several works attempt to address these issues BID35 BID33 BID34 BID5 , but none has managed to overcome these problems when scaling to a large number of workers.More crucially, many ASGD algorithms require re-tuning of hyperparameters when scaling to different numbers of workers, and several even introduce new hyperparameters that must also be tuned BID35 BID33 BID34 . In practice, the vast number of potential hyperparameter configurations means that tuning is often done in parallel, with each worker independently evaluating a single configuration using standard SGD. Once the optimal hyperparameters are selected, training is completed on larger clusters of workers. Any additional tuning for ASGD can thus be computationally expensive and time-consuming. Though many algorithms have been proposed to reduce the cost of tuning BID2 BID13 BID12 BID9 BID26 , hyperparameter search remains a significant obstacle, and many practitioners cannot afford to re-tune hyperparameters for distributed training.Our contribution: We propose Distributed Accelerated Nesterov ASGD (DANA), a new distributed ASGD algorithm that works out of the box: it achieves state-of-the-art accuracy on existing architectures without any additional hyperparameter tuning or changes to the training schedule, while scaling as well or better than existing ASGD approaches, and without any additional overhead. Our DANA implementation achieves state-of-the-art accuracy on ImageNet when training ResNet-50 with 16 and even 32 workers, as well as on CIFAR-10 and CIFAR-100. DANA is a new asynchronous SGD algorithm for training of neural networks. By mitigating the effect of gradient staleness, DANA scales out-of-the-box to large clusters using the same hyperparameters and learning schedule optimized for training on a single worker, while maintaining similar final accuracy, without adding any overhead at the master. DANA could be used to extend other non-distributed optimization procedures (e.g., Nadam BID7 ) to a distributed setting without adding parameters. Integrating DANA with DC-ASGD could further mitigate gradient staleness, though without eliminating tuning. Finally, we are working to extend DANA with separate, selfadjusting weights per worker to address settings with heterogeneous workers while avoiding tuning.",Distributed computing can significantly reduce training time neural networks. Despite potential however distributed training has not been widely adopted:scaling training process is difficult existing SGD methods require substantial tuning hyperparameters learning schedules achieve sufficient accuracy when increasing number workers. practice tuning can be prohibitively expensive given huge number potential hyperparameter configurations effort required test one. propose DANA novel approach scales out-of-the-box large clusters using hyperparameters learning schedule optimized training single worker maintaining similar final accuracy without additional overhead. DANA estimates future value model parameters adapting Nesterov Accelerated Gradient distributed setting mitigates effect gradient staleness one main difficulties scaling SGD workers. Evaluation three state-of-the-art network architectures three datasets shows DANA scales well better existing work without tune hyperparameters tweak learning schedule. example DANA achieves 75.73 accuracy ImageNet when training ResNet-50 16 workers similar non-distributed baseline. Modern deep neural networks are comprised millions parameters which require massive amounts data time learn. Steady growth networks years has made impractical train scratch single GPU. Distributing computations several GPUs can drastically reduce training time. Unfortunately stochastic gradient descent SGD typically used train networks is an inherently sequential algorithm. result training deep neural networks multiple workers computational devices is difficult especially when trying maintain high efficiency scalability final accuracy.Data Parallelism is a common practice distributing computation:data is split across multiple workers worker computes data. Synchronous SGD SSGD is the most straightforward method distribute training process neural networks:worker computes gradients separate mini-batches which are then aggregated update single model. result is identical multiplying batch sizeB number workersN effective batch size isB·N. severely limits scalability reduces model accuracy if not handled carefully BID25 BID6 BID8. Furthermore synchronization limits SSGD progress slowest worker:workers must finish current mini-batch update parameter server can proceed next mini-batch.Asynchronous SGD ASGD addresses drawbacks removing synchronization workers BID5. Unfortunately suffers gradient staleness:gradients sent workers are often based parameters are older master's parameter server current parameters. Hence distributed ASGD suffers slow convergence reduced final accuracy may converge if the number workers is high BID34. Several works attempt address issues BID35 BID33 BID34 BID5 none has managed overcome problems when scaling large number workers.More crucially many ASGD algorithms require re-tuning hyperparameters when scaling different numbers workers several even introduce new hyperparameters must also tuned BID35 BID33 BID34. practice vast number potential hyperparameter configurations means tuning is often done parallel worker independently evaluating single configuration using standard SGD. optimal hyperparameters are selected training is completed larger clusters workers. additional tuning ASGD can thus computationally expensive time-consuming Though many algorithms have been proposed reduce cost tuning BID2 BID13 BID12 BID9 BID26 hyperparameter search remains significant obstacle many practitioners cannot afford re-tune hyperparameters distributed training.Our contribution:propose Distributed Accelerated Nesterov ASGD DANA new distributed ASGD algorithm works box:achieves state-of-the-art accuracy existing architectures without additional hyperparameter tuning changes training schedule scaling well better existing ASGD approaches without additional overhead. DANA implementation achieves state-of-the-art accuracy ImageNet when training ResNet-50 16 even 32 workers well CIFAR-10 CIFAR-100 DANA is a new asynchronous SGD algorithm training neural networks. mitigating effect gradient staleness DANA scales out-of-the-box large clusters using hyperparameters learning schedule optimized training single worker maintaining similar final accuracy without adding overhead master. DANA could used extend non-distributed optimization procedures e.g Nadam BID7 distributed setting without adding parameters. Integrating DANA DC-ASGD could mitigate gradient staleness though without eliminating tuning. Finally are working extend DANA separate selfadjusting weights per worker address settings heterogeneous workers avoiding tuning.,1035,747,288,0.009,1.386,2025/11/05 17:19:01,0.0,1.382,0.1744548286604356,316.882
"This paper proposes a novel approach to train deep neural networks by unlocking the layer-wise dependency of backpropagation training. The approach employs additional modules called local critic networks besides the main network model to be trained, which are used to obtain error gradients without complete feedforward and backward propagation processes. We propose a cascaded learning strategy for these local networks. In addition, the approach is also useful from multi-model perspectives, including structural optimization of neural networks, computationally efficient progressive inference, and ensemble classification for performance improvement. Experimental results show the effectiveness of the proposed approach and suggest guidelines for determining appropriate algorithm parameters. In recent days, deep learning has been remarkably advanced and successfully applied in numerous fields BID14 . A key mechanism behind the success of deep neural networks is that they are capable of extracting useful information progressively through their layered structures. It is an increasing trend that more and more complex deep neural network structures are developed in order to solve challenging real-world problems, e.g., BID7 . Training of deep neural networks is based on backpropagation in most cases, which basically works in a sequential and synchronous manner. During the feedforward pass, the input data is processed through the hidden layers to produce the network output; during the feedback pass, the error gradient is propagated back through the layers to update each layer's weight parameters. Therefore, training of each layer has dependency on all the other layers, which causes the issue of locking BID9 . This is undesirable in some cases, e.g., a system consisting of several interacting models, a model distributed across multiple computing nodes, etc.There have been attempts to remove the locking constraint. In BID0 , the method of auxiliary coordinates (MAC) is proposed. It replaces the original loss minimization problem with an equality-constrained optimization problem by introducing an auxiliary variable for each data and each hidden unit. Then, solving the problem is formulated as iteratively solving several sub-problems independently. A similar approach using the alternating direction method of multipliers (ADMM) is proposed in BID17 . It also employs an equality-constrained optimization but with different auxiliary variables, so that resulting sub-problems have closed form solutions. However, these methods are not scalable to deep learning architectures such as convolutional neural networks (CNNs).The method proposed in BID9 , called decoupled neural interface (DNI), directly synthesizes estimated error gradients, called synthetic gradients, using an additional small neural network for training a layer's weight parameters. As long as the synthetic gradients are close to the actual backpropagated gradients, each layer does not need to wait until the error at the output layer is backpropagated through the preceding layers, which allows independent training of each layer. However , this method suffers from performance degradation when compared to regular backpropagation BID2 . The idea of having additional modules supporting the layers of the main model is also adopted in BID2 , where the additional modules are trained to approximate the main model's outputs instead of error gradients. Due to this , however, the method does not resolve the issue of update locking, and in fact, the work does not intend to design a non-sequential learning algorithm. BID9 and the proposed local critic training. The black, green , and blue arrows indicate feedforward passes, an error gradient flow, and loss comparison, respectively.In this paper, we propose a novel approach for non-sequential learning, called local critic training. The key idea is that additional modules besides the main neural network model are employed, which we call local critics, in order to indirectly deliver error gradients to the main model for training without backpropagation. In other words, a local critic located at a certain layer group is trained in such a way that the derivative of its output serves as the error gradient for training of the corresponding layers' weight parameters. Thus, the error gradient does not need to be backpropagated, and the feedforward operations and gradient-descent learning can be performed independently. Through extensive experiments, we examine the influences of the network structure, update frequency, and total number of local critics, which provide not only insight into operation characteristics but also guidelines for performance optimization of the proposed method.In addition to the capability of implementing training without locking, the proposed approach can be exploited for additional important applications. First, we show that applying the proposed method automatically performs structural optimization of neural networks for a given problem, which has been a challenging issue in the machine learning field. Second, a progressive inference algorithm using the network trained with the proposed method is presented, which can adaptively reduce the computational complexity during the inference process (i.e., test phase) depending on the given data. Third, the network trained by the proposed method naturally enables ensemble inference that can improve the classification performance. In this paper, we proposed the local critic training approach for removing the inter-layer locking constraint in training of deep neural networks. In addition, we proposed three applications of the local critic training method: structural optimization of neural networks, progressive inference, and ensemble classification. It was demonstrated that the proposed method can successfully train CNNs with local critic networks having extremely simple structures. The performance of the method was also evaluated in various aspects, including effects of structures and update intervals of local critic networks and influences of the sizes of layer groups. Finally, it was shown that structural optimization, progressive inference, and ensemble classification can be performed directly using the models trained with the proposed approach without additional procedures. A ADDITIONAL RESULTS",paper proposes novel approach train deep neural networks unlocking layer-wise dependency backpropagation training. approach employs additional modules called local critic networks besides main network model trained which are used obtain error gradients without complete feedforward backward propagation processes. propose cascaded learning strategy local networks. addition approach is also useful multi-model perspectives including structural optimization neural networks computationally efficient progressive inference ensemble classification performance improvement. Experimental results show effectiveness proposed approach suggest guidelines determining appropriate algorithm parameters. recent days deep learning has been remarkably advanced successfully applied numerous fields BID14. key mechanism behind success deep neural networks is that they are capable extracting useful information progressively layered structures. is an increasing trend complex deep neural network structures are developed order solve challenging real-world problems e.g BID7. Training deep neural networks is based backpropagation cases which basically works sequential synchronous manner. feedforward pass input data is processed hidden layers produce network output;feedback pass error gradient is propagated back layers update layer's weight parameters. Therefore training layer has dependency layers which causes issue locking BID9. is undesirable cases e.g system consisting several interacting models model distributed across multiple computing nodes etc.There have been attempts remove locking constraint. BID0 method auxiliary coordinates MAC is proposed. replaces original loss minimization problem equality-constrained optimization problem introducing auxiliary variable data hidden unit. solving problem is formulated iteratively solving several sub-problems independently. similar approach using alternating direction method multipliers ADMM is proposed BID17. also employs equality-constrained optimization different auxiliary variables resulting sub-problems have closed form solutions. However methods are not scalable deep learning architectures convolutional neural networks CNNs.The method proposed BID9 called decoupled neural interface DNI directly synthesizes estimated error gradients called synthetic gradients using additional small neural network training layer's weight parameters. long synthetic gradients are close actual backpropagated gradients layer does not need wait error output layer is backpropagated preceding layers which allows independent training layer. However method suffers performance degradation when compared regular backpropagation BID2. idea additional modules supporting layers main model is also adopted BID2 where the additional modules are trained approximate main model's outputs instead error gradients. Due however method does not resolve issue update locking fact work does not intend design non-sequential learning algorithm. BID9 proposed local critic training. black green blue arrows indicate feedforward passes error gradient flow loss comparison respectively.In paper propose novel approach non-sequential learning called local critic training. key idea is that additional modules besides main neural network model are employed which we call local critics order indirectly deliver error gradients main model training without backpropagation. words local critic located certain layer group is trained way derivative output serves error gradient training corresponding layers' weight parameters. Thus error gradient does not need backpropagated feedforward operations gradient-descent learning can be performed independently. extensive experiments examine influences network structure update frequency total number local critics which provide insight operation characteristics also guidelines performance optimization proposed method.In addition capability implementing training without locking proposed approach can be exploited additional important applications. First show applying proposed method automatically performs structural optimization neural networks given problem which has been challenging issue machine learning field. Second progressive inference algorithm using network trained proposed method is presented which can adaptively reduce computational complexity inference process.e test phase depending given data. Third network trained proposed method naturally enables ensemble inference can improve classification performance. paper proposed local critic training approach removing inter-layer locking constraint training deep neural networks. addition proposed three applications local critic training method:structural optimization neural networks progressive inference ensemble classification. was demonstrated proposed method can successfully train CNNs local critic networks extremely simple structures. performance method was also evaluated various aspects including effects structures update intervals local critic networks influences sizes layer groups. Finally was shown structural optimization progressive inference ensemble classification can be performed directly using models trained proposed approach without additional procedures. ADDITIONAL RESULTS,1093,748,345,0.011,1.461,2025/11/05 17:19:01,0.01,1.452,0.4080996884735203,343.958
"\emph{Truncated Backpropagation Through Time} (truncated BPTT, \cite{jaeger2002tutorial}) is a widespread method for learning recurrent computational graphs. Truncated BPTT keeps the computational benefits of \emph{Backpropagation Through Time} (BPTT \cite{werbos:bptt}) while relieving the need for a complete backtrack through the whole data sequence at every step.   However, truncation favors short-term dependencies: the gradient estimate of truncated BPTT is biased, so that it does not benefit from the convergence guarantees from stochastic gradient theory. We introduce \emph{Anticipated Reweighted Truncated Backpropagation} (ARTBP), an algorithm that keeps the computational benefits of truncated BPTT, while providing unbiasedness. ARTBP works by using variable truncation lengths together with carefully chosen compensation factors in the backpropagation equation. We check the viability of ARTBP on two tasks. First, a simple synthetic task where careful balancing of temporal dependencies at different scales is needed: truncated BPTT displays unreliable performance, and in worst case scenarios, divergence, while ARTBP converges reliably. Second, on Penn Treebank character-level language modelling \cite{ptb_proc}, ARTBP slightly outperforms truncated BPTT.
 We have shown that the bias introduced by truncation in the backpropagation through time algorithm can be compensated by the simple mathematical trick of randomizing the truncation points and introducing compensation factors in the backpropagation equation. The algorithm is experimentally viable, and provides proper balancing of the effects of different time scales when training recurrent models.",\emph Truncated Backpropagation Time truncated BPTT \cite jaeger2002tutorial is a widespread method learning recurrent computational graphs. Truncated BPTT keeps computational benefits \emph Backpropagation Time BPTT \cite werbos:bptt relieving need complete backtrack whole data sequence every step. However truncation favors short-term dependencies:gradient estimate truncated BPTT is biased does not benefit convergence guarantees stochastic gradient theory. introduce \emph Anticipated Reweighted Truncated Backpropagation ARTBP algorithm keeps computational benefits truncated BPTT providing unbiasedness. ARTBP works using variable truncation lengths together carefully chosen compensation factors backpropagation equation. check viability ARTBP two tasks. First simple synthetic task where careful balancing temporal dependencies different scales is needed:truncated BPTT displays unreliable performance worst case scenarios divergence ARTBP converges reliably. Second Penn Treebank character-level language modelling \cite ptb_proc ARTBP slightly outperforms truncated BPTT. have shown bias introduced truncation backpropagation time algorithm can be compensated simple mathematical trick randomizing truncation points introducing compensation factors backpropagation equation. algorithm is experimentally viable provides proper balancing effects different time scales when training recurrent models.,332,245,87,0.003,1.355,2025/11/05 17:19:01,0.0,1.333,0.0778816199376944,98.88
"Graph convolutional networks (GCNs) have been widely used for classifying graph nodes in the semi-supervised setting.
 Previous works have shown that GCNs are vulnerable to the perturbation on adjacency and feature matrices of existing nodes. However, it is unrealistic to change the connections of  existing nodes in many applications, such as existing users in social networks. In this paper, we investigate methods attacking GCNs by adding fake nodes. A greedy algorithm is proposed to generate adjacency and feature matrices of fake nodes, aiming to minimize the classification accuracy on the existing ones. In additional, we introduce a discriminator to classify fake nodes from real nodes, and propose a Greedy-GAN algorithm to simultaneously update the discriminator and the attacker, to make fake nodes indistinguishable to the real ones.   Our non-targeted attack decreases the accuracy of GCN down to 0.10, and our targeted attack reaches a success rate of 0.99 for attacking the whole datasets, and 0.94 on average for attacking a single node. Graphs play a very important role in many real world applications, such as social networks (Facebook and Twitter), biological networks (protein-protein interaction networks and gene interaction networks), as well as attribute graphs (PubMed and Arxiv) BID12 BID32 BID26 . Node classification is one of the most important tasks on graphs-given a graph with labels associated with a subset of nodes, predict the labels for rest of the nodes. For this node classification task, deep learning models on graphs, such as Graph Convoltional Networks (GCNs), have achieved state of the art performance BID16 . Moreover, GCNs have wide applications in cyber security, where they can learn a close-to-correct node labeling semiautonomously. This reduces the load on security experts and helps to manage networks that add or remove nodes dynamically, such as, WiFi networks in universities and web services in companies.The wide applicability of GCNs motivates recent studies about their robustness. BID34 BID6 developed algorithms to attack GCNs, showing that by altering a small amount of edges and features, the classification accuracy of GCNs can be reduced to chance-level. However, changing edges or features associated with existing nodes is impractical in many cases. For example, in social network applications, an attacker has to login to the users' accounts to change existing connections and features, and gaining login accesses is almost impossible. In comparison, adding fake nodes that correspond to fake accounts or users, can be much easier in practice. But the key question is can we interfere the classification results of existing nodes by adding fake nodes to the network? We answer this question affirmative by introducing novel algorithms to design fake nodes that successfully reduce GCN's performance on existing nodes.To design the adjacency and feature matrices associated with fake nodes, we have to address two challenges. First, the edges and features are usually discrete 0/1 variables. Although there have been many algorithms proposed for attacking image classifiers, such as FGSM, C&W and PGD attacks BID11 BID1 BID21 , they all assume continuous input space and cannot be directly applied to problems with discrete input space. Second, it's not easy to make the fake nodes ""looked"" like the real ones? For example, if we add a fake node that connects to all existing nodes, the system can easily detect and disable such fake node. In this paper, we propose two algorithms, Greedy attack and Greedy-GAN attack, to address these two challenges. Our contributions can be summarized below:• To the best of our knowledge, this is the first paper studying how to add fake nodes to attack GCNs. We do not need to manipulate existing nodes' adjacency and feature matrices.• We propose a Greedy attack algorithm to address the discrete input space problem in designing fake nodes' adjacency and feature matrices.• We introduce a discriminator to classify fake nodes from real nodes, and propose a Greedy-GAN algorithm to simultaneous optimize the discriminator and the attacker. Despite a lower successful rate, this approach can make fake nodes harder to detect.• We conduct experiments on several real datasets. For non-targeted attack, we get accuracy down to 0.10 for the Cora dataset, and 0.14 for the Citeseer dataset. For targeted attack on whole datasets, Greedy attack have up to 99% success rate on Cora and 90% on Citeseer.For targeted attack on a single node, it could reach 94% success rate on Cora and 0.80% success rate on Citeseer. We present two algorithms, Greedy and Greedy-GAN, on adversarial attacks of GCNs by adding fake nodes, without changing any existing edges or features, for both non-targeted and targeted attacks. We successfully attacked existing GCN implementations, and explored parameter sensitives, such as number of fake nodes and different label rates of fake nodes. To make the attack unnoticeable, we added a discriminator using the Greedy-GAN algorithm to generate features of fake nodes. We noticed that data cleaning before training is crucial, and adding a discriminator makes the impact of attacks weaker. There is a trade-off between the efficiency of attack and realness of fake nodes' features.",Graph convolutional networks GCNs have been widely used classifying graph nodes semi-supervised setting. Previous works have shown GCNs are vulnerable perturbation adjacency feature matrices existing nodes. However is unrealistic change connections existing nodes many applications existing users social networks. paper investigate methods attacking GCNs adding fake nodes. greedy algorithm is proposed generate adjacency feature matrices fake nodes aiming minimize classification accuracy existing ones. additional introduce discriminator classify fake nodes real nodes propose Greedy-GAN algorithm simultaneously update discriminator attacker make fake nodes indistinguishable real ones. non-targeted attack decreases accuracy GCN 0.10 targeted attack reaches success rate 0.99 attacking whole datasets 0.94 average attacking single node. Graphs play important role many real world applications social networks Facebook Twitter biological networks protein-protein interaction networks gene interaction networks well attribute graphs PubMed Arxiv BID12 BID32 BID26. Node classification is one important tasks graphs-given graph labels associated subset nodes predict labels rest nodes. node classification task deep learning models graphs Graph Convoltional Networks GCNs have achieved state art performance BID16. Moreover GCNs have wide applications cyber security where they can learn close-to-correct node labeling semiautonomously. reduces load security experts helps manage networks add remove nodes dynamically WiFi networks universities web services companies.The wide applicability GCNs motivates recent studies robustness. BID34 BID6 developed algorithms attack GCNs showing altering small amount edges features classification accuracy GCNs can be reduced chance-level However changing edges features associated existing nodes is impractical many cases. example social network applications attacker has to login users' accounts change existing connections features gaining login accesses is almost impossible. comparison adding fake nodes correspond fake accounts users can be much easier practice. key question is can we interfere classification results existing nodes adding fake nodes network? answer question affirmative introducing novel algorithms design fake nodes successfully reduce GCN's performance existing nodes.To design adjacency feature matrices associated fake nodes have to address two challenges. First edges features are usually discrete0/1 variables. Although have been many algorithms proposed attacking image classifiers FGSM C W PGD attacks BID11 BID1 BID21 assume continuous input space cannot directly applied problems discrete input space. Second easy make fake nodes looked like real ones? example if we add fake node connects existing nodes system can easily detect disable fake node. paper propose two algorithms Greedy attack Greedy-GAN attack have to address two challenges. contributions can be summarized below:• best knowledge is the first paper studying how to add fake nodes attack GCNs. do not need manipulate existing nodes' adjacency feature matrices.• propose Greedy attack algorithm address discrete input space problem designing fake nodes' adjacency feature matrices.• introduce discriminator classify fake nodes real nodes propose Greedy-GAN algorithm simultaneous optimize discriminator attacker. Despite lower successful rate approach can make fake nodes harder detect.• conduct experiments several real datasets. non-targeted attack get accuracy 0.10 Cora dataset 0.14 Citeseer dataset. targeted attack whole datasets Greedy attack haveupto99% success rate Cora 90% Citeseer.For targeted attack single node could reach94% success rate Cora 0.80 success rate Citeseer. present two algorithms Greedy Greedy-GAN adversarial attacks GCNs adding fake nodes without changing existing edges features non-targeted targeted attacks. successfully attacked existing GCN implementations explored parameter sensitives number fake nodes different label rates fake nodes. make attack unnoticeable added discriminator using Greedy-GAN algorithm generate features fake nodes. noticed data cleaning training is crucial adding discriminator makes impact attacks weaker. is a trade-off efficiency attack realness fake nodes' features.,1066,732,334,0.011,1.456,2025/11/05 17:19:01,0.01,1.643,0.392523364485981,323.002
"Transfer learning aims to solve the data sparsity for a specific domain by applying information of another domain. Given a sequence (e.g. a natural language sentence), the transfer learning, usually enabled by recurrent neural network (RNN), represent the sequential information transfer. RNN uses a chain of repeating cells to model the sequence data. However, previous studies of neural network based transfer learning simply transfer the information across the whole layers, which are unfeasible for seq2seq and sequence labeling. Meanwhile, such layer-wise transfer learning mechanisms also lose the fine-grained cell-level information from the source domain.

 In this paper, we proposed the aligned recurrent transfer, ART, to achieve cell-level information transfer. ART is in a recurrent manner that different cells share the same parameters. Besides transferring the corresponding information at the same position, ART transfers information from all collocated words in the source domain. This strategy enables ART to capture the word collocation across domains in a more flexible way. We conducted extensive experiments on both sequence labeling tasks (POS tagging, NER) and sentence classification (sentiment analysis). ART outperforms the state-of-the-arts over all experiments.
 Most previous NLP studies focus on open domain tasks. But due to the variety and ambiguity of natural language BID7 BID18 , models for one domain usually incur more errors when adapting to another domain. This is even worse for neural networks since embeddingbased neural network models usually suffer from overfitting BID12 . While existing NLP models are usually trained by the open domain, they suffer from severe performance degeneration when adapting to specific domains. This motivates us to train specific models for specific domains.The key issue of training a specific domain is the insufficiency of labeled data. Transfer learning is one promising way to solve the insufficiency BID8 . Existing studies BID3 BID8 have shown that (1) NLP models in different domains still share many common features (e.g. common vocabularies, similar word semantics, similar sentence syntaxes), and (2) the corpus of the open domain is usually much richer than that of a specific domain.Our transfer learning model is under the pre-training framework. We first pre-train the model for the source domain. Then we fine-tune the model for the target domain. Recently, some pre-trained models (e.g. BERT BID4 , ELMo (Peters et al., 2018) , GPT-2 (Radford et al., 2019) ) successfully learns general knowledge for text. The difference is that these models use a large scale and domain-independent corpus for pre-training. In this paper, we use a small scale but domaindependent corpus as the source domain for pre-training. We argue that, for the pre-training corpus, the domain relevance will overcome the disadvantage of limited scale.Most previous transfer learning approaches BID11 BID6 only transfer information across the whole layers. This causes the information loss from cells in the source domain. ''Layer-wise transfer learning"" indicates that the approach represents the whole sentence by a single vector. So the transfer mechanism is only applied to the vector. We highlight the effectiveness of precisely capturing and transferring information of each cell from the source domain in two cases. First, in seq2seq (e.g. machine translation) or sequence labeling (e.g. POS tagging) tasks, all cells directly affect the results. So layer-wise information transfer is unfeasible for these tasks. Second, even for the sentence classification, cells in the source domain provide more fine-grained information to understand the target domain. For example, in figure 1, parameters for ""hate"" are insufficiently trained. The model transfers the state of ""hate"" from the source domain to understand it better.Target: Sometimes I really hate RIBs.Source: Sometimes I really hate RIBs. Figure 1 : Motivation of ART. The orange words ""sometimes"" and ""hate"" are with insufficiently trained parameters. The red line indicates the information transfer from the corresponding position. The blue line indicates the information transfer from a collocated word. Besides transferring the corresponding position's information, the transfer learning algorithm captures the cross-domain long-term dependency. Two words that have a strong dependency on each other can have a long gap between them. Being in the insufficiently trained target domain, a word needs to represent its precise meaning by incorporating the information from its collocated words. Here ""collocate"" indicates that a word's semantics can have long-term dependency on other words. To understand a word in the target domain, we need to precisely represent its collocated words from the source domain. We learn the collocated words via the attention mechanism BID1 . For example, in figure 1, ""hate"" is modified by the adverb ""sometimes"", which implies the act of hating is not serious. But the ""sometimes"" in the target domain is trained insufficiently. We need to transfer the semantics of ""sometimes"" in the source domain to understand the implication. Therefore, we need to carefully align word collocations between the source domain and the target domain to represent the long-term dependency.In this paper, we proposed ART (aligned recurrent transfer), a novel transfer learning mechanism, to transfer cell-level information by learning to collocate cross-domain words. ART allows the celllevel information transfer by directly extending each RNN cell. ART incorporates the hidden state representation corresponding to the same position and a function of the hidden states for all words weighted by their attention scores.Cell-Level Recurrent Transfer ART extends each recurrent cell by taking the states from the source domain as an extra input. While traditional layer-wise transfer learning approaches discard states of the intermediate cells, ART uses cell-level information transfer, which means each cell is affected by the transferred information. For example, in figure 1, the state of ""hate"" in the target domain is affected by ""sometimes"" and ""hate"" in the source domain. Thus ART transfers more fine-grained information.Learn to Collocate and Transfer For each word in the target domain, ART learns to incorporate two types of information from the source domain: (a) the hidden state corresponding to the same word, and (b) the hidden states for all words in the sequence. Information (b) enables ART to capture the cross-domain long-term dependency. ART learns to incorporate information (b) based on the attention scores BID1 of all words from the source domain. Before learning to transfer, we first pre-train the neural network of the source domain. Therefore ART is able to leverage the pre-trained information from the source domain. In this paper, we study the problem of transfer learning for sequences. We proposed the ART model to collocate and transfer cell-level information. ART has three advantages: (1) it transfers more fine-grained cell-level information, and thus can be adapted to seq2seq or sequence labeling tasks; (2) it aligns and transfers a set of collocated words in the source sentence to represent the cross domain long-term dependency; (3) it is general and can be applied to different tasks. Besides, ART verified the effectiveness of pre-training models with the limited but relevant training corpus.",Transfer learning aims solve data sparsity specific domain applying information another domain. Given sequence e.g natural language sentence transfer learning usually enabled recurrent neural network RNN represent sequential information transfer. RNN uses chain repeating cells model sequence data. However previous studies neural network based transfer learning simply transfer information across whole layers which are unfeasible seq2seq sequence labeling. Meanwhile layer-wise transfer learning mechanisms also lose fine-grained cell-level information source domain. paper proposed aligned recurrent transfer ART achieve cell-level information transfer. ART is in a recurrent manner different cells share parameters. Besides transferring corresponding information position ART transfers information collocated words source domain. strategy enables ART capture word collocation across domains flexible way. conducted extensive experiments sequence labeling tasks POS tagging NER sentence classification sentiment analysis ART outperforms state-of-the-arts experiments. previous NLP studies focus open domain tasks. due variety ambiguity natural language BID7 BID18 models one domain usually incur errors when adapting another domain. is even worse neural networks since embeddingbased neural network models usually suffer overfitting BID12. existing NLP models are usually trained open domain suffer severe performance degeneration when adapting specific domains. motivatesus train specific models specific domains.The key issue training specific domain is the insufficiency labeled data. Transfer learning is one promising way solve insufficiency BID8. Existing studies BID3 BID8 have shown 1 NLP models different domains still share many common features e.g common vocabularies similar word semantics similar sentence syntaxes 2 corpus open domain is usually much richer specific domain.Our transfer learning model is under the pre-training framework. first pre-train model source domain. fine-tune model target domain. Recently pre-trained models e.g BERT BID4 ELMo Petersetal. 2018 GPT-2 Radfordetal. 2019 successfully learns general knowledge text. difference is that these models use large scale domain-independent corpus pre-training paper use small scale domaindependent corpus source domain pre-training argue pre-training corpus domain relevance will overcome disadvantage limited scale.Most previous transfer learning approaches BID11 BID6 transfer information across whole layers. causes information loss cells source domain. Layer-wise transfer learning indicates approach represents whole sentence single vector. transfer mechanism is only applied vector. highlight effectiveness precisely capturing transferring information cell source domain two cases. First seq2seq e.g machine translation sequence labeling e.g POS tagging tasks cells directly affect results. layer-wise information transfer is unfeasible tasks. Second even sentence classification cells source domain provide fine-grained information understand target domain. example figure1 parameters hate are are with insufficiently trained. model transfers state hate source domain understand better.Target:Sometimes really hate RIBs.Source:Sometimes really hate RIBs. Figure1:Motivation ART. orange words sometimes hate are are with insufficiently trained parameters. red line indicates information transfer corresponding position. blue line indicates information transfer collocated word. Besides transferring corresponding position's information transfer learning algorithm captures cross-domain long-term dependency. Two words have a strong dependency can havea long gap them. insufficiently trained target domain word needs represent precise meaning incorporating information collocated words. collocate indicates word's semantics can have long-term dependency words. understand word target domain need precisely represent collocated words source domain. learn collocated words via attention mechanism BID1. example figure1 hate is modified adverb sometimes which implies act hating is not serious. sometimes target domain is trained insufficiently. need transfer semantics sometimes source domain understand implication. Therefore need carefully align word collocations source domain target domain represent long-term dependency.In paper proposed ART aligned recurrent transfer novel transfer learning mechanism transfer cell-level information learning collocate cross-domain words. ART allows celllevel information transfer directly extending RNN cell. ART incorporates hidden state representation corresponding position function hidden states words weighted attention scores.Cell-Level Recurrent Transfer ART extends recurrent cell taking states source domain extra input. traditional layer-wise transfer learning approaches discard states intermediate cells ART uses cell-level information transfer which means cell is affected transferred information. example figure1 state hate target domain is affected sometimes hate source domain. Thus ART transfers fine-grained information.Learn Collocate Transfer word target domain ART learns incorporate two types information source domain:hidden state corresponding word b hidden states words sequence. Information b enables ART capture cross-domain long-term dependency. ART learns incorporate information b based attention scores BID1 words source domain. learning transfer first pre-train neural network source domain. Therefore ART is able leverage pre-trained information source domain. paper study problem transfer learning sequences. proposed ART model collocate transfer cell-level information. ART has three advantages:1 transfers fine-grained cell-level information thus can be adapted seq2seq sequence labeling tasks;2 aligns transfers set collocated words source sentence represent cross domain long-term dependency;3 is general can be applied different tasks. Besides ART verified effectiveness pre-training models limited relevant training corpus.,1439,961,478,0.016,1.497,2025/11/05 17:19:01,0.01,1.516,0.5202492211838008,449.62
"Addressing uncertainty is critical for autonomous systems to robustly adapt to the real world. We formulate the problem of model uncertainty as a continuous Bayes-Adaptive Markov Decision Process (BAMDP), where an agent maintains a posterior distribution over latent model parameters given a history of observations and maximizes its expected long-term reward with respect to this belief distribution. Our algorithm, Bayesian Policy Optimization, builds on recent policy optimization algorithms to learn a universal policy that navigates the exploration-exploitation trade-off to maximize the Bayesian value function. To address challenges from discretizing the continuous latent parameter space, we propose a new policy network architecture that encodes the belief distribution independently from the observable state. Our method significantly outperforms algorithms that address model uncertainty without explicitly reasoning about belief distributions and is competitive with state-of-the-art Partially Observable Markov Decision Process solvers. At its core, real-world robotics focuses on operating under uncertainty. An autonomous car must drive alongside unpredictable human drivers under road conditions that change from day to day. An assistive home robot must simultaneously infer users' intended goals as it helps them. A robot arm must recognize and manipulate varied objects. These examples share common themes: (1) an underlying dynamical system with unknown latent parameters (road conditions, human goals, object identities), (2) an agent that can probe the system via exploration, while ultimately (3) maximizing an expected long-term reward via exploitation.The Bayes-Adaptive Markov Decision Process (BAMDP) framework BID9 elegantly captures the exploration-exploitation dilemma that the agent faces. Here, the agent maintains a belief, which is a posterior distribution over the latent parameters φ given a history of observations. A BAMDP can be cast as a Partially Observable Markov Decision Process (POMDP) BID7 whose state is (s, φ), where s corresponds to the observable world state. By planning in the belief space of this POMDP, the agent balances explorative and exploitative actions. In this paper, we focus on BAMDP problems in which the latent parameter space is either a discrete finite set or a bounded continuous set that can be approximated via discretization. For this class of BAMDPs, the belief is a categorical distribution, allowing us to represent it using a vector of weights.The core problem for BAMDPs with continuous state-action spaces is how to explore the reachable belief space. In particular, discretizing the latent space can result in an arbitrarily large belief vector, which causes the belief space to grow exponentially. Approximating the value function over the reachable belief space can be challenging: although point-based value approximations BID16 BID26 have been largely successful for approximating value functions of discrete POMDP problems, these approaches do not easily extend to continuous state-action spaces. Monte-Carlo Tree Search approaches (Silver & Veness, 2010; BID10 are also prohibitively expensive in continuous state-action spaces: the width of the search tree after a single iteration is too large, preventing an adequate search depth from being reached.Our key insight is that we can bypass learning the value function and directly learn a policy that maps beliefs to actions by leveraging the latest advancements in batch policy optimization algorithms BID32 . Inspired by previous approaches that train learning algorithms with an ensemble of models BID30 BID43 , we examine model uncertainty through a BAMDP lens. Although our approach provides only locally optimal policies, we believe that it offers a practical and scalable solution for continuous BAMDPs.Our method, Bayesian Policy Optimization (BPO), is a batch policy optimization method which utilizes a black-box Bayesian filter and augmented state-belief representation. During offline training, BPO simulates the policy on multiple latent models sampled from the source distribution FIG0 ). At each simulation timestep, it computes the posterior belief using a Bayes filter and inputs the state-belief pair (s, b) to the policy. Our algorithm only needs to update the posterior along the simulated trajectory in each sampled model, rather than branching at each possible action and observation as in MCTS-based approaches.Our key contribution is the following. We introduce a Bayesian policy optimization algorithm to learn policies that directly reason about model uncertainty while maximizing the expected long-term reward (Section 4). To address the challenge of large belief representations, we introduce two encoder networks that balance the size of belief and state embeddings in the policy network FIG0 . In addition, we show that our method, while designed for BAMDPs, can be applied to continuous POMDPs when a compact belief representation is available (Section 4.2). Through experiments on classical POMDP problems and BAMDP variants of OpenAI Gym benchmarks, we show that BPO significantly outperforms algorithms that address model uncertainty without explicitly reasoning about beliefs and is competitive with state-of-the-art POMDP algorithms (Section 5). Bayesian Policy Optimization is a practical and scalable approach for continuous BAMDP problems. We demonstrate that BPO learns policies that achieve performance comparable to state-of-the-art discrete POMDP solvers. They also outperform state-of-the-art robust policy gradient algorithms that address model uncertainty without formulating it as a BAMDP problem. Our network architecture scales well with respect to the degree of latent parameter space discretization due to its independent encoding of state and belief. We highlight that BPO is agnostic to the choice of batch policy optimization subroutine. Although we used TRPO in this work, we can also use more recent policy optimization algorithms, such as PPO BID33 , and leverage improvements in variance-reduction techniques BID42 ).BPO outperforms algorithms that do not explicitly reason about belief distributions. Our Bayesian approach is necessary for environments where uncertainty must actively be reduced, as shown in FIG1 and FIG2 . If all actions are informative (as with MuJoCo, Chain) and the posterior belief distribution easily collapses into a unimodal distribution, UP-MLE provides a lightweight alternative.BPO scales to fine-grained discretizations of latent space. However , our experiments also suggest that each problem has an optimal discretization level, beyond which further discretization may degrade performance. As a result , it may be preferable to perform variable-resolution discretization rather than an extremely fine, single-resolution discretization. Adapting iterative densification ideas previously explored in motion planning BID8 and optimal control BID20 to the discretization of latent space may yield a more compact belief representation while enabling further improved performance.An alternative to the model-based Bayes filter and belief encoder components of BPO is learning to directly map a history of observations to a lower-dimensional belief embedding, analogous to BID25 . This would enable a policy to learn a meaningful belief embedding without losing information from our a priori choice of discretization. Combining a recurrent policy for unidentified parameters with a Bayes filter for identified parameters offers an intriguing future direction for research efforts.","Addressing uncertainty is critical autonomous systems robustly adapt real world. formulate problem model uncertainty continuous Bayes-Adaptive Markov Decision Process BAMDP where an agent maintains posterior distribution latent model parameters given history observations maximizes expected long-term reward respect belief distribution. algorithm Bayesian Policy Optimization builds recent policy optimization algorithms learn universal policy navigates exploration-exploitation trade-off maximize Bayesian value function. address challenges discretizing continuous latent parameter space propose new policy network architecture encodes belief distribution independently observable state. method significantly outperforms algorithms address model uncertainty without explicitly reasoning belief distributions is competitive state-of-the-art Partially Observable Markov Decision Process solvers. core real-world robotics focuses operating uncertainty. autonomous car must drive alongside unpredictable human drivers road conditions change day day. assistive home robot must simultaneously infer users' intended goals helps them. robot arm must recognize manipulate varied objects. examples share common themes:1 underlying dynamical system unknown latent parameters road conditions human goals object identities 2 where an agent can probe system via exploration ultimately 3 maximizing expected long-term reward via exploitation.The Bayes-Adaptive Markov Decision Process BAMDP framework BID9 elegantly captures exploration-exploitation dilemma agent faces. agent maintains belief which is a posterior distribution latent parameters φ given history observations. BAMDP can be cast Partially Observable Markov Decision Process POMDP BID7 whose state is(s,φ where s corresponds observable world state. planning belief space POMDP agent balances explorative exploitative actions. paper focus BAMDP problems which the latent parameter space is either discrete finite set bounded continuous set can be approximated via discretization. class BAMDPs belief is a categorical distribution allowingus represent using vector weights.The core problem BAMDPs continuous state-action spaces is how to explore reachable belief space. particular discretizing latent space can result arbitrarily large belief vector which causes belief space grow exponentially. Approximating value function reachable belief space can be challenging:although point-based value approximations BID16 BID26 have been largely successful approximating value functions discrete POMDP problems approaches do not easily extend continuous state-action spaces. Monte-Carlo Tree Search approaches Silver Veness 2010;BID10 are also prohibitively expensive continuous state-action spaces:width search tree single iteration is too large preventing adequate search depth reached.Our key insight is that we can bypass learning value function directly learn policy maps beliefs actions leveraging latest advancements batch policy optimization algorithms BID32. Inspired previous approaches train learning algorithms ensemble models BID30 BID43 examine model uncertainty BAMDP lens. Although approach provides locally optimal policies believe offers practical scalable solution continuous BAMDPs.Our method Bayesian Policy Optimization BPO is a batch policy optimization method which utilizes black-box Bayesian filter augmented state-belief representation. offline training BPO simulates policy multiple latent models sampled source distribution FIG0 simulation timestep computes posterior belief using Bayes filter inputs state-belief pair b policy. algorithm needs update posterior along simulated trajectory sampled model rather branching possible action observation MCTS-based approaches.Our key contribution is the following. introduce Bayesian policy optimization algorithm learn policies directly reason model uncertainty maximizing expected long-term reward Section4 address challenge large belief representations introduce two encoder networks balance size belief state embeddings policy network FIG0. addition show method designed BAMDPs can be applied continuous POMDPs when a compact belief representation is available Section 4.2 experiments classical POMDP problems BAMDP variants OpenAI Gym benchmarks show BPO significantly outperforms algorithms address model uncertainty without explicitly reasoning beliefs is competitive state-of-the-art POMDP algorithms Section5 Bayesian Policy Optimization is a practical scalable approach continuous BAMDP problems. demonstrate BPO learns policies achieve performance comparable state-of-the-art discrete POMDP solvers. also outperform state-of-the-art robust policy gradient algorithms address model uncertainty without formulating BAMDP problem. network architecture scales well respect degree latent parameter space discretization due independent encoding state belief. highlight BPO is agnostic choice batch policy optimization subroutine. Although used TRPO work can also use recent policy optimization algorithms PPO BID33 leverage improvements variance-reduction techniques BID42.BPO outperforms algorithms do not explicitly reason belief distributions. Bayesian approach is necessary environments where uncertainty must actively reduced shown FIG1 FIG2. If all actions are informative MuJoCo Chain posterior belief distribution easily collapses unimodal distribution UP-MLE provides lightweight alternative.BPO scales fine-grained discretizations latent space. However experiments also suggest problem has an optimal discretization level beyond which further discretization may degrade performance. result may preferable perform variable-resolution discretization rather extremely fine single-resolution discretization. Adapting iterative densification ideas previously explored motion planning BID8 optimal control BID20 discretization latent space may yield compact belief representation enabling improved performance.An alternative model-based Bayes filter belief encoder components BPO is learning directly map history observations lower-dimensional belief embedding analogous BID25. would enable policy learn meaningful belief embedding without losing information priori choice discretization. Combining recurrent policy unidentified parameters Bayes filter identified parameters offers intriguing future direction research efforts.",1372,991,381,0.013,1.384,2025/11/05 17:19:01,0.01,1.763,0.16822429906542,408.837
"For many evaluation metrics commonly used as benchmarks for unconditional image generation, trivially memorizing the training set attains a better score than models which are considered state-of-the-art; we consider this problematic.
 We clarify a necessary condition for an evaluation metric not to behave this way: estimating the function must require a large sample from the model. In search of such a metric, we turn to neural network divergences (NNDs), which are defined in terms of a neural network trained to distinguish between distributions. The resulting benchmarks cannot be ``won'' by training set memorization, while still being perceptually correlated and computable only from samples. We survey past work on using NNDs for evaluation, implement an example black-box metric based on these ideas, and validate experimentally that it can measure a notion of generalization.
 In machine learning, it is often difficult to directly measure progress towards our goals (e.g. ""classify images correctly in the real world"", ""generate valid translations of text""). To enable progress despite this difficulty, it is useful to define a standardized benchmark task which is easy to evaluate and serves as a proxy for some final task. This enables much stronger claims of improvement (albeit towards a somewhat artificial task) by reducing the risk of inadequate baselines or evaluation mistakes, with the hope that progress on the benchmark will yield discoveries and methods which are useful towards the final task. This approach requires that a benchmark task satisfy two properties:1. It should define a straightforward and objective evaluation procedure, such that strong claims of improvement can be made. Any off-limits methods of obtaining a high score (e.g. abusing a test set) should be clearly defined. 2. Improved performance on the benchmark should require insights which are likely to be helpful towards the final task. The benchmark should, by construction, reflect at least some of the kinds of difficulty inherent in the final task.Together these imply that a benchmark should at least be nontrivial: we should not know a priori how to obtain an arbitrarily high score, except perhaps by clearly-off-limits methods. Crucial to a useful benchmark is an evaluation metric which measures what we care about for the final task and which satisfies the requirements outlined above.This paper deals with unconditional generation of natural images, which has been the goal of much recent work in generative modeling (e.g. BID35 BID25 . Our ideas are general, but we hope to improve evaluation practice in models like Generative Adversarial Networks (GANs) BID14 . Generative modeling has many possible final tasks BID47 . Of these, unconditional image generation is perhaps not very useful directly, but the insights and methods discovered in its pursuit have proven useful to other tasks like domain adaptation BID42 , disentangled representation learning , and imitation learning BID21 .Some notion of generalization is crucial to why unconditional generation is difficult (and hence interesting). Otherwise , simply memorizing the training data exactly would yield perfect ""generations"" Figure 1 : Common GAN benchmarks prefer training set memorization (p train , red) to a model (q, green) which imperfectly fits the true distribution (p, blue) but covers more of p's support. and the task would be meaningless. One might argue that some work-particularly recent GAN research-merely aims to improve convergence properties of the learning algorithm, and so generalization isn't a big concern. However, generalization is an important part of why GANs themselves are interesting. A GAN with better convergence properties but no ability to generalize is arguably not a very interesting GAN; we believe our definition of the task, and our benchmarks, should reflect this.Because our task is to generate samples, and often our models only permit sampling, recent work (e.g. BID23 BID17 BID48 ) has adopted benchmarks based on evaluation metrics BID20 which measure the perceptual quality and diversity of samples. However these particular metrics are, by construction, trivially ""won"" by a model which memorizes the training set. In other words , they mostly ignore any notion of generalization, which is central to why the task is difficult to begin with. This idea is illustrated in Figure 1 . In this sense they give rise to ""trivial"" benchmark tasks which can lead to less convincing claims of improvement, and ultimately less progress towards useful methods. While ""nontrivial "" benchmark tasks based on downstream applications can be used, the goals of these tasks are at best indirectly related to, and at worst opposite from, sample generation (e.g. for semi-supervised learning BID10 ).This paper considers evaluation metrics for generative models which give rise to nontrivial benchmarks, and which are aligned with the final task of generating novel, perceptually realistic and diverse data. We stress the difference between evaluating models and defining benchmarks. The former assumes that models have been chosen ahead of time, independently of the metric. The latter assumes that models will be developed with the metric in mind, and so seeks to avoid falsely high scores resulting from exploiting undesirable solutions to the benchmark (e.g. memorizing the training set). Our goal is to define benchmarks , and many of our decisions follow from this. Our contributions are as follows:• We establish a framework for sample-based evaluation that permits a meaningful notion of generalization. We clarify a necessary condition for the ability to measure generalization: That the evaluation requires a large sample from the model. • We investigate using neural network divergences as evaluation metrics which have attractive properties for this application. We survey past work exploring the use of neural network divergences for evaluation.• We study an example neural network divergence called ""CNN divergence"" (D CNN ) experimentally.We demonstrate that it can detect and penalize memorization and that it measures diversity relatively more than other evaluation functions. We believe our experiments show that the NNDs are a promising direction for evaluating generative models. They are not trivially solved by memorizing the training set, which satisfies our argument (Section 3) that measuring generalization ability is linked to whether the metric requires a large collection of samples. They also appear to prefer diversity relatively more than the IS and FID metrics. We note that NNDs are almost certainly not the only evaluation metric under which models can meaningfully generalize, and encourage work on alternative metrics.Ultimately, models should be evaluated according to their intended final task BID47 . In our work we assume that our final task is not usefully solved by memorizing the training set, but for many tasks such memorization is a completely valid solution. If so, the evaluation should reflect this: we do not need our model to be closer to the true distribution than the training set, Definition 1 does not apply, and we might be free to consider evaluations which look at only a small sample from the model.","many evaluation metrics commonly used benchmarks unconditional image generation trivially memorizing training set attains better score models which are considered considered state-of-the-art consider problematic. clarify necessary condition evaluation metric behave way:estimating function must require large sample model. search metric turn neural network divergences NNDs which are defined terms neural network trained distinguish distributions. resulting benchmarks cannot training set memorization still perceptually correlated computable samples. survey past work using NNDs evaluation implement example black-box metric based ideas validate experimentally can measure notion generalization. machine learning is often difficult directly measure progress towards goals e.g classify images correctly real world generate valid translations text enable progress despite difficulty is useful define standardized benchmark task which is easy evaluate serves proxy final task. enables much stronger claims improvement albeit towards somewhat artificial task reducing risk inadequate baselines evaluation mistakes hope progress benchmark will yield discoveries methods which are useful towards final task. approach requires benchmark task satisfy two properties:1 should define straightforward objective evaluation procedure strong claims improvement can be made. off-limits methods obtaining high score e.g abusing test set should be clearly defined. 2. Improved performance benchmark should require insights which are likely helpful towards final task. benchmark should,by construction should reflect least kinds difficulty inherent final task.Together imply benchmark should at least nontrivial:should not know priori how to obtain arbitrarily high score except perhaps clearly-off-limits methods. Crucial useful benchmark is an evaluation metric which measures what we care final task which satisfies requirements outlined above.This paper deals unconditional generation natural images which has been goal much recent work generative modeling e.g BID35 BID25. ideas are general hope improve evaluation practice models like Generative Adversarial Networks GANs BID14. Generative modeling has many possible final tasks BID47. unconditional image generation is perhaps useful directly insights methods discovered pursuit have proven useful tasks like domain adaptation BID42 disentangled representation learning imitation learning BID21.Some notion generalization is crucial why unconditional generation is difficult hence interesting Otherwise simply memorizing training data exactly would yield perfect generations Figure 1:Common GAN benchmarks prefer training set memorization p train red model q green which imperfectly fits true distribution p blue covers p's support. task would meaningless. One might argue work-particularly recent GAN research-merely aims improve convergence properties learning algorithm generalization big concern. However generalization is an important part why GANs are interesting. GAN better convergence properties ability generalize is arguably interesting GAN;believe definition task benchmarks should reflect this.Because task is to generate samples is often models permit sampling recent work e.g BID23 BID17 BID48 has adopted benchmarks based evaluation metrics BID20 which measure perceptual quality diversity samples. However particular metrics are,by construction trivially model which memorizes training set. words mostly ignore notion generalization which is central why the task is difficult begin with. idea is illustrated Figure1. sense give rise trivial benchmark tasks which can lead less convincing claims improvement ultimately less progress towards useful methods. nontrivial benchmark tasks based downstream applications can be used goals tasks are at best indirectly related worst opposite sample generation e.g semi-supervised learning BID10.This paper considers evaluation metrics generative models which give rise nontrivial benchmarks which are aligned final task generating novel perceptually realistic diverse data. stress difference evaluating models defining benchmarks. former assumes models have been chosen ahead time independently metric. latter assumes models will be developed metric mind seeks avoid falsely high scores resulting exploiting undesirable solutions benchmark e.g memorizing training set goal is to define benchmarks many decisions follow this. contributions are as follows:• establish framework sample-based evaluation permits meaningful notion generalization. clarify necessary condition ability measure generalization:evaluation requires large sample model. • investigate using neural network divergences evaluation metrics which have attractive properties application. survey past work exploring use neural network divergences evaluation.• study example neural network divergence called CNN divergence CNN experimentally.We demonstrate can detect penalize memorization measures diversity relatively evaluation functions. believe experiments show NNDs are a promising direction evaluating generative models. are not trivially solved memorizing training set which satisfies argument Section3 measuring generalization ability is linked whether metric requires large collection samples. also appear prefer diversity relatively IS FID metrics. note NNDs are almost certainly evaluation metric which models can meaningfully generalize encourage work alternative metrics.Ultimately models should be evaluated according intended final task BID47. work assume final task is not usefully solved memorizing training set many tasks memorization is a completely valid solution. If so,the evaluation should reflect this:do not need model closer true distribution training set Definition1 does not apply might free consider evaluations which look small sample model.",1372,922,450,0.014,1.488,2025/11/05 17:19:01,0.01,1.6,0.4922118380062303,450.265
"Conventional methods model open domain dialogue generation as a black box through end-to-end learning from large scale conversation data. In this work, we make the first step to open the black box by introducing dialogue acts into open domain dialogue generation. The dialogue acts are generally designed and reveal how people engage in social chat. Inspired by analysis on real data, we propose jointly modeling dialogue act selection and response generation, and perform learning with human-human conversations tagged with a dialogue act classifier and a reinforcement approach to further optimizing the model for long-term conversation. With the dialogue acts, we not only achieve significant improvement over state-of-the-art methods on response quality for given contexts and long-term conversation in both machine-machine simulation and human-machine conversation, but also are capable of explaining why such achievements can be made. Conversational agents are becoming ubiquitous recently. Through human-machine conversation, such agents either help users complete specific tasks BID39 or engage them in social chat BID30 . Depending on application scenarios, various conversational agents have been designed including chatbots, personal assistants, and automated customer service, etc.Traditional research on conversational agents focuses on task-oriented dialogue systems BID39 where task specific dialogue acts are handcrafted in a form of slot-value pairs. On the one hand, through slot-filling, the dialogue acts make conversations in such systems interpretable and controllable; on the other hand, they also hinder scaling such systems to new domains. To escape from the limitation, recent interest of research moves to end-to-end dialogue learning without any assumptions on dialogue acts. Most of the effort is paid to non-task-oriented chit-chat BID30 , and there are also a few studies on task-oriented dialogues BID1 BID4 . Without dialogue acts, these work directly constructs a response by learning from large scale data with neural networks, and thus is easy to scale to new domains. On the other hand, due to the absence of dialogue acts, it is hard to interpret the emergence of a response to a dialogue context and predict where the conversation will flow to.In this work, we aim to achieve interpretability and controllability in non-task-oriented dialogues. To this end, we introduce dialogue acts into open domain dialogue generation. Open domain dialogue generation has been widely applied to chatbots which aim at engaging users by keeping conversation going. Existing work concentrates on generating relevant and diverse responses for a static context. However, it is not clear if relevance and diversity are sufficient to engagement in dynamic interactions. Therefore, we investigate the following problems: (1) if we can properly design dialogue acts that can enable us to understand engagement in human-human open domain conversation; (2) how to learn a dialogue generation model with the dialogue acts; and (3) how the model performs in practice and if the performance can be explained by the dialogue acts.To examine how people engage in social chat, we establish a general dialogue act taxonomy for open domain conversation by extending the existing work with high-level dialogue acts regarding to conversational context. The taxonomy, when applied to real data, gives rise to an interesting finding that in addition to replying with relevance and diversity , people are used to driving their social chat by constantly switching to new contexts and properly asking questions. Such behaviors are less explored before, and thus are difficult for the existing end-to-end learning methods to imitate. To mimic human behaviors, we propose jointly modeling dialogue act selection and response generation in open domain dialogue generation. The dialogue model is specified with neural networks. We propose learning from human-human interactions by fitting the model to large scale real world dialogues tagged with a dialogue act classifier and further optimizing the policy of act selection for long-term conversation through a reinforcement learning approach. Our model enjoys several advantages over the existing models: (1) the dialogue acts provide interpretation to response generation from a discourse perspective; (2) the dialogue acts enhance diversity of responses by expanding the search space from language to act × language; (3) the dialogue acts manage the flow of humanmachine conversations and thus enhance human engagement; and (4) the dialogue act selection is compatible with post-engineering work (e.g., combination with rules), and thus allows engineers to flexibly control their systems through picking responses from their desired dialogue acts. Evaluation results on large scale test data indicate that our model can significantly outperform state-of-the-art methods in terms of quality of generated responses regarding to given contexts and lead to longterm conversation in both machine-machine simulation and human-machine conversation in a way similar to how human behave in their interactions.Our contributions in this work include: (1) design of dialogue acts that represent human behavior regarding to conversational context and insights from analysis of human-human interactions with the design; (2) joint modeling of dialogue act selection and response generation in open domain dialogue generation; (3) proposal of a supervised learning approach and a reinforcement learning approach for model optimization; (4) empirical verification of the effectiveness of the model through automatic metrics, human annotations, machine-machine simulation, and human-machine conversation. A response or an answer to the previous utterances in the current context. ""this summer."" after ""when are you going to Tokyo?"". Finally, we study how the generated responses are affected by the dialogue acts. We collect generated responses from a specific dialogue act for the contexts of the test dialogues, and characterize the responses with the following metrics: (1) distinct-1 and distinct-2; (2) words out of context (OOC): ratio of words that are in the generated responses but not contained by the contexts; and (3) average length of the generated responses (Ave Len). TAB9 reports the results 4 . In general, responses generated from CS. * are longer, more informative, and contain more new words than responses generated from CM. *, which has been illustrated by the example in TAB7 . Another interesting finding is that statements and answers are generally more informative than questions in both CS. * and CM.*. In addition to these metrics, we also calculate BLEU scores and embedding based metrics, but do not observe significant difference among responses from different dialogue acts. The reason might be that these metrics are based on comparsion of the generated responses and human responses, but human responses in the test set are inherently mixture of responses from different dialogue acts. We study open domain dialogue generation with generally designed dialogue acts that can describe human behavior in social interactions. To mimic such behavior, we propose jointly modeling dialogue act selection and response generation, and perform both supervised learning with a learned dialogue act classifier and reinforcement learning for long-term conversation. Empirical studies on response generation for given contexts, machine-machine simulation, and human-machine conversation show that the proposed models can significantly outperform state-of-the-art methods.",Conventional methods model open domain dialogue generation black box end-to-end learning large scale conversation data. work make first step open black box introducing dialogue acts open domain dialogue generation. dialogue acts are generally designed reveal how people engage social chat. Inspired analysis real data propose jointly modeling dialogue act selection response generation perform learning human-human conversations tagged dialogue act classifier reinforcement approach optimizing model long-term conversation. dialogue acts achieve significant improvement state-of-the-art methods response quality given contexts long-term conversation machine-machine simulation human-machine conversation are also are capable explaining why such achievements can be made. Conversational agents are becoming ubiquitous recently. human-machine conversation agents either help users complete specific tasks BID39 engage social chat BID30. Depending application scenarios various conversational agents have been designed including chatbots personal assistants automated customer service etc.Traditional research conversational agents focuses task-oriented dialogue systems BID39 where task specific dialogue acts are handcrafted form slot-value pairs. one hand slot-filling dialogue acts make conversations systems interpretable controllable;hand are also hinder scaling systems new domains. escape limitation recent interest research moves end-to-end dialogue learning without assumptions dialogue acts. effort is paid non-task-oriented chit-chat BID30 are also studies task-oriented dialogues BID1 BID4. Without dialogue acts work directly constructs response learning large scale data neural networks thus is easy scale new domains. hand due absence dialogue acts is hard interpret emergence response dialogue context predict where the conversation will flow to.In work aim achieve interpretability controllability non-task-oriented dialogues. end introduce dialogue acts open domain dialogue generation. Open domain dialogue generation has been widely applied chatbots which aim engaging users keeping conversation going. Existing work concentrates generating relevant diverse responses static context. However is not clear if relevance diversity are sufficient engagement dynamic interactions. Therefore investigate following problems:1 if we can properly design dialogue acts can enableus understand engagement human-human open domain conversation;2 how to learn dialogue generation model dialogue acts;3 how the model performs practice if the performance can be explained dialogue acts.To examine how people engage social chat establish general dialogue act taxonomy open domain conversation extending existing work high-level dialogue acts regarding conversational context. taxonomy when applied real data gives rise interesting finding addition replying relevance diversity people are used driving social chat constantly switching new contexts properly asking questions. behaviors are less explored thus are difficult existing end-to-end learning methods imitate. mimic human behaviors propose jointly modeling dialogue act selection response generation open domain dialogue generation. dialogue model is specified neural networks. propose learning human-human interactions fitting model large scale real world dialogues tagged dialogue act classifier optimizing policy act selection long-term conversation reinforcement learning approach. model enjoys several advantages existing models:1 dialogue acts provide interpretation response generation discourse perspective;2 dialogue acts enhance diversity responses expanding search space language act × language;3 dialogue acts manage flow humanmachine conversations thus enhance human engagement;4 dialogue act selection is compatible post-engineering work e.g combination rules thus allows engineers flexibly control systems picking responses desired dialogue acts. Evaluation results large scale test data indicate model can significantly outperform state-of-the-art methods terms quality generated responses regarding given contexts lead longterm conversation machine-machine simulation human-machine conversation way similar how human behave interactions.Our contributions work include:1 design dialogue acts represent human behavior regarding conversational context insights analysis human-human interactions design;2 joint modeling dialogue act selection response generation open domain dialogue generation;3 proposal supervised learning approach reinforcement learning approach model optimization;4 empirical verification effectiveness model automatic metrics human annotations machine-machine simulation human-machine conversation. response answer previous utterances current context. summer. when are you going Tokyo? Finally study how the generated responses are affected dialogue acts. collect generated responses specific dialogue act contexts test dialogues characterize responses following metrics:1 distinct-1 distinct-2 2 words context OOC ratio words are in the generated responses contained contexts;3 average length generated responses Ave Len TAB9 reports results4. general responses generated CS. * are longer informative contain new words responses generated CM. * which has been illustrated example TAB7. Another interesting finding is that statements answers are generally informative questions CS. * CM. * addition metrics are also calculate BLEU scores embedding based metrics do not observe significant difference among responses different dialogue acts. reason might metrics are based comparsion generated responses human responses human responses test set are inherently mixture responses different dialogue acts. study open domain dialogue generation generally designed dialogue acts can describe human behavior social interactions. mimic behavior propose jointly modeling dialogue act selection response generation perform supervised learning learned dialogue act classifier reinforcement learning long-term conversation. Empirical studies response generation given contexts machine-machine simulation human-machine conversation show proposed models can significantly outperform state-of-the-art methods.,1334,908,426,0.014,1.469,2025/11/05 17:19:01,0.01,1.467,0.4330218068535826,450.097
"We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any definition of the semantic information, the problem might seem ill-posed. Specifically, in typical cases, it seems possible to build infinitely many alternative mappings  from every target mapping. This apparent ambiguity stands in sharp contrast to the recent empirical success in solving this problem.

 We identify the abstract notion of aligning two domains in a semantic way with concrete terms of minimal relative complexity. A theoretical framework for measuring the complexity of compositions of functions is developed in order to show that it is reasonable to expect the minimal complexity mapping to be unique. The measured complexity used is directly related to the depth of the neural networks being learned and a semantically aligned mapping could then be captured simply by learning using architectures that are not much bigger than the minimal architecture.

 Various predictions are made based on the hypothesis that semantic alignment can be captured by the minimal mapping. These are verified extensively. In addition, a new mapping algorithm is proposed and shown to lead to better mapping results. Multiple recent reports (Xia et al., 2016; BID13 BID12 Yi et al., 2017) convincingly demonstrated that one can learn to map between two domains that are each specified merely by a set of unlabeled examples. For example, given a set of unlabeled images of horses, and a set of unlabeled images of zebras, CycleGAN (Zhu et al., 2017) creates the analog zebra image for a new image of a horse and vice versa.These recent methods employ two types of constraints. First, when mapping from one domain to another, the output has to be indistinguishable from the samples of the new domain. This is enforced using GANs BID9 and is applied at the distribution level: the mapping of horse images to the zebra domain should create images that are indistinguishable from the training images of zebras and vice versa. The second type of constraint enforces that for every single sample, transforming it to the other domain and back (by a composition of the mappings in the two directions) results in the original sample. This is enforced for each training sample from either domain: every training image of a horse (zebra), which is mapped to a zebra (horse) image and then back to the source domain, should be as similar as possible to the original input image.In another example, taken from DiscoGAN BID13 , a function is learned to map a handbag to a shoe of a similar style. One may wonder why striped bags are not mapped, for example, to shoes with a checkerboard pattern. If every striped pattern in either domain is mapped to a checkerboard pattern in the other and vice-versa, then both the distribution constraints and the circularity constraints might hold. The former could hold since both striped and checkerboard patterned objects would be generated. Circularity could hold since, for example, a striped object would be mapped to a checkerboard object in the other domain and then back to the original striped object.One may claim that the distribution of striped bags is similar to those of striped shoes and that the distribution of checkerboard patterns is also the same in both domains. In this case, the alignment follows from fitting the shapes of the distributions. This explanation is unlikely, since no effort is being made to create handbags and shoes that have the same distributions of these properties, as well as many other properties.Our work is dedicated to the alternative hypothesis that the target mapping is implicitly defined by being approximated by the lowest-complexity mapping that has a low discrepancy between the mapped samples and the target distribution, i.e., the property that even a good discriminator cannot distinguish between the generated samples and the target ones. In Sec. 2 we explore the inherent ambiguity of cross domain mapping. In Sec. 3, we present the hypothesis and two verifiable predictions, as well as a new unsupervised mapping algorithm. In Sec. 4, we show that the number of minimal complexity mappings is expected to be small. Sec. 5 verifies the various predictions. Some context to our work, including classical ideas such as Occam's Razor, MDL, and Kolmogorov complexity are discussed in Sec. 6. Our stratified complexity model is related to structural risk minimization (SRM) by Vapnik & Chervonenkis (1971a) , which employs a hierarchy of nested subsets of hypothesis classes in order of increasing complexity. In our stratification, which is based on the number of layers, the complexity classes are not necessarily nested. A major emphasis in SRM is the dependence on the number of samples: the algorithm selects the hypothesis from one of the nested hypothesis classes depending on the amount of training data. In our case, one can expect higher values of k 2 to be beneficial as the number of training samples grows. However, the exact characterization of this relation is left for future work.Alg. 1 can be seen as a form of distillation. The first step of the algorithm finds the minimal complexity for mapping between the two domains and obtains the first generator. Then, a second generator, with a large complexity, is trained while being encouraged to output images which are close to the output of the first generator. This resembles the distillation methods proposed by BID11 and later analyzed by BID10 .Since the method depicted in Alg. 1 optimizes , among other things, the architecture of the network, our method is somewhat related to work that learn the network's structure during training, e.g., (Saxena & Verbeek, 2016; Wen et al., 2016; Liu et al., 2015; BID7 BID15 . This body of work, which deals exclusively with supervised learning, optimizes the networks loss by modifying both the parameters and the hyperparameters. For GAN based loss, this would not work, since with more capacity, one can reduce the discrepancy but quickly lose the alignment.Indeed, we point to a key difference between supervised learning and unsupervised learning. While in the former, deeper networks, which can learn even random labels, work well (Zhang et al., 2017) , unsupervised learning requires a careful control of the network capacity. This realization , which echoes the application of MDL for model selection in unsupervised learning (Zemel, 1994) , was overshadowed by the overgeneralized belief that deeper networks lead to higher accuracy.The limitations of unsupervised based learning that are due to symmetry, are also a part of our model. For example, the mapping of cars in one pose to cars in the mirrored pose that sometimes happens in BID13 , is similar in nature to the mapping of x to 1 − x in the simple example given in Sec. 3.1. Such symmetries occur when we can divide y AB into two functions y AB = y 2 • y 1 such that a function W is a linear mapping and also a DPM of y 1 • D A and, therefore, DISPLAYFORM0 While we focus on unsupervised learning, the emergence of semantics when learning with a restricted capacity is widely applicable, such as with autoencoders, transfer learning, semi-supervised learning and elsewhere. As an extreme example , Sutskever et al. FORMULA0 present empirical evidence that a meaningful mapper can be learned, even from very few examples, if the network trained is kept small. The recent success in mapping between two domains in an unsupervised way and without any existing knowledge, other than network hyperparameters, is nothing less than extraordinary and has far reaching consequences. As far as we know, nothing in the existing machine learning or cognitive science literature suggests that this would be possible.We provide an intuitive definition of function complexity and employ it in order to identify minimal complexity mappings, which we conjecture play a pivotal role in this success. If our hypothesis is correct, simply by training networks that are not too complex, the target mapping stands out from all other alternative mappings.Our analysis leads directly to a new unsupervised cross domain mapping algorithm that is able to avoid the ambiguity of such mapping, yet enjoy the expressiveness of deep neural networks. The experiments demonstrate that the analogies become richer in details and more complex, while maintaining the alignment.We show that the number of low-discrepancy mappings that are of low-complexity is expected to be small. Our main proof is based on the assumption of identifiability, which constitutes an open question. We hope that there would be a renewed interest in this problem, which has been open for decades for networks with more than a single hidden layer and is unexplored for modern activation functions. FIG1 : Results for mapping Males to itself (B=A) using a DiscoGAN architecture and enforcing that the mapping is not the identity mapping. The odd rows present the learned mapping h, and the even rows present the full cycle h • h.",discuss feasibility following learning problem:given unmatched samples two domains nothing else which can learn mapping two which preserves semantics. Due lack paired samples without definition semantic information problem might seem ill-posed Specifically typical cases seems possible build infinitely many alternative mappings every target mapping. apparent ambiguity stands sharp contrast recent empirical success solving problem. identify abstract notion aligning two domains semantic way concrete terms minimal relative complexity. theoretical framework measuring complexity compositions functions is developed order show is reasonable expect minimal complexity mapping unique. measured complexity used is directly related depth neural networks learned semantically aligned mapping could captured simply learning using architectures are not much bigger minimal architecture. Various predictions are made based hypothesis semantic alignment can be captured minimal mapping. are verified extensively. addition new mapping algorithm is proposed shown lead better mapping results. Multiple recent reports Xiaetal. 2016;BID13 BID12Yiet al. 2017 convincingly demonstrated one can learn map two domains are each specified merely set unlabeled examples. example given set unlabeled images horses set unlabeled images zebras CycleGAN Zhuetal. 2017 creates analog zebra image new image horse vice versa.These recent methods employ two types constraints. First when mapping one domain another output has to be indistinguishable samples new domain. is enforced using GANs BID9 is applied distribution level:mapping horse images zebra domain should create images are indistinguishable training images zebras vice versa. second type constraint enforces every single sample transforming domain back composition mappings two directions results original sample. is enforced training sample either domain:every training image horse zebra which is mapped zebra horse image back source domain should be as is similar possible original input image.In another example taken DiscoGAN BID13 function is learned map handbag shoe similar style. One may wonder why striped bags are not mapped example shoes checkerboard pattern. If every striped pattern either domain is mapped checkerboard pattern vice-versa distribution constraints circularity constraints might hold. former could hold since striped checkerboard patterned objects would generated. Circularity could hold since example striped object would mapped checkerboard object domain back original striped object.One may claim distribution striped bags is similar striped shoes distribution checkerboard patterns is also domains. case alignment follows fitting shapes distributions. explanation is unlikely since effort is being made create handbags shoes have the same distributions properties well many properties.Our work is dedicated alternative hypothesis target mapping is implicitly defined approximated lowest-complexity mapping has a low discrepancy mapped samples target distribution.e property even good discriminator cannot distinguish generated samples target ones. Sec. 2 explore inherent ambiguity cross domain mapping. Sec. 3 present hypothesis two verifiable predictions well new unsupervised mapping algorithm. Sec. 4 show number minimal complexity mappings is expected small. Sec. 5 verifies various predictions. context work including classical ideas Occam's Razor MDL Kolmogorov complexity are discussed Sec. 6. stratified complexity model is related structural risk minimization SRM Vapnik Chervonenkis 1971a which employs hierarchy nested subsets hypothesis classes order increasing complexity. stratification which is based number layers complexity classes are not necessarily nested. major emphasis SRM is the dependence number samples:algorithm selects hypothesis one nested hypothesis classes depending amount training data. case one can expect higher values k2 beneficial number training samples grows. However exact characterization relation is left future work.Alg.1 can be seen form distillation. first step algorithm finds minimal complexity mapping two domains obtains first generator. second generator large complexity is trained encouraged output images which are close output first generator. resembles distillation methods proposed BID11 later analyzed BID10.Since method depicted Alg. 1 optimizes among things architecture network method is somewhat related work learn network's structure training e.g Saxena Verbeek 2016;Wenetal. 2016;Liuetal. 2015;BID7 BID15. body work which deals exclusively supervised learning optimizes networks loss modifying parameters hyperparameters. GAN based loss would work since capacity one can reduce discrepancy quickly lose alignment.Indeed point key difference supervised learning unsupervised learning. former deeper networks which can learn even random labels work well Zhangetal. 2017 unsupervised learning requires careful control network capacity. realization which echoes application MDL model selection unsupervised learning Zemel 1994 was overshadowed overgeneralized belief deeper networks lead higher accuracy.The limitations unsupervised based learning are due symmetry are also part model. example when mapping cars one pose cars mirrored pose sometimes happens BID13 should be as is similar nature mapping x 1−x simple example given Sec. 3.1 symmetries occur when we can divide AB two functions AB 2• 1 functionW is a linear mapping also DPM 1• therefore DISPLAYFORM0 focus unsupervised learning emergence semantics when learning restricted capacity is widely applicable autoencoders transfer learning semi-supervised learning elsewhere. extreme example Sutskeveretal. FORMULA0 present empirical evidence meaningful mapper can be learned even examples if the network trained is kept small. recent success mapping two domains unsupervised way without existing knowledge if the network hyperparameters is nothing less extraordinary has far reaching consequences. far know is nothing existing machine learning cognitive science literature suggests would possible.We provide intuitive definition function complexity employ order identify minimal complexity mappings which we conjecture play pivotal role success. If our hypothesis is correct simply training networks are not too complex target mapping stands alternative mappings.Our analysis leads directly new unsupervised cross domain mapping algorithm is able avoid ambiguity mapping yet enjoy expressiveness deep neural networks. experiments demonstrate analogies become richer details complex maintaining alignment.We show number low-discrepancy mappings are of low-complexity is expected small. main proof is based assumption identifiability which constitutes open question. hope would renewed interest problem which has been open decades networks single hidden layer is unexplored modern activation functions. FIG1:Results mapping Males B=A using DiscoGAN architecture enforcing mapping is not the identity mapping. odd rows present learned mappingh even rows present full cycleh• h.,1832,1199,633,0.023,1.528,2025/11/05 17:19:01,0.01,1.452,0.616822429906542,686.019
"We present a novel approach for the certification of neural networks against adversarial perturbations which combines scalable overapproximation methods with precise (mixed integer) linear programming. This results in significantly better precision than state-of-the-art verifiers on challenging feedforward and convolutional neural networks with piecewise linear activation functions. Neural networks are increasingly applied in critical domains such as autonomous driving BID1 , medical diagnosis BID0 , and speech recognition BID13 . However, it has been shown by BID11 that neural networks can be vulnerable against adversarial attacks, i.e., imperceptible input perturbations cause neural networks to misclassify. To address this challenge and prove that a network is free of adversarial examples (usually, in a region around a given input), recent work has started investigating the use of certification techniques. Current verifiers can be broadly classified as either complete or incomplete.Complete verifiers are exact, i.e., if the verifier fails to certify a network then the network is nonrobust (and vice-versa) . Existing complete verifiers are based on Mixed Integer Linear Programming (MILP) BID19 BID8 BID5 BID3 or SMT solvers BID16 BID7 . Although precise, these can only handle networks with a small number of layers and neurons. To scale, incomplete verifiers usually employ overapproximation methods and hence they are sound but may fail to prove robustness even if it holds. Incomplete verifiers use methods such as duality BID6 , abstract interpretation BID23 , linear approximations BID29 , semidefinite relaxations BID21 , combination of linear and non-linear approximation BID30 , or search space discretization BID14 . Incomplete verifiers are more scalable than complete ones, but can suffer from precision loss for deeper networks. In principle, incomplete verifiers can be made asymptotically complete by iteratively refining the input space BID26 or the neurons BID27 ; however, in the worst case, this may eliminate any scalability gains and thus defeat the purpose of using overapproximation in the first place.This work: boosting complete and incomplete verifiers. A key challenge then is to design a verifier which improves the precision of incomplete methods and the scalability of complete ones. In this work, we make a step towards addressing this challenge based on two key ideas: (i) a combination of state-of-the-art overapproximation techniques used by incomplete methods, including LP relaxations, together with MILP solvers, often employed in complete verifiers; (ii) a novel heuristic, which points to neurons whose approximated bounds should be refined. We implemented these ideas in a system called RefineZono, and showed that is is faster than state-of-the-art complete verifiers on small networks while improving precision of existing incomplete verifiers on larger networks.The recent works of BID27 and BID25 have also explored the combination of linear programming with overapproximation. However, both use simpler and coarser overapproximations than ours. Our evaluation shows that RefineZono is faster than both for complete verification. For example, RefineZono is faster than the work of BID25 for the complete x 7x 8 x 9x 10 x 11x 12x 13 Figure 1 : Robustness analysis of a toy example neural network using our method. Here, approximation results computed with DeepZ (blue box) are refined using MILP whereas those in green are refined using LP. verification of a 3 × 50 network, while for the larger 9 × 200 network their method does not finish within multiple days on images which RefineZono verifies in ≈ 14 minutes. DISPLAYFORM0 We presented a novel refinement-based approach for effectively combining overapproximation techniques used by incomplete verifiers with linear-programming-based methods used in complete verifiers. We implemented our method in a system called RefineZono and showed its effectiveness on verification tasks involving feedforward and convolutional neural networks with ReLU activations.Our evaluation demonstrates that RefineZono can certify robustness properties beyond the reach of existing state-of-the-art complete verifiers (these can fail due to scalability issues) while simultaneously improving on the precision of existing incomplete verifiers (which can fail due to using too coarse of an overapproximation).Overall , we believe combining the strengths of overapproximation methods with those of mixed integer linear programming as done in this work is a promising direction for further advancing the state-of-the-art in neural network verification.",present novel approach certification neural networks adversarial perturbations which combines scalable overapproximation methods precise mixed integer linear programming. results significantly better precision state-of-the-art verifiers challenging feedforward convolutional neural networks piecewise linear activation functions. Neural networks are increasingly applied critical domains autonomous driving BID1 medical diagnosis BID0 speech recognition BID13. However has been shown BID11 neural networks can be vulnerable adversarial attacks.e imperceptible input perturbations cause neural networks misclassify. address challenge prove network is free adversarial examples usually region around given input recent work has started investigating use certification techniques. Current verifiers can be broadly classified either complete incomplete.Complete verifiers are exact.e if the verifier fails certify network network is nonrobust vice-versa Existing complete verifiers are based Mixed Integer Linear Programming MILP BID19 BID8 BID5 BID3 SMT solvers BID16 BID7. Although precise can only handle networks small number layers neurons. scale incomplete verifiers usually employ overapproximation methods hence are sound may fail prove robustness even if it holds. Incomplete verifiers use methods duality BID6 abstract interpretation BID23 linear approximations BID29 semidefinite relaxations BID21 combination linear non-linear approximation BID30 search space discretization BID14. Incomplete verifiers are more scalable complete ones can suffer precision loss deeper networks. principle incomplete verifiers can be made asymptotically complete iteratively refining input space BID26 neurons BID27;however worst case may eliminate scalability gains thus defeat purpose using overapproximation first place.This work:boosting complete incomplete verifiers. key challenge is to design verifier which improves precision incomplete methods scalability complete ones. work make step towards addressing challenge based two key ideas:combination state-of-the-art overapproximation techniques used incomplete methods including LP relaxations together MILP solvers often employed complete verifiers;ii novel heuristic which points neurons whose approximated bounds should be refined. implemented ideas system called RefineZono showed is is faster state-of-the-art complete verifiers small networks improving precision existing incomplete verifiers larger networks.The recent works BID27 BID25 have also explored combination linear programming overapproximation. However use simpler coarser overapproximations ours. evaluation shows RefineZono is faster complete verification. example RefineZono is faster work BID25 completex7x8 x9x10x 11x 12x 13 Figure 1:Robustness analysis toy example neural network using method. approximation results computed DeepZ blue box are refined using MILP whereas green are refined usingLP. verification 3 × 50 network larger 9 × 200 network method does not finish within multiple days images which RefineZono verifies ≈ 14 minutes. DISPLAYFORM0 presented novel refinement-based approach effectively combining overapproximation techniques used incomplete verifiers linear-programming-based methods used complete verifiers. implemented method system called RefineZono showed effectiveness verification tasks involving feedforward convolutional neural networks ReLU activations.Our evaluation demonstrates RefineZono can certify robustness properties beyond reach existing state-of-the-art complete verifiers can which can fail due scalability issues simultaneously improving precision existing incomplete verifiers can which can fail due using coarse overapproximation.Overall believe combining strengths overapproximation methods mixed integer linear programming done work is a promising direction advancing state-of-the-art neural network verification.,903,671,232,0.008,1.346,2025/11/05 17:19:01,0.0,1.438,0.0498442367601246,277.113
"A distinct commonality between HMMs and RNNs is that they both learn hidden representations for sequential data. In addition, it has been noted that the backward computation of the Baum-Welch algorithm for HMMs is a special case of the back-propagation algorithm used for neural networks (Eisner (2016)). Do these observations suggest that, despite their many apparent differences, HMMs are a special case of RNNs? In this paper, we show that that is indeed the case, and investigate a series of architectural transformations between HMMs and RNNs, both through theoretical derivations and empirical hybridization. In particular, we investigate three key design factors—independence assumptions between the hidden states and the observation, the placement of softmaxes, and the use of non-linearities—in order to pin down their empirical effects. We present a comprehensive empirical study to provide insights into the interplay between expressivity and interpretability in this model family with respect to language modeling and parts-of-speech induction. The sequence is a common structure among many forms of naturally occurring data, including speech, text, video, and DNA. As such, sequence modeling has long been a core research problem across several fields of machine learning and AI. By far the most widely used approach for decades is Hidden Markov Models BID1 BID10 , which assumes a sequence of discrete latent variables to generate a sequence of observed variables. When the latent variables are unobserved, unsupervised training of HMMs can be performed via the Baum-Welch algorithm (which, in turn, is based on the forward-backward algorithm), as a special case of Expectation-Maximization (EM) BID4 . Importantly, the discrete nature of the latent variables has the benefit of interpretability, as they recover contextual clustering of the output variables. In contrast, Recurrent Neural Networks (RNNs) BID11 BID6 introduced later assume continuous latent representations. Their hidden states have no probabilistic interpretation, regardless of many different architectural variants, such as LSTMs BID9 , GRUs BID3 and RANs BID13 .Despite their many apparent differences, both HMMs and RNNs model hidden representations for sequential data. At the heart of both models are: a state at time t, a transition function f : h t−1 → h t in latent space, and an emission function g : h t → x t . In addition , it has been noted that the backward computation in the Baum-Welch algorithm is a special case of back-propagation for neural networks BID5 . Therefore, a natural question arises as to the fundamental relationship between HMMs and RNNs. Might HMMs be a special case of RNNs?In this paper , we investigate a series of architectural transformations between HMMs and RNNsboth through theoretical derivations and empirical hybridization. In particular , we demonstrate that forward marginal inference for an HMM-accumulating forward probabilities to compute the marginal emission and hidden state distributions at each time step-can be reformulated as equations for computing an RNN cell. In addition, we investigate three key design factors-independence Figure 1 : Above each of the models we indicate the type of transition and emission cells used. H for HMM, R for RNN/Elman and F is a novel Fusion defined in §3.3. It is particularly important to track when a vector is a distribution (resides in a simplex) versus in the unit cube (e.g. after a sigmoid non-linearity). These are indicated by c i and c i , respectively. SM stands for softmax rows.assumptions between the hidden states and observations, the placement of softmaxes, and the use of non-linearities-in order to pin down their empirical effects. While we focus on HMMs with discrete outputs, our analysis framework could be extended to HMMs over continuous observations.Our work builds on earlier work that have also noted the connection between RNNs and HMMs BID23 BID25 (see §7). Our contribution is to provide the first thorough theoretical investigation into the model variants, carefully controlling for every design choices, along with comprehensive empirical analysis over the spectrum of possible hybridization between HMMs and RNNs.We find that the key elements to better performance of the HMMs are the use of a sigmoid instead of softmax linearity in the recurrent cell, and the use of an unnormalized output distribution matrix in the emission computation. On the other hand, multiplicative integration of the previous hidden state and input embedding, and intermediate normalizations in the cell computation are less consequential. We also find that HMMs outperform other RNNs variants for unsupervised prediction of the next POS tag, demonstrating the advantages of discrete bottlenecks for increased interpretability.The paper is structured as follows. First, we present the derivation of HMM marginal inference as a special case of RNN computation ( §2). Next we explore a gradual transformation of HMMs into RNNs ( §3), followed by the reverse transformation of Elman RNNs back to HMMs ( §4). Finally we provide empirical analysis in §5 and §6 to pin point the effects of varying design choices over possible hybridizations between HMMs and RNNs.","distinct commonality HMMs RNNs is that they both learn hidden representations sequential data. addition has been noted backward computation Baum-Welch algorithm HMMs is a special case back-propagation algorithm used neural networks Eisner 2016 Do observations suggest despite many apparent differences HMMs are a special case RNNs? paper show is indeed case investigate series architectural transformations HMMs RNNs theoretical derivations empirical hybridization. particular investigate three key design factors independence assumptions hidden states observation placement softmaxes use non-linearities order pin empirical effects. present comprehensive empirical study provide insights interplay expressivity interpretability model family respect language modeling parts-of-speech induction. sequence is a common structure among many forms naturally occurring data including speech text video DNA. sequence modeling has long core research problem across several fields machine learning AI. far widely used approach decades is Hidden Markov Models BID1 BID10 which assumes sequence discrete latent variables generate sequence observed variables. When the latent variables are unobserved unsupervised training HMMs can be performed via Baum-Welch algorithm which,in turn is based forward-backward algorithm special case Expectation-Maximization EM BID4. Importantly discrete nature latent variables has the benefit interpretability recover contextual clustering output variables. contrast Recurrent Neural Networks RNNs BID11 BID6 introduced later assume continuous latent representations. hidden states have no probabilistic interpretation regardless many different architectural variants LSTMs BID9 GRUs BID3 RANs BID13.Despite many apparent differences HMMs RNNs model hidden representations sequential data. heart models are:state time transition functionf:h t−1→h latent space emission functiong:h →x t. addition has been noted backward computation Baum-Welch algorithm is a special case back-propagation neural networks BID5. Therefore natural question arises fundamental relationship HMMs RNNs. Might HMMs special case RNNs? paper investigate series architectural transformations HMMs RNNsboth theoretical derivations empirical hybridization. particular demonstrate forward marginal inference HMM-accumulating forward probabilities compute marginal emission hidden state distributions time step-can reformulated equations computing RNN cell. addition investigate three key design factors-independence Figure1:models indicate type transition emission cells used. H HMM R RNN/Elman F is a novel Fusion defined §3.3 is particularly important track when a vector is a distribution resides simplex versus unit cube e.g sigmoid non-linearity are indicated c c respectively. SM stands softmax rows.assumptions hidden states observations placement softmaxes use non-linearities-in order pin empirical effects. focus HMMs discrete outputs analysis framework could extended HMMs continuous observations.Our work builds earlier work have also noted connection RNNs HMMs BID23 BID25 see§7 contribution is to provide first thorough theoretical investigation model variants carefully controlling every design choices along comprehensive empirical analysis spectrum possible hybridization HMMs RNNs.We find key elements better performance HMMs are the use sigmoid instead softmax linearity recurrent cell use unnormalized output distribution matrix emission computation. hand multiplicative integration previous hidden state input embedding intermediate normalizations cell computation are less consequential. also find HMMs outperform RNNs variants unsupervised prediction next POS tag demonstrating advantages discrete bottlenecks increased interpretability.The paper is structured follows. First present derivation HMM marginal inference special case RNN computation §2 Next explore gradual transformation HMMs RNNs §3 followed reverse transformation Elman RNNs back HMMs §4 Finally provide empirical analysis §5 §6 pin point effects varying design choices possible hybridizations HMMs RNNs.",1087,737,350,0.011,1.475,2025/11/05 17:19:01,0.01,1.667,0.4517133956386294,322.267
"Deep neural networks have been tremendously successful in a number of tasks.
 One of the main reasons for this is their capability to automatically
 learn representations of data in levels of abstraction,
 increasingly disentangling the data as the internal transformations are applied.
 In this paper we propose a novel regularization method that penalize covariance between dimensions of the hidden layers in a network, something that benefits the disentanglement.
 This makes the network learn nonlinear representations that are linearly uncorrelated, yet allows the model to obtain good results on a number of tasks, as demonstrated by our experimental evaluation.
 The proposed technique can be used to find the dimensionality of the underlying data, because it effectively disables dimensions that aren't needed.
 Our approach is simple and computationally cheap, as it can be applied as a regularizer to any gradient-based learning model. A good data representation should ultimately uncover underlying factors in the raw data while being useful for a model to solve some task. Deep neural networks learn representations that are increasingly abstract in deeper layers, disentangling the causes of variation in the underlying data BID1 . Formal definitions of disentanglement are lacking, although Ver BID17 ; BID0 both use the total correlation as a measure of disentanglement. Inspired by this, we consider a simpler objective: a representation disentangles the data well when its components do not correlate, and we explore the effects of penalizing this linear dependence between different dimensions in the representation. Ensuring independence in the representation space results in a distribution that is factorizable and thus easy to model BID8 BID14 .We propose a novel regularization scheme that penalizes the cross-correlation between the dimensions of the learned representations, and helps artificial neural networks learn disentangled representations. The approach is very versatile and can be applied to any gradient-based machine learning model that learns its own distributed vector representations. A large body of literature have been published about techniques for learning non-linear independent representations BID12 BID5 BID3 , but in comparison our approach is simpler, and does not impose restrictions on the model used. The proposed technique penalizes representations with correlated activations. It strongly encourages the model to find the dimensionality of the data, and thus to disable superfluous dimensions in the resulting representations. The experimental evaluation on synthetic data verifies this: the model is able to learn all useful dimensions in the data, and after convergence, these are the only ones that are active. This can be of great utility when pruning a network, or to decide when a network needs a larger capacity. The disabling of activations in the internal representation can be viewed as (and used for) dimensionality reduction. The proposed approach allows for interpretability of the activations computed in the model, such as isolating specific underlying factors. The solution is computationally cheap, and can be applied without modification to many gradient-based machine learning models that learns distributed representations.Moreover, we present an extensive experimental evaluation on a range of tasks on different data modalities, which shows that the proposed approach disentangles the data well; we do get uncorrelated components in the resulting internal representations, while retaining the performance of the models on their respective task.Figure 1: When data is distributed along non-linear manifolds, a linear model cannot describe the data well (left). However, with a non-linear model (right), it is possible to capture the variations of the data in a more reasonable way and unfold it into a compact orthogonal representation space.The main contributions of this work include: L Σ regularization, a novel approach penalizing the covariance between dimensions in a representation (see Section 2). The regularizer encourages a model to use the minimal number of dimensions needed in the representation. The approach is computationally cheap and can be applied without any restrictions on the model. The experimental evaluation shows how different models can benefit from using L Σ regularization. From autoencoders on synthetic data to deep convolutional autoencoders trained on CIFAR-10, we show that L Σ helps us learn uncorrelated and disentangled representations (see Section 3). In this paper, we have presented L Σ regularization, a novel regularization scheme based on penalizing the covariance between dimensions of the internal representation learned in a hierarchical model. The proposed regularization scheme helps models learn linearly uncorrelated variables in a non-linear space. While techniques for learning independent components follow criteria that are more strict, our solution is flexible and portable, and can be applied to any feature-learning model that is trained with gradient descent. Our method has no penalty on the performance on tasks evaluated in the experiments, while it does disentangle the data.",Deep neural networks have been tremendously successful number tasks. One main reasons is their capability automatically learn representations data levels abstraction increasingly disentangling data internal transformations are applied. paper propose novel regularization method penalize covariance dimensions hidden layers network something benefits disentanglement. makes network learn nonlinear representations are linearly uncorrelated yet allows model obtain good results number tasks demonstrated experimental evaluation. proposed technique can be used find dimensionality underlying data effectively disables dimensions needed. approach is simple computationally cheap can canbe applied regularizer gradient-based learning model. good data representation should ultimately uncover underlying factors raw data useful model solve task. Deep neural networks learn representations are increasingly abstract deeper layers disentangling causes variation underlying data BID1. Formal definitions disentanglement are lacking although Ver BID17;BID0 use total correlation measure disentanglement. Inspired consider simpler objective:representation disentangles data well when its components do not correlate explore effects penalizing linear dependence different dimensions representation. Ensuring independence representation space results distribution is factorizable thus easy model BID8 BID14.We propose novel regularization scheme penalizes cross-correlation dimensions learned representations helps artificial neural networks learn disentangled representations. approach is very versatile can be applied gradient-based machine learning model learns distributed vector representations. large body literature have been published techniques learning non-linear independent representations BID12 BID5 BID3 comparison approach is simpler does not impose restrictions model used. proposed technique penalizes representations correlated activations. strongly encourages model find dimensionality data thus disable superfluous dimensions resulting representations. experimental evaluation synthetic data verifies this:model is able learn useful dimensions data convergence are the ones are active. can be of great utility when pruning network decide when a network needs larger capacity. disabling activations internal representation can be viewed used dimensionality reduction. proposed approach allows interpretability activations computed model isolating specific underlying factors. solution is computationally cheap can can be applied without modification many gradient-based machine learning models learns distributed representations.Moreover present extensive experimental evaluation range tasks different data modalities which shows proposed approach disentangles data well;do get uncorrelated components resulting internal representations retaining performance models respective task.Figure1:When data is distributed along non-linear manifolds linear model cannot describe data well left However non-linear model right is possible capture variations data reasonable way unfold compact orthogonal representation space.The main contributions work include:L Σ regularization novel approach penalizing covariance dimensions representation see Section2 regularizer encourages model use minimal number dimensions needed representation. approach is computationally cheap can be applied without restrictions model. experimental evaluation shows how different models can benefit using L Σ regularization. autoencoders synthetic data deep convolutional autoencoders trained CIFAR-10 show L Σ helpsus learn uncorrelated disentangled representations see Section3 paper have presented L Σ regularization novel regularization scheme based penalizing covariance dimensions internal representation learned hierarchical model. proposed regularization scheme helps models learn linearly uncorrelated variables non-linear space. techniques learning independent components follow criteria are more strict solution is flexible portable can can be applied feature-learning model is trained gradient descent. method has no penalty performance tasks evaluated experiments does disentangle data.,930,622,308,0.009,1.495,2025/11/05 17:19:02,0.0,1.425,0.5140186915887852,304.302
"This report introduces a training and recognition scheme, in which classification is realized via class-wise discerning. Trained with datasets whose labels are randomly shuffled except for one class of interest, a neural network learns class-wise parameter values, and remolds itself from a feature sorter into feature filters, each of which discerns objects belonging to one of the classes only. Classification of an input can be inferred from the maximum response of the filters. A multiple check with multiple versions of filters can diminish fluctuation and yields better performance. This scheme of discerning, maximum response and multiple check is a method of general viability to improve performance of feedforward networks, and the filter training itself is a promising feature abstraction procedure. In contrast to the direct sorting, the scheme mimics the classification process mediated by a series of one component picking. Suppose given a task of sorting a bunch of colored balls, we can usually do it in two ways. One is to randomly pick up a ball and deposit it to one of the groups according to its color. Or we can collect balls of the same color at a time until the last two colors are separated. Standard neural networks for classification tasks work in the former manner, for which it is an implied principle that every class should be on an equal footing and biases are harmful. This is the reason why the training data contain subsets of identical sample number or close in size for each class. The scheme introduced in this work is an analogue of the latter, in which the networks do not respond equally to features of different classes. Rather, they function more like filters, and ascription of an object is inferred from how strong their responses are.The filter networks are obtained by filter training, from which we have a group of networks or more specifically a batch of parameter values, number of which is equal to the number of classes. Ensemblization appears to be a built-in trait of this recognition scheme. Since a prediction should not refer to a preassigned label, a quantitative evaluation of how each filter responds to an input should be defined on an equal footing. As long as one of the alternative filters scores higher than the correct one, the prediction is wrong. Fluctuation makes the correct filter the weaker in this one to many contest. To do it a favour we introduce another hierarchy of ensemblization that is a batch of versions for the filters, in the hope that the correct filter could be the overall winner in this tournament. These three steps constitute a classification procedure of discerning, maximum response, and multiple check (DMM).The DMM scheme can improve accuracy of mediocre networks, networks already having high accuracy, and those trained with small-scale data. Fundamental reason for the increase is that in the filter training a multiclass problem is reduced to a pseudo binary classification, the class of interest and the others. Intuitively , we have the feeling that telling a component from a mixture is easier than sorting all the ingredients. The pseudo reduction mitigates workload. Depending on capacity of networks and amount of training samples, the increase of accuracy varies. Nevertheless , as performance improvement due to the mitigation is almost sure, the scheme can be a general route to enhance feedforward networks. Moreover, since a filter is specifically trained for one class, the filter training is a feature abstraction procedure in itself.In the following, we first investigate the mechanism of filter training and how it works through a toy model. From this classification of points in a 2D plane, we can clearly view how the decision boundaries are reshaped. Then, we give a probabilistic argument why the maximum response is a proper criterion to infer classification. After remarking on its relation with related works, we experiment MMD on the CIFAR-10 and MNIST datasets. Motivated by the classification process via one component discerning, we propose the filter training and maximum response. The multiple check can build up an increment of performance if the fluctuation in the responses are properly distributed among filter versions. How to deal with the two types of fluctuations is the major concern for it to work well. DMM constitutes a special ensemble learning scheme, which itself can be incorporated into other schemes as an additional hierarchy of ensemblization. It is beneficial if similar mechanism can be integrated into other network architectures, since task simplification is a common strategy in intellegence activities.",report introduces training recognition scheme which classification is realized via class-wise discerning. Trained datasets whose labels are randomly shuffled except one class interest neural network learns class-wise parameter values remolds feature sorter feature filters which discerns objects belonging one classes only. Classification input can be inferred maximum response filters. multiple check multiple versions filters can diminish fluctuation yields better performance. scheme discerning maximum response multiple check is a method general viability improve performance feedforward networks filter training is a promising feature abstraction procedure. contrast direct sorting scheme mimics classification process mediated series one component picking. Suppose given task sorting bunch colored balls can usually do it in two ways. One is to randomly pick ball deposit one groups according color. can collect balls color time last two colors are separated. Standard neural networks classification tasks work former manner whichit isan implied principle every class should be on an equal footing biases are harmful. is the reason why the training data contain subsets identical sample number close size class. scheme introduced work is an analogue latter which the networks do not respond equally features different classes. Rather function like filters ascription object is inferred how strong responses are.The filter networks are obtained filter training whichwe havea group networks specifically batch parameter values number which is equal number classes. Ensemblization appears built-in trait recognition scheme. Since prediction should not refer preassigned label quantitative evaluation how each filter responds input should be defined equal footing. long one alternative filters scores higher correct one prediction is wrong. Fluctuation makes correct filter weaker one many contest. do it a favour introduce another hierarchy ensemblization is a batch versions filters hope correct filter could overall winner tournament. three steps constitute classification procedure discerning maximum response multiple check DMM.The DMM scheme can improve accuracy mediocre networks which the networks already high accuracy trained small-scale data. Fundamental reason increase is that in the filter training multiclass problem is reduced pseudo binary classification class interest others. Intuitively have the feeling telling component mixture is easier sorting ingredients. pseudo reduction mitigates workload. Depending capacity networks amount training samples increase accuracy varies. Nevertheless performance improvement due mitigation is almost sure scheme can be a general route enhance feedforward networks. Moreover since filter is specifically trained one class filter training is a feature abstraction procedure itself.In following first investigate mechanism how each filter training how it works toy model. classification points 2D plane can clearly view how the decision boundaries are reshaped. give probabilistic argument why the maximum response is a proper criterion infer classification. remarking relation related works experiment MMD CIFAR-10 MNIST datasets. Motivated classification process via one component discerning propose filter training maximum response. multiple check can build increment performance if the fluctuation responses are properly distributed among filter versions. How to deal two types fluctuations is the major concern work well. DMM constitutes special ensemble learning scheme which itself can incorporated schemes additional hierarchy ensemblization. is beneficial if similar mechanism can be integrated network architectures since task simplification is a common strategy intellegence activities.,863,587,276,0.009,1.47,2025/11/05 17:19:02,0.0,1.729,0.4361370716510901,308.434
"A long-held conventional wisdom states that larger models train more slowly when using gradient descent. This work challenges this widely-held belief, showing that larger models can potentially train faster despite the increasing computational requirements of each training step. In particular, we study the effect of network structure (depth and width) on halting time and show that larger models---wider models in particular---take fewer training steps to converge.

 We design simple experiments to quantitatively characterize the effect of overparametrization on weight space traversal. Results show that halting time improves when growing model's width for three different applications, and the improvement comes from each factor: The distance from initialized weights to converged weights shrinks with a power-law-like relationship, the average step size grows with a power-law-like relationship, and gradient vectors become more aligned with each other during traversal.
 How does overparametrization affect the convergence? BID1 have shown that for a simple LNN increasing depth can accelerate optimization, but increasing width does not affect convergence. However, the conclusion of ""width does not matter"" is a consequence of an implicit assumption that minimum width is larger than input dimensionality. If hidden dimension is wide enough to absorb all the information within the input data, increasing width obviously would not affect convergence. For many real problems, however we are operating in a regime where hidden dimension is generally smaller than input dimension. In particular, RNN operate in this regime.Using the machinery introduced in the work of BID18 , we will show that convergence rate is a function of direct distance from initialization point to final point, average step size and the average angle between gradient vectors and the path that connects current weights to final wights.In this paper, we present a variety of experiments designed to characterize the effect of width on error surface. These experiments are designed to qualitatively answer simple questions. How does width affect the convergence? Why does wider network converge faster? Which factors contribute more to the convergence, increase in the step size, better alignment of gradient vectors towards the final weights or the reduction in direct distance? Is the improvement the result of increasing model capacity or there is a true acceleration phenomenon? Why does the convergence improvement slows down beyond a certain model size?We study the characteristics of convergence curve and show that it can be characterized into a powerlaw region within which the number of gradient updates to convergence has a reciprocal relationship to model size and linear relationship to dataset size, and a flat region within which increasing model size does not affect convergence.We analyze the error surface characteristics of overparametrized models. Our qualitative results suggest that as models get wider (1) direct distance from initial weight to final weights shrinks.(2) Total path length traveled gets shrinks. (3) path length shrinks faster than direct distance. (4) step size gets larger. These results collectively suggests that number of local minimas in higher dimensional space grows asymmetrically wrt. origin and there exists a shorter path within the extra dimension to the newly-found local minimas. We also provide a simple theoretical analysis for a simplified problem of LNN and show that direct distance is expected to shrink as models get wider.",long-held conventional wisdom states larger models train slowly when using gradient descent. work challenges widely-held belief showing larger models can potentially train faster despite increasing computational requirements training step. particular study effect network structure depth width halting time show larger models -wider models particular -take fewer training steps converge. design simple experiments quantitatively characterize effect overparametrization weight space traversal. Results show halting time improves when growing model's width three different applications improvement comes factor:distance initialized weights converged weights shrinks power-law-like relationship average step size grows power-law-like relationship gradient vectors become aligned traversal. How does overparametrization affect convergence? BID1 have shown simple LNN increasing depth can accelerate optimization increasing width does not affect convergence. However conclusion width does not matter is a consequence implicit assumption minimum width is larger input dimensionality. If hidden dimension is wide enough absorb information within input data increasing width obviously would affect convergence. many real problems however are operating regime where hidden dimension is generally smaller input dimension. particular RNN operate regime.Using machinery introduced work BID18 will show convergence rate is a function direct distance initialization point final point average step size average angle gradient vectors path connects current weights final wights.In paper present variety experiments designed characterize effect width error surface. experiments are designed qualitatively answer simple questions. How does width affect convergence? Why does wider network converge faster? Which factors contribute convergence increase step size better alignment gradient vectors towards final weights reduction direct distance? Is the improvement result increasing model capacity is a true acceleration phenomenon? Why does the convergence improvement slows beyond certain model size? study characteristics convergence curve show can be characterized powerlaw region within which the number gradient updates convergence has a reciprocal relationship model size linear relationship dataset size flat region within which increasing model size does not affect convergence.We analyze error surface characteristics overparametrized models. qualitative results suggest models get wider 1 direct distance initial weight final weights shrinks. 2 Total path length traveled gets shrinks. 3 path length shrinks faster direct distance. 4 step size gets larger. results collectively suggests number local minimas higher dimensional space grows asymmetrically wrt. origin exists shorter path within extra dimension newly-found local minimas. also provide simple theoretical analysis simplified problem LNN show direct distance is expected shrink models get wider.,632,456,176,0.007,1.386,2025/11/05 17:19:02,0.0,1.483,0.1744548286604356,226.183
"Due to its potential to improve programmer productivity and software quality, automated program repair has been an active topic of research. Newer techniques harness neural networks to learn directly from examples of buggy programs and their fixes. In this work, we consider a recently identified class of bugs called variable-misuse bugs. The state-of-the-art solution for variable misuse enumerates potential fixes for all possible bug locations in a program, before selecting the best prediction. We show that it is beneficial to train a model that jointly and directly localizes and repairs variable-misuse bugs. We present multi-headed pointer networks for this purpose, with one head each for localization and repair. The experimental results show that the joint model significantly outperforms an enumerative solution that uses a pointer based model for repair alone. Advances in machine learning and the availability of large corpora of source code have led to growing interest in the development of neural representations of programs for performing program analyses. In particular, different representations based on token sequences BID10 BID1 , program parse trees BID18 BID16 , program traces (Reed & de Freitas, 2015; BID3 BID26 , and graphs BID0 have been proposed for a variety of tasks including repair BID5 BID0 , optimization BID2 , and synthesis BID17 BID4 .In recent work, BID0 proposed the problem of variable misuse (VARMISUSE): given a program, find program locations where variables are used, and predict the correct variables that should be in those locations. A VARMISUSE bug exists when the correct variable differs from the current one at a location. BID0 show that variable misuses occur in practice, e.g., when a programmer copies some code into a new context, but forgets to rename a variable from the older context, or when two variable names within the same scope are easily confused. FIG0 shows an example derived from a real bug. The programmer copied line 5 to line 6, but forgot to rename object name to subject name. FIG0 shows the correct version. BID0 proposed an enumerative solution to the VARMISUSE problem. They train a model based on graph neural networks that learns to predict a correct variable (among all type-1 def validate_sources(sources): 2 object_name = get_content(sources, 'obj') 3 subject_name = get_content(sources, 'subj') 4 result = Result() 5 result.objects.append(object name) 6 result.subjects.append(object name) 7 return result (a) An example of VARMISUSE shown in red text. At test time, one prediction task is generated for each of the variable-use locations (Blue boxes).1 def validate_sources(sources): 2 object_name = get_content(sources, 'obj') 3 subject_name = get_content(sources, 'subj') 4 result = Result() 5 result.objects.append(object name) 6 result.subjects.append(subject name) 7 return result (b ) The corrected version of FIG0 . If used at train time, one example would be generated for each of the variable-use locations (Blue boxes). correct variables available in the scope) for each slot in a program. A slot is a placeholder in a program where a variable is used. The model is trained on a synthetic dataset containing a training example for each slot in the programs from a corpus of correct source files, and teaching the model to predict the correct, existing variable for each slot. At inference time, a program of unknown correctness is turned into n prediction tasks, one for each of its n slots. Each prediction task is then performed by the trained model and predictions of high probability that differ from the existing variable in the corresponding slot are provided to the programmer as likely VARMISUSE bugs.Unfortunately, this enumerative strategy has some key technical drawbacks. First, it approximates the repair process for a given program by enumerating over a number of independent prediction problems, where important shared context among the dependent predictions is lost. Second, in the training process, the synthetic bug is always only at the position of the slot. If for example, the program in FIG0 were used for training, then five training examples, one corresponding to each identifier in a blue box (a variable read, in this case), would be generated. In each of them, the synthetic bug is exactly at the slot position. However, during inference, the model generates one prediction problem for each variable use in the program. In only one of these prediction problems does the slot coincide with the bug location; in the rest, the model now encounters a situation where there is a bug somewhere else, at a location other than the slot. This differs from the cases it has been trained on. For example, in FIG0 , the prediction problem corresponding to the slot on line 5 contains a bug elsewhere (at line 6) and not in the slot. Only the problem corresponding to the slot on line 6 would match how the model was trained. This mismatch between training and test distributions hampers the prediction accuracy of the model. In our experiments, it leads to an accuracy drop of 4% to 14%, even in the non-enumerative setting, i.e., when the exact location of the bug is provided. Since the enumerative approach uses the prediction of the same variable as the original variable for declaring no bugs at that location, this phenomenon contributes to its worse performance. Another drawback of the enumerative approach is that it produces one prediction per slot in a program, rather than one prediction per program. BID0 deal with this by manually selecting a numerical threshold and reporting a bug (and its repair) only if the predicted probability for a repair is higher than that threshold. Setting a suitable threshold is difficult: too low a threshold can increase false positives and too high a threshold can cause false negatives.In order to deal with these drawbacks, we present a model that jointly learns to perform: 1) classification of the program as either faulty or correct (with respect to VARMISUSE bugs), 2) localization of the bug when the program is classified as faulty, and 3) repair of the localized bug. One of the key insights of our joint model is the observation that, in a program containing a single VARMISUSE bug, a variable token can only be one of the following: 1) a buggy variable (the faulty location), 2) some occurrence of the correct variable that should be copied over the incorrect variable into the faulty location (a repair location), or 3) neither the faulty location nor a repair location. This arises from the fact that the variable in the fault location cannot contribute to the repair of any other variablethere is only one fault location -and a variable in a repair location cannot be buggy at the same time. This observation leads us to a pointer model that can point at locations in the input BID25 by learning distributions over input tokens. The hypothesis that a program that contains a bug at a location likely contains ingredients of the repair elsewhere in the program BID6 has been used quite effectively in practice (Le BID13 . Mechanisms based on pointer networks can play a useful role to exploit this observation for repairing programs.We formulate the problem of classification as pointing to a special no-fault location in the program. To solve the joint prediction problem of classification, localization, and repair, we lift the usual pointer-network architecture to multi-headed pointer networks, where one pointer head points to the faulty location (including the no-fault location when the program is predicted to be non-faulty) and another to the repair location. We compare our joint prediction model to an enumerative approach for repair. Our results show that the joint model not only achieves a higher classification, localization , and repair accuracy, but also results in high true positive score.Furthermore, we study how a pointer network on top of a recurrent neural network compares to the graph neural network used previously by BID0 . The comparison is performed for program repair given an a priori known bug location, the very same task used by that work. Limited to only syntactic inputs, our model outperforms the graph-based one by 7 percentage points . Although encouraging, this comparison is only limited to syntactic inputs; in contrast, the graph model uses both syntax and semantics to achieve state-of-the-art repair accuracy. In future work we plan to study how jointly predicting bug location and repair might improve the graph model when bug location is unknown, as well as how our pointer-network-based model compares to the graphbased one when given semantics, in addition to syntax; the latter is particularly interesting, given the relatively simpler model architecture compared to message-passing networks BID8 . In summary, this paper makes the following key contributions: 1) it presents a solution to the general variable-misuse problem in which enumerative search is replaced by a neural network that jointly localizes and repairs faults; 2) it shows that pointer networks over program tokens provide a suitable framework for solving the VARMISUSE problem; and 3) it presents extensive experimental evaluation over multiple large datasets of programs to empirically validate the claims. BID0 proposed an enumerative approach for solving the VARMISUSE problem by making individual predictions for each variable use in a program and reporting back all variable discrepancies above a threshold, using a graph neural network on syntactic and semantic information. We contrast this paper to that work at length in the previous section. BID5 propose a neural model for semantic code repair where one of the classes of bugs they consider is VARREPLACE, which is similar to the VARMISUSE problem. This model also performs an enumerative search as it predicts repairs for all program locations and then computes a scoring of the repairs to select the best one. As a result, it also suffers from a similar training/test data mismatch issue as BID0 . Similar to us, they use a pooled pointer model to perform the repair task. However, our model uses multi-headed pointers to perform classification, localization, and repair jointly. In this paper, we present an approach that jointly learns to localize and repair bugs. We use a key insight of the VARMISUSE problem that both the bug and repair must exist in the original program to design a multi-headed pointer model over a sequential encoding of program token sequences. The joint model is shown to significantly outperform an enumerative approach using a model that can predict a repair given a potential bug location. In the future, we want to explore joint localization and repair using other models such as graph models and combinations of pointer and graph models, possibly with using more semantic information about programs.",Due potential improve programmer productivity software quality automated program repair has been an active topic research. Newer techniques harness neural networks learn directly examples buggy programs fixes. work consider recently identified class bugs called variable-misuse bugs. state-of-the-art solution variable misuse enumerates potential fixes possible bug locations program selecting best prediction. show is beneficial train model jointly directly localizes repairs variable-misuse bugs. present multi-headed pointer networks purpose where one head localization repair. experimental results show joint model significantly outperforms enumerative solution uses pointer based model repair alone. Advances machine learning availability large corpora source code have led growing interest development neural representations programs performing program analyses. particular different representations based token sequences BID10 BID1 program parse trees BID18 BID16 program traces Reed de Freitas 2015;BID3 BID26 graphs BID0 have been proposed variety tasks including repair BID5 BID0 optimization BID2 synthesis BID17 BID4.In recent work BID0 proposed problem variable misuse VARMISUSE given program find program locations where variables are used predict correct variables shouldbein locations. VARMISUSE bug exists when the correct variable differs current one location. BID0 show variable misuses occur practice e.g when a programmer copies code new context forgets rename variable older context when two variable names within scope are easily confused. FIG0 shows example derived real bug. programmer copied line5 line6 forgot rename object name subject name. FIG0 shows correct version. BID0 proposed enumerative solution VARMISUSE problem. train model based graph neural networks learns predict correct variable among type-1 def validate_sources sources 2 object_name get_content sources 'obj' 3 subject_name get_content sources 'subj' 4 result Result 5 result.objects.append object name 6 result.subjects.append object name 7 return result example VARMISUSE shown red text. test time where one prediction task is generated variable-use locations Blue boxes .1 def validate_sources sources 2 object_name get_content sources 'obj' 3 subject_name get_content sources 'subj' 4 result Result 5 result.objects.append object name 6 result.subjects.append subject name 7 return result b corrected version FIG0. If used train time where one example would generated variable-use locations Blue boxes correct variables available scope slot program. slot is a placeholder program where a variable is used. model is trained synthetic dataset containing training example slot programs corpus correct source files teaching model predict correct existing variable slot. inference time program unknown correctness is turned n prediction tasks where one n slots. prediction task is then is performed trained model predictions high probability differ existing variable corresponding slot are provided programmer likely VARMISUSE bugs.Unfortunately enumerative strategy has some key technical drawbacks. First approximates repair process given program enumerating number independent prediction problems where important shared context among dependent predictions is lost. Second training process synthetic bug is always position slot. If for example program FIG0 were used training five training examples where one corresponding identifier blue box variable read case would generated. synthetic bug is exactly slot position. However inference model generates one prediction problem variable use program. one prediction problems does the slot coincide bug location;rest model encounters situation where there is a bug somewhere else location slot. differs cases has been trained on. example FIG0 prediction problem corresponding slot line 5 contains bug elsewhere line6 slot. problem corresponding slot line 6 would match how the model was trained. mismatch training test distributions hampers prediction accuracy model. experiments leads accuracy drop 4% 14% even non-enumerative setting.e when the exact location bug is provided. Since enumerative approach uses prediction variable original variable declaring bugs location phenomenon contributes worse performance. Another drawback enumerative approach is that it produces one prediction per slot program rather one prediction per program. BID0 deal manually selecting numerical threshold reporting bug repair if the predicted probability repair is higher threshold. Setting suitable threshold is difficult:low threshold can increase false positives high threshold can cause false negatives.In order deal drawbacks present model jointly learns perform:1 classification program either faulty correct respect VARMISUSE bugs 2 localization bug when the program is classified faulty 3 repair localized bug. One key insights joint model is the observation program containing single VARMISUSE bug variable token can only be one following:1 buggy variable faulty location 2 occurrence correct variable should be copied incorrect variable faulty location repair location 3 neither faulty location repair location. arises fact variable fault location cannot contribute repair variablethere is only one fault location -and variable repair location cannot buggy time. observation leadsus pointer model can point locations input BID25 learning distributions input tokens. hypothesis program contains bug location likely contains ingredients repair elsewhere program BID6 has been used quite effectively practice Le BID13. Mechanisms based pointer networks can play useful role exploit observation repairing programs.We formulate problem classification pointing special no-fault location program. solve joint prediction problem classification localization repair lift usual pointer-network architecture multi-headed pointer networks where one pointer head points faulty location including no-fault location when the program is predicted non-faulty another repair location. compare joint prediction model enumerative approach repair. results show joint model achieves higher classification localization repair accuracy also results high true positive score.Furthermore study how a pointer network top recurrent neural network compares graph neural network used previously BID0. comparison is then is performed program repair given priori known bug location task used work. Limited syntactic inputs model outperforms graph-based one 7 percentage points. Although encouraging comparison is only limited syntactic inputs;contrast graph model uses syntax semantics achieve state-of-the-art repair accuracy. future work plan study how jointly predicting bug location repair might improve graph model when bug location is unknown well how our pointer-network-based model compares graphbased one when given semantics addition syntax;latter is particularly interesting given relatively simpler model architecture compared message-passing networks BID8. summary paper makes following key contributions:1 presents solution general variable-misuse problem which enumerative search is replaced neural network jointly localizes repairs faults;2 shows pointer networks program tokens provide suitable framework solving VARMISUSE problem;3 presents extensive experimental evaluation multiple large datasets programs empirically validate claims. BID0 proposed enumerative approach solving VARMISUSE problem making individual predictions variable use program reporting back variable discrepancies threshold using graph neural network syntactic semantic information. contrast paper work length previous section. BID5 propose neural model semantic code repair where one classes bugs consider is VARREPLACE which is similar VARMISUSE problem. model also performs enumerative search predicts repairs program locations computes scoring repairs select best one. result also suffers similar training/test data mismatch issue BID0. Similar us use pooled pointer model perform repair task. However model uses multi-headed pointers perform classification localization repair jointly. paper present approach jointly learns localize repair bugs. use key insight VARMISUSE problem bug repair must exist original program design multi-headed pointer model sequential encoding program token sequences. joint model is shown significantly outperform enumerative approach using model can predict repair given potential bug location. future want explore joint localization repair using models graph models combinations pointer graph models possibly using semantic information programs.,2141,1403,738,0.029,1.526,2025/11/05 17:19:02,0.01,1.493,0.6105919003115264,759.73
"Classification and clustering have been studied separately in machine learning and computer vision. Inspired by the recent success of deep learning models in solving various vision problems (e.g., object recognition, semantic segmentation) and the fact that humans serve as the gold standard in assessing clustering algorithms, here, we advocate for a unified treatment of the two problems and suggest that hierarchical frameworks that progressively build complex patterns on top of the simpler ones (e.g., convolutional neural networks) offer a promising solution. We do not dwell much on the learning mechanisms in these frameworks as they are still a matter of debate, with respect to biological constraints. Instead, we emphasize on the compositionality of the real world structures and objects. In particular, we show that CNNs, trained end to end using back propagation with noisy labels, are able to cluster data points belonging to several overlapping shapes, and do so much better than the state of the art algorithms. The main takeaway lesson from our study is that mechanisms of human vision, particularly the hierarchal organization of the visual ventral stream should be taken into account in clustering algorithms (e.g., for learning representations in an unsupervised manner or with minimum supervision) to reach human level clustering performance. This, by no means, suggests that other methods do not hold merits. For example, methods relying on pairwise affinities (e.g., spectral clustering) have been very successful in many cases but still fail in some cases (e.g., overlapping clusters). Clustering, a.k.a unsupervised classification or nonparametric density estimation, is central to many data-driven domains and has been studied heavily in the past. The task in clustering is to group a given collection of unlabeled patterns into meaningful clusters such that objects within a cluster are more similar to each other than they are to objects in other clusters. Clustering provides a summary representation of data at a coarse level and is used widely in many disciplines (e.g., computer version, bioinformatics, text processing) for exploratory data analysis (a.k.a pattern mining) as well as representation learning (e.g., bag of words). Despite the introduction of thousands of clustering algorithms in the past BID0 , some challenges still remain. For instance, existing algorithms fall short in dealing with different cluster shapes, high dimensions, automatically determining the number of clusters or other parameters, large amounts of data, choosing the appropriate similarity measure, incorporating domain knowledge, and cluster evaluation. Further, no clustering algorithm can consistently win over other algorithms, handle all test cases, and perform at the level of humans.Deep neural networks have become a dominant approach to solve various tasks across many fields. They have been proven successful in several domains including computer vision BID16 , natural language processing BID6 , and speech recognition BID8 for tasks such as scene and object classification BID16 , pixel-level labeling for image segmentation BID21 ; BID34 , modeling attention ; , image generation BID11 , robot arm control BID19 , speech recognition BID12 , playing Atari games BID23 and beating the Go champion. BID28 adopted in this work.Deep Convolutional Neural Networks (CNNs) BID17 have been particularly successful over vision problems. One reason is that nearby pixels in natural scenes are highly correlated. Further natural objects are compositional. These facts allow applying the same filters across spatial locations (and hence share weights), and build complex filters from simpler ones to detect highlevel patterns (e.g., object parts, objects). We advocate that these properties are highly appealing when dealing with clustering problems. For instance, the classic two half moons example can be solved by applying a filter that is selective to each half moon. Or, when two clusters with different shapes overlap, the problem can be solved by having filters responding to each shape. Solving these cases is very challenging by just looking at local regions around points and being blind to the high-level patterns. Incorporating domain knowledge, while working in some cases, does not give a general solution for solving all clustering problems. The human visual system easily solves these 2D problems because it is a general system with a rich set of learned or evolved filters. We believe that deep CNNs, although imperfect models of the human vision as they lack feedback and lateral connections carry a huge promise for solving clustering tasks. Further, as we will argue, they offer a unified solution to both classification and clustering tasks.The current demarcation between classification and clustering becomes murky when we notice that researchers often refer to human judgments in evaluating the outcomes of clustering algorithms. Indeed, humans learn quite a lot about the visual world during their life time. Moreover, the structure of the visual system has been fine-tuned through the evolution. Thus, certainly, there is a learning component involved which has been often neglected in formulating clustering algorithms. While this is sensible from an application point of view (e.g., pattern mining), not only it limits the pursuit for stronger algorithms but also narrows our understanding of human vision.Learning techniques have been utilized for clustering in the past (e.g., BID1 ; BID25 ), for example for tuning parameters (e.g., BID1 ). Deep networks have also been exploited for clustering (e.g., BID14 ; BID13 BID32 ). However, to our knowledge, while CNNs have been already adopted for image segmentation, so far they have not been exploited for generic clustering. Our goal is to investigate such possibility. To this end, instead of borrowing from clustering to do image segmentation, we follow the opposite direction and propose a deep learning based approach to clustering.Our method builds on the fully convolutional network literature, in particular, recent work on edge detection and semantic segmentation which utilize multi-scale local and non-local cues BID28 . Thanks to a high volume of labeled data, high capacity of deep networks, powerful optimization algorithms, and high computational power, deep models win on these tasks. We are also strongly inspired by the works showing the high resemblance between human vision mechanisms and CNNs from behavioral, electrophysiological, and computational aspects (e.g., BID33 BID9 ; BID17 ; BID16 ; BID3 . Our study enriches our understanding of the concept of clustering and its relation to classification. We argued that deep neural networks, especially CNNs, hold a great promise for data clustering. We are motivated by the fact that human vision (and learning) is a general system capable of solving both classification and clustering tasks thus blurring the current dichotomy in treating these problems. Our results show that CNNs can successfully handle complex and occluded clusters much better than other algorithms. This means that a learning mechanism, unsupervised or with minimal supervision, seems inevitable in capturing complex cluster shapes.While our formulation is supervised, feeding the labels to the network is not always consistent. This is where our work differs from semantic segmentation and instance level segmentation. We exploited the mean squared loss to train the network. It might be possible to define other loss functions to teach the network more efficiency using less number of training data or even with weaker labels. One possibility is the pairwise accuracy that we used here for evaluation. Instead of correctly classifying labels, the emphasis can be placed on correctly predicting whether two points belong to the same cluster, regardless of cluster identities (i.e., class labels may vary).Notice that while here we focused on synthetic stimuli, variations of the proposed CNN architecture, have been successfully applied to natural image segmentation. Thus, CNNs offer a unified solution that can be applied to different data modalities and even to higher dimensional data. Further work is needed to extend this line of work to higher dimensions, and more versatile types of cluster shapes (e.g., free form curves, Gestalt examples, density-based clusters). In this regard, adopting CNNs trained on natural images containing a rich set of intermediate-and high-level patterns can give invaluable insights.",Classification clustering have been studied separately machine learning computer vision. Inspired recent success deep learning models solving various vision problems e.g object recognition semantic segmentation fact humans serve gold standard assessing clustering algorithms advocate unified treatment two problems suggest hierarchical frameworks progressively build complex patterns top simpler ones e.g convolutional neural networks offer promising solution. do not dwell much learning mechanisms frameworks are still matter debate respect biological constraints. Instead emphasize compositionality real world structures objects. particular show CNNs trained end end using back propagation noisy labels are able cluster data points belonging several overlapping shapes do so much better state art algorithms. main takeaway lesson study is that mechanisms human vision particularly hierarchal organization visual ventral stream should be taken account clustering algorithms e.g is a learning representations unsupervised manner minimum supervision reach human level clustering performance. means suggests methods do not hold merits. example methods relying pairwise affinities e.g spectral clustering have been very successful many cases still fail cases e.g overlapping clusters Clustering.k.a unsupervised classification nonparametric density estimation is central many data-driven domains has been studied heavily past. task clustering is to group given collection unlabeled patterns meaningful clusters objects within cluster are more similar areto objects clusters. Clustering provides summary representation data coarse level is used widely many disciplines e.g computer version bioinformatics text processing exploratory data analysis.k.a pattern mining well representation learning e.g bag words Despite introduction thousands clustering algorithms past BID0 challenges still remain. instance existing algorithms fall short dealing different cluster shapes high dimensions automatically determining number clusters parameters large amounts data choosing appropriate similarity measure incorporating domain knowledge cluster evaluation. clustering algorithm can consistently win algorithms handle test cases perform level humans.Deep neural networks have become dominant approach solve various tasks across many fields. have been proven successful several domains including computer vision BID16 natural language processing BID6 speech recognition BID8 tasks scene object classification BID16 pixel-level labeling image segmentation BID21;BID34 modeling attention;image generation BID11 robot arm control BID19 speech recognition BID12 playing Atari games BID23 beating Go champion. BID28 adopted work.Deep Convolutional Neural Networks CNNs BID17 have been particularly successful vision problems. One reason is that nearby pixels natural scenes are highly correlated. natural objects are compositional. facts allow applying filters across spatial locations hence share weights build complex filters simpler ones detect highlevel patterns e.g object parts objects advocate properties are highly appealing when dealing clustering problems. instance classic two half moons example can be solved applying filter is selective half moon. when two clusters different shapes overlap problem can be solved filters responding shape. Solving cases is very challenging looking local regions around points blind high-level patterns. Incorporating domain knowledge working cases does not give general solution solving clustering problems. human visual system easily solves 2D problems is a general system rich set learned evolved filters. believe deep CNNs although imperfect models human vision lack feedback lateral connections carry huge promise solving clustering tasks. will argue offer unified solution classification clustering tasks.The current demarcation classification clustering becomes murky when we notice researchers often refer human judgments evaluating outcomes clustering algorithms. Indeed humans learn quite lot visual world life time. Moreover structure visual system has been fine-tuned evolution. Thus certainly is a learning component involved which has been often neglected formulating clustering algorithms. is sensible application point view e.g pattern mining limits pursuit stronger algorithms also narrows understanding human vision.Learning techniques have been utilized clustering past e.g BID1;BID25 example tuning parameters e.g BID1 Deep networks have also exploited clustering e.g BID14;BID13 BID32 However knowledge CNNs have been already adopted image segmentation far have not been exploited generic clustering. goal is to investigate possibility. end instead borrowing clustering do image segmentation follow opposite direction propose deep learning based approach clustering.Our method builds fully convolutional network literature particular recent work edge detection semantic segmentation which utilize multi-scale local non-local cues BID28. Thanks high volume labeled data high capacity deep networks powerful optimization algorithms high computational power deep models win tasks. are also strongly inspired works showing high resemblance human vision mechanisms CNNs behavioral electrophysiological computational aspects e.g BID33 BID9;BID17;BID16;BID3. study enriches understanding concept clustering relation classification. argued deep neural networks especially CNNs hold great promise data clustering. are motivated fact human vision learning is a general system capable solving classification clustering tasks thus blurring current dichotomy treating problems. results show CNNs can successfully handle complex occluded clusters much better algorithms. means learning mechanism unsupervised minimal supervision seems inevitable capturing complex cluster shapes.While formulation is supervised feeding labels network is not always consistent. is where our work differs semantic segmentation instance level segmentation. exploited mean squared loss train network. might possible define loss functions teach network efficiency using less number training data even weaker labels. One possibility is the pairwise accuracy used evaluation. Instead correctly classifying labels emphasis can be placed correctly predicting whether two points belong cluster regardless cluster identities.e class labels may vary.Notice focused synthetic stimuli variations proposed CNN architecture have been successfully applied natural image segmentation. Thus CNNs offer unified solution can be applied different data modalities even higher dimensional data. work is needed extend line work higher dimensions versatile types cluster shapes e.g free form curves Gestalt examples density-based clusters regard adopting CNNs trained natural images containing rich set intermediate-and high-level patterns can give invaluable insights.,1568,1058,510,0.022,1.482,2025/11/05 17:19:02,0.01,1.673,0.4735202492211836,530.315
"Instancewise feature scoring is a method for model interpretation, which yields, for each test instance, a vector of importance scores associated with features. Methods based on the Shapley score have been proposed as a fair way of computing feature attributions, but incur an exponential complexity in the number of features.   This combinatorial explosion arises from the definition of Shapley value and prevents these methods from being scalable to large data sets and complex models. We focus on settings in which the data have a graph structure, and the contribution of features to the target variable is well-approximated by a graph-structured factorization.   In such settings, we develop two algorithms with linear complexity for instancewise feature importance scoring on black-box models.   We establish the relationship of our methods to the Shapley value and a closely related concept known as the Myerson value from cooperative game theory. We demonstrate on both language and image data that our algorithms compare favorably with other methods using both quantitative metrics and human evaluation. Although many black box machine learning models, such as random forests, deep neural networks, and kernel methods, can produce highly accurate prediction in many applications, such prediction often comes at the cost of interpretability. Ease of interpretation is a crucial criterion when these tools are applied in areas such as medicine, financial markets, and criminal justice; for more background, see the discussion paper by Lipton (2016) as well as references therein.In this paper, we study instancewise feature importance scoring as a specific approach to the problem of interpreting the predictions of black-box models. Given a predictive model, such a method yields, for each instance to which the model is applied, a vector of importance scores associated with the underlying features. The instancewise property means that this vector, and hence the relative importance of each feature, is allowed to vary across instances. Thus, the importance scores can act as an explanation for the specific instance, indicating which features are the key for the model to make its prediction on that instance.There is now a large body of research focused on the problem of scoring input features based on the prediction of a given instance (see, e.g., Shrikumar et al., 2017; BID0 Ribeiro et al., 2016; Lundberg & Lee, 2017; Štrumbelj & Kononenko, 2010; BID1 BID4 Sundararajan et al., 2017) . Of most relevance to this paper is a line of recent work (Štrumbelj & Kononenko, 2010; Lundberg & Lee, 2017; BID4 ) that has developed methods for model interpretation based on Shapley value (Shapley, 1953) from cooperative game theory. The Shapley value was originally proposed as an axiomatic characterization of a fair distribution of a total surplus from all the players, and can be applied to predictive models, in which case each feature is modeled as a player in the underlying game. While the Shapley value approach is conceptually appealing, it is also computationally challenging: in general, each evaluation of a Shapley value requires an exponential number of model evaluations. Different approaches to circumventing this complexity barrier have been proposed, including those based on Monte Carlo approximation (Štrumbelj & Kononenko, 2010; BID4 and methods based on sampled least-squares with weights (Lundberg & Lee, 2017) .In this paper, we take a complementary point of view, arguing that the problem of explanation is best approached within a model-based paradigm. In this view, explanations are cast in terms of a model, which may or may not be the same model as used to fit the data. Criteria such as Shapley value, which are intractable to compute when no assumptions are made, can be more effectively computed or approximated within the framework of a model. We focus specifically on settings in which a graph structure is appropriate for describing the relations between features in the data (e.g., chains for sequences and grids for images), and distant features according to the graph have weak interaction during the computation of Shapley values. We propose two methods for instancewise feature importance scoring in this framework, which we term L-Shapley and C-Shapley; here the abbreviations ""L"" and ""C"" refer to ""local"" and ""connected,"" respectively. By exploiting the underlying graph structure, the number of model evaluations is reduced to linear-as opposed to exponential-in the number of features. We demonstrate the relationship of these measures with a constrained form of Shapley value, and we additionally relate C-Shapley with another solution concept from cooperative game theory, known as the Myerson value (Myerson, 1977) . The Myerson value is commonly used in graph-restricted games, under a local additivity assumption of the model on disconnected subsets of features. Finally, we apply our feature scoring methods to several state-of-the-art models for both language and image data, and find that our scoring algorithms compare favorably to several existing sampling-based algorithms for instancewise feature importance scoring. We have proposed two new algorithms-L-Shapley and C-Shapley-for instancewise feature importance scoring, making use of a graphical representation of the data. We have demonstrated the superior performance of these algorithms compared to other methods on black-box models for instancewise feature importance scoring in both text and image classification with both quantitative metrics and human evaluation.Geoffrey Hinton, Nitish Srivastava, and Kevin Swersky. Neural networks for machine learninglecture 6a-overview of mini-batch gradient descent. et al., 2011) , which contains 50, 000 binary labeled movie reviews, with a split of 25, 000 for training and 25, 000 for testing.AG news with Char-CNN The AG news corpus is composed of titles and descriptions of 196, 000 news articles from 2, 000 news sources (Zhang et al., 2015) . It is segmented into four classes, each containing 30, 000 training samples and 1, 900 testing samples.Yahoo! Answers with LSTM The corpus of Yahoo! Answers Topic Classification Dataset is divided into ten categories, each class containing 140, 000 training samples and 5, 000 testing samples.Each input text includes the question title, content and best answer.MNIST The MNIST data set contains 28 × 28 images of handwritten digits with ten categories 0 − 9 (LeCun et al., 1998). A subset of MNIST data set composed of digits 3 and 8 is used for better visualization, with 12, 000 images for training and 1, 000 images for testing.",Instancewise feature scoring is a method model interpretation which yields test instance vector importance scores associated features. Methods based Shapley score have been proposed fair way computing feature attributions incur exponential complexity number features. combinatorial explosion arises definition Shapley value prevents methods scalable large data sets complex models. focus settings which the data have a graph structure contribution features target variable is well-approximated graph-structured factorization. settings develop two algorithms linear complexity instancewise feature importance scoring black-box models. establish relationship methods Shapley value closely related concept known Myerson value cooperative game theory. demonstrate language image data algorithms compare favorably methods using quantitative metrics human evaluation. Although many black box machine learning models random forests deep neural networks kernel methods can produce highly accurate prediction many applications prediction often comes cost interpretability. Ease interpretation is a crucial criterion when these tools are applied areas medicine financial markets criminal justice;background see discussion paper Lipton 2016 well references therein.In paper study instancewise feature importance scoring specific approach problem interpreting predictions black-box models. Given predictive model method yields instance which the model is applied vector importance scores associated underlying features. instancewise property means vector hence relative importance feature is allowed vary across instances. Thus importance scores can act explanation specific instance indicating which features are the key model make prediction instance.There is now a large body research focused problem scoring input features based prediction given instance see e.g Shrikumaretal. 2017;BID0 Ribeiroetal. 2016;Lundberg Lee 2017;Štrumbelj Kononenko 2010;BID1 BID4 Sundararajanet al. 2017 relevance paper is a line recent work Štrumbelj Kononenko 2010;Lundberg Lee 2017;BID4 has developed methods model interpretation based Shapley value Shapley 1953 cooperative game theory. Shapley value was originally proposed axiomatic characterization fair distribution total surplus players can be applied predictive models which case feature is modeled player underlying game. Shapley value approach is conceptually appealing is also computationally challenging:general evaluation Shapley value requires exponential number model evaluations. Different approaches circumventing complexity barrier have been proposed including based Monte Carlo approximation Štrumbelj Kononenko 2010;BID4 methods based sampled least-squares weights Lundberg Lee 2017.In paper take complementary point view arguing problem explanation is best approached within model-based paradigm. view explanations are cast terms model may may model used fit data. Criteria Shapley value which are intractable compute when no assumptions are made can be more effectively computed approximated within framework model. focus specifically settings which a graph structure is appropriate describing relations features which the data e.g chains sequences grids images distant features according graph have weak interaction computation Shapley values. propose two methods instancewise feature importance scoring framework which we term L-Shapley C-Shapley abbreviationsL C refer local connected respectively. exploiting underlying graph structure number model evaluations is reduced linear-as opposed exponential-in number features. demonstrate relationship measures constrained form Shapley value additionally relate C-Shapley another solution concept cooperative game theory known Myerson value Myerson 1977 Myerson value is commonly used graph-restricted games local additivity assumption model disconnected subsets features. Finally apply feature scoring methods several state-of-the-art models language image data find scoring algorithms compare favorably several existing sampling-based algorithms instancewise feature importance scoring. have proposed two new algorithms-L-Shapley C-Shapley-for instancewise feature importance scoring making use graphical representation data. have demonstrated superior performance algorithms compared methods black-box models instancewise feature importance scoring text image classification quantitative metrics human evaluation.Geoffrey Hinton Nitish Srivastava Kevin Swersky. Neural networks machine learninglecture 6a-overview mini-batch gradient descent. etal. 2011 which contains50 000 binary labeled movie reviews split 25 000 training 25 000 testing.AG news Char-CNN AG news corpus is composed titles descriptions 196 000 news articles 2 000 news sources Zhangetal. 2015 is segmented four classes containing30 000 training samples 1 900 testing samples.Yahoo Answers LSTM corpus Yahoo! Answers Topic Classification Dataset is divided ten categories class containing 140 000 training samples 5 000 testing samples.Each input text includes question title content best answer.MNIST MNIST data set contains 28 × 28 images handwritten digits ten categories0− 9 LeCunetal. 1998 subset MNIST data set composed digits3 8 is used better visualization 12 000 images training 1 000 images testing.,1380,939,441,0.015,1.47,2025/11/05 17:19:02,0.01,1.409,0.4361370716510901,437.838
"According to parallel distributed processing (PDP) theory in psychology, neural networks (NN) learn distributed rather than interpretable localist representations. This view has been held so strongly that few researchers have analysed single units to determine if this assumption is correct. However, recent results from psychology, neuroscience and computer science have shown the occasional existence of local codes emerging in artificial and biological neural networks. In this paper, we undertake the first systematic survey of when local codes emerge in a feed-forward neural network, using generated input and output data with known qualities. We find that the number of local codes that emerge from a NN follows a well-defined distribution across the number of hidden layer neurons, with a peak determined by the size of input data, number of examples presented and the sparsity of input data. Using a 1-hot output code drastically decreases the number of local codes on the hidden layer. The number of emergent local codes increases with the percentage of dropout applied to the hidden layer, suggesting that the localist encoding may offer a resilience to noisy networks. This data suggests that localist coding can emerge from feed-forward PDP networks and suggests some of the conditions that may lead to interpretable localist representations in the cortex. The findings highlight how local codes should not be dismissed out of hand. Local neural network models, which are often argued to be biologically implausible, have nevertheless been built or discussed by psychologists such as BID11 ; BID16 ; BID13 , and a few researchers like BID1 have done single neuron probing studies (the equivalent of the neuroscience approach) on their neural networks. However, as parallel distributed processing (PDP) neural networks (NN), as discussed by BID17 b) and BID15 , are generally assumed to learn distributed encodings across all situations, it is often believed that a single neuron in an artificial neural network is not interpretable, and experiments to test if this is true are rarely performed.Recently, however, there has been evidence emerging from neuroscience and modern artificial neural networks that demonstrate the existence of interpretable, local codes. BID10 argued that the neurons in the hippocampus codes for information in a highly selective manner in order to learn quickly without forgetting (catastrophic interference), and BID4 argued that some neurons in cortex are highly selective in order to encode multiple items at the same time in shortterm memory (solving the so-called superposition catastrophe). BID14 reported single cells that fire frequently in response to one stimulus, which suggests that individual neurons can be usefully interpreted.Localist codes have been found in artificial neural networks, see BID2 for full reviews, some examples are Le (2013); BID7 ). BID4 have shown that PDP models learn localist codes when trained to co-activate multiple items at the same time. Deep networks learn selective codes under some conditions. For example, BID8 's found quote mark detectors in RNNs. And there is also some evidence from feed-forward models. For example, BID12 have found that probing individual hidden layer neurons (HLNs) with noise and using activation maximisation they can produce a picture of what that neuron will respond most to, and from this they identified HLNs that act as feature detectors, such as those that only responding to creases (in clothing) or eyes or faces and so on.We would like to elucidate the conditions in which simple networks learn selective units, as this may provide further insight into the conditions in which neurons in cortex respond selectively, and, as we expect such codes are learned for sound information theoretic reasons, we expect that these conditions will also apply to when neural networks might learn them as well. Thus, in this paper, we undertake a study of simple feed-forward neural networks to investigate whether local codes, LCs, do actually emerge in PDP networks, and (as we shall show that they do) we then look at what inhibits or promotes the emergence of LCs by designing input and output data with known properties. And, as this data is structured to have some invariance within a class and some randomness, it is proposed that these experiments could as be modelling the layers within the deep neural network above those which transform the input data from pixel space to feature space.To be clear, we consider a neuron to be interpretable if probing of the activation state of it could give correct and useful information about the classification of the input. We look for information about the presence or absence of a category in the hidden layer (category selective HLNs). We separate the qualitative measure (selective) of whether or not a HLN encodes category presence, from the quantitative measure of how much the HLN responds to a category (selectivity). Thus, a HLN is selective if it encodes the presence/absence of a category. Examples are shown in figure 1, as the neuron encodes the presence or absence of the category shown as red circles, equivalently, it could be claimed that these neurons are selective for that category. As biological neurons use energy to encode information, a selective neuron is usually 'selectively on' (see figure 1(left)), but as there is no energy cost in neural networks 'selectively off' units (figure 1(right)) have also been observed. We use the word 'selectivity' as a quantitative measure of the difference between activations for the two categories, A and not-A, where A is the category a neuron is selective for (and not-A being all other categories). Specifically: DISPLAYFORM0 The important point is the qualitative measure of whether or not a neuron is selective, not how much it is selective by, as we are interested in counting the number of local codes that emerge. Note that the chance that all the members of A would emerge disjoint from the members of not-A is 50 50 / 500 50 is tiny (4.32 × 10 −71 ). Furthermore, we found that the selectivity increased with training as the neural network minimised the loss function, but that the number of selective codes did not change once the neural network achieved 100% accuracy.A criticism often made of a grandmother cell hypothesis is that even if a cell fires consistently to a single class, it is not possible to know that it would not have fired to a stimulus that was not presented. For example, although BID14 found a neuron that responded selectively to images of Jennifer Aniston, the authors only presented approximately 100 images to the human participant, and it is possible that other non-tested images would also drive the neuron. BID20 estimated that between 50-150 other images would drive this neuron. Obviously an experimenter cannot present every possible combination of visual inputs to a patient. However, in neural networks with small datasets, we can present all the possible stimuli to the network. We consider a neuron to be selective if it is selective over all the data it is reasonable to expect the network to differentiate between. For example, it is reasonable to do the test over all training data, and it is reasonable to do it over all test and all verification data or even other data of a similar form (such as different photos of the same class), and choosing what constitutes a reasonable set of data is a decision to be made by the experimenters and reviewers. In this work, we chose to use a simple pattern classification task, rather than an image recognition task, as we could then test the NN with all possible patterns. We have demonstrated that interpretable localised encodings of the presence/absence of some categories can emerge from the hidden layer of a feed-forward neural network. As the number of local codes follows a well-defined pattern with the size of the hidden layer, and it is affected by modifications of the input and output data, it suggests that the number of local codes is related to the computing capacity of the neural network and the difficulty of the problem presented to it, suggesting that the local codes offer some modification to the computing power of the neural network.Furthermore, as the hidden layer size increases, there is so much extra capacity that local codes are not needed. Our results suggest that local codes require more effort to train, but offer more efficient use of the available capacity.As the number of local codes shared invariants within a categories, it does imply that the local codes have some function associated with recognising these invariants. As the average number and range of LCs generally increases with dropout, and the LCs are repressed by a fully locally encoded output layer, it suggests that some local codes are good to have, and that number increases with noisy networks. The fact that the dropout data seems to contain multiple overlapping peaks, and, in our tests, peak numbers of LCs are seen at 500 and 1000 (and 2000 for the S R = 1 9 data) HLNs implies that there are more than one qualitative approaches for the neural network to solve the problem, and tuning the problem and neural network parameters nudges the solution to different distributions of local codes. Do these simple networks tell us anything about deep neural networks? The data presented here was designed to have invariant feature 'short-cuts' that the neural network could make use of in classifying input data into classes and the argument could well be made that the data passed between layers of a deep neural network is not of the same quality. Whilst an obvious next experiment for us is to investigate the qualities of the data passed within a neural network, preliminary feed-forward neural network training on standard simple neural network data (such as the Iris dataset from Fisher (1936)) results also show the emergence of local codes when there is a 'short-cut' in the data (publication in preparation). The observations that local codes are seen under dropout, with distributed input and output codes, when there are invariant features and local codes are inhibited with 1-hot output encodings, suggests that local codes might be found in a the middle and higher layers of a deep network, and not the penultimate layer where the 1-hot output could inhibit them or the early layers where invariant features common to a class have not yet been identified. Another interesting question is whether the local codes might have a diagnostic use, for example, is it the case that they increased in networks that generalise or are they, perhaps, an indicator of over-training? Answering this would also highlight when and where we should expect invariants in the data, as learning an invariant feature, such as, 'presence of eyes implies presence of face', could help with generalisation and classification, however learning an irrelevant invariant feature, such as, presence of 'blue sky implies tanks' would not. Discriminating a blue-sky selective neuron from a tank-selective neuron in such a case would require careful thought about what we should consider reasonable data to test for selectivity.","According parallel distributed processing PDP theory psychology neural networks NN learn distributed rather interpretable localist representations. view has been held strongly researchers have analysed single units determine if this assumption is correct. However recent results psychology neuroscience computer science have shown occasional existence when local codes emerging artificial biological neural networks. paper undertake first systematic survey when local codes emerge feed-forward neural network using generated input output data known qualities. find number when local codes emerge NN follows well-defined distribution across number hidden layer neurons peak determined size input data number examples presented sparsity input data. Using 1-hot output code drastically decreases number when local codes hidden layer. number emergent local codes increases percentage dropout applied hidden layer suggesting localist encoding may offer resilience noisy networks. data suggests localist coding can emerge feed-forward PDP networks suggests conditions may lead interpretable localist representations cortex. findings highlight how local codes should not be dismissed hand. Local neural network models which are is often argued biologically implausible have nevertheless built discussed psychologists BID11;BID16;BID13 researchers like BID1 have done single neuron probing studies equivalent neuroscience approach neural networks. However parallel distributed processing PDP neural networks NN discussed BID17b BID15 are generally assumed learn distributed encodings across situations which are is often believed single neuron artificial neural network is not interpretable experiments do the do it over test if this is true are rarely performed.Recently however has been evidence emerging neuroscience modern artificial neural networks demonstrate existence interpretable local codes. BID10 argued neurons hippocampus codes information highly selective manner order learn quickly without forgetting catastrophic interference BID4 argued neurons cortex are highly selective order encode multiple items time shortterm memory solving so-called superposition catastrophe BID14 reported single cells fire frequently response one stimulus which suggests individual neurons can be usefully interpreted.Localist codes have been have found artificial neural networks see BID2 full reviews examples areLe 2013 BID7 BID4 have shown PDP models learn localist codes when trained co-activate multiple items time. Deep networks learn selective codes conditions. example BID8 's found quote mark detectors RNNs. is also evidence feed-forward models. example BID12 have been have found probing individual hidden layer neurons HLNs noise using activation maximisation can produce picture what that neuron will respond identified HLNs act feature detectors responding creases clothing eyes faces on.We would like elucidate conditions which simple networks learn selective units may provide insight conditions which neurons cortex respond selectively expect codes are learned sound information theoretic reasons expect conditions will also apply when neural networks might learn well. Thus paper undertake study simple feed-forward neural networks investigate whether local codes LCs do actually emerge PDP networks shall show do)look what inhibits promotes emergence LCs designing input output data known properties. data is structured have some invariance within class randomness is proposed experiments could modelling layers within deep neural network which transform input data pixel space feature space.To clear consider neuron interpretable if probing activation state could give correct useful information classification input. look information presence absence category hidden layer category selective HLNs separate qualitative measure selective whether HLN encodes category presence quantitative measure how much HLN responds category selectivity Thus HLN is selective if it encodes presence/absence category. Examples are shown figure1 neuron encodes presence absence category shown red circles equivalently could claimed neurons are selective category. biological neurons use energy encode information selective neuron is usually 'selectively on' see figure1 left isno energy cost neural networks 'selectively off' units figure1 right have also observed. use word 'selectivity' quantitative measure difference activations two categories not-A whereAis category neuron is selective not-A categories Specifically:DISPLAYFORM0 important point is the qualitative measure whether neuron is selective how is so much is selective are interested counting number when local codes emerge. Note chance members would emerge disjoint members not-A is 50 50/500 50 is tiny 4.32 × 10 −71 Furthermore found selectivity increased training neural network minimised loss function number selective codes did not change neural network achieved 100% accuracy.A criticism often made grandmother cell hypothesis is that even if a cell fires consistently single class is not is possible know would have fired stimulus was not presented. example although BID14 found neuron responded selectively images Jennifer Aniston authors presented approximately 100 images human participant is not is possible non-tested images would also drive neuron. BID20 estimated 50-150 images would drive neuron. Obviously experimenter cannot present every possible combination visual inputs patient. However neural networks small datasets can present possible stimuli network. consider neuron selective if it is selective data is reasonable expect network differentiate between. example is is reasonable do the do it over test training data is is reasonable do the do it over test verification data even data similar form different photos class choosing what constitutes reasonable set data is a decision made experimenters reviewers. work chose use simple pattern classification task rather image recognition task could test NN possible patterns. have demonstrated interpretable localised encodings presence/absence categories can emerge hidden layer feed-forward neural network. number when local codes follows well-defined pattern size hidden layer is affected modifications input output data which suggests number when local codes is related computing capacity neural network difficulty problem presented suggesting local codes offer modification computing power neural network.Furthermore hidden layer size increases how is so much extra capacity local codes are not needed. results suggest local codes require effort train offer efficient use available capacity.As number when local codes shared invariants within categories does imply local codes have some function associated recognising invariants. average number range LCs generally increases dropout LCs are repressed fully locally encoded output layer which suggests local codes are good have,and number increases noisy networks. fact dropout data seems contain multiple overlapping peaks tests peak numbers LCs are seen 500 1000 2000 R 1 9 data HLNs implies are more one qualitative approaches neural network solve problem tuning problem neural network parameters nudges solution different distributions when local codes. Do these simple networks tellus anything deep neural networks? data presented was designed have invariant feature 'short-cuts' neural network could make use classifying input data classes argument could well made data passed layers deep neural network is not of the quality. Whilst obvious next experiment us is to investigate qualities data passed within neural network preliminary feed-forward neural network training standard simple neural network data Iris dataset Fisher 1936 results also show emergence when local codes when there is a 'short-cut' data publication preparation observations local codes are seen dropout distributed input output codes when there are invariant features local codes are inhibited 1-hot output encodings which suggests local codes might found middle higher layers deep network penultimate layer where the 1-hot output could inhibit early layers where invariant features common class have not yet identified. Another interesting question is whether local codes might have a diagnostic use example is it the case increased networks generalise are they,perhaps indicator over-training Answering would also highlight when and wherewe should expect invariants data learning invariant feature 'presence eyes implies presence face' could help generalisation classification however learning irrelevant invariant feature presence 'blue sky implies tanks' would not. Discriminating blue-sky selective neuron tank-selective neuron case would require careful thought what we should consider reasonable data do the do it over test selectivity.",2177,1436,741,0.034,1.516,2025/11/05 17:19:02,0.01,1.563,0.5794392523364484,783.17
"Representing entities and relations in an embedding space is a well-studied approach for machine learning on relational data. Existing approaches however primarily focus on simple link structure between a finite set of entities, ignoring the variety of data types that are often used in relational databases, such as text, images, and numerical values. In our approach, we propose a multimodal embedding using different neural encoders for this variety of data, and combine with existing models to learn embeddings of the entities. We extend existing datasets to create two novel benchmarks, YAGO-10-plus and MovieLens-100k-plus, that contain additional relations such as textual descriptions and images of the original entities. We demonstrate that our model utilizes the additional information effectively to provide further gains in accuracy. Moreover, we test our learned multimodal embeddings by using them to predict missing multimodal attributes. Knowledge bases (KB) are an essential part of many computational systems with applications in variety of domains, such as search, structured data management, recommendations, question answering, and information retrieval. However, KBs often suffer from incompleteness, noise in their entries, and inefficient inference. Due to these deficiencies, learning the relational knowledge representation has been a focus of active research BID1 BID10 BID21 BID29 BID4 . These approaches represent relational triples, consisting of a subject entity, relation, and an object entity, by estimating fixed, low-dimensional representations for each entity and relation from observations, thus encode the uncertainty and infer missing facts accurately and efficiently. The subject and the object entities come from a fixed, enumerable set of entities that appear in the knowledge base.Knowledge bases in the real world, however, are rich with a variety of different data types. Apart from a fixed set of entities, the relations often not only include numerical attributes (such as ages, dates, financial, and geoinformation), but also textual attributes (such as names, descriptions, and titles/designations) and images (profile photos, flags, posters, etc.) . Although these different types of relations cannot directly be represented as links in a graph over a fixed set of nodes, they can be crucial pieces of evidences for knowledge base completion. For example the textual descriptions and images might provide evidence for a person's age, profession, and designation. Further, this additional information still contains similar limitations as the conventional link data; they are often missing, may be noisy when observed, and for some applications, may need to be predicted in order to address a query. There is thus a crucial need for relational modeling that goes beyond just the link-based, graph view of knowledge-base completion, is able to utilize all the observed information, and represent the uncertainty of multimodal relational evidence.In this paper, we introduce a multimodal embedding approach for modeling knowledge bases that contains a variety of data types, such as textual, images, numerical, and categorical values. Although we propose a general framework that can be used to extend many of the existing relational modeling approaches, here we primary apply our method to the DistMult approach . We extend this approach that learns a vector for each entity and relation by augmenting it with additional neural encoders for different evidence data types. For example, when the object of a triple is an image, we encode it into a fixed-length vector using a CNN, while the textual attributes are encoded using sequential embedding approaches like LSTMs. The scoring module remains identical; given the vector representations of the subject, relation, and object of a triple, this module produces a score indicating the probability that the triple is correct. This unified model allows for flow of the information across the different relation types, enabling more accurate modeling of relational data.We provide an evaluation of our proposed approach on two relational databases. Since we are introducing a novel formulation in the relational setting, we introduce two benchmarks, created by extending the existing YAGO-10 and MovieLens-100k datasets to include additional relations such as textual descriptions, numerical attributes, and images of the original entities. In our evaluation, we demonstrate that our model utilizes the additional information effectively to provide gains in link-prediction accuracy, and present a breakdown of how much each relation benefits from each type of the additional information. We also present results that indicate the learned multimodal embeddings are capable of predicting the object entities for different types of data which is based on the similarity between those entities. Motivated by the need to utilize multiple source of information to achieve more accurate link prediction we presented a novel neural approach to multimodal relational learning. In this paper we introduced a universal link prediction model that uses different types of information to model knowledge bases. We proposed a compositional encoding component to learn unified entity embedding that encode the variety of information available for each entity. In our analysis we show that our model in comparison to a common link predictor, DistMult, can achieve higher accuracy, showing the importance of employing the available variety of information for each entity. Since all the existing datasets are designed for previous methods, they lack mentioned kind of extra information. In result, we introduced two new benchmarks YAGO-10-plus and MovieLens-100k-plus, that are extend version of existing datasets. Further, in our evaluation, we showed that our model effectively utilizes the extra information in order to benefit existing relations. We will release the datasets and the open-source implementation of our models publicly.There are number of avenues for future work. We will investigate the performance of our model in completing link prediction task using different scoring function and more elaborate encoding component and objective function. We are also interested in modeling decoding of multimodal values in the model itself, to be able to query these values directly. Further, we plan to explore efficient query algorithms for embedded knowledge bases, to compete with practical database systems.",Representing entities relations embedding space is a well-studied approach machine learning relational data. Existing approaches however primarily focus simple link structure finite set entities ignoring variety data types are often used relational databases text images numerical values. approach propose multimodal embedding using different neural encoders variety data combine existing models learn embeddings entities. extend existing datasets create two novel benchmarks YAGO-10-plus MovieLens-100k-plus contain additional relations textual descriptions images original entities. demonstrate model utilizes additional information effectively provide gains accuracy. Moreover test learned multimodal embeddings using predict missing multimodal attributes. Knowledge bases KB are an essential part many computational systems applications variety domains search structured data management recommendations question answering information retrieval. However KBs often suffer incompleteness noise entries inefficient inference. Due deficiencies learning relational knowledge representation has been a focus active research BID1 BID10 BID21 BID29 BID4. approaches represent relational triples consisting subject entity relation when the object entity estimating fixed low-dimensional representations entity relation observations thus encode uncertainty infer missing facts accurately efficiently. subject object entities come fixed enumerable set entities appear knowledge base.Knowledge bases real world however are rich variety different data types. Apart fixed set entities relations often include numerical attributes ages dates financial geoinformation also textual attributes names descriptions titles/designations images profile photos flags posters etc. Although different types relations cannot directly represented links graph fixed set nodes can be crucial pieces evidences knowledge base completion. example textual descriptions images might provide evidence person's age profession designation. additional information still contains similar limitations conventional link data;are often missing may noisy when observed applications may need predicted order address query. is thus crucial need relational modeling goes beyond link-based graph view knowledge-base completion is able utilize observed information represent uncertainty multimodal relational evidence.In paper introduce multimodal embedding approach modeling knowledge bases contains variety data types textual images numerical categorical values. Although propose general framework can be used extend many existing relational modeling approaches primary apply method DistMult approach. extend approach learns vector entity relation augmenting additional neural encoders different evidence data types. example when the object triple is an image encode fixed-length vector using CNN textual attributes are encoded using sequential embedding approaches like LSTMs. scoring module remains identical;given vector representations subject relation when the object triple module produces score indicating probability triple is correct. unified model allows flow information across different relation types enabling accurate modeling relational data.We provide evaluation proposed approach two relational databases. Since are introducing novel formulation relational setting introduce two benchmarks created extending existing YAGO-10 MovieLens-100k datasets include additional relations textual descriptions numerical attributes images original entities. evaluation demonstrate model utilizes additional information effectively provide gains link-prediction accuracy present breakdown how much relation benefits type additional information. are also present results indicate learned multimodal embeddings are capable predicting object entities different types data which is based similarity entities. Motivated need utilize multiple source information achieve accurate link prediction presented novel neural approach multimodal relational learning. paper introduced universal link prediction model uses different types information model knowledge bases. proposed compositional encoding component learn unified entity embedding encode variety information available entity. analysis show model comparison common link predictor DistMult can achieve higher accuracy showing importance employing available variety information entity. Since existing datasets are designed previous methods lack mentioned kind extra information. result introduced two new benchmarks YAGO-10-plus MovieLens-100k-plus are extend version existing datasets. evaluation showed model effectively utilizes extra information order benefit existing relations. will release datasets open-source implementation models publicly.There are number avenues future work. will investigate performance model completing link prediction task using different scoring function elaborate encoding component objective function. are also interested modeling decoding multimodal values model able query values directly. plan explore efficient query algorithms embedded knowledge bases compete practical database systems.,1152,728,424,0.013,1.582,2025/11/05 17:19:02,0.01,1.346,0.7850467289719627,365.911
"An ensemble of neural networks is known to be more robust and accurate than an individual network, however usually with linearly-increased cost in both training and testing. 
 In this work, we propose a two-stage method to learn Sparse Structured Ensembles (SSEs) for neural networks.
 In the first stage, we run SG-MCMC with group sparse priors to draw an ensemble of samples from the posterior distribution of network parameters. In the second stage, we apply weight-pruning to each sampled network and then perform retraining over the remained connections.
 In this way of learning SSEs with SG-MCMC and pruning, we not only achieve high prediction accuracy since SG-MCMC enhances exploration of the model-parameter space, but also reduce memory and computation cost significantly in both training and testing of NN ensembles.
 This is thoroughly evaluated in the experiments of learning SSE ensembles of both FNNs and LSTMs.
 For example, in LSTM based language modeling (LM), we obtain 21\% relative reduction in LM perplexity by learning a SSE of 4 large LSTM models, which has only 30\% of model parameters and 70\% of computations in total, as compared to the baseline large LSTM LM.
 To the best of our knowledge, this work represents the first methodology and empirical study of integrating SG-MCMC, group sparse prior and network pruning together for learning NN ensembles. Recently there are increasing interests in using ensembles of Deep Neural Networks (DNNs) BID19 ; BID17 ), which are known to be more robust and accurate than individual networks. An explanation stems from the fact that learning neural networks is an optimization problem with many local minima BID13 ). Multiple models obtained from applying stochastic optimization, e.g. the widely used Stochastic Gradient Descent (SGD) and its variants, converge to different local minima and tend to make different errors. Due to this diversity, the collective prediction produced by an ensemble is less likely to be in error than individual predictions. The collective prediction is usually performed by averaging the predictions of the multiple neural networks.On the other hand, the improved prediction accuracy of such model averaging can be understood from the principled perspective of Bayesian inference with Bayesian neural networks. Specifically, for each test pointx, we consider the predictive distribution P (ỹ|x, D) = ∫ P (ỹ|x, θ)P (θ|D)dθ, by integrating the model distribution P (ỹ|x, θ) with the posterior distribution over the model parameters P (θ|D) given training data D. The predictive distribution is then approximated by Monte Carlo integration P (ỹ|x, D) ≈ DISPLAYFORM0 , where θ (m) ∼ P (θ|D), m = 1, · · · , M , are posterior samples of model parameters. It is well known that such Bayesian model averaging is more accurate in prediction and robust to over-fitting than point estimates of model parameters BID3 ; ; BID9 ).Despite the obvious advantages as seen from both perspectives, a practical problem that hinders the use of DNN ensembles in real-world tasks is that an ensemble requires too much computation in both training and testing. Traditionally , multiple neural networks are trained, e.g. with different random initialization of model parameters. Recent studies in BID21 ; BID17 ) propose to learn an ensemble which consists of multiple snapshot models along the op- timization path within a single training process, by leveraging a special cyclic learning rate schedule. This reduces the training cost, but the testing cost is still high.In this paper we also aim at learning an ensemble within a single training process, but by leveraging the recent progress in Bayesian posterior sampling, namely the Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) algorithms. Moreover, we apply group sparse priors in training to enforce group-level sparsity on the network's connections. Subsequently we can further use model pruning to compress the networks so that the testing cost is reduced with no loss of accuracy.Figure 1 presents a high-level overview of our two-stage method to learn Sparse Structured Ensembles (SSEs) for DNNs. Specifically, in the first stage, we run SG-MCMC with group sparse priors to draw an ensemble of samples from the posterior distribution of network parameters. In the second stage, we apply weight-pruning to each sampled network and then perform retraining over the remained connections as fine-tuning. In this way of learning SSEs with SG-MCMC and pruning, we reduce memory and computation cost significantly in both training and testing of NN ensembles, while maintaining high prediction accuracy. This is empirically verified in our experiments of learning SSE ensembles of both FNNs and LSTMs.We evaluate the performance of the proposed method on two experiments with different types of neural networks. The first is an image classification experiment, which uses Feed-forward Neural Networks (FNNs) on the well-known MNIST dataset (Deng (2012) ). Second, we experiment with the more challenging task of Long Short-term Memory (LSTM, BID15 ) based language modeling, which is conducted on the Penn Treebank dataset BID22 ). It is found that the proposed method works well across both tasks. For example, we obtain 12% relative reduction (from 78.4 to 68.6) in LM perplexity by learning a SSE of 4 large LSTM models, which has only 40% of model parameters and 90% of computations in total, as compared to the large LSTM LM in BID34 . Furthermore, when the embedding weights of input and output are shared as in BID18 , we obtain a perplexity of 62.1 (achieving 21% reduction from 78.4) by 4 large LSTMs with only 30% of model parameters and 70% of computations in total. In this work, we propose a novel method of learning NN ensembles efficiently and cost-friendly by integrating three mutually enhanced techniques: SG-MCMC sampling, group sparse prior and network pruning. The resulting SGLD+GSP+PR method is easy to implement, yet surprisingly effective. This is thoroughly evaluated in the experiments of learning SSE ensembles of both FNNs and LSTMs. The Sparse Structured Ensembles (SSEs) learned by our method gain better prediction performance with reduced training and test cost when compared to traditional methods of learning NN ensembles. Moreover, by proper controlling the number of models used in the ensemble, the method can also be used to produce SSE, which outperforms baseline NN significantly without increasing the model size and computation cost.Some interesting future works: (1) interleaving model sampling and model pruning; (2) application of this new method, as a new powerful tool of learning ensembles, to more tasks.",ensemble neural networks is known robust accurate individual network however usually linearly-increased cost training testing. work propose two-stage method learn Sparse Structured Ensembles SSEs neural networks. first stage run SG-MCMC group sparse priors draw ensemble samples posterior distribution network parameters. second stage apply weight-pruning sampled network perform retraining remained connections. way learning SSEs SG-MCMC pruning achieve high prediction accuracy since SG-MCMC enhances exploration model-parameter space also reduce memory computation cost significantly training testing NN ensembles. is thoroughly evaluated experiments learning SSE ensembles FNNs LSTMs. example LSTM based language modeling LM obtain 21\ relative reduction LM perplexity learning SSE 4 large LSTM models which has only 30\ model parameters 70\ computations total compared baseline large LSTMLM. best knowledge work represents first methodology empirical study integrating SG-MCMC group sparse prior network pruning together learning NN ensembles. Recently are increasing interests using ensembles Deep Neural Networks DNNs BID19;BID17 which are known robust accurate individual networks. explanation stems fact learning neural networks is an optimization problem many local minima BID13 Multiple models obtained applying stochastic optimization e.g widely used Stochastic Gradient Descent SGD variants converge different local minima tend make different errors. Due diversity collective prediction produced ensemble is less likely error individual predictions. collective prediction is usually performed averaging predictions multiple neural networks.On hand improved prediction accuracy model averaging can be understood principled perspective Bayesian inference Bayesian neural networks. Specifically test pointx consider predictive distributionP ỹ|x ∫P ỹ|x whereθ P θ|D dθ integrating model distributionP ỹ|x whereθ posterior distribution model parametersP θ|D given training data D. predictive distribution is then approximated Monte Carlo integrationP ỹ|x ≈ DISPLAYFORM0 whereθ ∼P θ|D 1 ··· are posterior samples model parameters. is well known Bayesian model averaging is more accurate prediction robust over-fitting point estimates model parameters BID3;BID9.Despite obvious advantages seen perspectives practical problem hinders use DNN ensembles real-world tasks is that an ensemble requires much computation training testing. Traditionally multiple neural networks are trained e.g different random initialization model parameters. Recent studies BID21;BID17 propose learn ensemble which consists multiple snapshot models along op- timization path within single training process leveraging special cyclic learning rate schedule. reduces training cost testing cost is still high.In paper also aim learning ensemble within single training process leveraging recent progress Bayesian posterior sampling namely Stochastic Gradient Markov Chain Monte Carlo SG-MCMC algorithms. Moreover apply group sparse priors training enforce group-level sparsity network's connections. Subsequently can further use model pruning compress networks testing cost is reduced loss accuracy.Figure 1 presents high-level overview two-stage method learn Sparse Structured Ensembles SSEs DNNs. Specifically first stage run SG-MCMC group sparse priors draw ensemble samples posterior distribution network parameters. second stage apply weight-pruning sampled network perform retraining remained connections fine-tuning way learning SSEs SG-MCMC pruning reduce memory computation cost significantly training testing NN ensembles maintaining high prediction accuracy. is empirically verified experiments learning SSE ensembles FNNs LSTMs.We evaluate performance proposed method two experiments different types neural networks. first is an image classification experiment which uses Feed-forward Neural Networks FNNs well-known MNIST dataset Deng 2012 Second experiment challenging task Long Short-term Memory LSTM BID15 based language modeling which is conducted Penn Treebank dataset BID22 is found proposed method works well across tasks. example obtain12% relative reduction 78.4 68.6 LM perplexity learning SSE 4 large LSTM models which has only40% model parameters 90% computations total compared large LSTMLM BID34. Furthermore when the embedding weights input output are shared BID18 obtain perplexity 62.1 achieving21% reduction 78.4 4 large LSTMs 30% model parameters 70% computations total. work propose novel method learning NN ensembles efficiently cost-friendly integrating three mutually enhanced techniques:SG-MCMC sampling group sparse prior network pruning. resulting SGLD+GSP+PR method is easy implement yet surprisingly effective. is thoroughly evaluated experiments learning SSE ensembles FNNs LSTMs. Sparse Structured Ensembles SSEs learned method gain better prediction performance reduced training test cost when compared traditional methods learning NN ensembles. Moreover proper controlling number models used ensemble method can also used produce SSE which outperforms baseline NN significantly without increasing model size computation cost.Some interesting future works:1 interleaving model sampling model pruning;2 application new method new powerful tool learning ensembles tasks.,1378,924,454,0.015,1.491,2025/11/05 17:19:02,0.01,1.469,0.5015576323987541,438.342
"This paper introduces a new framework for data efficient and versatile learning. Specifically:
 1) We develop ML-PIP, a general framework for Meta-Learning approximate Probabilistic Inference for Prediction. ML-PIP extends existing probabilistic interpretations of meta-learning to cover a broad class of methods. 
 2) We introduce \Versa{}, an instance of the framework employing a flexible and versatile amortization network that takes few-shot learning datasets as inputs, with arbitrary numbers of shots, and outputs a distribution over task-specific parameters in a single forward pass. \Versa{} substitutes optimization at test time with forward passes through inference networks, amortizing the cost of inference and relieving the need for second derivatives during training.
 3) We evaluate \Versa{} on benchmark datasets where the method sets new state-of-the-art results, and can handle arbitrary number of shots, and for classification, arbitrary numbers of classes at train and test time. The power of the approach is then demonstrated through a challenging few-shot ShapeNet view reconstruction task. Many applications require predictions to be made on myriad small, but related datasets. In such cases, it is natural to desire learners that can rapidly adapt to new datasets at test time. These applications have given rise to vast interest in few-shot learning BID9 BID32 , which emphasizes data efficiency via information sharing across related tasks. Despite recent advances, notably in meta-learning based approaches BID44 BID54 BID8 BID10 , there remains a lack of general purpose methods for flexible, data-efficient learning.Due to the ubiquity of recent work, a unifying view is needed to understand and improve these methods. Existing frameworks BID16 are limited to specific families of approaches. In this paper we develop a framework for meta-learning approximate probabilistic inference for prediction (ML-PIP), providing this view in terms of amortizing posterior predictive distributions. In Section 4, we show that ML-PIP re-frames and extends existing point-estimate probabilistic interpretations of meta-learning BID16 to cover a broader class of methods, including gradient based meta-learning BID10 BID44 , metric based meta-learning BID48 , amortized MAP inference BID43 and conditional probability modelling BID13 .The framework incorporates three key elements. First , we leverage shared statistical structure between tasks via hierarchical probabilistic models developed for multi-task and transfer learning BID18 BID0 . Second , we share information between tasks about how to learn and perform inference using meta-learning BID37 BID50 BID47 . Since uncertainty is rife in small datasets, we provide a procedure for metalearning probabilistic inference. Third , we enable fast learning that can flexibly handle a wide range of tasks and learning settings via amortization .Building on the framework, we propose a new method -VERSA -which substitutes optimization procedures at test time with forward passes through inference networks. This amortizes the cost of inference, resulting in faster test-time performance, and relieves the need for second derivatives during training. VERSA employs a flexible amortization network that takes few-shot learning datasets, and outputs a distribution over task-specific parameters in a single forward pass. The network can handle arbitrary numbers of shots, and for classification, arbitrary numbers of classes at train and test time (see Section 3). In Section 5, we evaluate VERSA on (i) standard benchmarks where the method sets new state-of-the-art results, (ii) settings where test conditions (shot and way) differ from training, and (iii) a challenging one-shot view reconstruction task. We have introduced ML-PIP, a probabilistic framework for meta-learning. ML-PIP unifies a broad class of recently proposed meta-learning methods, and suggests alternative approaches. Building on ML-PIP, we developed VERSA, a few-shot learning algorithm that avoids the use of gradient based optimization at test time by amortizing posterior inference of task-specific parameters. We evaluated VERSA on several few-shot learning tasks and demonstrated state-of-the-art performance and compelling visual results on a challenging 1-shot view reconstruction task. a We report the performance of Prototypical Networks when training and testing with the same ""shot"" and ""way"", which is consistent with the experimental protocol of the other methods listed. We note that Prototypical Networks perform better when trained on higher ""way"" than that of testing. In particular, when trained on 20-way classification and tested on 5-way, the model achieves 68.20 ± 0.66%.",paper introduces new framework data efficient versatile learning. Specifically:1 develop ML-PIP general framework Meta-Learning approximate Probabilistic Inference Prediction. ML-PIP extends existing probabilistic interpretations meta-learning cover broad class methods. 2 introduce \Versa instance framework employing flexible versatile amortization network takes few-shot learning datasets inputs arbitrary numbers shots outputs distribution task-specific parameters single forward pass. \Versa substitutes optimization test time forward passes inference networks amortizing cost inference relieving need second derivatives training. 3 evaluate \Versa benchmark datasets where the method sets new state-of-the-art results can handle arbitrary number shots classification arbitrary numbers classes train test time. power approach is then demonstrated challenging few-shot ShapeNet view reconstruction task. Many applications require predictions made myriad small related datasets. cases is natural desire learners can rapidly adapt new datasets test time. applications have given rise vast interest few-shot learning BID9 BID32 which emphasizes data efficiency via information sharing across related tasks. Despite recent advances notably meta-learning based approaches BID44 BID54 BID8 BID10 remains lack general purpose methods flexible data-efficient learning.Due ubiquity recent work unifying view is needed understand improve methods. Existing frameworks BID16 are limited specific families approaches. paper develop framework meta-learning approximate probabilistic inference prediction ML-PIP providing view terms amortizing posterior predictive distributions. Section4 show ML-PIP re-frames extends existing point-estimate probabilistic interpretations meta-learning BID16 cover broader class methods including gradient based meta-learning BID10 BID44 metric based meta-learning BID48 amortized MAP inference BID43 conditional probability modelling BID13.The framework incorporates three key elements. First leverage shared statistical structure tasks via hierarchical probabilistic models developed multi-task transfer learning BID18 BID0. Second share information tasks how to learn perform inference using meta-learning BID37 BID50 BID47. Since uncertainty is rife small datasets provide procedure metalearning probabilistic inference. Third enable fast learning can flexibly handle wide range tasks learning settings via amortization.Building framework propose new method -VERSA -which substitutes optimization procedures test time forward passes inference networks. amortizes cost inference resulting faster test-time performance relieves need second derivatives training. VERSA employs flexible amortization network takes few-shot learning datasets outputs distribution task-specific parameters single forward pass. network can handle arbitrary numbers shots classification arbitrary numbers classes train test time see Section3 Section5 evaluate VERSA standard benchmarks where the method sets new state-of-the-art results ii settings where test conditions shot way differ training iii challenging one-shot view reconstruction task. have introduced ML-PIP probabilistic framework meta-learning ML-PIP unifies broad class recently proposed meta-learning methods suggests alternative approaches. Building ML-PIP developed VERSA few-shot learning algorithm avoids use gradient based optimization test time amortizing posterior inference task-specific parameters. evaluated VERSA several few-shot learning tasks demonstrated state-of-the-art performance compelling visual results challenging 1-shot view reconstruction task. report performance Prototypical Networks when training testing shot way which is consistent experimental protocol methods listed. note Prototypical Networks perform better when trained higher way testing. particular when trained 20-way classification tested 5-way model achieves 68.20± 0.66,900,635,265,0.008,1.417,2025/11/05 17:19:02,0.0,1.211,0.2710280373831775,281.426
"In recent years, softmax together with its fast approximations has become the de-facto loss function for deep neural networks with multiclass predictions. However, softmax is used in many problems that do not fully fit the multiclass framework and where the softmax assumption of mutually exclusive outcomes can lead to biased results. This is often the case for applications such as language modeling, next event prediction and matrix factorization, where many of the potential outcomes are not mutually exclusive, but are more likely to be independent conditionally on the state. To this end, for the set of problems with positive and unlabeled data, we propose a relaxation of the original softmax formulation, where, given the observed state, each of the outcomes are conditionally independent but share a common set of negatives. Since we operate in a regime where explicit negatives are missing, we create an adversarially-trained model of negatives and derive a new negative sampling and weighting scheme which we denote as Cooperative Importance Sampling (CIS). We show empirically the advantages of our newly introduced negative sampling scheme by pluging it in the Word2Vec algorithm and benching it extensively against other negative sampling schemes on both language modeling and matrix factorization tasks and show large lifts in performance. Learning from positive and unlabeled data is a well-defined task in machine learning, known as positive-unlabeled (PU) learning BID6 ; BID14 ; BID13 ; BID22 ; BID19 ). The applications of PU learning are numerous, as in many fields negative data is either too expensive to obtain or too hard to define. This is the case in language modeling, where one only observes examples of valid sentences and documents, and tries to learn a generative process. Similarly, in computer vision, with the recent work on Generative Adversarial Networks (GANs), one tries to learn the underlying generative process that produces meaningful images. In both cases, the space of negatives (e.g., non-sentences or non-images) is not clear. Similarly, in matrix factorization, most of the matrices contain pairs of observed interactions, and there are no available explicit negatives.In all of the applications enumerated above, it is quite common to encounter solutions that are based on a softmax loss function. In language modeling, and more recently in matrix factorization, the Word2Vec algorithm (see BID15 ) models the conditional probability of observing all possible items in the vicinity of a context item as a categorical distribution using the softmax loss.However, modeling the probability of co-occurrence as a categorical distribution is a very biased assumption that is clearly refuted by the data, since for all context words there are multiple words that co-occur at the same time.In our paper we propose Partially Mutual Exclusive Softmax (PMES), a new model that relaxes the mutual exclusivity constraint over the outcomes. PMES relaxes this constraint by splitting the set of all outcomes into a set of possible outcomes that are conditionally independent given the context, and a set of impossible outcomes which become negative examples.The context-dependent negative set is hypothesized but not known, so in our method we introduce a model for negatives that is used to weight the sampled candidate negatives. The training algorithm is based on the simultaneous training of two neural networks. The first network is a generator that fits the positives and the sampled negatives. The second network is the discriminator, which is trained to separate the true positive pairs from generated pairs, and is used as the model of the probability that an example would receive a negative label.The resulting solution has many similarities with other recent negative sampling methods for approximating full softmax. However, unlike most of the previous methods, our method is not trying to faithfully approximate the full softmax formulation, but to fix some of its over-simplifying assumptions. Furthermore, we believe that the observed lift in performance of some of the negative sampling work over the full softmax can be explained through the prism of Partially Mutual Exclusive Softmax.Our hypothesis is further confirmed by experiments on language modeling and matrix factorization, where we show a big lift in performance over previous work on negative sampling and full softmax. We validate some of our intuitions on the advantages of our sampling procedure on an artificial dataset where the support sets are known, and show that our sampling scheme correctly approximates the support, which is not the case for other softmax variants.Overall, the main contributions of this paper are the following:• We propose Partially Mutual Exclusive (PME) Softmax, a modified version of the softmax loss that is a better fit for problems with positive and unlabeled data.• We derive a new negative sampling scheme based on an cooperatively-trained models of negatives which we denote as Cooperative Importance Sampling (CIS)• We show empirically the validity of our proposed approach by plugging our new loss into the Word2Vec model, and evaluating this enhanced Word2Vec model against classical sampling schemes for Word2Vec on language modeling and matrix factorization tasks across six real-world datasets.We discuss related work on Word2Vec, negative sampling schemes for softmax and GANs in Section 2 of this paper. In Section 3 we formally introduce our PME-Softmax loss and the associated CIS negative sampling scheme, and describe the training algorithm. We highlight the performance of our method in Section 4, and conclude with ideas and directions for future work in Section 5. In this paper, we have proposed Partially Mutual Exclusive Softmax, a relaxed version of the full softmax that is more suited in cases with no explicit negatives, e.g., in cases with positive and unlabeled data. In order to model the new softmax we proposed a cooperative negative sampling algorithm. Based on recent progress made on GANs in discrete data settings, our cooperative training approach can be easily applied to models that use standard sampled softmax training, where the generator and discriminator can be of the same family of models. In future work we will investigate the effectiveness of this training procedure on more complex models, and also try to make our mutually exclusive set model more contextual and dependent on both objects i and j within a pair. For example, for a given pair context/target, one might want to use the closest neighbors of the target in the embedding space as negatives. This could enable us to obtain a negative distribution that fits both the context and the target.","recent years softmax together fast approximations has become de-facto loss function deep neural networks multiclass predictions. However softmax is used many problems do not fully fit multiclass framework where the softmax assumption mutually exclusive outcomes can lead biased results. is often case applications language modeling next event prediction matrix factorization where many potential outcomes are not mutually exclusive are more likely independent conditionally state. end set problems positive unlabeled data propose relaxation original softmax formulation where,given observed state outcomes are conditionally independent share common set negatives. Since operate regime where explicit negatives are missing create adversarially-trained model negatives derive new negative sampling weighting scheme which we denote Cooperative Importance Sampling CIS show empirically advantages newly introduced negative sampling scheme pluging Word2Vec algorithm benching extensively negative sampling schemes language modeling matrix factorization tasks show large lifts performance. Learning positive unlabeled data is a well-defined task machine learning known positive-unlabeled PU learning BID6;BID14;BID13;BID22;BID19 applications PU learning are numerous where many fields negative data is either expensive obtain hard define. is the case language modeling where one observes examples valid sentences documents tries learn generative process. Similarly computer vision recent work Generative Adversarial Networks GANs one tries learn underlying generative process produces meaningful images. cases space negatives e.g non-sentences non-images is not clear. Similarly matrix factorization matrices contain pairs observed interactions are available explicit negatives.In applications enumerated is quite common encounter solutions are based softmax loss function. language modeling recently matrix factorization Word2Vec algorithm see BID15 models conditional probability observing possible items vicinity context item categorical distribution using softmax loss.However modeling probability co-occurrence categorical distribution is a very biased assumption is clearly refuted data since context words are multiple words co-occur time.In paper propose Partially Mutual Exclusive Softmax PMES new model relaxes mutual exclusivity constraint outcomes. PMES relaxes constraint splitting set outcomes set possible outcomes are conditionally independent given context set impossible outcomes which become negative examples.The context-dependent negative set is hypothesized known method introduce model negatives is used weight sampled candidate negatives. training algorithm is based simultaneous training two neural networks. first network is a generator fits positives sampled negatives. second network is the discriminator which is trained separate true positive pairs generated pairs is used model probability example would receive negative label.The resulting solution has many similarities recent negative sampling methods approximating full softmax. However unlike previous methods method is not trying faithfully approximate full softmax formulation fix over-simplifying assumptions. Furthermore believe observed lift performance negative sampling work full softmax can be explained prism Partially Mutual Exclusive Softmax.Our hypothesis is further confirmed experiments language modeling matrix factorization where we show big lift performance previous work negative sampling full softmax. validate intuitions advantages sampling procedure artificial dataset where the support sets are known where we show sampling scheme correctly approximates support which is not case softmax variants.Overall main contributions paper are the following:• propose Partially Mutual Exclusive PME Softmax modified version softmax loss is a better fit problems positive unlabeled data.• derive new negative sampling scheme based cooperatively-trained models negatives which we denote Cooperative Importance Sampling CIS • show empirically validity proposed approach plugging new loss Word2Vec model evaluating enhanced Word2Vec model classical sampling schemes Word2Vec language modeling matrix factorization tasks across six real-world datasets.We discuss related work Word2Vec negative sampling schemes softmax GANs Section2 paper. Section3 formally introduce PME-Softmax loss associated CIS negative sampling scheme describe training algorithm. highlight performance method Section4 conclude ideas directions future work Section5. paper have proposed Partially Mutual Exclusive Softmax relaxed version full softmax is more suited cases explicit negatives e.g cases positive unlabeled data. order model new softmax proposed cooperative negative sampling algorithm. Based recent progress made GANs discrete data settings cooperative training approach can be easily applied models use standard sampled softmax training where the generator discriminator can be of the family models. future work will investigate effectiveness training procedure complex models also try make mutually exclusive set model contextual dependent objects j within pair. example where,given pair context/target where one might want use closest neighbors target embedding space negatives. could enableus obtain negative distribution fits context target.",1281,846,435,0.014,1.514,2025/11/05 17:19:02,0.01,1.569,0.5732087227414329,428.662
"Over the past few years, various tasks involving videos such as classification, description, summarization and question answering have received a lot of attention. Current models for these tasks compute an encoding of the video by treating it as a sequence of images and going over every image in the sequence, which becomes computationally expensive for longer videos. In this paper, we focus on the task of video classification and aim to reduce the computational cost by using the idea of distillation. Specifically, we propose a Teacher-Student network wherein the teacher looks at all the frames in the video but the student looks at only a small fraction of the frames in the video. The idea is to then train the student to minimize  (i)  the difference between the final representation computed by the student and the teacher and/or (ii) the difference between the distributions predicted by the teacher and the student. This smaller student network which involves fewer computations but still learns to mimic the teacher can then be employed at inference time for video classification. We experiment with the YouTube-8M dataset and show  that the proposed student network can reduce the inference time by upto 30% with a negligent drop in the performance. Today video content has become extremely prevalent on the internet influencing all aspects of our life such as education, entertainment, communication etc. This has led to an increasing interest in automatic video processing with the aim of identifying activities BID16 BID24 , generating textual descriptions BID5 , generating summaries BID25 BID13 , answering questions BID8 and so on. On one hand, with the availability of large scale datasets BID18 BID19 BID9 BID0 BID23 for various video processing tasks, it has now become possible to train increasingly complex models which have high memory and computational needs but on the other hand there is a demand for running these models on low power devices such as mobile phones and tablets with stringent constraints on latency and computational cost. It is important to balance the two and design models which can learn from large amounts of data but still be computationally cheap at inference time.With the above motivation, we focus on the task of video classification BID0 and aim to reduce the computational cost at inference time. Current state of the art models for video classification (Yue-Hei BID24 BID10 BID17 treat the video as a sequence of images (or frames) and compute a representation of the video by using a Recurrent Neural Network (RNN). The input to the RNN at every time step is an encoding of the corresponding image (frame) at that time step as obtained from a Convolutional Neural Network. Computing such a representation for longer videos can be computationally very expensive as it requires running the RNN for many time steps. Further, for every time step the corresponding frame from the video needs to pass through a convolutional neural network to get its representation. Such computations are still feasible on a GPU but become infeasible on low end devices which have power, memory and computational constraints.Typically, one can afford more computational resources at training time but a less expensive model is desired at test time. We propose to achieve this by using the idea of distillation wherein we train a computationally expensive teacher network which computes a representation for the video by processing all frames in the video. We then train a relatively inexpensive student network whose objective is to process only a few frames of the video and produce a representation which is very similar to the representation computed by the teacher. This is achieved by minimizing (i) the squared error loss between the representations of the student network and the teacher network and/or (ii) by minimizing the difference between the output distributions (class probabilities) predicted by the two networks. We refer to this as the matching loss. FIG2 illustrates this idea where the teacher sees every frame of the video but the student sees fewer frames, i.e., every j-th frame of the video. At inference time, we then use the student network for classification thereby reducing the time required for processing the video.We experiment with two different methods of training the Teacher-Student network. In the first method (which we call Serial Training), the teacher is trained independently and then the student is trained to match the teacher with or without an appropriate regularizer to account for the classification loss. In the second method (which we call Parallel Training), the teacher and student are trained jointly using the classification loss as well as the matching loss. We experiment with the YouTube-8M dataset and show that the smaller student network reduces the inference time by upto 30% while still achieving a classification performance which is very close to that of the expensive teacher network. The results of our experiments are summarized mainly in Tables 1 (performance) and 4 (computation time). We also report some additional results in Table 2 equally spaced k frames performs better than all the other baselines. The performance gap between Uniform-k and the other baselines is even more significant when the value of k is small. The main purpose of this experiment was to decide the right way of selecting frames for the student network.Based on these results, we ensured that for all our experiments, we fed equally spaced k frames to the student. Also, these experiments suggest that Uniform-k is a strong baseline to compare against.2. Comparing Teacher-Student Network with Uniform-k Baseline: As mentioned above, the Uniform-k is a simple but effective way of reducing the number of frames to be processed. We observe that all the teacher-student models outperform this strong baseline. Further, in a separate experiment as reported in Table 3 we observe that when we reduce the number of training examples seen by the teacher and the student, then the performance of the Uniform-k baseline drops and is much lower than that of the corresponding teacher student network. This suggests that the teacher student network can be even more useful when the amount of training data is limited.3. Serial Versus Parallel Training of Teacher-Student: While the best results in Table 1 are obtained using Serial training, if we compare the corresponding rows of Serial and Parallel training we observe that there is not much difference between the two. We found this to be surprising and investigated this further. In particular, we compared the performance of the teacher after different epochs in the Parallel training setup with the performance of the a static teacher trained independently (Serial). We plotted this performance in FIG3 and observed that after 3-4 epochs of training, the Parallel teacher is able to perform at par with Serial teacher (the constant blue line). As a result, the Parallel student now learns from this trained teacher for a few more epochs and is almost able to match the performance of the Serial student. This trend is same across the different combinations of loss functions that we used. We proposed a method to reduce the computation time for video classification using the idea of distillation. Specifically, we first train a teacher network which computes a representation of the video using all the frames in the video. We then train a student network which only processes k frames of the video. We use different combinations of loss functions which ensures that (i) the final representation produced by the student is the same as that produced by the teacher and (ii) the output probability distributions produced by the student are similar to those produced by the teacher. We compare the proposed models with a strong baseline and skyline and show that the proposed model outperforms the baseline and gives a significant reduction in terms of computational time and cost when compared to the skyline. In particular, We evaluate our model on the YouTube-8M dataset and show that the computationally less expensive student network can reduce the computation time by upto 30% while giving similar performance as the teacher network.As future work, we would like to evaluate our model on other video processing tasks such as summarization, question answering and captioning. We would also like to experiment with more complex and different teacher networks other than the hierarchical RNN considered in this work. We would also like to independently train an agent which learns to select the most favorable k frames of the video as opposed to simply using equally spaced k frames.",past years various tasks involving videos classification description summarization question answering have received lot attention. Current models tasks compute encoding video treating sequence images going every image sequence which becomes computationally expensive longer videos. paper focus task video classification aim reduce computational cost using idea distillation. Specifically propose Teacher-Student network wherein teacher looks frames video student looks small fraction frames video. idea is to then train student minimize difference final representation computed student teacher/ii difference distributions predicted teacher student. smaller student network which involves fewer computations still learns mimic teacher can then be employed inference time video classification. experiment YouTube-8M dataset show proposed student network can reduce inference time upto30% negligent drop performance. Today video content has become extremely prevalent internet influencing aspects life education entertainment communication etc. has led increasing interest automatic video processing aim identifying activities BID16 BID24 generating textual descriptions BID5 generating summaries BID25 BID13 answering questions BID8 on. one hand availability large scale datasets BID18 BID19 BID9 BID0 BID23 various video processing tasks has now become possible train increasingly complex models which have high memory computational needs hand is a demand running models low power devices mobile phones tablets stringent constraints latency computational cost. is important balance two design models which can learn large amounts data still computationally cheap inference time.With motivation focus task video classification BID0 aim reduce computational cost inference time. Current state art models video classification Yue-Hei BID24 BID10 BID17 treat video sequence images frames compute representation video using Recurrent Neural Network RNN input RNN every time step is an encoding corresponding image frame time step obtained Convolutional Neural Network. Computing representation longer videos can be computationally expensive requires running RNN many time steps. every time step corresponding frame video needs pass convolutional neural network get representation. computations are still feasible GPU become infeasible low end devices which have power memory computational constraints.Typically one can afford computational resources training time less expensive model is desired test time. propose achieve using idea distillation wherein train computationally expensive teacher network which computes representation video processing frames video. train relatively inexpensive student network whose objective is to process frames video produce representation which is very similar representation computed teacher. is achieved minimizing squared error loss representations student network teacher network/ii minimizing difference output distributions class probabilities predicted two networks. refer matching loss. FIG2 illustrates idea where the teacher sees every frame video student sees fewer frames.e every j-th frame video. inference time use student network classification thereby reducing time required processing video.We experiment two different methods training Teacher-Student network. first method which we call Serial Training teacher is trained independently student is trained match teacher without appropriate regularizer account classification loss. second method which we call Parallel Training teacher student are trained jointly using classification loss well matching loss. experiment YouTube-8M dataset show smaller student network reduces inference time upto30% still achieving classification performance which is very close expensive teacher network. results experiments are summarized mainly Tables1 performance 4 computation time also report additional results Table 2 equally spaced k frames performs better baselines. performance gap Uniform-k baselines is even significant when the value k is small. main purpose experiment was to decide right way selecting frames student network.Based results ensured experiments fed equally spacedk frames student. Also experiments suggest Uniform-k is a strong baseline compare against.2 Comparing Teacher-Student Network Uniform-k Baseline:mentioned Uniform-k is a simple effective way reducing number frames processed. observe teacher-student models outperform strong baseline. separate experiment reported Table3 observe when we reduce number training examples seen teacher student performance Uniform-k baseline drops is much lower corresponding teacher student network. suggests teacher student network can be even useful when the amount training data is limited.3 limited.3 Serial Versus Parallel Training Teacher-Student best results Table1 are obtained using Serial training if we compare corresponding rows Serial Parallel training observe is not much difference two. found surprising investigated further. particular compared performance teacher different epochs Parallel training setup performance static teacher trained independently Serial plotted performance FIG3 observed 3-4 epochs training Parallel teacher is able perform par Serial teacher constant blue line result Parallel student learns trained teacher epochs is almost able match performance Serial student. trend is same across different combinations loss functions used. proposed method reduce computation time video classification using idea distillation. Specifically first train teacher network which computes representation video using frames video. train student network which only processes k frames video. use different combinations loss functions which ensures final representation produced student is the sameas produced teacher ii output probability distributions produced student are similar produced teacher. compare proposed models strong baseline skyline show proposed model outperforms baseline gives significant reduction terms computational time cost when compared skyline. particular evaluate model YouTube-8M dataset show computationally less expensive student network can reduce computation time upto30% giving similar performance teacher network.As future work would like evaluate model video processing tasks summarization question answering captioning. would also like experiment complex different teacher networks hierarchical RNN considered work. would also like independently train agent which learns select favorable k frames video opposed simply using equally spaced k frames.,1621,997,624,0.021,1.626,2025/11/05 17:19:02,0.01,1.635,0.9221183800623048,534.895
"Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as powerful frameworks for deep generative model learning, have largely been considered as two distinct paradigms and received extensive independent studies respectively. This paper aims to establish formal connections between GANs and VAEs through a new formulation of them. We interpret sample generation in GANs as performing posterior inference, and show that GANs and VAEs involve minimizing KL divergences of respective posterior and inference distributions with opposite directions, extending the two learning phases of classic wake-sleep algorithm, respectively. The unified view provides a powerful tool to analyze a diverse set of existing model variants, and enables to transfer techniques across research lines in a principled way. For example, we apply the importance weighting method in VAE literatures for improved GAN learning, and enhance VAEs with an adversarial mechanism that leverages generated samples. Experiments show generality and effectiveness of the transfered techniques. Deep generative models define distributions over a set of variables organized in multiple layers. Early forms of such models dated back to works on hierarchical Bayesian models BID30 and neural network models such as Helmholtz machines , originally studied in the context of unsupervised learning, latent space modeling, etc. Such models are usually trained via an EM style framework, using either a variational inference (Jordan et al., 1999) or a data augmentation BID35 algorithm. Of particular relevance to this paper is the classic wake-sleep algorithm dates by for training Helmholtz machines, as it explored an idea of minimizing a pair of KL divergences in opposite directions of the posterior and its approximation.In recent years there has been a resurgence of interests in deep generative modeling. The emerging approaches, including Variational Autoencoders (VAEs) BID18 , Generative Adversarial Networks (GANs) BID12 , Generative Moment Matching Networks (GMMNs) BID24 BID10 , auto-regressive neural networks BID21 BID37 , and so forth, have led to impressive results in a myriad of applications, such as image and text generation (Radford et al., 2015; Hu et al., 2017; BID37 , disentangled representation learning BID7 BID20 , and semi-supervised learning (Salimans et al., 2016; BID19 . The deep generative model literature has largely viewed these approaches as distinct model training paradigms. For instance, GANs aim to achieve an equilibrium between a generator and a discriminator; while VAEs are devoted to maximizing a variational lower bound of the data log-likelihood. A rich array of theoretical analyses and model extensions have been developed independently for GANs BID0 BID1 Salimans et al., 2016; BID31 and VAEs BID4 BID8 Hu et al., 2017) , respectively. A few works attempt to combine the two objectives in a single model for improved inference and sample generation BID26 BID22 BID25 BID34 . Despite the significant progress specific to each method, it remains unclear how these apparently divergent approaches connect to each other in a principled way.In this paper, we present a new formulation of GANs and VAEs that connects them under a unified view, and links them back to the classic wake-sleep algorithm. We show that GANs and VAEs involve minimizing opposite KL divergences of respective posterior and inference distributions, and extending the sleep and wake phases, respectively, for generative model learning. More specifically, we develop a reformulation of GANs that interprets generation of samples as performing posterior inference, leading to an objective that resembles variational inference as in VAEs. As a counterpart, VAEs in our interpretation contain a degenerated adversarial mechanism that blocks out generated samples and only allows real examples for model training.The proposed interpretation provides a useful tool to analyze the broad class of recent GAN-and VAEbased algorithms, enabling perhaps a more principled and unified view of the landscape of generative modeling. For instance, one can easily extend our formulation to subsume InfoGAN BID7 that additionally infers hidden representations of examples, VAE/GAN joint models BID22 BID5 ) that offer improved generation and reduced mode missing, and adversarial domain adaptation (ADA) BID11 Purushotham et al., 2017) that is traditionally framed in the discriminative setting.The close parallelisms between GANs and VAEs further ease transferring techniques that were originally developed for improving each individual class of models, to in turn benefit the other class. We provide two examples in such spirit: 1) Drawn inspiration from importance weighted VAE (IWAE) BID4 , we straightforwardly derive importance weighted GAN (IWGAN) that maximizes a tighter lower bound on the marginal likelihood compared to the vanilla GAN. 2) Motivated by the GAN adversarial game we activate the originally degenerated discriminator in VAEs, resulting in a full-fledged model that adaptively leverages both real and fake examples for learning. Empirical results show that the techniques imported from the other class are generally applicable to the base model and its variants, yielding consistently better performance. Our new interpretations of GANs and VAEs have revealed strong connections between them, and linked the emerging new approaches to the classic wake-sleep algorithm. The generality of the proposed formulation offers a unified statistical insight of the broad landscape of deep generative modeling, and encourages mutual exchange of techniques across research lines. One of the key ideas in our formulation is to interpret sample generation in GANs as performing posterior inference. This section provides a more general discussion of this point.Traditional modeling approaches usually distinguish between latent and visible variables clearly and treat them in very different ways. One of the key thoughts in our formulation is that it is not necessary to make clear boundary between the two types of variables (and between generation and inference), but instead, treating them as a symmetric pair helps with modeling and understanding. For instance, we treat the generation space x in GANs as latent, which immediately reveals the connection between GANs and adversarial domain adaptation, and provides a variational inference interpretation of the generation. A second example is the classic wake-sleep algorithm, where the wake phase reconstructs visibles conditioned on latents, while the sleep phase reconstructs latents conditioned on visibles (i.e., generated samples). Hence, visible and latent variables are treated in a completely symmetric manner.• Empirical data distributions are usually implicit, i.e., easy to sample from but intractable for evaluating likelihood. In contrast, priors are usually defined as explicit distributions, amiable for likelihood evaluation.• The complexity of the two distributions are different. Visible space is usually complex while latent space tends (or is designed) to be simpler.However, the adversarial approach in GANs and other techniques such as density ratio estimation (Mohamed & Lakshminarayanan, 2016) and approximate Bayesian computation BID2 have provided useful tools to bridge the gap in the first point. For instance , implicit generative models such as GANs require only simulation of the generative process without explicit likelihood evaluation, hence the prior distributions over latent variables are used in the same way as the empirical data distributions, namely, generating samples from the distributions. For explicit likelihood-based models, adversarial autoencoder (AAE) leverages the adversarial approach to allow implicit prior distributions over latent space. Besides, a few most recent work BID26 BID36 BID34 Rosca et al., 2017) extends VAEs by using implicit variational distributions as the inference model. Indeed, the reparameterization trick in VAEs already resembles construction of implicit variational distributions (as also seen in the derivations of IWGANs in Eq.37). In these algorithms, adversarial approach is used to replace intractable minimization of the KL divergence between implicit variational distributions and priors.The second difference in terms of space complexity guides us to choose appropriate tools (e.g., adversarial approach v.s. reconstruction optimization, etc) to minimize the distance between distributions to learn and their targets. However, the tools chosen do not affect the underlying modeling mechanism.For instance, VAEs and adversarial autoencoder both regularize the model by minimizing the distance between the variational posterior and certain prior, though VAEs choose KL divergence loss while AAE selects adversarial loss.We can further extend the symmetric treatment of visible/latent x/z pair to data/label x/t pair, leading to a unified view of the generative and discriminative paradigms for unsupervised and semi-supervised learning. Specifically, conditional generative models create (data, label) pairs by generating data x given label t. These pairs can be used for classifier training (Hu et al., 2017; BID32 . In parallel, discriminative approaches such as knowledge distillation BID14 BID17 create (data, label) pairs by generating label t conditioned on data x. With the symmetric view of x and t spaces , and neural network based black-box mappings across spaces, we can see the two approaches are essentially the same. A ADVERSARIAL DOMAIN ADAPTATION (ADA)ADA aims to transfer prediction knowledge learned from a source domain with labeled data to a target domain without labels, by learning domain-invariant features. Let D φ (x) = q φ (y|x) be the domain discriminator . The conventional formulation of ADA is as following : DISPLAYFORM0 Further add the supervision objective of predicting label t(z) of data z in the source domain, with a classifier f ω (t|x) parameterized with π: DISPLAYFORM1 We then obtain the conventional formulation of adversarial domain adaptation used or similar in BID11 Purushotham et al., 2017) .B PROOF OF LEMMA 1Proof. DISPLAYFORM2 where DISPLAYFORM3 Note that p θ (x|y = 0) = p g θ (x), and p θ (x|y = 1) = p data (x). DISPLAYFORM4 . Eq.(21) can be simplified as: DISPLAYFORM5 On the other hand , DISPLAYFORM6 Note that DISPLAYFORM7 Taking derivatives of Eq. FORMULA1 w.r.t θ at θ 0 we get DISPLAYFORM8 Taking derivatives of the both sides of Eq. FORMULA1 at w.r.t θ at θ 0 and plugging the last equation of Eq. FORMULA1 , we obtain the desired results. We show that, in Lemma.1 (Eq.6), the JSD term is upper bounded by the KL term, i.e., DISPLAYFORM9 DISPLAYFORM10 Proof. From Eq. FORMULA1 , we have DISPLAYFORM11 From Eq. FORMULA1 and Eq. FORMULA1 , we have DISPLAYFORM12 Eq. FORMULA1 and Eq. FORMULA1",Deep generative models have achieved impressive success recent years. Generative Adversarial Networks GANs Variational Autoencoders VAEs powerful frameworks deep generative model learning have largely considered two distinct paradigms received extensive independent studies respectively. paper aims establish formal connections GANs VAEs new formulation them. interpret sample generation GANs performing posterior inference show GANs VAEs involve minimizingKL divergences respective posterior inference distributions opposite directions extending two learning phases classic wake-sleep algorithm respectively. unified view provides powerful tool analyze diverse set existing model variants enables transfer techniques across research lines principled way. example apply importance weighting method VAE literatures improved GAN learning enhance VAEs adversarial mechanism leverages generated samples. Experiments show generality effectiveness transfered techniques. Deep generative models define distributions set variables organized multiple layers. Early forms models dated back works hierarchical Bayesian models BID30 neural network models Helmholtz machines originally studied context unsupervised learning latent space modeling etc. models are usually trained via EM style framework using either variational inference Jordanetal. 1999 data augmentation BID35 algorithm. particular relevance paper is the classic wake-sleep algorithm dates training Helmholtz machines explored idea minimizing pair KL divergences opposite directions posterior approximation.In recent years has been a resurgence interests deep generative modeling. emerging approaches including Variational Autoencoders VAEs BID18 Generative Adversarial Networks GANs BID12 Generative Moment Matching Networks GMMNs BID24 BID10 auto-regressive neural networks BID21 BID37 forth have led impressive results myriad applications image text generation Radfordetal. 2015;Huetal. 2017;BID37 disentangled representation learning BID7 BID20 semi-supervised learning Salimansetal. 2016;BID19. deep generative model literature has largely viewed approaches distinct model training paradigms. instance GANs aim achieve equilibrium generator discriminator;VAEs are devoted maximizing variational lower bound data log-likelihood rich array theoretical analyses model extensions have been developed independently GANs BID0 BID1 Salimans etal. 2016;BID31 VAEs BID4 BID8Hu etal. 2017 respectively. works attempt combine two objectives single model improved inference sample generation BID26 BID22 BID25 BID34. Despite significant progress specific method remains unclear how these apparently divergent approaches connect principled way.In paper present new formulation GANs VAEs connects unified view links back classic wake-sleep algorithm. show GANs VAEs involve minimizing opposite KL divergences respective posterior inference distributions extending sleep wake phases respectively generative model learning. specifically develop reformulation GANs interprets generation samples performing posterior inference leading objective resembles variational inference VAEs. counterpart VAEs interpretation contain degenerated adversarial mechanism blocks generated samples allows real examples model training.The proposed interpretation provides useful tool analyze broad class recent GAN-and VAEbased algorithms enabling perhaps principled unified view landscape generative modeling. instance one can easily extend formulation subsume InfoGAN BID7 additionally infers hidden representations examples VAE/GAN joint models BID22 BID5 offer improved generation reduced mode missing adversarial domain adaptation ADA BID11 Purushothametal. 2017 is traditionally framed discriminative setting.The close parallelisms GANs VAEs ease transferring techniques were originally developed improving individual class models turn benefit class. provide two examples spirit:1 Drawn inspiration importance weighted VAE IWAE BID4 straightforwardly derive importance weighted GAN IWGAN maximizes tighter lower bound marginal likelihood compared vanilla GAN. 2 Motivated GAN adversarial game activate originally degenerated discriminator VAEs resulting full-fledged model adaptively leverages real fake examples learning. Empirical results show techniques imported class are generally applicable base model variants yielding consistently better performance. new interpretations GANs VAEs have revealed strong connections linked emerging new approaches classic wake-sleep algorithm. generality proposed formulation offers unified statistical insight broad landscape deep generative modeling encourages mutual exchange techniques across research lines. One key ideas formulation is to interpret sample generation GANs performing posterior inference. section provides general discussion point.Traditional modeling approaches usually distinguish latent visible variables clearly treat different ways. One key thoughts formulation is thatitis necessary make clear boundary two types variables generation inference instead treating symmetric pair helps modeling understanding. instance treat generation spacex GANs latent which immediately reveals connection GANs adversarial domain adaptation provides variational inference interpretation generation. second example is the classic wake-sleep algorithm where the wake phase reconstructs visibles conditioned latents sleep phase reconstructs latents conditioned visibles.e generated samples Hence visible latent variables are treated completely symmetric manner.• Empirical data distributions are usually implicit.e easy sample intractable evaluating likelihood. contrast priors are usually defined explicit distributions amiable likelihood evaluation.• complexity two distributions are different. Visible space is usually complex latent space tends is designed simpler.However adversarial approach GANs techniques density ratio estimation Mohamed Lakshminarayanan 2016 approximate Bayesian computation BID2 have provided useful tools bridge gap first point. instance implicit generative models GANs require simulation generative process without explicit likelihood evaluation hence prior distributions latent variables are used way empirical data distributions namely generating samples distributions. explicit likelihood-based models adversarial autoencoder AAE leverages adversarial approach allow implicit prior distributions latent space. Besides recent work BID26 BID36 BID34 Roscaetal. 2017 extends VAEs using implicit variational distributions inference model. Indeed reparameterization trick VAEs already resembles construction implicit variational distributions also seen derivations IWGANs Eq.37 algorithms adversarial approach is used replace intractable minimization KL divergence implicit variational distributions priors.The second difference terms space complexity guidesus choose appropriate tools e.g adversarial approachv.s reconstruction optimization etc minimize distance distributions learn targets. However tools chosen do not affect underlying modeling mechanism.For instance VAEs adversarial autoencoder regularize model minimizing distance variational posterior certain prior though VAEs chooseKL divergence loss AAE selects adversarial loss.We can further extend symmetric treatment visible/latentx/z pair data/labelx/pair leading unified view generative discriminative paradigms unsupervised semi-supervised learning. Specifically conditional generative models create data label pairs generating data x given label t. pairs can be used classifier training Huetal. 2017;BID32. parallel discriminative approaches knowledge distillation BID14 BID17 create data label pairs generating label conditioned datax. symmetric view x spaces neural network based black-box mappings across spaces can see two approaches are essentially same. ADVERSARIAL DOMAIN ADAPTATION ADA ADA aims transfer prediction knowledge learned source domain labeled data target domain without labels learning domain-invariant features. Let φ x qφ y|x domain discriminator. conventional formulation ADA is as following:DISPLAYFORM0 add supervision objective predicting label z dataz source domain classifierfω t|x parameterized π:DISPLAYFORM1 obtain conventional formulation adversarial domain adaptation used similar BID11 Purushothametal. 2017.B PROOF LEMMA 1Proof. DISPLAYFORM2 where DISPLAYFORM3 Note pθ x|y 0 pgθ x pθ x|y 1 p data x DISPLAYFORM4. Eq. 21 can be simplified as:DISPLAYFORM5 hand DISPLAYFORM6 Note DISPLAYFORM7 Taking derivatives Eq. FORMULA1w.r.t θ θ0 get DISPLAYFORM8 Taking derivatives sides Eq. FORMULA1 w.r.tθ θ0 plugging last equation Eq. FORMULA1 obtain desired results. show Lemma.1 Eq.6 JSD term is upper bounded KL term.e DISPLAYFORM9 DISPLAYFORM10 Proof. Eq. FORMULA1 have DISPLAYFORM11 Eq. FORMULA1 Eq. FORMULA1 have DISPLAYFORM12Eq. FORMULA1 Eq. FORMULA1,2201,1542,659,0.027,1.427,2025/11/05 17:19:02,0.01,1.405,0.3021806853582554,710.745
"Deep neural networks have demonstrated promising prediction and classification performance on many healthcare applications. However, the interpretability of those models are often lacking. On the other hand, classical interpretable models such as rule lists or decision trees do not lead to the same level of accuracy as deep neural networks and can often be too complex to interpret (due to the potentially large depth of rule lists). In this work, we present PEARL,  Prototype lEArning via Rule Lists, which iteratively uses rule lists to guide a neural network to learn representative data prototypes. The resulting prototype neural network provides  accurate prediction, and the prediction can be easily explained by  prototype and its guiding rule lists. Thanks to the prediction power of neural networks, the rule lists from				 prototypes are more concise and hence provide better interpretability. On two real-world electronic healthcare records (EHR) datasets, PEARL consistently outperforms all baselines across both datasets, especially achieving performance improvement over conventional rule learning by up to 28% and over prototype learning by up to 3%. Experimental results also show the resulting interpretation of PEARL is  simpler than the standard rule learning. The rapid growth of sizes and complexities of electronic health records (EHR) data has motivated the use of deep learning models, which demonstrated state-of-the-art performance in many tasks, including diagnostics and disease detection BID7 BID38 , medication prediction BID16 , risk prediction BID9 Xiao et al., 2018b) , and patient subtyping BID1 BID4 . Although deep learning models can produce accurate predictions and classifications, they are often treated as black-box models that lack interpretability and transparency of their inner working BID20 . This is a critical problem as it can limit the adoption of deep learning in medical decision making.Recently, there have been great efforts of trying to explain black-box deep models, including via attention mechanism BID7 BID40 , visualization BID31 , and explanation by examples or prototypes BID17 . To bring deep models into real clinical practice, clinicians often need to understand why a certain output is produced and how the model generates this output for a given input BID24 . Rule learning and prototype learning are two promising directions to achieve clinical model interpretability.Rule learning generates a set of rules from training data, in which its prediction is done at leaf levels via simple models such as majority vote or regression. For example, the results of rule learning are rule lists composed of multiple if-then statements BID0 . Those rules can be interpretable to domain experts as they are expressed in simple logical forms BID30 BID3 . However, because of such a simple prediction model, the accuracy of rule-based models is often lower than deep neural networks. Moreover, the interpretability can be undermined as the depth of rules becomes very large and thus incomprehensible for human with tens or hundreds of levels of the rules.Prototype learning is another interpretable model inspired by case-based reasoning BID14 , where observations are classified based on their proximity to a prototype point in the dataset. Many machine learning models have incorporated prototype concepts BID28 BID2 BID12 , and learn to compute prototypes (as actual data points or synthetic points) that can represent a set of similar points. However prototypes alone may not lead to interpretable models as we still need an intuitive way to represent and explain what a prototype is, especially given recent deep prototype works BID17 .Both approaches were explored in healthcare applications. For example, rule learning was employed to identify how likely patients were to be readmitted to a hospital after they had been released, each probability associated with a set of rules as criteria BID35 . While prototype could be selected from actual patients and genes for clinicians to make sense of large patient cohort or gene data BID2 . However , there are still open challenges: How to construct simple rules with more accurate prediction and classification performance? How to produce accurate and intuitive definitions of prototypes?In this work, we propose Prototype lEArning via Rule List (PEARL), which combines rule learning and prototype learning on deep neural networks to harness the benefits of both approaches and alleviate their shortcomings for an accurate and interpretable prediction model. In particular , we iteratively learn rule lists, via a data reweighing procedure using prototypes, and then update prototypes via neural networks with learned rules. PEARL not only generates simple and interpretable rule lists and prototypes, but also provides neural network models which can infer the similarity of a query datum to all the prototypes. To summarize, we make the following contributions in this paper.1. We propose an integrative method to combine rule list and prototype learning, enabling PEARL to harness the power of these methods.2. PEARL automatically learns prototypes corresponding to rules in a rule list, which are more concise than conventional rule list learning methods and more explainable than prototype learning methods by providing logic reasoning.3. On real-world electronic health record datasets, PEARL demonstrates both accurate prediction performance and simple interpretation. In this paper, we proposed PEARL, an integrative prototype learning neural network that combines rule learning and prototype learning on deep neural networks to harness the benefits of these methods. We empirically demonstrated that PEARL is more accurate , thanks to an iterative data reweighing algorithm, and more interpretable than rule learning, since it explains diagnostic decisions using much fewer clinical variables. PEARL is an initial attempt to combine traditional rule learning with deep neural networks. In future research, we will try to extend PEARL to other interpretable models.","Deep neural networks have demonstrated promising prediction classification performance many healthcare applications. However interpretability models are often lacking. hand classical interpretable models rule lists decision trees do not lead level accuracy deep neural networks can often complex interpret due potentially large depth rule lists work present PEARL Prototype lEArning via Rule Lists which iteratively uses rule lists guide neural network learn representative data prototypes. resulting prototype neural network provides accurate prediction which its prediction can be easily explained prototype guiding rule lists. Thanks prediction power neural networks rule lists prototypes are more concise hence provide better interpretability. two real-world electronic healthcare records EHR datasets PEARL consistently outperforms baselines across datasets especially achieving performance improvement conventional rule learning 28% prototype learning 3%. Experimental results also show resulting interpretation PEARL is simpler standard rule learning. rapid growth sizes complexities electronic health records EHR data has motivated use deep learning models which demonstrated state-of-the-art performance many tasks including diagnostics disease detection BID7 BID38 medication prediction BID16 risk prediction BID9 Xiao etal. 2018b patient subtyping BID1 BID4. Although deep learning models can produce accurate predictions classifications are often treated black-box models lack interpretability transparency inner working BID20. is a critical problem can limit adoption deep learning medical decision making.Recently have been great efforts trying explain black-box deep models including via attention mechanism BID7 BID40 visualization BID31 explanation examples prototypes BID17. bring deep models real clinical practice clinicians often need understand why a certain output is produced how the model generates output given input BID24. Rule learning prototype learning are two promising directions achieve clinical model interpretability.Rule learning generates set rules training data which its prediction is done leaf levels via simple models majority vote regression. example results rule learning are rule lists composed multiple if-then statements BID0. rules can be interpretable domain experts are expressed simple logical forms BID30 BID3. However simple prediction model accuracy rule-based models is often lower deep neural networks. Moreover interpretability can be undermined depth rules becomes large thus incomprehensible human tens hundreds levels rules.Prototype learning is another interpretable model inspired case-based reasoning BID14 where observations are classified based proximity prototype point dataset. Many machine learning models have incorporated prototype concepts BID28 BID2 BID12 learn compute prototypes actual data points synthetic points can represent set similar points. However prototypes alone may lead interpretable models still need intuitive way represent explain what a prototype is,especially given recent deep prototype works BID17.Both approaches were explored healthcare applications. example rule learning was employed identify how likely patients were to be readmitted hospital had been released probability associated set rules criteria BID35. prototype could selected actual patients genes clinicians make sense large patient cohort gene data BID2. However are still open challenges:How to construct simple rules accurate prediction classification performance? How to produce accurate intuitive definitions prototypes? work propose Prototype lEArning via Rule List PEARL which combines rule learning prototype learning deep neural networks harness benefits approaches alleviate shortcomings accurate interpretable prediction model. particular which iteratively learn rule lists via data reweighing procedure using prototypes update prototypes via neural networks learned rules. PEARL generates simple interpretable rule lists prototypes also provides neural network models which can infer similarity query datum prototypes. summarize make following contributions paper.1 propose integrative method combine rule list prototype learning enabling PEARL harness power methods.2 PEARL automatically learns prototypes corresponding rules rule list which are more concise conventional rule list learning methods explainable prototype learning methods providing logic reasoning.3 real-world electronic health record datasets PEARL demonstrates accurate prediction performance simple interpretation. paper proposed PEARL integrative prototype learning neural network combines rule learning prototype learning deep neural networks harness benefits methods. empirically demonstrated PEARL is more accurate thanks iterative data reweighing algorithm interpretable rule learning since explains diagnostic decisions using much fewer clinical variables. PEARL is an initial attempt combine traditional rule learning deep neural networks. future research will try extend PEARL interpretable models.",1116,797,319,0.01,1.4,2025/11/05 17:19:02,0.0,1.468,0.2180685358255447,335.463
"Generative Adversarial Networks (GANs) are powerful tools for realistic image generation. However, a major drawback of GANs is that they are especially hard to train, often requiring large amounts of data and long training time. In this paper we propose the Deli-Fisher GAN, a GAN that generates photo-realistic images by enforcing structure on the latent generative space using similar approaches in \cite{deligan}. The structure of the latent space we consider in this paper is modeled as a mixture of Gaussians, whose parameters are learned in the training process. Furthermore, to improve stability and efficiency, we use the Fisher Integral Probability Metric as the divergence measure in our GAN model, instead of the Jensen-Shannon divergence. We show by experiments that the Deli-Fisher GAN performs better than DCGAN, WGAN, and the Fisher GAN as measured by inception score. Generative Adversarial Networks (GAN) are powerful unsupervised learning models that have recently achieved great success in learning high-dimensional distributions BID1 ). In the field of image and vision sciences in particular, GAN models are capable of generating ""fake"" images that look authentic to human observers.The basic framework of a GAN model consists of two parts: a generator G = G θ (z) that generates images by translating random input noise z into a particular distribution of interest, and a discriminator D = D p (x) which calculates the probability that an image x is an authentic image as opposed to a generated ""fake"" image from the generator. While the generator G and discriminator D can be modeled as any smooth functions, these two components are usually modeled as two neural networks in practical applications. During the training process, we optimize the generator and the discriminator alternately against each other. Within each step, we first keep D fixed and optimize G so as to improve its capability of generating images that look real to D. Then, we keep G fixed and train D to improve the discriminator's ability to distinguish real and G-generated images. The two parts G and D play a two-player game against each other. At the end of the training, we would be able to have a generator that is capable of generating photo-realistic images.In mathematical form, a GAN model can be described as an optimization problem, as follows: DISPLAYFORM0 where V (D, G) is the objective function measuring the divergence between the two distributions: the distribution of the real existing data D(x), and the that of the generated data D(G(z)), where x follows the distribution of real images and z follows the distribution of input noise. Depending on the choice of function V (D, G), different GAN models have been proposed over time (see BID1 , , BID4 ) to increase stability and achieve faster convergence rates.",Generative Adversarial Networks GANs are powerful tools realistic image generation. However major drawback GANs is that they are especially hard train often requiring large amounts data long training time. paper propose Deli-Fisher GAN GAN generates photo-realistic images enforcing structure latent generative space using similar approaches \cite deligan structure latent space consider paper is modeled mixture Gaussians whose parameters are learned training process. Furthermore improve stability efficiency use Fisher Integral Probability Metric divergence measure GAN model instead Jensen-Shannon divergence. show experiments Deli-Fisher GAN performs better DCGAN WGAN Fisher GAN measured inception score. Generative Adversarial Networks GAN are powerful unsupervised learning models have recently achieved great success learning high-dimensional distributions BID1 field image vision sciences particular GAN models are capable generating fake images look authentic human observers.The basic framework GAN model consists two parts:generatorG Gθ z generates images translating random input noise z particular distribution interest discriminator p x which calculates probability imagex is an authentic image opposed generated fake image generator. generatorG discriminator can be modeled smooth functions two components are usually modeled two neural networks practical applications. training process optimize generator discriminator alternately other. Within step first keep fixed optimizeG improve capability generating images look real D. keep G fixed train improve discriminator's ability distinguish real G-generated images. two partsG play two-player game other. end training would able have a generator is capable generating photo-realistic images.In mathematical form GAN model can be described optimization problem follows:DISPLAYFORM0 whereV G is the objective function measuring divergence two distributions:distribution real existing data x generated data G z where x follows distribution real images z follows distribution input noise. Depending choice functionV G different GAN models have been proposed time see BID1 BID4 increase stability achieve faster convergence rates.,558,353,205,0.006,1.581,2025/11/05 17:19:02,0.0,1.529,0.7819314641744546,189.981
"Recent work on encoder-decoder models for sequence-to-sequence mapping has shown that integrating both temporal and spatial attentional mechanisms into neural networks increases the performance of the system substantially. We report on a new modular network architecture that applies an attentional mechanism not on temporal and spatial regions of the input, but on sensor selection for multi-sensor setups. This network called the sensor transformation attention network (STAN) is evaluated in scenarios which include the presence of natural noise or synthetic dynamic noise. We demonstrate how the attentional signal responds dynamically to changing noise levels and sensor-specific noise, leading to reduced word error rates (WERs) on both audio and visual tasks using TIDIGITS and GRID; and also on CHiME-3, a multi-microphone real-world noisy dataset. The improvement grows as more channels are corrupted as demonstrated on the CHiME-3 dataset. Moreover, the proposed STAN architecture naturally introduces a number of advantages including ease of removing sensors from existing architectures, attentional interpretability, and increased robustness to a variety of noise environments. Attentional mechanisms have shown improved performance as part of the encoder-decoder based sequence-to-sequence framework for applications such as image captioning BID22 , speech recognition BID1 BID3 , and machine translation BID0 BID21 . Dynamic and shifting attention, for example, on salient attributes within an image helps in image captioning as demonstrated by the state-of-art results on multiple benchmark datasets BID22 . Similarly, an attention-based recurrent sequence generator network can replace the Hidden Markov Model (HMM) typically used in a large vocabulary continuous speech recognition system, allowing an HMM-free RNN-based network to be trained for end-to-end speech recognition BID1 .While attentional mechanisms have mostly been applied to both spatial and temporal features, this work focuses on attention used in sensor selection. We introduce the STAN architecture that embeds an attentional mechanism for sensor selection and supports multi-sensor as well as multi-modal inputs. This attentional mechanism allows STANs to dynamically focus on sensors with higher signal-to-noise ratio (SNR) and its output is highly interpretable. Because of their inherently modular architecture, STANs remain operational even when sensors are removed after training. The same modularity makes STANs attractive for tasks that make use of multi-sensor integration. The STAN architecture can be seen as a generalization of existing less-modular network types that include attention in multi-sensor setups BID11 BID10 .This work consists of three main sections. First, we formally introduce the STAN architecture in section 2. In the first evaluation phase in section 3, we demonstrate the proper function of the attentional mechanism in synthetic noise environments with multiple audio sensors (TIDIGITS dataset) and multiple video sensors (GRID). The second evaluation phase in section 4 covers the multi-microphone real world dataset CHiME-3, where we show the proper functioning of the STAN attentional mechanism on natural noise and the robustness of STANs with respect to altered sensor configurations. The sensor transformation attention network (STAN) architecture has a number of interesting features for sensor selection which we explored in this work. By equipping each sensor with an attentional mechanism for distinguishing meaningful features, networks can learn how to select, transform, and interpret the output of their sensors. Firstly, and by design, we show that STANs exhibit remarkable robustness to both real-world and synthetic dynamic noise sources. By challenging these networks during training with dynamic and persistent noise sources, the networks learn to rapidly isolate sensors corrupted by noise sources. Secondly, we show that this form of training results in even better accuracy performance from STANs than simply concatenating the sensor inputs. This is best demonstrated on the heavily noise corrupted STR environment of the CHiME-3 real-data evaluation set, where STANs achieve 23% lower WER than concatenation models for the 50 most corrupted samples. Thirdly, we find that the output of the attention modules is highly informative, clearly indicating a sub-optimal sensor placement for a sensor pointing away from the speaker on the CHiME-3 dataset. Remarkably, this outcome is even obtained when sharing the weights of the attention modules across sensors, implying that these attention modules learned to successfully differentiate between sensors with higher and lower SNR data in presence of natural noise.Due to their modular architecture, STANs are also remarkably flexible with respect to the sensor configuration, even performing well with the removal of sensors after training. One can train STANs to solve a task with a multi-sensor setup and after training, remove the less informative sensors, with possibly savings of energy consumption and computational load on multi-sensor hardware systems with restricted computational power such as mobile robots. In the case of a defect, a sensor could be removed and STANs would remain operational with the remaining sensors.",Recent work encoder-decoder models sequence-to-sequence mapping has shown integrating temporal spatial attentional mechanisms neural networks increases performance system substantially. report new modular network architecture applies attentional mechanism temporal spatial regions input sensor selection multi-sensor setups. network called sensor transformation attention network STAN is evaluated scenarios which include presence natural noise synthetic dynamic noise. demonstrate how the attentional signal responds dynamically changing noise levels sensor-specific noise leading reduced word error rates WERs audio visual tasks using TIDIGITS GRID;also CHiME-3 multi-microphone real-world noisy dataset. improvement grows channels are corrupted demonstrated CHiME-3 dataset. Moreover proposed STAN architecture naturally introduces number advantages including ease removing sensors existing architectures attentional interpretability increased robustness variety noise environments. Attentional mechanisms have shown improved performance part encoder-decoder based sequence-to-sequence framework applications image captioning BID22 speech recognition BID1 BID3 machine translation BID0 BID21. Dynamic shifting attention example salient attributes within image helps image captioning demonstrated state-of-art results multiple benchmark datasets BID22. Similarly attention-based recurrent sequence generator network can replace Hidden Markov Model HMM typically used large vocabulary continuous speech recognition system allowing HMM-free RNN-based network trained end-to-end speech recognition BID1.While attentional mechanisms have mostly applied spatial temporal features work focuses attention used sensor selection. introduce STAN architecture embeds attentional mechanism sensor selection supports multi-sensor well multi-modal inputs. attentional mechanism allows STANs dynamically focus sensors higher signal-to-noise ratio SNR output is highly interpretable. inherently modular architecture where STANs remain operational even when sensors are removed training. modularity makes STANs attractive tasks make use multi-sensor integration. STAN architecture can be seen generalization existing less-modular network types include attention multi-sensor setups BID11 BID10.This work consists three main sections. First formally introduce STAN architecture section2. first evaluation phase section3 demonstrate proper function attentional mechanism synthetic noise environments multiple audio sensors TIDIGITS dataset multiple video sensors GRID second evaluation phase section 4 covers multi-microphone real world dataset CHiME-3 where we show proper functioning STAN attentional mechanism natural noise robustness STANs respect altered sensor configurations. sensor transformation attention network STAN architecture has a number interesting features sensor selection which we explored work. equipping sensor attentional mechanism distinguishing meaningful features networks can learn how to select transform interpret output sensors. Firstly design where we show STANs exhibit remarkable robustness real-world synthetic dynamic noise sources. challenging networks training dynamic persistent noise sources networks learn rapidly isolate sensors corrupted noise sources. Secondly where we show form training results even better accuracy performance STANs simply concatenating sensor inputs. is best demonstrated heavily noise corrupted STR environment CHiME-3 real-data evaluation set where STANs achieve23% lower WER concatenation models 50 corrupted samples. Thirdly find output attention modules is highly informative clearly indicating sub-optimal sensor placement sensor pointing away speaker CHiME-3 dataset. Remarkably outcome is even obtained when sharing weights attention modules across sensors implying attention modules learned successfully differentiate sensors higher lower SNR data presence natural noise.Due modular architecture where STANs are also remarkably flexible respect sensor configuration even performing well removal sensors training. One can train STANs solve task multi-sensor setup training remove less informative sensors possibly savings energy consumption computational load multi-sensor hardware systems restricted computational power mobile robots. case defect sensor could removed STANs would remain operational remaining sensors.,988,701,287,0.009,1.409,2025/11/05 17:19:02,0.0,1.261,0.2461059190031151,297.83
"Massive data exist among user local platforms that usually cannot support deep neural network (DNN) training due to computation and storage resource constraints. Cloud-based training schemes provide beneficial services but suffer from potential privacy risks due to excessive user data collection. To enable cloud-based DNN training while protecting the data privacy simultaneously, we propose to leverage the intermediate representations of the data, which is achieved by splitting the DNNs and deploying them separately onto local platforms and the cloud. The local neural network (NN) is used to generate the feature representations. To avoid local training and protect data privacy, the local NN is derived from pre-trained NNs. The cloud NN is then trained based on the extracted intermediate representations for the target learning task. We validate the idea of DNN splitting by characterizing the dependency of privacy loss and classification accuracy on the local NN topology for a convolutional NN (CNN) based image classification task. Based on the characterization, we further propose PrivyNet to determine the local NN topology, which optimizes the accuracy of the target learning task under the constraints on privacy loss, local computation, and storage. The efficiency and effectiveness of PrivyNet are demonstrated with CIFAR-10 dataset. With the pervasiveness of sensors, cameras, and mobile devices, massive data are generated and stored on local platforms. While useful information can be extracted from the data, the training process can be too computationally intensive that local platforms are not able to support. Cloud-based services provide a viable alternative to enable deep model training but rely on excessive user data collection, which suffers from potential privacy risks and policy violations.To enable the cloud-based training scheme while simultaneously protecting user data privacy, different data pre-processing schemes are proposed. Instead of releasing the original data, transformed representations are usually generated locally and then, uploaded for the target learning tasks. For the intermediate representations to be effective, there are two requirements, i.e. utility and privacy. The utility requirement urges that the target learning task can be accomplished accurately based on the released representations, while the privacy requirement forces the leakage of private information to be constrained within a satisfiable range. Furthermore, the transformation scheme should also be flexible enough for platforms with different computation and storage capabilities and for different types of data, which can be either high dimensional and continuous, like videos or images, or discrete.Related Works Privacy and utility trade-off has been one of the main questions in the privacy research. Different measures of privacy and utility are proposed based on the rate-distortion theory BID18 BID16 du Pin Calmon & Fawaz, 2012) , statistical estimation BID21 , and learnability BID10 . To actively explore the trade-off between privacy and utility, in recent years, many different transformations have been proposed. Syntactic anonymization methods, including k-anonymity BID22 , l-diversity BID14 and t-closeness BID13 , are proposed to anonymize quasiidentifiers and protect sensitive attributes in a static database. However, syntactic anonymization is hard to apply to high-dimensional continuous data because quasi-identifiers and sensitive attributes become hard to define.Differential privacy is proposed to provide a more formal privacy guarantee and can be easily achieved by adding noise BID3 BID4 . However, because differential privacy only prevents an adversary from gaining additional knowledge by inclusion/exclusion of an individual data BID5 , the total information leakage from the released representations is not limited BID8 . Meanwhile, to achieve differential privacy, existing works BID19 BID0 usually require local platforms to get involved in the backward propagation process, which makes it hard to deploy them on lightweight platforms.Non-invertible linear and non-linear transformations are also proposed for data anonymization. Existing linear transformations rely on the covariance between data and labels BID6 or the linear discriminant analysis (LDA) BID24 to filter the training data. However, linear transformations usually suffer from limited privacy protection since the original data can be reconstructed given the released representations. Recently proposed nonlinear transformations based on minimax filter BID8 or Siamese networks BID15 can provide better privacy protection. However, they can only be applied to protect privacy in the inference stage since iteractive training scheme is required between the cloud and local platforms, for which privacy loss becomes very hard to control. Figure 1: The proposed PrivyNet framework: the local NN is derived from pre-trained NNs for feature extraction and the cloud NN is trained for the target learning task. Privacy and utility trade-off is controlled by the topology of the local NN.Contribution To this end, we propose PrivyNet, a flexible DNN training framework to achieve a fine-grained control of the trade-off between privacy and utility. PrivyNet divides a DNN model into two parts and deploys them onto the local platforms and the cloud separately. As shown in Figure 1 , the local NN is used to generate intermediate representations while the cloud NN is trained for the learning task based on the released intermediate representations. The privacy protection is achieved through the transformation realized by the local NN, which is non-linear and consists of different lossy operations, including convolution, pooling, and so on. To avoid local training, we derive the local NN from pre-trained NNs. Our key insight here is that the initial layers of a DNN are usually used to extract general features that are not application specific and can enable different learning tasks. Therefore, by deriving the local NN from pre-trained NNs, a good utility can be achieved since useful features are embedded in the released representations, while privacy can be protected by selecting the topology of the local NN to control the specific features to release. Our main contributions are summarized as follows:• We propose PrivyNet, a novel framework to split DNN model to enable cloud-based training with a fine-grained control of privacy loss.• We characterize the privacy loss and utility of using CNN as the local NN in detail, based on which three key factors that determine the privacy and utility trade-off are identified and compared.• A hierarchical strategy is proposed to determine the topology of the local NN to optimize the utility considering constraints on local computation, storage, and privacy loss.• We verify PrivyNet by using the CNN-based image classification as an example and demonstrate its efficiency and effectiveness. In this section, we provide detailed discussions on the adversarial model adopted in the paper.According to the adversarial model we have defined in Section 3, the transformation induced by the FEN is assumed to be unknown to the attackers. This helps prevent more powerful attacks and enable a better privacy protection. However, because the FEN is derived from the pre-trained NNs, the structure and weights of which are also available to the attackers, we need to provide strategies to protect the anonymity of the FEN. In our framework, we consider the following two methods for the protection of the FEN:• Build a pool of pre-trained NNs to enable FEN derivation from NNs. In our characterization framework, we use VGG16 as an example. The same procedure can be applied to VGG19 BID20 , ResNet BID9 , Inception BID23 . By enlarging the pool, it becomes harder for the attacker to guess how the FEN is derived.• Apply the channel selection procedure to both output channels and intermediate channels.After the channel selection, the number of channels and the subset of selected channels in each layer become unknown to the attackers. Therefore , even if the attackers know the pre-trained NN, from which the FEN is derived, it becomes much harder to guess the channels that form the FEN.One important requirement for the intermediate channel selection is that the utility is not sacrificed and the privacy loss is not increased. We verify the change of privacy and utility empirically. We take the first 6 layers of VGG16, including 4 convolution layers and 2 max-pooling layers, and set the depth of output channel to 8. We use CIFAR-10 dataset and the same ICN and IRN as in Section 2. We first gradually reduce the channel depth of the first convolution layer from 64 to 16. As shown in FIG12 , the privacy and utility are rarely impacted by the change of the channel depth of first convolution layer. Meanwhile, we can observe the dramatic reduction on the runtime. We then gradually reduce the channel depth for each convolution layer. As shown in FIG4 , after we reduce the channel depth for each layer to half of its original depth, we still get similar privacy and utility with a dramatic reduction of the runtime. , 64, 128, 8}, { 32, 32, 128, 8}, {32, 32, 64, 8}, respectively By channel selection for intermediate layers, even if the attackers can know the pre-trained NN that our FEN is derived from, it is still very hard to determine the number of layers for the FEN and the number of channels for each layer. In this way, the anonymity of the FEN can be well protected.",Massive data exist among user local platforms usually cannot support deep neural network DNN training due computation storage resource constraints. Cloud-based training schemes provide beneficial services suffer potential privacy risks due excessive user data collection. enable cloud-based DNN training protecting data privacy simultaneously propose leverage intermediate representations data which is achieved splitting DNNs deploying separately onto local platforms cloud. local neural network NN is used generate feature representations. avoid local training protect data privacy localNN is derived pre-trained NNs. cloudNN is then is trained based extracted intermediate representations target learning task. validate idea DNN splitting characterizing dependency privacy loss classification accuracy local NN topology convolutionalNN CNN based image classification task. Based characterization propose PrivyNet determine local NN topology which optimizes accuracy target learning task constraints privacy loss local computation storage. efficiency effectiveness PrivyNet are demonstrated CIFAR-10 dataset. pervasiveness sensors cameras mobile devices massive data are generated stored local platforms. useful information can be extracted data training process can be too computationally intensive local platforms are not able support. Cloud-based services provide viable alternative enable deep model training rely excessive user data collection which suffers potential privacy risks policy violations.To enable cloud-based training scheme simultaneously protecting user data privacy different data pre-processing schemes are proposed. Instead releasing original data transformed representations are usually generated locally uploaded target learning tasks. intermediate representations effective are two requirements.e utility privacy. utility requirement urges target learning task can be accomplished accurately based released representations which privacy requirement forces leakage private information constrained within satisfiable range. Furthermore transformation scheme should also flexible enough platforms different computation storage capabilities different types data which can be either high dimensional continuous like videos images discrete.Related Works Privacy utility trade-off has been one main questions privacy research. Different measures privacy utility are proposed based rate-distortion theory BID18 BID16 du Pin Calmon Fawaz 2012 statistical estimation BID21 learnability BID10. actively explore trade-off privacy utility recent years many different transformations have been proposed. Syntactic anonymization methods including k-anonymity BID22 l-diversity BID14 t-closeness BID13 are proposed anonymize quasiidentifiers protect sensitive attributes static database. However syntactic anonymization is hard apply high-dimensional continuous data quasi-identifiers sensitive attributes become hard define.Differential privacy is proposed provide formal privacy guarantee can be easily achieved adding noise BID3 BID4. However differential privacy prevents adversary gaining additional knowledge inclusion/exclusion individual data BID5 total information leakage released representations is not limited BID8. Meanwhile achieve differential privacy existing works BID19 BID0 usually require local platforms get involved backward propagation process which makes hard deploy lightweight platforms.Non-invertible linear non-linear transformations are also proposed data anonymization. Existing linear transformations rely covariance data labels BID6 linear discriminant analysis LDA BID24 filter training data. However linear transformations usually suffer limited privacy protection since original data can be reconstructed given released representations. Recently proposed nonlinear transformations based minimax filter BID8 Siamese networks BID15 can provide better privacy protection. However can only applied protect privacy inference stage since iteractive training scheme is required cloud local platforms which privacy loss becomes hard control. Figure1:proposed PrivyNet framework:localNN is derived pre-trained NNs feature extraction cloudNN is then is trained target learning task. Privacy utility trade-off is controlled topology local NN.Contribution end propose PrivyNet flexible DNN training framework achieve fine-grained control trade-off privacy utility. PrivyNet divides DNN model two parts deploys onto local platforms cloud separately. shown Figure1 localNN is used generate intermediate representations cloudNN is then is trained learning task based released intermediate representations. privacy protection is achieved transformation realized localNN which is non-linear consists different lossy operations including convolution pooling on. avoid local training derive localNN pre-trained NNs. key insight is that the initial layers DNN are usually used extract general features are not application specific can enable different learning tasks. Therefore deriving localNN pre-trained NNs good utility can be achieved since useful features are embedded released representations which privacy can be protected selecting topology localNN control specific features release. main contributions are summarized follows:• propose PrivyNet novel framework split DNN model enable cloud-based training fine-grained control privacy loss.• characterize privacy loss utility using CNN localNN detail based which three key factors determine privacy utility trade-off are identified compared.• hierarchical strategy is proposed determine topology localNN optimize utility considering constraints local computation storage which privacy loss.• verify PrivyNet using CNN-based image classification example demonstrate efficiency effectiveness. section provide detailed discussions adversarial model adopted paper.According adversarial model have defined Section3 transformation induced FEN is assumed unknown attackers. helps prevent powerful attacks can enable better privacy protection. However which the FEN is derived pre-trained NNs structure weights which are also available attackers need provide strategies protect anonymity FEN. framework consider following two methods protection FEN:• Build pool pre-trained NNs enable FEN derivation NNs. characterization framework use VGG16 example. procedure can be applied VGG19 BID20 ResNet BID9 Inception BID23. enlarging pool becomes harder attacker guess how the FEN is derived.• Apply channel selection procedure output channels intermediate channels.After channel selection number channels subset selected channels layer become unknown attackers. Therefore even if the attackers know pre-trainedNN which the FEN is derived becomes much harder guess channels form FEN.One important requirement intermediate channel selection is that the utility is not sacrificed privacy loss is not increased. verify change privacy utility empirically. take first 6 layers VGG16 including 4 convolution layers 2 max-pooling layers set depth output channel 8. use CIFAR-10 dataset ICN IRN Section2. first gradually reduce channel depth first convolution layer 64 16. shown FIG12 which privacy utility are rarely impacted change channel depth first convolution layer. Meanwhile can observe dramatic reduction runtime. gradually reduce channel depth convolution layer. shown FIG4 reduce channel depth layer half original depth still get similar privacy utility dramatic reduction runtime. 64 128 8 32 32 128 8 32 32 64 8 respectively channel selection intermediate layers even if the attackers can know pre-trainedNN FEN is derived is still hard determine number layers FEN number channels layer. way anonymity FEN can be well protected.,1818,1254,564,0.024,1.45,2025/11/05 17:19:02,0.01,1.517,0.3738317757009343,569.499
"Generative Adversarial Networks (GANs) have shown remarkable success as a framework for training models to produce realistic-looking data. In this work, we propose a Recurrent GAN (RGAN) and Recurrent Conditional GAN (RCGAN) to produce realistic real-valued multi-dimensional time series, with an emphasis on their application to medical data. RGANs make use of recurrent neural networks (RNNs) in the generator and the discriminator. In the case of RCGANs, both of these RNNs are conditioned on auxiliary information. We demonstrate our models in a set of toy datasets, where we show visually and quantitatively (using sample likelihood and maximum mean discrepancy) that they can successfully generate realistic time-series. We also describe novel evaluation methods for GANs, where we generate a synthetic labelled training dataset, and evaluate on a real test set the performance of a model trained on the synthetic data, and vice-versa. We illustrate with these metrics that RCGANs can generate time-series data useful for supervised training, with only minor degradation in performance on real test data. This is demonstrated on digit classification from ‘serialised’ MNIST and by training an early warning system on a medical dataset of 17,000 patients from an intensive care unit. We further discuss and analyse the privacy concerns that may arise when using RCGANs to generate realistic synthetic medical time series data, and demonstrate results from differentially private training of the RCGAN. Access to data is one of the bottlenecks in the development of machine learning solutions to domainspecific problems. The availability of standard datasets (with associated tasks) has helped to advance the capabilities of learning systems in multiple tasks. However, progress appears to lag in other fields, such as medicine. It is tempting to suggest that tasks in medicine are simply harder -the data more complex, more noisy, the prediction problems less clearly defined. Regardless of this, the dearth of data accessible to researchers hinders model comparisons, reproducibility and ultimately scientific progress. However, due to the highly sensitive nature of medical data, its access is typically highly controlled, or require involved and likely imperfect de-identification. The motivation for this work is therefore to exploit and develop the framework of generative adversarial networks (GANs) to generate realistic synthetic medical data. This data could be shared and published without privacy concerns, or even used to augment or enrich similar datasets collected in different or smaller cohorts of patients. Moreover, building a system capable of synthesizing realistic medical data implies modelling the processes that generates such information, and therefore it can represent the first step towards developing a new approach for creating predictive systems in medical environments.Beyond the utility to the machine learning research community, such a tool stands to benefit the medical community for use in training simulators. In this work, we focus on synthesising real-valued time-series data as from an Intensive Care Unit (ICU). In ICUs, doctors have to make snap decisions under time pressure, where they cannot afford to hesitate. It is already standard in medical training to use simulations to train doctors, but these simulations often rely on hand-engineered rules and physical props. Thus, a model capable of generating diverse and realistic ICU situations could have an immediate application, especially when given the ability to condition on underlying 'states' of the patient.The success of GANs in generating realistic-looking images BID29 BID20 BID12 BID30 suggests their applicability for this task, however limited work has exploited them for generating time-series data. In addition, evaluation of GANs remains a largely-unsolved problem, with researchers often relying on visual evaluation of generated examples, an approach which is both impractical and inappropriate for multi-dimensional medical time series. For example BID35 ) present a method to use convolutional GANs specifically designed to generate video sequences, and the results were visually evaluated with Amazon Mechanical Turk. In BID25 , authors present a method for voice synthesis based on dilated convolutions, which is also evaluated by humans. This voice synthesis model has been very recently improved by introducing an RNN-based network that generates the spectrogram of the signal BID32 .The primary contributions of this work are:1. Demonstration of a method to generate multivariate real-valued sequences using adversarial training and recurrent neural networks.2. Showing novel approaches for evaluating GANs.3. Generating synthetic medical time series data.4. Empirical privacy analysis of both GANs and differential private GANs. We have described, trained and evaluated a recurrent GAN architecture for generating real-valued sequential data, which we call RGAN. We have additionally developed a conditional variant (RCGAN) to generate synthetic datasets, consisting of real-valued time-series data with associated labels. As this task poses new challenges, we have presented novel solutions to deal with evaluation and questions of privacy. By generating labelled training data -by conditioning on the labels and generating the corresponding samples, we can evaluate the quality of the model using the 'TSTR technique', where we train a model on the synthetic data, and evaluate it on a real, held-out test set. We have demonstrated this approach using 'serialised' multivariate MNIST, and on a dataset of real ICU patients, where models trained on the synthetic dataset achieved performance at times comparable to that of the real data. In domains such as medicine, where privacy concerns hinder the sharing of data, this implies that with refinement of these techniques, models could be developed on synthetic data that are still valuable for real tasks. This could enable the development of synthetic 'benchmarking' datasets for medicine (or other sensitive domains), of the kind which have enabled great progress in other areas. We have additionally illustrated that such a synthetic dataset does not pose a major privacy concern or constitute a data leak for the original sensitive training data, and that for stricter privacy guarantees, differential privacy can be used in training the RCGAN with some loss to performance. : Data from three real eICU patients (purple, blue, gold) of the first five hours after admission. Noise from N (0, σ 2 e ) for σ e = 0.1σ has been added to protect privacy, where σ is the standard deviation of the true data (for that variable). We compare the data at its original sampling resolution with downsampled to one measurement every 15 minutes (the setting used in this paper) and 30 minutes. High-frequency fluctuations are lost through downsampling, but general trends and some variability are preserved in the 15 minute case. These patients were selected randomly from the set of patients with minimal missing data during the time period and so are representative of the cohort used to generate the training data. : Three random samples from the generator trained on eICU data. These samples are from the synthetic datasets used in the TSTR experiments in section 5.1. The generator produces data in [−1, 1], so to obtain medically relevant values, the inverse of the scaling transformation used on the training data has been applied. This transformation was to scale each variable at each time-point independently to the range [−1, 1]. An unusually high value (likely an artefact) in the mean arterial pressure at 135 minutes after admission is responsible for the apparent downward spike in the generated data. A scaling transformation T is applied to the real data (independently for each variable at each timepoint), and the synthetic data is as produced by the generator. , and zooming in. The synthetic data consists of the generated datasets from all five replicates of the TSTR experiment in eICU described in section 5.1 with TSTR results reported in Table 2a . The real data is the training set for those expeirments. between synthetic and real data. The synthetic data is that used in the TSTR experiments (five replicates) in section 5.1.","Generative Adversarial Networks GANs have shown remarkable success framework training models produce realistic-looking data. work propose Recurrent GAN RGAN Recurrent Conditional GAN RCGAN produce realistic real-valued multi-dimensional time series emphasis application medical data. RGANs make use recurrent neural networks RNNs generator discriminator. case RCGANs RNNs are conditioned auxiliary information. demonstrate models set toy datasets where we show visually quantitatively using sample likelihood maximum mean discrepancy can successfully generate realistic time-series also describe novel evaluation methods GANs where we generate synthetic labelled training dataset can evaluate real test set performance model trained synthetic data vice-versa illustrate metrics RCGANs can generate time-series data useful supervised training minor degradation performance real test data. is demonstrated digit classification serialised MNIST training early warning system medical dataset 17,000 patients intensive care unit. discuss analyse privacy concerns may arise when using RCGANs generate realistic synthetic medical time series data demonstrate results differentially private training RCGAN. Access data is one bottlenecks development machine learning solutions domainspecific problems. availability standard datasets associated tasks has helped advance capabilities learning systems multiple tasks. However progress appears lag fields medicine. is tempting suggest tasks medicine are simply harder -the data complex noisy prediction problems less clearly defined. Regardless dearth data accessible researchers hinders model comparisons reproducibility ultimately scientific progress. However due highly sensitive nature medical data access is typically highly controlled require involved likely imperfect de-identification motivation work is therefore exploit develop framework generative adversarial networks GANs generate realistic synthetic medical data. data could shared published without privacy concerns even used augment enrich similar datasets collected different smaller cohorts patients. Moreover building system capable synthesizing realistic medical data implies modelling processes generates information therefore can represent first step towards developing new approach creating predictive systems medical environments.Beyond utility machine learning research community tool stands benefit medical community use training simulators. work focus synthesising real-valued time-series data Intensive Care Unit ICU ICUs doctors have to make snap decisions time pressure where they cannot afford hesitate. is already standard medical training use simulations train doctors simulations often rely hand-engineered rules physical props. Thus model capable generating diverse realistic ICU situations could have an immediate application especially when given ability condition underlying 'states' patient.The success GANs generating realistic-looking images BID29 BID20 BID12 BID30 suggests applicability task however limited work has exploited generating time-series data. addition evaluation GANs remains largely-unsolved problem researchers often relying visual evaluation generated examples approach which is both impractical inappropriate multi-dimensional medical time series. example BID35 present method use convolutional GANs specifically designed generate video sequences results were visually evaluated Amazon Mechanical Turk. BID25 authors present method voice synthesis based dilated convolutions which is also evaluated humans. voice synthesis model has been very recently improved introducing RNN-based network generates spectrogram signal BID32.The primary contributions work are:1 Demonstration method generate multivariate real-valued sequences using adversarial training recurrent neural networks.2 Showing novel approaches evaluating GANs.3 Generating synthetic medical time series data.4 Empirical privacy analysis GANs differential private GANs. have described trained evaluated recurrent GAN architecture generating real-valued sequential data which we call RGAN. have additionally developed conditional variant RCGAN generate synthetic datasets consisting real-valued time-series data associated labels. task poses new challenges have presented novel solutions deal evaluation questions privacy. generating labelled training data -by conditioning labels generating corresponding samples can evaluate quality model using 'TSTR technique' where we train model synthetic data can evaluate real held-out test set. have demonstrated approach using 'serialised' multivariate MNIST dataset real ICU patients where models trained synthetic dataset achieved performance times comparable real data. domains medicine where privacy concerns hinder sharing data implies refinement techniques where models could developed synthetic data are still valuable real tasks. could enable development synthetic 'benchmarking' datasets medicine sensitive domains kind which have enabled great progress areas. have additionally illustrated synthetic dataset does not pose major privacy concern constitute data leak original sensitive training data stricter privacy guarantees differential privacy can be used training RCGAN loss performance. Data three real eICU patients purple blue gold first five hours admission. Noise N 0 whereσ2e σe 0.1σ has been added protect privacy whereσ is the standard deviation true data variable compare data original sampling resolution downsampled one measurement every15 minutes setting used paper 30 minutes. High-frequency fluctuations are lost downsampling general trends variability are preserved 15 minute case. patients were selected randomly set patients minimal missing data time period are representative cohort used generate training data. Three random samples generator trained eICU data. samples are from the synthetic datasets used TSTR experiments section 5.1 generator produces data −1 1 obtain medically relevant values inverse scaling transformation used training data has been applied. transformation was to scale variable time-point independently range −1 1 unusually high value likely artefact mean arterial pressure 135 minutes admission is responsible apparent downward spike generated data. scaling transformation is applied real data independently variable timepoint synthetic data is as produced generator. zooming in. synthetic data consists generated datasets five replicates TSTR experiment eICU described section 5.1 TSTR results reported Table2a. real data is the training set expeirments. synthetic real data. synthetic data is that used TSTR experiments five replicates section 5.1",1596,1069,527,0.016,1.493,2025/11/05 17:19:02,0.01,1.453,0.5077881619937696,496.507
"Emphasis effects – visual changes that make certain elements more
 prominent – are commonly used in information visualization to draw
 the user’s attention or to indicate importance. Although theoretical
 frameworks of emphasis exist (that link visually diverse emphasis
 effects through the idea of visual prominence compared to background
 elements), most metrics for predicting how emphasis effects
 will be perceived by users come from abstract models of human
 vision which may not apply to visualization design. In particular,
 it is difficult for designers to know, when designing a visualization,
 how different emphasis effects will compare and what level of one
 effect is equivalent to what level of another. To address this gap,
 we carried out two studies that provide empirical evidence about
 how users perceive different emphasis effects, using three visual
 variables (colour, size, and blur/focus) and eight strength levels.
 Results from gaze tracking, mouse clicks, and subjective responses
 show that there are significant differences between visual variables
 and between levels, and allow us to develop an initial understanding
 of perceptual equivalence. We developed a model from the data in
 our first study, and used it to predict the results in the second; the
 model was accurate, with high correlations between predictions and
 real values. Our studies and empirical models provide valuable new
 information for designers who want to understand and control how
 emphasis effects will be perceived by users. Emphasis effects are visual changes that make certain elements more prominent, and are commonly used in information visualization to draw the user's attention or to indicate importance. Emphasizing important data points is a common method used by designers to support the user when gradually exploring the data -or in narrative visualization [25] , when known aspects of the data are presented to the users. An effective emphasis effect will alter a data point's visual features [4, 22] , such that a viewer's attention will be guided to the region of interest [61] . The goal of emphasis is to alter important data points to appear more visually prominent and can be achieved through the use of a variety of visual effects [17, 22, 23, 59] . For example, a visualization can use colour changes to emphasize some data points, and differences in the visual prominence of the selected data points will be achieved from variations in color, a visual variable known to guide a user's attention [24] . Although theoretical frameworks of emphasis exist that link visually diverse emphasis effects through the idea of visual prominence compared to background elements [22] , we still know little about how emphasis effects will be perceived by users. In particular, we know little about what visual effects, and what magnitudes of those effects, will be most quickly recognized as emphasis by the viewer of a visualization; in addition, we know little about how different effects compare and what level of an effect is equivalent to what level of another. Many metrics for predicting how emphasis effects will be perceived by users come from abstract models of human vision which may not apply to visualization design. These abstract models from human vision are generally constructed using large and visually isolated stimuli under optimal conditions. Models of human visual attention are effective at predicting perceptibility in isolation but not within a field of distractors, and do not work well with even minor changes to the visual field [3, 58] . Visualizations, in contrast, often consist of large numbers of a variety of marks viewed using a wide range of devices and environments -and designers may use a variety of techniques to emphasize data points. Current guidelines do not address how different emphasis effects are perceived by viewers in visualizations, or provide an equivalence metric for perceived emphasis so designers can choose effects correctly. Without effective models of visual prominence in visualizations, designers lack information on know how different visual effects compare, and don't know what magnitude of effect to use to appropriately guide a viewer's attention to an area of interest. To address this gap, we carried out two studies that provide empirical evidence about how users perceive different emphasis effects, using three visual variables (colour, size, and blur/focus) and eight strength levels. It is important to note that the three emphasis effects are qualitatively different -for example, colour and size manipulate just the emphasized element, whereas blur/focus manipulates everything but the emphasized element -and so our goal is not simply to identify which effect is most perceivable, but rather to establish how the effects compare to one another at different magnitudes. To do this, our first study established a baseline of perceived visual prominence through eye-tracking data, interaction logs, and subjective ratings in simulated static scatterplot visualizations. We then built a model from the first study's data using logarithmic curves, that provides a prediction of equivalence between the three emphasis effects. Our second study then examined perceived emphasis in a more realistic context, by looking at visual prominence in complex visualizations that are taken from real-world applications (the MASSVIS dataset [7] ). We evaluated our model by using it to predict the results of the second study for three different measures; the model was accurate, with R 2 values as high as 0.96. Our two studies provide new findings about how people perceive three emphasis effects and their magnitudes in visualizations: • There were significant differences in both studies for emphasis effect: blur/focus was most prominent, and colour least prominent, with size in between depending on magnitude. • There were also significant differences between the magnitude levels for all effects, providing a graduated way to increase or decrease perceived prominence. • A predictive model based on logarithmic curves fit the Study 1 data well, and was accurate at predicting perceived emphasis in Study 2 (particularly in terms of subjective ratings). Our studies provide an initial empirical foundation for understanding how visual effects operate and are experienced by viewers when used for emphasis in visualizations -and although more work is needed to refine and broaden the models, our work provides useful new information for designers who want to control how emphasis effects will be perceived by users. Emphasis is essential to InfoVis and is used to highlight regions of interest in a visualization. While there is a large body of research in this domain, much of the work seeks to understand how the underlying perceptual system operates -limiting the possibility of extracting design lessons from low-level data and findings. We survey current empirical studies of perception from visualization and vision science to inform our work. Emphasis is an essential component of InfoVis, and is used by designers to draw a user's attention or to indicate importance. However, it is difficult for designers to know how different emphasis effects will compare and what level of one effect is equivalent to what level of another when designing visualizations. We carried out two user studies to evaluate the visual prominence of three emphasis effects (blur/focus, colour, and size) at various strength levels, and developed a predictive model that can indicate equivalence between effects. Results from our two studies provide the beginnings of an empirical foundation for understanding how visual effects operate and are experienced by viewers when used for emphasis in visualizations, and provide new information for designers who want to control how emphasis effects will be perceived by users.","Emphasis effects – visual changes make certain elements prominent– are commonly used information visualization draw users attention indicate importance. Although theoretical frameworks emphasis exist link visually diverse emphasis effects idea visual prominence compared background elements metrics predicting how emphasis effects will be perceived users come abstract models human vision may apply visualization design. particular is difficult designers know when designing visualization how different emphasis effects will compare what level one effect is equivalent what level another. address gap carried two studies provide empirical evidence how users perceive different emphasis effects using three visual variables colour size blur/focus eight strength levels. Results gaze tracking mouse clicks subjective responses show are significant differences visual variables levels allowus develop initial understanding perceptual equivalence. developed model data first study is used predict results second;model was accurate high correlations predictions real values. studies empirical models provide valuable new information designers who want understand control how emphasis effects will be perceived users. Emphasis effects are visual changes make certain elements prominent are commonly used information visualization draw user's attention indicate importance. Emphasizing important data points is a common method used designers support user when gradually exploring data -or narrative visualization 25 when known aspects data are presented users. effective emphasis effect will alter data point's visual features 4 22 viewer's attention will be guided region interest 61 goal emphasis is to alter important data points appear visually prominent can be achieved use variety visual effects 17 22 23 59 example visualization can use colour changes emphasize data points differences visual prominence selected data points will be achieved variations color visual variable known guide user's attention 24 Although theoretical frameworks emphasis exist link visually diverse emphasis effects idea visual prominence compared background elements 22 still know little how emphasis effects will be perceived users. particular know little what visual effects what magnitudes effects will be most quickly recognized emphasis viewer visualization;addition know little how different effects compare what level effect is equivalent what level another. Many metrics predicting how emphasis effects will be perceived users come abstract models human vision may apply visualization design. abstract models human vision are generally constructed using large visually isolated stimuli optimal conditions. Models human visual attention are effective predicting perceptibility isolation within field distractors do not work well even minor changes visual field 3 58 Visualizations contrast often consist large numbers variety marks viewed using wide range devices environments -and designers may use variety techniques emphasize data points. Current guidelines do not address how different emphasis effects are perceived viewers visualizations provide equivalence metric perceived emphasis designers can choose effects correctly. Without effective models visual prominence visualizations designers lack information know how different visual effects compare know what magnitude effect use appropriately guide viewer's attention area interest. address gap carried two studies provide empirical evidence how users perceive different emphasis effects using three visual variables colour size blur/focus eight strength levels. is important note three emphasis effects are qualitatively different -for example colour size manipulate emphasized element whereas blur/focus manipulates everything emphasized element -and goal is not simply identify which effect is most perceivable rather establish how the effects compare one another different magnitudes. do this,first study established baseline perceived visual prominence eye-tracking data interaction logs subjective ratings simulated static scatterplot visualizations. built model first study's data using logarithmic curves provides prediction equivalence three emphasis effects. second study examined perceived emphasis realistic context looking visual prominence complex visualizations are taken real-world applications MASSVIS dataset 7 evaluated model using predict results second study three different measures;model was accurate R 2 values high 0.96 two studies provide new findings how people perceive three emphasis effects magnitudes visualizations:• were significant differences studies emphasis effect:blur/focus was most prominent colour least prominent size depending magnitude. • were also significant differences magnitude levels effects providing graduated way increase decrease perceived prominence. • predictive model based logarithmic curves fit Study 1 data well was accurate predicting perceived emphasis Study2 particularly terms subjective ratings studies provide initial empirical foundation understanding how visual effects operate are experienced viewers when used emphasis visualizations -and although work is needed refine broaden models do not work provides useful new information designers who want control how emphasis effects will be perceived users. Emphasis is is an essential InfoVis is used highlight regions interest visualization. is a large body research domain much work seeks understand how the underlying perceptual system operates -limiting possibility extracting design lessons low-level data findings. survey current empirical studies perception visualization vision science inform work. Emphasis is is an essential component InfoVis is used designers draw user's attention indicate importance. However is difficult designers know how different emphasis effects will compare what level one effect is equivalent what level another when designing visualizations. carried two user studies evaluate visual prominence three emphasis effects blur/focus colour size various strength levels developed predictive model can indicate equivalence effects. Results two studies provide beginnings empirical foundation understanding how visual effects operate are experienced viewers when used emphasis visualizations provide new information designers who want control how emphasis effects will be perceived users.",1430,961,469,0.018,1.488,2025/11/05 17:19:02,0.01,1.297,0.4922118380062303,500.256
"Memory Network based models have shown a remarkable progress on the task of relational reasoning.
 Recently, a simpler yet powerful neural network module called Relation Network (RN) has been introduced. 
 Despite its architectural simplicity, the time complexity of relation network grows quadratically with data, hence limiting its application to tasks with a large-scaled memory.
 We introduce Related Memory Network, an end-to-end neural network architecture exploiting both memory network and relation network structures. 
 We follow memory network's four components while each component operates similar to the relation network without taking a pair of objects. 
 As a result, our model is as simple as RN but the computational complexity is reduced to linear time.
 It achieves the state-of-the-art results in jointly trained bAbI-10k story-based question answering and  bAbI dialog dataset. Neural network has made an enormous progress on the two major challenges in artificial intelligence: seeing and reading. In both areas, embedding methods have served as the main vehicle to process and analyze text and image data for solving classification problems. As for the task of logical reasoning, however, more complex and careful handling of features is called for. A reasoning task requires the machine to answer a simple question upon the delivery of a series of sequential information. For example, imagine that the machine is given the following three sentences: ""Mary got the milk there."", ""John moved to the bedroom."", and ""Mary traveled to the hallway."" Once prompted with the question, ""Where is the milk?"", the machine then needs to sequentially focus on the two supporting sentences, ""Mary got the milk there."" and ""Mary traveled to the hallway."" in order to successfully determine that the milk is located in the hallway.Inspired by this reasoning mechanism, J. has introduced the memory network (MemNN), which consists of an external memory and four components: input feature map (I), generalization (G), output feature map (O), and response (R). The external memory enables the model to deal with a knowledge base without loss of information. Input feature map embeds the incoming sentences. Generalization updates old memories given the new input and output feature map finds relevant information from the memory. Finally, response produces the final output.Based on the memory network architecture, neural network based models like end-to-end memory network (MemN2N) BID11 , gated end-to-end memory network (GMemN2N) BID7 , dynamic memory network (DMN) BID6 , and dynamic memory network + (DMN+) BID13 are proposed. Since strong reasoning ability depends on whether the model is able to sequentially catching the right supporting sentences that lead to the answer, the most important thing that discriminates those models is the way of constructing the output feature map. As the output feature map becomes more complex, it is able to learn patterns for more complicate relations. For example, MemN2N, which has the lowest performance among the four models, measures the relatedness between question and sentence by the inner product, while the best performing DMN+ uses inner product and absolute difference with two embedding matrices.Recently, a new architecture called Relation Network (RN) BID9 has been proposed as a general solution to relational reasoning. The design philosophy behind it is to directly capture the supporting relation between the sentences through the multi-layer perceptron (MLP). Despite its simplicity, RN achieves better performance than previous models without any catastrophic failure.The interesting thing we found is that RN can also be interpreted in terms of MemNN. It is composed of O and R where each corresponds to MLP which focuses on the related pair and another MLP which infers the answer. RN does not need to have G because it directly finds all the supporting sentences at once. In this point of view, the significant component would be MLP-based output feature map. As MLP is enough to recognize highly non-linear pattern, RN could find the proper relation better than previous models to answer the given question.However, as RN considers a pair at a time unlike MemNN, the number of relations that RN learns is n 2 when the number of input sentence is n. When n is small, the cost of learning relation is reduced by n times compared to MemNN based models, which enables more data-efficient learning BID9 . However, when n increases, the performance becomes worse than the previous models. In this case, the pair-wise operation increases the number of non-related sentence pairs more than the related sentence pair, thereby confuses RN's learning. BID9 has suggested attention mechanisms as a solution to filter out unimportant relations; however, since it interrupts the reasoning operation, it may not be the most optimal solution to the problem.Our proposed model, ""Relation Memory Network"" (RMN), is able to find complex relation even when a lot of information is given. It uses MLP to find out relevant information with a new generalization which simply erase the information already used. In other words, RMN inherits RN's MLP-based output feature map on Memory Network architecture. Experiments show its state-ofthe-art result on the text-based question answering tasks.",Memory Network based models have shown remarkable progress task relational reasoning. Recently simpler yet powerful neural network module called Relation Network RN has been introduced. Despite architectural simplicity time complexity relation network grows quadratically data hence limiting application tasks large-scaled memory. introduce Related Memory Network end-to-end neural network architecture exploiting memory network relation network structures. follow memory network's four components component operates similar relation network without taking pair objects. result model is as simple RN computational complexity is reduced linear time. achieves state-of-the-art results jointly trained bAbI-10k story-based question answering bAbI dialog dataset. Neural network has made enormous progress two major challenges artificial intelligence:seeing reading. areas embedding methods have served main vehicle process analyze text image data solving classification problems. task logical reasoning however complex careful handling features is called for. reasoning task requires machine answer simple question upon delivery series sequential information. example imagine machine is given following three sentences:Mary got milk there. John moved bedroom. Mary traveled hallway. prompted question Where is the milk? machine needs sequentially focus two supporting sentences Mary got milk there. Mary traveled hallway. order successfully determine milk is located hallway.Inspired reasoning mechanism J. has introduced memory network MemNN which consists external memory four components:input feature map generalization G output feature map response R external memory enables model deal knowledge base without loss information. Input feature map embeds incoming sentences. Generalization updates old memories given new input output feature map finds relevant information memory. Finally response produces final output.Based memory network architecture neural network based models like end-to-end memory network MemN2N BID11 gated end-to-end memory network GMemN2N BID7 dynamic memory network DMN BID6 dynamic memory network+DMN+BID13 are proposed. Since strong reasoning ability depends whether model is able sequentially catching right supporting sentences lead answer important thing discriminates models is the way constructing output feature map. output feature map becomes complex is able learn patterns complicate relations. example MemN2N which has the lowest performance among four models measures relatedness question sentence inner product best performing DMN+uses inner product absolute difference two embedding matrices.Recently new architecture called Relation Network RN BID9 has been proposed general solution relational reasoning. design philosophy behind is to directly capture supporting relation sentences multi-layer perceptron MLP Despite simplicity RN achieves better performance previous models without catastrophic failure.The interesting thing found is thatRN can also interpreted terms MemNN. is composed R where each corresponds MLP which focuses related pair another MLP which infers answer. RN does not need haveG directly finds supporting sentences once. point view significant component would MLP-based output feature map. MLP is enough recognize highly non-linear pattern RN could find proper relation better previous models answer given question.However RN considers pair time unlike MemNN number relations RN learns isn2 when the number input sentence isn. Whenn is small cost learning relation is reduced n times compared MemNN based models which enables data-efficient learning BID9. However when n increases performance becomes worse previous models. case pair-wise operation increases number non-related sentence pairs related sentence pair thereby confuses RN's learning. BID9 has suggested attention mechanisms solution filter unimportant relations;however since interrupts reasoning operation may optimal solution problem.Our proposed model Relation Memory Network RMN is able find complex relation even when a lot information is given. uses MLP find relevant information new generalization which simply erase information already used. words RMN inherits RN's MLP-based output feature map Memory Network architecture. Experiments show state-ofthe-art result text-based question answering tasks.,1034,714,320,0.01,1.448,2025/11/05 17:19:02,0.0,1.368,0.3676012461059186,323.035
"We investigate in this paper the architecture of deep convolutional networks. Building on existing state of the art models, we propose a reconfiguration of the model parameters into several parallel branches at the global network level, with each branch being a standalone CNN. We show that this arrangement is an efficient way to significantly reduce the number of parameters while at the same time improving the performance. The use of branches brings an additional form of regularization. In addition to splitting the parameters into parallel branches, we propose a tighter coupling of these branches by averaging their log-probabilities. The tighter coupling favours the learning of better representations, even at the level of the individual branches, as compared to when each branch is trained independently. We refer to this branched architecture as ""coupled ensembles"". The approach is very generic and can be applied with almost any neural network architecture. With coupled ensembles of DenseNet-BC and parameter budget of 25M, we obtain error rates of 2.92%, 15.68% and 1.50% respectively on CIFAR-10, CIFAR-100 and SVHN tasks. For the same parameter budget, DenseNet-BC has an error rate of 3.46%, 17.18%, and 1.8% respectively.   With ensembles of coupled ensembles, of DenseNet-BC networks, with 50M total parameters, we obtain error rates of 2.72%, 15.13% and 1.42% respectively on these tasks. The design of early convolutional architectures (CNN) involved choices of hyper-parameters such as: filter size, number of filters at each layer, and padding BID15 BID14 . Since the introduction of the VGGNet BID20 ) the design has moved towards following a template: fixed filter size of 3 × 3 and N features maps, down-sample to half the input resolution only by the use of either maxpool or strided convolutions BID21 , and double the number the computed feature maps following each down-sampling operation. This philosophy is used by state of the art models like ResNet BID8 and DenseNet BID11 . The last two architectures extended the template to include the use of ""skip-connections"" between non-contiguous layers.Our work extends this template by adding another element, which we refer to as ""coupled ensembling"". In this set-up, the network is decomposed into several branches, each branch being functionally similar to a complete CNN. The proposed template achieves performance comparable to state of the art models with a significantly lower parameter count.In this paper, we make the following contributions: (i) we show that given a parameter budget, it is better to have the parameters split among branches rather than having a single branch (which is the case for all current networks), (ii) we compare different ways to combine the activations of the parallel branches and find that it is best to take an arithmetic mean of the individual logprobabilities (iii) combining these elements, we significantly match and improve the performance of convolutional networks on CIFAR and SVHN datasets, with a heavily reduced parameter count. (iv) Further ensembling of coupled ensembles lead to more improvement. This paper is organised as follows: in section 2, we discuss related work; in section 3, we introduce the concept of coupled ensembles and the motivation behind the idea; in section 4, we evaluate the proposed approach and compare it with the state of the art; and we conclude and discuss future work in section 5. The proposed approach consists in replacing a single deep convolutional network by a number of ""element blocks"" which resemble standalone CNN models. The intermediate score vectors produced by each of the elements blocks are coupled via a ""fuse layer"". At training time, this is done by taking an arithmetic average of their log-probabilities for the targets. At test time the score vectors are averaged following the output from each score vector. Both of these aspects leads to a significant performance improvement over a single branch configuration. This improvement comes at the cost of a small increase in the training and prediction times. The proposed approach leads to the best performance for a given parameter budget as can be seen in tables 3 and 4, and in figure 2. Additionally, the individual ""element block"" performance is better as compared to when they are trained independently.The increase in training and prediction times is mostly due to the sequential processing of branches during the forward and backward passes. The smaller size of the branches makes the data parallelism on GPUs less efficient. This effect is not as pronounced for larger models. This could be solved in two ways. First, as there is no data dependency between the branches (before the averaging layer) it is possible to extend the data parallelism to the branches, restoring the initial level of parallelism. This can be done by through a parallel implementation of multiple 2D convolutions at the same time. Second or alternatively, when multiple GPUs are used, it is possible to spread the branches over the GPUs.Preliminary experiments on ImageNet (Russakovsky et al., 2015) show that coupled ensembles have a lower error for the same parameter budget as compared to single branch models. We will expand on these experiments in the future.",investigate paper architecture deep convolutional networks. Building existing state art models propose reconfiguration model parameters several parallel branches global network level branch standalone CNN. show arrangement is an efficient way significantly reduce number parameters time improving performance. use branches brings additional form regularization. addition splitting parameters parallel branches propose tighter coupling branches averaging log-probabilities tighter coupling favours learning better representations even level individual branches compared when each branch is trained independently. refer branched architecture coupled ensembles. approach is very generic can be applied almost neural network architecture. coupled ensembles DenseNet-BC parameter budget 25M obtain error rates 2.92 15.68 1.50 respectively CIFAR-10 CIFAR-100 SVHN tasks. parameter budget DenseNet-BC has an error rate 3.46 17.18 1.8 respectively. ensembles coupled ensembles DenseNet-BC networks 50M total parameters obtain error rates 2.72 15.13 1.42 respectively tasks. design early convolutional architectures CNN involved choices hyper-parameters as:filter size number filters layer padding BID15 BID14. Since introduction VGGNet BID20 design has moved towards following template:fixed filter size 3×3 N features maps down-sample half input resolution use either maxpool strided convolutions BID21 double number computed feature maps following down-sampling operation. philosophy is used state art models like ResNet BID8 DenseNet BID11. last two architectures extended template include use skip-connections non-contiguous layers.Our work extends template adding another element which we refer coupled ensembling. set-up network is decomposed several branches branch functionally similar complete CNN. proposed template achieves performance comparable state art models significantly lower parameter count.In paper make following contributions:show given parameter budget is better have the parameters split among branches rather single branch which is the case current networks ii compare different ways combine activations parallel branches find is best take arithmetic mean individual logprobabilities iii combining elements significantly match improve performance convolutional networks CIFAR SVHN datasets heavily reduced parameter count. iv ensembling coupled ensembles lead improvement. paper is organised follows:section2 discuss related work;section3 introduce concept coupled ensembles motivation behind idea;section4 evaluate proposed approach compare state art;conclude discuss future work section5. proposed approach consists replacing single deep convolutional network number element blocks which resemble standalone CNN models. intermediate score vectors produced elements blocks are coupled via fuse layer. training time is done taking arithmetic average log-probabilities targets. test time score vectors are averaged following output score vector. aspects leads significant performance improvement single branch configuration. improvement comes cost small increase training prediction times. proposed approach leads best performance given parameter budget can be seen tables3 4 figure2. Additionally individual element block performance is better compared when they are trained independently.The increase training prediction times is mostly due sequential processing branches forward backward passes. smaller size branches makes data parallelism GPUs less efficient. effect is not as pronounced larger models. could solved two ways. First is data dependency branches averaging layer is possible extend data parallelism branches restoring initial level parallelism. can be done parallel implementation multiple 2D convolutions time. Second alternatively when multiple GPUs are used is possible spread branches GPUs.Preliminary experiments ImageNet Russakovskyetal. 2015 show coupled ensembles have a lower error parameter budget compared single branch models. will expand experiments future.,1065,674,391,0.01,1.58,2025/11/05 17:19:02,0.01,1.5,0.7788161993769471,326.164
"Convolutional Neural Networks (CNN) are very popular in many fields including computer vision, speech recognition, natural language processing, to name a few. Though deep learning leads to groundbreaking performance in these domains, the networks used are very demanding computationally and are far from real-time even on a GPU, which is not power efficient and therefore does not suit low power systems such as mobile devices. To overcome this challenge, some solutions have been proposed for quantizing the weights and activations of these networks, which accelerate the runtime significantly. Yet, this acceleration comes at the cost of a larger error. The NICE method proposed in this work trains quantized neural networks by noise injection and a learned clamping, which improve the accuracy. This leads to state-of-the-art results on various regression and classification tasks, e.g., ImageNet classification with architectures such as ResNet-18/34/50 with low as 3-bit weights and 3 -bit activations. We implement the proposed solution on an FPGA to demonstrate its applicability for low power real-time applications.",Convolutional Neural Networks CNN are very popular many fields including computer vision speech recognition natural language processing name few. Though deep learning leads groundbreaking performance domains networks used are very demanding computationally are far real-time even GPU which is not power efficient therefore does not suit low power systems mobile devices. overcome challenge solutions have been proposed quantizing weights activations networks which accelerate runtime significantly. Yet acceleration comes cost larger error. NICE method proposed work trains quantized neural networks noise injection learned clamping which improve accuracy. leads state-of-the-art results various regression classification tasks e.g ImageNet classification architectures ResNet-18/34/50 low 3-bit weights 3 -bit activations. implement proposed solution FPGA demonstrate applicability low power real-time applications.,212,147,65,0.002,1.442,2025/11/05 17:19:02,0.0,1.75,0.3489096573208719,81.694
"In complex transfer learning scenarios new tasks might not be tightly linked to previous tasks. Approaches that transfer information contained only in the final parameters of a source model will therefore struggle. Instead, transfer learning at at higher level of abstraction is needed. We propose Leap, a framework that achieves this by transferring knowledge across learning processes. We associate each task with a manifold on which the training process travels from initialization to final parameters and construct a meta-learning objective that minimizes the expected length of this path. Our framework leverages only information obtained during training and can be computed on the fly at negligible cost. We demonstrate that our framework outperforms competing methods, both in meta-learning and transfer learning, on a set of computer vision tasks. Finally, we demonstrate that Leap can transfer knowledge across learning processes in demanding reinforcement learning environments (Atari) that involve millions of gradient steps. Transfer learning is the process of transferring knowledge encoded in one model trained on one set of tasks to another model that is applied to a new task. Since a trained model encodes information in its learned parameters, transfer learning typically transfers knowledge by encouraging the target model's parameters to resemble those of a previous (set of) model(s) (Pan & Yang, 2009 ). This approach limits transfer learning to settings where good parameters for a new task can be found in the neighborhood of parameters that were learned from a previous task. For this to be a viable assumption, the two tasks must have a high degree of structural affinity, such as when a new task can be learned by extracting features from a pretrained model BID12 BID14 Mahajan et al., 2018) . If not, this approach has been observed to limit knowledge transfer since the training process on one task will discard information that was irrelevant for the task at hand, but that would be relevant for another task BID15 BID1 .We argue that such information can be harnessed, even when the downstream task is unknown, by transferring knowledge of the learning process itself. In particular, we propose a meta-learning framework for aggregating information across task geometries as they are observed during training. These geometries, formalized as the loss surface, encode all information seen during training and thus avoid catastrophic information loss. Moreover , by transferring knowledge across learning processes, information from previous tasks is distilled to explicitly facilitate the learning of new tasks.Meta learning frames the learning of a new task as a learning problem itself, typically in the few-shot learning paradigm BID20 Santoro et al., 2016; Vinyals et al., 2016) . In this environment, learning is a problem of rapid adaptation and can be solved by training a meta-learner by backpropagating through the entire training process (Ravi & Larochelle, 2016; BID6 BID11 . For more demanding tasks, meta-learning in this manner is challenging; backpropagating through thousands of gradient steps is both impractical and susceptible to instability. On the other hand, truncating backpropagation to a few initial steps induces a short-horizon bias (Wu et al., 2018) . We argue that as the training process grows longer in terms of the distance traversed on the loss landscape, the geometry of this landscape grows increasingly important. When adapting to a new task through a single or a handful of gradient steps, the geometry can largely be ignored. In contrast, with more gradient steps, it is the dominant feature of the training process.To scale meta-learning beyond few-shot learning, we propose Leap, a light-weight framework for meta-learning over task manifolds that does not need any forward-or backward-passes beyond those already performed by the underlying training process. We demonstrate empirically that Leap is a superior method to similar meta and transfer learning methods when learning a task requires more than a handful of training steps. Finally, we evaluate Leap in a reinforcement Learning environment (Atari 2600; BID8 , demonstrating that it can transfer knowledge across learning processes that require millions of gradient steps to converge. Transfer learning typically ignores the learning process itself, restricting knowledge transfer to scenarios where target tasks are very similar to source tasks. In this paper, we present Leap, a framework for knowledge transfer at a higher level of abstraction. By formalizing knowledge transfer as minimizing the expected length of gradient paths, we propose a method for meta-learning that scales to highly demanding problems. We find empirically that Leap has superior generalizing properties to finetuning and competing meta-learners.",complex transfer learning scenarios new tasks might tightly linked previous tasks. Approaches can transfer information contained final parameters source model will therefore struggle. Instead transfer learning higher level abstraction is needed. propose Leap framework achieves transferring knowledge across learning processes. associate task manifold which the training process travels initialization final parameters construct meta-learning objective minimizes expected length path. framework leverages information obtained training can be computed fly negligible cost. demonstrate framework outperforms competing methods meta-learning transfer learning set computer vision tasks. Finally demonstrate Leap can transfer knowledge across learning processes demanding reinforcement learning environments Atari involve millions gradient steps. Transfer learning is the process transferring knowledge encoded one model trained one set tasks another model is applied new task. Since trained model encodes information learned parameters transfer learning typically transfers knowledge encouraging target model's parameters resemble previous set model Pan Yang 2009 If not approach limits transfer learning settings where good parameters new task can be found neighborhood parameters were learned previous task. viable assumption two tasks must have a high degree structural affinity when new task can be learned extracting features pretrained model BID12 BID14 Mahajanetal. 2018 If not approach has been observed limit knowledge transfer since training process one task will discard information was irrelevant task hand would relevant another task BID15 BID1.We argue information can be harnessed even when the downstream task is unknown transferring knowledge learning process itself. particular propose meta-learning framework aggregating information across task geometries are observed training. geometries formalized loss surface encode information seen training thus avoid catastrophic information loss. Moreover transferring knowledge across learning processes information previous tasks is distilled explicitly facilitate learning new tasks.Meta learning frames learning new task learning problem typically few-shot learning paradigm BID20 Santoroetal. 2016;Vinyalsetal. 2016 environment learning is a problem rapid adaptation can be solved training meta-learner backpropagating entire training process Ravi Larochelle 2016;BID6 BID11. demanding tasks meta-learning manner is challenging;backpropagating thousands gradient steps is both impractical susceptible instability. hand truncating backpropagation initial steps induces short-horizon bias Wuetal. 2018 argue training process grows longer terms distance traversed loss landscape geometry landscape grows increasingly important. When adapting new task single handful gradient steps geometry can largely ignored. contrast gradient steps is the dominant feature training process.To scale meta-learning beyond few-shot learning propose Leap light-weight framework meta-learning task manifolds does not need forward-or backward-passes beyond already performed underlying training process. demonstrate empirically Leap is a superior method similar meta transfer learning methods when learning task requires handful training steps. Finally evaluate Leap reinforcement Learning environment Atari 2600;BID8 demonstrating can transfer knowledge across learning processes require millions gradient steps converge. Transfer learning typically ignores learning process restricting knowledge transfer scenarios where target tasks are very similar source tasks. paper present Leap framework knowledge transfer higher level abstraction. formalizing knowledge transfer minimizing expected length gradient paths propose method meta-learning scales highly demanding problems. find empirically Leap has superior generalizing properties finetuning competing meta-learners,900,605,295,0.009,1.488,2025/11/05 17:19:02,0.0,1.472,0.4922118380062303,296.113
"Given an existing trained neural network, it is often desirable to learn new capabilities without hindering performance of those already learned. Existing approaches either learn sub-optimal solutions, require joint training, or incur a substantial increment in the number of parameters for each added task, typically as many as the original network. We propose a method called Deep Adaptation Networks (DAN) that constrains newly learned filters to be linear combinations of existing ones. DANs preserve performance on the original task, require a fraction (typically 13%) of the number of parameters compared to standard fine-tuning procedures and converge in less cycles of training to a comparable or better level of performance. When coupled with standard network quantization techniques, we further reduce the parameter cost to around 3% of the original with negligible or no loss in accuracy. The learned architecture can be controlled to switch between various learned representations, enabling a single network to solve a task from multiple different domains. We conduct extensive experiments showing the effectiveness of our method on a range of image classification tasks and explore different aspects of its behavior. While deep neural networks continue to show remarkable performance gains in various areas such as image classification BID20 ), semantic segmentation BID24 ), object detection BID9 ), speech recognition BID13 )medical image analysis BID23 ) -and many more -it is still the case that typically, a separate model needs to be trained for each new task. Given two tasks of a totally different modality or nature, such as predicting the next word in a sequence of words versus predicting the class of an object in an image, it stands to reason that each would require a different architecture or computation. However, for a set of related tasks such as classifying images from different domains it is natural to expect that solutions will (1) Utilize the same computational pipeline; (2) Require a modest increment in the number of required parameters for each added task; (3) Be learned without hindering performance of already learned tasks (a.k.a catastrophic forgetting) and (4) Be learned incrementally, dropping the requirement for joint training such as in cases where the training data for previously learned tasks is no longer available.Our goal is to enable a network to learn a set of related tasks one by one while adhering to the above requirements. We do so by augmenting a network learned for one task with controller modules which utilize already learned representations for another. The parameters of the controller modules are optimized to minimize a loss on a new task. The training data for the original task is not required at this stage. The network's output on the original task data stays exactly as it was; any number of controller modules may be added to each layer so that a single network can simultaneously encode multiple distinct tasks, where the transition from one task to another can be done by setting a binary switching variable or controlled automatically. The resultant architecture is coined DAN, standing for Deep Adaptation Networks. We demonstrate the effectiveness of our method on the recently introduced Visual Decathlon Challenge (Rebuffi et al. (2017) ) whose task is to produce a classifier to work well on ten different image classification datasets. Though adding only 13% of the number of original parameters for each newly learned task (the specific number depends on the network architecture), the average performance surpasses that of fine tuning all parameters -without the negative side effects of doubling the number of parameters and catastrophic forgetting. In this work, we focus on the task of image classification on various datasets, hence in our experiments the word ""task"" refers to a specific dataset.Our main contribution is the introduction of an improved alternative to transfer learning, which is as effective as fine-tuning all network parameters towards a new task, precisely preserves old task performance, requires a fraction (network dependent, typically 13%) of the cost in terms of new weights and is able to switch between any number of learned tasks.We introduce two variants of the method, a fully-parametrized version, whose merits are described above and one with far fewer parameters, which significantly outperforms shallow transfer learning (i.e. feature extraction) for a comparable number of parameters. In the next section, we review some related work. Sec. 3 details the proposed method. In Sec. 4 we present various experiments, including comparison to related methods, as well as exploring various strategies on how to make our method more effective, followed by some discussion & concluding remarks. We have observed that the proposed method converges to a a reasonably good solution faster than vanilla fine-tuning and eventually attains slightly better performance. This is despite the network's expressive power, which is limited by our construction. We conjecture that constraining each layer to be expressed as a linear combination of the corresponding layer in the original network serves to regularize the space of solutions and is beneficial when the tasks are sufficiently related to each other. One could come up with simple examples where the proposed method would likely fail: if the required solutions to two tasks are disjoint. For example, one task requires counting of horizontal lines and the other requires counting of vertical ones, and such examples are all that appear in the training sets, then the proposed method will likely work far worse than vanilla fine-tuning or training from scratch. We leave the investigation of this issue, as well as finding ways between striking a balance between reusing features and learning new ones as future work. We have presented a method for transfer learning thats adapts an existing network to new tasks while fully preserving the existing representation. Our method matches or outperforms vanilla finetuning, though requiring a fraction of the parameters, which when combined with net compression Our method achieve better performance over baselines for a large range of parameter budgets. For very few parameters diagonal (ours) outperforms features extraction. To obtain maximal accuracy our full method requires far fewer parameters (see linear vs finetune). (b) Our method (linear) converges to a high accuracy faster than fine-tuning. The weaker variant of our method converges as fast as feature-extraction but reaches an overall higher accuracy (3 (a)). (c) zoom in on top-right of (b).reaches 3% of the original parameters with no loss of accuracy. The method converges quickly to high accuracy while being on par or outperforming other methods with the same goal. Built into our method is the ability to easily switch the representation between the various learned tasks, enabling a single network to perform seamlessly on various domains. The control parameter α can be cast as a real-valued vector, allowing a smooth transition between representations of different tasks. An example of the effect of such a smooth transition can be seen in FIG2 where α is used to linearly interpolate between the representation of differently learned tasks, allowing one to smoothly control transitions between different behaviors. Allowing each added task to use a convex combination of already existing controllers will potentially utilize controllers more efficiently and decouple the number of controllers from the number of tasks.",Given existing trained neural network is often desirable learn new capabilities without hindering performance already learned. Existing approaches either learn sub-optimal solutions require joint training incur substantial increment number parameters added task typically many original network. propose method called Deep Adaptation Networks DAN constrains newly learned filters linear combinations existing ones. DANs preserve performance original task require fraction typically13% number parameters compared standard fine-tuning procedures converge less cycles training comparable better level performance. When coupled standard network quantization techniques reduce parameter cost around3% original negligible loss accuracy. learned architecture can be controlled switch various learned representations enabling single network solve task multiple different domains. conduct extensive experiments showing effectiveness method range image classification tasks explore different aspects behavior. deep neural networks continue show remarkable performance gains various areas image classification BID20 semantic segmentation BID24 object detection BID9 speech recognition BID13 medical image analysis BID23 -and many -it is still case typically separate model needs trained new task. Given two tasks totally different modality nature predicting next word sequence words versus predicting class object image stands reason would require different architecture computation. However set related tasks classifying images different domains is natural expect solutions will(1 Utilize computational pipeline;2 Require modest increment number required parameters added task;3 learned without hindering performance already learned tasks.k.a catastrophic forgetting 4 learned incrementally dropping requirement joint training cases where the training data previously learned tasks is no longer available.Our goal is to enable network learn set related tasks one one adhering requirements. do so by augmenting network learned one task controller modules which utilize already learned representations another. parameters controller modules are optimized minimize loss new task. training data original task is not required stage. network's output original task data stays exactly was;number controller modules may added layer single network can simultaneously encode multiple distinct tasks where the transition one task another can be done setting binary switching variable controlled automatically. resultant architecture is coined DAN standing Deep Adaptation Networks. demonstrate effectiveness method recently introduced Visual Decathlon Challenge Rebuffietal. 2017 whose task is to produce classifier work well ten different image classification datasets. Though adding 13% number original parameters newly learned task specific number depends network architecture average performance surpasses fine tuning parameters -without negative side effects doubling number parameters catastrophic forgetting. work focus task image classification various datasets hence experiments word task refers specific dataset.Our main contribution is the introduction improved alternative transfer learning which is as effective fine-tuning network parameters towards new task precisely preserves old task performance requires fraction network dependent typically13% cost terms new weights is able switch number learned tasks.We introduce two variants method fully-parametrized version whose merits are described one far fewer parameters which significantly outperforms shallow transfer learning.e feature extraction comparable number parameters. next section review related work. Sec. 3 details proposed method. Sec. 4 present various experiments including comparison related methods well exploring various strategies how to make method effective followed discussion concluding remarks. have observed proposed method converges reasonably good solution faster vanilla fine-tuning eventually attains slightly better performance. is despite network's expressive power which is limited construction. conjecture constraining layer expressed linear combination corresponding layer original network serves regularize space solutions is beneficial when the tasks are sufficiently related other. One could come simple examples where the proposed method would likely fail:if the required solutions two tasks are disjoint. example one task requires counting horizontal lines requires counting vertical ones examples are all that appear training sets proposed method will likely work far worse vanilla fine-tuning training scratch. leave investigation issue well finding ways striking balance reusing features learning new ones future work. have presented method transfer learning thats adapts existing network new tasks fully preserving existing representation. method matches outperforms vanilla finetuning though requiring fraction parameters which when combined net compression method achieve better performance baselines large range parameter budgets. parameters diagonal outperforms features extraction. obtain maximal accuracy full method requires far fewer parameters see linear vs finetune b method linear converges high accuracy faster fine-tuning weaker variant method converges fast feature-extraction reaches overall higher accuracy 3 c zoom top-right b.reaches3% original parameters loss accuracy. method converges quickly high accuracy par outperforming methods goal. Built method is the ability easily switch representation various learned tasks enabling single network perform seamlessly various domains. control parameterα can be cast real-valued vector allowing smooth transition representations different tasks. example effect smooth transition can be seen FIG2 whereα is used linearly interpolate representation differently learned tasks allowing one smoothly control transitions different behaviors. Allowing added task use convex combination already existing controllers will potentially utilize controllers efficiently decouple number controllers number tasks.,1397,910,487,0.017,1.535,2025/11/05 17:19:02,0.01,1.581,0.6386292834890962,472.515
"High throughput and low latency inference of deep neural networks are critical for the deployment of deep learning applications. This paper presents a general technique toward 8-bit low precision inference of convolutional neural networks, including 1) channel-wise scale factors of weights, especially for depthwise convolution, 2) Winograd convolution, and 3) topology-wise 8-bit support. We experiment the techniques on top of a widely-used deep learning framework. The 8-bit optimized model is automatically generated with a calibration process from FP32 model without the need of fine-tuning or retraining. We perform a systematical and comprehensive study on 18 widely-used convolutional neural networks and demonstrate the effectiveness of 8-bit low precision inference across a wide range of applications and use cases, including image classification, object detection, image segmentation, and super resolution. We show that the inference throughput
 and latency are improved by 1.6X and 1.5X respectively with minimal within 0.6%1to no loss in accuracy from FP32 baseline. We believe the methodology can provide the guidance and reference design of 8-bit low precision inference for other frameworks. All the code and models will be publicly available soon. While convolutional neural networks (CNN) shows state-of-the-art (SOTA) accuracy for wide range of computation vision tasks, it still faces challenges during industrial deployment due to its high computational complexity of inference. Low precision is one of the key techniques being actively studied recently to conquer the problem BID29 BID8 ; BID20 ; BID18 ; BID17 . With hardware acceleration support, low precision inference can compute more operations per second, reduce the memory access pressure and better utilize the cache, and deliver higher throughput and lower latency.Convolution is the primary operation in CNN models and it is a common practice to enable 8-bit low precision (INT8) inference for convolution in deep learning frameworks (e.g., TensorFlow, MXNet, and TensorRT). To make it work, convolution utilizes INT8 computation, which requires two scale factors for activation and weight, respectively. It is workable for standard convolution with single group and two groups BID13 . However, it does not work well for convolution with large groups, especially for depthwise convolution BID0 . In addition to direct convolution, it is worthwhile to explore INT8 Winograd convolution BID14 for better performance, which is absent in previous research 2 . Although recent work have demonstrated INT8 inference with minimal accuracy loss across various models BID29 BID4 ; ; BID11 , INT8 inference is limited due to more complex topology primarily introduced by sum operation in residual block and concatenation operation in inception block BID0 . Existing solutions need to convert the convolution output from INT8 to FP32, and apply the sum or concatenation operation on FP32. The sacrifice of memory bandwidth and frequent data conversion lead to considerable performance overhead and therefore limit the real deployment. Moreover, there is no systematical study of INT8 inference on various use cases, including image classification BID13 ; BID25 ; BID0 ; ), object detection Ren et al. (2015 ; BID1 ; BID15 , image segmentation BID16 ; BID15 , etc.In this paper, we present a general technique towards efficient INT8 inference of CNN models. We experiment the technique on top of a widely-used deep learning framework. To the best of our knowledge, our work is the first attempt to address the above problems. We summarize our contributions below:1. We provide a systematical approach to channel-wise quantization of convolution, which is essential to keep the accuracy for depthwise convolution. Top1 accuracy of INT8 inference on MobileNet-V1 and MobileNet-V2 is improved by 1.98% and 70.6%, respectively. 2. We explore the approach of INT8 Winograd convolution and present the calibration details that cannot be trivially derived from direct convolution. Our experiment on VGG-16 shows Top1 and Top5 accuracy loss with INT8 Winograd convolution is minimal within 0.30% and 0.25% from FP32 baseline, reducing from 5.31% and 3.38%, respectively. 3. We add the support of sum in residual block, concatenation in inception block, and convolution for classification. We also fuse the memory-bound operation convolution with a rectified linear unit (ReLU) BID19 and fold the parameters of batch normalization BID10 into convolution kernels. With topology-wise INT8 support, inference speed is greatly improved by data conversion reduction and memory saving. 4. To our knowledge, this is the first time such a systematic study is applied to and empirical result is reported on many CNN use cases and models. We develop a calibration tool that automatically generates optimized INT8 model from FP32 model without the need of fine-tuning or retraining for easy and repeatable deployment. We perform a comprehensive study on 18 widely-used CNN models and demonstrate the effectiveness of INT8 inference across a wide range of applications, including image classification, object detection, image segmentation, and super resolution. The inference throughput and latency are improved by 1.6X and 1.5X respectively, while the accuracy loss is minimal within 0.6% to no loss from FP32 baseline.We believe our methodology is general for CNN models and can provide the guide and reference on other frameworks. All the code and models will be publicly available soon.The rest of the paper is organized as follows, Section 2 discusses related work on low-precision inference in deep learning. Section 3 describes INT8 inference quantization approach and recipe for CNN models. Section 4 includes experimental results, comprehensive study, and related discussion. Finally, Section 5 concludes the summary with results and future directions. To align the model with best accuracy, the above performance in TAB2 does not include INT8 Winograd convolution. We expect to deliver similar performance improvement of Winograd on INT8 as FP32 BID14 during our development. Different from previous work BID29 BID26 , we also experiment the first convolution using INT8 than FP32, which shows reasonable accuracy within 1% loss.Our experimental results also demonstrate the impact of calibration process on accuracy with different sampling iteration, different calibration algorithm, or different scale factor mode. We summarize our findings: (1) Channel-wise scaling factors can always deliver better accuracy than single scale factor, especially for depthwise convolution; (2) Direct algorithm is more effective in most cases than KL, while KL algorithm can deliver better accuracy than FP32 baseline in some cases; and (3) More sampling iterations show more stable dynamic data rage and therefore better accuracy. How to select the optimal calibration strategy is an interesting topic as one of our future directions. In this paper, we propose the general recipe of INT8 inference and experiment the techniques on a widely-used deep learning framework. We develop an automatic calibration tool for optimized INT8 model generation and demonstrate the effectiveness on 18 CNN models across a wide range of use cases. The inference throughput and latency are improved by 1.6X and 1.5X respectively, while the accuracy loss is minimal within 0.6% to no loss from FP32 baseline. We believe our methodology is general for CNN models and can provide the guide and reference on other frameworks.",High throughput low latency inference deep neural networks are critical deployment deep learning applications. paper presents general technique toward 8-bit low precision inference convolutional neural networks including1 channel-wise scale factors weights especially depthwise convolution 2 Winograd convolution 3 topology-wise 8-bit support. experiment techniques top widely-used deep learning framework. 8-bit optimized model is automatically generated calibration process FP32 model without need fine-tuning retraining. perform systematical comprehensive study 18 widely-used convolutional neural networks demonstrate effectiveness 8-bit low precision inference across wide range applications use cases including image classification object detection image segmentation super resolution. show inference throughput latency are improved 1.6X 1.5X respectively minimal within 0.6%1to loss accuracy FP32 baseline. believe methodology can provide guidance reference design 8-bit low precision inference frameworks. code models will be publicly available soon. convolutional neural networks CNN shows state-of-the-art SOTA accuracy wide range computation vision tasks still faces challenges industrial deployment due high computational complexity inference. Low precision is one key techniques actively studied recently conquer problem BID29 BID8;BID20;BID18;BID17. hardware acceleration support low precision inference can compute operations per second reduce memory access pressure better utilize cache deliver higher throughput lower latency.Convolution is the primary operation CNN models is a common practice enable 8-bit low precision INT8 inference convolution deep learning frameworks e.g TensorFlow MXNet TensorRT make work convolution utilizes INT8 computation which requires two scale factors activation weight respectively. is workable standard convolution single group two groups BID13. However does not work well convolution large groups especially depthwise convolution BID0. addition direct convolution is worthwhile explore INT8 Winograd convolution BID14 better performance which is absent previous research2. Although recent work have demonstrated INT8 inference minimal accuracy loss across various models BID29 BID4;BID11 INT8 inference is limited due complex topology primarily introduced sum operation residual block concatenation operation inception block BID0. Existing solutions need convert convolution output INT8 FP32 apply sum concatenation operation FP32. sacrifice memory bandwidth frequent data conversion lead considerable performance overhead therefore limit real deployment. Moreover is no systematical study INT8 inference various use cases including image classification BID13;BID25;BID0;object detection Renet al. 2015;BID1;BID15 image segmentation BID16;BID15 etc.In paper present general technique towards efficient INT8 inference CNN models. experiment technique top widely-used deep learning framework. best knowledge does not work is the first attempt address problems. summarize contributions below:1 provide systematical approach channel-wise quantization convolution which is essential keep accuracy depthwise convolution. Top1 accuracy INT8 inference MobileNet-V1 MobileNet-V2 is improved 1.98 70.6 respectively. 2. explore approach INT8 Winograd convolution present calibration details cannot trivially derived direct convolution. experiment VGG-16 shows Top1 Top5 accuracy loss INT8 Winograd convolution is minimal minimal within 0.30 0.25 FP32 baseline reducing 5.31 3.38 respectively. 3. add support sum residual block concatenation inception block convolution classification. also fuse memory-bound operation convolution rectified linear unit ReLU BID19 fold parameters batch normalization BID10 convolution kernels. topology-wise INT8 support inference speed is greatly improved data conversion reduction memory saving. 4. knowledge is the first time systematic study is applied empirical result is reported many CNN use cases models. develop calibration tool automatically generates optimized INT8 model FP32 model without need fine-tuning retraining easy repeatable deployment. perform comprehensive study 18 widely-used CNN models demonstrate effectiveness INT8 inference across wide range applications including image classification object detection image segmentation super resolution. inference throughput latency are improved 1.6X 1.5X respectively accuracy loss is minimal minimal within 0.6 loss FP32 baseline.We believe methodology is general CNN models can provide guide reference frameworks. code models will be publicly available soon.The rest paper is organized follows Section 2 discusses related work low-precision inference deep learning. Section 3 describes INT8 inference quantization approach recipe CNN models. Section 4 includes experimental results comprehensive study related discussion. Finally Section 5 concludes summary results future directions. align model best accuracy performance TAB2 does not include INT8 Winograd convolution. expect deliver similar performance improvement Winograd INT8 FP32 BID14 development. Different previous work BID29 BID26 also experiment first convolution using INT8 FP32 which shows reasonable accuracy within 1% loss.Our experimental results also demonstrate impact calibration process accuracy different sampling iteration different calibration algorithm different scale factor mode. summarize findings:1 Channel-wise scaling factors can always deliver better accuracy single scale factor especially depthwise convolution;2 Direct algorithm is more effective cases KL KL algorithm can deliver better accuracy FP32 baseline cases;3 sampling iterations show stable dynamic data rage therefore better accuracy. How to select optimal calibration strategy is an interesting topic one future directions. paper propose general recipe INT8 inference experiment techniques widely-used deep learning framework. develop automatic calibration tool optimized INT8 model generation demonstrate effectiveness 18 CNN models across wide range use cases. inference throughput latency are improved 1.6X 1.5X respectively accuracy loss is minimal minimal within 0.6 loss FP32 baseline. believe methodology is general CNN models can provide guide reference frameworks.,1478,1085,393,0.015,1.362,2025/11/05 17:19:02,0.01,1.4,0.0996884735202493,460.534
"Recent approaches have successfully demonstrated the benefits of learning the parameters of shallow networks in hyperbolic space. We extend this line of work by imposing hyperbolic geometry on the embeddings used to compute the ubiquitous attention mechanisms for different neural networks architectures. By only changing the geometry of embedding of object representations, we can use the embedding space more efficiently without increasing the number of parameters of the model. Mainly as the number of objects grows exponentially for any semantic distance from the query, hyperbolic geometry  --as opposed to Euclidean geometry-- can encode those objects without having any interference. Our method shows improvements in generalization on neural machine translation on WMT'14 (English to German), learning on graphs (both on synthetic and real-world graph tasks) and visual question answering (CLEVR) tasks while keeping the neural representations compact. The focus of this work is to endow neural network representations with suitable geometry to capture fundamental properties of data, including hierarchy and clustering behaviour. These properties emerge in many real-world scenarios that approximately follow power-law distributions BID28 BID9 ). This includes a wide range of natural phenomena in physics BID23 , biology BID26 , and even human-made structures such as metabolic-mass relationships BID4 , social networks , and frequencies of words BID33 BID32 BID38 ).Complex networks , which connect distinguishable heterogeneous sets of elements represented as nodes, provide us an intuitive way of understanding these structures. They will also serve as our starting point for introducing hyperbolic geometry, which is by itself difficult to visualize. Nodes in complex networks are referred to as heterogeneous, in the sense that they can be divided into sub-nodes which are themselves distinguishable from each other. The scale-free structure of natural data manifests itself as a power law distribution on the node degrees of the complex network that describes it.Complex networks can be approximated with tree-like structures, such as taxonomies and dendrograms, and as lucidly presented by , hyperbolic spaces can be thought of as smooth trees abstracting the hierarchical organization of complex networks. Let us begin by recalling a simple property of n-ary trees that will help us understand hyperbolic space and why hyperbolic geometry is well suited to model relational data.In an n-ary tree, the number of nodes at distance r from the root and the number of nodes at distance no more than r from the root both grow as n r . Similarly, in a two-dimensional hyperbolic space with curvature −ζ 2 ,ζ > 0, the circumference and area of a disc of radius r grows as 2πsinh(ζr) and 2π(cosh(ζr)−1), respectively, both of are exponential in r BID20 . The growth of volume in hyperbolic space should be contrasted with Euclidean space where the corresponding quantities expand polynomially, circumference as 2πr and area as πr 2 .In the two-dimensional example of Figure 1 , the expanding rings show examples at a fixed semantic distance from the central object (""pug""). The number of concepts grows quickly with semantic distance forcing each successive ring to be more crowded in order to maintain a fixed distance to the center. In contrast, the extra volume of hyperbolic spheres (depicted by reducing the size of the examples) allows all of the examples to remain well separated from their semantic neighbours. Figure 1: An intuitive depiction of how images might be embedded in 2D. The location of the embeddings reflects the similarity between each image and that of a pug. Since the number of instances within a given semantic distance from the central object grows exponentially, the Euclidean space is not able to compactly represent such structure (left). In hyperbolic space (right) the volume grows exponentially, allowing for sufficient room to embed the images. For visualization, we have shrunk the images in this Euclidean diagram, a trick also used by Escher.Mechanically, the computed embeddings by a random network for objects at a given semantic distance might still seem epsilon distance away from each other (or crowded) as the ones obtained by using Euclidean geometry. However, enforcing hyperbolic geometry intuitively means that all operations with these embeddings take into account, the density in that particular region of the space. For example, any noise introduced in the system (e.g., in gradients) will also be corrected by the density. In contrast to working in Euclidean space , this means that the embeddings will be equally distinguishable regardless of the density.The intimate connection between hyperbolic space and scale free networks (where node degree follows a power law) is made more precise in . In particular, there it is shown that the heterogeneous topology implies hyperbolic geometry, and conversely hyperbolic geometry yields heterogeneous topology. Moreover, Sarkar (2011) describes a construction that embeds trees in two-dimensional hyperbolic space with arbitrarily low distortion, which is not possible in Euclidean space of any dimension BID24 . Following this exciting line of research, recently the machine learning community has gained interest in learning non-Euclidean embeddings directly from data BID29 BID7 BID34 BID30 BID39 BID5 .Fuelled by the desire of increasing the capacity of neural networks without increasing the number of trainable parameters so as to match the complexity of data, we propose hyperbolic attention networks. As opposed to previous approaches, which impose hyperbolic geometry on the parameters of shallow networks BID29 BID7 , we impose hyperbolic geometry on the activations of deep networks. This allows us to exploit hyperbolic geometry to reason about embeddings produced by deep networks. We introduce efficient hyperbolic operations to express the popular , ubiquitous mechanism of attention BID1 BID12 BID42 BID47 . Our method shows improvements in terms of generalization on neural machine translation BID42 , learning on graphs and visual question answering BID0 BID25 BID16 tasks while keeping the representations compact. Simultaneously to our work, BID8 proposed a method to learn SVMs in the hyperboloid model of hyperbolic space, and Nickel and Kiela (2018) proposed a method to learn shallow embeddings of graphs in hyperbolic space by using the hyperboloid model. We have presented a novel way to impose the inductive biases from hyperbolic geometry on the activations of deep neural networks. Our proposed hyperbolic attention operation makes use of hyperbolic geometry in both the computation of the attention weights, and in the aggregation operation over values. We implemented our proposed hyperbolic attention mechanism in both Relation Networks and the Transformer and showed that we achieve improved performance on a diverse set of tasks. We have shown improved performance on link prediction and shortest path length prediction in scale free graphs, on two visual question answering datasets, real-world graph transduction tasks and finally on English to German machine translation. The gains are particularly prominent in relatively small models, which confirms our hypothesis that hyperbolic geometry induces more compact representations.Yang and Rush (2016) have proposed to imposed the activations of the neural network to lie on a Lie-group manifold in the memory. Similarly as a future work, an interesting potential future direction is to use hyperbolic geometry as an inductive bias for the activation of neural networks in the memory.",Recent approaches have successfully demonstrated benefits learning parameters shallow networks hyperbolic space. extend line work imposing hyperbolic geometry embeddings used compute ubiquitous attention mechanisms different neural networks architectures. changing geometry embedding object representations can use embedding space efficiently without increasing number parameters model. Mainly number objects grows exponentially semantic distance query hyperbolic geometry opposed Euclidean geometry can encode objects without interference. method shows improvements generalization neural machine translation WMT'14 English German learning graphs synthetic real-world graph tasks visual question answering CLEVR tasks keeping neural representations compact. focus work is to endow neural network representations suitable geometry capture fundamental properties data including hierarchy clustering behaviour. properties emerge many real-world scenarios approximately follow power-law distributions BID28 BID9 includes wide range natural phenomena physics BID23 biology BID26 even human-made structures metabolic-mass relationships BID4 social networks frequencies words BID33 BID32 BID38.Complex networks which connect distinguishable heterogeneous sets elements represented nodes provideus intuitive way understanding structures. will also serve starting point introducing hyperbolic geometry whichisby difficult visualize. Nodes complex networks are referred heterogeneous sense can be divided sub-nodes which are themselves distinguishable other. scale-free structure natural data manifests power law distribution node degrees complex network describes it.Complex networks can be approximated tree-like structures taxonomies dendrograms lucidly presented hyperbolic spaces can be thought smooth trees abstracting hierarchical organization complex networks. Let us begin recalling simple property n-ary trees will help us understand hyperbolic space why hyperbolic geometry is well suited model relational data.In n-ary tree number nodes distancer root number nodes distance r root grow nr. Similarly two-dimensional hyperbolic space curvature−ζ2 ζ 0 circumference area disc radius r grows 2πsinh ζr 2π cosh ζr −1 respectively are exponential r BID20. growth volume hyperbolic space should be contrasted Euclidean space where the corresponding quantities expand polynomially circumference 2πr area πr 2.In two-dimensional example Figure1 expanding rings show examples fixed semantic distance central object pug number concepts grows quickly semantic distance forcing successive ring crowded order maintain fixed distance center. contrast extra volume hyperbolic spheres depicted reducing size examples allows examples remain well separated semantic neighbours. Figure1:intuitive depiction how images might embedded 2D. location embeddings reflects similarity image pug. Since number instances within given semantic distance central object grows exponentially Euclidean space is not able compactly represent structure left hyperbolic space right volume grows exponentially allowing sufficient room embed images. visualization have shrunk images Euclidean diagram trick also used Escher.Mechanically computed embeddings random network objects given semantic distance might still seem epsilon distance away crowded ones obtained using Euclidean geometry. However enforcing hyperbolic geometry intuitively means operations embeddings take account density particular region space. example noise introduced system e.g gradients will also corrected density. contrast working Euclidean space means embeddings will be equally distinguishable regardless density.The intimate connection hyperbolic space scale free networks where node degree follows power law is made precise in. particular is shown heterogeneous topology implies hyperbolic geometry conversely hyperbolic geometry yields heterogeneous topology. Moreover Sarkar 2011 describes construction embeds trees two-dimensional hyperbolic space arbitrarily low distortion which is not possible Euclidean space dimension BID24. Following exciting line research recently machine learning community has gained interest learning non-Euclidean embeddings directly data BID29 BID7 BID34 BID30 BID39 BID5.Fuelled desire increasing capacity neural networks without increasing number trainable parameters match complexity data propose hyperbolic attention networks. opposed previous approaches which impose hyperbolic geometry parameters shallow networks BID29 BID7 which impose hyperbolic geometry activations deep networks. allowsus exploit hyperbolic geometry reason embeddings produced deep networks. introduce efficient hyperbolic operations express popular ubiquitous mechanism attention BID1 BID12 BID42 BID47. method shows improvements terms generalization neural machine translation BID42 learning graphs visual question answering BID0 BID25 BID16 tasks keeping representations compact. Simultaneously work BID8 proposed method learn SVMs hyperboloid model hyperbolic space Nickel Kiela 2018 have proposed method learn shallow embeddings graphs hyperbolic space using hyperboloid model. have presented novel way impose inductive biases hyperbolic geometry activations deep neural networks. proposed hyperbolic attention operation makes use hyperbolic geometry computation attention weights aggregation operation values. implemented proposed hyperbolic attention mechanism Relation Networks Transformer showed achieve improved performance diverse set tasks. have shown improved performance link prediction shortest path length prediction scale free graphs two visual question answering datasets real-world graph transduction tasks finally English German machine translation. gains are particularly prominent relatively small models which confirms hypothesis hyperbolic geometry induces compact representations.Yang Rush 2016 have proposed imposed activations neural network lie Lie-group manifold memory. Similarly future work interesting potential future direction is to use hyperbolic geometry inductive bias activation neural networks memory.,1468,982,486,0.016,1.495,2025/11/05 17:19:02,0.01,1.429,0.5140186915887852,464.835
"We present a method for evaluating the sensitivity of deep reinforcement learning (RL) policies. We also formulate a zero-sum dynamic game for designing robust deep reinforcement learning policies. Our approach mitigates the brittleness of policies when agents are trained in a simulated environment and are later exposed to the real world where it is hazardous to employ RL policies. This framework for training deep RL policies involve a zero-sum  dynamic game against an adversarial agent, where the goal is to drive the system dynamics to a saddle region. Using a variant of the guided policy search algorithm, our agent learns to adopt robust policies that require less samples for learning the dynamics and performs better than the GPS algorithm. Without loss of generality, we demonstrate that deep RL policies trained in this fashion will be maximally robust to a ``worst"" possible adversarial disturbances. Deep reinforcement learning (RL) for complex agent behavior in realistic environments usually combines function approximation techniques with learning-based control. A good RL controller should guarantee fulfillment of performance specifications under external disturbances, or modeling errors. Quite often in practice, however, this is not the case -with deep RL policies not often generalizing well to real-world scenarios. This can be attributed to the inherent differences between the training and testing environments. Recently, there have been efforts at integrating function approximation techniques with learning-based control, in an end-to-end fashion, in order to have systems that optimize objectives while guaranteeing generalization to environmental uncertainties. Examples include trajectory-based optimization for known dynamics ( BID16 BID25 ), or trajectory optimization for unknown dynamics such as guided policy search algorithms BID0 BID13 BID15 .While these methods produce performance efficiency for agent tasks in the real world, there are sensitivity questions of such policies that need to be addressed such as, how to guarantee maximally robust deep RL policies in the presence of external disturbances, or modeling errors. A typical approach employed in minimizing sample inefficiency is to engineer an agent's policy in a simulated environment, and later transfer such policies to physical environments. However, questions of robustness persist in such scenarios as the agent often has to cope with modeling errors and new sensory inputs from a different environment. For continuous control tasks, learned policies may become brittle in the presence of external perturbations, or a slight change in the system dynamics may significantly affect the performance of the learned controller BID20 -defeating the purpose of having a robust policy that is learned through environmental interaction .The contribution of this paper is two-fold:• first, we provide a framework that demonstrates the brittleness of a state-of-the-art deep RL policy; specifically, given a trained RL policy, we pose an adversarial agent against the fixed trained policy; the goal is to perturb the parameter space of the learned policy. We demonstrate that the most sophisticated deep policies fail in the presence of adversarial perturbations.• second, we formulate an iterative dynamic zero-sum, two player game, where each agent executes an opposite reaction to its pair: a concave-convex problem follows explicitly, and our goal is to achieve a saddle point equilibrium, where the state is everywhere defined but possibly infinite-valued).Noting that lack of generalization of learned reward functions to the real-world can be thought of as external disturbance that perturb the system dynamics, we formulate the learning of robust control policies as a zero-sum two player Markov game -an iterative dynamic game (iDG) -that pits an adversarial agent against a protagonist agent.The controller aims to minimize a given cost while the second agent, an adversary aims to maximize the given cost in the presence of an additive disturbance. We run the algorithm in finite episodic settings and show a dynamic game approach aimed at generating policies that are maximally robust.The content of this paper is thus organized: we review relevant literature to our contribution in Sec. 2; we then provide an H ∞ background in Sec. BID2 . This H ∞ technical introduction will be used in formulating the design of perturbation signals in Sec. BID3 . Without loss of generality, we provide a formal treatment of the iDG algorithm within the guided policy search framework in Sec. 5. Experimental evaluation on multiple robots is provided in Sec. 6 followed by conclusions in Sec. 7. We have evaluated the sensitivity of select deep reinforcement learning algorithms and shown that despite the most carefully designed policies, such policies implemented on real-world agents exhibit a potential for disastrous performances when unexpected such as when there exist modeling errors and discrepancy between training environment and real-world roll-outs (as evidenced by the results from the two dynamics the agent faces in our sensitivity experiment). We then test the dynamic trajectory optimization two-player algorithm on a robot motor task using Levine et al's BID13 's guided policy search algorithm. In our implementation of the dynamic game algorithm, we focus on the robustness parameters that cause the robot's policy to fail in the presence of the erstwhile sensysensitivity parameter. We demonstrate that our two-player game framework allows agents operating under nonlinear dynamics to learn the underlying dynamics under significantly more finite samples than vanilla GPS algorithm does -thus improving upon the Gaussian model mixture method used in BID0 and BID13 .Having agents that are robust to unmodeled nonlinearities, dynamics, and high frequency modes in a nonlinear dynamical system has long been a fundamental question that control theory strives to achieve. To the best of our knowledge, we are not aware of other works that addresses the robustness of deep policies that are trained end-to-end from a maximal robustness perspective. In future work, we hope to replace the crude Gaussian Mixture Model for the dynamics with a more sophisticated nonlinear model, and evaluate how the agent behaves in the presence of unknown dynamics.",present method evaluating sensitivity deep reinforcement learning RL policies. also formulate zero-sum dynamic game designing robust deep reinforcement learning policies. approach mitigates brittleness policies when agents are trained simulated environment are later exposed real world where it is hazardous employ RL policies. framework training deep RL policies involve zero-sum dynamic game adversarial agent where the goal is to drive system dynamics saddle region. Using variant guided policy search algorithm where each agent learns adopt robust policies require less samples learning dynamics performs better GPS algorithm. Without loss generality demonstrate deep RL policies trained fashion will be maximally robust worst possible adversarial disturbances. Deep reinforcement learning RL complex agent behavior realistic environments usually combines function approximation techniques learning-based control. good RL controller should guarantee fulfillment performance specifications external disturbances modeling errors. Quite often practice however is not case -with deepRL policies often generalizing well real-world scenarios. can be attributed inherent differences training testing environments. Recently have been efforts integrating function approximation techniques learning-based control end-to-end fashion order have systems optimize objectives guaranteeing generalization environmental uncertainties. Examples include trajectory-based optimization known dynamics BID16 BID25 trajectory optimization unknown dynamics guided policy search algorithms BID0 BID13 BID15.While methods produce performance efficiency agent tasks real world are sensitivity questions policies need addressed how guarantee maximally robust deep RL policies presence external disturbances modeling errors. typical approach employed minimizing sample inefficiency is to engineer agent's policy simulated environment later transfer policies physical environments. However questions robustness persist scenarios agent often has to cope modeling errors new sensory inputs different environment. continuous control tasks learned policies may become brittle presence external perturbations slight change system dynamics may significantly affect performance learned controller BID20 -defeating purpose robust policy is learned environmental interaction.The contribution paper is two-fold two-fold • first provide framework demonstrates brittleness state-of-the-art deep RL policy;specifically given trained RL policy pose adversarial agent fixed trained policy;goal is to perturb parameter space learned policy. demonstrate sophisticated deep policies fail presence adversarial perturbations.• second formulate iterative dynamic zero-sum two player game where each agent executes opposite reaction pair:concave-convex problem follows explicitly where the goal is to achieve saddle point equilibrium where the state is everywhere defined possibly infinite-valued.Noting lack generalization learned reward functions real-world can be thought external disturbance perturb system dynamics formulate learning robust control policies zero-sum two player Markov game -an iterative dynamic game iDG -that pits adversarial agent protagonist agent.The controller aims minimize given cost second agent adversary aims maximize given cost presence additive disturbance. run algorithm finite episodic settings show dynamic game approach aimed generating policies are maximally robust.The content paper is thus organized:review relevant literature contribution Sec. 2;provide H ∞ background Sec. BID2. H ∞ technical introduction will be used formulating design perturbation signals Sec. BID3. Without loss generality provide formal treatment iDG algorithm within guided policy search framework Sec. 5. Experimental evaluation multiple robots is provided Sec. 6 followed conclusions Sec. 7. have evaluated sensitivity select deep reinforcement learning algorithms shown despite carefully designed policies policies implemented real-world agents exhibit potential disastrous performances when unexpected when there exist modeling errors discrepancy training environment real-world roll-outs evidenced results two dynamics agent faces sensitivity experiment test dynamic trajectory optimization two-player algorithm robot motor task using Levine et al's BID13 's guided policy search algorithm. implementation dynamic game algorithm focus robustness parameters cause robot's policy fail presence erstwhile sensysensitivity parameter. demonstrate two-player game framework allows agents operating nonlinear dynamics learn underlying dynamics significantly finite samples vanilla GPS algorithm does -thus improving upon Gaussian model mixture method used BID0 BID13.Having agents are robust unmodeled nonlinearities dynamics high frequency modes nonlinear dynamical system has long fundamental question control theory strives achieve. best knowledge are not aware works addresses robustness deep policies are trained end-to-end maximal robustness perspective. future work hope replace crude Gaussian Mixture Model dynamics sophisticated nonlinear model evaluate how the agent behaves presence unknown dynamics.,1143,787,356,0.012,1.452,2025/11/05 17:19:02,0.01,1.541,0.3800623052959498,346.046
"Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we provide a quantitative analysis of the robustness of classifiers to universal perturbations, and draw a formal link between the robustness to universal perturbations, and the geometry of the decision boundary. Specifically, we establish theoretical bounds on the robustness of classifiers under two decision boundary models (flat and curved models). We show in particular that the robustness of deep networks to universal perturbations is driven by a key property of their curvature: there exist shared directions along which the decision boundary of deep networks is systematically positively curved. Under such conditions, we prove the existence of small universal perturbations. Our analysis further provides a novel geometric method for computing universal perturbations, in addition to explaining their properties. Despite the success of deep neural networks in solving complex visual tasks BID11 ; BID15 , these classifiers have recently been shown to be highly vulnerable to perturbations in the input space. In BID24 , state-of-the-art classifiers are empirically shown to be vulnerable to universal perturbations: there exist very small imageagnostic perturbations that cause most natural images to be misclassified. The existence of universal perturbation is further shown in Hendrik BID12 to extend to other visual tasks, such as semantic segmentation. Universal perturbations fundamentally differ from the random noise regime, and exploit essential properties of deep networks to misclassify most natural images with perturbations of very small magnitude. Why are state-of-the-art classifiers highly vulnerable to these specific directions in the input space? What do these directions represent? To answer these questions, we follow a theoretical approach and find the causes of this vulnerability in the geometry of the decision boundaries induced by deep neural networks. For deep networks, we show that the key to answering these questions lies in the existence of shared directions (across different datapoints) along which the decision boundary is highly curved. This establishes fundamental connections between geometry and robustness to universal perturbations, and thereby reveals new properties of the decision boundaries induced by deep networks.Our aim here is to derive an analysis of the vulnerability to universal perturbations in terms of the geometric properties of the boundary. To this end, we introduce two decision boundary models: 1) the locally flat model assumes that the first order linear approximation of the decision boundary holds locally in the vicinity of the natural images, and 2) the locally curved model provides a second order local description of the decision boundary, and takes into account the curvature information. We summarize our contributions as follows:• Under the locally flat decision boundary model, we show that classifiers are vulnerable to universal directions as long as the normals to the decision boundaries in the vicinity of natural images are correlated (i.e., they approximately span a low dimensional space). This result formalizes and proves some of the empirical observations made in BID24 .• Under the locally curved decision boundary model, the robustness to universal perturbations is instead driven by the curvature of the decision boundary; we show that the existence of shared directions along which the decision boundary is positively 1 curved implies the existence of very small universal perturbations.• We show that state-of-the-art deep nets remarkably satisfy the assumption of our theorem derived for the locally curved model: there actually exist shared directions along which the decision boundary of deep neural networks are positively curved. Our theoretical result consequently captures the large vulnerability of state-of-the-art deep networks to universal perturbations.• We finally show that the developed theoretical framework provides a novel (geometric) method for computing universal perturbations, and further explains some of the properties observed in BID24 (e.g., diversity, transferability) regarding the robustness to universal perturbations. In this paper, we analyzed the robustness of classifiers to universal perturbations, under two decision boundary models: Locally flat and curved. We showed that the first are not robust to universal directions, provided the normal vectors in the vicinity of natural images are correlated. While this model explains the vulnerability for e.g., linear classifiers, this model discards the curvature information, which is essential to fully analyze the robustness of deep nets to universal perturbations. The second, classifiers with curved decision boundaries, are instead not robust to universal perturbations, provided the existence of a shared subspace along which the decision boundary is positively curved (for most 7 We used m = 1 in this experiment as the matrix H is prohibitively large for ImageNet. Figure 9 : Diversity of universal perturbations randomly sampled from the subspace S c . The normalized inner product between two perturbations is less than 0.1. directions). We empirically verify this assumption for deep nets. Our analysis hence explains the existence of universal perturbations, and further provides a purely geometric approach for computing such perturbations, in addition to explaining properties of perturbations, such as their diversity.Other authors have focused on the analysis of the robustness properties of SVM classifiers (e.g., BID33 ) and new approaches for constructing robust classifiers (based on robust optimization) Caramanis et al. FORMULA2 ; BID16 . More recently, some have assessed the robustness of deep neural networks to different regimes such as adversarial perturbations BID29 ; BID1 , random noise , and occlusions BID28 BID5 . The robustness of classifiers to adversarial perturbations has been specifically studied in BID29 ; BID8 ; ; BID2 ; BID0 , followed by works to improve the robustness BID20 ; BID10 BID26 ; BID3 , and attempts at explaining the phenomenon in BID8 ; BID6 ; BID30 ; BID31 . This paper however differs from these previous works as we study universal (imageagnostic) perturbations that can fool every image in a dataset, as opposed to image-specific adversarial perturbations that are not universal across datapoints (as shown in BID24 ). Moreover, explanations that hinge on the output of a deep network being well approximated by a linear function of the inputs f (x) = W x + b are inconclusive, as the assumption is violated even for relatively small networks. We show here that it is precisely the large curvature of the decision boundary that causes vulnerability to universal perturbations. Our bounds indeed show an increasing vulnerability with respect to the curvature of the decision boundary, and represent up to our knowledge the first quantitative result showing tight links between robustness and curvature. In addition, we show empirically that the first-order approximation of the decision boundary is not sufficient to explain the high vulnerability to universal perturbations ( Fig. 7 (b) ). Recent works have further proposed new methods for computing universal perturbations Mopuri et al. FORMULA2 ; BID14 ; instead, we focus here on an analysis of the phenomenon of vulnerability to universal perturbations, while also providing a constructive approach to compute universal perturbations leveraging our curvature analysis. Finally, it should be noted that recent works have studied properties of deep networks from a geometric perspective (such as their expressivity BID27 ; BID22 ); our focus is different in this paper as we analyze the robustness with the geometry of the decision boundary.Our analysis hence shows that to construct classifiers that are robust to universal perturbations, it is key to suppress this subspace of shared positive directions, which can possibly be done through regularization of the objective function. This will be the subject of future works.",Deep networks have recently shown vulnerable universal perturbations:exist small image-agnostic perturbations cause natural images misclassified classifiers. paper provide quantitative analysis robustness classifiers universal perturbations draw formal link robustness universal perturbations geometry decision boundary. Specifically establish theoretical bounds robustness classifiers two decision boundary models flat curved models show particular robustness deep networks universal perturbations is driven key property curvature:exist shared directions along which the decision boundary deep networks is systematically positively curved. conditions prove existence small universal perturbations. analysis provides novel geometric method computing universal perturbations addition explaining properties. Despite success deep neural networks solving complex visual tasks BID11;BID15 classifiers have recently shown highly vulnerable perturbations input space. BID24 state-of-the-art classifiers are empirically shown vulnerable universal perturbations:exist small imageagnostic perturbations cause natural images misclassified. existence universal perturbation is further shown Hendrik BID12 extend visual tasks semantic segmentation. Universal perturbations fundamentally differ random noise regime exploit essential properties deep networks misclassify natural images perturbations small magnitude. Why are state-of-the-art classifiers highly vulnerable specific directions input space? What do these directions represent? answer questions follow theoretical approach find causes vulnerability geometry decision boundaries induced deep neural networks. deep networks show key answering questions lies existence shared directions across different datapoints along which the decision boundary is highly curved. establishes fundamental connections geometry robustness universal perturbations thereby reveals new properties decision boundaries induced deep networks.Our aim is to derive analysis vulnerability universal perturbations terms geometric properties boundary. end introduce two decision boundary models:1 locally flat model assumes first order linear approximation decision boundary holds locally vicinity natural images 2 locally curved model provides second order local description decision boundary takes account curvature information. summarize contributions follows:• locally flat decision boundary model show classifiers are vulnerable universal directions long normals decision boundaries vicinity natural images are correlated.e approximately span low dimensional space result formalizes proves empirical observations made BID24.• locally curved decision boundary model robustness universal perturbations is instead driven curvature decision boundary;show existence shared directions along which the decision boundary is positively 1 curved implies existence small universal perturbations.• show state-of-the-art deep nets remarkably satisfy assumption theorem derived locally curved model:actually exist shared directions along which the decision boundary deep neural networks are positively curved. theoretical result consequently captures large vulnerability state-of-the-art deep networks universal perturbations.• finally show developed theoretical framework provides novel geometric method computing universal perturbations explains properties observed BID24 e.g diversity transferability regarding robustness universal perturbations. paper analyzed robustness classifiers universal perturbations two decision boundary models:Locally flat curved. showed first are not robust universal directions provided normal vectors vicinity natural images are correlated. model explains vulnerability e.g linear classifiers model discards curvature information which is essential fully analyze robustness deep nets universal perturbations. second classifiers curved decision boundaries are instead robust universal perturbations provided existence shared subspace along which the decision boundary is positively curved 7 used 1 experiment matrixH is prohibitively large ImageNet. Figure9:Diversity universal perturbations randomly sampled subspace c. normalized inner product two perturbations is less 0.1 directions empirically verify assumption deep nets. analysis hence explains existence universal perturbations provides purely geometric approach computing perturbations addition explaining properties perturbations diversity.Other authors have focused analysis robustness properties SVM classifiers e.g BID33 new approaches constructing robust classifiers based robust optimization Caramanisetal. FORMULA2;BID16. recently have assessed robustness deep neural networks different regimes adversarial perturbations BID29;BID1 random noise occlusions BID28 BID5. robustness classifiers adversarial perturbations has been specifically studied BID29;BID8;BID2;BID0 followed works improve robustness BID20;BID10 BID26;BID3 attempts explaining phenomenon BID8;BID6;BID30;BID31. paper however differs previous works study universal imageagnostic perturbations can fool every image dataset opposed image-specific adversarial perturbations are not universal across datapoints shown BID24 Moreover explanations hinge output deep network well approximated linear function inputsf x Wx+b are inconclusive assumption is violated even relatively small networks. show is precisely large curvature decision boundary causes vulnerability universal perturbations. bounds indeed show increasing vulnerability respect curvature decision boundary represent knowledge first quantitative result showing tight links robustness curvature. addition show empirically first-order approximation decision boundary is not sufficient explain high vulnerability universal perturbations Fig. 7 b Recent works have further proposed new methods computing universal perturbations Mopuri etal. FORMULA2;BID14;instead focus analysis phenomenon vulnerability universal perturbations also providing constructive approach compute universal perturbations leveraging curvature analysis. Finally should be noted recent works have studied properties deep networks geometric perspective expressivity BID27;BID22 focus is different paper analyze robustness geometry decision boundary.Our analysis hence shows construct classifiers are robust universal perturbations is key suppress subspace shared positive directions which can possibly done regularization objective function. will be the subject future works.,1485,984,501,0.023,1.509,2025/11/05 17:19:02,0.01,1.432,0.5576323987538936,490.02
"Behavioral skills or policies for autonomous agents are conventionally learned from reward functions, via reinforcement learning, or from demonstrations, via imitation learning. However, both modes of task specification have their disadvantages: reward functions require manual engineering, while demonstrations require a human expert to be able to actually perform the task in order to generate the demonstration. Instruction following from natural language instructions provides an appealing alternative: in the same way that we can specify goals to other humans simply by speaking or writing, we would like to be able to specify tasks for our machines. However, a single instruction may be insufficient to fully communicate our intent or, even if it is, may be insufficient for an autonomous agent to actually understand how to perform the desired task. In this work, we propose an interactive formulation of the task specification problem, where iterative language corrections are provided to an autonomous agent, guiding it in acquiring the desired skill. Our proposed language-guided policy learning algorithm can integrate an instruction and a sequence of corrections to acquire new skills very quickly. In our experiments, we show that this method can enable a policy to follow instructions and corrections for simulated navigation and manipulation tasks, substantially outperforming direct, non-interactive instruction following. Behavioral skills or policies for autonomous agents are typically specified in terms of reward functions (in the case of reinforcement learning) or demonstrations (in the case of imitation learning). However, both reward functions and demonstrations have downsides as mechanisms for communicating goals. Reward functions must be engineered manually, which can be challenging in real-world environments, especially when the learned policies operate directly on raw sensory perception. Sometimes, simply defining the goal of the task requires engineering the very perception system that end-to-end deep learning is supposed to acquire. Demonstrations sidestep this challenge, but require a human demonstrator to actually be able to perform the task, which can be cumbersome or even impossible. When humans must communicate goals to each other, we often use language. Considerable research has also focused on building autonomous agents that can follow instructions provided via language BID7 ; BID8 ). However, a single instruction may be insufficient to fully communicate the full intent of a desired behavior. For example, if we would like a robot to position an object on a table in a particular place, we might find it easier to guide it by telling it which way to move, rather than verbally defining a coordinate in space. Furthermore, an autonomous agent might be unable to deduce how to perform a task from a single instruction, even if it is very precise. In both cases, interactive and iterative corrections can help resolve confusion and ambiguity, and indeed humans often employ corrections when communicating task goals to each other.In this paper, our goal is to enable an autonomous agent to accept instructions and then iteratively adjust its policy by incorporating interactive corrections (illustrated in Figure 1 ). This type of in-theloop supervision can guide the learner out of local optima, provide fine-grained task definition, and is natural for humans to provide to the agent. As we discuss in Section 2, iterative language corrections can be substantially more informative than simpler forms of supervision, such as preferences, while being substantially easier and more natural to provide than reward functions or demonstrations.Figure 1: An example where corrections disambiguate an instruction. The agent is unable to fully deduce the user's intent from the instruction alone and iterative language corrections guide the agent to the correct position. Our method is concerned with meta-learning policies that can ground language corrections in their environment and use them to improve through iterative feedback.In order to effectively use language corrections, the agent must be able to ground these corrections to concrete behavioral patterns. We propose an end-to-end algorithm for grounding iterative language corrections by using a multi-task setup to meta-train a model that can ingest its own past behavior and a correction, and then correct its behavior to produce better actions. During a meta-training phase, this model is iteratively retrained on its own behavior (and the corresponding correction) on a wide distribution of known tasks. The model learns to correct the types of mistakes that it actually tends to make in the world, by interpreting the language input. At meta-test time, this model can then generalize to new tasks, and learn those tasks quickly through iterative language corrections.The main contributions of our work are the formulation of guided policies with language (GPL) via meta-learning, as well as a practical GPL meta-learning algorithm and model. We train on English sentences sampled from a hand-designed grammar as a first step towards real human-in-the-loop supervision. We evaluate our approach on two simulated tasks -multi-room object manipulation and robotic object relocation. The first domain involves navigating a complex world with partial observation, seeking out objects and delivering them to user-specified locations. The second domain involves controlling a robotic gripper in a continuous state and action space to move objects to precise locations in relation to other objects. This requires the policy to ground the corrections in terms of objects and places, and to control and correct complex behavior. We presented meta-learning for guided policies with language (GPL), a framework for interactive learning of tasks with in-the-loop language corrections. In GPL , the policy attempts successive trials in the environment, and receives language corrections that suggest how to improve the next trial over the previous one. The GPL model is trained via meta-learning, using a dataset of other tasks to learn how to ground language corrections in terms of behaviors and objects. While our method currently uses fake language, future work could incorporate real language at training time. To scale corrections to real-world tasks, it is vital to handle new concepts, in terms of actions or objects, not seen at training time. Approachs to handling these new concepts could be innovations at the model level, such as using meta-learning, or at the interface level, allowing humans to describe new objects to help the agent. It is possible to visualize failure cases, which illuminate the behavior of the algorithm on challenging tasks. In the failure case in FIG9 , we note that the agent is able to successfully enter the purple room, pickup the green ball, and exit. However, after it receives the fourth correction telling it to go to the green goal, it forgets to pick up the green ball. This behavior can likely be improved by varying corrections more at training time, and providing different corrections if an agent is unable to comprehend the first one.Additionally, we present a success case in Figure 9 , where the agent successfully learns to solve the task through iterative corrections, making further progress in each frame.",Behavioral skills policies autonomous agents are conventionally learned reward functions via reinforcement learning demonstrations via imitation learning. However modes task specification have their disadvantages:reward functions require manual engineering demonstrations require human expert able actually perform task order generate demonstration. Instruction following natural language instructions provides appealing alternative:way can specify goals humans simply speaking writing would like able specify tasks machines. However single instruction may insufficient fully communicate intent even may insufficient autonomous agent actually understand how to perform desired task. work propose interactive formulation task specification problem where iterative language corrections are provided autonomous agent guiding acquiring desired skill. proposed language-guided policy learning algorithm can integrate instruction sequence corrections acquire new skills quickly. experiments show method can enable policy follow instructions corrections simulated navigation manipulation tasks substantially outperforming direct non-interactive instruction following. Behavioral skills policies autonomous agents are typically specified terms reward functions case reinforcement learning demonstrations case imitation learning However reward functions demonstrations have downsides mechanisms communicating goals. Reward functions must engineered manually which can be challenging real-world environments especially when the learned policies operate directly raw sensory perception. Sometimes simply defining goal task requires engineering perception system end-to-end deep learning is supposed acquire. Demonstrations sidestep challenge require human demonstrator actually able perform task which can be cumbersome even impossible. When humans must communicate goals often use language. Considerable research has also focused building autonomous agents can follow instructions provided via language BID7;BID8 However single instruction may insufficient fully communicate full intent desired behavior. example would like robot position object table particular place might find easier guide telling which way move rather verbally defining coordinate space. Furthermore autonomous agent might unable deduce how to perform task single instruction even if it is very precise. cases interactive iterative corrections can help resolve confusion ambiguity indeed humans often employ corrections when communicating task goals other.In paper goal is to enable autonomous agent accept instructions iteratively adjust policy incorporating interactive corrections illustrated Figure1 type in-theloop supervision can guide learner local optima provide fine-grained task definition is natural humans provide agent. discuss Section2 where iterative language corrections can be substantially informative simpler forms supervision preferences substantially easier natural provide reward functions demonstrations.Figure1:example where corrections disambiguate instruction. agent is unable fully deduce user's intent instruction alone iterative language corrections guide agent correct position. method is concerned meta-learning policies can ground language corrections environment use improve iterative feedback.In order effectively use language corrections where the agent must able ground corrections concrete behavioral patterns. propose end-to-end algorithm grounding iterative language corrections using multi-task setup meta-train model can ingest past behavior correction correct behavior produce better actions. meta-training phase model is iteratively retrained behavior corresponding correction wide distribution known tasks. model learns correct types mistakes actually tends make world interpreting language input. meta-test time model can then generalize new tasks learn tasks quickly iterative language corrections.The main contributions work are the formulation guided policies language GPL via meta-learning well practical GPL meta-learning algorithm model. train English sentences sampled hand-designed grammar first step towards real human-in-the-loop supervision. evaluate approach two simulated tasks -multi-room object manipulation robotic object relocation. first domain involves navigating complex world partial observation seeking objects delivering user-specified locations. second domain involves controlling robotic gripper continuous state action space move objects precise locations relation objects. requires policy ground corrections terms objects places control correct complex behavior. presented meta-learning guided policies language GPL framework interactive learning tasks in-the-loop language corrections. GPL policy attempts successive trials environment receives language corrections suggest how to improve next trial previous one. GPL model is trained via meta-learning using dataset tasks learn how to ground language corrections terms behaviors objects. method currently uses fake language future work could incorporate real language training time. scale corrections real-world tasks is vital handle new concepts terms actions objects seen training time. Approachs handling new concepts could innovations model level using meta-learning interface level allowing humans describe new objects help agent. is possible visualize failure cases which illuminate behavior algorithm challenging tasks. failure case FIG9 note agent is able successfully enter purple room pickup green ball exit. However receives fourth correction telling go green goal forgets pick green ball. behavior can likely improved varying corrections training time providing different corrections if an agent is unable comprehend first one.Additionally present success case Figure9 where the agent successfully learns solve task iterative corrections making progress frame.,1308,835,473,0.015,1.566,2025/11/05 17:19:02,0.01,1.419,0.7352024922118381,458.354
"Deep generative models such as Generative Adversarial Networks (GANs) and
 Variational Auto-Encoders (VAEs) are important tools to capture and investigate
 the properties of complex empirical data. However, the complexity of their inner
 elements makes their functionment challenging to assess and modify. In this
 respect, these architectures behave as black box models. In order to better
 understand the function of such networks, we analyze their modularity based on
 the counterfactual manipulation of their internal variables. Our experiments on the
 generation of human faces with VAEs and GANs support that modularity between
 activation maps distributed over channels of generator architectures is achieved
 to some degree, can be used to better understand how these systems operate and allow meaningful transformations of the generated images without further training.
 erate and edit the content of generated images. Deep generative models have proven powerful in learning to design realistic images in a variety of complex domains (handwritten digits, human faces, interior scenes). Complex neural architectures are now used to learn complex empirical data distributions by designing a non-linear function mapping a latent space to the space observations. In particular, two distinct approaches have recently emerged as state of the art: Generative Adversarial Networks (GANs) BID4 , and Variational Autoencoders (VAEs) BID8 BID17 . Such architectures relate to a question that work in Neuroscience and Computer vision have long since tried to address: the relation between an observed scene and its high level internal representation. This has been framed using two objects: (1) the mapping of a 3D scene to its perceived (2D) image, called forward optics, (2) the converse mapping, called inverse optics, (see e.g. BID7 ). Many computer vision algorithms have relied on inverse graphics approaches that model both forward and inverse optics simultaneously BID9 . In recent years, emphasis has been put on producing compact descriptions of the scene in terms of high level features reflecting a disentangled latent representation that can be mapped back to the image. However, the fundamental asymmetry between the structure of original forward and inverse optics mappings has received less attention. A key difference is that forward optics can be concisely described with a restricted set of equations taking into account physical parameters of the scene, while inverse optics does not have an explicit form and relies heavily on prior assumptions to be solved numerically. The simplicity of the forward optics may allow an agent to efficiently manipulate and update internal representations, for instance to plan interactions with the outside world, following a predictive coding principle BID16 . This supports that modularity of generative models should be assessed and enforced in order to understand and manipulate representations.Achieving this aim for deep architectures is challenging, because they mostly behave as black boxes, making it difficult for users to interact with the generative process. Indeed, we can act on how the network is trained (e.g. the optimized objective), what it learns to generate, but not on how the learned generative process operates. For example, to use a face generator to create a face combining the eyes of one generated face with remaining features of another one may be achieved by either additional training or complex manipulation of the network's input or output. Directly influencing the generative process learned by the network on the other hand is made difficult due to the complexity of the function class entailed by the networks' non-linearities and high dimensional parameter space. To grasp the properties of such a system, a possible approach is to intervene on parts of the architecture that implements the generative function. Ideally, the effect of such interventions on the output would be interpretable. This suggests we should uncover a modular structure in those architectures, such that each part of a network can be assigned a specific function.In this paper, we propose that modularity can be quantified and exploited in a causal framework to infer whether modules within the architecture can be further disentangled. This hypothesis relies on the general principle of Independence of Mechanisms stating that the various mechanisms involved in generating the observed data can be modified individually without affecting each other BID14 . It has been recently demonstrated that this principle can be applied to generative models encountered in machine learning BID0 . One key aspect of causality frameworks is to allow evaluating with counterfactuals how the outcome of a observed system would have changed, provided some variables would have taken different values. We use such counterfactuals to assess the role of specific internal variables in the overall functioning of trained deep generative models and uncover the modular structure of these systems. We start by introducing this perspective formally with the notion of intrinsic disentanglement, and show that it extends the classical notion of disentangled representation investigated in the deep learning literature. Then, we introduce tools to analyze this disentanglement in existing systems. We show empirically how VAEs and GANs trained on a human face dataset express a form of modularity with intermediate activation maps responsible for encoding different parts of the generated images.Related work. The issue of interpretability in convolutional neural networks has been the topic of intensive investigation. Most of that research however has focused on discriminative neural networks, not generative ones. In the discriminative case, efforts have been made to find optimal activation patterns for filters BID20 , BID2 ), to find correlation between intermediate feature space and data features BID3 , BID23 or to disentangle patterns detected by various filters to compute an explanatory graph BID22 . Furthermore, explicitly enforcing modularity in networks has been tried recently with Capsule networks architectures BID18 ), although Capsule network explicitly separate the architecture in different modules before training. A more detailed overview can found in review BID21 . It is important to emphasize discriminative and generative processes differ significantly, and working on generative processes allows to directly observe the effect of changes in intermediate representations on the generated picture rather than having to correlate it back input images. The recent InfoGAN network BID1 ) and other works BID11 ; BID9 ; BID5 ) in disentanglement of latent variables in generative models can be seen as what we define as extrinsic disentanglement. As such, we believe our intrinsic disentanglement perspective should be complementary with such approaches and are not in direct competition. Finally our approach relates to modularity and invariance principles formulated in the field of causality, in particular as formalized by BID0 . The purpose of this paper was to introduce a methodology to assess modularity in deep networks. Modularity may involve different aspects, and strongly depends on the nature of the modeled data. In this paper, we focused on features of the image that preferentially occur in specific parts of the generated images. This is a reasonable assumption for the CelebA dataset, given that the faces are spatially aligned. To some extent this is also true for the CIFAR10 dataset, where objects preferentially appear at the center of the image and the soil and sky in the background will be found at the bottom and top respectively. This approach may however have some limitations when looking at different datasets deprived from such spatial organization. In this case, capturing the structure of output variations induced by hybridization may require a more general approach. In principle, multidimensional technique such as Principal Component Analysis and non-linear generalizations may be able to characterize counterfactuals of each channels in order to further generate relevant modules following the steps described in the present work.Another aspect that is left to further work is how to optimize modularity in deep generative networks. We believe that classical (extrinsic) disentanglement approaches will not help, as they focus on the input of the network without control on its internal structure. While current generative models seem to exhibit some amount of modularity, improving it may require specific learning objectives as well as an appropriate choice of architectures.",Deep generative models Generative Adversarial Networks GANs Variational Auto-Encoders VAEs are important tools capture investigate properties complex empirical data. However complexity inner elements makes functionment challenging assess modify. respect architectures behave black box models. order better understand function networks analyze modularity based counterfactual manipulation internal variables. experiments generation human faces VAEs GANs support modularity activation maps distributed channels generator architectures is achieved degree can be used better understand how these systems operate allow meaningful transformations generated images without training. erate edit content generated images. Deep generative models have proven powerful learning design realistic images variety complex domains handwritten digits human faces interior scenes Complex neural architectures are now used learn complex empirical data distributions designing non-linear function mapping latent space space observations. particular two distinct approaches have recently emerged state art:Generative Adversarial Networks GANs BID4 Variational Autoencoders VAEs BID8 BID17. architectures relate question work Neuroscience Computer vision have long since tried address:relation observed scene high level internal representation. has been framed using two objects:1 mapping 3D scene perceived 2D image called forward optics 2 converse mapping called inverse optics see e.g BID7 Many computer vision algorithms have relied inverse graphics approaches model forward inverse optics simultaneously BID9. recent years emphasis has been put producing compact descriptions scene terms high level features reflecting disentangled latent representation can be mapped back image. However fundamental asymmetry structure original forward inverse optics mappings has received less attention. key difference is that forward optics can be concisely described restricted set equations taking account physical parameters scene inverse optics does not have an explicit form relies heavily prior assumptions solved numerically. simplicity forward optics may allow agent efficiently manipulate update internal representations instance plan interactions outside world following predictive coding principle BID16. supports modularity generative models should be assessed enforced order understand manipulate representations.Achieving aim deep architectures is challenging mostly behave black boxes making difficult users interact generative process. Indeed can act how the network is trained e.g optimized objective what it learns generate how the learned generative process operates. example use face generator create face combining eyes one generated face remaining features another one may achieved either additional training complex manipulation network's input output. Directly influencing generative process learned network hand is made difficult due complexity function class entailed networks' non-linearities high dimensional parameter space. grasp properties system possible approach is to intervene parts architecture implements generative function. Ideally effect interventions output would interpretable. suggests should uncover modular structure architectures part network can be assigned specific function.In paper propose modularity can be quantified exploited causal framework infer whether modules within architecture can be further disentangled. hypothesis relies general principle Independence Mechanisms stating various mechanisms involved generating observed data can be modified individually without affecting BID14. has been recently demonstrated principle can be applied generative models encountered machine learning BID0. One key aspect causality frameworks is to allow evaluating counterfactuals how the outcome observed system would have changed provided variables would have taken different values. use counterfactuals assess role specific internal variables overall functioning trained deep generative models uncover modular structure systems. start introducing perspective formally notion intrinsic disentanglement show extends classical notion disentangled representation investigated deep learning literature. introduce tools analyze disentanglement existing systems. show empirically how VAEs GANs trained human face dataset express form modularity intermediate activation maps responsible encoding different parts generated images.Related work. issue interpretability convolutional neural networks has been the topic intensive investigation. research however has focused discriminative neural networks generative ones. discriminative case efforts have been made find optimal activation patterns filters BID20 BID2 find correlation intermediate feature space data features BID3 BID23 disentangle patterns detected various filters compute explanatory graph BID22. Furthermore explicitly enforcing modularity networks has been tried recently Capsule networks architectures BID18 although Capsule network explicitly separate architecture different modules training. detailed overview can found review BID21. is important emphasize discriminative generative processes differ significantly working generative processes allows directly observe effect changes intermediate representations generated picture rather correlate back input images. recent InfoGAN network BID1 works BID11;BID9;BID5 disentanglement latent variables generative models can be seen what we define extrinsic disentanglement. believe intrinsic disentanglement perspective should be complementary approaches are not in direct competition. Finally approach relates modularity invariance principles formulated field causality particular formalized BID0. purpose paper was to introduce methodology assess modularity deep networks. Modularity may involve different aspects strongly depends nature modeled data. paper focused features image preferentially occur specific parts generated images. is a reasonable assumption CelebA dataset given faces are spatially aligned. extent is also true CIFAR10 dataset where objects preferentially appear center image soil sky background will be found bottom top respectively. approach may however have some limitations when looking different datasets deprived spatial organization. case capturing structure output variations induced hybridization may require general approach. principle multidimensional technique Principal Component Analysis non-linear generalizations may able characterize counterfactuals channels order generate relevant modules following steps described present work.Another aspect is left work is how to optimize modularity deep generative networks. believe classical extrinsic disentanglement approaches will not help focus input network without control internal structure. current generative models seem exhibit amount modularity improving may require specific learning objectives well appropriate choice architectures.,1571,1059,512,0.017,1.483,2025/11/05 17:19:02,0.01,1.707,0.4766355140186917,519.668
"Relational databases store a significant amount of the worlds data. However, accessing this data currently requires users to understand a query language such as SQL. We propose Seq2SQL, a deep neural network for translating natural language questions to corresponding SQL queries. Our model uses rewards from in the loop query execution over the database to learn a policy to generate the query, which contains unordered parts that are less suitable for optimization via cross entropy loss. Moreover, Seq2SQL leverages the structure of SQL to prune the space of generated queries and significantly simplify the generation problem. In addition to the model, we release WikiSQL, a dataset of 80654 hand-annotated examples of questions and SQL queries distributed across 24241 tables fromWikipedia that is an order of magnitude larger than comparable datasets. By applying policy based reinforcement learning with a query execution environment to WikiSQL, Seq2SQL outperforms a state-of-the-art semantic parser, improving execution accuracy from 35.9% to 59.4% and logical form accuracy from 23.4% to 48.3%. Relational databases store a vast amount of today's information and provide the foundation of applications such as medical records BID12 , financial markets BID3 , and customer relations management BID20 ). However, accessing relational databases requires an understanding of query languages such as SQL, which, while powerful, is difficult to master. Natural language interfaces (NLI), a research area at the intersection of natural language processing and human-computer interactions, seeks to provide means for humans to interact with computers through the use of natural language BID0 . We investigate one particular aspect of NLI applied to relational databases: translating natural language questions to SQL queries.Our main contributions in this work are two-fold. First, we introduce Seq2SQL, a deep neural network for translating natural language questions to corresponding SQL queries. Seq2SQL, shown in FIG0 , consists of three components that leverage the structure of SQL to prune the output space of generated queries. Moreover, it uses policy-based reinforcement learning (RL) to generate the conditions of the query, which are unsuitable for optimization using cross entropy loss due to their unordered nature. We train Seq2SQL using a mixed objective, combining cross entropy losses and RL rewards from in-the-loop query execution on a database. These characteristics allow Seq2SQL to achieve state-of-the-art results on query generation.Next, we release WikiSQL, a corpus of 80654 hand-annotated instances of natural language questions, SQL queries, and SQL tables extracted from 24241 HTML tables from Wikipedia. WikiSQL is an order of magnitude larger than previous semantic parsing datasets that provide logical forms along with natural language utterances. We release the tables used in WikiSQL both in raw JSON format as well as in the form of a SQL database. Along with WikiSQL, we release a query execution engine for the database used for in-the-loop query execution to learn the policy. On WikiSQL, Seq2SQL outperforms a previously state-of-the-art semantic parsing model by BID8 , which obtains 35.9% execution accuracy, as well as an augmented pointer network baseline, which obtains 53.3% execution accuracy. By leveraging the inherent structure of We proposed Seq2SQL, a deep neural network for translating questions to SQL queries. Our model leverages the structure of SQL queries to reduce the output space of the model. To train Seq2SQL, we applied in-the-loop query execution to learn a policy for generating the conditions of the SQL query, which is unordered and unsuitable for optimization via cross entropy loss. We also introduced WikiSQL, a dataset of questions and SQL queries that is an order of magnitude larger than comparable datasets. Finally, we showed that Seq2SQL outperforms a state-of-the-art semantic parser on WikiSQL, improving execution accuracy from 35.9% to 59.4% and logical form accuracy from 23.4% to 48.3%.","Relational databases store significant amount worlds data. However accessing data currently requires users understand query language SQL. propose Seq2SQL deep neural network translating natural language questions corresponding SQL queries. model uses rewards loop query execution database learn policy generate query which contains unordered parts are less suitable optimization via cross entropy loss. Moreover Seq2SQL leverages structure SQL prune space generated queries significantly simplify generation problem. addition model release WikiSQL dataset 80654 hand-annotated examples questions SQL queries distributed across 24241 tables fromWikipedia is an order magnitude larger comparable datasets. applying policy based reinforcement learning query execution environment WikiSQL Seq2SQL outperforms state-of-the-art semantic parser improving execution accuracy 35.9 59.4 logical form accuracy 23.4 48.3%. Relational databases store vast amount today's information provide foundation applications medical records BID12 financial markets BID3 customer relations management BID20 However accessing relational databases requires understanding query languages SQL which,while powerful is difficult master. Natural language interfaces NLI research area intersection natural language processing human-computer interactions seeks provide means humans interact computers use natural language BID0. investigate one particular aspect NLI applied relational databases:translating natural language questions SQL queries.Our main contributions work are two-fold two-fold First introduce Seq2SQL deep neural network translating natural language questions corresponding SQL queries. Seq2SQL shown FIG0 consists three components leverage structure SQL prune output space generated queries. Moreover uses policy-based reinforcement learning RL generate conditions query which are unsuitable optimization using cross entropy loss due unordered nature. train Seq2SQL using mixed objective combining cross entropy losses RL rewards in-the-loop query execution database. characteristics allow Seq2SQL achieve state-of-the-art results query generation.Next release WikiSQL corpus 80654 hand-annotated instances natural language questions SQL queries SQL tables extracted 24241 HTML tables Wikipedia. WikiSQL is an order magnitude larger previous semantic parsing datasets provide logical forms along natural language utterances. release tables used WikiSQL raw JSON format well form SQL database. Along WikiSQL release query execution engine database used in-the-loop query execution learn policy. WikiSQL Seq2SQL outperforms previously state-of-the-art semantic parsing model BID8 which obtains obtains 35.9 execution accuracy well augmented pointer network baseline which obtains obtains 53.3 execution accuracy. leveraging inherent structure proposed Seq2SQL deep neural network translating questions SQL queries. model leverages structure SQL queries reduce output space model. train Seq2SQL applied in-the-loop query execution learn policy generating conditions SQL query which is unordered unsuitable optimization via cross entropy loss. also introduced WikiSQL dataset questions SQL queries is an order magnitude larger comparable datasets. Finally showed Seq2SQL outperforms state-of-the-art semantic parser WikiSQL improving execution accuracy 35.9 59.4 logical form accuracy 23.4 48.3",797,564,233,0.007,1.413,2025/11/05 17:19:02,0.0,1.8,0.2585669781931463,260.893
"We introduce Explainable Adversarial Learning, ExL, an approach for training neural networks that are intrinsically robust to adversarial attacks. We find that the implicit generative modeling of random noise with the same loss function used during posterior maximization, improves a model's understanding of the data manifold furthering adversarial robustness. We prove our approach's efficacy and provide a simplistic visualization tool for understanding adversarial data, using Principal Component Analysis. Our analysis reveals that adversarial robustness, in general, manifests in models with higher variance along the high-ranked principal components. We show that models learnt with our approach perform remarkably well against a wide-range of attacks. Furthermore, combining ExL with state-of-the-art adversarial training extends the robustness of a model, even beyond what it is adversarially trained for, in both white-box and black-box attack scenarios. Despite surpassing human performance on several perception tasks, Machine Learning (ML) models remain vulnerable to adversarial examples: slightly perturbed inputs that are specifically designed to fool a model during test time BID2 BID29 BID6 BID23 . Recent works have demonstrated the security danger adversarial attacks pose across several platforms with ML backend such as computer vision BID29 BID6 BID22 BID15 BID19 , malware detectors BID16 BID33 BID7 BID10 and gaming environments BID11 BID1 . Even worse, adversarial inputs transfer across models: same inputs are misclassified by different models trained for the same task, thus enabling simple Black-Box (BB) 1 attacks against deployed ML systems .Several works BID14 BID24 BID3 demonstrating improved adversarial robustness have been shown to fail against stronger attacks BID0 . The state-of-the-art approach for BB defense is ensemble adversarial training that augments the training dataset of the target model with adversarial examples transferred from other pre-trained models BID30 . BID21 showed that models can even be made robust to White-Box (WB) 1 attacks by closely maximizing the model's loss with Projected Gradient Descent (PGD) based adversarial training. Despite this progress, errors still appear for perturbations beyond what the model is adversarially trained for BID27 .There have been several hypotheses explaining the susceptibility of ML models to such attacks. The most common one suggests that the overly linear behavior of deep neural models in a high dimensional input space causes adversarial examples BID6 BID20 . Another hypothesis suggests that adversarial examples are off the data manifold BID28 BID18 . Combining the two, we infer that excessive linearity causes models to extrapolate their behavior beyond the data manifold yielding pathological results for slightly perturbed inputs. A question worth asking here is: Can we improve the viability of the model to generalize better on such out-of-sample data?In this paper, we propose Explainable Adversarial Learning (ExL), wherein we introduce multiplicative noise into the training inputs and optimize it with Stochastic Gradient Descent (SGD) while minimizing the overall cost function over the training data. Essentially, the input noise (randomly initialized at the beginning) is gradually learnt during the training procedure. As a result, the noise approximately models the input distribution to effectively maximize the likelihood of the class labels given the inputs. FIG0 shows the input noise learnt during different stages of training by a simple convolutional network (ConvN et2 architecture discussed in Section 3 below), learning handwritten digits from MNIST dataset BID17 . We observe that the noise gradually transforms and finally assumes a shape that highlights the most dominant features in the MNIST training data. For instance, the MNIST images are centered digits on a black background. Noise, in fact, learnt this centered characteristic . This suggests that the model not only finds the right prediction but also the right explanation. Noise inculcates this explainable behavior by discovering some knowledge about the input/output distribution during training. FIG0 shows the noise learnt with ExL on colored CIFAR10 images BID13 ) (on ResNet18 architecture BID8 ), which reveals that noise template (also RGB) learns prominent color blobs on a greyish-black background, that de-emphasizes background pixels. A recent theory BID4 suggests that adversarial examples (off manifold misclassified points) occur in close proximity to randomly chosen inputs on the data manifold that are, in fact, correctly classified. With ExL, we hypothesize that the model learns to look in the vicinity of the onmanifold data points and thereby incorporate more out-of-sample data (without using any direct data augmentation) that, in turn, improves its generalization capability in the off-manifold input space. We empirically evaluate this hypothesis by visualizing and studying the relationship between the adversarial and the clean inputs using Principal Component Analysis (PCA). Examining the intermediate layer's output, we discover that models exhibiting adversarial robustness yield significantly lower distance between adversarial and clean inputs in the Principal Component (PC) subspace.We further harness this result to establish that ExL noise modeling, indeed, acquires an improved realization of the input/output distribution characteristics that enables it to generalize better. To further substantiate our hypothesis, we also show that ExL globally reduces the dimensionality of the space of adversarial examples BID31 . We evaluate our approach on classification tasks such as MNIST, CIFAR10 and CIFAR100 and show that models trained with ExL are extensively more adversarially robust. We also show that combining ExL with ensemble/PGD adversarial training significantly extends the robustness of a model, even beyond what it is adversarially trained for, in both BB/WB attack scenarios. We proposed Explainable Adversarial Learning, ExL, as a reliable method for improving adversarial robustness. Specifically, our key findings are: 1) We show that noise modeling at the input during discriminative training improves a model's ability to generalize better for out-of-sample adversarial data (without explicit data augmentation). 2) Our PCA variance and cosine distance analysis provides a significant perspective to visualize and quantify a model's response to adversarial/clean data.A crucial question one can ask is, How to break ExL defense? The recent work BID0 shows that many defense methods cause 'gradient masking' that eventually fail. We reiterate that, ExL alone does not give a strong BB/WB defense. However, the smoothening effect of noise modeling on the loss FIG3 suggests that noise modeling decreases the magnitude of the gradient masking effect. ExL does not change the classification model that makes it easy to be scaled to larger datasets while integrating with other adversarial defense techniques. Coupled with other defense, ExL performs remarkably (even for larger values). We combine ExL with EnsAdv & PGDAdv, which do not cause obfuscated gradients and hence can withstand strong attacks, however, upto a certain point. For WB perturbations much greater than the training value, ExL+PGDAdv also breaks. In fact, for adaptive BB adversaries BID30 or adversaries that query the model to yield full prediction confidence (not just the label), ExL+EnsAdv will be vulnerable. Note, advantage with ExL is, being independent of the attack/defense method, ExL can be potentially combined with stronger attacks developed in future, to create stronger defenses.While variance and principal subspace analysis help us understand a model's behavior, we cannot fully describe the structure of the manifold learnt by the linear subspace view. However, PCA does provide a basic intuition about the generalization capability of complex image models. In fact, our PC results establish the superiority of adversarial training methods (SGD ens ; SGD P GD : BID30 ; BID21 and can be used as a valid metric to gauge adversarial susceptibility in future proposals. Finally, as our likelihood theory (Eqn.1) indicates, better noise modeling techniques with improved gradient penalties can further improve robustness and requires further investigation. Also, performing noise modeling at intermediate layers to improve variance/explainability, and hence robustness, are other future work directions.A APPENDIX A: JUSTIFICATION OF X + N VS X × N AND USE OF ∇L N ≤ 0 FOR NOISE MODELING FIG0 : For MNIST dataset, we show the noise template learnt when we use multiplicative/additive noise (N ) for Explainable Learning. The final noise-integrated image (for a sample digit '9') that is fed to the network before and after training is also shown. Additive noise disrupts the image drastically. Multiplicative noise, on the other hand, enhances the relevant pixels while eliminating the background. Accuracy corrsponding to each scenario is also shown and compared against standard SGD training scenario (without any noise). Here, we train a simple convolutional architecture (ConvNet: 10C-M-20C-M-320FC) of 2 Convolutional (C) layers with 10, 20 filters, each followed by 2×2 Max-pooling (M) and a Fully-Connected (FC) layer of size 320. We use mini-batch SGD with momentum of 0.5, learning rate (η=0.1) decayed by 0.1 every 15 epochs and batchsize 64 to learn the network parameters. We trained 3 ConvNet models independently corresponding to each scenario for 30 epochs. For the ExL scenarios, we conduct noise modelling with only negative loss gradients (∇LN ≤ 0) with noise learning rate, ηnoise = 0.001, throughout the training process. Note, the noise image shown is the average across all 64 noise templates. Figure A2 : Here, we showcase the noise learnt by a simple convolutional network (ConvNet: 10C-M-20C-M-320FC), learning the CIFAR10 data with ExL (multiplicative noise) under different gradient update conditions. As with MNIST ( FIG0 , we observe that the noise learnt enhances the region of interest while deemphasizing the background pixels. Note, the noise in this case has RGB components as a result of which we see some prominent color blobs in the noise template after training. The performance table shows that using only negative gradients (i.e. ∇LN ≤ 0) during backpropagation for noise modelling yields minimal loss in accuracy as compared to a standard SGD trained model. We use mini-batch SGD with momentum of 0.9, weight decay 5e-4, learning rate (η=0.01) decayed by 0.2 every 10 epochs and batch-size 64 to learn the network parameters. We trained 4 ConvNet models independently corresponding to each scenario for 30 epochs. For the ExL scenarios, we conduct noise modelling by backpropagating the corresponding gradient with noise learning rate (ηnoise = 0.001) throughout the training process. Note, the noise image shown is the average across all 64 noise templates. We observe that ExL noise increases the explainability (or variance) along the high rank PCs. Also, as we go deeper into the network, the absolute difference of the variance values between SGD/ExL decreases. This is expected as the contribution of input noise on the overall representations decreases as we go deeper into the network. Moreover, there is a generic-to-specific transition in the hierarchy of learnt features of a deep neural network. Thus, the linear PC subspace analysis to quantify a model's knowledge of the data manifold is more applicable in the earlier layers, since they learn more general input-related characteristics. Nonetheless, we see that ExL model yields widened explainability than SGD for each intermediate layer except the final Block4 that feeds into the output layer. We use mini-batch SGD with momentum of 0.9, weight decay 5e-4, learning rate (η=0.1) decayed by 0.1 every 30 epochs and batch-size 64 to learn the network parameters. We trained 2 ResNet-18 models independently corresponding to each scenario for 60 epochs. For noise modelling, we use ηnoise = 0.001 decayed by 0.1 every 30 epochs. Note, we used a sample set of 700 test images to conduct the PCA. FIG2 : Here, we show the variance captured in the leading Principal Component (PC) dimensions for the Conv1 and Block1 learnt activations in response to both clean and adversarial inputs for ResNet-18 models correponding to the scenarios discussed in FIG1 . The model's variance for both clean and adversarial inputs are exactly same in case of ExL/SGD for Conv1 layers. For Block1, the adversarial input variance is slighlty lower in case of SGD than that of clean input. With ExL, the variance is still the same for Block1. This indicates that PC variance statistics cannot differentiate between a model's knowledge of on-/off-manifold data. It only tells us whether a model's underlying representation has acquired more knowledge about the data manifold. To analyze a model's understanding of adversarial data, we need to look into the relationship between the clean and adversarial projection onto the PC subspace and measure the cosine distance. Note, we used the Fast Gradient Sign Method (FGSM) method BID6 to create BB adversaries with a step size of 8/255, from another independently trained ResNet-18 model (source) with standard SGD. The source attack model has the same hyperparameters as the SGD model in FIG1 and is trained for 40 epochs.","introduce Explainable Adversarial Learning ExL approach training neural networks are intrinsically robust adversarial attacks. find implicit generative modeling random noise loss function used posterior maximization improves model's understanding data manifold furthering adversarial robustness. prove approach's efficacy provide simplistic visualization tool understanding adversarial data using Principal Component Analysis. analysis reveals adversarial robustness general manifests models higher variance along high-ranked principal components. show models learnt approach perform remarkably well wide-range attacks. Furthermore combining ExL state-of-the-art adversarial training extends robustness model even beyond what it is adversarially trained white-box black-box attack scenarios. Despite surpassing human performance several perception tasks Machine Learning ML models remain vulnerable adversarial examples:slightly perturbed inputs are specifically designed fool model test time BID2 BID29 BID6 BID23. Recent works have demonstrated security danger adversarial attacks pose across several platforms ML backend computer vision BID29 BID6 BID22 BID15 BID19 malware detectors BID16 BID33 BID7 BID10 gaming environments BID11 BID1. Even worse adversarial inputs transfer across models:inputs are misclassified different models trained task thus enabling simple Black-Box BB 1 attacks deployed ML systems.Several works BID14 BID24 BID3 demonstrating improved adversarial robustness have been shown fail stronger attacks BID0. state-of-the-art approach BB defense is ensemble adversarial training augments training dataset target model adversarial examples transferred pre-trained models BID30. BID21 showed models can even made robust White-Box WB 1 attacks closely maximizing model's loss Projected Gradient Descent PGD based adversarial training. Despite progress errors still appear perturbations beyond what the model is adversarially trained BID27.There have been several hypotheses explaining susceptibility ML models attacks. common one suggests overly linear behavior deep neural models high dimensional input space causes adversarial examples BID6 BID20. Another hypothesis suggests adversarial examples are off the data manifold BID28 BID18. Combining two infer excessive linearity causes models extrapolate behavior beyond data manifold yielding pathological results slightly perturbed inputs. question worth asking is:Can we improve viability model generalize better out-of-sample data? paper propose Explainable Adversarial Learning ExL wherein introduce multiplicative noise training inputs optimize Stochastic Gradient Descent SGD minimizing overall cost function training data. Essentially input noise randomly initialized beginning is gradually learnt training procedure. result noise approximately models input distribution effectively maximize likelihood class labels given inputs. FIG0 shows input noise learnt different stages training simple convolutional network ConvN et2 architecture discussed Section3 learning handwritten digits MNIST dataset BID17. observe noise gradually transforms finally assumes shape highlights dominant features MNIST training data. instance MNIST images are centered digits black background. Noise fact learnt centered characteristic. suggests model finds right prediction also right explanation. Noise inculcates explainable behavior discovering knowledge input/output distribution training. FIG0 shows noise learnt ExL colored CIFAR10 images BID13 ResNet18 architecture BID8 which reveals noise template also RGB learns prominent color blobs greyish-black background de-emphasizes background pixels. recent theory BID4 suggests adversarial examples manifold misclassified points occur close proximity randomly chosen inputs data manifold are,in fact correctly classified. ExL hypothesize model learns look vicinity onmanifold data points thereby incorporate out-of-sample data without using direct data augmentation turn improves generalization capability off-manifold input space. empirically evaluate hypothesis visualizing studying relationship adversarial clean inputs using Principal Component Analysis PCA Examining intermediate layer's output discover models exhibiting adversarial robustness yield significantly lower distance adversarial clean inputs Principal Component PC subspace.We harness result establish ExL noise modeling indeed acquires improved realization input/output distribution characteristics enables generalize better. substantiate hypothesis also show ExL globally reduces dimensionality space adversarial examples BID31. evaluate approach classification tasks MNIST CIFAR10 CIFAR100 show models trained ExL are extensively adversarially robust. also show combining ExL ensemble/PGD adversarial training significantly extends robustness model even beyond what it is adversarially trained BB/WB attack scenarios. proposed Explainable Adversarial Learning ExL reliable method improving adversarial robustness. Specifically key findings are:1 show noise modeling input discriminative training improves model's ability generalize better out-of-sample adversarial data without explicit data augmentation 2 PCA variance cosine distance analysis provides significant perspective visualize quantify model's response adversarial/clean data.A crucial question one can ask is,How to break ExL defense? recent work BID0 shows many defense methods cause 'gradient masking' eventually fail. reiterate ExL alone does not give strongBB/WB defense. However smoothening effect noise modeling loss FIG3 suggests noise modeling decreases magnitude gradient masking effect. ExL does not change classification model makes easy scaled larger datasets integrating adversarial defense techniques. Coupled defense ExL performs remarkably even larger values combine ExL EnsAdv PGDAdv which do not cause obfuscated gradients hence can withstand strong attacks however upto certain point. WB perturbations much greater training value ExL+PGDAdv also breaks. fact adaptive BB adversaries BID30 adversaries query model yield full prediction confidence label ExL+EnsAdv will be vulnerable. Note advantage ExL is,being independent attack/defense method ExL can be potentially combined stronger attacks developed future create stronger defenses.While variance principal subspace analysis help us understand model's behavior cannot fully describe structure manifold learnt linear subspace view. However PCA does provide basic intuition generalization capability complex image models. fact PC results establish superiority adversarial training methods SGD ens;SGDPGD:BID30;BID21 can be used valid metric gauge adversarial susceptibility future proposals. Finally likelihood theory Eqn.1 indicates better noise modeling techniques improved gradient penalties can further improve robustness requires investigation. Also performing noise modeling intermediate layers improve variance/explainability hence robustness are other future work directions.A APPENDIX A:JUSTIFICATION X+NVS X×N USE ∇LN≤0 NOISE MODELING FIG0:MNIST dataset show noise template learnt when we use multiplicative/additive noise N Explainable Learning. final noise-integrated image sample digit '9' is fed network training is also shown. Additive noise disrupts image drastically. Multiplicative noise hand enhances relevant pixels eliminating background. Accuracy corrsponding scenario is also shown compared standard SGD training scenario without noise train simple convolutional architecture ConvNet:10C-M-20C-M-320FC 2 Convolutional C layers 10 20 filters followed 2×2 Max-pooling Fully-Connected FC layer size 320. use mini-batch SGD momentum 0.5 learning rate η=0.1 decayed 0.1 every 15 epochs batchsize64 learn network parameters. trained 3 ConvNet models independently corresponding scenario 30 epochs. ExL scenarios conduct noise modelling negative loss gradients ∇LN≤0 noise learning rate ηnoise 0.001 throughout training process. Note noise image shown is the average across 64 noise templates. FigureA2:showcase noise learnt simple convolutional network ConvNet:10C-M-20C-M-320FC learning CIFAR10 data ExL multiplicative noise different gradient update conditions. MNIST FIG0 observe noise learnt enhances region interest deemphasizing background pixels. Note noise case has RGB components result which we see prominent color blobs noise template training. performance table shows using negative gradients.e ∇LN≤0 backpropagation noise modelling yields minimal loss accuracy compared standard SGD trained model. use mini-batch SGD momentum 0.9 weight decay 5e-4 learning rate η=0.01 decayed 0.2 every 10 epochs batch-size64 learn network parameters. trained 4 ConvNet models independently corresponding scenario 30 epochs. ExL scenarios conduct noise modelling backpropagating corresponding gradient noise learning rate ηnoise 0.001 throughout training process. Note noise image shown is the average across 64 noise templates. observe ExL noise increases explainability variance along high rank PCs. Also go deeper network absolute difference variance values SGD/ExL decreases. is expected contribution input noise overall representations decreases go deeper network. Moreover is a generic-to-specific transition hierarchy learnt features deep neural network. Thus linear PC subspace analysis quantify model's knowledge data manifold is more applicable earlier layers since learn general input-related characteristics. Nonetheless see ExL model yields widened explainability SGD intermediate layer except final Block4 feeds output layer. use mini-batch SGD momentum 0.9 weight decay 5e-4 learning rate η=0.1 decayed 0.1 every 30 epochs batch-size64 learn network parameters. trained 2 ResNet-18 models independently corresponding scenario 60 epochs. noise modelling use ηnoise 0.001 decayed 0.1 every 30 epochs. Note used sample set 700 test images conduct PCA. FIG2:show variance captured leading Principal Component PC dimensions Conv1 Block1 learnt activations response clean adversarial inputs ResNet-18 models correponding scenarios discussed FIG1. model's variance clean adversarial inputs are exactly case ExL/SGD Conv1 layers. Block1 adversarial input variance is slighlty lower case SGD clean input. ExL variance is still Block1. indicates PC variance statistics cannot differentiate model's knowledge on-/off-manifold data. tells us whether model's underlying representation has acquired knowledge data manifold. analyze model's understanding adversarial data need look relationship clean adversarial projection onto PC subspace measure cosine distance. Note used Fast Gradient Sign Method FGSM method BID6 create BB adversaries step size 8/255 another independently trained ResNet-18 model source standard SGD. source attack model has the same hyperparameters SGD model FIG1 is trained 40 epochs.",2758,1961,797,0.034,1.406,2025/11/05 17:19:03,0.01,1.674,0.2367601246105914,866.911
"We propose a method which can visually explain the classification decision of deep neural networks (DNNs). There are many proposed methods in machine learning and computer vision seeking to clarify the decision of machine learning black boxes, specifically DNNs.   All of these methods try to gain insight into why the network ""chose class A"" as an answer. Humans, when searching for explanations, ask two types of questions. The first question is, ""Why did you choose this answer? "" The second question asks, ""Why did you not choose answer B over A?"" The previously proposed methods are either not able to provide the latter directly or efficiently.

 We introduce a method capable of answering the second question both directly and efficiently. In this work, we limit the inputs to be images. In general, the proposed method generates explanations in the input space of any model capable of efficient evaluation and gradient evaluation. We provide results, showing the superiority of this approach for gaining insight into the inner representation of machine learning models. Deep neural networks (DNN) have shown extraordinary performance on computer vision tasks such as image classification BID25 BID23 BID24 BID7 , image segmentation BID3 , and image denoising BID29 . The first example of such a performance was on image classification, where it outperformed other computer vision methods which were carefully handcrafted for image classification BID12 . Following this success, DNNs continued to grow in popularity. Although the performances of DNNs on different tasks are getting close to human expertise BID17 and in some cases surpass them BID24 , there is hesitation to use them when interpretability of the results is important. Accuracy is a well-defined criterion but does not provide useful understandings of the actual inner workings of the network. If the deployment of a network may result in inputs whose distribution differs from that of the training or testing data, interpretability or explanations of the network's decisions can be important for securing human trust in the network.Explanations are important in settings such as medical treatments, system verification, and human training and teaching. Naturally, one way of getting an explanation is asking the direct question, ""Why did the DNN choose this answer?"" Humans often also seek contrasting explanations. For instance, they maybe more familiar with the contrasting answer, or they want to find the subtle differences in input which change the given answer to the contrasting one. This way of questioning can be phrased as, ""Why did the DNN not choose B (over A)?"" In this work, we present a framework to answer this type of question. We learn a model over the input space which is capable of generating synthetic samples similar to the input. Then, we ask how we can alter this synthetic input to change the classification outcome. Our proposed framework is not based on heuristics, does not need to change the given network, is applicable as long as the given model can handle backpropagation (no further requirements for layers), and can run much faster than methods with input perturbation. The only overhead of this method is the assumed availability of a latent model over the input. If this latent model is not available, we can learn such a model using generative adversarial methods or variational auto encoders. Learning this latent space needs to be done only a single time and is independent of the learned classifier to be explained. Our constrastive explanation method (CDeepEx) provides an effective method for querying a learned network to discover its learned representations and biases. We demonstrated the quality of our method, compared to other current methods and illustrated how these contrastive explanations can shed light on the robustness of a learned network.Asking a network contrastive questions of the form, ""Why is this example not of class B?"" can yield important information about how the network is making its decisions. Most previous explanation methods do not address this problem directly, and modifying their output to attempt to answer constrastive questions fails.Our formulation draws on three ideas: The explanation should be in the space of natural inputs, should be an example that is maximally ambiguous between the true and probe classes, and should not be confused with other classes. The method does not require knowledge of or heuristics related to the architecture or modality of the network. The explanations can point to unintended correlations in the input data that are expressed in the resulting learned network.","propose method which can visually explain classification decision deep neural networks DNNs are many proposed methods machine learning computer vision seeking clarify decision machine learning black boxes specifically DNNs. methods try gain insight why the network chose class answer. Humans when searching explanations ask two types questions. first question is,Why did choose answer? second question asks Why did you choose answerB A? previously proposed methods are either able provide latter directly efficiently. introduce method capable answering second question directly efficiently. work limit inputs images. general proposed method generates explanations input space model capable efficient evaluation gradient evaluation. provide results showing superiority approach gaining insight inner representation machine learning models. Deep neural networks DNN have shown extraordinary performance computer vision tasks image classification BID25 BID23 BID24 BID7 image segmentation BID3 image denoising BID29. first example performance was on image classification where it outperformed computer vision methods which were carefully handcrafted image classification BID12. Following success DNNs continued grow popularity. Although performances DNNs different tasks are getting close human expertise BID17 cases surpass BID24 is hesitation use when interpretability results is important. Accuracy is a well-defined criterion does not provide useful understandings actual inner workings network. If the deployment network may result inputs whose distribution differs training testing data interpretability explanations network's decisions can be important securing human trust network.Explanations are important settings medical treatments system verification human training teaching. Naturally one way getting explanation is asking direct question Why did the DNN choose answer? Humans often also seek contrasting explanations. instance maybe familiar contrasting answer want find subtle differences input which change given answer contrasting one. way questioning can be phrased Why did DNN chooseB work present framework answer type question. learn model input space which is capable generating synthetic samples similar input. ask how we can alter synthetic input change classification outcome. proposed framework is not based heuristics does not need change given network is applicable long given model can handle backpropagation requirements layers can run much faster methods input perturbation. overhead method is the assumed availability latent model input. If this latent model is not available can learn model using generative adversarial methods variational auto encoders. Learning latent space needs done single time is independent learned classifier explained. constrastive explanation method CDeepEx provides effective method querying learned network discover learned representations biases. demonstrated quality method compared current methods illustrated how these contrastive explanations can shed light robustness learned network.Asking network contrastive questions form Why is this should be an example classB? can yield important information how the network is making decisions. previous explanation methods do not address problem directly modifying output attempt answer constrastive questions fails.Our formulation draws three ideas:explanation should be in the space natural inputs Why is this should be an example is maximally ambiguous true probe classes should not confused classes. method does not require knowledge heuristics related architecture modality network. explanations can point unintended correlations input data are expressed resulting learned network.",869,582,287,0.009,1.493,2025/11/05 17:19:03,0.0,1.745,0.5077881619937696,301.376
"We flip the usual approach to study invariance and robustness of neural networks by considering the non-uniqueness and instability of the inverse mapping. We provide theoretical and numerical results on the inverse of ReLU-layers. First, we derive a necessary and sufficient condition on the existence of invariance that provides a geometric interpretation. Next, we move to robustness via analyzing local effects on the inverse. To conclude, we show how this reverse point of view not only provides insights into key effects, but also enables to view adversarial examples from different perspectives. Invariance and stability/robustness are two of the most important properties characterizing the behavior of a neural network. Due to growing requirements like robustness to adversarial examples BID16 and the increasing use of deep learning in safety-critical applications, there has been a surge in interest in these properties. Invariance and stability are considered to be the key mechanisms in dealing with uninformative properties of the input BID0 BID6 and are studied from the information theoretical perspective in form of the loss of information about the input BID17 BID11 .Invariance and stability are also tightly linked to robustness against adversarial attacks (Cisse et al., 2017; BID18 BID14 , generalization BID15 Gouk et al., 2018) and even the training of Generative Adversarial Networks BID7 . In general , stability is studied via two basic properties: 1) locally via a norm of the Jacobian BID15 BID14 , 2) globally via the Lipschitz constant (Cisse et al., 2017; BID7 BID18 ). From a high-level perspective, both of these approaches study an upper bound on stability as the Lipschitz constant and a Jacobian norm quantifies the highest possible change under a perturbation with a given magnitude. We, unlike the approaches above, aim to broaden our understanding by analyzing the lowest possible change under a perturbation.More formally, we study which perturbations ∆x do not (or only little) affect the outcome of a network F . Our analysis considers a given input data point x and investigates the ∆x's, such that DISPLAYFORM0 where a small ε > 0 is given. While these properties can be crucial for many discriminative tasks BID6 , the model could be flawed if perturbations that alter the semantics have only a minor impact on the features. This is a reverse perspective on adversarial examples BID16 , which commonly considers small input perturbations that lead to large changes and thus to arbitrary decisions of the network.This flipped view and the study of smallest changes calls for a different approach: we study the instabilities of the inverse instead of the stabilities of the forward mapping. In particular, if F is invariant to perturbations ∆x, then x and x + ∆x lie in the preimage of the output z = F (x), i.e. F is not uniquely invertible. Robustness towards large perturbations induces an instable inverse mapping as small changes in the output can be due to large changes in the input.Based on the piecewise linear nature of ReLU networks BID8 , we characterize the preimage of ReLU-activations as a single point, finite (bounded) or infinite (unbounded) . Further, we study the stability of the linearization of rectifier networks via its singular values. To illustrate these locally changing properties and to demonstrate their tight connection, we visualize the behavior on a synthetic problem in FIG0 . As ReLU-layers are piecewise linear, the local behavior is constant on polytopes. Further, the regions with infinite/finite preimages correspond to regions with condition number of one or zero, while singleton preimages link to condition numbers larger than one. Thus, both properties are tightly connected and investigating one property alone yields an incomplete picture.Our contributions are as follows:• We derive conditions when the preimage of an output of a ReLU-layer has finite or infinite volume or is a single point. Based on these conditions, we derive an algorithm to check these conditions and exemplify its usability by applying it to investigate the preimages of a trained network. (See Section 2.) • We study the stability of the inverse via analyzing the linearization at a point in input space, which is accurate within a polytope. We provide upper bounds on the smallest singular value of a linearization and prove how the removal of uncorrelated features could effect the stability of the inverse mapping. Based on these ideas, we experimentally demonstrate how singular values evolve over the different layers in rectifier networks. (See Section 3.) • We introduce a reverse view on adversarial examples and connect it to invariance and robustness by leveraging our analysis of preimages. (see Section 5) We presented the inverse as an approach to tackle the invariance and robustness properties of ReLU networks. Particularly, we studied two main effects: 1) conditions under which the preimage of a ReLU layer is a point, finite or infinite and 2) how ReLU can effect the inverse stability of the linearization. By deriving approaches to numerically examine these effects, we highlighted the broad range of possible effects. Moreover, controlling such properties may be desirable as our experiment on adversarial examples showed.Besides the open questions on how to control the structure of preimages and inverse stability via architecture design or regularization, we envision several theoretical directions based on our work. Especially, incorporate nonlinear effects like moving between linear regions of rectifier networks could lift the analysis closer to practice. Furthermore, studying similarities of omnidirectionality as a geometrical property and singular values could further strengthen the link between these two crucial properties. Proof (Corollary 2, Equivalences of omnidirectionality) We show the equivalences by proving i) DISPLAYFORM0 Let A ∈ R m×n be omnidirectional, i.e. for every x = 0, it holds that Ax 0. This is equivalent to DISPLAYFORM1 which is ii). The implications from ii) to iii) and from iii) to iv) are obvious. From iv), we have that DISPLAYFORM2 which is equivalent to i), the omnidirectionality of A. Altogether, this shows the equivalence of all four points.Definition 10 (Convex hull) For A ∈ R m×n , the convex hull is defined as DISPLAYFORM3 where a i ∈ R n are the rows of A.Theorem 11 (Stiemke's theorem, see Dantzig (1963) ) Let A ∈ R m×n be a matrix, then the following two expressions are equivalent.• y : Ay 0 DISPLAYFORM4 Here z 0 means that 0 = z 0 . Proof (Theorem 12, Singleton solutions of inequality systems) ""⇐"" Let (A| I , b| I ) be omnirectional for x 0 . Then it holds that A| I x + b| I = A| I (x − x 0 ) 0. Due to the omnidirectionality of A| I , x 0 is the unique solution of the inequality system A| I x + b| I 0. The existence of a solution for the whole system Ax + b 0 is guaranteed by assumption and therefore x 0 is the unique solution of Ax + b 0. ""⇒"" Here we will prove "" I : (A| I , b| I ) omnidirectional for some p ⇒ solution non-unique"".We will start by doing the following logical transformations: This means that A| I is not omnidirectional, because otherwise A| I x 0 + b| I = 0 due to the definition of I, which would lead to the contradiction that (A| I , b| I ) is omnidirectional for x 0 . But this means ∃x = 0 : A| I x 0 as a result of Corollary 2. Since A| I c x 0 + b| I c ≺ 0, we also have ∀x ∃ > 0 : A| I c (x 0 + x) + b| I c ≺ 0. This holds in particular for x , so we define accordingly x * := εx = 0. Therefore, we have A| I c (x 0 + x * ) + b| I c ≺ 0 as well as DISPLAYFORM5 DISPLAYFORM6 Altogether it holds that A(x 0 + x * ) + b 0 with x * = 0, which means that x 0 is a non-unique solution for the inequality system Ax + b 0.Proof (Theorem 4, Preimages of ReLU-layers) We consider the ReLU-layer DISPLAYFORM7 given its output y ∈ R m with A ∈ R m×n , b ∈ R m and x ∈ R n . Clearly, this equation can also be written as the mixed linear system DISPLAYFORM8 This allows us to consider the two cases N (A| y 0 ) = {0} and N (A| y 0 ) = {0}.In the first case , we have a linear system which allows us to calculate x uniquely, i.e. we can do retrieval. This leads us to the second case, the interesting one. In this case we can only recover x uniquely if and only if the system of inequalities ""pins down"" P N (A|y 0) x, where P V is the orthogonal projection into the closed space V . Formally this requires DISPLAYFORM9 to have a unique solution for x ∈ R n and P N (A|y 0) ⊥ x fixed (given via the equality system). By defining b := b| y 0 + A| y 0 (P N (A|y 0 ) ⊥ x) we have DISPLAYFORM10",flip usual approach study invariance robustness neural networks considering non-uniqueness instability inverse mapping. provide theoretical numerical results inverse ReLU-layers First derive necessary sufficient condition existence invariance provides geometric interpretation. Next move robustness via analyzing local effects inverse. conclude show how this reverse point view provides insights key effects also enables view adversarial examples different perspectives. Invariance stability/robustness are two important properties characterizing behavior neural network. Due growing requirements like robustness adversarial examples BID16 increasing use deep learning safety-critical applications has been surge interest properties. Invariance stability are considered key mechanisms dealing uninformative properties input BID0 BID6 are studied information theoretical perspective form loss information input BID17 BID11.Invariance stability are also tightly linked robustness adversarial attacks Cisseetal. 2017;BID18 BID14 generalization BID15 Gouket al. 2018 even training Generative Adversarial Networks BID7. general stability is studied via two basic properties:1 locally via norm Jacobian BID15 BID14 2 globally via Lipschitz constant Cisseetal. 2017;BID7 BID18 high-level perspective approaches study upper bound stability Lipschitz constant Jacobian norm quantifies highest possible change perturbation given magnitude. unlike approaches aim broaden understanding analyzing lowest possible change perturbation.More formally study which perturbations∆x do not(or little affect outcome networkF. analysis considers given input data point x investigates ∆x's DISPLAYFORM0 where a smallε 0 is given. properties can be crucial many discriminative tasks BID6 model could flawed if perturbations alter semantics have only a minor impact features. is a reverse perspective adversarial examples BID16 which commonly considers small input perturbations lead large changes thus arbitrary decisions network.This flipped view study smallest changes calls different approach:study instabilities inverse instead stabilities forward mapping. particular ifF is invariant perturbations∆x x x+∆x lie preimage outputz F x.eF is not uniquely invertible. Robustness towards large perturbations induces instable inverse mapping small changes output can be due large changes input.Based piecewise linear nature ReLU networks BID8 characterize preimage ReLU-activations single point finite bounded infinite unbounded study stability linearization rectifier networks via singular values. illustrate locally changing properties demonstrate tight connection visualize behavior synthetic problem FIG0. ReLU-layers are piecewise linear local behavior is constant polytopes. regions infinite/finite preimages correspond regions condition number one zero singleton preimages link condition numbers larger one. Thus properties are tightly connected investigating one property alone yields incomplete picture.Our contributions are as follows:• derive conditions when the preimage output ReLU-layer has finite infinite volume is a single point. Based conditions derive algorithm check conditions exemplify usability applying investigate preimages trained network. See Section2. • study stability inverse via analyzing linearization point input space which is accurate within polytope. provide upper bounds smallest singular value linearization prove how the removal uncorrelated features could effect stability inverse mapping. Based ideas experimentally demonstrate how singular values evolve different layers rectifier networks. See Section3. • introduce reverse view adversarial examples connect invariance robustness leveraging analysis preimages. see Section5 presented inverse approach tackle invariance robustness properties ReLU networks. Particularly studied two main effects:1 conditions which the preimage ReLU layer is a point finite infinite 2 how ReLU can effect inverse stability linearization. deriving approaches numerically examine effects highlighted broad range possible effects. Moreover controlling properties may desirable experiment adversarial examples showed.Besides open questions how to control structure preimages inverse stability via architecture design regularization envision several theoretical directions based work. Especially incorporate nonlinear effects like moving linear regions rectifier networks could lift analysis closer practice. Furthermore studying similarities omnidirectionality geometrical property singular values could strengthen link two crucial properties. Proof Corollary2 Equivalences omnidirectionality show equivalences proving DISPLAYFORM0 Let ∈ R m×n omnidirectional.e everyx 0 holds Ax0. is equivalent DISPLAYFORM1 whichisii implications ii iii iii iv are obvious. iv have DISPLAYFORM2 which is equivalent omnidirectionality A. Altogether shows equivalence four points.Definition10 Convex hull ∈ R m×n convex hull is defined DISPLAYFORM3 whereai∈Rn are the rows A.Theorem11 Stiemke's theorem see Dantzig 1963 Let ∈ R m×n matrix following two expressions are equivalent.• y:Ay 0 DISPLAYFORM4 z 0 means 0 z0. Proof Theorem12 Singleton solutions inequality systems ⇐ Let A| b| omnirectional x0. holds A| x+b| A| x−x0 0. Due omnidirectionality A| x0 is the unique solution inequality systemA| x+b| 0. existence solution whole systemAx+b0 is guaranteed assumption thereforex0 is the unique solution Ax+b0. ⇒ will prove I:A| b| is not is omnidirectional p ⇒ solution non-unique.We will start following logical transformations:means A| is not is omnidirectional otherwiseA| x0+b| 0 due definition would lead contradiction A| b| is not is omnidirectional x0. means∃x 0:A| x0 result Corollary2. SinceA| cx0+b| c≺0 also have∀x∃ 0:A| c x0+x+b| c≺0. holds particular x define accordinglyx* εx 0. Therefore haveA| c x0+x *+b| c≺0 well DISPLAYFORM5 DISPLAYFORM6 Altogether holds x0+x *+b0 x* 0 which means x0 is a non-unique solution inequality systemAx+b 0.Proof Theorem4 Preimages ReLU-layers consider ReLU-layer DISPLAYFORM7 given output ∈R ∈ R m×n b∈R x∈Rn. Clearly equation can also written mixed linear system DISPLAYFORM8 allowsus consider two casesN A| 0 0 N A| 0 0.In first case have a linear system which allowsus calculate x uniquely.e can do retrieval. leadsus second case interesting one. case can only recover x uniquely if and onlyif system inequalities pins PN A|y0 x wherePV is the orthogonal projection closed spaceV. Formally requires DISPLAYFORM9 have a unique solution x∈Rn PN A|y0 ⊥ x fixed given via equality system definingb:b| 0+A| 0 PN A|y0 ⊥x have DISPLAYFORM10,2041,1348,693,0.024,1.514,2025/11/05 17:19:03,0.01,1.562,0.5732087227414329,686.569
"While deep learning has led to remarkable results on a number of challenging problems, researchers have discovered a vulnerability of neural networks in adversarial settings, where small but carefully chosen perturbations to the input can make the models produce extremely inaccurate outputs. This makes these models particularly unsuitable for safety-critical application domains (e.g. self-driving cars) where robustness is extremely important. Recent work has shown that augmenting training with adversarially generated data provides some degree of robustness against test-time attacks. In this paper we investigate how this approach scales as we increase the computational budget given to the defender. We show that increasing the number of parameters in adversarially-trained models increases their robustness, and in particular that ensembling smaller models while adversarially training the entire ensemble as a single model is a more efficient way of spending said budget than simply using a larger single model. Crucially, we show that it is the adversarial training of the ensemble, rather than the ensembling of adversarially trained models, which provides robustness. Deep neural networks have demonstrated state-of-the-art performance in a wide range of application domains BID13 . However, researchers have discovered that deep networks are in some sense 'brittle', in that small changes to their inputs can result in wildly different outputs BID8 BID10 BID27 . For instance, practically imperceptible (to human) modifications to images can result in misclassification of the image with high confidence. Not only are networks susceptible to these 'attacks', but these attacks are also relatively easy to compute using standard optimization techniques BID5 BID6 . These changes are often referred to as adversarial perturbations, in the sense that an adversary could craft a very small change to the input in order to create an undesirable outcome. This phenomenon is not unique to image classification, nor to particular network architectures, nor to particular training algorithms BID23 .Adversarial attacks can be broken into different categories depending on how much knowledge of the underlying model the adversary has access to. In 'white-box ' attacks the adversary has full access to the model, and can perform both forward and backwards passes (though not change the weights or logic of the network) BID4 BID6 . In the 'black-box ' setting the adversary has no access to the model, but perhaps knows the dataset that the model was trained on BID23 . Despite several recent papers demonstrating new defences against adversarial attacks BID1 BID7 BID16 BID26 BID29 BID31 BID32 BID33 , recent papers have demonstrated that most of these new defences are still susceptible to attacks and largely just obfuscate the gradients that the attacker can follow, and that non-gradient based attacks are still effective BID30 ; BID2 . In this section we briefly discuss the possible reasons for the behaviours observed. As we saw, an ensemble of models trained adversarially outperforms the other setups at test time. We suspect, that this might be happening due to a mechanism described below.When the model is being trained, it is exposed to pairs of images, both ""clean"" and adversarially modified. The adversarial training exploits the fact that the original image is close to the decision boundary of the model. The model then, when provided with both clean and adversarial image would attempt to modify the decision boundary in order to engulf them both. It is relatively easy to imagine why SingleAdv would be weaker then the other models-it simply has less parameters than the competition. In order to accommodate the adversarial example it has to compromise the decision boundary somewhere else, pulling it close to other clean images, making it vulnerable to subsequent attack. This is illustrated in Figure 3a .The possible reason why Ensemble2Adv outperforms DoubleAdv is more elusive. Both models have the same number of parameters, so one could expect them to display a similar performance. As Ensemble2Adv is more robust to white box attack during test time we argue, that this might be due to the fact that in abundance of flexibility DoubleAdv tends often to spread out thin ""tentacles"" Figure 3: Different responses of various architectures to adversarial training. Solid lines represent decision boundary of the models that see only ""clean"" images. Dashed lines are the boundaries modified due to the presence of adversarial training. The black dot is a clean image, the red dot is its adversarial modification. In the presence of two models Model 1 is blue and Model 2 is green. In case it needs to be specified with respect to which model the adversarial example is constructed the red dot has a circle in an appropriate color around it.( Figure 3b ) which do not cover up too much of a space. On the other hand, given that Ensemble2Adv is comprised of two separate models they are both subject to lesser ability to overfit following from the smaller number of parameters available in them. Thus we argue, that in most cases the modification of the model with adversarial training covers the adversarial example by modifying one model more than the other. This way the decision boundary of the model modified to a lesser degree still ""provides protection"" for ""clean"" images, while at the same time the ""tentacle"" generated by the model modified more is thicker than the one DoubleAdv creates. We illustrate that with Figure 3c .Finally, it was shown that SeparateEnsemble2Adv is outperformed by a Ensemble2Adv trained ""jointly"". We think that this is due to the fact that the adversarial training has to weaken both of the submodels simultaneously. Figure 3d illustrates that.For a further illustration of the effects of adversarial training we plotted actual images of the decision boundaries for non-adversarially and adversarially trained Baseline and 2-Ensemble models (Figure 4) . DISPLAYFORM0 Figure 4: Decision boundaries for various architectures/training methods. Each column shows the decision regions of two models on the same 2-dimensional plane in the space of all images. On every picture the black dot corresponds to the datapoint-an unaltered (ship ) image from the test dataset. The light rectangle superimposed over the dot represents the bounds of the permitted attack region within the region. The two red arrows are the two vectors-attack directions on the base image, with respect to respectively the first and second tested model. The red dots are the images resulting from the attack. The plane presented is then the ( unique) 2-dimensional plane containing those 3 points. Dark grey is void (outside the slice boundaries), and all other pixels are generated by a forward pass of the model at those coordinates, with the colour used representing the majority class.Decision regions of the models are 3072-dimensional sets, so visualizing them itself poses a challenge. What we present are color-coded values of the models restricted to 2-dimensional planes in the space of all images, chosen so that the original image and the closest adversarial example (or attempt to find one) for both models in a pair being compared are co-planar. We observe, amongst other things, some support for the hypothesis put forward in Figure 3 : adversarial training adds ""thickness"" around the natural image points, pushing the boundary further away from them, and in doing so, making adversarial examples harder to find (even within the test set); ensembling makes some classes more ""consistent"" within the decision plane, but introduce small ""pockets"" or ""tentacles"" of other classes; and the combinator thereof removes said pockets to create large regions of the correct class around images. We believe that such an approach of choosing a good plane and plotting the values of models on it is a more informative way of visualizing phenomena taking place in the universe of robustness and adversarial examples than more traditional approaches like t-SNE plots BID18 . In this paper, we provide an empirical study of the effect of increasing the number of parameters in a model trained with adversarial training methods, with regard to its robustness to test-time adversarial attacks. We showed that while increasing parameters improves robustness, it is better to do so by ensembling smaller models than by producing one larger model. Through our experiments, we show that this result is not only due to ensembling alone, or to the implicit robustness of an ensemble of adversarially trained models, but specifically to due to the adversarial training of an ensemble as if it were a single model. We proposed a high level interpretation of why this phenomenon might occur. Further work should seek to determine whether scaling the number of models in the ensemble while controlling for number of parameters produces significant improvements over the minimal ensembles studied here in an attempt to draw conclusions about why such architectures are generally more robust than larger single models, even under adversarial training.",deep learning has led remarkable results number challenging problems researchers have discovered vulnerability neural networks adversarial settings where small carefully chosen perturbations input can make models produce extremely inaccurate outputs. makes models particularly unsuitable safety-critical application domains e.g self-driving cars where robustness is extremely important. Recent work has shown augmenting training adversarially generated data provides degree robustness test-time attacks. paper investigate how this approach scales increase computational budget given defender. show increasing number parameters adversarially-trained models increases robustness particular ensembling smaller models adversarially training entire ensemble if it were single model is a more efficient way spending said budget simply using larger single model. Crucially show is the adversarial training ensemble rather ensembling adversarially trained models which provides robustness. Deep neural networks have demonstrated state-of-the-art performance wide range application domains BID13. However researchers have discovered deep networks are in some sense 'brittle' where small changes inputs can result wildly different outputs BID8 BID10 BID27. instance practically imperceptible human modifications images can result misclassification image high confidence. are networks susceptible 'attacks' attacks are also relatively easy compute using standard optimization techniques BID5 BID6. changes are often referred adversarial perturbations sense adversary could craft small change input order create undesirable outcome. phenomenon is not is then the(unique image classification particular network architectures particular training algorithms BID23.Adversarial attacks can be broken different categories depending how much knowledge underlying model adversary has has no access to. 'white-box attacks adversary has full access which model can perform forward backwards passes though change weights logic network BID4 BID6. 'black-box setting adversary has has no access which model perhaps knows dataset model was trained BID23. Despite several recent papers demonstrating new defences adversarial attacks BID1 BID7 BID16 BID26 BID29 BID31 BID32 BID33 recent papers have demonstrated new defences are still susceptible attacks largely obfuscate gradients attacker can follow non-gradient based attacks are still effective BID30;BID2. section briefly discuss possible reasons behaviours observed. saw ensemble models trained adversarially outperforms setups test time. suspect might happening due mechanism described below.When model is being trained is exposed pairs images clean adversarially modified. adversarial training exploits fact original image is close decision boundary model. model when provided clean adversarial image would attempt modify decision boundary order engulf both. is relatively easy imagine why SingleAdv would weaker models-it simply has less parameters competition. order accommodate adversarial example has to compromise decision boundary somewhere else pulling close clean images making vulnerable subsequent attack. is illustrated Figure 3a.The possible reason why Ensemble2Adv outperforms DoubleAdv is more elusive. models have the same number parameters one could expect display similar performance. Ensemble2Adv is more robust white box attack test time argue might due fact abundance flexibility DoubleAdv tends often spread thin tentacles Figure3:Different responses various architectures adversarial training. Solid lines represent decision boundary models see clean images. Dashed lines are the boundaries modified due presence adversarial training. black dot is a clean image red dot is its adversarial modification. presence two models Model1 is blue Model2 is green. case needs specified respect which model adversarial example is constructed red dot has a circle appropriate color around it. Figure3b which do not cover much space. hand given Ensemble2Adv is comprised two separate models are both subject lesser ability overfit following smaller number parameters available them. Thus argue cases modification model adversarial training covers adversarial example modifying one model other. way decision boundary model modified lesser degree still provides protection clean images time tentacle generated model modified is thicker one DoubleAdv creates. illustrate Figure 3c.Finally was shown SeparateEnsemble2Adv is outperformed Ensemble2Adv trained jointly. think is due fact is the adversarial training has to weaken submodels simultaneously. Figure 3d illustrates that.For illustration effects adversarial training plotted actual images decision boundaries non-adversarially adversarially trained Baseline 2-Ensemble models Figure4 DISPLAYFORM0 Figure4:Decision boundaries various architectures/training methods. column shows decision regions two models 2-dimensional plane space images. every picture black dot corresponds datapoint-an unaltered ship image test dataset. light rectangle superimposed dot represents bounds permitted attack region within region. two red arrows are the two vectors-attack directions base image respect respectively first second tested model. red dots are the images resulting attack. plane presented is not is then the(unique 2-dimensional plane containing 3 points. Dark grey is void outside slice boundaries pixels are generated forward pass model coordinates colour used representing majority class.Decision regions models are 3072-dimensional sets visualizing poses challenge. What we present are color-coded values models restricted 2-dimensional planes space images chosen original image closest adversarial example attempt find one models pair compared are co-planar co-planar observe amongst things support hypothesis put forward Figure3:adversarial training adds thickness around natural image points pushing boundary away making adversarial examples harder find even within test set ensembling makes classes consistent within decision plane introduce small pockets tentacles classes;combinator thereof removes said pockets create large regions correct class around images. believe approach choosing good plane plotting values models isa informative way visualizing phenomena taking place universe robustness adversarial examples traditional approaches like t-SNE plots BID18. paper provide empirical study effect increasing number parameters model trained adversarial training methods regard robustness test-time adversarial attacks. showed increasing parameters improves robustness is better do so by ensembling smaller models producing one larger model. experiments show result is not only due do so by ensembling alone implicit robustness ensemble adversarially trained models specifically due adversarial training ensemble if it were single model. proposed high level interpretation why this phenomenon might occur. work should seek determine whether scaling number models ensemble controlling number parameters produces significant improvements minimal ensembles studied attempt draw conclusions why such architectures are generally robust larger single models even adversarial training.,1768,1184,584,0.02,1.493,2025/11/05 17:19:03,0.01,1.527,0.5077881619937696,554.409
"Multi-task learning (MTL) with neural networks leverages commonalities in tasks to improve performance, but often suffers from task interference which reduces the benefits of transfer. To address this issue we introduce the routing network paradigm, a novel neural network and training algorithm. A routing network is a kind of self-organizing neural network consisting of two components: a router and a set of one or more function blocks. A function block may be any neural network – for example a fully-connected or a convolutional layer. Given an input the router makes a routing decision, choosing a function block to apply and passing the output back to the router recursively, terminating when a fixed recursion depth is reached. In this way the routing network dynamically composes different function blocks for each input. We employ a collaborative multi-agent reinforcement learning (MARL) approach to jointly train the router and function blocks. We evaluate our model against cross-stitch networks and shared-layer baselines on multi-task settings of the MNIST, mini-imagenet, and CIFAR-100 datasets. Our experiments demonstrate a significant improvement in accuracy, with sharper convergence. In addition, routing networks have nearly constant per-task training cost while cross-stitch networks scale linearly with the number of tasks. On CIFAR100 (20 tasks) we obtain cross-stitch performance levels with an 85% average reduction in training time.
 Multi-task learning (MTL) is a paradigm in which multiple tasks must be learned simultaneously. Tasks are typically separate prediction problems, each with their own data distribution. In an early formulation of the problem, BID7 describes the goal of MTL as improving generalization performance by ""leveraging the domain-specific information contained in the training signals of related tasks."" This means a model must leverage commonalities in the tasks (positive transfer) while minimizing interference (negative transfer). In this paper we propose a new architecture for MTL problems called a routing network, which consists of two trainable components: a router and a set of function blocks. Given an input, the router selects a function block from the set, applies it to the input, and passes the result back to the router, recursively up to a fixed recursion depth. If the router needs fewer iterations then it can decide to take a PASS action which leaves the current state unchanged. Intuitively, the architecture allows the network to dynamically self-organize in response to the input, sharing function blocks for different tasks when positive transfer is possible, and using separate blocks to prevent negative transfer.The architecture is very general allowing many possible router implementations. For example, the router can condition its decision on both the current activation and a task label or just one or the other. It can also condition on the depth (number of router invocations), filtering the function module choices to allow layering. In addition, it can condition its decision for one instance on what was historically decided for other instances, to encourage re-use of existing functions for improved compression. The function blocks may be simple fully-connected neural network layers or whole networks as long as the dimensionality of each function block allows composition with the previous function block choice. They needn't even be the same type of layer. Any neural network or part of a network can be ""routed"" by adding its layers to the set of function blocks, making the architecture applicable to a wide range of problems. Because the routers make a sequence of hard decisions, which are not differentiable, we use reinforcement learning (RL) to train them. We discuss the training algorithm in Section 3.1, but one way we have modeled this as an RL problem is to create a separate RL agent for each task (assuming task labels are available in the dataset). Each such task agent learns its own policy for routing instances of that task through the function blocks.To evaluate we have created a ""routed"" version of the convnet used in BID26 and use three image classification datasets adapted for MTL learning: a multi-task MNIST dataset that we created, a Mini-imagenet data split as introduced in BID32 , and CIFAR-100 BID18 , where each of the 20 label superclasses are treated as different tasks. 1 We conduct extensive experiments comparing against cross-stitch networks BID23 and the popular strategy of joint training with layer sharing as described in BID7 . Our results indicate a significant improvement in accuracy over these strong baselines with a speedup in convergence and often orders of magnitude improvement in training time over cross-stitch networks.",Multi-task learning MTL neural networks leverages commonalities tasks improve performance often suffers task interference which reduces benefits transfer. address issue introduce routing network paradigm novel neural network training algorithm. routing network is a kind self-organizing neural network consisting two components:router set one function blocks. function block may neural network– example fully-connected convolutional layer. Given input router makes routing decision choosing function block apply passing output back router recursively terminating when a fixed recursion depth is reached. way routing network dynamically composes different function blocks input. employ collaborative multi-agent reinforcement learning MARL approach jointly train router function blocks. evaluate model cross-stitch networks shared-layer baselines multi-task settings MNIST mini-imagenet CIFAR-100 datasets. experiments demonstrate significant improvement accuracy sharper convergence. addition routing networks have nearly constant per-task training cost cross-stitch networks scale linearly number tasks. CIFAR100 20 tasks obtain cross-stitch performance levels 85% average reduction training time. Multi-task learning MTL is a paradigm which multiple tasks must learned simultaneously. Tasks are typically separate prediction problems data distribution. early formulation problem BID7 describes goal MTL improving generalization performance leveraging domain-specific information contained training signals related tasks. means model must leverage commonalities tasks positive transfer minimizing interference negative transfer paper propose new architecture MTL problems called routing network which consists two trainable components:router set function blocks. Given input router selects function block set applies input passes result back router recursively fixed recursion depth. If the router needs fewer iterations can decide take PASS action which leaves current state unchanged. Intuitively architecture allows network dynamically self-organize response input sharing function blocks different tasks when positive transfer is possible using separate blocks prevent negative transfer.The architecture is very general allowing many possible router implementations. example router can condition decision current activation task label one other. can also condition depth number router invocations filtering function module choices allow layering. addition can condition decision one instance what was historically decided instances encourage re-use existing functions improved compression. function blocks may simple fully-connected neural network layers whole networks long dimensionality function block allows composition previous function block choice. even type layer. neural network part network can be routed adding layers set function blocks making architecture applicable wide range problems. routers make sequence hard decisions which are not differentiable use reinforcement learning RL train them. discuss training algorithm Section 3.1 one way have modeled RL problem is to create separate RL agent task assuming task labels are available dataset task agent learns policy routing instances task function blocks.To evaluate have created routed version convnet used BID26 use three image classification datasets adapted MTL learning:multi-task MNIST dataset created Mini-imagenet data split introduced BID32 CIFAR-100 BID18 where eachof 20 label superclasses are treated different tasks. 1 conduct extensive experiments comparing cross-stitch networks BID23 popular strategy joint training layer sharing described BID7. results indicate significant improvement accuracy strong baselines speedup convergence often orders magnitude improvement training time cross-stitch networks.,901,593,308,0.009,1.519,2025/11/05 17:19:03,0.0,1.444,0.5887850467289715,293.798
"We propose a practical method for $L_0$ norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of $L_0$ regularization. However, since the $L_0$ norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected $L_0$ regularized objective is differentiable with respect to the distribution parameters. We further propose the \emph{hard concrete} distribution for the gates, which is obtained by ``stretching'' a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer. Deep neural networks are flexible function approximators that have been very successful in a broad range of tasks. They can easily scale to millions of parameters while allowing for tractable optimization with mini-batch stochastic gradient descent (SGD), graphical processing units (GPUs) and parallel computation. Nevertheless they do have drawbacks. Firstly, it has been shown in recent works BID6 that they are greatly overparametrized as they can be pruned significantly without any loss in accuracy; this exhibits unnecessary computation and resources. Secondly, they can easily overfit and even memorize random patterns in the data BID39 , if not properly regularized. This overfitting can lead to poor generalization in practice.A way to address both of these issues is by employing model compression and sparsification techniques. By sparsifying the model, we can avoid unnecessary computation and resources, since irrelevant degrees of freedom are pruned away and do not need to be computed. Furthermore, we reduce its complexity, thus penalizing memorization and alleviating overfitting.A conceptually attractive approach is the L 0 norm regularization of (blocks of) parameters; this explicitly penalizes parameters for being different than zero with no further restrictions. However, the combinatorial nature of this problem makes for an intractable optimization for large models.In this paper we propose a general framework for surrogate L 0 regularized objectives. It is realized by smoothing the expected L 0 regularized objective with continuous distributions in a way that can maintain the exact zeros in the parameters while still allowing for efficient gradient based optimization. This is achieved by transforming continuous random variables (r.v.s) with a hard nonlinearity, the Figure 1 : L p norm penalties for a parameter θ according to different values of p. It is easily observed that both weight decay and Lasso, p = 2 and p = 1 respectively, impose shrinkage for large values of θ. By gradually allowing p < 1 we observe that the shrinkage is reduced and at the limit of p = 0 we observe that the penalty is a constant for θ = 0.hard-sigmoid. We further propose and employ a novel distribution obtained by this procedure; the hard concrete. It is obtained by ""stretching"" a binary concrete random variable BID19 BID12 and then passing its samples through a hard-sigmoid. We demonstrate the effectiveness of this simple procedure in various experiments.2 MINIMIZING THE L 0 NORM OF PARAMETRIC MODELS One way to sparsify parametric models, such as deep neural networks, with the least assumptions about the parameters is the following; let D be a dataset consisting of N i.i.d. input output pairs {(x 1 , y 1 ), . . . , (x N , y N )} and consider a regularized empirical risk minimization procedure with an L 0 regularization on the parameters θ of a hypothesis (e.g. a neural network) h(·; θ) 1 : DISPLAYFORM0 DISPLAYFORM1 where |θ| is the dimensionality of the parameters, λ is a weighting factor for the regularization and L(·) corresponds to a loss function, e.g. cross-entropy loss for classification or mean-squared error for regression. The L 0 norm penalizes the number of non-zero entries of the parameter vector and thus encourages sparsity in the final estimates θ * . The Akaike Information Criterion (AIC) BID0 ) and the Bayesian Information Criterion (BIC) BID28 , well-known model selection criteria, correspond to specific choices of λ. Notice that the L 0 norm induces no shrinkage on the actual values of the parameters θ; this is in contrast to e.g. L 1 regularization and the Lasso BID32 , where the sparsity is due to shrinking the actual values of θ. We provide a visualization of this effect in Figure 1 .Unfortunately , optimization under this penalty is computationally intractable due to the nondifferentiability and combinatorial nature of 2 |θ| possible states of the parameter vector θ. How can we relax the discrete nature of the L 0 penalty such that we allow for efficient continuous optimization of Eq. 1, while allowing for exact zeros in the parameters? This section will present the necessary details of our approach. We have described a general recipe that allows for optimizing the L 0 norm of parametric models in a principled and effective manner. The method is based on smoothing the combinatorial problem with continuous distributions followed by a hard-sigmoid. To this end, we also proposed a novel distribution which we coin as the hard concrete; it is a ""stretched"" binary concrete distribution, the samples of which are transformed by a hard-sigmoid. This in turn better mimics the binary nature of Bernoulli distributions while still allowing for efficient gradient based optimization. In experiments we have shown that the proposed L 0 minimization process leads to neural network sparsification that is competitive with current approaches while theoretically allowing for speedup in training. We have further shown that this process can provide a good inductive bias and regularizer, as on the CIFAR experiments with wide residual networks we improved upon dropout.As for future work; better harnessing the power of conditional computation for efficiently training very large neural networks with learned sparsity patterns is a potential research direction. It would be also interesting to adopt a full Bayesian treatment over the parameters θ, such as the one employed at ; BID18 . This would then allow for further speedup and compression due to the ability of automatically learning the bit precision of each weight. Finally, it would be interesting to explore the behavior of hard concrete r.v.s at binary latent variable models, since they can be used as a drop in replacement that allow us to maintain both the discrete nature as well as the efficient reparametrization gradient optimization.",propose practical method $L_0 norm regularization neural networks:pruning network training encouraging weights become exactly zero. regularization is interesting since 1 can greatly speed training inference 2 can improve generalization. AIC BIC well-known model selection criteria are special cases $L_0 regularization. However since $L_0 norm weights is non-differentiable cannot incorporate directly regularization term objective function. propose solution inclusion collection non-negative stochastic gates which collectively determine which weights set zero. show somewhat surprisingly certain distributions gates expected $L_0 regularized objective is differentiable respect distribution parameters. propose \emph hard concrete distribution gates which is obtained stretching binary concrete distribution transforming samples hard-sigmoid parameters distribution gates can then be jointly optimized original network parameters. result method allows straightforward efficient learning model structures stochastic gradient descent allows conditional computation principled way. perform various experiments demonstrate effectiveness resulting approach regularizer. Deep neural networks are flexible function approximators have been very successful broad range tasks. can easily scale millions parameters allowing tractable optimization mini-batch stochastic gradient descent SGD graphical processing units GPUs parallel computation. Nevertheless do have drawbacks. Firstly has been shown recent works BID6 are greatly overparametrized can be pruned significantly without loss accuracy;exhibits unnecessary computation resources. Secondly can easily overfit even memorize random patterns data BID39 if not properly regularized. overfitting can lead poor generalization practice.A way address issues is by employing model compression sparsification techniques. sparsifying model can avoid unnecessary computation resources since irrelevant degrees freedom are pruned away do not need computed. Furthermore reduce complexity thus penalizing memorization alleviating overfitting.A conceptually attractive approach is the L 0 norm regularization blocks parameters;explicitly penalizes parameters different zero restrictions. However combinatorial nature problem makes intractable optimization large models.In paper propose general framework surrogate L 0 regularized objectives. is realized smoothing expected L 0 regularized objective continuous distributions way can maintain exact zeros parameters still allowing efficient gradient based optimization. is achieved transforming continuous random variables r.v.s hard nonlinearity Figure1:L p norm penalties parameter θ according different values p. is easily observed weight decay Lasso p 2 p 1 respectively impose shrinkage large values θ. gradually allowingp 1 observe shrinkage is reduced limit p 0 observe penalty is a constant θ 0.hard-sigmoid. propose employ novel distribution obtained procedure;hard concrete. is obtained stretching binary concrete random variable BID19 BID12 passing samples hard-sigmoid demonstrate effectiveness simple procedure various experiments.2 MINIMIZING L 0 NORM PARAMETRIC MODELS One way sparsify parametric models deep neural networks least assumptions parameters is the following;let dataset consisting N.i.d input output pairs x1 1 xN N consider regularized empirical risk minimization procedure L 0 regularization parametersθ hypothesis e.g neural network h ·θ 1:DISPLAYFORM0 DISPLAYFORM1 where |θ| is the dimensionality parameters λ is a weighting factor regularization L · corresponds loss function e.g cross-entropy loss classification mean-squared error regression. L 0 norm penalizes number non-zero entries parameter vector thus encourages sparsity final estimatesθ* Akaike Information Criterion AIC BID0 Bayesian Information Criterion BIC BID28 well-known model selection criteria correspond specific choices λ. Notice L 0 norm induces shrinkage actual values parametersθ;is in contrast e.gL1 regularization Lasso BID32 where the sparsity is due shrinking actual values θ. provide visualization effect Figure 1.Unfortunately optimization penalty is computationally intractable due nondifferentiability combinatorial nature 2 |θ| possible states parameter vectorθ. How can we relax discrete nature L 0 penalty allow efficient continuous optimization Eq. 1 allowing exact zeros parameters? section will present necessary details approach. have described general recipe allows optimizing L 0 norm parametric models principled effective manner. method is based smoothing combinatorial problem continuous distributions followed hard-sigmoid end also proposed novel distribution which we coin hard concrete;is a stretched binary concrete distribution samples which are transformed hard-sigmoid turn better mimics binary nature Bernoulli distributions still allowing efficient gradient based optimization. experiments have shown proposed L 0 minimization process leads neural network sparsification is competitive current approaches theoretically allowing speedup training. have further shown process can provide good inductive bias regularizer CIFAR experiments wide residual networks improved upon dropout.As future work;better harnessing power conditional computation efficiently training large neural networks learned sparsity patterns is a potential research direction. would also interesting adopt full Bayesian treatment parametersθ one employed at;BID18. would allow speedup compression due ability automatically learning bit precision weight. Finally would interesting explore behavior hard concreter.v.s binary latent variable models since can be used drop replacement allowus maintain discrete nature well efficient reparametrization gradient optimization.,1471,985,486,0.015,1.493,2025/11/05 17:19:03,0.01,1.491,0.5077881619937696,455.177
"Recently popularized graph neural networks achieve the state-of-the-art accuracy on a number of standard benchmark datasets for graph-based semi-supervised learning, improving significantly over existing approaches. These architectures alternate between a propagation layer that aggregates the hidden states of the local neighborhood and a fully-connected layer. Perhaps surprisingly, we show that a linear model, that removes all the intermediate fully-connected layers, is still able to achieve a performance comparable to the state-of-the-art models. This significantly reduces the number of parameters, which is critical for semi-supervised learning where number of labeled examples are small. This in turn allows a room for designing more innovative propagation layers. Based on this insight, we propose a novel graph neural network that removes all the intermediate fully-connected layers, and replaces the propagation layers with attention mechanisms that respect the structure of the graph. The attention mechanism allows us to learn a dynamic and adaptive local summary of the neighborhood to achieve more accurate predictions. In a number of experiments on benchmark citation networks datasets, we demonstrate that our approach outperforms competing methods. By examining the attention weights among neighbors, we show that our model provides some interesting insights on how neighbors influence each other. One of the major bottlenecks in applying machine learning in practice is collecting sizable and reliable labeled data, essential for accurate predictions. One way to overcome the problem of limited labeled data is semi-supervised learning, using additional unlabeled data that might be freely available. In this paper, we are interested in a scenario when this additional unlabeled data is available in a form of a graph. The graph provides underlying pairwise relations among the data points, both labeled and unlabeled.Of particular interest are those applications where the presence or absence of an edge between two data points is determined by nature, for instance as a result of human activities or natural relations. As a concrete example, consider a citation network. Each node in the graph is a published research paper, associated with a bag-of-words feature vector. An (directed) edge indicates a citation link. Presence of an edge indicates that the authors of a paper have consciously determined to refer to the other paper, and hence captures some underlying relation that might not be inferred from the bag-of-words feature vectors alone. Such external graph data are available in several applications of interest, such as classifying users connected via a social network, items and customers connected by purchase history, users and movies connected by viewing history, and entities in a knowledge graph connected by relationships. In this paper, we are interested in the setting where the graph is explicitly given and represents additional information not present in the feature vectors.The goal of such graph-based semi-supervised learning problems is to classify the nodes in a graph using a small subset of labeled nodes and all the node features. There is a long line of literature on this topic since BID6 which seeks graph cuts that preserve the known labels and BID50 which uses graph Laplacian to regularize the nearby nodes to have similar labels. However, BID27 recently demonstrated that the existing approaches can be significantly improved upon on a number of standard benchmark datasets, using an innovative neural network architecture on graph-based data known collectively as graph neural networks.Inspired by this success, we seek to understand the reason behind the power of graph neural networks, to guide our design of a novel architecture for semi-supervised learning on graphs. To this end, we first found that a linear classifier of multinomial logistic regression achieves the accuracy comparable to the best known graph neural network. This linear classifier removes all intermediate non-linear activation layers, and only keeps the linear propagation function from neighbors in graph neural networks. This suggests the importance of aggregation information form the neighbors in the graph. This further motivates us to design a new way of aggregating neighborhood information through attention mechanism since, intuitively, neighbors might not be equally important. This proposed attention-based graph neural network captures this intuition and (a) greatly reduces the model complexity, with only a single scalar parameter at each intermediate layer; (b) discovers dynamically and adaptively which nodes are relevant to the target node for classification; and (c) improves upon state-of-the-art methods in terms of accuracy on standard benchmark datasets. Further, the learned attention strengths provide some form of interpretability. They provide insights on why a particular prediction is made on a target node and which neighbors are more relevant in making that decision. In this paper, we present an attention-based graph neural network model for semi-supervised classification on a graph. We demonstrate that our method consistently outperforms competing methods on the standard benchmark citation network datasets. We also show that the learned attention also provides interesting insights on how neighbors influence each other. In training, we have tried more",Recently popularized graph neural networks achieve state-of-the-art accuracy number standard benchmark datasets graph-based semi-supervised learning improving significantly existing approaches. architectures alternate propagation layer aggregates hidden states local neighborhood fully-connected layer. Perhaps surprisingly show linear model removes intermediate fully-connected layers is still able achieve performance comparable state-of-the-art models. significantly reduces number parameters which is critical semi-supervised learning where number labeled examples are small. turn allows room designing innovative propagation layers. Based insight propose novel graph neural network removes intermediate fully-connected layers replaces propagation layers attention mechanisms respect structure graph. attention mechanism allowsus learn dynamic adaptive local summary neighborhood achieve accurate predictions. number experiments benchmark citation networks datasets demonstrate approach outperforms competing methods. examining attention weights among neighbors show model provides interesting insights how neighbors influence other. One major bottlenecks applying machine learning practice is collecting sizable reliable labeled data essential accurate predictions. One way overcome problem limited labeled data is semi-supervised learning using additional unlabeled data might freely available. paper are interested scenario when this additional unlabeled data is available form graph. graph provides underlying pairwise relations among data points labeled unlabeled.Of particular interest are those applications where the presence absence edge two data points is determined nature instance result human activities natural relations. concrete example consider citation network. node graph is a published research paper associated bag-of-words feature vector. directed edge indicates citation link. Presence edge indicates authors paper have consciously determined refer paper hence captures underlying relation might inferred bag-of-words feature vectors alone. external graph data are available several applications interest classifying users connected via social network items customers connected purchase history users movies connected viewing history entities knowledge graph connected relationships. paper are interested setting where the graph is explicitly given represents additional information present feature vectors.The goal graph-based semi-supervised learning problems is to classify nodes graph using small subset labeled nodes node features. is a long line literature topic since BID6 which seeks graph cuts preserve known labels BID50 which uses graph Laplacian regularize nearby nodes have similar labels. However BID27 recently demonstrated existing approaches can be significantly improved upon number standard benchmark datasets using innovative neural network architecture graph-based data known collectively graph neural networks.Inspired success seek understand reason behind power graph neural networks guide design novel architecture semi-supervised learning graphs. end first found linear classifier multinomial logistic regression achieves accuracy comparable best known graph neural network. linear classifier removes intermediate non-linear activation layers keeps linear propagation function neighbors graph neural networks. suggests importance aggregation information form neighbors graph. motivatesus design new way aggregating neighborhood information attention mechanism since intuitively neighbors might equally important. proposed attention-based graph neural network captures intuition greatly reduces model complexity single scalar parameter intermediate layer;b discovers dynamically adaptively which nodes are are more relevant target node classification;c improves upon state-of-the-art methods terms accuracy standard benchmark datasets. learned attention strengths provide form interpretability. provide insights why a particular prediction is made target node which neighbors are are more relevant making decision. paper present attention-based graph neural network model semi-supervised classification graph. demonstrate method consistently outperforms competing methods standard benchmark citation network datasets. also show learned attention also provides interesting insights how neighbors influence other. training have tried,941,623,318,0.009,1.51,2025/11/05 17:19:03,0.0,1.355,0.5607476635514017,308.679
"Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimensionality of data can be much lower than the ambient dimensionality. We argue that this discrepancy may contribute to the difficulties in training generative models. We therefore propose to map both the generated and target distributions to the latent space using the encoder of a standard autoencoder, and train the generator (or decoder) to match the target distribution in the latent space. The resulting method, perceptual generative autoencoder (PGA), is then incorporated with maximum likelihood or variational autoencoder (VAE) objective to train the generative model. With maximum likelihood, PGA generalizes the idea of reversible generative models to unrestricted neural network architectures and arbitrary latent dimensionalities. When combined with VAE, PGA can generate sharper samples than vanilla VAE. Recent years have witnessed great interest in generative models, mainly due to the success of generative adversarial networks (GANs) BID7 BID12 BID1 . Despite the prevalence, the adversarial nature of GANs can lead to a number of challenges, such as unstable training dynamics and mode collapse. Since the advent of GANs, substantial efforts have been devoted to addressing these challenges BID21 BID9 BID19 , while non-adversarial approaches that are free of these issues have also gained attention. Examples include variational autoencoders (VAEs) BID13 , reversible generative models BID5 BID14 , and Wasserstein autoencoders (WAEs) BID22 .However , non-adversarial approaches often have significant limitations. For instance , VAEs tend to generate blurry samples, while reversible generative models require restricted neural network architectures or solving neural differential equations BID8 . Furthermore , to use the change of variable formula, the latent space of a reversible model must have the same dimensionality as the data space, which is unreasonable considering that real-world, high-dimensional data (e.g., images) tends to lie on low-dimensional manifolds, and thus results in redundant latent dimensions and variability. Intriguingly , recent research BID3 suggests that the discrepancy between the intrinsic and ambient dimensionalities of data also contributes to the difficulties in training GANs and VAEs.In this work, we present a novel framework for training autoencoder-based generative models, with non-adversarial losses and unrestricted neural network architectures. Given a standard autoencoder and a target data distribution, instead of matching the target distribution in the data space, we map both the generated and target distributions to the latent space using the encoder, and train the generator (or decoder) to minimize the divergence between the mapped distributions. We prove, under mild assumptions, that by minimizing a form of latent reconstruction error, matching the target distribution in the latent space implies matching it in the data space. We call this framework perceptual generative autoencoder (PGA). We show that PGA enables training generative autoencoders with maximum likelihood, without restrictions on architectures or latent dimensionalities. In addition, when combined with VAE, PGA can generate sharper samples than vanilla VAE. 1 2 METHODS 2.1 PERCEPTUAL GENERATIVE MODEL Let f : R D → R H be the encoder parameterized by φ, and g : R H → R D be the decoder parameterized by θ. Our goal is to obtain a generative model, which maps a simple prior distribution to the data distribution, D. Throughout this paper, we use N (0, I) as the prior distribution.For z ∈ R H , the output of the decoder, g (z), lies in a manifold that is at most H-dimensional. Therefore, if we train the autoencoder to minimize DISPLAYFORM0 DISPLAYFORM1 , thenx can be seen as a projection of the input data, x, onto the manifold of g (z). LetD denote the distribution ofx. Given enough capacity of the encoder,D is the best approximation to D (in terms of L2 distance), that we can obtain from the decoder, and thus can serve as a surrogate target for training the generator.Due to the difficulty of directly training the generator to matchD, we seek to mapD to the latent space, and train the generator to match the mapped distribution,Ĥ, in the latent space. To this end, we reuse the encoder for mappingD toĤ, and train the generator such that h (·) = f (g (·)) maps N (0, I) toĤ. In addition, to ensure that g maps N (0, I) toD, we minimize the following latent reconstruction loss with respect to (w.r.t.) φ: DISPLAYFORM2 Formally, let Z (x) be the set of all z's that are mapped to the same x by the decoder, we have the following theorem: Theorem 1. Assuming the convexity of Z (x) for all x ∈ R D , and sufficient capacity of the encoder; for z ∼ N (0, I), if Eq. (2) is minimized and h (z) ∼Ĥ, then g (z) ∼D.Proof. We first show that any different x's generated by the decoder are mapped to different z's by the encoder. Let x 1 = g (z 1 ), x 2 = g (z 2 ), and x 1 = x 2 . Since the encoder has sufficient capacity and Eq. (2) is minimized, we have f ( DISPLAYFORM3 For z ∼ N (0, I), denote the distributions of g (z) and h (z), respectively, by D and H. We then consider the case where D andD are discrete distributions. If g (z) D , then there exists an x, DISPLAYFORM4 The result still holds when D andD approach continuous distributions.Note that the two distributions compared in Theorem 1, D andD, are mapped respectively from N (0, I) and H. While N (0, I) is supported on the whole R H , there can be z's with low probabilities in N (0, I), but with high probabilities in H, which are not well covered by Eq. (2). Therefore, it is sometimes helpful to minimize another latent reconstruction loss on H: DISPLAYFORM5 By Theorem 1, the problem of training the generative model reduces to training h to map N (0, I) tô H, which we refer to as the perceptual generative model. In the subsequent subsections, we present a maximum likelihood approach, as well as a VAE-based approach, to train the perceptual generative model. We proposed a framework, PGA, for training autoencoder-based generative models, with nonadversarial losses and unrestricted neural network architectures. By matching target distributions in the latent space, PGA trained with maximum likelihood generalizes the idea of reversible generative models to unrestricted neural network architectures and arbitrary latent dimensionalities. In addition, it improves the performance of VAE when combined together.In principle, PGA can be combined with any method that can train the perceptual generative model. While we have only considered two non-adversarial approaches, an interesting future work would be to combine PGA with an adversarial discriminator trained on latent representations. Moreover, the compatibility issue with batch normalization deserves further investigation.",Modern generative models are usually designed match target distributions directly data space where the intrinsic dimensionality data can be much lower ambient dimensionality. argue discrepancy may contribute difficulties training generative models. therefore propose map generated target distributions latent space using encoder standard autoencoder if we train generator decoder match target distribution latent space. resulting method perceptual generative autoencoder PGA is then incorporated maximum likelihood variational autoencoder VAE objective train generative model. maximum likelihood PGA generalizes idea reversible generative models unrestricted neural network architectures arbitrary latent dimensionalities. When combined VAE PGA can generate sharper samples vanilla VAE. Recent years have witnessed great interest generative models mainly due success generative adversarial networks GANs BID7 BID12 BID1. Despite prevalence adversarial nature GANs can lead number challenges unstable training dynamics mode collapse. Since advent GANs substantial efforts have been devoted addressing challenges BID21 BID9 BID19 non-adversarial approaches are free issues have also gained attention. Examples include variational autoencoders VAEs BID13 reversible generative models BID5 BID14 Wasserstein autoencoders WAEs BID22.However non-adversarial approaches often have significant limitations. instance VAEs tend generate blurry samples reversible generative models require restricted neural network architectures solving neural differential equations BID8. Furthermore use change variable formula latent space reversible model must have the same dimensionality data space which is unreasonable considering real-world high-dimensional data e.g images tends lie low-dimensional manifolds thus results redundant latent dimensions variability. Intriguingly recent research BID3 suggests discrepancy intrinsic ambient dimensionalities data also contributes difficulties training GANs VAEs.In work present novel framework training autoencoder-based generative models non-adversarial losses unrestricted neural network architectures. Given standard autoencoder target data distribution instead matching target distribution data space map generated target distributions latent space using encoder if we train generator decoder minimize divergence mapped distributions. prove mild assumptions minimizing form latent reconstruction error matching target distribution latent space implies matching data space. call framework perceptual generative autoencoder PGA show PGA enables training generative autoencoders maximum likelihood without restrictions architectures latent dimensionalities. addition when combined VAE PGA can generate sharper samples vanilla VAE. 1 2 METHODS 2.1 PERCEPTUAL GENERATIVE MODEL Let f:R →RH encoder parameterized φ g:RH→R decoder parameterized θ. goal is to obtain generative model which maps simple prior distribution data distribution D. Throughout paper useN 0 prior distribution.Forz∈ RH output decoder g z lies manifold is at most H-dimensional Therefore if we train autoencoder minimize DISPLAYFORM0 DISPLAYFORM1 thenx can be seen projection input data x onto manifold g z LetD denote distribution ofx. Given enough capacity encoder is the best approximation terms L2 distance can obtain decoder thus can serve surrogate target training generator.Due difficulty directly training generator matchD seek mapD latent space if we train generator match mapped distribution Ĥ latent space. end reuse encoder mappingD toĤ if we train generator h · f g · mapsN 0 toĤ. addition ensure g mapsN 0 toD minimize following latent reconstruction loss respect w.r.t φ:DISPLAYFORM2 Formally letZ x set z's are mapped x decoder have the following theorem:Theorem1. Assuming convexity Z x x∈R sufficient capacity encoder;z∼N 0 if Eq. 2 is minimized h z ∼Ĥ g z ∼D.Proof. first show different x's generated decoder are mapped different z's encoder. Letx1 g z1 x2 g z2 x1 x2. Since encoder has sufficient capacity Eq. 2 is minimized havef DISPLAYFORM3 z∼N 0 denote distributions g z h z respectively H. consider case where D andD are discrete distributions. Ifg z exists x DISPLAYFORM4 result still holds when D andD approach continuous distributions.Note two distributions compared Theorem1 andD are mapped respectively N 0 H. N 0 is supported wholeRH can be z's low probabilities N 0 high probabilities H which are not well covered Eq. 2 Therefore is sometimes helpful minimize another latent reconstruction loss H:DISPLAYFORM5 Theorem1 problem training generative model reduces trainingh mapN 0 tôH which we refer perceptual generative model. subsequent subsections present maximum likelihood approach which are not well VAE-based approach if we train perceptual generative model. proposed framework PGA training autoencoder-based generative models nonadversarial losses unrestricted neural network architectures. matching target distributions latent space PGA trained maximum likelihood generalizes idea reversible generative models unrestricted neural network architectures arbitrary latent dimensionalities. addition improves performance VAE when combined together.In principle PGA can be combined method can train perceptual generative model. have only considered two non-adversarial approaches interesting future work would combine PGA adversarial discriminator trained latent representations. Moreover compatibility issue batch normalization deserves investigation.,1494,989,505,0.02,1.511,2025/11/05 17:19:03,0.01,1.5,0.5638629283489092,474.986
"The quality of the representations achieved by embeddings is determined by how well the geometry of the embedding space matches the structure of the data.
 Euclidean space has been the workhorse for embeddings; recently hyperbolic and spherical spaces have gained popularity due to their ability to better embed new types of structured data---such as hierarchical data---but most data is not structured so uniformly.
 We address this problem by proposing learning embeddings in a product manifold combining multiple copies of these model spaces (spherical, hyperbolic, Euclidean), providing a space of heterogeneous curvature suitable for a wide variety of structures.
 We introduce a heuristic to estimate the sectional curvature of graph data and directly determine an appropriate signature---the number of component spaces and their dimensions---of the product manifold.
 Empirically, we jointly learn the curvature and the embedding in the product space via Riemannian optimization.
 We discuss how to define and compute intrinsic quantities such as means---a challenging notion for product manifolds---and provably learnable optimization functions.
 On a range of datasets and reconstruction tasks, our product space embeddings outperform single Euclidean or hyperbolic spaces used in previous works, reducing distortion by 32.55% on a Facebook social network dataset. We learn word embeddings and find that a product of hyperbolic spaces in 50 dimensions consistently improves on baseline Euclidean and hyperbolic embeddings, by 2.6
 points in Spearman rank correlation on similarity tasks
 and 3.4 points on analogy accuracy.
 With four decades of use, Euclidean space is the venerable elder of embedding spaces. Recently, non-Euclidean spaces-hyperbolic BID27 BID33 and spherical BID42 BID24 )-have gained attention by providing better representations for certain types of structured data. The resulting embeddings offer better reconstruction metrics: higher mean average precision (mAP) and lower distortion compared to their Euclidean counterparts. These three spaces are the model spaces of constant curvature BID21 , and this improvement in representation fidelity arises from the correspondence between the structure of the data (hierarchical, cyclical) and the geometry of non-Euclidean space (hyperbolic: negatively curved, spherical: positively curved). The notion of curvature plays the key role.To improve representations for a variety of types of data-beyond hierarchical or cyclical-we seek spaces with heterogeneous curvature. The motivation for such mixed spaces is intuitive: our data may have complicated, varying structure, in some regions tree-like, in others cyclical, and we seek the best of all worlds. We expect mixed spaces to match the geometry of the data and thus provide higher quality representations. However, to employ these spaces, we face several key obstacles. We must perform a challenging manifold optimization to learn both the curvature and the embedding. Afterwards, we also wish to operate on the embedded points. For example, analogy operations for word embeddings in Euclidean vector space (e.g., a − b + c) must be lifted to manifolds. 2 , Euclidean plane E 2 , and hyperboloid H 2 . Thick lines are geodesics; these get closer in positively curved (K = +1) space S 2 , remain equidistant in flat (K = 0) space E 2 , and get farther apart in negatively curved (K = −1) space H 2 .We propose embedding into product spaces in which each component has constant curvature. As we show, this allows us to capture a wider range of curvatures than traditional embeddings, while retaining the ability to globally optimize and operate on the resulting embeddings. Specifically , we form a Riemannian product manifold combining hyperbolic, spherical, and Euclidean components and equip it with a decomposable Riemannian metric. While each component space in the product has constant curvature (positive for spherical, negative for hyperbolic, and zero for Euclidean), the resulting mixed space has non-constant curvature. However, selecting appropriate curvatures for the embedding space is a potential challenge. We directly learn the curvature for each component space along with the embedding (via Riemannian optimization), recovering the correct curvature, and thus the matching geometry, directly from data. We show empirically that we can indeed recover non-uniform curvatures and improve performance on reconstruction metrics.Another technical challenge is to select the underlying number of components and dimensions of the product space; we call this the signature. This concept is vacuous in Euclidean space: the product of E r1 , . . . , E rn is identical to the single space E r1+...+rn . However, this is not the case with spherical and hyperbolic spaces. For example, the product of the spherical space S 1 (the circle) with itself is the torus S 1 × S 1 , which is topologically distinct from the sphere S 2 . We address this challenge by introducing a theory-guided heuristic estimator for the signature. We do so by matching an empirical notion of discrete curvature in our data with the theoretical distribution of the sectional curvature, a fine-grained measure of curvature on Riemannian manifolds that is amenable to analysis in products. We verify that this approach recovers the correct signature on reconstruction tasks.Standard techniques such as PCA require centering so that the embedded directions capture components of variation. Centering in turn needs an appropriate generalization of the mean. We develop a formulation of mean for embedded points that exploits the decomposability of the distance and has theoretical guarantees. For T = {p 1 , . . . , p n } in a manifold M with dimension r, the mean is µ(T ) := arg min p i d 2 M (p, p i ). We give a global existence result: under symmetry conditions on the distribution of the points in T on the spherical components, gradient descent recovers µ(T ) with error ε in time O(nr log ε −1 ).We demonstrate the advantages of product space embeddings through a variety of experiments; products are at least as good as single spaces, but can offer significant improvements when applied to structures not suitable for single spaces. We measure reconstruction quality (via mAP and distortion ) for synthetic and real datasets over various allocations of embedding spaces. We observe a 32.55% improvement in distortion versus any single space on a Facebook social network graph. Beyond reconstruction, we apply product spaces to skip-gram word embeddings, a popular technique with numerous downstream applications, which crucially require the use of the manifold structure. We find that products of hyperbolic spaces improve performance on benchmark evaluations-suggesting that words form multiple smaller hierarchies rather than one larger one. We see an improvement of 3.4 points over baseline single spaces on the Google word analogy benchmark and of 2.6 points in Spearman rank correlation on a word similarity task using the WS-353 corpus. Our results and initial exploration suggest that mixed product spaces are a promising area for future study. Product spaces enable improved representations by better matching the geometry of the embedding space to the structure of the data. We introduced a tractable Riemannian product manifold class that combines Euclidean, spherical, and hyperbolic spaces. We showed how to learn embeddings and curvatures, estimate the product signature, and defined a tractable formulation of mean. We hope that our techniques encourage further research on non-Euclidean embedding spaces. Table 5 : Accuracy on the Google word analogy dataset. Taking products of smaller hyperbolic spaces significantly improves performance. Unlike conventional embeddings, the operations in hyperbolic and product spaces are defined solely through distances and manifold operations. The Appendix starts with a glossary of symbols and a discussion of related work. Afterwards, we provide the proof of Lemma 2. We continue with a more in-depth treatment of the curvature estimation algorithm. We then introduce two combinatorial constructions-embedding techniques that do not require optimization-that rely on the alternative product distances. We give additional details on our experimental setup. Finally, we additionally evaluate the interpretability of these embeddings (i.e., do the separate components in the embedding manifold capture intrinsic qualities of the data?) through visualizations of the synthetic example from FIG0 . DISPLAYFORM0",quality representations achieved embeddings is determined how well geometry embedding space matches structure data. Euclidean space has been the workhorse embeddings;recently hyperbolic spherical spaces have gained popularity due ability better embed new types structured data -such hierarchical data -but data is not structured uniformly. address problem proposing learning embeddings product manifold combining multiple copies model spaces spherical hyperbolic Euclidean providing space heterogeneous curvature suitable wide variety structures. introduce heuristic estimate sectional curvature graph data directly determine appropriate signature -the number component spaces dimensions -of product manifold. Empirically jointly learn curvature embedding product space via Riemannian optimization. discuss how to define compute intrinsic quantities means -a challenging notion product manifolds -and provably learnable optimization functions. range datasets reconstruction tasks product space embeddings outperform single Euclidean hyperbolic spaces used previous works reducing distortion 32.55 Facebook social network dataset. learn word embeddings find product hyperbolic spaces 50 dimensions consistently improves baseline Euclidean hyperbolic embeddings 2.6 points Spearman rank correlation similarity tasks 3.4 points analogy accuracy. four decades use Euclidean space is the venerable elder embedding spaces. Recently non-Euclidean spaces-hyperbolic BID27 BID33 spherical BID42 BID24 -have gained attention providing better representations certain types structured data. resulting embeddings offer better reconstruction metrics:higher mean average precision mAP lower distortion compared Euclidean counterparts. three spaces are the model spaces constant curvature BID21 improvement representation fidelity arises correspondence structure data hierarchical cyclical geometry non-Euclidean space hyperbolic:negatively curved spherical:positively curved notion curvature plays key role.To improve representations variety types data-beyond hierarchical cyclical-we seek spaces heterogeneous curvature. motivation mixed spaces is intuitive:data may have complicated varying structure regions tree-like others cyclical seek best worlds. expect mixed spaces match geometry data thus provide higher quality representations. However employ spaces face several key obstacles. must perform challenging manifold optimization learn curvature embedding. Afterwards also wish operate embedded points. example analogy operations word embeddings Euclidean vector space e.g −b+c must lifted manifolds. 2 Euclidean planeE2 hyperboloidH2. Thick lines are geodesics;get closer positively curved K+1 space 2 remain equidistant flat K 0 spaceE2 get farther apart negatively curved K −1 space H 2.We propose embedding product spaces which each component has constant curvature. show allowsus capture wider range curvatures traditional embeddings retaining ability globally optimize operate resulting embeddings. Specifically form Riemannian product manifold combining hyperbolic spherical Euclidean components equip decomposable Riemannian metric. component space product has constant curvature positive spherical negative hyperbolic zero Euclidean resulting mixed space has non-constant curvature. However selecting appropriate curvatures embedding space is a potential challenge. directly learn curvature component space along embedding via Riemannian optimization recovering correct curvature thus matching geometry directly data. show empirically can indeed recover non-uniform curvatures improve performance reconstruction metrics.Another technical challenge is to select underlying number components dimensions product space;call signature. concept is vacuous Euclidean space:product Er1 Ern is identical single spaceEr1+...+rn. However is not case spherical hyperbolic spaces. example product spherical space 1 circle is torus 1× 1 which is topologically distinct sphere 2. address challenge introducing theory-guided heuristic estimator signature. do so by matching empirical notion discrete curvature data theoretical distribution sectional curvature fine-grained measure curvature Riemannian manifolds is amenable analysis products. verify approach recovers correct signature reconstruction tasks.Standard techniques PCA require centering embedded directions capture components variation. Centering turn needs appropriate generalization mean. develop formulation mean embedded points exploits decomposability distance has theoretical guarantees. p1 pn manifold dimensionr mean isµ arg minp 2 p p give global existence result:symmetry conditions distribution points spherical components gradient descent recoversµ errorε time nr logε−1.We demonstrate advantages product space embeddings variety experiments;products are at least good single spaces can offer significant improvements when applied structures suitable single spaces. measure reconstruction quality via mAP distortion synthetic real datasets various allocations embedding spaces. observe 32.55 improvement distortion versus single space Facebook social network graph. Beyond reconstruction apply product spaces skip-gram word embeddings popular technique numerous downstream applications which crucially require use manifold structure. find products hyperbolic spaces improve performance benchmark evaluations-suggesting words form multiple smaller hierarchies rather one larger one. see improvement 3.4 points baseline single spaces Google word analogy benchmark 2.6 points Spearman rank correlation word similarity task using WS-353 corpus. results initial exploration suggest mixed product spaces are a promising area future study. Product spaces enable improved representations better matching geometry embedding space structure data. introduced tractable Riemannian product manifold class combines Euclidean spherical hyperbolic spaces. showed how to learn embeddings curvatures estimate product signature defined tractable formulation mean. hope techniques encourage research non-Euclidean embedding spaces. Table5:Accuracy Google word analogy dataset. Taking products smaller hyperbolic spaces significantly improves performance. Unlike conventional embeddings operations hyperbolic product spaces are defined solely distances manifold operations. Appendix starts glossary symbols discussion related work. Afterwards provide proof Lemma2. continue in-depth treatment curvature estimation algorithm. introduce two combinatorial constructions-embedding techniques do not require optimization-that rely alternative product distances. give additional details experimental setup. Finally additionally evaluate interpretability embeddings.e do the separate components embedding manifold capture intrinsic qualities data? visualizations synthetic example FIG0. DISPLAYFORM0,1663,1118,545,0.019,1.487,2025/11/05 17:19:03,0.01,1.514,0.4890965732087229,502.816
"Synthesizing user-intended programs from a small number of input-output exam-
 ples is a challenging problem with several important applications like spreadsheet
 manipulation, data wrangling and code refactoring. Existing synthesis systems
 either completely rely on deductive logic techniques that are extensively hand-
 engineered or on purely statistical models that need massive amounts of data, and in
 general fail to provide real-time synthesis on challenging benchmarks. In this work,
 we propose Neural Guided Deductive Search (NGDS), a hybrid synthesis technique
 that combines the best of both symbolic logic techniques and statistical models.
 Thus, it produces programs that satisfy the provided specifications by construction
 and generalize well on unseen examples, similar to data-driven systems. Our
 technique effectively utilizes the deductive search framework to reduce the learning
 problem of the neural component to a simple supervised learning setup. Further,
 this allows us to both train on sparingly available real-world data and still leverage
 powerful recurrent neural network encoders. We demonstrate the effectiveness
 of our method by evaluating on real-world customer scenarios by synthesizing
 accurate programs with up to 12× speed-up compared to state-of-the-art systems. Automatic synthesis of programs that satisfy a given specification is a classical problem in AI BID29 , with extensive literature in both machine learning and programming languages communities. Recently, this area has gathered widespread interest, mainly spurred by the emergence of a sub-area -Programming by Examples (PBE) BID10 . A PBE system synthesizes programs that map a given set of example inputs to their specified example outputs. Such systems make many tasks accessible to a wider audience as example-based specifications can be easily provided even by end users without programming skills. See Figure 1 for an example. PBE systems are usually evaluated on three key criteria: (a) correctness: whether the synthesized program We studied the problem of real-time program synthesis with a small number of input-output examples. For this problem, we proposed a neural-guided system that builds upon PROSE, a state-of-the-art symbolic logic based system. Our system avoids top-down enumerative grammar exploration required by PROSE thus providing impressive synthesis performance while still retaining key advantages of a deductive system. That is, compared to existing neural synthesis techniques, our system enjoys following advantages: a) correctness: programs generated by our system are guaranteed to satisfy the given input-output specification, b) generalization: our system learns the user-intended program with just one input-output example in around 60% test cases while existing neural systems learn such a program in only 16% test cases, c) synthesis time: our system can solve most of the test cases in less than 0.1 sec and provide impressive performance gains over both neural as well symbolic systems.The key take-home message of this work is that a deep integration of a symbolic deductive inference based system with statistical techniques leads to best of both the worlds where we can avoid extensive engineering effort required by symbolic systems without compromising the quality of generated programs, and at the same time provide significant performance (when measured as synthesis time) gains. For future work, exploring better learning models for production rule selection and applying our technique to diverse and more powerful grammars should be important research directions.A ROBUSTFILL PERFORMANCE WITH DIFFERENT BEAM SIZES","Synthesizing user-intended programs small number input-output exam- ples is a challenging problem several important applications like spreadsheet manipulation data wrangling code refactoring. Existing synthesis systems either completely rely deductive logic techniques are extensively hand- engineered purely statistical models need massive amounts data general fail provide real-time synthesis challenging benchmarks. work propose Neural Guided Deductive Search NGDS hybrid synthesis technique combines best symbolic logic techniques statistical models. Thus produces programs satisfy provided specifications construction generalize well unseen examples similar data-driven systems. technique effectively utilizes deductive search framework reduce learning problem neural component simple supervised learning setup. allowsus train sparingly available real-world data still leverage powerful recurrent neural network encoders. demonstrate effectiveness method evaluating real-world customer scenarios synthesizing accurate programs 12× speed-up compared state-of-the-art systems. Automatic synthesis programs satisfy given specification is a classical problem AI BID29 extensive literature machine learning programming languages communities. Recently area has gathered widespread interest mainly spurred emergence sub-area -Programming Examples PBE BID10. PBE system synthesizes programs map given set example inputs specified example outputs. systems make many tasks accessible wider audience example-based specifications can be easily provided even end users without programming skills. See Figure1 example. PBE systems are usually evaluated three key criteria:correctness:whether synthesized program studied problem real-time program synthesis small number input-output examples. problem proposed neural-guided system builds upon PROSE state-of-the-art symbolic logic based system. system avoids top-down enumerative grammar exploration required PROSE thus providing impressive synthesis performance still retaining key advantages deductive system. is,compared existing neural synthesis techniques system enjoys following advantages:correctness:programs generated system are guaranteed satisfy given input-output specification b generalization:system learns user-intended program one input-output example around60% test cases existing neural systems learn program 16% test cases c synthesis time:system can solve test cases less 0.1 sec provide impressive performance gains neural well symbolic systems.The key take-home message work is that a deep integration symbolic deductive inference based system statistical techniques leads best worlds where we can avoid extensive engineering effort required symbolic systems without compromising quality generated programs time provide significant performance when measured synthesis time gains. future work exploring better learning models production rule selection applying technique diverse powerful grammars should be important research directions.A ROBUSTFILL PERFORMANCE DIFFERENT BEAM SIZES",661,470,191,0.006,1.406,2025/11/05 17:19:03,0.0,1.692,0.2367601246105914,190.658
"Variational auto-encoders
 (VAEs) offer a tractable approach when performing approximate inference in otherwise intractable generative models. However, standard VAEs often produce latent codes that are disperse and lack interpretability, thus making the resulting representations unsuitable for auxiliary tasks (e.g. classification) and human interpretation. We address these issues by merging ideas from variational auto-encoders and sparse coding, and propose to explicitly model sparsity in the latent space of a VAE with a Spike and Slab prior distribution. We derive the evidence lower bound using a discrete mixture recognition function thereby making approximate posterior inference as computational efficient as in the standard VAE case. With the new approach, we are able to infer truly sparse representations with generally intractable non-linear probabilistic models. We show that these sparse representations are advantageous over standard VAE representations on two benchmark classification tasks (MNIST and Fashion-MNIST) by demonstrating improved classification accuracy and significantly increased robustness to the number of latent dimensions. Furthermore, we demonstrate qualitatively that the sparse elements capture subjectively understandable sources of variation. Variational auto-encoders (VAEs) offer an efficient way of performing approximate posterior inference with otherwise intractable generative models and yield probabilistic encoding functions that can map complicated high-dimensional data to lower dimensional representations BID11 BID26 BID31 BID25 . Making such representations meaningful and efficient, however, is a particularly difficult task and currently a major challenge in representation learning BID8 BID2 BID9 BID33 . Large latent spaces often give rise to many latent dimensions that do not carry any information, and obtaining codes that properly capture the complexity of the observed data is generally problematic BID33 BID6 BID2 .In the case of linear mappings, sparse coding offers an elegant solution to the aforementioned problem; the representation space is induced to be sparse. In such a way, the encoding function is encouraged to use the minimum number of non-zero elements necessary to describe each observation and condense information in few active variables, different for each sample BID22 BID7 . In fact, due to their efficiency of representation, sparse codes have been used in many learning and recognition systems, as they provide easier interpretation BID14 BID1 BID18 BID0 and increased efficiency in, for example, classification, clustering, and transmission tasks when used as learning inputs BID38 BID35 BID12 .In this work, we aim to extent the aforementioned capability of linear sparse coding to non-linear probabilistic generative models thus allowing efficient, informative and interpretable representations in the general case. To this end we formulate a new variation of the classical VAE in which we employ a sparsity inducing prior in the latent space based on the Spike and Slab distribution. We match this by a discrete mixture recognition function that can map observations to sparse latent vectors. Efficient inference, comparable in complexity to that of standard VAEs, is achieved by deriving an evidence lower bound (ELBO) for the new model which is optimized using standard gradient methods to recover the encoding and decoding functions. In our experiments , we consider two benchmark dataset (MNIST and Fashion-MNIST) and show how the resulting ELBO is able to recover sparse, informative and interpretable representations regardless of the predefined number of latent dimensions. The ability to adjust to data complexity allows to automatically discover the sources of variation in given observations, without the need to carefully adjust the architecture of a model to the given representation task. We demonstrate these properties by first performing classification experiments using latent vectors as inputs, where we demonstrate that VSC representations marginally outperform VAE ones and display greatly improved robustness over large variations in latent space dimensionality. Secondly we show that many sparse elements in retrieved codes control subjectively recognisable features in the generated observations. 2 BACKGROUND AND RELATED WORK 2.1 SPARSE CODING Sparse coding aims to approximately represent input vectors x i with a weighted linear combination of few unknown basis vectors b j BID14 BID1 BID15 . The problem of determining the optimal basis and weights is generally formulated as the minimisation of an objective function of the following form arg min DISPLAYFORM0 where X ∈ R M ×N is the matrix of data, having as columns the input vectors x i ∈ R M ×1 , B ∈ R M ×J is the matrix having as columns the basis vectors b j ∈ R M ×1 , Z ∈ R J×N is the sparse codes matrix, having as columns the sparse codes z i ∈ R J×1 corresponding to the inputs x i , λ is a real positive parameter and φ(z i ) is a sparsity inducing function.Sparse coding can be probabilistically interpreted as a generative model, where the observed vectors x i are generated from the unobserved latent variables z i through the linear process x i = Bz i + , where is the observation noise and is drawn from an isotropic normal distribution with zero mean BID14 BID1 . The model can then be described with the following prior and likelihood distributions DISPLAYFORM1 where β is a real positive parameter, σ is the standard deviation of the observation noise and I is the identity matrix. Performing maximum a posteriori (MAP) estimation with this model results in the minimisation shown in equation 1 with λ = σ 2 β.In contrast to the MAP formulation, we are interested in maximising the marginal likelihood p(x) = p(x i ) and being able to perform such optimisation for arbitrarily complicated likelihood functions p(x|z).Previous work has demonstrated variational EM inference for such maximisation in the linear generative model case, with a particular choice of sparsity inducing prior BID32 BID4 . However, EM inference becomes intractable for more complicated non-linear posteriors and a large number of input vectors BID11 , making such an approach unsuitable to scale to our desired model. Conversely, some work has been done in generalising sparse coding to non-linear transformations, by defining sparsity on Riemannian manifolds BID7 BID3 . These generalisations, however, perform MAP inference as they define a non-linear equivalent of the objective function in equation 1 and are limited to simple manifolds due to the need to compute the manifold's logarithmic map. In this paper, we lay the general framework to induce sparsity in the latent space of VAEs, allowing approximate variational inference with arbitrarily complicated and probabilistic sparse coding models. We derived a lower bound which is of clear interpretation and efficient to estimate and optimise, as the ELBO of a standard VAE. With the resulting encoders, we recovered efficient sparse codes, which proved to be optimal learning inputs in standard classification benchmarks and exhibit good interpretation in many of their non-zero components. We conclude that inducing sparsity in the latent space of generative models appears to be a promising route to obtaining useful codes, interpretable representations and controlled data synthesis, which are all outstanding challenges in VAEs and representation learning in general. In future work, we aim to further study the properties of a sparse latent space with respect to its interpretation and features disentanglement capability. We expect VSC to be able to model huge ensembles of varied data by sparsely populating large latent spaces, hence isolating the features that govern variability among similar objects in widely diverse aggregates of data.",Variational auto-encoders VAEs offer tractable approach when performing approximate inference otherwise intractable generative models. However standard VAEs often produce latent codes are disperse lack interpretability thus making resulting representations unsuitable auxiliary tasks e.g classification human interpretation. address issues merging ideas variational auto-encoders sparse coding propose explicitly model sparsity latent space VAE Spike Slab prior distribution. derive evidence lower bound using discrete mixture recognition function thereby making approximate posterior inference computational efficient standard VAE case. new approach are able infer truly sparse representations generally intractable non-linear probabilistic models. show sparse representations are advantageous standard VAE representations two benchmark classification tasks MNIST Fashion-MNIST demonstrating improved classification accuracy significantly increased robustness number latent dimensions. Furthermore where we demonstrate qualitatively sparse elements capture subjectively understandable sources variation. Variational auto-encoders VAEs offer efficient way performing approximate posterior inference otherwise intractable generative models yield probabilistic encoding functions can map complicated high-dimensional data lower dimensional representations BID11 BID26 BID31 BID25. Making representations meaningful efficient however is a particularly difficult task currently major challenge representation learning BID8 BID2 BID9 BID33. Large latent spaces often give rise many latent dimensions do not carry information obtaining codes properly capture complexity observed data is generally problematic BID33 BID6 BID2.In case linear mappings sparse coding offers elegant solution aforementioned problem;representation space is induced sparse. way encoding function is encouraged use minimum number non-zero elements necessary describe observation condense information active variables different sample BID22 BID7. fact due efficiency representation sparse codes have been used many learning recognition systems provide easier interpretation BID14 BID1 BID18 BID0 increased efficiency example classification clustering transmission tasks when used learning inputs BID38 BID35 BID12.In work aim extent aforementioned capability linear sparse coding non-linear probabilistic generative models thus allowing efficient informative interpretable representations general case. end formulate new variation classical VAE which we employ sparsity inducing prior latent space based Spike Slab distribution. match discrete mixture recognition function can map observations sparse latent vectors. Efficient inference comparable complexity standard VAEs is achieved deriving evidence lower bound ELBO new model which is optimized using standard gradient methods recover encoding decoding functions. experiments consider two benchmark dataset MNIST Fashion-MNIST show how the resulting ELBO is able recover sparse informative interpretable representations regardless predefined number latent dimensions. ability adjust data complexity allows automatically discover sources variation given observations without need carefully adjust architecture model given representation task. demonstrate properties first performing classification experiments using latent vectors inputs where we demonstrate VSC representations marginally outperform VAE ones display greatly improved robustness large variations latent space dimensionality. Secondly show many sparse elements retrieved codes control subjectively recognisable features generated observations. 2 BACKGROUND RELATED WORK 2.1 SPARSE CODING Sparse coding aims approximately represent input vectors x weighted linear combination unknown basis vectorsb j BID14 BID1 BID15. problem determining optimal basis weights is generally formulated minimisation objective function following form arg min DISPLAYFORM0 whereX∈R ×N is the matrix data columns input vectorsx ∈R ×1 B∈R ×J is the matrix columns basis vectorsbj ∈R ×1 Z ∈ R J×N is the sparse codes matrix columns sparse codesz ∈ R J×1 corresponding inputsx λ is a real positive parameter φ z is a sparsity inducing function.Sparse coding can be probabilistically interpreted generative model where the observed vectorsx are generated unobserved latent variablesz linear processx Bz+where is the observation noise is drawn isotropic normal distribution zero mean BID14 BID1. model can then be described following prior likelihood distributions DISPLAYFORM1 whereβ is a real positive parameter σ is the standard deviation observation noise is the identity matrix. Performing maximum posteriori MAP estimation model results minimisation shown equation1 λ σ 2 β.In contrast MAP formulation are interested maximising marginal likelihoodp x p x able perform optimisation arbitrarily complicated likelihood functions p x|z.Previous work has demonstrated variational EM inference maximisation linear generative model case particular choice sparsity inducing prior BID32 BID4. However EM inference becomes intractable complicated non-linear posteriors large number input vectors BID11 making approach unsuitable scale desired model. Conversely work has been done generalising sparse coding non-linear transformations defining sparsity Riemannian manifolds BID7 BID3. generalisations however perform MAP inference define non-linear equivalent objective function equation1 are limited simple manifolds due need compute manifold's logarithmic map. paper lay general framework induce sparsity latent space VAEs allowing approximate variational inference arbitrarily complicated probabilistic sparse coding models. derived lower bound which is of clear interpretation efficient estimate optimise ELBO standard VAE. resulting encoders recovered efficient sparse codes which proved optimal learning inputs standard classification benchmarks exhibit good interpretation many non-zero components. conclude inducing sparsity latent space generative models appears promising route obtaining useful codes interpretable representations controlled data synthesis which are all outstanding challenges VAEs representation learning general. future work aim study properties sparse latent space respect interpretation features disentanglement capability. expect VSC able model huge ensembles varied data sparsely populating large latent spaces hence isolating features govern variability among similar objects widely diverse aggregates data.,1486,1056,430,0.014,1.407,2025/11/05 17:19:03,0.01,1.615,0.2398753894080995,449.569
"A widely observed phenomenon in deep learning is the degradation problem: increasing
 the depth of a network leads to a decrease in performance on both test and training data. Novel architectures such as ResNets and Highway networks have addressed this issue by introducing various flavors of skip-connections or gating mechanisms. However, the degradation problem persists in the context of plain feed-forward networks. In this work we propose a simple method to address this issue. The proposed method poses the learning of weights in deep networks as a constrained optimization problem where the presence of skip-connections is penalized by Lagrange multipliers. This allows for skip-connections to be introduced during the early stages of training and subsequently phased out in a principled manner. We demonstrate the benefits of such an approach with experiments on MNIST, fashion-MNIST, CIFAR-10 and CIFAR-100 where the proposed method is shown to greatly decrease the degradation effect (compared to plain networks) and is often competitive with ResNets. The representation view of deep learning suggests that neural networks learn an increasingly abstract representation of input data in a hierarchical fashion BID26 BID6 BID7 . Such representations may then be exploited to perform various tasks such as image classification, machine translation and speech recognition.A natural conclusion of the representation view is that deeper networks will learn more detailed and abstract representations as a result of their increased capacity. However, in the case of feed-forward networks it has been observed that performance deteriorates beyond a certain depth, even when the network is applied to training data. Recently, Residual Networks (ResNets; BID9 and Highway Networks BID22 have demonstrated that introducing various flavors of skip-connections or gating mechanisms makes it possible to train increasingly deep networks. However, the aforementioned degradation problem persists in the case of plain deep networks (i.e., networks without skip-connections of some form).A widely held hypothesis explaining the success of ResNets is that the introduction of skipconnections serves to improve the conditioning of the optimization manifold as well as the statistical properties of gradients employed during training. BID19 and BID21 show that the introduction of specially designed skip-connections serves to diagonalize the Fisher information matrix, thereby bringing standard gradient steps closer to the natural gradient. More recently, BID0 demonstrated that the introduction of skip-connections helps retain the correlation structure across gradients. This is contrary to the gradients of deep feed-forward networks, which resemble white noise. More generally, the skip-connections are thought to reduce the effects of vanishing gradients by introducing a linear term BID10 .The goal of this work is to address the degradation issue in plain feed-forward networks by leveraging some of the desirable optimization properties of ResNets. We approach the task of learning parameters for a deep network under the framework of constrained optimization. This strategy allows us to introduce skip-connections penalized by Lagrange multipliers into the architecture of our network. In our setting , skip-connections play an important role during the initial training of the network and are subsequently removed in a principled manner. Throughout a series of experiments we demonstrate that such an approach leads to improvements in generalization error when compared to architectures without skip-connections and is competitive with ResNets in some cases.The contributions of this work are as follows:• We propose alternative training strategy for plain feed-forward networks which reduces the degradation in performance as the depth of the network increases. The proposed method introduces skip-connections which are penalized by Lagrange multipliers. This allows for the presence of skip-connections to be iteratively phased out during training in a principled manner. The proposed method is thereby able to enjoy the optimization benefits associated with skip-connections during the early stages of training.• A number of benchmark datasets are used to demonstrate the empirical capabilities of the proposed method. In particular , the proposed method greatly reduces the degradation effect compared to plain networks and is on several occasions competitive with ResNets. This manuscript presents a simple method for training deep feed-forward networks which greatly reduces the degradation problem. In the past, the degradation issue has been successfully addressed via the introduction of skip-connections. As such, the goal of this work is to propose a new training regime which retains the optimization benefits associated with ResNets while ultimately phasing out skip-connections. This is achieved by posing network training as a constrained optimization problem where skip-connections are introduced during the early stages of training and subsequently phased out in a principled manner using Lagrange multipliers.Throughout a series of experiments we demonstrate that the performance of VAN networks is stable, displaying a far smaller drop in performance as depth increases and thereby largely mitigating the degradation problem.",widely observed phenomenon deep learning is the degradation problem:increasing depth network leads decrease performance test training data. Novel architectures ResNets Highway networks have addressed issue introducing various flavors skip-connections gating mechanisms. However degradation problem persists context plain feed-forward networks. work propose simple method address issue. proposed method poses learning weights deep networks constrained optimization problem where the presence skip-connections is penalized Lagrange multipliers. allows skip-connections introduced early stages training are subsequently phased principled manner. demonstrate benefits approach experiments MNIST fashion-MNIST CIFAR-10 CIFAR-100 where the proposed method is shown greatly decrease degradation effect compared plain networks is often competitive ResNets. representation view deep learning suggests neural networks learn increasingly abstract representation input data hierarchical fashion BID26 BID6 BID7. representations may exploited perform various tasks image classification machine translation speech recognition.A natural conclusion representation view is that deeper networks will learn detailed abstract representations result increased capacity. However case feed-forward networks has been observed performance deteriorates beyond certain depth even when the network is applied training data. Recently Residual Networks ResNets;BID9 Highway Networks BID22 have demonstrated introducing various flavors skip-connections gating mechanisms makes possible train increasingly deep networks. However aforementioned degradation problem persists case plain deep networks.e networks without skip-connections form.A widely held hypothesis explaining success ResNets is that the introduction skipconnections serves improve conditioning optimization manifold well statistical properties gradients employed training. BID19 BID21 show introduction specially designed skip-connections serves diagonalize Fisher information matrix thereby bringing standard gradient steps closer natural gradient. recently BID0 demonstrated introduction skip-connections helps retain correlation structure across gradients. is contrary gradients deep feed-forward networks which resemble white noise. generally skip-connections are thought reduce effects vanishing gradients introducing linear term BID10.The goal work is to address degradation issue plain feed-forward networks leveraging desirable optimization properties ResNets. approach task learning parameters deep network framework constrained optimization. strategy allowsus introduce skip-connections penalized Lagrange multipliers architecture network. setting skip-connections play important role initial training network are subsequently removed principled manner. Throughout series experiments demonstrate approach leads improvements generalization error when compared architectures without skip-connections is competitive ResNets cases.The contributions work are as follows:• propose alternative training strategy plain feed-forward networks which reduces degradation performance depth network increases. proposed method introduces skip-connections which are penalized Lagrange multipliers. allows presence skip-connections iteratively phased training principled manner. proposed method is thereby able enjoy optimization benefits associated skip-connections early stages training.• number benchmark datasets are used demonstrate empirical capabilities proposed method. particular proposed method greatly reduces degradation effect compared plain networks is on several occasions competitive ResNets. manuscript presents simple method training deep feed-forward networks which greatly reduces degradation problem. past degradation issue has been successfully addressed via introduction skip-connections goal work is to propose new training regime which retains optimization benefits associated ResNets ultimately phasing skip-connections is achieved posing network training constrained optimization problem where skip-connections are introduced early stages training are subsequently phased principled manner using Lagrange multipliers.Throughout series experiments demonstrate performance VAN networks is stable displaying far smaller drop performance depth increases thereby largely mitigating degradation problem.,932,642,290,0.01,1.452,2025/11/05 17:19:03,0.0,1.4,0.3800623052959498,307.933
"Deep learning is becoming more widespread in its application due to its power in solving complex classification problems. However, deep learning models often require large memory and energy consumption, which may prevent them from being deployed effectively on embedded platforms, limiting their applications. This work addresses the problem by proposing methods {\em Weight Reduction Quantisation} for compressing the memory footprint of the models, including reducing the number of weights and the number of bits to store each weight. Beside, applying with sparsity-inducing regularization, our work focuses on speeding up stochastic variance reduced gradients (SVRG) optimization on non-convex problem. Our method that mini-batch SVRG with $\ell$1 regularization on non-convex problem has faster and smoother convergence rates than SGD by using adaptive learning rates. Experimental evaluation of our approach uses MNIST and CIFAR-10 datasets on LeNet-300-100 and LeNet-5 models, showing our approach can reduce the memory requirements both in the convolutional and fully connected layers by up to 60$\times$ without affecting their test accuracy. Artificial intelligence is finding wider application across a number of domains where computational resources can vary from large data centres to mobile devices. However, state-ofthe-art techniques such as deep learning BID14 require significant resources, including large memory requirements and energy consumption. Reducing the size of the deep learning model to a compact model that has small memory footprint without compromising its performance is a desirable research aim to address the challenges for deploying these leading approaches on mobile devices. 1 regularization can be used as a penalty to train models to prevent the model from over-fitting the training data. As well as providing, 1 regularization is a powerful compression techniques to penalize some weights to be zero. As the results, our research focus on improving the method based on 1 regularization to reduce memory requirements. Moreover, as deep neural network optimization is a non-convex problem, the optimization can be stuck in local-minimal, which can reduce the performance. To address the problem, we improve SGD optimization for non-convex function to enhancing sparse representations obtained with 1 regularization. In this paper, we propose our compression method Weight Reduction Quantisation which reduces both the number of weights and bits-depth of model without sacrificing accuracy. To reduces the number of weights, our method employs sparsity-inducing 1 regularization to encourage many connections in both convolutional and fully connected layers to be zero during the training process. Formally, in this paper we consider the following unconstrained minimization problem, Given training labels y 1 , y 2 , ..., y N as correct outputs for input data x 1 , x 2 , ..., x N , the optimization problem to estimate the weights in all layers, W, is defined by DISPLAYFORM0 L(y i , f(x i ; W)) + λr(W),where λ is a hyper-parameter controlling the degree of regularization and the weights in all layers is given by W. The problem 1 can be strongly convex or possibly non-convex BID2 . Following update rule, the mini-batch SGD method with 1 regularization is a popular approach for performing the optimization, and the weight update rule is given by DISPLAYFORM1 where each weight of network can be represented by w j ,the total number of weights is M. k is the iteration counter and η k is the learning rate and B is mini-batch size (1 < B < N) used to approximate the full gradient. However, SGD optimization with 1 regularization has two challenges: firstly, it inefficiently encourages weight to be zero due to fluctuations generated by SGD BID18 . Secondly, SGD optimization slowing down convergence rate due to the high variance of gradients. The two methods of cumulative 1 regularization and SVRG can solve the two challenges respectively:Cumulative 1 regularization BID18 proposed a method cumulating the 1 penalties to resolve the problem. The method clips regularization at zero, which avoids the derivative DISPLAYFORM2 being non-differentiable when w j = 0 and provides a more stable convergence for the weights. Moreover, the cumulative penalty can reduce the weight to zero more quickly.Mini-batch SVRG As SGD optimization has slow convergence asymptotically due to noise, BID12 proposed SVRG that can efficiently decrease the noise of SGD by reducing the variance of gradients by: DISPLAYFORM3 whereμ j is the average gradient of sub-optimal weightsw j which is the weight after every m SGD iterationsμ DISPLAYFORM4 whereW is the sub-optimal weights after m SGD iterations in all layers. For succinctness we also write ∇ψ i (w DISPLAYFORM5 . They determined that reduction of variance helps initial weights w 0 close to global minima at the beginning in order to boost the convergence rate of SGD in strongly convex problems. BID12 further prove that the performance of SGD degrades with mini-batching by the theoretical result of complexity. Specifically, for batch size of B, SGD has a 1/ √ B dependence on the batch size. In contrast, SVRG in a parallel setting has 1/B dependence on the batch size which is much better than SGD. Hence, SVRG allows more efficient mini-batching. However, for non-strongly convex problems, global minimization of non-convex function is NP-hard BID1 . BID12 have a assumption that SVRG can also be applied in neural networks to accelerate the local convergence rate of SGD. Further, Allen BID1 prove non-asymptotic rates of convergence of SVRG for non-convex optimization and proposed improved SVRG that is provably faster than SGD. Hence, a promising approach is to use mini-batch SVRG instead of SGD with cumulative 1 regularization. In this paper, we proposed Weight Reduction Quantisation that efficiently compressed neural networks without scarifying accuracy. Our method has two stages that reduce the number of weights and reduce the number of bits to store each weight. We show that SVRG and cumulative 1 regularization can improve over SGD and 1-regularization. By combining them, we have presented a new compression method Delicate-SVRG-cumulative-1 that can efficiently reduce the number of parameters by the separate adaptive learning rates. The three adaptive learning rates are applied on SVRG and cumulative 1 penalty, which provides a high accuracy and reduced number of weights. Besides, our method improved SVRG that can be used on non-convex problem with fast convergence rate. In our experiments on LeNet-300-100 and LeNet-5, our method can significantly reduce the memory requirements up to 60× without accuracy loss. After compression by our method, a compact deep neural network can be efficiently deployed on an embedded device with performance of the original model.Algorithm 1 Delicate-SVRG-cumulative-1: Stochastic descent training with cumulative 1 penalty procedure Train( λ) u ← 0 µ ← 0 Initial w j and q j with zero for all number of weights M for k=0 to Maximal Iterations do DISPLAYFORM0 end for u ← u + ηλ/M end for for j ∈ features used in sample i do randomly select m features from train samples DISPLAYFORM1 (∇ψ i (w j ) -∇ψ i (w j )) + β kμ ∇ψ i (w j ) = ∇ψ i (w j ) if w j andw j converge to the same weights theñ µ = 0 end if µ ←μ + The results showed in Figure4.7.3 Using multiple initializations to compare the performance of our method and other three methods.The experiments were run with multiple initializations and there was some small variability in the results. However, the relative performance of the our method is always better than SVRG and SGD combining with cumulative 1 regularization. The results showed in (b) The test loss: MNIST dataset on LeNet-5 (left) and CIFAR-10 dataset on LeNet-300-100 (middle) and Figure 4: Estimate the convergence rate when using four compression methods, including our method Delicate-SVRG-cumulative-1, Delicate-SVRG-cumulative-1 (without BiasPruning) that without bias-based pruning in 1 regularization,SVRG-cumulative-1 and SGD-cumulative-1, on LeNet-300-100 and LeNet-5 models with MNIST and CIFAR-10 datasets. Here we choose the compression rate that equal 90% to observe training and test loss. For MNIST dataset, we did not notice subtle difference train and test loss on LeNet-300-100 model generated by four methods. Figure 5: Using three types of initial weights, we compare our method with other three methods. D-SVRG-C-L1 and D-SVRG-C-L1(wo BiasPruning) are always better than other two methods. This experiment also can verify the our view that the performance of SVRG is better or worse than SGD that depends on the number of training samples. In our experiment, if choosing small dataset (e.g. MNIST), SVRG is better than SGD. Otherwise, if choosing relatively large dataset (e.g. CIFAR-10), SVRG is worse than SGD.",Deep learning is becoming widespread application due power solving complex classification problems. However deep learning models often require large memory energy consumption may prevent deployed effectively embedded platforms limiting applications. work addresses problem proposing methods \em Weight Reduction Quantisation compressing memory footprint models including reducing number weights number bits store weight. Beside applying sparsity-inducing regularization work focuses speeding stochastic variance reduced gradients SVRG optimization non-convex problem. method mini-batch SVRG $\ell $1 regularization non-convex problem has faster smoother convergence rates SGD using adaptive learning rates. Experimental evaluation approach uses MNIST CIFAR-10 datasets LeNet-300-100 LeNet-5 models showing approach can reduce memory requirements convolutional fully connected layers 60 $\times without affecting test accuracy. Artificial intelligence is finding wider application across number domains where computational resources can vary large data centres mobile devices. However state-ofthe-art techniques deep learning BID14 require significant resources including large memory requirements energy consumption. Reducing size deep learning model compact model has small memory footprint without compromising performance is a desirable research aim address challenges deploying leading approaches mobile devices. 1 regularization can be used penalty train models prevent model over-fitting training data. well providing 1 regularization is a powerful compression techniques penalize weights zero. results research focus improving method based 1 regularization reduce memory requirements. Moreover deep neural network optimization is a non-convex problem optimization can be stuck local-minimal which can reduce performance. address problem improve SGD optimization non-convex function enhancing sparse representations obtained 1 regularization. paper propose compression method Weight Reduction Quantisation which reduces number weights bits-depth model without sacrificing accuracy. reduces number weights method employs sparsity-inducing1 regularization encourage many connections convolutional fully connected layers zero training process. Formally paper consider following unconstrained minimization problem Given training labels 1 2... N correct outputs input datax1 x2... xN optimization problem estimate weights layers W is defined DISPLAYFORM0L f x i;W+λr W whereλ is a hyper-parameter controlling degree regularization weights layers is given W. problem1 can be strongly convex possibly non-convex BID2. Following update rule mini-batch SGD method 1 regularization is a popular approach performing optimization weight update rule is given DISPLAYFORM1 where each weight network can be represented wj total number weights isM. k is the iteration counter ηk is the learning rate B is mini-batch size 1 B N used approximate full gradient. However SGD optimization 1 regularization has two challenges:firstly inefficiently encourages weight zero due fluctuations generated SGD BID18. Secondly SGD optimization slowing convergence rate due high variance gradients. two methods cumulative 1 regularization SVRG can solve two challenges respectively:Cumulative 1 regularization BID18 proposed method cumulating 1 penalties resolve problem. method clips regularization zero which avoids derivative DISPLAYFORM2 non-differentiable whenwj 0 provides stable convergence weights. Moreover cumulative penalty can reduce weight zero quickly.Mini-batch SVRG SGD optimization has slow convergence asymptotically due noise BID12 proposed SVRG can efficiently decrease noise SGD reducing variance gradients by:DISPLAYFORM3 whereμj is the average gradient sub-optimal weightswj which is the weight every SGD iterationsμ DISPLAYFORM4 whereW is the sub-optimal weights SGD iterations layers. succinctness also write∇ψ w DISPLAYFORM5. determined reduction variance helps initial weights w 0 close global minima beginning order boost convergence rate SGD strongly convex problems. BID12 prove performance SGD degrades mini-batching theoretical result complexity. Specifically batch size B SGD has a has1/√B dependence batch size. contrast SVRG parallel setting has a has 1/B dependence batch size which is much better SGD. Hence SVRG allows efficient mini-batching However non-strongly convex problems global minimization non-convex function is NP-hard BID1. BID12 have a assumption SVRG can also applied neural networks accelerate local convergence rate SGD. Allen BID1 prove non-asymptotic rates convergence SVRG non-convex optimization proposed improved SVRG is provably faster SGD. Hence promising approach is to use mini-batch SVRG instead SGD cumulative 1 regularization. paper proposed Weight Reduction Quantisation can efficiently compressed neural networks without scarifying accuracy. method has two stages reduce number weights reduce number bits store weight. show SVRG cumulative 1 regularization can improve SGD 1-regularization combining have presented new compression method Delicate-SVRG-cumulative-1 can efficiently reduce number parameters separate adaptive learning rates. three adaptive learning rates are applied SVRG cumulative 1 penalty which provides high accuracy reduced number weights. Besides method improved SVRG can be used non-convex problem fast convergence rate. experiments LeNet-300-100 LeNet-5 method can significantly reduce memory requirements 60× without accuracy loss. compression method compact deep neural network can be efficiently deployed embedded device performance original model.Algorithm 1 Delicate-SVRG-cumulative-1 Stochastic descent training cumulative 1 penalty procedure Train λ u←0µ ← 0 Initialw j qj zero number weights k=0 Maximal Iterations do DISPLAYFORM0 end u←u+ηλ/end j ∈ features used sample do randomly select features train samples DISPLAYFORM1 ∇ψ wj -∇ψ wj+βkμ∇ψ wj ∇ψ wj if w j andwj converge weights theñµ 0 end ifµ←μ+results showed Figure4.7.3 Using multiple initializations compare performance method three methods.The experiments were run multiple initializations was some small variability results. However relative performance method is always better SVRG SGD combining cumulative 1 regularization. results showed b test loss:MNIST dataset LeNet-5 left CIFAR-10 dataset LeNet-300-100 middle Figure4:Estimate convergence rate when using four compression methods including method Delicate-SVRG-cumulative-1 Delicate-SVRG-cumulative-1 without BiasPruning without bias-based pruning 1 regularization SVRG-cumulative-1 SGD-cumulative-1 LeNet-300-100 LeNet-5 models MNIST CIFAR-10 datasets. choose compression rate equal90% observe training test loss. MNIST dataset did not notice subtle difference train test loss LeNet-300-100 model generated four methods. Figure5:Using three types initial weights compare method three methods. D-SVRG-C-L1 D-SVRG-C-L1 wo BiasPruning are always better two methods. experiment also can verify view performance SVRG is better worse SGD depends number training samples. experiment if choosing small dataset e.g MNIST SVRG is better SGD. Otherwise if choosing relatively large dataset e.g CIFAR-10 SVRG is worse SGD.,1901,1380,521,0.021,1.378,2025/11/05 17:19:03,0.01,1.391,0.1495327102803733,537.938
"It has been argued that the brain is a prediction machine that continuously learns how to make better predictions about the stimuli received from the external environment. For this purpose, it builds a model of the world around us and uses this model to infer the external stimulus. Predictive coding has been proposed as a mechanism through which the brain might be able to build such a model of the external environment. However, it is not clear how predictive coding can be used to build deep neural network models of the brain while complying with the architectural constraints imposed by the brain. In this paper, we describe an algorithm to build a deep generative model using predictive coding that can be used to infer latent representations about the stimuli received from external environment. Specifically, we used predictive coding to train a deep neural network on real-world images in a unsupervised learning paradigm. To understand the capacity of the network with regards to modeling the external environment, we studied the latent representations generated by the model on images of objects that are never presented to the model during training. Despite the novel features of these objects the model is able to infer the latent representations for them. Furthermore, the reconstructions of the original images obtained from these latent representations preserve the important details of these objects. The general idea of predictive coding BID8 BID9 BID11 postulates that the brain is continuously trying to predict the information it receives from external environment. An implementation of predictive coding was first proposed as a model of visual information processing in the brain BID12 . Recently, it was described as an implementation of the free-energy principle in the brain BID1 . Predictive coding models the visual information processing pathways as a recurrently connected hierarchical neural network. Feedback connections from higher to lower level areas convey predictions about the activities of the lower level neurons and feedforward connections convey the residual errors in these predictions to higher level areas.Several studies have focused on the biological plausibility of predictive coding and its relation to other learning approaches. In BID14 , the author showed that a model of biased competition BID0 that uses lateral inhibition to suppress the input of other nodes is equivalent to the linear model of predictive coding. An extension to predictive coding has been proposed in BID13 that relaxes the requirement of symmetric weights between two adjacent layers in the network. In a similar study, it was shown that the error-backpropagation and predictive coding use similar forms of weight changes during learning BID16 .From the perspective of training deep neural networks, predictive coding is an approach that is widely supported by neurophysiological data BID3 ) and adheres to the architectural and locality (in terms of learning) constraints imposed by the brain. Existing studies on predictive coding has focused on small neural network models to study the development of orientation selective receptive fields in primary visual cortex BID12 BID13 . It is unclear how predictive coding can be used to build deep neural network models of the brain to study more complicated brain processes like attention, memory, etc. Another important question that arises while building models of the brain is how can we comply with the architectural constraints applicable in the brain like the retinotopic arrangement of receptive fields that is found in the sensory cortical areas. At present, mostly neural networks with fully connected layers are used, which implies that the receptive fields of neurons are as big as the field of view. To overcome this, neural network models are trained on patches from real world images. This approach works well when training small neural network models but it is difficult to extend it for training deep neural networks.In this paper, we present a systematic approach for training deep neural networks using predictive coding in a biologically plausible manner. The network is used to learn hierarchical latent representations for a given input stimulus. The architecture of these neural networks is inspired by convolutional neural networks BID5 . However, to comply with the retinotopic arrangement of receptive fields observed in sensory cortical areas, we employ neural networks in which filters are not applied across the entire layer, similar to locally connected layers used in BID15 . Instead, filters are applied only to a small receptive field which allows us to train the filters associated with different receptive fields independently. This approach can be easily scaled to train deep neural networks for modeling information processing along the sensory processing pathways.In general, the approach proposed in this paper can be used for stimuli in any modality. To illustrate the effectiveness of the approach, we trained a deep neural network using predictive coding on 1000 real-world images of horses and ships from the CIFAR-10 data set. The model is trained in an unsupervised learning paradigm to build a generative model for real-world images and is used to infer latent representations for real-world. To estimate the capacity of the network in modeling real-world images, we used the model to infer latent representations for new images of horses and ships as well as objects that are never presented to the network during training. The model is able to reconstruct the original real-world images from the inferred latent representations while retaining the important features of the objects in these images. This shows that the model can capture the causal regularities in real-world images.The paper is organized as follows: Section 2 describes the architecture and the predictive coding based learning algorithm used for training deep neural network models. Section 3 describes the results of studies conducted using the trained models. Section 4 discusses the computational implications of deep predictive coding and its relationship with other approaches in machine learning. Section 5 summarizes the conclusions from the experiments reported in this paper. In this section, we discuss the computational implications of the algorithm presented in this paper and the similarities it shares with existing approaches in machine learning.Deep neural networks have improved the state-of-the-art performances in many problems related to image processing like classification, semantic segmentation, etc. These improvements have been achieved by exploiting the availability of cheap computational power. However, with increases in the complexity of neural network architectures, the problem of developing efficient learning algorithms has become prominent. A large body of work in machine learning literature has been dedicated to improving the speed of error-backpropagation which is one of the most used learning algorithms for training deep neural networks. However, an inherent property of error-backpropagation is to systematically propagate information through the network in the forward direction and during learning, propagate the error gradients in the backward direction. This imposes restrictions on the extent of parallelization that can be achieved with error back-propagation.In this respect, the proposed learning algorithm can be extensively parallelized. It can be observed from Equations 6 and 7 that the latent representations for the neurons in a given layer depend only on the error in predicting the latent representations at the layer below. This aspect of the learning algorithm can be leveraged to update the latent representations and filters at each layer in the network in parallel. Thus the feedforward and feedback processes can be performed at each layer in parallel. Further, the use of a network architecture with retinotopical arrangement of receptive fields allows us to update the latent representations and filters associated with all positions in a given layer in parallel. Thus, the learning algorithm proposed in this paper is amenable to parallelization and can be useful for speeding up the training of deep neural architectures.Another interesting aspect of the predictive coding is its proximity to the idea of deconvolutional neural networks BID17 . Deconvolutional neural networks have also been used to learn the latent representations for a given input image and have been used for the problem of semantic segmentation BID10 . The problem of learning latent representations is inherently an ill-posed problem as there is no unique solution for a given input stimulus. To overcome this issue deconvolutional neural networks optimize on auxiliary variables and the generated latent representations in alternation. A continuation parameter β is continuously increased during the learning process until the latent representations are strongly clamped to the auxiliary variables. This requires carefully controlling the learning process and increases the computational requirements of the learning algorithm due to an extra optimization step on auxiliary variables. Predictive coding provides an alternate solution to this problem. In Equation 6, the update term associated with td constraint the learning algorithm to generate latent representations that can be easily predicted by the successive layers in the network. The effect of this constraint on the learning algorithm is same as that of the auxiliary variables in deconvolutional neural networks and impart numerical stability to the learning process. This approach provides a more simpler solution to the problem of learning latent representations without imposing the additional computational effort of optimizing auxiliary variables. In this paper, we describe a method to train deep neural networks using predictive coding for modeling information processing along cortical sensory hierarchies. The approach uses a neural network in which neurons project only to neurons in their respective receptive fields. This kind of architecture respects the retinotopic arrangement of receptive fields observed in the visual cortical areas.The method can be used to build a deep generative model for data in any modality. For illustration, we trained the model on a set of real-world images and then used the trained model to infer hierarchical latent representations. Even though the model is trained on a small data set of 1000 images of horses and ships, it can infer effective latent representations for images of other objects like sparrow, cats, trucks, cars, etc. This shows that the trained model is able to capture the statistical regularities present in the real-world images. In this regards, the generalization ability of the model is better than most existing algorithms that usually rely on large amount of data to achieve better generalization.",has been argued brain is a prediction machine continuously learns how to make better predictions stimuli received external environment. purpose builds model world aroundus uses model infer external stimulus. Predictive coding has been proposed mechanism which the brain might able build model external environment. However is not clear how predictive coding can be used build deep neural network models brain complying architectural constraints imposed brain. paper describe algorithm build deep generative model using predictive coding can be used infer latent representations stimuli received external environment. Specifically used predictive coding train deep neural network real-world images unsupervised learning paradigm. understand capacity network regards modeling external environment studied latent representations generated model images objects are never presented model training. Despite novel features objects model is able infer latent representations them. Furthermore reconstructions original images obtained latent representations preserve important details objects. general idea predictive coding BID8 BID9 BID11 postulates brain is continuously trying predict information receives external environment. implementation predictive coding was first proposed model visual information processing brain BID12. Recently was described implementation free-energy principle brain BID1. Predictive coding models visual information processing pathways recurrently connected hierarchical neural network. Feedback connections higher lower level areas convey predictions activities lower level neurons feedforward connections convey residual errors predictions higher level areas.Several studies have focused biological plausibility predictive coding relation learning approaches. BID14 author showed model biased competition BID0 uses lateral inhibition suppress input nodes is equivalent linear model predictive coding. extension predictive coding has been proposed BID13 relaxes requirement symmetric weights two adjacent layers network. similar study was shown error-backpropagation predictive coding use similar forms weight changes learning BID16.From perspective training deep neural networks predictive coding is an approach is widely supported neurophysiological data BID3 adheres architectural locality terms learning constraints imposed brain. Existing studies predictive coding has focused small neural network models study development orientation selective receptive fields primary visual cortex BID12 BID13. is unclear how predictive coding can be used build deep neural network models brain study complicated brain processes like attention memory etc. Another important question arises building models brain is how can we comply architectural constraints applicable brain like retinotopic arrangement receptive fields is found sensory cortical areas. present mostly neural networks fully connected layers are used which implies receptive fields neurons are as big field view. overcome neural network models are trained patches real world images. approach works well when training small neural network models is difficult extend training deep neural networks.In paper present systematic approach training deep neural networks using predictive coding biologically plausible manner. network is used learn hierarchical latent representations given input stimulus. architecture neural networks is inspired convolutional neural networks BID5. However comply retinotopic arrangement receptive fields observed sensory cortical areas employ neural networks which filters are not are applied across entire layer similar locally connected layers used BID15. Instead filters are not are applied small receptive field which allowsus train filters associated different receptive fields independently. approach can be easily scaled train deep neural networks modeling information processing along sensory processing pathways.In general approach proposed paper can be used stimuli modality. illustrate effectiveness approach trained deep neural network using predictive coding 1000 real-world images horses ships CIFAR-10 data set. model is trained unsupervised learning paradigm build generative model real-world images is have been used infer latent representations real-world estimate capacity network modeling real-world images used model infer latent representations new images horses ships well objects are never presented network training. model is able reconstruct original real-world images inferred latent representations retaining important features objects images. shows model can capture causal regularities real-world images.The paper is organized follows:Section 2 describes architecture predictive coding based learning algorithm used training deep neural network models. Section 3 describes results studies conducted using trained models. Section 4 discusses computational implications deep predictive coding relationship approaches machine learning. Section 5 summarizes conclusions experiments reported paper. section discuss computational implications algorithm presented paper similarities shares existing approaches machine learning.Deep neural networks have improved state-of-the-art performances many problems related image processing like classification semantic segmentation etc. improvements have been achieved exploiting availability cheap computational power. However increases complexity neural network architectures problem developing efficient learning algorithms has become prominent. large body work machine learning literature has been dedicated improving speed error-backpropagation which is one used learning algorithms training deep neural networks. However inherent property error-backpropagation is to systematically propagate information network forward direction learning propagate error gradients backward direction. imposes restrictions extent parallelization can be achieved error back-propagation.In respect proposed learning algorithm can be extensively parallelized. can be observed Equations6 7 latent representations neurons given layer depend error predicting latent representations layer below. aspect learning algorithm can be leveraged update latent representations filters layer network parallel. Thus feedforward feedback processes can be performed layer parallel. use network architecture retinotopical arrangement receptive fields allowsus update latent representations filters associated positions given layer parallel. Thus learning algorithm proposed paper is amenable parallelization can be useful speeding training deep neural architectures.Another interesting aspect predictive coding is its proximity idea deconvolutional neural networks BID17. Deconvolutional neural networks have also used learn latent representations given input image is have been used problem semantic segmentation BID10. problem learning latent representations is inherently ill-posed problem is no unique solution given input stimulus. overcome issue deconvolutional neural networks optimize auxiliary variables generated latent representations alternation. continuation parameterβ is continuously increased learning process latent representations are strongly clamped auxiliary variables. requires carefully controlling learning process increases computational requirements learning algorithm due extra optimization step auxiliary variables. Predictive coding provides alternate solution problem. Equation6 update term associated td constraint learning algorithm generate latent representations can be easily predicted successive layers network. effect constraint learning algorithm is same as that auxiliary variables deconvolutional neural networks impart numerical stability learning process. approach provides simpler solution problem learning latent representations without imposing additional computational effort optimizing auxiliary variables. paper describe method train deep neural networks using predictive coding modeling information processing along cortical sensory hierarchies. approach uses neural network which neurons project neurons respective receptive fields. kind architecture respects retinotopic arrangement receptive fields observed visual cortical areas.The method can be used build deep generative model data modality. illustration trained model set real-world images is have been used trained model infer hierarchical latent representations. Even though model is trained small data set 1000 images horses ships can infer effective latent representations images objects like sparrow cats trucks cars etc. shows trained model is able capture statistical regularities present real-world images. regards generalization ability model is better existing algorithms usually rely large amount data achieve better generalization.,1895,1282,613,0.19,1.478,2025/11/05 17:19:03,0.01,1.5,0.4610591900311524,694.684
"In this paper, we propose deep convolutional generative adversarial networks (DCGAN) that learn to produce a 'mental image' of the input image as internal representation of a certain category of input data distribution.   This mental image is what the DCGAN 'imagines' that the input image might look like under ideal conditions.   The mental image contains a version of the input that is iconic, without any peculiarities that do not contribute to the ideal representation of the input data distribution within a category. A DCGAN learns this association by training an encoder to capture salient features from the original image and a decoder to convert salient features into its associated mental image representation.   Our new approach, which we refer to as a Mental Image DCGAN (MIDCGAN), learns features that are useful for recognizing entire classes of objects, and that this in turn has the benefit of helping single and zero shot recognition.   We demonstrate our approach on object instance recognition and handwritten digit recognition tasks. Deep convolutional neural networks have had a revolutionary impact on machine learning and computer vision, yet we still fall dramatically short when it comes to learning in a manner that is most similar to people. Consider the way that children interact with objects when they are very young Yu et al., 2009 ): during their interaction, children look at objects from many different perspectives. Eventually they build up a preference for certain viewpoints after examining objects for a long period of time. In this paper, we consider the question of what would happen if we were to train a deep convolutional generative adversarial network in the same manner. For this, we provide the mental image (i.e., an ideal representation), and then provide samples of many different variations of the input image. The Mental Image DCGAN (MIDCGAN) is trained to associate each of these samples in a specific input distribution back to the mental image. This association is learned using a GAN architecture (see FIG1 ) with a generator composed of an encoder and decoder. MID-CGAN trains the encoder to learn salient bottleneck features for each class while the decoder learns to generate a mental image from bottleneck features. We will show that MIDCGAN bottleneck features are better suited for learning than those features that are generated without the benefit of using a mental image.Stated more formally, a typical learning task seeks to learn the data distribution, p(x) mapping to a class or category label y or p(y|x). The diversity of samples in the training data are limiting in the way the learner represents the category class internally. The MIDCGAN approach on the other hand provides a mental imagex as target to be learned and stored as representation of a category target distribution. The learner maps the input data distribution, p(x), to this canonical representation of the category,x, i.e p(x|x). During this mapping process, the MIDCGAN creates an internal bottleneck feature vector that is best representative of the input distribution mapping to the mental image.We demonstrate the effectiveness of mental image DCGANs (MIDCGAN) on two different problems. First, we demonstrate this for handwritten digits as proof of concept. In this case, we assume that a helpful tutor has provided an ideal representation of the digit, so the mental image is a stencil FIG2 . When the MIDCGAN sees a digit, it is trained to think of how it might look if it were looking at the stencil. We mainly demonstrate the performance of MIDCGAN on instance based object recognition. In this case, the helpful tutor provides the system with an iconic view of the object. The MIDCGAN observes the objects from different viewpoints, but at each time it is trained to think of how the object might look like if it were looking at the object from an ideal or iconic perspective. BID22 .We evaluate this in three different ways. First , we evaluate quantitatively the usefulness of the bottleneck features from MIDCGAN on learning tasks (comparing to DCGAN features trained without a mental image). Second , we evaluate qualitatively MIDCGAN's ability to generate mental images. Finally , we evaluate MIDCGAN's ability to perform few shot recognition on objects whose mental image was not learned or transfer learning. More precisely how does MIDCGAN perform when asked to imagine what an object in its frontal view, when it has never seen the object before. In this section, we will present and discuss the four major experiments. In the first two, MNIST and SVHN are evaluated using stencils targets as mental images. In the final two, we evaluate object instance recognition using the Big Berkeley Instance Recognition Database (BigBIRD) and the University of Washington Kinects Objects Dataset. In the first experiment, we learn mental images for each of the objects. In the second experiment, we use the features learned previously to recognize an entirely new database. In all experiments, we show that learning in this manner outperforms features learned from a typical DCGAN architecture. We have demonstrated the use of mental model autoencoder-based DCGAN (MIDCGAN) on digit classification (MNIST), and object recognition on both the Kinects Objects Dataset (RGB-D) and the Bigbird Dataset. Although MIDCGAN was demonstrated on representative viewpoints, the selection of the mental target image could be arbitrary. In cases when MIDCGAN was not sure about the object, the generated image did not resemble the actual representative image, or important details about the representative image were omitted. In essence, it could potentially provide another way to determine the confidence in the prediction of the object class.MIDCGAN can be used on robotics platform with real images in the wild. Given the growing interest in active object manipulation and recognition in the robotics community BID2 . Incorporating real manipulation of objects as separate modality with MIDCGAN could permit robots to learn about objects in their environment with minimal supervision. The mental images described in this paper map very well to the concept of prototype learning in the cognitive science community. Several improvements could be made to MIDCGAN in the future. First, we have generally assumed the availability of a tutor to select a mental image. Autonomous selection of the mental images is an inherent extension to allow semi-supervised and fully unsupervised MIDCGAN training. Alternatively, prototype images can be selected in some systematic manner using some heuristics related to the objects (i.e., a cup holds liquid so prototype is face up, the handle is to be grabbed so that should be visible).",paper propose deep convolutional generative adversarial networks DCGAN learn produce 'mental image' input image internal representation certain category input data distribution. mental image is what the DCGAN 'imagines' input image might look like ideal conditions. mental image contains version input is iconic without peculiarities do not contribute ideal representation input data distribution within category. DCGAN learns association training encoder capture salient features original image decoder convert salient features associated mental image representation. new approach which we refer Mental Image DCGAN MIDCGAN learns features are useful recognizing entire classes objects turn has the benefit helping single zero shot recognition. demonstrate approach object instance recognition handwritten digit recognition tasks. Deep convolutional neural networks have had a revolutionary impact machine learning computer vision yet still fall dramatically short when it comes learning manner is most similar people. Consider way children interact objects when they are very youngYuetal. 2009 interaction children look objects many different perspectives. Eventually build preference certain viewpoints examining objects long period time. paper consider question would happen if we were to train deep convolutional generative adversarial network manner. provide mental image.e ideal representation provide samples many different variations input image. Mental Image DCGAN MIDCGAN is trained associate samples specific input distribution back mental image. association is learned using GAN architecture see FIG1 generator composed encoder decoder. MID-CGAN trains encoder learn salient bottleneck features class decoder learns generate mental image bottleneck features. will show MIDCGAN bottleneck features are better suited learning features are generated without benefit using mental image.Stated formally typical learning task seeks learn data distribution p x mapping class category label p y|x diversity samples training data are limiting way learner represents category class internally. MIDCGAN approach hand provides mental imagex target learned stored representation category target distribution. learner maps input data distribution p x canonical representation category x.ep x|x mapping process MIDCGAN creates internal bottleneck feature vector is best representative input distribution mapping mental image.We demonstrate effectiveness mental image DCGANs MIDCGAN two different problems. First demonstrate handwritten digits proof concept. case assume helpful tutor has provided ideal representation digit mental image is a stencil FIG2. When the MIDCGAN sees digit is trained think might look if it were looking stencil. mainly demonstrate performance MIDCGAN instance based object recognition. case helpful tutor provides system iconic view how the object. MIDCGAN observes objects different viewpoints time is trained think how the object might look like if it were looking object ideal iconic perspective. BID22.We evaluate three different ways. First evaluate quantitatively usefulness bottleneck features MIDCGAN learning tasks comparing DCGAN features trained without mental image Second evaluate qualitatively MIDCGAN's ability generate mental images. Finally evaluate MIDCGAN's ability perform shot recognition objects whose mental image was not learned transfer learning. precisely how does MIDCGAN perform when asked imagine what an object frontal view when it has never seen object before. section will present discuss four major experiments. first two MNIST SVHN are evaluated using stencils targets mental images. final two evaluate object instance recognition using Big Berkeley Instance Recognition Database BigBIRD University Washington Kinects Objects Dataset. first experiment learn mental images objects. second experiment use features learned previously recognize entirely new database. experiments show learning manner outperforms features learned typical DCGAN architecture. have demonstrated use mental model autoencoder-based DCGAN MIDCGAN digit classification MNIST object recognition Kinects Objects Dataset RGB-D Bigbird Dataset. Although MIDCGAN was demonstrated representative viewpoints selection mental target image could arbitrary. cases when MIDCGAN was not sure object generated image did not resemble actual representative image important details representative image were omitted. essence could potentially provide another way determine confidence prediction how the object class.MIDCGAN can be used robotics platform real images wild. Given growing interest active object manipulation recognition robotics community BID2. Incorporating real manipulation objects separate modality MIDCGAN could permit robots learn objects environment minimal supervision. mental images described paper map well concept prototype learning cognitive science community. Several improvements could made MIDCGAN future. First have generally assumed availability tutor select mental image. Autonomous selection mental images is an inherent extension allow semi-supervised fully unsupervised MIDCGAN training. Alternatively prototype images can be selected systematic manner using heuristics related objects.e cup holds liquid prototype is face handle is to be grabbed should be visible,1302,857,445,0.015,1.519,2025/11/05 17:19:03,0.01,1.733,0.5887850467289715,423.963
"An obstacle that prevents the wide adoption of (deep) reinforcement learning (RL) in control systems is its need for a large number of interactions with the environment in order to master a skill. The learned skill usually generalizes poorly across domains and re-training is often necessary when presented with a new task. We present a framework that combines techniques in \textit{formal methods} with \textit{hierarchical reinforcement learning} (HRL). The set of techniques we provide allows for the convenient specification of tasks with logical expressions, learns hierarchical policies (meta-controller and low-level controllers) with well-defined intrinsic rewards using any RL methods and is able to construct new skills from existing ones without additional learning. We evaluate the proposed methods in a simple grid world simulation as well as simulation on a Baxter robot. Reinforcement learning has received much attention in the recent years because of its achievements in games BID17 , , robotics manipulation Jang et al., , BID5 and autonomous driving BID8 , BID16 . However, training a policy that sufficiently masters a skill requires an enormous amount of interactions with the environment and acquiring such experience can be difficult on physical systems. Moreover, most learned policies are tailored to mastering one skill (by maximizing the reward) and are hardly reusable on a new skill.Skill composition is the idea of constructing new skills out of existing skills (and hence their policies) with little to no additional learning. In stochastic optimal control, this idea has been adopted by authors of BID25 and BID4 to construct provably optimal control laws based on linearly solvable Markov decision processes. Authors of BID6 , Tang & Haarnoja have showed in simulated manipulation tasks that approximately optimal policies can result from adding the Q-functions of the existing policies.Hierarchical reinforcement learning is an effective means of achieving transfer among tasks. The goal is to obtain task-invariant low-level policies, and by re-training the meta-policy that schedules over the low-level policies, different skills can be obtain with less samples than training from scratch. Authors of BID7 have adopted this idea in learning locomotor controllers and have shown successful transfer among simulated locomotion tasks. Authors of BID18 have utilized a deep hierarchical architecture for multi-task learning using natural language instructions.Temporal logic is a formal language commonly used in software and digital circuit verification BID1 as well as formal synthesis BID2 . It allows for convenient expression of complex behaviors and causal relationships. TL has been used by BID19 , BID13 to synthesize provably correct control policies. Authors of BID0 have also combined TL with Q-learning to learn satisfiable policies in discrete state and action spaces.In this work, we focus on hierarchical skill acquisition and zero-shot skill composition. Once a set of skills is acquired, we provide a technique that can synthesize new skills without the need to further interact with the environment (given the state and action spaces as well as the transition remain the same). We adopt temporal logic as the task specification language. Compared to most heuristic reward structures used in the RL literature to specify tasks, formal specification language excels at its semantic rigor and interpretability of specified behaviors. Our main contributions are:• We take advantage of the transformation between TL formula and finite state automata (FSA) to construct deterministic meta-controllers directly from the task specification without the necessity for additional learning. We show that by adding one discrete dimension to the original state space, structurally simple parameterized policies such as feed-forward neural networks can be used to learn tasks that require complex temporal reasoning.• Intrinsic motivation has been shown to help RL agents learn complicated behaviors with less interactions with the environment BID22 , BID11 BID9 . However , designing a well-behaved intrinsic reward that aligns with the extrinsic reward takes effort and experience. In our work, we construct intrinsic rewards directly from the input alphabets of the FSA (a component of the automaton), which guarantees that maximizing each intrinsic reward makes positive progress towards satisfying the entire task specification. From a user's perspective, the intrinsic rewards are constructed automatically from the TL formula.• In our framework, each FSA represents a hierarchical policy with low-level controllers that can be re-modulated to achieve different tasks. Skill composition is achieved by manipulating the FSA that results from their TL specifications in a deterministic fashion. Instead of interpolating/extrapolating among existing skills, we present a simple policy switching scheme based on graph manipulation of the FSA. Therefore, the compositional outcome is much more transparent. We introduce a method that allows learning of such hierarchical policies with any non-hierarchical RL algorithm. Compared with previous work on skill composition , we impose no constraints on the policy representation or the problem class. In this paper, we proposed the FSA augmented MDP, a product MDP that enables effective learning of hierarchical policies using any RL algorithm for tasks specified by scTLTL. We also introduced automata guided skill composition, a technique that combines existing skills to create new skills without additional learning. We show in robotic simulations that using the proposed methods we enable simple policies to perform logically complex tasks.Limitations of the current framework include discontinuity at the point of switching (for Equation (15)), which makes this method suitable for high level decision tasks but not for low level control tasks. The technique only compares robustness at the current step and chooses to follow a sub-policy for one time-step, making the switching policy short-sighted and may miss long term opportunities. One way to address this is to impose a termination condition for following each sub-policy and terminate only when the condition is triggered (as in the original options framework). This termination condition can be hand designed or learned",obstacle prevents wide adoption deep reinforcement learning RL control systems is its need large number interactions environment order master skill. learned skill usually generalizes poorly across domains re-training is often necessary when presented new task. present framework combines techniques \textit formal methods \textit hierarchical reinforcement learning HRL set techniques provide allows convenient specification tasks logical expressions learns hierarchical policies meta-controller low-level controllers well-defined intrinsic rewards using RL methods is able construct new skills existing ones without additional learning. evaluate proposed methods simple grid world simulation well simulation Baxter robot. Reinforcement learning has received much attention recent years achievements games BID17 robotics manipulation Janget al. BID5 autonomous driving BID8 BID16. However training policy sufficiently masters skill requires enormous amount interactions environment acquiring experience can be difficult physical systems. Moreover learned policies are tailored mastering one skill maximizing reward are hardly reusable new skill.Skill composition is the idea constructing new skills existing skills hence policies little additional learning. stochastic optimal control idea has been adopted authors BID25 BID4 construct provably optimal control laws based linearly solvable Markov decision processes. Authors BID6 Tang Haarnoja have showed simulated manipulation tasks approximately optimal policies can result adding Q-functions existing policies.Hierarchical reinforcement learning is an effective means achieving transfer among tasks. goal is to obtain task-invariant low-level policies re-training meta-policy schedules low-level policies different skills can be obtain less samples training scratch. Authors BID7 have adopted idea learning locomotor controllers have shown successful transfer among simulated locomotion tasks. Authors BID18 have utilized deep hierarchical architecture multi-task learning using natural language instructions.Temporal logic is a formal language commonly used software digital circuit verification BID1 well formal synthesis BID2. allows convenient expression complex behaviors causal relationships. TL has been used BID19 BID13 synthesize provably correct control policies. Authors BID0 have also combinedTL Q-learning learn satisfiable policies discrete state action spaces.In work focus hierarchical skill acquisition zero-shot skill composition. set skills is acquired provide technique can synthesize new skills without need interact environment given state action spaces well transition remain adopt temporal logic task specification language. Compared heuristic reward structures used RL literature specify tasks formal specification language excels semantic rigor interpretability specified behaviors. main contributions are:• take advantage transformation TL formula finite state automata FSA construct deterministic meta-controllers directly task specification without necessity additional learning. show adding one discrete dimension original state space structurally simple parameterized policies feed-forward neural networks can be used learn tasks require complex temporal reasoning.• Intrinsic motivation has been shown help RL agents learn complicated behaviors less interactions environment BID22 BID11 BID9. However designing well-behaved intrinsic reward aligns extrinsic reward takes effort experience. work construct intrinsic rewards directly input alphabets FSA component automaton which guarantees maximizing intrinsic reward makes positive progress towards satisfying entire task specification. user's perspective intrinsic rewards are constructed automatically TL formula.• framework FSA represents hierarchical policy low-level controllers can be re-modulated achieve different tasks. Skill composition is achieved manipulating FSA results TL specifications deterministic fashion. Instead interpolating/extrapolating among existing skills present simple policy switching scheme based graph manipulation FSA. Therefore compositional outcome is much transparent. introduce method allows learning hierarchical policies non-hierarchical RL algorithm. Compared previous work skill composition impose constraints policy representation problem class. paper proposed FSA augmented MDP product MDP enables effective learning hierarchical policies using RL algorithm tasks specified scTLTL. also introduced automata guided skill composition technique combines existing skills create new skills without additional learning. show robotic simulations using proposed methods enable simple policies perform logically complex tasks.Limitations current framework include discontinuity point switching Equation 15 which makes method suitable high level decision tasks low level control tasks. technique compares robustness current step chooses follow sub-policy one time-step making switching policy short-sighted may miss long term opportunities. One way address is to impose termination condition following sub-policy terminate when the condition is triggered original options framework termination condition can be hand designed learned,1129,781,348,0.011,1.446,2025/11/05 17:19:03,0.01,1.429,0.3613707165109031,345.023
"The tremendous memory and computational complexity of Convolutional Neural Networks (CNNs) prevents the inference deployment on resource-constrained systems. As a result, recent research focused on CNN optimization techniques, in particular quantization, which allows weights and activations of layers to be represented with just a few bits while achieving impressive prediction performance. However, aggressive quantization techniques still fail to achieve full-precision prediction performance on state-of-the-art CNN architectures on large-scale classification tasks. In this work we propose a method for weight and activation quantization that is scalable in terms of quantization levels (n-ary representations) and easy to compute while maintaining the performance close to full-precision CNNs. Our weight quantization scheme is based on trainable scaling factors and a nested-means clustering strategy which is robust to weight updates and therefore exhibits good convergence properties. The flexibility of nested-means clustering enables exploration of various n-ary weight representations with the potential of high parameter compression. For activations, we propose a linear quantization strategy that takes the statistical properties of batch normalization into account. We demonstrate the effectiveness of our approach using state-of-the-art models on ImageNet. The increasing computational complexity and memory requirements of Convolutional Neural Networks (CNNs) have motivated recent research efforts in efficient representation and processing of CNNs. Several optimization and inference approaches have been proposed with the objective of model compression and inference acceleration. The primary aim of model compression is to enable on-device storage (e.g., mobile phones and other resource-constrained devices) and to leverage on-chip memory in order to reduce energy consumption BID13 , latency and bandwidth of parameter accesses. Inference acceleration can be achieved by lowering the precision of computations in terms of resolution, removing connections within networks (pruning), and specialized software/hardware architectures.Quantized Neural Networks are optimization techniques where weights and/or activations of a neural network are transformed from 32-bit floating point into a lower resolution; for aggressive quantization techniques down to binary BID7 BID22 or ternary BID16 BID31 representations. Although prior quantization techniques achieve fullprecision accuracy on highly over-parameterized architectures (e.g., AlexNet, VGG) or toy tasks (e.g., MNIST, SVHN, CIFAR-10), there is still an unacceptable gap between extremely low bitwidth representations and state-of-the-art architectures for real-world tasks. Furthermore, aggressive quantization approaches are usually designed for specific representations (e.g., binary or ternary), and are not scalable in the sense that they do not allow for more quantization levels (i.e., weight values) if required. Thus, accuracy degradation cannot be compensated without changes in the baseline architecture which includes deepening or widening the neural network, and/or using full-precision weights in the input and output layers, respectively.In this work, we address the issue of accuracy degradation by introducing a scalable non-uniform quantization method for weights that is based on trainable scaling factors in combination with a nested-means clustering approach. In particular, nested-means splits the weight distribution iteratively into several quantization intervals until a pre-defined discretization level is reached. Subsequently, all weights within a certain quantization interval are assigned the same weight (i.e., the scaling factor). Nested-means clustering tends to assign small weights to larger quantization intervals while less frequent larger weights are assigned to smaller quantization intervals. This improves classification performance which is in line with recent observations that larger weights carry more information than smaller weights BID9 . We evaluate our approach on state-of-theart CNN architectures in terms of computational requirements and prediction accuracy using the ImageNet classification task.The paper is structured as follows. In Sec. 2 and Sec. 3 related work and background on inference acceleration is discussed. Weight and activation quantization is presented in Sec. 4 and Sec. 5, respectively. Experimental results for ImageNet are shown in Sec. 6. Sec. 7 concludes the paper. We have presented a novel approach for compressing CNNs through quantization and connection pruning, which reduces the resolution of weights and activations and is scalable in terms of the number of quantization levels. As a result, the computational complexity and memory requirements of DNNs are substantially reduced, and an execution on resource-constrained devices is more feasible. We introduced a nested-means clustering algorithm for weight quantization that finds suitable interval thresholds that are subsequently used to assign each weight to a trainable scaling factor. Our approach exhibits both a low computational complexity and robustness to weight updates, which makes it an attractive alternative to other clustering methods. Furthermore, the proposed quantization method is flexible as it allows for various numbers of quantization levels, enabling high compression rates while achieving prediction accuracies close to single-precision floating-point weights.For instance, we utilize this flexibility to add an extra quantization level to ternary weights (quaternary weights), resulting in an improvement in prediction accuracy while keeping the bit width at two. For activation quantization, we developed an approximation based on statistical attributes that have been observed when batch normalization is employed. Experiments using state-of-the-art DNN architectures on real-world tasks, including ResNet-18 and ImageNet, show the effectiveness of our approach.",tremendous memory computational complexity Convolutional Neural Networks CNNs prevents inference deployment resource-constrained systems. result recent research focused CNN optimization techniques particular quantization which allows weights activations layers represented bits achieving impressive prediction performance. However aggressive quantization techniques still fail achieve full-precision prediction performance state-of-the-art CNN architectures large-scale classification tasks. work propose method weight activation quantization is scalable terms quantization levels n-ary representations easy compute maintaining performance close full-precision CNNs. weight quantization scheme is based trainable scaling factors nested-means clustering strategy which is robust weight updates therefore exhibits good convergence properties. flexibility nested-means clustering enables exploration various n-ary weight representations potential high parameter compression. activations propose linear quantization strategy takes statistical properties batch normalization account. demonstrate effectiveness approach using state-of-the-art models ImageNet. increasing computational complexity memory requirements Convolutional Neural Networks CNNs have motivated recent research efforts efficient representation processing CNNs. Several optimization inference approaches have been proposed objective model compression inference acceleration. primary aim model compression is to enable on-device storage e.g mobile phones resource-constrained devices leverage on-chip memory order reduce energy consumption BID13 latency bandwidth parameter accesses. Inference acceleration can be achieved lowering precision computations terms resolution removing connections within networks pruning specialized software/hardware architectures.Quantized Neural Networks are optimization techniques where weights/activations neural network are transformed 32-bit floating point lower resolution;aggressive quantization techniques binary BID7 BID22 ternary BID16 BID31 representations. Although prior quantization techniques achieve fullprecision accuracy highly over-parameterized architectures e.g AlexNet VGG toy tasks e.g MNIST SVHN CIFAR-10 is still unacceptable gap extremely low bitwidth representations state-of-the-art architectures real-world tasks. Furthermore aggressive quantization approaches are usually designed specific representations e.g binary ternary are scalable sense do not allow quantization levels.e weight values if required. Thus accuracy degradation cannot compensated without changes baseline architecture which includes deepening widening neural network/using full-precision weights input output layers respectively.In work address issue accuracy degradation introducing scalable non-uniform quantization method weights is based trainable scaling factors combination nested-means clustering approach. particular nested-means splits weight distribution iteratively several quantization intervals pre-defined discretization level is reached. Subsequently weights within certain quantization interval are assigned weight.e scaling factor Nested-means clustering tends assign small weights larger quantization intervals less frequent larger weights are assigned smaller quantization intervals. improves classification performance which is in line recent observations larger weights carry information smaller weights BID9. evaluate approach state-of-theart CNN architectures terms computational requirements prediction accuracy using ImageNet classification task.The paper is structured follows. Sec. 2 Sec. 3 related work background inference acceleration is discussed. Weight activation quantization is presented Sec. 4 Sec. 5 respectively. Experimental results ImageNet are shown Sec. 6. Sec. 7 concludes paper. have presented novel approach compressing CNNs quantization connection pruning which reduces resolution weights activations is scalable terms number quantization levels. result computational complexity memory requirements DNNs are substantially reduced execution resource-constrained devices is more feasible. introduced nested-means clustering algorithm weight quantization finds suitable interval thresholds are subsequently used assign weight trainable scaling factor. approach exhibits low computational complexity robustness weight updates which makes attractive alternative clustering methods. Furthermore proposed quantization method is flexible allows various numbers quantization levels enabling high compression rates achieving prediction accuracies close single-precision floating-point weights.For instance utilize flexibility add extra quantization level ternary weights quaternary weights resulting improvement prediction accuracy keeping bit width two. activation quantization developed approximation based statistical attributes have been observed when batch normalization is employed. Experiments using state-of-the-art DNN architectures real-world tasks including ResNet-18 ImageNet show effectiveness approach.,1055,761,294,0.01,1.386,2025/11/05 17:19:03,0.0,1.25,0.1744548286604356,323.646
"Reinforcement learning (RL) agents optimize only the features specified in a reward function and are indifferent to anything left out inadvertently. This means that we must not only specify what to do, but also the much larger space of what not to do. It is easy to forget these preferences, since these preferences are already satisfied in our environment. This motivates our key insight: when a robot is deployed in an environment that humans act in, the state of the environment is already optimized for what humans want. We can therefore use this implicit preference information from the state to fill in the blanks. We develop an algorithm based on Maximum Causal Entropy IRL and use it to evaluate the idea in a suite of proof-of-concept environments designed to show its properties. We find that information from the initial state can be used to infer both side effects that should be avoided as well as preferences for how the environment should be organized. Our code can be found at https://github.com/HumanCompatibleAI/rlsp. Deep reinforcement learning (deep RL) has been shown to succeed at a wide variety of complex tasks given a correctly specified reward function. Unfortunately, for many real-world tasks it can be challenging to specify a reward function that captures human preferences, particularly the preference for avoiding unnecessary side effects while still accomplishing the goal BID2 . As a result, there has been much recent work BID8 BID13 Sadigh et al., 2017) that aims to learn specifications for tasks a robot should perform.Typically when learning about what people want and don't want, we look to human action as evidence: what reward they specify BID14 , how they perform a task (Ziebart et al., 2010; BID13 , what choices they make BID8 Sadigh et al., 2017) , or how they rate certain options BID9 . Here, we argue that there is an additional source of information that is potentially rather helpful, but that we have been ignoring thus far:The key insight of this paper is that when a robot is deployed in an environment that humans have been acting in, the state of the environment is already optimized for what humans want.For example, consider an environment in which a household robot must navigate to a goal location without breaking any vases in its path, illustrated in FIG5 . The human operator, Alice, asks the robot to go to the purple door, forgetting to specify that it should also avoid breaking vases along the way. However, since the robot has been deployed in a state that only contains unbroken vases, it can infer that while acting in the environment (prior to robot's deployment), Alice was using one of the relatively few policies that do not break vases, and so must have cared about keeping vases intact. Figure 1: An illustration of learning preferences from an initial state. Alice attempts to accomplish a goal in an environment with an easily breakable vase in the center. The robot observes the state of the environment, s 0 , after Alice has acted for some time from an even earlier state s −T . It considers multiple possible human reward functions, and infers that states where vases are intact usually occur when Alice's reward penalizes breaking vases. In contrast, it doesn't matter much what the reward function says about carpets, as we would observe the same final state either way. Note that while we consider a specific s −T for clarity here, the robot could also reason using a distribution over s −T .The initial state s 0 can contain information about arbitrary preferences, including tasks that the robot should actively perform. For example, if the robot observes a basket full of apples near an apple tree, it can reasonably infer that Alice wants to harvest apples. However , s 0 is particularly useful for inferring which side effects humans care about. Recent approaches avoid unnecessary side effects by penalizing changes from an inaction baseline (Krakovna et al., 2018; Turner, 2018) . However , this penalizes all side effects. The inaction baseline is appealing precisely because the initial state has already been optimized for human preferences, and action is more likely to ruin s 0 than inaction. If our robot infers preferences from s 0 , it can avoid negative side effects while allowing positive ones.This work is about highlighting the potential of this observation, and as such makes unrealistic assumptions, such as known dynamics and hand-coded features. Given just s 0 , these assumptions are necessary: without dynamics, it is hard to tell whether some feature of s 0 was created by humans or not. Nonetheless, we are optimistic that these assumptions can be relaxed, so that this insight can be used to improve deep RL systems. We suggest some approaches in our discussion.Our contributions are threefold. First, we identify the state of the world at initialization as a source of information about human preferences. Second, we leverage this insight to derive an algorithm, Reward Learning by Simulating the Past (RLSP), which infers reward from initial state based on a Maximum Causal Entropy (Ziebart et al., 2010) model of human behavior. Third, we demonstrate the properties and limitations of RLSP on a suite of proof-of-concept environments: we use it to avoid side effects, as well as to learn implicit preferences that require active action. In FIG5 the robot moves to the purple door without breaking the vase, despite the lack of a penalty for breaking vases.","Reinforcement learning RL agents optimize features specified reward function are indifferent anything left inadvertently. means must specify whattodo,also much larger space do. is easy forget preferences since preferences are already satisfied environment. motivates key insight:when a robot is deployed environment humans act state environment is already optimized what humans want. can therefore use implicit preference information state fill blanks. develop algorithm based Maximum Causal Entropy IRL use evaluate idea suite proof-of-concept environments designed show properties. find information initial state can be used infer side effects should be avoided well preferences how the environment should be organized. code can be found https://github.com/HumanCompatibleAI/rlsp. Deep reinforcement learning deepRL has been shown succeed wide variety complex tasks given correctly specified reward function. Unfortunately many real-world tasks can be challenging specify reward function captures human preferences particularly preference avoiding unnecessary side effects still accomplishing goal BID2. result has been much recent work BID8 BID13 Sadighetal. 2017 aims learn specifications tasks robot should perform.Typically when learning what people want want look human action evidence:what what the reward specify BID14 how they perform task Ziebartetal. 2010;BID13 what choices make BID8 Sadighet al. 2017 how rate certain options BID9. argue is an additional source information is potentially rather helpful have been ignoring thus far:key insight paper is that when a robot is deployed environment humans have been acting state environment is already optimized what humans want.For example consider environment which a household robot must navigate goal location without breaking vases path illustrated FIG5. human operator Alice asks robot go purple door forgetting specify should also avoid breaking vases along way. However since robot has been deployed state contains unbroken vases can infer acting environment prior robot's deployment Alice was using one relatively policies do not break vases must have cared keeping vases intact. Figure1:illustration learning preferences initial state. Alice attempts accomplish goal environment easily breakable vase center. robot observes state environment 0 Alice has acted time even earlier state −T considers multiple possible human reward functions infers states where vases are intact usually occur when Alice's reward penalizes breaking vases. contrast matter much what what the reward function says carpets would observe final state either way. Note consider specific −T clarity robot could also reason using distribution −T.The initial state 0 can contain information arbitrary preferences including tasks robot should actively perform. example if the robot observes basket full apples near apple tree can reasonably infer Alice wants harvest apples. However 0 is particularly useful inferring which side effects humans care about. Recent approaches avoid unnecessary side effects penalizing changes inaction baseline Krakovnaetal. 2018;Turner 2018 However penalizes side effects. inaction baseline is appealing precisely initial state has already optimized human preferences action is more likely ruin 0 inaction. If our robot infers preferences 0 can avoid negative side effects allowing positive ones.This work is about highlighting potential observation makes unrealistic assumptions known dynamics hand-coded features. Given 0 assumptions are necessary:without dynamics is hard tell whether feature 0 was created humans not. Nonetheless are optimistic assumptions can be relaxed insight can be used improve deep RL systems. suggest approaches discussion.Our contributions are threefold. First identify state world initialization source information human preferences. Second leverage insight derive algorithm Reward Learning Simulating Past RLSP which infers reward initial state based Maximum Causal Entropy Ziebartetal. 2010 model human behavior. Third demonstrate properties limitations RLSP suite proof-of-concept environments:use avoid side effects well learn implicit preferences require active action. FIG5 robot moves purple door without breaking vase despite lack penalty breaking vases.",1103,738,365,0.011,1.495,2025/11/05 17:19:03,0.01,1.467,0.5140186915887852,354.749
"Regularization is one of the crucial ingredients of deep learning, yet the term regularization has various definitions, and regularization methods are often studied separately from each other. In our work we present a novel, systematic, unifying taxonomy to categorize existing methods. We distinguish methods that affect data, network architectures, error terms, regularization terms, and optimization procedures. We identify the atomic building blocks of existing methods, and decouple the assumptions they enforce from the mathematical tools they rely on. We do not provide all details about the listed methods; instead, we present an overview of how the methods can be sorted into meaningful categories and sub-categories. This helps revealing links and fundamental similarities between them. Finally, we include practical recommendations both for users and for developers of new regularization methods. Regularization is one of the key elements of machine learning, particularly of deep learning BID37 , allowing to generalize well to unseen data even when training on a finite training set or with an imperfect optimization procedure. In the traditional sense of optimization and also in older neural networks literature, the term ""regularization"" is reserved solely for a penalty term in the loss function BID12 . Recently, the term has adopted a broader meaning: Goodfellow et al. (2016, Chap. 5 ) loosely define it as ""any modification we make to a learning algorithm that is intended to reduce its test error but not its training error"". We find this definition slightly restrictive and present our working definition of regularization, since many techniques considered as regularization do reduce the training error (e.g. weight decay in AlexNet ). Definition 1. Regularization is any supplementary technique that aims at making the model generalize better, i.e. produce better results on the test set.This can include various properties of the loss function, the loss optimization algorithm, or other techniques. Note that this definition is more in line with machine learning literature than with inverse problems literature, the latter using a more restrictive definition.In this work, we create a novel, systematic, unifying taxonomy of regularization methods for deep learning. We analyze existing methods and identify their atomic building blocks. This leads to decoupling of two important concepts: Which assumptions the methods rely on (and try to enforce), and which mathematical and algorithmic tools they use. In turn, this enables better understanding of existing methods and speeds up development of new ones: The researchers can focus either on finding new, better ways of enforcing existing assumptions, or focus on discovery of new assumptions that can be enforced in some existing way.Before we proceed to the presentation of our taxonomy, we revisit some basic machine learning theory in Section 2. This will provide a justification of the top level of the taxonomy. In Sections 3-7, we continue with a finer division of the individual classes of the regularization techniques, aiming at separating as many clearly separable concepts as possible and isolating atomic building blocks of individual methods. Finally, in Section 8 we present our practical recommendations for using existing methods and designing new methods. We are aware that the many research works discussed in this taxonomy cannot be summarized in a single sentence. For the sake of structuring the multitude of papers, we decided to merely describe a certain subset of their properties according to the focus of our taxonomy.",Regularization is one crucial ingredients deep learning yet term regularization has various definitions regularization methods are often studied separately other. work present novel systematic unifying taxonomy categorize existing methods. distinguish methods affect data network architectures error terms regularization terms optimization procedures. identify atomic building blocks existing methods decouple assumptions enforce mathematical tools rely on. do not provide details listed methods;instead present overview how the methods can be sorted meaningful categories sub-categories helps revealing links fundamental similarities them. Finally include practical recommendations users developers new regularization methods. Regularization is one key elements machine learning particularly deep learning BID37 allowing generalize well unseen data even when training finite training set imperfect optimization procedure. traditional sense optimization also older neural networks literature term regularization is reserved solely penalty term loss function BID12. Recently term has adopted broader meaning:Goodfellowetal. 2016 Chap. 5 loosely define modification make learning algorithm is intended reduce test error training error. find definition slightly restrictive present working definition regularization since many techniques considered regularization do reduce training error e.g weight decay AlexNet Definition1. Regularization is any supplementary technique aims making model generalize better.e produce better results test set.This can include various properties loss function loss optimization algorithm techniques. Note definition is more in line machine learning literature inverse problems literature latter using restrictive definition.In work create novel systematic unifying taxonomy regularization methods deep learning. analyze existing methods identify atomic building blocks. leads decoupling two important concepts:Which assumptions methods rely try enforce which mathematical algorithmic tools use. turn enables better understanding existing methods speeds development new ones:researchers can focus either finding new better ways enforcing existing assumptions focus discovery new assumptions can be enforced existing way.Before proceed presentation taxonomy revisit basic machine learning theory Section2. will provide justification top level taxonomy. Sections 3-7 continue finer division individual classes regularization techniques aiming separating many clearly separable concepts possible isolating atomic building blocks individual methods. Finally Section8 present practical recommendations using existing methods designing new methods. are aware many research works discussed taxonomy cannot summarized single sentence. sake structuring multitude papers decided merely describe certain subset properties according focus taxonomy.,660,423,237,0.007,1.56,2025/11/05 17:19:03,0.0,1.35,0.7165109034267914,249.621
"Deep neural networks are surprisingly efficient at solving practical tasks,
 but the theory behind this phenomenon is only starting to catch up with
 the practice. Numerous works show that depth is the key to this efficiency.
 A certain class of deep convolutional networks – namely those that correspond
 to the Hierarchical Tucker (HT) tensor decomposition – has been
 proven to have exponentially higher expressive power than shallow networks.
 I.e. a shallow network of exponential width is required to realize
 the same score function as computed by the deep architecture. In this paper,
 we prove the expressive power theorem (an exponential lower bound on
 the width of the equivalent shallow network) for a class of recurrent neural
 networks – ones that correspond to the Tensor Train (TT) decomposition.
 This means that even processing an image patch by patch with an RNN
 can be exponentially more efficient than a (shallow) convolutional network
 with one hidden layer. Using theoretical results on the relation between
 the tensor decompositions we compare expressive powers of the HT- and
 TT-Networks. We also implement the recurrent TT-Networks and provide
 numerical evidence of their expressivity. Deep neural networks solve many practical problems both in computer vision via Convolutional Neural Networks (CNNs) BID19 ; BID31 ; BID14 ) and in audio and text processing via Recurrent Neural Networks (RNNs) BID11 ; BID21 BID8 ). However, although many works focus on expanding the theoretical explanation of neural networks success BID20 ; BID6 ; ), the full theory is yet to be developed.One line of work focuses on expressive power, i.e. proving that some architectures are more expressive than others. showed the connection between Hierarchical Tucker (HT) tensor decomposition and CNNs, and used this connection to prove that deep CNNs are exponentially more expressive than their shallow counterparts. However, no such result exists for Recurrent Neural Networks. The contributions of this paper are three-fold.1. We show the connection between recurrent neural networks and Tensor Train decomposition (see Sec. 4); 2. We formulate and prove the expressive power theorem for the Tensor Train decomposition (see Sec. 5), which -on the language of RNNs -can be interpreted as follows: to (exactly) emulate a recurrent neural network, a shallow (non-recurrent) architecture of exponentially larger width is required; DISPLAYFORM0 Figure 1: Recurrent-type neural architecture that corresponds to the Tensor Train decomposition. Gray circles are bilinear maps (for details see Section 4). In this paper, we explored the connection between recurrent neural networks and Tensor Train decomposition and used it to prove the expressive power theorem, which states that a shallow network of exponentially large width is required to mimic a recurrent neural network. The downsides of this approach is that it provides worst-case analysis and do not take optimization issues into account. In the future work, we would like to address the optimization issues by exploiting the Riemannian geometry properties of the set of TT-tensors of fixed rank and extend the analysis to networks with non-linearity functions inside the recurrent connections (as was done for CNNs in ).",Deep neural networks are surprisingly efficient solving practical tasks theory behind phenomenon is only starting catch practice. Numerous works show depth is the key efficiency. certain class deep convolutional networks– namely correspond Hierarchical Tucker HT tensor decomposition– has been proven have exponentially higher expressive power shallow networks. .e shallow network exponential width is required realize score function computed deep architecture. paper prove expressive power theorem exponential lower bound width equivalent shallow network class recurrent neural networks– ones correspond Tensor Train TT decomposition. means even processing image patch patch RNN can be exponentially efficient shallow convolutional network one hidden layer. Using theoretical results relation tensor decompositions compare expressive powers HT- TT-Networks also implement recurrent TT-Networks provide numerical evidence expressivity. Deep neural networks solve many practical problems computer vision via Convolutional Neural Networks CNNs BID19;BID31;BID14 audio text processing via Recurrent Neural Networks RNNs BID11;BID21 BID8 However although many works focus expanding theoretical explanation neural networks success BID20;BID6;full theory is yet developed.One line work focuses expressive power.e proving architectures are more expressive others. showed connection Hierarchical Tucker HT tensor decomposition CNNs used connection prove deep CNNs are exponentially expressive shallow counterparts. However result exists Recurrent Neural Networks. contributions paper are three-fold.1 three-fold.1 show connection recurrent neural networks Tensor Train decomposition see Sec. 4 2. formulate prove expressive power theorem Tensor Train decomposition see Sec. 5 which -on language RNNs -can interpreted follows:exactly emulate recurrent neural network shallow non-recurrent architecture exponentially larger width is required;DISPLAYFORM0 Figure1:Recurrent-type neural architecture corresponds Tensor Train decomposition. Gray circles are bilinear maps details see Section4 paper explored connection recurrent neural networks Tensor Train decomposition used prove expressive power theorem which states shallow network exponentially large width is required mimic recurrent neural network. downsides approach is that it provides worst-case analysis do not take optimization issues account. future work would like address optimization issues exploiting Riemannian geometry properties set TT-tensors fixed rank extend analysis networks non-linearity functions inside recurrent connections was done CNNs,636,429,207,0.006,1.483,2025/11/05 17:19:03,0.0,1.529,0.4766355140186917,215.033
"Probabilistic modelling is a principled framework to perform model aggregation, which has been a primary mechanism to combat mode collapse in the context of Generative Adversarial Networks (GAN). In this paper, we propose a novel probabilistic framework for GANs, ProbGAN, which iteratively learns a distribution over generators with a carefully crafted prior. Learning is efficiently triggered by a tailored stochastic gradient Hamiltonian Monte Carlo with a novel gradient approximation to perform Bayesian inference. Our theoretical analysis further reveals that our treatment is the first probabilistic framework that yields an equilibrium where generator distributions are faithful to the data distribution. Empirical evidence on synthetic high-dimensional multi-modal data and image databases (CIFAR-10, STL-10, and ImageNet) demonstrates the superiority of our method over both start-of-the-art multi-generator GANs and other probabilistic treatment for GANs. Generative Adversarial Networks (GAN) BID9 is notoriously hard to train and suffers from mode collapse. There has been a series of works attempting to address these issues. One noticeable thread focuses on objective design, which improves the original JensenShannon divergence with more stable pseudo-metrics such as f -divergence (Nowozin et al., 2016) , χ 2 -divergence (Mao et al., 2017) , and Wasserstein distance BID0 . However, such treatment is inherently limited when a single generator does not include enough model capacity to capture the granularity in data distribution in practice. Clearly, such a generator can hardly produce accurate samples regardless of the choice of objectives.An alternative remedy is to learn multiple generators instead of a single one. This type of methods (Hoang et al., 2018; Tolstikhin et al., 2017; Wang et al., 2016b ) is motivated by a straightforward intuition that multiple generators can better model multi-modal distributions since each generator only needs to capture a subset of the modes. To entail model aggregation, probabilistic modelling is a natural and principled framework to articulate the aggregation process.Recently, Saatci & Wilson (2017) propose Bayesian GAN, a probabilistic framework for GAN under Bayesian inference. It shows that modelling the distribution of generator helps alleviate mode collapse and motivates the interpretability of the learned generators. This probabilistic framework is built upon Bayesian models for generator and discriminator, whose maximum likelihood estimation can be realized as a metaphor of typical GAN objectives.While empirical study on semi-supervised image classification tasks shows the effectiveness of Bayesian GAN, a critical theoretical question on this framework remains unanswered: Does it really converge to the generator distribution that produces the real data distribution? Indeed, our theoretical analysis and experimental results on a simple toy dataset reveal that the current Bayesian GAN falls short of convergence guarantee.With this observation, we follow the prior work to exploit probabilistic modelling as a principled way to realize model aggregation, but approach this problem from a theoretical perspective. We analyze the developed treatment, including the choice of priors, approximate inference, as well as its convergence property, and simultaneously propose a new probabilistic framework with the desirable convergence guarantee and consequently superior empirical performance.Our main contributions are:• We theoretically establish, to our best knowledge, the first probabilistic treatment of GANs such that any generator distribution faithful to the data distribution is an equilibrium.• We prove the previous Bayesian method (Saatci & Wilson, 2017) for any minimax GAN objective induces incompatibility of its defined conditional distributions.• We propose two special Monte Carlo inference algorithms for our probabilistic model which efficiently approximate the gradient of a non-differentiable criterion.• Empirical studies on synthetic high-dimensional multi-modal data and benchmark image datasets, CIFAR-10, STL-10, and ImageNet, demonstrate the superiority of the proposed framework over the state-of-the-art GAN methods. In this paper, we propose ProbGAN, a novel probabilistic modelling framework for GAN. From the perspective of Bayesian Modelling, it contributes a novel likelihood function establishing a connection to existing GAN models and a novel prior stabilizing the inference process. We also design scalable and asymptotically correct inference algorithms for ProbGAN. In the future work, we plan to extend the proposed framework to non-parametric Bayesian modelling and investigate more theoretical properties of GANs in the probabilistic modelling context.Developing Bayesian generalization for deep learning models is not a recent idea and happens in many fields other than generative models such as adversarial training (Ye & Zhu, 2018) and Bayesian neural networks (Wang et al., 2016a) . By this work, we emphasize the importance of going beyond the intuition and understanding the theoretical behavior of the Bayesian model. We hope that our work helps inspire continued exploration into Bayesian deep learning (Wang & Yeung, 2016 ) from a more rigorous perspective. A OMITTED PROOFS Theorem 1. This theorem is general and holds when the GAN objective and the discriminator space have symmetry. The symmetry of GAN objective means its functions φ 1 and φ 2 satisfy that ∃c ∈ R, ∀x ∈ R, φ 1 (x) ≡ φ 2 (c − x). While the symmetry of discriminator space DISPLAYFORM0 Note that the symmetry condition are very weak, first it holds for all the common choices of GAN objectives such as those listed in TAB0 . Second, it holds for neural network which is the most common parameterization for discriminator in practice. DISPLAYFORM1 DISPLAYFORM2 Eqn. 11 and Eqn. 12 prove that q * DISPLAYFORM3 Thus the generator distribution will not change based on the dynamics in Eqn. 2 since q * DISPLAYFORM4 ).",Probabilistic modelling is a principled framework perform model aggregation which has been primary mechanism combat mode collapse context Generative Adversarial Networks GAN paper propose novel probabilistic framework GANs ProbGAN which iteratively learns distribution generators carefully crafted prior. Learning is efficiently triggered tailored stochastic gradient Hamiltonian Monte Carlo novel gradient approximation perform Bayesian inference. theoretical analysis reveals treatment is the first probabilistic framework yields equilibrium where generator distributions are faithful data distribution. Empirical evidence synthetic high-dimensional multi-modal data image databases CIFAR-10 STL-10 ImageNet demonstrates superiority method start-of-the-art multi-generator GANs probabilistic treatment GANs. Generative Adversarial Networks GAN BID9 is notoriously hard train suffers mode collapse. has been a series works attempting address issues. One noticeable thread focuses objective design which improves original JensenShannon divergence stable pseudo-metrics f -divergence Nowozinetal. 2016 χ 2 -divergence Maoetal. 2017 Wasserstein distance BID0. However treatment is inherently limited when a single generator does not include enough model capacity capture granularity data distribution practice. Clearly generator can hardly produce accurate samples regardless choice objectives.An alternative remedy is to learn multiple generators instead single one. type methods Hoangetal. 2018;Tolstikhinetal. 2017;Wangetal. 2016b is motivated straightforward intuition multiple generators can better model multi-modal distributions since generator needs capture subset modes. entail model aggregation probabilistic modelling is a natural principled framework articulate aggregation process.Recently Saatci Wilson 2017 propose Bayesian GAN probabilistic framework GAN Bayesian inference. shows modelling distribution generator helps alleviate mode collapse motivates interpretability learned generators. probabilistic framework is built upon Bayesian models generator discriminator whose maximum likelihood estimation can be realized metaphor typical GAN objectives.While empirical study semi-supervised image classification tasks shows effectiveness Bayesian GAN critical theoretical question framework remains unanswered:Does it really converge generator distribution produces real data distribution? Indeed theoretical analysis experimental results simple toy dataset reveal current Bayesian GAN falls short convergence guarantee.With observation follow prior work exploit probabilistic modelling principled way realize model aggregation approach problem theoretical perspective. analyze developed treatment including choice priors approximate inference well convergence property simultaneously propose new probabilistic framework desirable convergence guarantee consequently superior empirical performance.Our main contributions are:• theoretically establish best knowledge first probabilistic treatment GANs generator distribution faithful data distribution is an equilibrium.• prove previous Bayesian method Saatci Wilson 2017 minimax GAN objective induces incompatibility defined conditional distributions.• propose two special Monte Carlo inference algorithms probabilistic model which efficiently approximate gradient non-differentiable criterion.• Empirical studies synthetic high-dimensional multi-modal data benchmark image datasets CIFAR-10 STL-10 ImageNet demonstrate superiority proposed framework state-of-the-art GAN methods. paper propose ProbGAN novel probabilistic modelling framework GAN. perspective Bayesian Modelling contributes novel likelihood function establishing connection existing GAN models novel prior stabilizing inference process. also design scalable asymptotically correct inference algorithms ProbGAN. future work plan extend proposed framework non-parametric Bayesian modelling investigate theoretical properties GANs probabilistic modelling context.Developing Bayesian generalization deep learning models is not a recent idea happens many fields generative models adversarial training Ye Zhu 2018 Bayesian neural networks Wangetal. 2016a work emphasize importance going beyond intuition understanding theoretical behavior Bayesian model. hope work helps inspire continued exploration Bayesian deep learning Wang Yeung 2016 rigorous perspective. OMITTED PROOFS Theorem1. theorem is general holds when the GAN objective discriminator space have symmetry. symmetry GAN objective means functionsφ1 φ 2 satisfy ∃c∈R ∀x∈R φ1 x ≡φ2 c−x symmetry discriminator space DISPLAYFORM0 Note symmetry condition are very weak first holds common choices GAN objectives listed TAB0. Second holds neural network which is the most common parameterization discriminator practice. DISPLAYFORM1 DISPLAYFORM2 Eqn. 11 Eqn. 12 prove q * DISPLAYFORM3 Thus generator distribution will not change based dynamics Eqn. 2 sinceq* DISPLAYFORM4,1154,814,340,0.011,1.418,2025/11/05 17:19:03,0.01,1.7,0.2741433021806849,329.494
"In the adversarial-perturbation problem of neural networks, an adversary starts with a neural network model $F$ and a point $\bfx$ that $F$ classifies correctly, and applies a \emph{small perturbation} to  $\bfx$ to produce another point $\bfx'$ that $F$ classifies \emph{incorrectly}.  In this paper, we propose taking into account \emph{the inherent confidence information} produced by models when studying adversarial perturbations, where a natural measure of ``confidence'' is \|F(\bfx)\|_\infty$ (i.e. how confident $F$ is about its prediction?) . Motivated by a thought experiment based on the manifold assumption, we propose a ``goodness property'' of models which states that \emph{confident regions of a good model should be well separated}. We give formalizations of this property and examine existing robust training objectives in view of them. Interestingly, we find that a recent objective by Madry et al. encourages training a model that satisfies well our formal version of the goodness property, but has a weak control of points that are wrong but with low confidence. However, if Madry et al.'s model is indeed a good solution to their objective, then good and bad points are now distinguishable and we can try to embed uncertain points back to the closest confident region to get (hopefully) correct predictions. We thus propose embedding objectives and algorithms, and perform an empirical study using this method. Our experimental results are encouraging: Madry et al.'s model wrapped with our embedding procedure achieves almost perfect success rate in defending against attacks that the base model fails on, while retaining good generalization behavior.
 In the adversarial perturbation problem of neural networks, an adversary starts with a neural network model F and a point x that F classifies correctly (we assume that F ends with a softmax layer, which is common in the literature), and applies a small perturbation to x to produce another point x that F classifies incorrectly. BID17 first noticed the vulnerability of existing (deep) neural networks to adversarial perturbations, which is a somewhat surprising phenomenon given the great generalization capability of these networks. Since then, a line of research (see, for example, BID5 ; BID14 ; BID9 ; BID8 ) has been devoted to harden neural networks against adversarial perturbation. However, while modest progress has been made, until now there is still a large gap in successfully defending against more advanced attacks, such as attack by BID4 .In this paper, we propose taking into account the inherent confidence information produced by models when studying adversarial perturbations. To this end, a natural measure of confidence is F (x) ∞ (i.e., how confident F is about its prediction?) We motivate this consideration with a thought experiment based on the manifold assumption BID18 ; man) that is commonly made in unsupervised and semi-supervised learning, which states that natural data points lie on (or near to) separate low dimensional manifolds for different classes. Essentially , if one believes that deep neural networks learn to approximate well these low dimensional manifolds, then an ideal model should have the property that it can confidently distinguish points from natural manifolds as they are well separated due to the assumption. Moreover, since the learner never sees points that are far away from the natural manifolds, an ideal model should not claim confidence there.Taking this perspective, we propose a goodness property which states that confident regions of a good model should be well separated. We give formalizations of this property and examine existing robust training objectives in view of them. Interestingly, we find that a recent objective function by BID8 encourages training a model that satisfies well our formal version of the goodness property, in the sense that high-confidence predictions of different classes are well separated. On the other hand, our analysis also indicates that there could be many points with wrong but low-confidence predictions. Therefore, if Madry et al.' s model is indeed a good solution to their objective, then we can distinguish between good and bad points with confidence, and try to embed a low-confidence point back to confident regions to get (hopefully) the correct prediction.We propose two embedding objectives: (1) δ-Most Confident Neighbor (MCN δ ), where MCN δ (F, x) = arg max z∈N (x,δ) F (z) ∞ for a point x, a radius parameter δ > 0, and N (x, δ) the δ-neighborhood around x. (2) p-Nearest Confident Neighbor (NCN p ), where NCN p (F, x) = arg min z z − x subject to F (z) ∞ ≥ p, for a point x and a confidence parameter p ∈ (0, 1). With these, the end to end predictions become F (MCN δ (F, x)) and F (NCN p (F, x)). We note that these objectives are semantic: They fail only when the model has a confident but wrong prediction in the neighborhood.We perform an empirical study over CIFAR10. We first empirically validate that Madry et al.' s model is better, in view of our goodness property, than models trained without a robustness objective. We then give end-to-end defense results based on our method. Specifically, we propose using gradient based optimization, such as Carlini-Wagner attacks BID4 (which, however, are now used for defense) to solve MCN δ or NCN p . Our empirical results are encouraging : (1) It achieves almost perfect success rate in defending against attacks that the base model fails on, and (2) It also retains the good generalization behavior of the base model.The rest of the paper is organized as follows: We first discuss important prior work in Section 2 and some preliminaries in Section 3. Then Section 4 proposes the goodness property, and examines Madry et al.'s robust training objective function in view of the property. We then present embedding objectives and algorithms for handling low-confidence points in Section 5. Section 6 performs an empirical study where we validate that Madry et al.'s robust model satisfies well our goodness property, and then give defense results for our technique. Section 7 concludes with discussions on implications of our method. BID17 first observed the susceptibility of deep neural networks to adversarial perturbations. Since then, a large body of work have been devoted to studying hardening neural networks for this problem (a subset of work in this direction is BID5 BID14 ; BID9 ). Simultaneously, another line of work have been devoted to devise more effective or efficient attacks (a small set of work in this direction is BID10 BID13 BID4 ). Unfortunately, there still seems to be a large gap for the defense methods to defend against more sophisticated attacks, such as CarliniWagner attacks BID4 . For example, while the recent robust residual network constructed by BID8 achieves encouraging robustness results on MNIST, on CIFAR10 the accuracy against a strong adversary, such as attacks by BID4 , can be as low as 45.8%. We now discuss our method and results. (a) Base model on x, unconfident prediction ""automobile"" DISPLAYFORM0 (e) A valid ""ship"" that resembles the ""automobile""(f ) Base model on x, unconfident prediction ""airplane"" ( g) CarliniWagnerShell on x, unconfident prediction ""ship"" (h) Base model on x , unconfident prediction ""ship"" (i) CarliniWagnerShell on x , unconfident prediction ""airplane"" (j) A valid ""ship"" image that resembles the ""airplane"" Figure 2 : The images (a) and (e) are the points where our CarliniWagnerShell makes a wrong prediction. We show the original image on the first column, CarliniWagnerShell perturbations of the original images on the second column, adversarial perturbed images on the third column, and CarliniWagnerShell perturbations of the adversarial examples on the fourth column. Example ship images are presented on the last row for comparison.Our technical contributions. Our first technical contribution is the proposal to take into account the inherent confidence information produced by models when studying adversarial perturbations. Our second technical contribution is a formulation of a goodness property of models, and an analysis of existing models in view of the property. Interestingly, and somewhat surprisingly, we find that a recent robust training objective function by BID8 encourages good separation of highconfidence points, but has essentially no control of low-confidence points. Our third contribution is the proposal of embedding to handle low-confidence points. Our final contribution is a first empirical study that validates Madry et al.'s model in terms of the goodness property, and further demonstrates that a good model, when wrapped with embedding, simultaneously achieves good generalization and almost perfect robustness.Interpretations of our results. One interpretation of our results is that adversarial perturbations can naturally coexist with good generalization. While this is manifested in our analysis of Madry et al.'s objective function, we think that this phenomenon naturally and generally exists if one takes again a manifold point of view: Since natural manifolds reside in low dimensions, it seems much more challenging to control the confidence boundary, where ""adversarial perturbations"" exist in abundance, than controlling separation of the learned structures (i.e. confident regions that approximate the underlying manifolds).On the other hand, if all one cares about is robustness (decision does not change in a small neighborhood), then adversarial perturbation problem can be resolved by combining goodness property with embedding. For example, consider the following ""good model:"" If a data point is from the training set, then it outputs the correct label with confidence 1, otherwise it outputs a uniform distribution over labels. In other words, this model learns nothing but fitting the training set. We note that in this case, the adversarial perturbation problem is only well defined around the training points. Moreover , embedding now becomes 1-nearest neighbor search among the training points. As a result , the model is still perfectly robust with our method if training points are well separated.Highly confident predictions on random noises. We note that several work shows that neural networks can have highly confident predictions on random noises (e.g., BID11 ). In view of our work it is somewhat not surprising that neural networks can have such behaviors: These points are essentially ones that are far away from the ""universe"" the learner is asked to learn, and so if we do not control the training of neural networks to not claim confidence over the structure it has never seen, then it is valid to fit a model that has good behaviors on natural manifolds but also divergent behaviors outside. After all, why is a network supposed to work on points that are far away from the underlying natural manifolds, which is essentially the data generating distribution? Finally, we note that the adversarial perturbation problem is not well defined even near those points.","adversarial-perturbation problem neural networks adversary starts neural network model$F point $\bfx $F classifies correctly applies \emph small perturbation $\bfx produce another point $\bfx' $F classifies \emph incorrectly paper propose taking account \emph inherent confidence information produced models when studying adversarial perturbations where a natural measure confidence is \|F \bfx \|_\infty.e how confident confident$F is about its prediction? Motivated thought experiment based manifold assumption propose goodness property models which states \emph confident regions good model should be well separated give formalizations property examine existing robust training objectives view them. Interestingly find recent objective Madryetal. encourages training model satisfies well formal version goodness property has a weak control points are wrong low confidence. However if Madry et al.'s model is indeed good solution objective good bad points are now distinguishable can try embed uncertain points back closest confident region get hopefully correct predictions. thus propose embedding objectives algorithms perform empirical study using method. experimental results are encouraging:Madry et al.'s model wrapped embedding procedure achieves almost perfect success rate defending attacks base model fails retaining good generalization behavior. adversarial perturbation problem neural networks adversary starts neural network modelF pointx F classifies correctly assume F ends softmax layer which is common literature applies small perturbation x produce another pointx F classifies incorrectly. BID17 first noticed vulnerability existing deep neural networks adversarial perturbations which is a somewhat surprising phenomenon given great generalization capability networks. Since line research see example BID5;BID14;BID9;BID8 has been devoted harden neural networks adversarial perturbation. However modest progress has been made is still large gap successfully defending advanced attacks attack BID4.In paper propose taking account inherent confidence information produced models when studying adversarial perturbations. end where a natural measure confidence isF x ∞ .e how confidentF is about its prediction? motivate consideration thought experiment based manifold assumption BID18;man is commonly made unsupervised semi-supervised learning which states natural data points lie near separate low dimensional manifolds different classes. Essentially if if all one believes deep neural networks learn approximate well low dimensional manifolds ideal model should have the property can confidently distinguish points natural manifolds are well separated due assumption. Moreover since learner never sees points are far away natural manifolds ideal model should not claim confidence there.Taking perspective propose goodness property which states confident regions good model should be well separated. give formalizations property examine existing robust training objectives view them. Interestingly find recent objective function BID8 encourages training model satisfies well formal version goodness property sense high-confidence predictions different classes are well separated. hand analysis also indicates could many points wrong low-confidence predictions. Therefore if Madryetal.' model is indeed good solution objective can distinguish good bad points confidence try embed low-confidence point back confident regions get hopefully correct prediction.We propose two embedding objectives:1 δ-Most Confident Neighbor MCNδ where MCNδ F x arg max z∈N x δ F z ∞ pointx radius parameterδ 0 N x δ δ-neighborhood aroundx. 2 p-Nearest Confident Neighbor NCNp where NCNp F x arg minzz − x subject F z ∞≥p pointx confidence parameterp∈ 0 1 end end predictions becomeF MCNδ F x F NCNp F x note objectives are semantic:fail when the model has a confident wrong prediction neighborhood.We perform empirical study CIFAR10. first empirically validate Madryetal.' model is better view goodness property models trained without robustness objective. give end-to-end defense results based method. Specifically propose using gradient based optimization Carlini-Wagner attacks BID4 which,however are now used defense solve MCNδ NCNp. empirical results are encouraging:1 achieves almost perfect success rate defending attacks base model fails 2 also retains good generalization behavior base model.The rest paper is organized follows:first discuss important prior work Section2 preliminaries Section3. Section 4 proposes goodness property examines Madryetal.'s robust training objective function view property. present embedding objectives algorithms handling low-confidence points Section5. Section 6 performs empirical study where we validate Madry et al.'s robust model satisfies well goodness property give defense results technique. Section 7 concludes discussions implications method. BID17 first observed susceptibility deep neural networks adversarial perturbations. Since large body work have been devoted studying hardening neural networks problem subset work direction is BID5 BID14;BID9 Simultaneously another line work have been devoted devise effective efficient attacks small set work direction is BID10 BID13 BID4 Unfortunately still seems large gap defense methods defend sophisticated attacks CarliniWagner attacks BID4. example recent robust residual network constructed BID8 achieves encouraging robustness results MNIST CIFAR10 accuracy strong adversary attacks BID4 can be as low 45.8%. discuss method results. Base model x unconfident prediction automobile DISPLAYFORM0 e valid ship resembles automobile f Base model x unconfident prediction airplane g CarliniWagnerShell x unconfident prediction ship h Base model x unconfident prediction ship CarliniWagnerShell x unconfident prediction airplane j valid ship image resembles airplane Figure2:images e are the points where our CarliniWagnerShell makes wrong prediction. show original image first column CarliniWagnerShell perturbations original images second column where adversarial perturbed images third column CarliniWagnerShell perturbations adversarial examples fourth column. Example ship images are presented last row comparison.Our technical contributions. first technical contribution is the proposal take account inherent confidence information produced models when studying adversarial perturbations. second technical contribution is a formulation goodness property models analysis existing models view property. Interestingly which is a somewhat surprisingly find recent robust training objective function BID8 encourages good separation highconfidence points has which is essentially control low-confidence points. third contribution is the proposal embedding handle low-confidence points. final contribution is a first empirical study validates Madryetal.'s model terms goodness property demonstrates has good model when wrapped embedding simultaneously achieves good generalization almost perfect robustness.Interpretations results. One interpretation results is that adversarial perturbations can naturally coexist good generalization. is manifested analysis Madry et al.'s objective function think phenomenon naturally generally exists if one takes manifold point view:Since natural manifolds reside low dimensions seems much challenging control confidence boundary where adversarial perturbations exist abundance controlling separation learned structures.e confident regions approximate underlying manifolds.On hand if if all one cares is robustness decision does not change small neighborhood adversarial perturbation problem can be resolved combining goodness property embedding. example consider following good model:If a data point is from the training set outputs correct label confidence1 otherwise outputs uniform distribution labels. words model learns nothing fitting training set. note case where adversarial perturbation problem is only is not well defined around training points. Moreover embedding becomes 1-nearest neighbor search among training points. result model is still perfectly robust method if training points are well separated.Highly confident predictions random noises. note several work shows neural networks can have highly confident predictions random noises e.g BID11 view work is somewhat surprising neural networks can have such behaviors:points are essentially ones are far away universe learner is asked learn if do not control training neural networks claim confidence structure has never seen is valid fit model has good behaviors natural manifolds also divergent behaviors outside. why isa network supposed work points are far away underlying natural manifolds has which is essentially data generating distribution? Finally note adversarial perturbation problem is only is not well defined even near points.",2271,1521,750,0.031,1.493,2025/11/05 17:19:03,0.01,1.538,0.5077881619937696,766.871
"Recently Neural Architecture Search (NAS) has aroused great interest in both academia and industry, however it remains challenging because of its huge and non-continuous search space. Instead of applying evolutionary algorithm or reinforcement learning as previous works, this paper proposes a Direct Sparse Optimization NAS (DSO-NAS) method. In DSO-NAS, we provide a novel model pruning view to NAS problem. In specific, we start from a completely connected block, and then introduce scaling factors to scale the information flow between operations. Next, we impose sparse regularizations to prune useless connections in the architecture. Lastly, we derive an efficient and theoretically sound optimization method to solve it. Our method enjoys both advantages of differentiability and efficiency, therefore can be directly applied to large datasets like ImageNet. Particularly, On CIFAR-10 dataset, DSO-NAS achieves an average test error 2.84%, while on the ImageNet dataset DSO-NAS achieves 25.4% test error under 600M FLOPs with 8 GPUs in 18 hours. With no doubt, Deep Neural Networks (DNN) have been the engines for the AI renaissance in recent years. Dating back to 2012, DNN based methods have refreshed the records for many AI applications, such as image classification BID16 ; BID37 ; BID8 ), speech recognition ; BID4 ) and Go Game BID33 ). Considering its amazing representation power, DNNs have shifted the paradigm of these applications from manually designing the features and stagewise pipelines to end-to-end learning. Although DNNs have liberated researchers from such feature engineering, another tedious work has emerged -""network engineering"". In most cases, the neural networks need to be designed based on the specific tasks, which again leads to endless hyperparameters tuning and trails. Therefore, designing a suitable neural network architecture still requires considerable amounts of expertise and experience.To democratize the techniques, Neural Architecture Search (NAS) or more broadly, AutoML has been proposed. There are mainly two streams for NAS: The first one is to follow the pioneering work BID45 , which proposed a reinforcement learning algorithm to train a Recurrent Neural Network (RNN) controller that generates coded architectures ; BID29 ). The second one is the evolutionary algorithm, which iteratively evaluates and proposes new models for evaluation BID30 ; BID36 ). Despite their impressive performance, the search processes are incredibly resource-hungry and unpractical for large datasets like ImageNet, though some acceleration methods have been proposed BID44 ; BID29 ). Very recently, DARTS BID22 ) proposed a gradient-based method in which the connections are selected by a softmax classifier. Although DARTS achieves impressive performance with great acceleration, its search space is still limited to fix-length coding and blocksharing search as in previous works.In this work, we take another view to tackle these problems. We reformulate NAS as pruning the useless connections from a large network which contains the complete network architecture hypothesis space. Thus only one single model is trained and evaluated. Since the network structure is directly optimized during training, we call our method Direct Sparse Optimization NAS (DSO-NAS). We further demonstrate that this sparse regularized problem can be efficiently optimized by a modified accelerated proximal gradient method opposed to the inefficient reinforcement learning or revolutionary search. Notably, DSO-NAS is much simpler than the existing search methods as it unifies the neural network weight learning and architecture search into one single optimization problem. DSO-NAS does not need any controller BID45 ; ; BID29 ) or performance predictor BID21 ) or relaxation of the search space BID45 ; ; BID29 ; BID22 ). As a result of the efficiency and simplicity, DSO-NAS first demonstrate that NAS can be directly applied to large datasets like ImageNet with no block structure sharing. Our experiments show that DSO-NAS can achieve 2.84% average test error on CIFAR-10, as well as top-1 error 25.4% on ImageNet with FLOPs (the number of multiply-adds) under 600M.In summary, our contributions can be summarized as follows:• We propose a novel model pruning formulation for neural architecture search based on sparse optimization. Only one model needs to be trained during the search.• We propose a theoretically sound optimization method to solve this challenging optimization problem both effectively and efficiently.• We demonstrate the results of our proposed method are competitive or better than other NAS methods, while significantly simplifying and accelerating the search process. Neural Architecture Search has been the core technology for realizing AutoML. In this paper, we have proposed a Direct Sparse Optimization method for NAS. Our method is appealing to both academic research and industrial practice in two aspects: First, our unified weight and structure learning method is fully differentiable in contrast to most previous works. It provides a novel model pruning view to the NAS problem. Second, the induced optimization method is both efficient and effective. We have demonstrated state-of-the-art performance on both CIFAR and ILSVRC2012 image classification datasets, with affordable cost (single machine in one day).In the future, we would like to incorporate hardware features for network co-design, since the actual running speed of the same network may highly vary across different hardware because of cache size, memory bandwidth, etc. We believe our proposed DSO-NAS opens a new direction to pursue such objective. It could push a further step to AutoML for everyone's use.",Recently Neural Architecture Search NAS has aroused great interest academia industry however remains challenging huge non-continuous search space. Instead applying evolutionary algorithm reinforcement learning previous works paper proposes Direct Sparse Optimization NAS DSO-NAS method. DSO-NAS provide novel model pruning view NAS problem. specific start completely connected block introduce scaling factors scale information flow operations. Next impose sparse regularizations prune useless connections architecture. Lastly derive efficient theoretically sound optimization method solve it. method enjoys advantages differentiability efficiency therefore can be directly applied large datasets like ImageNet. Particularly CIFAR-10 dataset DSO-NAS achieves average test error 2.84 ImageNet dataset DSO-NAS achieves 25.4 test error 600M FLOPs 8 GPUs 18 hours. doubt Deep Neural Networks DNN have been the engines AI renaissance recent years. Dating back 2012 DNN based methods have refreshed records many AI applications image classification BID16;BID37;BID8 speech recognition;BID4 Go Game BID33 Considering amazing representation power DNNs have shifted paradigm applications manually designing features stagewise pipelines end-to-end learning. Although DNNs have liberated researchers feature engineering another tedious work has emerged -network engineering. cases neural networks need designed based specific tasks which again leads endless hyperparameters tuning trails. Therefore designing suitable neural network architecture still requires considerable amounts expertise experience.To democratize techniques Neural Architecture Search NAS broadly AutoML has been proposed. are mainly two streams NAS:first one is to follow pioneering work BID45 which have proposed reinforcement learning algorithm train Recurrent Neural Network RNN controller generates coded architectures;BID29 second one is the evolutionary algorithm which iteratively evaluates proposes new models evaluation BID30;BID36 Despite impressive performance search processes are incredibly resource-hungry unpractical large datasets like ImageNet though acceleration methods have been proposed BID44;BID29 recently DARTS BID22 proposed gradient-based method which the connections are selected softmax classifier. Although DARTS achieves impressive performance great acceleration search space is still limited fix-length coding blocksharing search previous works.In work take another view tackle problems. reformulate NAS pruning useless connections large network which contains complete network architecture hypothesis space. Thus one single model is trained evaluated. Since network structure is directly optimized training call method Direct Sparse Optimization NAS DSO-NAS demonstrate sparse regularized problem can be efficiently optimized modified accelerated proximal gradient method opposed inefficient reinforcement learning revolutionary search. Notably DSO-NAS is much simpler existing search methods unifies neural network weight learning architecture search one single optimization problem. DSO-NAS does not need controller BID45;BID29 performance predictor BID21 relaxation search space BID45;BID29;BID22 result efficiency simplicity DSO-NAS first demonstrate NAS can be directly applied large datasets like ImageNet block structure sharing. experiments show DSO-NAS can achieve achieve 2.84 average test error CIFAR-10 well top-1 error 25.4 ImageNet FLOPs number multiply-adds 600M.In summary contributions can be summarized follows:• propose novel model pruning formulation neural architecture search based sparse optimization. one model needs trained search.• propose theoretically sound optimization method solve challenging optimization problem effectively efficiently.• demonstrate results proposed method are competitive better NAS methods significantly simplifying accelerating search process. Neural Architecture Search has been the core technology realizing AutoML. paper which have proposed Direct Sparse Optimization method NAS. method is appealing academic research industrial practice two aspects:First unified weight structure learning method is fully differentiable contrast previous works. provides novel model pruning view NAS problem. Second induced optimization method is both efficient effective. have demonstrated state-of-the-art performance CIFAR ILSVRC2012 image classification datasets affordable cost single machine one day.In future would like incorporate hardware features network co-design since actual running speed network may highly vary across different hardware cache size memory bandwidth etc. believe proposed DSO-NAS opens new direction pursue objective. could push step AutoML everyone's use.,1092,789,303,0.01,1.384,2025/11/05 17:19:03,0.0,1.471,0.16822429906542,324.185
"Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. This paper focuses on this problem, and proposes two new compression methods, which jointly leverage weight quantization and distillation of larger teacher networks into smaller student networks. The first method we propose is called quantized distillation and leverages distillation during the training process, by incorporating distillation loss, expressed with respect to the teacher, into the training of a student network whose weights are quantized to a limited set of levels. The second method,  differentiable quantization, optimizes the location of quantization points through stochastic gradient descent, to better fit the behavior of the teacher model.   We validate both methods through experiments on convolutional and recurrent architectures. We show that quantized shallow students can reach similar accuracy levels to full-precision teacher models, while providing order of magnitude compression, and inference speedup that is linear in the depth reduction. In sum, our results enable DNNs for resource-constrained environments to leverage architecture and accuracy advances developed on more powerful devices.
 Background. Neural networks are extremely effective for solving several real world problems, like image classification BID20 BID10 , translation BID33 , voice synthesis BID27 or reinforcement learning BID26 BID30 . At the same time, modern neural network architectures are often compute, space and power hungry, typically requiring powerful GPUs to train and evaluate. The debate is still ongoing on whether large models are necessary for good accuracy. It is known that individual network weights can be redundant, and may not carry significant information, e.g. BID9 . At the same time, large models often have the ability to completely memorize datasets ), yet they do not, but instead appear to learn generic task solutions. A standing hypothesis for why overcomplete representations are necessary is that they make learning possible by transforming local minima into saddle points BID6 or to discover robust solutions, which do not rely on precise weight values BID13 BID16 .If large models are only needed for robustness during training, then significant compression of these models should be achievable, without impacting accuracy. This intuition is strengthened by two related, but slightly different research directions. The first direction is the work on training quantized neural networks, e.g. BID5 ; BID29 ; BID14 ; BID35 ; BID24 ; BID28 ; BID41 , which showed that neural networks can converge to good task solutions even when weights are constrained to having values from a set of integer levels. The second direction aims to compress already-trained models, while preserving their accuracy. To this end, various elegant compression techniques have been proposed, e.g. BID9 ; BID15 ; BID34 ; BID8 ; BID25 , which combine quantization, weight sharing, and careful coding of network weights, to reduce the size of state-of-the-art deep models by orders of magnitude, while at the same time speeding up inference.Both these research directions are extremely active, and have been shown to yield significant compression and accuracy improvements, which can be crucial when making such models available on embedded devices or phones. However , the literature on compressing deep networks focuses almost exclusively on finding good compression schemes for a given model, without significantly altering the structure of the model. On the other hand, recent parallel work BID3 BID12 introduces the process of distillation, which can be used for transferring the behaviour of a given model to any other structure. This can be used for compression, e.g. to obtain compact representations of ensembles BID12 . However the size of the student model needs to be large enough for allowing learning to succeed. A model that is too shallow, too narrow, or which misses necessary units, can result in considerable loss of accuracy BID31 .In this work, we examine whether distillation and quantization can be jointly leveraged for better compression. We start from the intuition that 1) the existence of highly-accurate, full-precision teacher models should be leveraged to improve the performance of quantized models, while 2) quantizing a model can provide better compression than a distillation process attempting the same space gains by purely decreasing the number of layers or layer width. While our approach is very natural, interesting research questions arise when these two ideas are combined.Contribution. We present two methods which allow the user to compound compression in terms of depth, by distilling a shallower student network with similar accuracy to a deeper teacher network, with compression in terms of width, by quantizing the weights of the student to a limited set of integer levels, and using less weights per layer. The basic idea is that quantized models can leverage distillation loss BID12 , the weighted average between the correct targets (represented by the labels) and soft targets (represented by the teacher's outputs).We implement this intuition via two different methods. The first, called quantized distillation, aims to leverage distillation loss during the training process, by incorporating it into the training of a student network whose weights are constrained to a limited set of levels. The second method, which we call differentiable quantization, takes a different approach, by attempting to converge to the optimal location of quantization points through stochastic gradient descent. We validate both methods empirically through a range of experiments on convolutional and recurrent network architectures. We show that quantized shallow students can reach similar accuracy levels to full-precision and deeper teacher models on datasets such as CIFAR and ImageNet (for image classification) and OpenNMT and WMT (for machine translation), while providing up to order of magnitude compression, and inference speedup that is linear in the depth. While the loss is continuous w.r.t. p, there are indirect effects when changing the way each weight gets quantized. This can have drastic effect on the learning process. As an extreme example, we could have degeneracies, where all weights get represented by the same quantization point, making learning impossible. Or diversity of p i gets reduced, resulting in very few weights being represented at a really high precision while the rest are forced to be represented in a much lower resolution.To avoid such issues, we rely on the following set of heuristics. Future work will look at adding a reinforcement learning loss for how the p i are assigned to weights.Choose good starting points. One way to initialize the starting quantization points is to make them uniformly spaced, which would correspond to use as a starting point the uniform quantization function. The differentiable quantization algorithm needs to be able to use a quantization point in order to update it; therefore, to make sure every quantization point is used we initialize the points to be the quantiles of the weight values. This ensures that every quantization point is associated with the same number of values and we are able to update it.Redistribute bits where it matters. Not all layers in the network need the same accuracy. A measure of how important each weight is to the final prediction is the norm of the gradient of each weight vector. So in an initial phase we run the forward and backward pass a certain number of times to estimate the gradient of the weight vectors in each layer, we compute the average gradient across multiple minibatches and compute the norm; we then allocate the number of points associated with each weight according to a simple linear proportion. In short we estimate DISPLAYFORM0 where l is the loss function,v is the vector of weights in a particular layer and DISPLAYFORM1 = ∂l ∂vi and we use this value to determine which layers are most sensitive to quantization.When using this process, we will use more than the indicated number of bits in some layers, and less in others. We can reduce the impact of this effect with the use of Huffman encoding, see Section 5; in any case, note that while the total number of points stays constant, allocating more points to a layer will increase bit complexity overall if the layer has a larger proportion of the weights.Use the distillation loss. In the algorithm delineated above, the loss refers to the loss we used to train the original model with. Another possible specification is to treat the unquantized model as the teacher model, the quantized model as the student, and to use as loss the distillation loss between the outputs of the unquantized and quantized model. In this case, then, we are optimizing our quantized model not to perform best with respect to the original loss, but to mimic the results of the unquantized model, which should be easier to learn for the model and provide better results.Hyperparameter optimization. The algorithm above is an optimization problem very similar to the original one. As usual, to obtain the best results one should experiment with hyperparameters optimization, and different variants of gradient descent. We have examined the impact of combining distillation and quantization when compressing deep neural networks. Our main finding is that, when quantizing, one can (and should) leverage large, accurate models via distillation loss, if such models are available. We have given two methods to do just that, namely quantized distillation, and differentiable quantization. The former acts directly on the training process of the student model, while the latter provides a way of optimizing the quantization of the student so as to best fit the teacher model.Our experimental results suggest that these methods can compress existing models by up to an order of magnitude in terms of size, on small image classification and NMT tasks, while preserving accuracy. At the same time, we note that distillation also provides an automatic improvement in inference speed, since it generates shallower models. One of our more surprising findings is that naive uniform quantization with bucketing appears to perform well in a wide range of scenarios. Our analysis in Section 2.2 suggests that this may be because bucketing provides a way to parametrize the Gaussian-like noise induced by quantization. Given its simplicity, it could be used consistently as a baseline method.In our experimental results, we performed manual architecture search for the depth and bit width of the student model, which is time-consuming and error-prone. In future work, we plan to examine the potential of reinforcement learning or evolution strategies to discover the structure of the student for best performance given a set of space and latency constraints. The second, and more immediate direction, is to examine the practical speedup potential of these methods, and use them together and in conjunction with existing compression methods such as weight sharing BID9 and with existing low-precision computation frameworks, such as NVIDIA TensorRT, or FPGA platforms.","Deep neural networks DNNs continue make significant advances solving tasks image classification translation reinforcement learning. One aspect field receiving considerable attention is efficiently executing deep models resource-constrained environments mobile embedded devices. paper focuses problem proposes two new compression methods which jointly leverage weight quantization distillation larger teacher networks smaller student networks. first method propose is called quantized distillation leverages distillation training process incorporating distillation loss expressed respect teacher training student network whose weights are quantized limited set levels. second method differentiable quantization optimizes location quantization points stochastic gradient descent better fit behavior teacher model. validate methods experiments convolutional recurrent architectures. show quantized shallow students can reach similar accuracy levels full-precision teacher models providing order magnitude compression inference speedup is linear depth reduction. sum results enable DNNs resource-constrained environments leverage architecture accuracy advances developed powerful devices. Background. Neural networks are extremely effective solving several real world problems like image classification BID20 BID10 translation BID33 voice synthesis BID27 reinforcement learning BID26 BID30. time modern neural network architectures are often compute space power hungry typically requiring powerful GPUs train evaluate. debate is still ongoing whether large models are necessary good accuracy. is known individual network weights can be redundant may carry significant information e.g BID9. time large models often have the ability completely memorize datasets yet do not,instead appear learn generic task solutions. standing hypothesis why overcomplete representations are necessary is that they is to make learning possible transforming local minima saddle points BID6 discover robust solutions which do not rely precise weight values BID13 BID16.If large models are only needed robustness training significant compression models should be achievable without impacting accuracy. intuition is strengthened two related slightly different research directions. first direction is the work training quantized neural networks e.g BID5;BID29;BID14;BID35;BID24;BID28;BID41 which showed neural networks can converge good task solutions even when weights are constrained values set integer levels. second direction aims compress already-trained models preserving accuracy. end various elegant compression techniques have been proposed e.g BID9;BID15;BID34;BID8;BID25 which combine quantization weight sharing careful coding network weights reduce size state-of-the-art deep models orders magnitude time speeding inference.Both research directions are extremely active have been shown yield significant compression accuracy improvements which can be crucial when making models available embedded devices phones. However literature compressing deep networks focuses almost exclusively finding good compression schemes given model without significantly altering structure model. hand recent parallel work BID3 BID12 introduces process distillation which can be used transferring behaviour given model structure. can be used compression e.g obtain compact representations ensembles BID12. However size student model needs large enough allowing learning succeed. model is too shallow narrow which misses necessary units can result considerable loss accuracy BID31.In work is to examine whether distillation quantization can be jointly leveraged better compression. start intuition 1 existence highly-accurate full-precision teacher models should be leveraged improve performance quantized models 2 quantizing model can provide better compression distillation process attempting space gains purely decreasing number layers layer width. approach is very natural interesting research questions arise when these two ideas are combined.Contribution. present two methods which allow user compound compression terms depth distilling shallower student network similar accuracy deeper teacher network compression terms width quantizing weights student limited set integer levels using less weights per layer. basic idea is that quantized models can can(and should leverage distillation loss BID12 weighted average correct targets represented labels soft targets represented teacher's outputs.We implement intuition via two different methods. first called quantized distillation aims leverage distillation loss training process incorporating training student network whose weights are constrained limited set levels. second method which we call differentiable quantization takes different approach attempting converge optimal location quantization points stochastic gradient descent. validate methods empirically range experiments convolutional recurrent network architectures. show quantized shallow students can reach similar accuracy levels full-precision deeper teacher models datasets CIFAR ImageNet image classification OpenNMT WMT machine translation providing order magnitude compression inference speedup is linear depth. loss is continuous continuousw.r.t p are indirect effects when changing way weight gets quantized. can have drastic effect learning process. extreme example could have degeneracies where all weights get represented quantization point making learning impossible. diversity p gets reduced resulting weights represented really high precision rest are forced represented much lower resolution.To avoid issues which do not rely following set heuristics. Future work will look adding reinforcement learning loss how thep are assigned weights.Choose good starting points. One way initialize starting quantization points is that they is to make uniformly spaced would correspond use starting point uniform quantization function. differentiable quantization algorithm needs able use quantization point order update it;therefore make sure every quantization point is used initialize points quantiles weight values. ensures every quantization point is associated number values are able update it.Redistribute bits where it matters. layers network need accuracy. measure how important weight is to the final prediction is the norm gradient weight vector. initial phase run forward backward pass certain number times estimate gradient weight vectors layer compute average gradient across multiple minibatches compute norm;allocate number points associated weight according simple linear proportion. short estimate DISPLAYFORM0 wherel is the loss function v is the vector weights particular layer DISPLAYFORM1 ∂l ∂vi use value determine which layers are most sensitive quantization.When using process will use indicated number bits layers less others. can reduce impact effect use Huffman encoding see Section5;case note total number points stays constant allocating points layer will increase bit complexity overall if the layer has a larger proportion weights.Use distillation loss. algorithm delineated loss refers loss used train original model with. Another possible specification is to treat unquantized model teacher model quantized model student will use loss distillation loss outputs unquantized quantized model. case are optimizing quantized model perform best respect original loss mimic results unquantized model which should be easier learn model provide better results.Hyperparameter optimization. algorithm is an optimization problem similar original one. usual obtain best results one should experiment hyperparameters optimization different variants gradient descent. have examined impact combining distillation quantization when compressing deep neural networks. main finding is that,when quantizing one can can(and should leverage large accurate models via distillation loss if such models are available. have given two methods do just that namely quantized distillation differentiable quantization. former acts directly training process student model latter provides way optimizing quantization student best fit teacher model.Our experimental results suggest methods can compress existing models order magnitude terms size small image classification NMT tasks preserving accuracy. time note distillation also provides automatic improvement inference speed since generates shallower models. One surprising findings is that naive uniform quantization bucketing appears perform well wide range scenarios. analysis Section 2.2 suggests may bucketing provides way parametrize Gaussian-like noise induced quantization. Given simplicity could used consistently baseline method.In experimental results performed manual architecture search depth bit width student model which is time-consuming error-prone future work plan examine potential reinforcement learning evolution strategies discover structure student best performance given set space latency constraints. second immediate direction is to examine practical speedup potential methods will use together conjunction existing compression methods weight sharing BID9 existing low-precision computation frameworks NVIDIA TensorRT FPGA platforms.",2149,1462,687,0.029,1.47,2025/11/05 17:19:03,0.01,1.611,0.4361370716510901,764.67
"Previous work has demonstrated the benefits of incorporating additional linguistic annotations such as syntactic trees into neural machine translation. However the cost of obtaining those syntactic annotations is expensive for many languages and the quality of unsupervised learning linguistic structures is too poor to be helpful. In this work, we aim to improve neural machine translation via source side dependency syntax but without explicit annotation. We propose a set of models that learn to induce dependency trees on the source side and learn to use that information on the target side. Importantly, we also show that our dependency trees capture important syntactic features of language and improve translation quality on two language pairs En-De and En-Ru.",Previous work has demonstrated benefits incorporating additional linguistic annotations syntactic trees neural machine translation. However cost obtaining syntactic annotations is expensive many languages quality unsupervised learning linguistic structures is too poor helpful. work aim improve neural machine translation via source side dependency syntax without explicit annotation. propose set models learn induce dependency trees source side learn use information target side. Importantly also show dependency trees capture important syntactic features language improve translation quality two language pairs En-De En-Ru,132,91,41,0.002,1.451,2025/11/05 17:19:03,0.0,1.333,0.3769470404984424,60.543
"Model-free reinforcement learning (RL) requires a large number of trials to learn a good policy, especially in environments with sparse rewards. We explore a method to improve the sample efficiency when we have access to demonstrations. Our approach, Backplay, uses a single demonstration to construct a curriculum for a given task. Rather than starting each training episode in the environment's fixed initial state, we start the agent near the end of the demonstration and move the starting point backwards during the course of training until we reach the initial state. Our contributions are that we analytically characterize the types of environments where Backplay can improve training speed, demonstrate the effectiveness of Backplay both in large grid worlds and a complex four player zero-sum game (Pommerman), and show that Backplay compares favorably to other competitive methods known to improve sample efficiency. This includes reward shaping, behavioral cloning, and reverse curriculum generation. An important goal of AI research is to construct agents that can learn well in new environments BID28 ). An increasingly popular paradigm for this task is deep reinforcement learning (deep RL, BID40 ; BID31 ; ). However, training an RL agent can take a very long time, particularly in environments with sparse rewards. In these settings, the agent typically requires a large number of episodes to stumble upon positive rewards and learn even a moderately effective policy that can then be refined. This is often resolved via hand-engineering a dense reward function. Such reward shaping, while effective, can also change the set of optimal policies and have unintended side effects BID34 BID7 .We consider an alternative technique for accelerating RL in sparse reward settings. The idea is to create a curriculum for the agent via reversing a single trajectory (i.e. state sequence) of reasonably good, but not necessarily optimal, behavior. We start our agent at the end of a demonstration and let it learn a policy in this easier setup. We then move the starting point backward until the agent is training only on the initial state of the task. We call this technique Backplay.Our contributions are threefold:1. We characterize analytically and qualitatively which environments Backplay will aid.2. We demonstrate Backplay's effectiveness on both a grid world task (to gain intuition) as well as the four player stochastic zero-sum game Pommerman BID32 .3. We empirically show that Backplay compares favorably to other methods that improve sample complexity.Besides requiring vastly fewer number of samples to learn a good policy, an agent trained with Backplay can outperform its demonstrator and even learn an optimal policy following a sub-optimal demonstration. Our experiments further show Backplay's strong performance relative to reward shaping (involves hand tuning reward functions), behavioral cloning (not intended for use with sub-optimal experts), and other forms of automatic curriculum generation BID12 , requires a reversable environment).2 RELATED WORK Figure 1 . Backplay : We first collect a demonstration, from which we build a curriculum over the states. We then sample a state according to that curriculum and initialize our agent accordingly.The most related work to ours is a blog post describing a method similar to Backplay used to obtain state-of-theart performance on the challenging Atari game Montezuma's Revenge (Salimans & Chen, 2018) . This work was independent of and concurrent to our own. In addition to reporting results on a different, complex stochastic multi-agent environment, we provide an analytic characterization of the method as well as an in depth discussion of what kinds of environments a practitioner can expect Backplay to out or underperform other existing methods.A popular method for improving RL with access to expert demonstrations is behavioral cloning/imitation learning. These methods explicitly encourage the learned policy to mimic an expert policy BID1 Ross et al., 2011; BID10 BID44 BID24 BID33 BID16 BID17 BID0 BID35 . Imitation learning requires access to both state and expert actions (whereas Backplay only requires states) and is designed to copy an expert, thus it cannot, without further adjustments (e.g. as proposed by BID14 ), surpass a suboptimal expert. We discuss the pros and cons of an imitation learning + adjustment vs. a Backplay-based approach in the main analysis section.Other algorithms BID38 BID29 BID8 , primarily in dialog, use a Backplay-like curriculum, albeit they utilize behavioral cloning for the first part of the trajectory. This is a major difference as we show that for many classes of problems, we only need to change the initial state distribution and do not see any gains from warm-starting with imitation learning. Backplay is more similar to Conservative Policy Iteration BID21 , a theoretical paper which presents an algorithm designed to operate with an explicit restart distribution.Also related to Backplay is the method of automatic reverse curriculum generation BID12 . These approaches assumes that the final goal state is known and that the environment is both resettable and reversible. The curricula are generated by taking random walks in the state space to generate starting states or by taking random actions starting at the goal state BID30 . These methods do not require an explicit 'good enough' demonstration as Backplay does. However, they require the environment to be reversible, an assumption that doesn't hold in many realistic tasks such as a robot manipulating breakable objects or complex video games such as Starcraft. In addition, they may fare poorly when random walks reach parts of the state space that are not actually relevant for learning a good policy. Thus, whether a practitioner wants to generate curricula from a trajectory or a random walk depends on the environment's properties. We discuss this in more detail in our analysis section and show empirical results suggesting that Backplay is superior.Hosu & Rebedea (2016) use uniformly random states of an expert demonstration as starting states for a policy. Like Backplay, they show that using a single loss function to learn a policy from both demonstrations and rewards can outperform the demonstrator and is robust to sub-optimal demonstrations. However, they do not impose a curriculum over the demonstration and are equivalent to the Uniform baseline in our experiments. BID46 We have introduced and analyzed Backplay, a technique which improves the sample efficiency of model-free RL by constructing a curriculum around a demonstration. We showed that Backplay agents can learn in complex environments where standard model-free RL fails, that they can outperform the 'expert' whose trajectories they use while training, and that they compare very favorably to related methods such as reversible curriculum generation. We also presented a theoretical analysis of its sample complexity gains in a simplified setting.An important future direction is combining Backplay with more complex and complementary methods such as Monte Carlo Tree Search (MCTS, BID5 BID42 ). There are many potential ways to do so, for example by using Backplay to warm-start MCTS.Another direction is to use Backplay to accelerate self-play learning in zero-sum games. However, special care needs to be taken to avoid policy correlation during training and thus to make sure that learned strategies are safe and not exploitable BID4 .A third direction is towards non-zero sum games. It is well known that standard independent multiagent learning does not produce agents that are able to cooperate in social dilemmas BID25 BID13 or risky coordination games BID43 . In contrast, humans are much better at finding these coordinating and cooperating equilibria BID3 BID22 . Thus , we conjecture that human demonstrations can be combined with Backplay to construct agents that perform well in such situations.Other future priorities are to gain further understanding into when Backplay works well, when it fails, and how we can make the procedure more efficient. Could we speed up Backplay by ascertaining confidence estimates of state values? Do the gains in sample complexity come from value estimation like our analysis suggests, from policy iteration, or from both? Is there an ideal rate for advancing the curriculum window and is there a better approach than a hand-tuned schedule?Stéphane Ross, Geoffrey Gordon, and Drew Bagnell. A reduction of imitation learning and structured prediction to no-regret online learning. In Proceedings of the fourteenth international conference on artificial intelligence and statistics, pp. 627-635, 2011. A APPENDIX","Model-free reinforcement learning RL requires large number trials learn good policy especially environments sparse rewards. explore method improve sample efficiency when we have access demonstrations. approach Backplay uses single demonstration construct curriculum given task. Rather starting training episode environment's fixed initial state start agent near end demonstration move starting point backwards course training reach initial state. contributions are that we analytically characterize types environments where Backplay can improve training speed demonstrate effectiveness Backplay large grid worlds complex four player zero-sum game Pommerman show Backplay compares favorably competitive methods known improve sample efficiency. includes reward shaping behavioral cloning reverse curriculum generation. important goal AI research is to construct agents can learn well new environments BID28 increasingly popular paradigm task is deep reinforcement learning deepRL BID40;BID31;However training RL agent can take long time particularly environments sparse rewards. settings agent typically requires large number episodes stumble upon positive rewards learn even moderately effective policy can then be refined. is often resolved via hand-engineering dense reward function. reward shaping effective can also change set optimal policies have unintended side effects BID34 BID7.We consider alternative technique acceleratingRL sparse reward settings. idea is to create curriculum agent via reversing single trajectory.e state sequence reasonably good necessarily optimal behavior. start agent end demonstration let learn policy easier setup. move starting point backward agent is training initial state task. call technique Backplay.Our contributions are threefold:1 threefold:1 characterize analytically qualitatively which environments Backplay will aid.2 aid.2 demonstrate Backplay's effectiveness grid world task gain intuition well four player stochastic zero-sum game Pommerman BID32.3 empirically show Backplay compares favorably methods improve sample complexity.Besides requiring vastly fewer number samples learn good policy agent trained Backplay can outperform demonstrator even learn optimal policy following sub-optimal demonstration. experiments show Backplay's strong performance relative reward shaping involves hand tuning reward functions behavioral cloning intended use sub-optimal experts forms automatic curriculum generation BID12 requires reversable environment .2 RELATED WORK Figure 1. Backplay:first collect demonstration which we build curriculum states. sample state according curriculum initialize agent accordingly.The related work is a blog post describing method similar Backplay used obtain state-of-theart performance challenging Atari game Montezuma's Revenge Salimans Chen 2018 work was independent concurrent own. addition reporting results different complex stochastic multi-agent environment provide analytic characterization method well depth discussion what kinds environments practitioner can expect Backplay underperform existing methods.A popular method improvingRL access expert demonstrations is behavioral cloning/imitation learning. methods explicitly encourage learned policy mimic expert policy BID1 Ross etal. 2011;BID10 BID44 BID24 BID33 BID16 BID17 BID0 BID35. Imitation learning requires access state expert actions whereas Backplay requires states is designed copy expert thus cannot without adjustments e.g proposed BID14 surpass suboptimal expert. discuss pros cons imitation learning+adjustment vs. Backplay-based approach main analysis section.Other algorithms BID38 BID29 BID8 primarily dialog use Backplay-like curriculum albeit utilize behavioral cloning first part trajectory. is a major difference show many classes problems need change initial state distribution do not see gains warm-starting imitation learning. Backplay is more similar Conservative Policy Iteration BID21 theoretical paper which presents algorithm designed operate explicit restart distribution.Also related Backplay is the method automatic reverse curriculum generation BID12. approaches assumes final goal state is known environment is both resettable reversible. curricula are generated taking random walks state space generate starting states taking random actions starting goal state BID30. methods do not require explicit 'good enough' demonstration Backplay does. However require environment reversible assumption hold many realistic tasks robot manipulating breakable objects complex video games Starcraft. addition may fare poorly when random walks reach parts state space are not actually relevant learning good policy. Thus whether practitioner wants generate curricula trajectory random walk depends environment's properties. discuss detail analysis section show empirical results suggesting Backplay is superior.Hosu Rebedea 2016 use uniformly random states expert demonstration starting states policy. Like Backplay show using single loss function learn policy demonstrations rewards can outperform demonstrator is robust sub-optimal demonstrations. However do not impose curriculum demonstration are equivalent Uniform baseline experiments. BID46 have introduced analyzed Backplay technique which improves sample efficiency model-freeRL constructing curriculum around demonstration. showed Backplay agents can learn complex environments where standard model-free RL fails can outperform 'expert' whose trajectories use training compare favorably related methods reversible curriculum generation. also presented theoretical analysis sample complexity gains simplified setting.An important future direction is combining Backplay complex complementary methods Monte Carlo Tree Search MCTS BID5 BID42 are many potential ways doso,example using Backplay warm-start MCTS.Another direction is to use Backplay accelerate self-play learning zero-sum games. However special care needs taken avoid policy correlation training thus make sure learned strategies are safe exploitable BID4.A third direction is towards non-zero sum games. is well known standard independent multiagent learning does not produce agents are able cooperate social dilemmas BID25 BID13 risky coordination games BID43. contrast humans are much better finding coordinating cooperating equilibria BID3 BID22. Thus conjecture human demonstrations can be combined Backplay construct agents perform well situations.Other future priorities are to gain understanding when Backplay works well when it fails howwe can make procedure efficient. Could speed Backplay ascertaining confidence estimates state values? Do the gains sample complexity come value estimation like analysis suggests policy iteration both? Is there an ideal rate advancing curriculum window is there a better approach hand-tuned schedule? Stéphane Ross Geoffrey Gordon Drew Bagnell. reduction imitation learning structured prediction no-regret online learning. Proceedings fourteenth international conference artificial intelligence statistics pp. 627-635 2011. APPENDIX",1650,1145,505,0.018,1.441,2025/11/05 17:19:03,0.01,1.516,0.3457943925233644,526.945
"Episodic memory is a psychology term which refers to the ability to recall specific events from the past. We suggest one advantage of this particular type of memory is the ability to easily assign credit to a specific state when remembered information is found to be useful. Inspired by this idea, and the increasing popularity of external memory mechanisms to handle long-term dependencies in deep learning systems, we propose a novel algorithm which uses a reservoir sampling procedure to maintain an external memory consisting of a fixed number of past states. The algorithm allows a deep reinforcement learning agent to learn online to preferentially remember those states which are found to be useful to recall later on. Critically this method allows for efficient online computation of gradient estimates with respect to the write process of the external memory. Thus unlike most prior mechanisms for external memory it is feasible to use in an online reinforcement learning setting.
 We present a novel algorithm for integrating a form of external memory with trainable reading and writing into a RL agent. The method depends on the observation that if we restrict the information stored in memory to be a set of past visited states, the information recorded also provides the context in which it was recorded. This means it is possible to assign credit to useful information without needing to backpropagate through time to when it was recorded. To achieve this we devise a reservoir sampling technique which uses a sampling procedure we introduce to generate a distribution over memory configurations for which we can derive gradient estimates. The whole algorithm is O(n) in both the number of trainable parameters and the size of the memory. In particular neither memory required nor computation time increase with history length, making it feasible to run in an online RL setting. We show that the resulting algorithm is able to achieve good performance on a toy problem we introduce designed to have sharp long-term dependencies which can be problematic for recurrent models.",Episodic memory is a psychology term which refers ability recall specific events past. suggest one advantage particular type memory is the ability easily assign credit specific state when remembered information is found useful. Inspired idea increasing popularity external memory mechanisms handle long-term dependencies deep learning systems propose novel algorithm which uses reservoir sampling procedure maintain external memory consisting fixed number past states. algorithm allows deep reinforcement learning agent learn online preferentially remember states which are found useful recall later on. Critically method allows efficient online computation gradient estimates respect write process external memory. Thus unlike prior mechanisms external memory is feasible use online reinforcement learning setting. present novel algorithm integrating form external memory trainable reading writing RL agent. method depends observation if we restrict information stored memory set past visited states information recorded also provides context which it was recorded. means is possible assign credit useful information without needing backpropagate time when it was recorded. achieve devise reservoir sampling technique which uses sampling procedure introduce generate distribution memory configurations which we can derive gradient estimates. whole algorithm isO(n number trainable parameters size memory. particular neither memory required computation time increase history length making is feasible run online RL setting. show resulting algorithm is able achieve good performance toy problem introduce designed have sharp long-term dependencies which can be problematic recurrent models.,366,247,119,0.004,1.482,2025/11/05 17:19:03,0.0,1.824,0.4735202492211836,125.636
"We achieve bias-variance decomposition for Boltzmann machines using an information geometric formulation. Our decomposition leads to an interesting phenomenon that the variance does not necessarily increase when more parameters are included in Boltzmann machines, while the bias always decreases. Our result gives a theoretical evidence of the generalization ability of deep learning architectures because it provides the possibility of increasing the representation power with avoiding the variance inflation. Understanding why the deep learning architectures can generalize well despite their high representation power with a large number of parameters is one of crucial problems in theoretical deep learning analysis, and there are a number of attempts to solve the problem with focusing on several aspects such as sharpness and robustness BID4 BID25 BID11 BID17 BID10 . However, the complete understanding of this phenomenon is not achieved yet due to the complex structure of deep learning architectures.To theoretically analyze the generalizability of the architectures, in this paper, we focus on Boltzmann machines BID0 and its generalization including higher-order Boltzmann machines BID20 BID14 , the fundamental probabilistic model of deep learning (see the book by Goodfellow et al. (2016, Chapter 20) for an excellent overview), and we firstly present bias-variance decomposition for Boltzmann machines. The key to achieve this analysis is to employ an information geometric formulation of a hierarchical probabilistic model, which was firstly explored by BID1 ; BID15 ; BID16 . In particular, the recent advances of the formulation by BID22 enables us to analytically obtain the Fisher information of parameters in Boltzmann machines, which is essential to give the lower bound of variances in bias-variance decomposition.We show an interesting phenomenon revealed by our bias-variance decomposition: The variance does not necessarily increase while the bias always monotonically decreases when we include more parameters in Boltzmann machines, which is caused by its hierarchical structure. Our result indicates the possibility of designing a deep learning architecture that can reduce both of bias and variance, leading to better generalization ability with keeping the representation power.The remainder of this paper is organized as follows: First we formulate the log-linear model of hierarchical probability distributions using an information geometric formulation in Section 2, which includes the traditional Boltzmann machines (Section 2.2) and arbitrary-order Boltzmann machines (Section 2.3). Then we present the main result of this paper, bias-variance decomposition for Boltzmann machines, in Section 3 and discuss its property. We empirically evaluate the tightness of our theoretical lower bound of the variance in Section 4. Finally, we conclude with summarizing the contribution of this paper in Section 5. In this paper, we have firstly achieved bias-variance decomposition of the KL divergence for Boltzmann machines using the information geometric formulation of hierarchical probability distributions. Our model is a generalization of the traditional Boltzmann machines, which can incorporate arbitrary order interactions of variables. Our bias-variance decomposition reveals the nonmonotonicity of the variance with respect to growth of parameter sets, which has been also reported elsewhere for non-linear models BID5 . This result indicates that it is possible to reduce both bias and variance when we include more higher-order parameters in the hierarchical deep learning architectures. To solve the open problem of the generalizability of the deep learning architectures, our finding can be fundamental for further theoretical development. Hidden layer 1 Hidden layer 2 1 2 3 4 {1} {2} {3} {4} {1,2} {1,2,3} {1,2,4} {1,3,4} {2,3,4} {1,3} {1,4} {2,3} {2,4} {1,2,3,4} {3,4} Ø {1} {2} {3} {4} {1,2} {1,2,3} {1,2,4} {1,3,4} {2,3,4} {1,3} {1,4} {2,3} {2,4} {1,2,3,4} {3,4} Ø Figure 3 : An example of a deep Boltzmann machine (left) with an input (visible) layer V = {1, 2} with two hidden layers H 1 = {3} and H 2 = {4}, and the corresponding domain set S V ∪H (right). In the right-hand side, the colored objects {1}, {2}, {3}, {4}, {1, 3}, {2, 3}, and {3, 4} denote the parameter set B, which correspond to nodes and edges of the DBM in the left-hand side.","achieve bias-variance decomposition Boltzmann machines using information geometric formulation. decomposition leads interesting phenomenon variance does not necessarily increase when more parameters are included Boltzmann machines bias always decreases. result gives theoretical evidence generalization ability deep learning architectures provides possibility increasing representation power avoiding variance inflation. Understanding why the deep learning architectures can generalize well despite high representation power large number parameters is one crucial problems theoretical deep learning analysis are number attempts solve problem focusing several aspects sharpness robustness BID4 BID25 BID11 BID17 BID10. However complete understanding phenomenon is not achieved yet due complex structure deep learning architectures.To theoretically analyze generalizability architectures paper focus Boltzmann machines BID0 generalization including higher-order Boltzmann machines BID20 BID14 fundamental probabilistic model deep learning see book Goodfellowetal. 2016 Chapter20 excellent overview firstly present bias-variance decomposition Boltzmann machines. key achieve analysis is to employ information geometric formulation hierarchical probabilistic model which was have firstly explored BID1;BID15;BID16. particular recent advances formulation BID22 enablesus analytically obtain Fisher information parameters Boltzmann machines which is essential give lower bound variances bias-variance decomposition.We show interesting phenomenon revealed bias-variance decomposition:variance does not necessarily increase bias always monotonically decreases when we include parameters Boltzmann machines which is caused hierarchical structure. result indicates possibility designing deep learning architecture can reduce bias variance leading better generalization ability keeping representation power.The remainder paper is organized follows:First formulate log-linear model hierarchical probability distributions using information geometric formulation Section2 which includes traditional Boltzmann machines Section 2.2 arbitrary-order Boltzmann machines Section 2.3 present main result paper bias-variance decomposition Boltzmann machines Section3 discuss property. empirically evaluate tightness theoretical lower bound variance Section4. Finally conclude summarizing contribution paper Section5. paper which was have firstly achieved bias-variance decomposition KL divergence Boltzmann machines using information geometric formulation hierarchical probability distributions. model is a generalization traditional Boltzmann machines which can incorporate arbitrary order interactions variables. bias-variance decomposition reveals nonmonotonicity variance respect growth parameter sets which has been also reported elsewhere non-linear models BID5. result indicates is possible reduce bias variance when we include higher-order parameters hierarchical deep learning architectures. solve open problem generalizability deep learning architectures finding can be fundamental theoretical development. Hidden layer 1 Hidden layer212 34 1 2 3 4 1,2 1,2,3 1,2,4 1,3,4 2,3,4 1,3 1,4 2,3 2,4 1,2,3,4 3,4 Ø 1 2 3 4 1,2 1,2,3 1,2,4 1,3,4 2,3,4 1,3 1,4 2,3 2,4 1,2,3,4 3,4 Ø Figure3:example deep Boltzmann machine left input visible layerV 1 2 two hidden layersH 1 3 H2 4 corresponding domain set V∪H right right-hand side colored objects 1 2 3 4 1 3 2 3 3 4 denote parameter setB which correspond nodes edges DBM left-hand side.",976,689,287,0.009,1.417,2025/11/05 17:19:04,0.0,1.609,0.2710280373831775,291.556
"Recurrent Neural Networks (RNNs) are powerful tools for solving sequence-based problems, but their efficacy and execution time are dependent on the size of the network.   Following recent work in simplifying these networks with model pruning and a novel mapping of work onto GPUs, we design an efficient implementation for sparse RNNs.   We investigate several optimizations and tradeoffs: Lamport timestamps, wide memory loads, and a bank-aware weight layout.   With these optimizations, we achieve speedups of over 6x over the next best algorithm for a hidden layer of size 2304, batch size of 4, and a density of 30%.   Further, our technique allows for models of over 5x the size to fit on a GPU for a speedup of 2x, enabling larger networks to help advance the state-of-the-art.   We perform case studies on NMT and speech recognition tasks in the appendix, accelerating their recurrent layers by up to 3x. Many sequence-based problems, including Speech Recognition BID0 and Neural Machine Translation (NMT) BID3 , can be solved effectively with Recurrent Neural Networks (RNNs). BID2 showed that these networks can run efficiently on massively parallel processors such as GPUs, and BID8 found that if the network is small enough to fit in the register file of a GPU, a persistent approach can be used to increase performance.In parallel, many network compression methods BID16 BID12 have been shown to reduce the model size of both Convolutional Neural Networks (CNNs) and RNNs. Recent work in this area has found that model pruning, in particular, can lead to significant reductions in the number of important network parameters for RNNs BID31 We present an approach that combines both of these techniques into an efficient and expandable approach. In particular, our work makes the following contributions:• Larger sparse RNNs can be run more efficiently on GPUs.• Sparse RNNs can be run with smaller batch sizes more efficiently on GPUs.• Various optimizations on top of the naïve implementation, necessary to achieve high performance.• Case studies using our technique showing 1 ) generalization to LSTMs, 2) practical network design considerations, and 3) speedups of up to 3× on two non-synthetic workloads.A naïve implementation of the idea, presented in Section 3, leads to limited benefit; we present a series of optimizations in Section 4 that help to achieve a high level of performance. Section 5 describes the experimental setup and results, and we discuss future work and our conclusions in Sections 6 and 7. The appendix presents a case study on a machine translation task.2 RELATED WORK 2.1 RNNS Recurrent Neural Networks (RNNs) are powerful tools for solving series-based problems, such as NMT BID3 BID18 BID0 BID26 , language modeling BID27 , and various NLP tasks BID7 . More complex recurrent networks have been devised to build on the basic RNN structure, such as Long/Short Term Memory networks (LSTMs) BID20 and Gated Recurrent Units (GRUs) BID6 . Though we focus on RNNs in this work for simplicity, our approach can extend to other recurrent network types, such as the LSTMs used in our case study. In particular, we build on a recent GPU-based method storing recurrent weights on-chip BID8 . Sparse persistent RNNs increase the performance of pruned networks, but without a series of optimizations we described in Section 4, the improvement is much lower. An optimized implementation is critical to achieve peak performance. After these optimizations, we see that our approach works best for sparser workloads, and, for most layer sizes, 10% density is sufficient to beat all other approaches, though for smaller layer sizes (up to 2304), our approach is the winner even up to a density of 30%. Different batch sizes can affect the efficiency of all techniques; in general, dense GEMMs and our approach scale the best, which tempers the benefit offered by other algorithms. Finally, the number of timesteps is largely immaterial to the relative performance of the various techniques.We have described an efficient algorithm for recurrent layers. To exploit this algorithm, one must first prune the recurrent layers of a target network. We perform this pruning during the training process for a nureal machine translation network BID22 , and we look to past work ) that has pruned a commercial speech recognition network, Deep Speech 2 BID0 . The results on these real workloads are promising: for a given accuracy, we show a speedup of between 2.0× to 3.1× in the machine translation network's recurrent layers pruned with load-balancing in mind, and a speedup of 1.2× to 2.9 on Deep Speech 2's recurrent layers pruned without load-balancing. Please refer to Appendix B for more details about the training processes and a full discussion of the results. We introduced sparse persistent RNNs, an efficient new algorithm for accelerating pruned recurrent networks. Further, we explored several optimizations that were needed to achieve these results on V100, a recent GPU. Our optimized technique allows for 7.3×, 3.4×, and 1.8× speedups against dense GEMM, sparse GEMM, and dense persistent implementations for a hidden layer of size 1792, batch size of 4, and a density of 10%. We show that much larger networks can be deployed onto a GPU of a fixed size with performance increases of around 5× over the next best solution for a density of 1-30% on a layer size of 2304; notably, this sparsity range includes denser workloads than typically perform worse with sparse optimizations. We also show promising results on much larger layers -7168 and 11520 achieve speedups of 1.9× for 2.6% and 1% densities, respectively. Our approach speeds up pruned NMT and speech recognition networks' recurrent layers by up to 3×. Finally, load-balanced pruning can significantly improve a network's throughput, and our technique is necessary to achieve both high performance and accuracy in some recurrent layers, as detailed in the case studies in our appendix. Without consideration of the accuracy of pruned networks and their execution speed (on state-of-theart algorithms) together, the conclusion that a large, sparse network is better than a small, dense one is not sufficiently proven. Our technique and these case studies show, among these insights, that this can be the case, however:• Our technique extends to LSTMs with little effort.• Our technique allows for pruned recurrent layers to run more efficiently than with any other existing algorithm.• Naïve pruning is not necessarily better than pruning with load-balancing in mind, especially when considering achievable performance.• Like past work, we see that a larger, sparse network can be more accurate than a smaller, dense one.• Comparisons against persistent kernels, which can beat non-resident sparse approaches,show that for a given accuracy or performance target, pruning a network and using our technique is the best choice.",Recurrent Neural Networks RNNs are powerful tools solving sequence-based problems efficacy execution time are dependent size network. Following recent work simplifying networks model pruning novel mapping work onto GPUs design efficient implementation sparse RNNs. investigate several optimizations tradeoffs:Lamport timestamps wide memory loads bank-aware weight layout. optimizations achieve speedups 6x next best algorithm hidden layer size 2304 batch size 4 density 30%. technique allows models 5x size fit GPU speedup 2x enabling larger networks help advance state-of-the-art perform case studies NMT speech recognition tasks appendix accelerating recurrent layers 3x. Many sequence-based problems including Speech Recognition BID0 Neural Machine Translation NMT BID3 can be solved effectively Recurrent Neural Networks RNNs BID2 showed networks can can be run efficiently massively parallel processors GPUs BID8 found if the network is small enough fit register file GPU persistent approach can be used increase performance.In parallel many network compression methods BID16 BID12 have been shown reduce model size Convolutional Neural Networks CNNs RNNs. Recent work area has found model pruning particular can lead significant reductions number important network parameters RNNs BID31 present approach combines techniques efficient expandable approach. particular work makes following contributions:• Larger sparse RNNs can can be run efficiently GPUs.• Sparse RNNs can can be run smaller batch sizes efficiently GPUs.• Various optimizations top naïve implementation necessary achieve high performance.• Case studies using technique showing1 generalization LSTMs 2 practical network design considerations 3 speedups 3× two non-synthetic workloads.A naïve implementation idea presented Section3 leads limited benefit;present series optimizations Section4 help achieve high level performance. Section 5 describes experimental setup results discuss future work conclusions Sections6 7. appendix presents case study machine translation task.2 RELATED WORK 2.1 RNNS Recurrent Neural Networks RNNs are powerful tools solving series-based problems NMT BID3 BID18 BID0 BID26 language modeling BID27 various NLP tasks BID7. complex recurrent networks have been devised build basic RNN structure Long/Short Term Memory networks LSTMs BID20 Gated Recurrent Units GRUs BID6. Though focus RNNs work simplicity approach can extend recurrent network types LSTMs used case study. particular build recent GPU-based method storing recurrent weights on-chip BID8. Sparse persistent RNNs increase performance pruned networks without series optimizations described Section4 improvement is much lower. optimized implementation is critical achieve peak performance. optimizations see approach works best sparser workloads layer sizes 10% density is sufficient beat approaches though smaller layer sizes 2304 approach is the winner even density 30%. Different batch sizes can affect efficiency techniques;general dense GEMMs approach scale best which tempers benefit offered algorithms. Finally number timesteps is largely immaterial relative performance various techniques.We have described efficient algorithm recurrent layers. exploit algorithm one must first prune recurrent layers target network. perform pruning training process nureal machine translation network BID22 look past work has pruned commercial speech recognition network Deep Speech 2 BID0. results real workloads are promising:given accuracy show speedup 2.0× 3.1× machine translation network's recurrent layers pruned load-balancing mind speedup 1.2× 2.9 Deep Speech 2's recurrent layers pruned without load-balancing Please refer AppendixB details training processes full discussion results. introduced sparse persistent RNNs efficient new algorithm accelerating pruned recurrent networks. explored several optimizations were needed achieve results V100 recent GPU. optimized technique allows 7.3× 3.4× 1.8× speedups dense GEMM sparse GEMM dense persistent implementations hidden layer size 1792 batch size 4 density 10%. show much larger networks can be deployed onto GPU fixed size performance increases around5× next best solution density 1-30 layer size 2304;notably sparsity range includes denser workloads typically perform worse sparse optimizations. also show promising results much larger layers -7168 11520 achieve speedups 1.9× 2.6 1% densities respectively. approach speeds pruned NMT speech recognition networks' recurrent layers 3×. Finally load-balanced pruning can significantly improve network's throughput technique is necessary achieve high performance accuracy recurrent layers detailed case studies appendix. Without consideration accuracy pruned networks execution speed state-of-theart algorithms together conclusion large sparse network is better small dense one is not sufficiently proven. technique case studies show among insights can case however:• technique extends LSTMs little effort.• technique allows pruned recurrent layers run efficiently existing algorithm.• Naïve pruning is not necessarily better pruning load-balancing mind especially when considering achievable performance.• Like past work see larger sparse network can be more accurate smaller dense one.• Comparisons persistent kernels which can beat non-resident sparse approaches show given accuracy performance target pruning network using technique is the best choice.,1468,992,476,0.015,1.48,2025/11/05 17:19:04,0.01,1.4,0.467289719626168,446.737
"Weight pruning has proven to be an effective method in reducing the model size and computation cost while not sacrificing the model accuracy. Conventional sparse matrix formats, however, involve irregular index structures with large storage requirement and sequential reconstruction process, resulting in inefficient use of highly parallel computing resources. Hence, pruning is usually restricted to inference with a batch size of one, for which an efficient parallel matrix-vector multiplication method exists. In this paper, a new class of sparse matrix representation utilizing Viterbi algorithm that has a high, and more importantly, fixed index compression ratio regardless of the pruning rate, is proposed. In this approach, numerous sparse matrix candidates are first generated by the Viterbi encoder, and then the one that aims to minimize the model accuracy degradation is selected by the Viterbi algorithm. The model pruning process based on the proposed Viterbi encoder and Viterbi algorithm is highly parallelizable, and can be implemented efficiently in hardware to achieve low-energy, high-performance index decoding process. Compared with the existing magnitude-based pruning methods, index data storage requirement can be further compressed by 85.2% in MNIST and 83.9% in AlexNet while achieving similar pruning rate. Even compared with the relative index compression technique, our method can still reduce the index storage requirement by 52.7% in MNIST and 35.5% in AlexNet. Deep neural networks (DNNs) demand an increasing number of parameters as the required complexity of tasks and supporting number of training data continue to grow BID2 . Correspondingly, DNN incurs a considerable number of computations and amount of memory footprint, and thus requires high performance parallel computing systems to meet the target response time. As an effort to realize energy-efficient DNN, researchers have suggested various low-cost hardware implementation techniques. Among them, pruning has been actively studied to reduce the redundant connections while not degrading the model accuracy. It has been shown that pruning can achieve 9× to 13× reduction in connections BID9 .After pruning, the remaining parameters are often stored in sparse matrix formats. Different ways of representing indices of non-zero values constitute the different sparse matrix format, and have a significant impact on the level of achievable computational parallelism when a sparse matrix is used as an input operand BID1 . If the format is not properly designed, then the performance of DNN with a sparse matrix can be even lower than the case with dense matrix BID28 . The two most important characteristics of a hardware-friendly sparse matrix format are 1) reducing index storage footprint and 2) parallelizable index decoding process. As a compromise between index size reduction and index decoding complexity, numerous formats have been proposed BID1 . DNN after pruning heavily involves sparse matrix-vector and matrix-matrix multiplications (SpMV and SpMM, respectively). Despite the sparse content , the computation time for SpMM is longer than that of dense matrix multiplication in the modern graphic processing unit (GPU), due to its serialized index decoding process and irregular memory access patterns. For example, the inference latency of AlexNet and VGG16 with SpMM can be increased by 2× to 5× on GPUs or CPUs BID10 . The traditional pruning technique , therefore, is only attractive in the case where SpMV can be utilized (i.e., batch size of 1) BID11 ) BID28 . Therefore, a sparse matrix representation associated with parallelizable dense-matrix reconstruction in a wide range of computing operations is the key to extending the use of pruning.We propose a new DNN-dedicated sparse matrix format and a new pruning method based on errorcorrection coding (ECC) techniques. A unique characteristic of this sparse matrix format is the fixed, yet high (as shown in Section 3) index compression ratio, regardless of the pruning rate. Moreover, sparse-to-dense matrix conversion employing the proposed format becomes a parallel process and is no longer the performance bottleneck. Notice that conventional sparse matrix formats entail at least one column or row index value for each non-zero parameter such that the amount of index data is larger than that of non-zero values. On the other hand, the proposed approach compresses the locations of non-zero values with a convolutional code which is a type of ECC code. Consequently, the size of the sparse matrix index becomes negligible.Conventional pruning approaches first identify the parameter candidates to be pruned, then construct a matrix (often sparse) using formats such as Compressed Sparse Row (CSR) to represent the survived parameters. On the contrary, in the proposed scheme, pruning is performed in a restricted manner since a specific sparse matrix format is first constructed. A DNN-specific Viterbi encoder takes an input pattern and generates a sequence of random-number, where a ""1"" indicates the parameter had survived, and had been pruned otherwise. Depending on the length of the input pattern, a vast (but limited) number of output patterns (hence candidates of the final sparse matrix representations) are considered. In this case, the input pattern is used as the sparse matrix index . The content of the input pattern, which generates a deterministic output random number sequence, is chosen such that the accuracy degradation is minimized based on a user-defined cost function (more details on Section 2). Both the Viterbi encoder and the algorithm have been shown to be computationally efficient with an inherent parallelizable characteristic, as demonstrated in the digital communication applications BID27 . In this work, we further extend its application and demonstrate how the Viterbi algorithm can be modified to perform energy-efficient DNN pruning.2 PRUNING USING VITERBI-BASED APPROACH Figure 1 illustrates the proposed Viterbi decompressor (VD), which is based on the Viterbi encoder widely used in digital communication. VD has a simple structure consisting only of FlipFlops (FFs) and XOR gates . In this configuration, VD takes one input bit and produces four output bits every clock cycle. Notice that FFs and XOR gates intermingle input bits and generate pseudo random number outputs. Assume that a dense matrix is formed after pruning, as shown in Figure 2 , and an input sequence of {0, 1, 1, 0} is applied to VD through four clock cycles to generate the outputs, where '1' implies that the corresponding parameter has survived. In this case, the overhead in the index for the proposed Viterbi-Compressible Matrix (VCM) format is significantly less than that of CSR. In the VCM format, the input sequence to the VD becomes the index information . This index size is independent of the number of non-zero values and can be determined in advance based on the target index compression ratio 1 . Unlike the CSR format, the available VD-compressible dense matrix representation is limited , meaning that not all possible dense matrix representations after conventional magnitude-based pruning (such as BID9 ) can be reconstructed by VD. Therefore, the pruning method considering VCM may result in a matrix that contains different survived parameters compared to a pruning method using the CSR format. Thus, the key to the success of VCM is to design a VD that allows diversified parameters to survive, and to efficiently search for the optimal VD input sequence that minimizes the accuracy degradation 2 . We proposed a new DNN-dedicated sparse matrix format and pruning method using the Viterbi encoder structure and Viterbi algorithm. Unlike previous methods, we first consider only limited choices of pruning results, all of which have the advantage of a significant index compression ratio by our proposed index decompressing structures. One particular pruning result is selected from the limited pruning solution space based on the Viterbi algorithm with user-defined branch metric equations that aim to minimize the accuracy degradation. As a result, our proposed sparse matrix, VCM, shows noticeable index storage reduction even compared with the relative index scheme. Fixed index compression ratio and inherently parallel reconstruction scheme allows a wide range of applications, such as SpMM, since sparse matrices can be converted into dense matrices efficiently.A APPENDIX",Weight pruning has proven effective method reducing model size computation cost sacrificing model accuracy. Conventional sparse matrix formats however involve irregular index structures large storage requirement sequential reconstruction process resulting inefficient use highly parallel computing resources. Hence pruning is usually restricted inference batch size one which an efficient parallel matrix-vector multiplication method exists. paper new class sparse matrix representation utilizing Viterbi algorithm has a high importantly fixed index compression ratio regardless pruning rate is proposed. approach numerous sparse matrix candidates are first generated Viterbi encoder one aims minimize model accuracy degradation is selected Viterbi algorithm. model pruning process based proposed Viterbi encoder Viterbi algorithm is highly parallelizable can be implemented efficiently hardware achieve low-energy high-performance index decoding process. Compared existing magnitude-based pruning methods index data storage requirement can be further compressed 85.2 MNIST 83.9 AlexNet achieving similar pruning rate. Even compared relative index compression technique method can still reduce index storage requirement 52.7 MNIST 35.5 AlexNet. Deep neural networks DNNs demand increasing number parameters required complexity tasks supporting number training data continue grow BID2. Correspondingly DNN incurs considerable number computations amount memory footprint thus requires high performance parallel computing systems meet target response time. effort realize energy-efficient DNN researchers have suggested various low-cost hardware implementation techniques. Among pruning has been actively studied reduce redundant connections degrading model accuracy. has been shown pruning can achieve9× 13× reduction connections BID9.After pruning remaining parameters are often stored sparse matrix formats. Different ways representing indices non-zero values constitute different sparse matrix format have a significant impact level achievable computational parallelism when a sparse matrix is used input operand BID1. If the format is not properly designed performance DNN sparse matrix can be even lower case dense matrix BID28. two important characteristics hardware-friendly sparse matrix format are1 reducing index storage footprint 2 parallelizable index decoding process. compromise index size reduction index decoding complexity numerous formats have been proposed BID1. DNN pruning heavily involves sparse matrix-vector matrix-matrix multiplications SpMV SpMM respectively Despite sparse content computation time SpMM is longer dense matrix multiplication modern graphic processing unit GPU due serialized index decoding process irregular memory access patterns. example inference latency AlexNet VGG16 SpMM can be increased 2× 5× GPUs CPUs BID10. traditional pruning technique therefore is only attractive case where SpMV can be utilized.e batch size 1 BID11 BID28. Therefore sparse matrix representation associated parallelizable dense-matrix reconstruction wide range computing operations is the key extending use pruning.We propose new DNN-dedicated sparse matrix format new pruning method based errorcorrection coding ECC techniques. unique characteristic sparse matrix format is the fixed yet high shown Section3 index compression ratio regardless pruning rate. Moreover sparse-to-dense matrix conversion employing proposed format becomes parallel process is no longer performance bottleneck. Notice conventional sparse matrix formats entail least one column row index value non-zero parameter amount index data is larger non-zero values. hand is proposed approach compresses locations non-zero values convolutional code which is a type ECC code. Consequently size sparse matrix index becomes negligible.Conventional pruning approaches first identify parameter candidates pruned construct matrix often sparse using formats Compressed Sparse Row CSR represent survived parameters. contrary is proposed scheme pruning is performed restricted manner since specific sparse matrix format is first constructed. DNN-specific Viterbi encoder takes input pattern generates sequence random-number where a 1 indicates parameter had survived had been pruned otherwise. Depending length input pattern vast limited number output patterns hence candidates final sparse matrix representations are considered. case input pattern is used sparse matrix index. content input pattern which generates deterministic output random number sequence is chosen accuracy degradation is minimized based user-defined cost function details Section2 Viterbi encoder algorithm have been shown computationally efficient inherent parallelizable characteristic demonstrated digital communication applications BID27. work extend application demonstrate how the Viterbi algorithm can be modified perform energy-efficient DNN pruning.2 PRUNING USING VITERBI-BASED APPROACH Figure 1 illustrates proposed Viterbi decompressor VD which is based Viterbi encoder widely used digital communication. VD has a simple structure consisting FlipFlops FFs XOR gates. configuration VD takes one input bit produces four output bits every clock cycle. Notice FFs XOR gates intermingle input bits generate pseudo random number outputs. Assume dense matrix is formed pruning shown Figure2 input sequence 0 wherea1 wherea1 0 is applied VD four clock cycles generate outputs where '1' implies corresponding parameter has survived. case overhead index proposed Viterbi-Compressible Matrix VCM format is significantly less CSR. VCM format input sequence VD becomes index information. index size is independent number non-zero values can be determined advance based target index compression ratio 1. Unlike CSR format available VD-compressible dense matrix representation is limited meaning possible dense matrix representations conventional magnitude-based pruning BID9 can be reconstructed VD. Therefore pruning method considering VCM may result matrix contains different survived parameters compared pruning method using CSR format. Thus key success VCM is to design VD allows diversified parameters survive efficiently search optimal VD input sequence minimizes accuracy degradation2. proposed new DNN-dedicated sparse matrix format pruning method using Viterbi encoder structure Viterbi algorithm. Unlike previous methods first consider limited choices pruning results which have the advantage significant index compression ratio proposed index decompressing structures. One particular pruning result is selected limited pruning solution space based Viterbi algorithm user-defined branch metric equations aim minimize accuracy degradation. result is proposed sparse matrix VCM shows noticeable index storage reduction even compared relative index scheme. Fixed index compression ratio inherently parallel reconstruction scheme allows wide range applications SpMM since sparse matrices can be converted dense matrices efficiently.A APPENDIX,1613,1133,480,0.018,1.424,2025/11/05 17:19:04,0.01,1.541,0.2928348909657317,485.271
"Learning policies for complex tasks that require multiple different skills is a major challenge in reinforcement learning (RL). It is also a requirement for its deployment in real-world scenarios. This paper proposes a novel framework for efficient multi-task reinforcement learning. Our framework trains agents to employ hierarchical policies that decide when to use a previously learned policy and when to learn a new skill. This enables agents to continually acquire new skills during different stages of training. Each learned task corresponds to a human language description. Because agents can only access previously learned skills through these descriptions, the agent can always provide a human-interpretable description of its choices. In order to help the agent learn the complex temporal dependencies necessary for the hierarchical policy, we provide it with a stochastic temporal grammar that modulates when to rely on previously learned skills and when to execute new skills. We validate our approach on Minecraft games designed to explicitly test the ability to reuse previously learned skills while simultaneously learning new skills. Deep reinforcement learning has demonstrated success in policy search for tasks in domains like game playing BID12 BID7 BID11 and robotic control BID9 b; BID16 . However, it is very difficult to accumulate multiple skills using just one policy network BID24 . Knowledge transfer techniques like distillation BID3 BID18 BID15 BID24 have been applied to train a policy network both to learn new skills while preserving previously learned skill as well as to combine single-task policies into a multi-task policy. Existing approaches usually treat all tasks independently. This often prevents full exploration of the underlying relations between different tasks. They also typically assume that all policies share the same state space and action space. This precludes transfer of previously learned simple skills to a new policy defined over a space with differing states or actions.When humans learn new skills, we often take advantage of our existing skills and build new capacities by composing or combining simpler ones. For instance, learning multi-digit multiplication relies on the knowledge of single-digit multiplication; learning how to properly prepare individual ingredients facilitates cooking dishes based on complex recipes.Inspired by this observation, we propose a hierarchical policy network which can reuse previously learned skills alongside and as subcomponents of new skills. It achieves this by discovering the underlying relations between skills.To represent the skills and their relations in an interpretable way, we also encode all tasks using human instructions such as ""put down."" This allows the agent to communicate its policy and generate plans using human language. Figure 1 illustrates an example: given the instruction ""Stack blue,"" our hierarchical policy learns to compose instructions and take multiple actions through a multi-level hierarchy in order to stack two blue blocks together. Steps from the top-level policy π 3 (i.e., the red Figure 1: Example of our multi-level hierarchical policy for a given task -stacking two blue blocks. Each arrow represents one step generated by a certain policy and the colors of arrows indicate the source policies. Note that at each step, a policy either utters an instruction for the lower-level policy or directly takes an action.branches) outline a learned high-level plan -""Get blue → Find blue → Put blue."" In addition, from lower level policies, we may also clearly see composed plans for other tasks. Based on policy π 2 , for instance, the task ""Get blue"" has two steps -""Find blue → action: turn left,"" whereas ""Put blue"" can be executed by a single action ""put down"" according to π 3 . Through this hierarchical model, we may i) accumulate tasks progressively from a terminal policy to a top-level policy and ii) unfold the global policy from top-level to basic actions.In order to better track temporal relationships between tasks, we train a stochastic temporal grammar (STG) model on the sequence of policy selections (previously learned skill or new skill) for positive episodes. The STG focuses on modeling priorities of tasks: for example, it is necessary to obtain an object before putting it down. Integrating the STG into the hierarchical policy boosts efficiency and accuracy by explicitly modeling such commonsense world knowledge.We validated our approach by testing it on object manipulation tasks implemented in a Minecraft world. Our experimental results demonstrate that this framework can (i) efficiently learn hierarchical policies and representations for multi-task RL; (ii) learn to utter human instructions to deploy pretrained policies, improve their explainability and reuse skills; and (iii) learn a stochastic temporal grammar via self-supervision to predict future actions. In this work, we have proposed a hierarchal policy modulated by a stochastic temporal grammar as a novel framework for efficient multi-task reinforcement learning through multiple training stages. Each task in our settings is described by a human instruction. The resulting global policy is able to reuse previously learned skills for new tasks by generating corresponding human instructions to inform base policies to execute relevant base tasks. We evaluate this framework in Minecraft games and have shown that our full model i) has a significantly higher learning efficiency than a flat policy does, ii) generalizes well in unseen environments, and iii) is capable of composing hierarchical plans in an interpretable manner.Currently, we rely on weak supervision from humans to define what skills to be learned in each training stage. In the future, we plan to automatically discover the optimal training procedures to increase the task set.A PSEUDO CODE OF OUR ALGORITHMS Algorithm 1 RUN(k, g) Input: Policy level k, task g ∈ G k Output: Episode trajectory Γ at the top level policy 1: t ← 0 2: Γ = ∅ 3: Get initial state s0 4: repeat 5:if k == 1 then 6:Sample at ∼ π k (·|st, g) and execute at 7:Get current state st+1 8:rt ← R(st+1, g) 9:Add st, at, rt, π k (·|st, g), g to Γ 10: else 11:Sample et and g t as in Section 3.3 for using STG as guidance 12:Sample at ∼ π aug k (·|st, g) 13:if et = 0 then 14:// Execute base policy π k−1 by giving instruction g t 15:RUN(k − 1, g t ) 16: else 17:Execute at 18: end if 19:Get current state st+1 20:rt ← R(st+1, g) 21:Add st, et, g t , at, rt, π DISPLAYFORM0 end if 23: if in curriculum learning phase 1 then 9: DISPLAYFORM1 Sample a task g from base task set G k−1 10: else 11:Sample a task g from global task set G k 12:end if 13://Run an episode 14: DISPLAYFORM2 if the maximum reward in Γ is +1 then 17: DISPLAYFORM3 Re-estimate the distributions of the STG based on updated D+ by MLE 19:end if 20:Sample n ∼ Possion(λ) 21:for j ∈ {1, · · · , n} do 22:Sample a mini-batch S from D 23:Update Θ based on (9) and the τ -th term in (8) 24:i ← i + 1 25:if i%M = 0 then 26:τ ← τ %3 + 1 27: end if 28: end for 29: until i ≥ N","Learning policies complex tasks require multiple different skills is a major challenge reinforcement learning RL is also requirement deployment real-world scenarios. paper proposes novel framework efficient multi-task reinforcement learning. framework trains agents employ hierarchical policies decide when to use previously learned policy when to learn new skill. enables agents continually acquire new skills different stages training. learned task corresponds human language description. agents can only access previously learned skills descriptions agent can always provide human-interpretable description choices. order help agent learn complex temporal dependencies necessary hierarchical policy provide stochastic temporal grammar modulates when to rely previously learned skills when to execute new skills. validate approach Minecraft games designed explicitly test ability reuse previously learned skills simultaneously learning new skills. Deep reinforcement learning has demonstrated success policy search tasks domains like game playing BID12 BID7 BID11 robotic control BID9b;BID16. However is very difficult accumulate multiple skills using one policy network BID24. Knowledge transfer techniques like distillation BID3 BID18 BID15 BID24 have been applied train policy network learn new skills preserving previously learned skill well combine single-task policies multi-task policy. Existing approaches usually treat tasks independently. often prevents full exploration underlying relations different tasks. also typically assume policies share state space action space. precludes transfer previously learned simple skills new policy defined space differing states actions.When humans learn new skills often take advantage existing skills build new capacities composing combining simpler ones. instance learning multi-digit multiplication relies knowledge single-digit multiplication;learning how to properly prepare individual ingredients facilitates cooking dishes based complex recipes.Inspired observation propose hierarchical policy network which can reuse previously learned skills alongside subcomponents new skills. achieves discovering underlying relations skills.To represent skills relations interpretable way also encode tasks using human instructions put down. allows agent communicate policy generate plans using human language. Figure 1 illustrates example:given instruction Stack blue hierarchical policy learns compose instructions take multiple actions multi-level hierarchy order stack two blue blocks together. Steps top-level policyπ3.e red Figure1:Example multi-level hierarchical policy given task -stacking two blue blocks. arrow represents one step generated certain policy colors arrows indicate source policies. Note step policy either utters instruction lower-level policy directly takes action.branches outline learned high-level plan -Get blue → Find blue → Put blue. addition lower level policies may also clearly see composed plans tasks. Based policyπ2 instance task Get blue has two steps -Find blue → action:turn left whereas Put blue can be executed single action put according π3. hierarchical model may accumulate tasks progressively terminal policy top-level policy ii unfold global policy top-level basic actions.In order better track temporal relationships tasks train stochastic temporal grammar STG model sequence policy selections previously learned skill new skill positive episodes. STG focuses modeling priorities tasks:example is necessary obtain object putting down. Integrating STG hierarchical policy boosts efficiency accuracy explicitly modeling commonsense world knowledge.We validated approach testing object manipulation tasks implemented Minecraft world. experimental results demonstrate framework can(i)efficiently learn hierarchical policies representations multi-taskRL;ii learn utter human instructions deploy pretrained policies improve explainability reuse skills;iii learn stochastic temporal grammar via self-supervision predict future actions. work have proposed hierarchal policy modulated stochastic temporal grammar novel framework efficient multi-task reinforcement learning multiple training stages. task settings is described human instruction. resulting global policy is able reuse previously learned skills new tasks generating corresponding human instructions inform base policies execute relevant base tasks. evaluate framework Minecraft games have shown full model has a significantly higher learning efficiency flat policy does,ii generalizes well unseen environments iii is capable composing hierarchical plans interpretable manner.Currently rely weak supervision humans define what skills learned training stage. future plan automatically discover optimal training procedures increase task set.A PSEUDO CODE ALGORITHMS Algorithm 1 RUN k g Input:Policy levelk taskg∈G k Output:Episode trajectoryΓ top level policy1:←02:Γ ∅3:Get initial states0 4:repeat5:ifk==1 6:Sample ∼πk ·|st g execute 7:Get current statest+18:rt←R st+1 g 9:Addst rt πk ·|st g g Γ10:else11:Sampleet g Section 3.3 using STG guidance12:Sample ∼ π augk ·|st g 13:ifet 0 14://Execute base policy π k−1 giving instructiong 15:RUN k−1 g 16:else17:Execute 18:end if19:Get current statest+120:rt←R st+1 g 21:Addst et g rt π DISPLAYFORM0 end if23:if in curriculum learning phase1 9:DISPLAYFORM1 Sample taskg base task setG k−110:else11:Sample taskg global task setG k12:end if13://Run episode14:DISPLAYFORM2 if the maximum reward Γ is+1 17:DISPLAYFORM3 Re-estimate distributions STG based updated+MLE19:end if20:Sample n ∼ Possion λ 21:j∈ 1 ··· n do22:Sample mini-batch 23:Update Θ based 9 τ -th term 8 24:←+125:ifi%M 0 26:τ←τ%3+127:end if28:end 29:≥N",1521,1062,459,0.014,1.432,2025/11/05 17:19:04,0.01,1.514,0.317757009345794,436.932
"Embeddings are a fundamental component of many modern machine learning and natural language processing models.
 Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior of the models.
 State of the art in analyzing embeddings consists in projecting them in two-dimensional planes without any interpretable semantics associated to the axes of the projection, which makes detailed analyses and comparison among multiple sets of embeddings challenging.
 In this work, we propose to use explicit axes defined as algebraic formulae over embeddings to project them into a lower dimensional, but semantically meaningful subspace, as a simple yet effective analysis and visualization methodology.
 This methodology assigns an interpretable semantics to the measures of variability and the axes of visualizations, allowing for both comparisons among different sets of embeddings and fine-grained inspection of the embedding spaces.
 We demonstrate the power of the proposed methodology through a series of case studies that make use of visualizations constructed around the underlying methodology and through a user study. The results show how the methodology is effective at providing more profound insights than classical projection methods and how it is widely applicable to many other use cases. Learning representations is an important part of modern machine learning and natural language processing research. Those representations are often real-valued vectors also called embeddings and are obtained both as byproducts of supervised learning or as the direct goal of unsupervised methods. Independently of how the embeddings are learned, there is much value in understanding what information they capture, how they relate to each other and how the data they are learned from influences them. A better understanding of the embedded space may lead to a better understanding of the data, of the problem and the behavior of the model, and may lead to critical insights in improving such models. Because of their high-dimensional nature, they are hard to visualize effectively, and the most adopted approach is to project them in a bi-dimensional space. Projections have a few shortcomings: 1) they may not preserve distance in the original space, 2) they are not comparable across models and 3) do not provide interpretable dimensions of variability to project to, preventing for more detailed analysis and understanding. For these reasons, there is value in mapping embeddings into a more specific, controllable and interpretable semantic space.Principal Component Analysis (PCA) BID27 and t-Distributed Stochastic Neighbor Embedding (t-SNE) BID30 are two projection techniques often used for visualizing embeddings in two dimensions, although other techniques can be used. PCA projects embeddings on a lower dimensional space that has the directions of the highest variance in the dataset as axes. Those dimensions do not carry any interpretable meaning, making interpretation difficult. By visualizing the first two dimensions of a PCA projection, the only insight obtainable is semantic relatedness BID5 between points by observing their relative closeness and therefore topical clusters can be identified. The downside is that embeddings that end up being close in the projected space may not be close in the original embedding space and vice versa. Moreover, as the directions of highest variance are different from embedding space to embedding space, the projections are incompatible among different embeddings spaces, and this makes them not comparable, a common issue among dimensionality reduction techniques. t-SNE, differently from PCA, optimizes a loss that encourages embeddings that are close in the original high-dimensional space to be close in the lower dimensional projection space. This helps in visualizing clusters better than with PCA, as t-SNE puts each point in the projected space so that distance in the original space with respect to its nearest neighbors is preserved as much as possible. Visualizations obtained in this way reflect more the original embedding space and topical clusters are more clearly distinguishable, but doesn't solve the issue of comparability of two different sets of embeddings, nor it solves the lack of interpretability of the axes and still doesn't allow for finegrained inspection. Moreover, t-SNE is pretty sensible to hyperparameters, making it unclear how much the projection reflects the data.In this paper, a new and simple method to inspect, explore and debug embedding spaces at a finegrained level is proposed. It consists in defining explicitly the axes of projection through formulae in vector algebra over the embeddings themselves. Explicit axis definition gives an interpretable and fine-grained semantics to the axes of projection. Defining axes explicitly makes it possible to analyze in a detailed way how embeddings relate to each other with respect to interpretable dimensions of variability, as carefully crafted formulas can map (to a certain extent) to semantically meaningful portions of the learned spaces. The explicit axes definition also allows for comparing of embeddings obtained from different datasets, as long as they have common labels.We demonstrate three visualizations for analyzing subspaces of interest of embedding spaces and a set of example case studies including bias detection, polysemy analysis and fine-grained embedding analysis. Additional tasks that may be performed using the proposed methodology and visualization are diachronic analysis and analysis of representations learned from graphs and knowledge bases. The proposed visualizations can moreover be used for debugging purposes and in general for obtaining a better understanding of the embedding spaces learned by different models and representation learning approaches. We are releasing an open-source 1 interactive tool that implements the proposed visualizations, in order to enable researchers in the fields of machine learning, computational linguistics, natural language processing, social sciences and digital humanities to perform exploratory analysis and better understand the semantics of their embeddings.The main contribution of this work lies in the use of explicit user-defined algebraic formulae as axes for projecting embedding spaces into semantically-meaningful subspaces that when visualized provide interpretable axes. We show how this methodology can be widely used through a series of case studies on well known models and data and we furthermore validate the how the visualizations are more interpretable through a user study. We presented a simple methodology for projecting embeddings into lower-dimensional semantically-meaningful subspaces through explicit vector algebra formulae operating on the embedding themselves. Classical projection methods are useful to gather on overall coarse-grained view of the embedding space and how embeddings cluster, but we showed how our approach allows goal-oriented analyses with more fine-grained comparison and enables cross-dataset comparison through a series of case studies and a user study. This is possible thanks to the ability of the proposed methodology to assign an explicit semantics to the measures of variability used as axes of the visualization that in turns makes them interpretable and widely applicable to many use cases in computational linguistics, natural language processing, machine learning, social sciences and digital humanities.A APPENDIX Figure 6 : Professions plotted on ""male"" and ""female"" axes in W ikipedia embeddings.",Embeddings are a fundamental component many modern machine learning natural language processing models. Understanding visualizing is essential gathering insights information capture behavior models. State art analyzing embeddings consists projecting two-dimensional planes without interpretable semantics associated axes projection which makes detailed analyses comparison among multiple sets how the embeddings challenging. work propose use explicit axes defined algebraic formulae embeddings project lower dimensional semantically meaningful subspace simple yet effective analysis visualization methodology. methodology assigns interpretable semantics measures variability axes visualizations allowing comparisons among different sets how the embeddings fine-grained inspection embedding spaces. demonstrate power proposed methodology series case studies make use visualizations constructed around underlying methodology user study. results show how the how this methodology is effective providing profound insights classical projection methods how it is widely applicable many use cases. Learning representations is an important part modern machine learning natural language processing research. representations are often real-valued vectors also called embeddings are obtained byproducts supervised learning direct goal unsupervised methods. Independently how the embeddings are learned is much value understanding what information capture how they relate how the data are learned influences them. better understanding embedded space may lead better understanding data problem behavior model may lead critical insights improving models. high-dimensional nature are hard visualize effectively adopted approach is to project bi-dimensional space. Projections have a few shortcomings:1 may preserve distance original space 2 are not comparable across models 3 do not provide interpretable dimensions variability project preventing detailed analysis understanding. reasons is value mapping embeddings specific controllable interpretable semantic space.Principal Component Analysis PCA BID27 t-Distributed Stochastic Neighbor Embedding t-SNE BID30 are two projection techniques often used visualizing embeddings two dimensions although techniques can be used. PCA projects embeddings lower dimensional space has the directions highest variance dataset axes. dimensions do not carry interpretable meaning making interpretation difficult. visualizing first two dimensions PCA projection insight obtainable is semantic relatedness BID5 points observing relative closeness therefore topical clusters can be identified. downside is that embeddings end close projected space may close original embedding space vice versa. Moreover directions highest variance are different embedding space embedding space projections are incompatible among different embeddings spaces which makes comparable common issue among dimensionality reduction techniques. t-SNE differently PCA optimizes loss encourages embeddings are close original high-dimensional space close lower dimensional projection space. helps visualizing clusters better PCA t-SNE puts point projected space distance original space respect nearest neighbors is preserved much possible. Visualizations obtained way reflect original embedding space topical clusters are more clearly distinguishable solve issue comparability two different sets how the embeddings solves lack interpretability axes still allow finegrained inspection. Moreover t-SNE is pretty sensible hyperparameters making unclear how much projection reflects data.In paper new simple method inspect explore debug embedding spaces finegrained level is proposed. consists defining explicitly axes projection formulae vector algebra embeddings themselves. Explicit axis definition gives interpretable fine-grained semantics axes projection. Defining axes explicitly makes possible analyze detailed way how embeddings relate respect interpretable dimensions variability carefully crafted formulas can map certain extent semantically meaningful portions learned spaces. explicit axes definition also allows comparing how the embeddings obtained different datasets long have common labels.We demonstrate three visualizations analyzing subspaces interest embedding spaces set example case studies including bias detection polysemy analysis fine-grained embedding analysis. Additional tasks may performed using proposed methodology visualization are diachronic analysis analysis representations learned graphs knowledge bases. proposed visualizations can moreover used debugging purposes general obtaining better understanding embedding spaces learned different models representation learning approaches. are releasing open-source 1 interactive tool implements proposed visualizations order enable researchers fields machine learning computational linguistics natural language processing social sciences digital humanities perform exploratory analysis better understand semantics embeddings.The main contribution work lies use explicit user-defined algebraic formulae axes projecting embedding spaces semantically-meaningful subspaces when visualized provide interpretable axes. show how the how this methodology can be widely used series case studies well known models data furthermore validate how the visualizations are more interpretable user study. presented simple methodology projecting embeddings lower-dimensional semantically-meaningful subspaces explicit vector algebra formulae operating embedding themselves. Classical projection methods are useful gather overall coarse-grained view embedding space how embeddings cluster showed how our approach allows goal-oriented analyses fine-grained comparison enables cross-dataset comparison series case studies user study. is possible thanks ability proposed methodology assign explicit semantics measures variability used axes visualization turns makes interpretable how it is widely applicable many use cases computational linguistics natural language processing machine learning social sciences digital humanities.A APPENDIX Figure6:Professions plotted male female axes W ikipedia embeddings.,1330,899,431,0.014,1.479,2025/11/05 17:19:04,0.01,1.462,0.4641744548286605,445.556
"Learning deep networks which can resist large variations between training andtesting data is essential to build accurate and robust image classifiers.   Towardsthis end, a typical strategy is to apply data augmentation to enlarge the trainingset.    However,  standard  data  augmentation  is  essentially  a  brute-force  strategywhich is inefficient,  as it performs all the pre-defined transformations  to everytraining sample. In this paper, we propose a principled approach to train networkswith  significantly  improved  resistance  to  large  variations  between  training  andtesting data.   This is achieved by embedding a learnable transformation moduleinto the introspective networks (Jin et al., 2017; Lazarow et al., 2017; Lee et al.,2018), which is a convolutional neural network (CNN) classifier empowered withgenerative capabilities.   Our approach alternatively synthesizes pseudo-negativesamples with learned transformations and enhances the classifier by retraining itwith synthesized samples.   Experimental results verify that our approach signif-icantly improves the ability of deep networks to resist large variations betweentraining and testing data and achieves classification accuracy improvements onseveral benchmark datasets, including MNIST, affNIST, SVHN and CIFAR-10. Classification problems have rapidly progressed with advancements in convolutional neural networks (CNNs) BID17 BID15 BID25 BID6 BID7 . CNNs are able to produce promising performance, given sufficient training data. However, when the training data is limited and unable to cover all the data variations in the testing data (e.g., the training set is MNIST, while the testing set is affNIST), the trained networks generalize poorly on the testing data. Consequently, how to learn deep networks which can resist large variations between training and testing data is a significant challenge for building accurate and robust image classifiers.To address this issue, a typical strategy is to apply data augmentation to enlarging the training set, i.e., applying various transformations, including random translations, rotations and flips as well as Gaussian noise injection, to the existing training data. This strategy is very effective in improving the performance, but it is essentially a brute-force strategy which is inefficient, as it exhaustively performs all these transformations to every training samples. Neither is it theoretically formulated.Alternatively, we realize that we can synthesize extra training samples with generative models. But, the problem is how to generate synthetic samples which are able to improve the robustness of CNNs to large variations between training and testing data. In this paper, we achieve this by embedding a learnable transformation module into introspective networks , a CNN classifier empowered with generative capabilities. We name our approach introspective transformation network (ITN), which performs training by a reclassification-by-synthesis algorithm. It alternatively synthesizes samples with learned transformations and enhances the classifier by retraining it with synthesized samples. We use a min-max formulation to learn our ITN, where the transformation module transforms the synthesized pseudo-negative samples to maximize their variations to the original training samples and the CNN classifier is updated by minimizing the classification loss of the transformed synthesized pseudo-negative samples. The transformation modules are learned jointly with the CNN classifier, which augments training data in an intelligent manner by narrowing down the search space for the variations.Our approach can work with any models that have generative and discriminative abilities, such as generative adversarial networks (GANs) and introspective networks. In this paper, we choose the introspective networks to generate extra training samples rather than GANs, because introspective networks have several advantages over GANs. Introspective learning framework maintains one single CNN discriminator that itself is also a generator while GANs have separate discriminators and generators. The generative and discriminative models are simultaneously refined over iterations. Additionally, Introspective networks are easier to train than GANs with gradient descent algorithms by avoiding adversarial learning.The main contribution of the paper is that we propose a principled approach that endows classifiers with the ability to resist larger variations between training and testing data in an intelligent and efficient manner. Experimental results show that our approach achieves better performance than standard data augmentation on both classification and cross-dataset generalization. Furthermore, we also show that our approach has great abilities in resisting different types of variations between training and testing data. We only briefly review introspective learning for binary-class problems, since the same idea can be easily extended to multi-class problems. Let us denote x ∈ R d as a data sample and y ∈ +1, −1 as the corresponding label of x. The goal of introspective learning is to model positive samples by learning the generative model p(x|y = +1). Under Bayes rule, we have DISPLAYFORM0 where p(y|x) is a discriminative model. For pedagogical simplicity, we assume p(y = 1) = p(y = −1) and this equation can be further simplified as: DISPLAYFORM1 The above equation suggests that a generative model for the positives p(x|y = +1) can be obtained from the discriminative model p(y|x) and a generative model p(x|y = −1) for the negatives. However, to faithfully learn p(x|y = +1), we need to have a representative p(x|y = −1), which is very difficult to obtain. A solution was provided in BID28 which learns p(x|y = −1) by using an iterative process starting from an initial reference distribution of the negatives p 0 (x|y = −1), e.g., p 0 (x|y = −1) = U (x), a Gaussian distribution on the entire space R d . This is updated by DISPLAYFORM2 where q t (y|x) is a discriminative model learned on a given set of positives and a limited number of pseudo-negatives sampled from p t (x|y = −1) and Z t =qt FORMULA0 qt(y=−1|x) p t (x|y = −1)dx is the normalizing factor. It has been proven that KL(p(x|y = +1)||p t+1 (x|y = −1)) ≤ KL(p(x|y = +1)||p t (x|y = −1))) (as long as each q t (y|x) makes a better-than-random prediction, the inequality holds) in BID28 , where KL(·||·) denotes the Kullback-Leibler divergences, which implies p t (x|y = −1) t=∞ → p(x|y = +1). Therefore, gradually learning p t (x|y = −1) by following this iterative process of Eqn.(3 ), the samples drawn from x ∼ p t (x|y = −1) become indistinguishable from the given training samples. Introspective Convolutional Networks (ICN) and Wasserstein Introspective Neural Networks (WINN) BID19 adopt the introspective learning framework and strengthen the classifiers by a reclassification-by-synthesis algorithm. However, both of them fail to capture large data variations between the training and testing data, since most of the generated pseudo-negatives are very similar to the original samples. But in practice, it is very common that the test data contain unseen variations that are not in training data, such as the same objects viewed from different angles and suffered from shape deformation.To address this issue, we present our approach building upon the introspective learning framework to resist large data variations between training and test data. Arguably, even large training sets cannot fully contains all the possible variations. Our goal is to quickly generate extra training samples with beneficial unseen variations that is not covered by the training data to help classifiers become robust. We assume that we can generates such training samples by applying a transformation function T (· ; σ) parametrized by learnable parameters σ to the original training samples. Let us denote g(· ; ψ) as the function that maps the samples x to the transformation parameters σ, where ψ is the model parameter of the function g. The generated samples still belong to the same category of the original samples, since the transformation function T only changes the high-level geometric properties of the samples. The outline of training procedures of ITN is presented in Algorithm 1. We denote S + = {(x + i , +1), i = 1... |S + |} as the positive sample set, DISPLAYFORM0 ; σ t )} as the transformed positive sample set at t th iteration with transformation parameter σ t and S DISPLAYFORM1 as the set of pseudonegatives drawn from p t (x|y = −1). We then will describe the detail of the training procedure.Discriminative model We first demonstrate the approach of building robust classifiers with given σ t . For a binary classification problem, at t th iteration, the discriminative model is represented as DISPLAYFORM2 Algorithm 1: Outline of ITN Training Algorithm 1: Input: Positive sample set S + , initial reference distribution p0(x|y = −1) and transformation function T 2: Output: Parameters θ, ω and ψ 3: Build S − 0 by sampling |S + | pseudo-negatives samples from p0(x|y = −1) 4: initialize parameters θ, ω and ψ, set t = 1 5: while not converge do 6:for each x DISPLAYFORM3 Compute transformation parameters σi = g(x DISPLAYFORM4 Choose i ∼ U (0, 1) and computexi = iT (x DISPLAYFORM5 9: end for 10:Compute θ, ω by Eqn.(6) 11:Compute ψ by Eqn. FORMULA0 Sample pseudo-negatives samples Zt = {z DISPLAYFORM6 Update all samples in Zt by Eqn. FORMULA0 Augment pseudo-negatives sample set S DISPLAYFORM7 .., |S + |} and t = t + 1 15: end while where θ t represents the model parameters at iteration t, and f t (x; θ t ) represents the model output at t th iteration. Note that, q t (y|x; θ t ) is trained on S + , T (S + ; σ t ) and pseudo-negatives drawn from p t (x|y = −1). In order to achieve stronger ability in resisting unseen variations, we want the distribution of T (S + ; σ t ) to be approximated by the distribution of pseudo negatives p t (x|y = −1), which can be achieved by minimizing the following Wasserstein distance BID5 : DISPLAYFORM8 where ω t is the extra parameter together with f t (·; θ t ) to compute the Wasserstein distance. Eachx in the setX t is computed with the formulax DISPLAYFORM9 2 is the gradient penalty that stabilizes the training procedure of the Wasserstein loss function.The goal of the discriminative model is to correctly classify any given x + , x T and x − . Thus, the objective function of learning the discriminative model at iteration t is DISPLAYFORM10 The classifiers obtain the strong ability in resisting unseen variations by training on the extra samples while preserving the ability to correctly classify the original samples. We discussed the binary classification case above. When dealing with multi-class classification problems, it is needed to adapt the above reclassification-by-synthesis scheme to the multi-class case. We can directly follow the strategies proposed in to extend ITN to deal with multi-class problems by learning a series of one-vs-all classifiers or a single CNN classifier.Exploring variations. The previous section describes how to learn the robust classifiers when the σ t is given. However, σ t is unknown and there are huge number of possibilities to selecting σ t . Now, the problem becomes how do we learn the σ t in a principled manner and apply it towards building robust classifiers? We solve this issue by forming a min-max problem upon the Eqn. FORMULA13 : DISPLAYFORM11 Here, we rewrite J(θ) and D(θ, ω) in Eqn. FORMULA11 and Eqn.(6) as J(θ, σ) and D(θ, ω, σ), since σ is now an unknown variable. We also subsequently drop the subscript t for notational simplicity. This formulation gives us a unified perspective that encompasses some prior work on building robust classifiers. The inner maximization part aims to find the transformation parameter σ that achieves the high loss values. On the other hand, the goal of the outer minimization is expected to find the the model parameters θ that enables discriminators to correctly classify x T and ω allows the negative distribution to well approximate the distribution of T (S + ; σ t ) . However, direclty solving Eqn. 7 is difficult. Thus, we break this learning process and first find a σ * that satisfies DISPLAYFORM12 where θ and ω are fixed. Then, θ and ω are learned with Eqn.(6) by keep σ = σ * . Empirically, the first term in the Eqn. 8 dominates over other terms, therefore we can drop the second and third terms to focus on learning more robust classifiers. The purpose of empirical approximation is to find the σ * that make x T hard to classify correctly. Instead of enumerating all possible examples in the data augmentation, Eqn.(8) efficiently and precisely finds a proper σ that increase the robustness of the current classifiers.We use g(· ; ψ) to learn σ, thus σ = g(x; ψ)+ζ, where ζ is random noise follows the standard normal distribution. The function parameter ψ is learned by Eqn.(8) . Notably, following the standard backpropagation procedure, we need to compute the derivative of the transformation function T in each step. In other words, the transformation function T (·; σ) need to be differentiable with respect to the parameter ψ to allow the gradients to flow through the transformation function T when learning by backpropagation.Generative model In the discriminative models, the updated discriminative model p(y|x) is learned by Eqn.(6). The updated discriminative model is then used to compute the generative model by the Eqn.(3) in section 3.1. The generative is learned by maximizing the likelihood function p(x). However, directly learning the generative model is cumbersome since we only need samples from the latest generative model. DISPLAYFORM13 where Z t indicates the normalizing factor at t th iteration. The random samples x are updated by increasing maximize the log likelihood of p − n (x). Note that maximizing log p Taking natural logarithm on both side of the equation above, we can get ln h t (x) = f t (x; θ t ). Therefore, log p − n (x) can be rewritten as DISPLAYFORM14 where C is the constant computed with normalizing factors Z t . This conversion allows us to maximize log p − n (x) by maximizing n−1 t=1 f t (x; θ t ). By taking the derivative of log p − n (x), the update step ∇x is: DISPLAYFORM15 where η ∼ N (0, 1) is the random Gaussian noise and λ is the step size that is annealed in the sampling process. In practice, we update from the samples generated from previous iterations to reduce time and memory complexity. An update threshold is introduced to guarantee the generated negative images are above certain criteria, which ensures the quality of negative samples. We modify the update threshold proposed in BID19 and keep track of the f t (x; θ t ) in every iteration. In particular, we build a set D by recording E[f t (x; θ t )], where x ∈ S + in every iteration. We form a normal distribution N (a, b) , where a and b represents mean and standard deviation computed from set D. The stop threshold is set to be a random number sampled from this normal distribution. The reason behind this threshold is to make sure the generated negative images are close to the majority of transformed positive images in the feature space. We proposed a principled and smart approach that endows the classifiers with the ability to resist larger variations between training and testing data. Our method, ITN strengthens the classifiers by generating unseen variations with various learned transformations. Experimental results show consistent performance improvements not only on the classification tasks but also on the other challenging classification tasks, such as cross dataset generalization. Moreover, ITN demonstrates its advantages in both effectiveness and efficiency over data augmentation. Our future work includes applying our approach to large scale datasets and extending it to generate samples with more types of variations.","Learning deep networks which can resist large variations training andtesting data is essential build accurate robust image classifiers. Towardsthis end typical strategy is to apply data augmentation enlarge trainingset. However standard data augmentation is essentially brute-force strategywhich is inefficient performs pre-defined transformations everytraining sample. paper propose principled approach train networkswith significantly improved resistance large variations training andtesting data. is achieved embedding learnable transformation moduleinto introspective networks Jinetal. 2017;Lazarowetal. 2017;Lee et al.,2018 whichis convolutional neural network CNN classifier empowered withgenerative capabilities. approach alternatively synthesizes pseudo-negativesamples learned transformations enhances classifier retraining itwith synthesized samples. Experimental results verify approach signif-icantly improves ability deep networks resist large variations betweentraining testing data achieves classification accuracy improvements onseveral benchmark datasets including MNIST affNIST SVHN CIFAR-10 Classification problems have rapidly progressed advancements convolutional neural networks CNNs BID17 BID15 BID25 BID6 BID7. CNNs are able produce promising performance given sufficient training data. However when the training data is limited unable cover data variations testing data e.g when the training set is MNIST testing set is affNIST trained networks generalize poorly testing data. Consequently how to learn deep networks which can resist large variations training testing data is a significant challenge building accurate robust image classifiers.To address issue typical strategy is to apply data augmentation enlarging training set.e applying various transformations including random translations rotations flips well Gaussian noise injection existing training data. strategy is very effective improving performance is essentially brute-force strategy which is inefficient exhaustively performs transformations every training samples. Neither is it theoretically formulated.Alternatively realize can synthesize extra training samples generative models. problem is how to generate synthetic samples which are able improve robustness CNNs large variations training testing data. paper achieve embedding learnable transformation module introspective networks CNN classifier empowered generative capabilities. name approach introspective transformation network ITN which performs training reclassification-by-synthesis algorithm. alternatively synthesizes samples learned transformations enhances classifier retraining synthesized samples. use min-max formulation learn ITN where the transformation module transforms synthesized pseudo-negative samples maximize variations original training samples CNN classifier is updated minimizing classification loss transformed synthesized pseudo-negative samples. transformation modules are learned jointly CNN classifier which augments training data intelligent manner narrowing search space variations.Our approach can work models have generative discriminative abilities generative adversarial networks GANs introspective networks. paper choose introspective networks generate extra training samples rather GANs introspective networks have several advantages GANs. Introspective learning framework maintains one single CNN discriminator is also generator GANs have separate discriminators generators. generative discriminative models are simultaneously refined iterations. Additionally Introspective networks are easier train GANs gradient descent algorithms avoiding adversarial learning.The main contribution paper is that we propose principled approach endows classifiers ability resist larger variations training testing data intelligent efficient manner. Experimental results show approach achieves better performance standard data augmentation classification cross-dataset generalization. Furthermore also show approach has great abilities resisting different types variations training testing data. briefly review introspective learning binary-class problems since idea can be easily extended multi-class problems. Let us denotex ∈R data sample ∈+1 −1 corresponding label x. goal introspective learning is to is the model positive samples learning generative modelp x|y+1 Bayes rule have DISPLAYFORM0 wherep y|x is a discriminative model. pedagogical simplicity assumep 1 p −1 equation can be further simplified as:DISPLAYFORM1 equation suggests have generative model positivesp x|y+1 can be obtained discriminative modelp y|x generative modelp x|y −1 negatives. However faithfully learnp x|y+1 need have a representativep x|y −1 whichis difficult obtain. solution was provided BID28 which learnsp x|y −1 using iterative process starting initial reference distribution negativesp0 x|y −1 e.g p0 x|y −1 U x Gaussian distribution entire spaceR d. is updated DISPLAYFORM2 whereq y|x is a discriminative model learned given set positives limited number pseudo-negatives sampled p x|y −1 Z =qt FORMULA0qt y=−1|x p x|y −1 dx is the normalizing factor. has been proven KL p x|y+1 ||p+1 x|y −1 ≤KL p x|y+1 ||p x|y −1 long q y|x makes better-than-random prediction inequality holds BID28 whereKL ·||· denotes Kullback-Leibler divergences which impliesp x|y −1 t=∞→p x|y+1 Therefore gradually learningp x|y −1 following iterative process Eqn. 3 samples drawn x∼p x|y −1 become indistinguishable given training samples. Introspective Convolutional Networks ICN Wasserstein Introspective Neural Networks WINN BID19 adopt introspective learning framework strengthen classifiers reclassification-by-synthesis algorithm. However fail capture large data variations training testing data since generated pseudo-negatives are very similar original samples. practice is very common test data contain unseen variations are not in training data objects viewed different angles suffered shape deformation.To address issue present approach building upon introspective learning framework resist large data variations training test data. Arguably even large training sets cannot fully contains possible variations. goal is to quickly generate extra training samples beneficial unseen variations is not covered training data help classifiers become robust. assume can generates training samples applying transformation function ·σ parametrized learnable parametersσ original training samples. Let us denoteg ·ψ function maps samplesx transformation parametersσ whereψ is to is the model parameter functiong. generated samples still belong category original samples since transformation function changes high-level geometric properties samples. outline training procedures ITN is presented Algorithm1. denote+x++1 1...|S+positive sample set have DISPLAYFORM0;σ transformed positive sample set th iteration transformation parameterσ DISPLAYFORM1 set pseudonegatives drawn p x|y −1 will describe detail training procedure.Discriminative model first demonstrate approach building robust classifiers givenσ t. binary classification problem th iteration discriminative model is represented DISPLAYFORM2 Algorithm1:Outline ITN Training Algorithm1:Input:Positive sample set+initial reference distributionp0 x|y −1 transformation function 2:Output:Parametersθ ω ψ3:Build −0 sampling|S+pseudo-negatives samples p0 x|y −1 4:initialize parametersθ ω ψ set 15:converge do6:x DISPLAYFORM3 Compute transformation parametersσi g x DISPLAYFORM4 Choose ∼U 0 1 computexi x DISPLAYFORM59:end 10:Computeθ ω Eqn. 6 11:Computeψ Eqn. FORMULA0 Sample pseudo-negatives samples Zt z DISPLAYFORM6 Update samples Zt Eqn. FORMULA0 Augment pseudo-negatives sample set DISPLAYFORM7.. |S++115:end whereθ represents model parameters iteration f x;θ represents model output th iteration. Note q y|xθ is trained++σ pseudo-negatives drawn p x|y −1 order achieve stronger ability resisting unseen variations want distribution+σ approximated distribution pseudo negativesp x|y −1 which can achieved minimizing following Wasserstein distance BID5:DISPLAYFORM8 whereω is the extra parameter together f ·θ compute Wasserstein distance. Eachx setX is computed formulax DISPLAYFORM92 is the gradient penalty stabilizes training procedure Wasserstein loss function.The goal discriminative model is to correctly classify givenx+x x − Thus objective function learning discriminative model iteration is DISPLAYFORM10 classifiers obtain strong ability resisting unseen variations training extra samples preserving ability correctly classify original samples. discussed binary classification case above. When dealing multi-class classification problems is needed adapt reclassification-by-synthesis scheme multi-class case. can directly follow strategies proposed extend ITN deal multi-class problems learning series one-vs-all classifiers single CNN classifier.Exploring variations. previous section describes how to how do we learn robust classifiers when theσ is given. However σ is unknown are huge number possibilities selectingσ t. problem becomes how to how do we learn σ principled manner apply towards building robust classifiers? solve issue forming min-max problem upon Eqn. FORMULA13:DISPLAYFORM11 rewriteJ θ θ ω Eqn. FORMULA11 Eqn. 6 J θ σ θ ω σ sinceσ is now an unknown variable. also subsequently drop subscript notational simplicity. formulation givesus unified perspective encompasses prior work building robust classifiers. inner maximization part aims find transformation parameterσ achieves high loss values. hand goal outer minimization is expected find model parametersθ enables discriminators correctly classifyx ω allows negative distribution well approximate distribution+σ However direclty solving Eqn. 7 is difficult. Thus break learning process first find σ* satisfies DISPLAYFORM12 whereθ ω are fixed. θ ω are learned Eqn. 6 keepσ σ * Empirically first term Eqn. 8 dominates terms therefore can drop second third terms focus learning robust classifiers. purpose empirical approximation is to find σ* makex hard classify correctly. Instead enumerating possible examples data augmentation Eqn. 8 efficiently precisely finds properσ increase robustness current classifiers.We useg ·ψ learnσ thusσ g x;ψ+ζ whereζ is random noise follows standard normal distribution. function parameterψ is learned Eqn. 8 Notably following standard backpropagation procedure need compute derivative transformation function step. words where the transformation function ·σ need differentiable respect parameterψ allow gradients flow transformation function when learning backpropagation.Generative model discriminative models updated discriminative modelp y|x is learned Eqn. 6 updated discriminative model is then used compute generative model Eqn. 3 section 3.1 generative is learned maximizing likelihood functionp x However directly learning generative model is cumbersome since need samples latest generative model. DISPLAYFORM13 whereZ indicates normalizing factor th iteration. random samplesx are updated increasing maximize log likelihood p−n x Note maximizing log p Taking natural logarithm side equation can getlnh x f x;θ Therefore logp−n x can be rewritten DISPLAYFORM14 whereC is the constant computed normalizing factorsZ t. conversion allowsus maximize logp− n x maximizing n−1 t=1f x;θ taking derivative logp−n x update step∇x is:DISPLAYFORM15 whereη∼N 0 1 is the random Gaussian noise λ is the step size is annealed sampling process. practice update samples generated previous iterations reduce time memory complexity. update threshold is introduced guarantee generated negative images are above certain criteria which ensures quality negative samples. modify update threshold proposed BID19 keep track f x;θ every iteration. particular build set recordingE f x;θ where x∈+every iteration. form normal distributionN b wherea b represents mean standard deviation computed set D. stop threshold is set random number sampled normal distribution. reason behind threshold is to make sure generated negative images are close majority transformed positive images feature space. proposed principled smart approach endows classifiers ability resist larger variations training testing data. method ITN strengthens classifiers generating unseen variations various learned transformations. Experimental results show consistent performance improvements classification tasks also challenging classification tasks cross dataset generalization. Moreover ITN demonstrates advantages effectiveness efficiency data augmentation. future work includes applying approach large scale datasets extending generate samples types variations.",3428,2335,1093,0.087,1.468,2025/11/05 17:19:04,0.02,1.443,0.4299065420560745,1160.025
"It is well known that it is possible to construct ""adversarial examples""
 for neural networks: inputs which are misclassified by the network
 yet indistinguishable from true data. We propose a simple
 modification to standard neural network architectures, thermometer
 encoding, which significantly increases the robustness of the network to
 adversarial examples. We demonstrate this robustness with experiments
 on the MNIST, CIFAR-10, CIFAR-100, and SVHN datasets, and show that
 models with thermometer-encoded inputs consistently have higher accuracy
 on adversarial examples, without decreasing generalization.
 State-of-the-art accuracy under the strongest known white-box attack was 
 increased from 93.20% to 94.30% on MNIST and 50.00% to 79.16% on CIFAR-10.
 We explore the properties of these networks, providing evidence
 that thermometer encodings help neural networks to
 find more-non-linear decision boundaries. Adversarial examples are inputs to machine learning models that are intentionally designed to cause the model to produce an incorrect output. The term was introduced by Szegedy et al. (2014) in the context of neural networks for computer vision. In the context of spam and malware detection, such inputs have been studied earlier under the name evasion attacks BID0 . Adversarial examples are interesting from a scientific perspective, because they demonstrate that even machine learning models that have superhuman performance on I.I.D. test sets fail catastrophically on inputs that are modified even slightly by an adversary. Adversarial examples also raise concerns in the emerging field of machine learning security because malicious attackers could use adversarial examples to cause undesired behavior BID15 .Unfortunately , there is not yet any known strong defense against adversarial examples. Adversarial examples that fool one model often fool another model, even if the two models are trained on different training examples (corresponding to the same task) or have different architectures (Szegedy et al., 2014) , so an attacker can fool a model without access to it. Attackers can improve their success rate by sending inputs to a model, observing its output, and fitting their own own copy of the model to the observed input-output pairs BID15 . Attackers can also improve their success rate by searching for adversarial examples that fool multiple different models-such adversarial examples are then much more likely to fool the unknown target model . Szegedy et al. (2014) proposed to defend the model using adversarial training (training on adversarial examples as well as regular examples) but it was not feasible to generate enough adversarial examples in the inner loop of the training process for the method to be effective at the time. Szegedy et al. (2014) used a large number of iterations of L-BFGS to produce their adversarial examples. BID3 developed the fast gradient sign method (FGSM) of generating adversarial examples and demonstrated that adversarial training is effective for reducing the error rate on adversarial examples. A major difficulty of adversarial training is that it tends to overfit to the method of adversarial example generation used at training time. For example, models trained to resist FGSM adversarial examples usually fail to resist L-BFGS adversarial examples. BID9 introduced the basic iterative method (BIM) which lies between FGSM and L-BFGS on a curve trading speed for effectiveness (the BIM consists of running FGSM for a medium number of iterations). Adversarial training using BIM still overfits to the BIM, unfortunately, and different iterative methods can still successfully attack the model. Recently, BID13 showed that adversarial training using adversarial examples created by adding random noise before running BIM results in a model that is highly robust against all known attacks on the MNIST dataset. However, it is less effective on more complex datasets, such as CIFAR. A strategy for training networks which are robust to adversarial attacks across all contexts is still unknown. In this work, we demonstrate that thermometer code discretization and one-hot code discretization of real-valued inputs to a model significantly improves its robustness to adversarial attack, advancing the state of the art in this field. In BID3 , the seeming linearity of deep neural networks was shown by visualizing the networks in several different ways. To test our hypothesis that discretization breaks some of this linearity, we replicate these visualizations and contrast them to visualizations of discretized models. See Appendix G for an illustration of these properties.For non-discretized, clean trained models, test-set examples always yield a linear boundary between correct and incorrect classification; in contrast, non-adversarially-trained models have a more interesting parabolic shape (see Figure 9 ). Loss for iterated white-box attacks on various models on a randomly chosen data point from MNIST. By step 40, which is where we evaluate, the loss of the point found by iterative attacks has converged. DISPLAYFORM0 When discretizing the input, we introduce C w · C h · C o · c · (k − 1) extra parameters, where c is the number of channels in the image, k is the number of levels of discretization, and C w , C h , C o are the width, height, and output channels of the first convolutional layer. Discretizing using 16 levels introduced 0.03% extra parameters for MNIST, 0.08% for CIFAR-10 and CIFAR-100, and 2.3% for SVHN. This increase is negligible, so it is likely that the robustness comes from the input discretization, and is not merely a byproduct of having a slightly higher-capacity model.",is well known is possible construct adversarial examples neural networks:inputs which are misclassified network yet indistinguishable true data. propose simple modification standard neural network architectures thermometer encoding which significantly increases robustness network adversarial examples. demonstrate robustness experiments MNIST CIFAR-10 CIFAR-100 SVHN datasets show models thermometer-encoded inputs consistently have higher accuracy adversarial examples without decreasing generalization. State-of-the-art accuracy strongest known white-box attack was increased 93.20 94.30 MNIST 50.00 79.16 CIFAR-10 explore properties networks providing evidence thermometer encodings help neural networks find more-non-linear decision boundaries. Adversarial examples are inputs machine learning models are intentionally designed cause model produce incorrect output. term was introduced Szegedyetal. 2014 context neural networks computer vision. context spam malware detection inputs have been studied earlier name evasion attacks BID0. Adversarial examples are interesting scientific perspective demonstrate even machine learning models have superhuman performance.I.D test sets fail catastrophically inputs are modified even slightly adversary. Adversarial examples also raise concerns emerging field machine learning security malicious attackers could use adversarial examples cause undesired behavior BID15.Unfortunately is not yet known strong defense adversarial examples. Adversarial examples fool one model often fool another model even if the two models are trained different training examples corresponding task have different architectures Szegedyetal. 2014 attacker can fool model without access it. Attackers can improve success rate sending inputs model observing output fitting copy model observed input-output pairs BID15. Attackers can also improve success rate searching adversarial examples fool multiple different models-such adversarial examples are then much likely fool unknown target model. Szegedyetal. 2014 proposed defend model using adversarial training training adversarial examples well regular examples was feasible generate enough adversarial examples inner loop training process method effective time. Szegedyetal. 2014 used large number iterations L-BFGS produce adversarial examples. BID3 developed fast gradient sign method FGSM generating adversarial examples demonstrated adversarial training is effective reducing error rate adversarial examples. major difficulty adversarial training is that it tends overfit method adversarial example generation used training time. example models trained resist FGSM adversarial examples usually fail resist L-BFGS adversarial examples. BID9 introduced basic iterative method BIM which lies FGSM L-BFGS curve trading speed effectiveness BIM consists running FGSM medium number iterations Adversarial training using BIM still overfits BIM unfortunately different iterative methods can still successfully attack model. Recently BID13 showed adversarial training using adversarial examples created adding random noise running BIM results model is highly robust known attacks MNIST dataset. However is less effective complex datasets CIFAR. strategy training networks which are robust adversarial attacks across contexts is still unknown. work demonstrate thermometer code discretization one-hot code discretization real-valued inputs model significantly improves robustness adversarial attack advancing state art field. BID3 seeming linearity deep neural networks was shown visualizing networks several different ways. test hypothesis discretization breaks linearity replicate visualizations contrast visualizations discretized models. See AppendixG illustration properties.For non-discretized clean trained models test-set examples always yield linear boundary correct incorrect classification;contrast non-adversarially-trained models have a more interesting parabolic shape see Figure9 Loss iterated white-box attacks various models randomly chosen data point MNIST. step40 which is where evaluate loss point found iterative attacks has converged. DISPLAYFORM0 When discretizing input introduceCw· Ch·C ·c· k−1 extra parameters wherec is the number channels image k is the number levels discretization Cw Ch C are the width height output channels first convolutional layer. Discretizing using 16 levels introduced 0.03 extra parameters MNIST 0.08 CIFAR-10 CIFAR-100 2.3 SVHN. increase is negligible is likely robustness comes input discretization is not merely byproduct slightly higher-capacity model.,1165,805,360,0.011,1.447,2025/11/05 17:19:04,0.01,1.366,0.3644859813084112,331.771
"Low-precision training is a promising way of decreasing the time and energy cost of training machine learning models.
 Previous work has analyzed low-precision training algorithms, such as low-precision stochastic gradient descent, and derived theoretical bounds on their convergence rates.
 These bounds tend to depend on the dimension of the model $d$ in that the number of bits needed to achieve a particular error bound increases as $d$ increases.
 This is undesirable because a motivating application for low-precision training is large-scale models, such as deep learning, where $d$ can be huge.
 In this paper, we prove dimension-independent bounds for low-precision training algorithms that use fixed-point arithmetic, which lets us better understand what affects the convergence of these algorithms as parameters scale.
 Our methods also generalize naturally to let us prove new convergence bounds on low-precision training with other quantization schemes, such as low-precision floating-point computation and logarithmic quantization. As machine learning models continue to scale to target larger problems on bigger data, the task of training these models quickly and efficiently becomes an ever-more-important problem. One promising technique for doing this is low-precision computation, which replaces the 32-bit or 64-bit floating point numbers that are usually used in ML computations with smaller numbers, often 8-bit or 16-bit fixed point numbers. Low-precision computation is a broadly applicable technique that has received a lot of attention, especially for deep learning, and specialized hardware accelerators have been developed to support it (Jouppi et al., 2017; Burger, 2017; Caulfield et al., 2017) .A major application for low-precision computation is the training of ML models using empirical risk minimization. This training is usually done using stochastic gradient descent (SGD), and most research in low-precision training has focused on low-precision versions of SGD. While most of this work is empirical (Wu et al., 2018; Das et al., 2018; Zhu et al., 2016; Köster et al., 2017; Lee et al., 2017; Hubara et al., 2016; Rastegari et al., 2016; Zhou et al., 2016; Gupta et al., 2015; Courbariaux et al., 2014; 2015; De Sa et al., 2017) , significant research has also been done in the theoretical analysis of low-precision training. This theoretical work has succeeded in proving bounds on the convergence rate of low-precision SGD and related low-precision methods in various settings, including for convex (De Sa et al., 2018; Zhang et al., 2017) and non-convex objectives (De Sa et al., 2015; Li et al., 2017; Alistarh et al., 2017) . One common characteristic of these results is that the bounds tend to depend on the dimension d of the model being learned (equivalently, d is the number of parameters). For example, (Li et al., 2017) gives the convergence bound DISPLAYFORM0 where the objective f is strongly convex with parameter µ, low-precision SGD outputsw T after T iterations, w * is the true global minimizer of the objective, σ 2 max is an upper bound on the second moment of the stochastic gradient samples E[ f (w) 2 2 ] ≤ σ 2 max , and δ is the quantization step, the difference between adjacent numbers in the low-precision format. Notice that, as T → ∞, this bound shows convergence down to a level of error that increases with the dimension d. Equivalently , in order to achieve the same level of error as d increases, we would need to use more bits of quantization to make δ smaller. Similar dimension-dependent results, where either the error or the number of bits needed increases with d, can also be seen in other work on low-precision training algorithms (Alistarh et al., 2017; Zhang et al., 2017; De Sa et al., 2018) . This dependence on d is unsatisfying because the motivation for low-precision training is to tackle large-scale problems on big data, where d can range up to 10 8 or more for commonly used models (Simonyan and Zisserman, Table 1 : Summary of our dimension-free results compared with prior work. The values report the number of bits needed, according to the theoretical bound, for the LP-SGD (Li et al., 2017) algorithm to achieve an expected objective gap (f (w) − f (w * )) of when we let step size α → 0, epoch length T → ∞. Here we let R denote the radius of the range of numbers representable in the low-precision format and assume w * 2 = Θ(R). The rest of the parameters can be found in the assumptions to be introduced later. log 2 O (Rσ/ε) · log 1 + σ1/σ 2014). For example, to compensate for a factor of d = 10 8 in (1), we could add bits to decrease the quantization step δ by a factor of √ d, but this would require adding log 2 (10 4 ) ≈ 13 bits, which is significant compared to the 8 or 16 bits that are commonly used in low-precision training. In this paper, we present dimension-independent bounds on the convergence of SGD when applied to low-precision training. We point out the conditions under which such bounds hold. We further extend our results to non-linear methods of quantization: logarithmic quantization and floating point quantization. We analyze the performance of SGD under logarithmic quantization and demonstrate that NLQ is a promising method for reducing the number of bits required in low-precision training. We also presented ways in which our theory could be used to suggest how to allocate bits between exponent and mantissa when FPQ is used. We hope that our work will encourage further investigation of non-linear quantization techniques. A ALGORITHMIn our work, we presented dimension-free bounds on the performance of low-precision SGD, here we present the algorithm in detail.",Low-precision training is a promising way decreasing time energy cost training machine learning models. Previous work has analyzed low-precision training algorithms low-precision stochastic gradient descent derived theoretical bounds convergence rates. bounds tend depend dimension model$d number bits needed achieve particular error bound increases $d increases. is undesirable motivating application is low-precision training is large-scale models deep learning where$d$d can be huge. paper prove dimension-independent bounds is low-precision training algorithms use fixed-point arithmetic which lets us better understand what affects convergence algorithms parameters scale. methods also generalize naturally let us prove new convergence bounds low-precision training quantization schemes low-precision floating-point computation logarithmic quantization. machine learning models continue scale target larger problems bigger data task training models quickly efficiently becomes ever-more-important problem. One promising technique is low-precision computation which replaces 32-bit 64-bit floating point numbers are usually used ML computations smaller numbers often 8-bit 16-bit fixed point numbers. Low-precision computation is a broadly applicable technique has received lot attention especially deep learning specialized hardware accelerators have been developed support Jouppietal. 2017;Burger 2017;Caulfieldetal. 2017.A major application is low-precision computation is the training ML models using empirical risk minimization. training is usually done using stochastic gradient descent SGD research low-precision training has focused low-precision versions SGD. work is empirical Wuetal. 2018;Dasetal. 2018;Zhuetal. 2016;Kösteretal. 2017;Leeetal. 2017;Hubaraetal. 2016;Rastegarietal. 2016;Zhouetal. 2016;Guptaetal. 2015;Courbariauxetal. 2014;2015;DeSaetal. 2017 significant research has also done theoretical analysis low-precision training. theoretical work has succeeded proving bounds convergence rate low-precision SGD related low-precision methods various settings including convex DeSaetal. 2018;Zhangetal. 2017 non-convex objectives DeSaetal. 2015;Lietal. 2017;Alistarhetal. 2017 One common characteristic results is that the bounds tend depend dimension model learned equivalently is the number parameters example Lietal. 2017 gives convergence bound DISPLAYFORM0 where the objectivef is strongly convex parameterµ low-precision SGD outputsw iterations w* is the true global minimizer objective σ 2 max is an upper bound second moment stochastic gradient samplesE f w 22 ≤ σ 2 max δ is the quantization step difference adjacent numbers low-precision format. Notice →∞ bound shows convergence level error increases dimension d. Equivalently order achieve level error increases would need use bits quantization make δ smaller. Similar dimension-dependent results where either error number bits needed increases can also seen work low-precision training algorithms Alistarhetal. 2017;Zhangetal. 2017;DeSaetal. 2018 dependence is unsatisfying motivation is low-precision training is to tackle large-scale problems big data where d can range 108 commonly used models Simonyan Zisserman Table1:Summary dimension-free results compared prior work. values report number bits needed according theoretical bound LP-SGD Lietal. 2017 algorithm achieve expected objective gap f w −f w* when let step sizeα →0 epoch length →∞. let R denote radius range numbers representable low-precision format assumew*2 Θ R rest parameters can be found assumptions introduced later. log2 Rσ/ε · log1+σ1/σ 2014 example compensate factor 108 1 could add bits decrease quantization stepδ factor √ would require adding log 2 104 ≈ 13 bits which is significant compared 8 16 bits are commonly used low-precision training. paper present dimension-independent bounds convergence SGD when applied low-precision training. point conditions which such bounds hold. extend results non-linear methods quantization:logarithmic quantization floating point quantization. analyze performance SGD logarithmic quantization demonstrate NLQ is a promising method reducing number bits required low-precision training. also presented ways which our theory could used suggest how to allocate bits exponent mantissa when FPQ is used. hope work will encourage investigation non-linear quantization techniques. ALGORITHMIn work presented dimension-free bounds performance low-precision SGD present algorithm detail.,1287,906,381,0.013,1.421,2025/11/05 17:19:04,0.01,1.488,0.2834890965732086,363.004
"We consider the problem of exploration in meta reinforcement learning. Two new meta reinforcement learning algorithms are suggested: E-MAML and ERL2. Results are presented on a novel environment we call 'Krazy World'  and a set of maze environments. We show E-MAML and ERL2 deliver better performance on tasks where exploration is important. Supervised learning algorithms typically have their accuracy measured against some held-out test set which did not appear at training time. A supervised learning model generalizes well if it maintains its accuracy under data that has non-trivial dissimilarity from the training data. This approach to evaluating algorithms based on their generalization ability contrasts the approach in reinforcement learning (RL), wherein there is usually no distinction between training and testing environments. Instead, an agent is trained on one environment, and results are reported on this same environment. Most RL algorithms thus favor mastery over generalization.Meta RL is the suggestion that RL should take generalization seriously. In Meta RL, agents are evaluated on their ability to quickly master new environments at test time. Thus, a meta RL agent must not learn how to master the environments it is given, but rather it must learn how to learn so that it can quickly train at test time. Recent advances in meta RL have introduced algorithms that are capable of generating large policy improvements at test time with minimal sample complexity requirements BID5 ; ; BID36 .One key question for meta RL that has been inadequately considered by BID5 ; is that of exploration (see BID10 for an overview of exploration in this context). A crucial step in learning to solve many environments is an initial period of exploration and system identification. Furthermore , we know that real-life agents become better at this exploratory phase with practice. Consider, for example, an individual playing an entirely new video game. They will first need to identify the objective of the game and its mechanics. Further, we would expect that individuals who have played many video games would have a significantly easier time learning new games. Similarly , we would expect a good meta RL agent to become more efficient at this exploratory period. Unfortunately , we have found existing algorithms deficient in this area. We hypothesize that this failure can at least partially be attributed to the tendency of existing algorithms to do greedy, local optimization at each step of meta-training, as discussed further below.To address the problem of exploration in meta RL, we introduce two new algorithms: E-MAML and E-RL 2 . It should come as no surprise that these algorithms are similar to their respective namesakes MAML and RL 2 . The algorithms are derived by reformulating the underlying meta-learning objective to account for the impact of initial sampling on future (post-meta-updated) returns. We show that our algorithms achieve better results than MAML and RL 2 on two environments: a Krazy World environment we developed to benchmark meta RL, and a set of maze environments. In the appendix to this work, we consider a more general form of our E-MAML derivation. This more general derivation suggests several promising directions for future work on exploration in meta-learning and highlights the novelty of our contributions. We considered the problem of exploration in meta reinforcement learning. Two new algorithms were derived and their properties were analyzed. In particular, we showed that these algorithms tend to learn more quickly and explore more efficiently than existing algorithms. It is likely that future work in this area will focus on meta-learning a curiosity signal which is robust and transfers across tasks. Perhaps this will enable meta agents which learn to explore rather than being forced to explore by mathematical trickery in their objectives. See appendix B for more explicit discussion on possible future directions. Figure 7 : Three heuristic metrics for exploration on Krazy World: Fraction of tile types visited during test time, number of times killed at a death square during test time, and number of goal squares visited. We see that E-MAML is consistently the most diligent algorithm at checking every tile type during test time. Beyond that, things are fuzzy with RL 2 and MAML both checking a majority of tile types at test time and E-RL 2 being sporadic in this regard. As for the number of times the death tile type was visited, we see that most algorithms start by dying in all three test episodes, and subsequently decrease to between one and two by the time they have converged. As mentioned above, RL 2 suffers from finding one goal and exploiting it, whereas the other algorithms regularly explore to find more goals. For the most part, the exploratory algorithms consistently deliver the best performance on these metrics. Performance on the death heuristic and the tile types found heuristic seem to indicate the meta learners are learning how to do at least some system identification. Figure 8 : MAML on the right and E-MAML on the left. A look at the number of gradient steps at test time vs reward on the Krazy World environment. Both MAML and E-MAML do not typically benefit from seeing more than one gradient step at test time. Hence, we only perform one gradient step at test time for the experiments in this paper.",consider problem exploration meta reinforcement learning. Two new meta reinforcement learning algorithms are suggested:E-MAML ERL2. Results are presented novel environment call 'Krazy World' set maze environments. show E-MAML ERL2 deliver better performance tasks where exploration is important. Supervised learning algorithms typically have their accuracy measured held-out test set which did not appear training time. supervised learning model generalizes well if it maintains accuracy data has non-trivial dissimilarity training data. approach evaluating algorithms based generalization ability contrasts approach reinforcement learning RL wherein is usually distinction training testing environments. Instead agent is trained one environment results are reported environment. RL algorithms thus favor mastery generalization.MetaRL is the suggestion RL should take generalization seriously. MetaRL agents are evaluated ability quickly master new environments test time. Thus meta RL agent must learn how to master environments is given rather must learn how to learn can quickly train test time. Recent advances metaRL have introduced algorithms are capable generating large policy improvements test time minimal sample complexity requirements BID5;BID36.One key question metaRL has been inadequately considered BID5;is that of exploration see BID10 overview exploration context crucial step learning solve many environments is an initial period exploration system identification. Furthermore know real-life agents become better exploratory phase practice. Consider example individual playing entirely new video game. will first need identify objective game mechanics. would expect individuals who have played many video games would have a significantly easier time learning new games. Similarly would expect good meta RL agent become efficient exploratory period. Unfortunately have found existing algorithms deficient area. hypothesize failure can at least partially attributed tendency existing algorithms do greedy local optimization step meta-training discussed below.To address problem exploration metaRL introduce two new algorithms:E-MAML E-RL2. should come surprise algorithms are similar respective namesakes MAML RL2. algorithms are derived reformulating underlying meta-learning objective account impact initial sampling future post-meta-updated returns. show algorithms achieve better results MAML RL2 two environments:Krazy World environment developed benchmark metaRL set maze environments. appendix work consider general form E-MAML derivation. general derivation suggests several promising directions future work exploration meta-learning highlights novelty contributions. considered problem exploration meta reinforcement learning. Two new algorithms were derived properties were analyzed. particular showed algorithms tend learn quickly explore efficiently existing algorithms. is likely future work area will focus meta-learning curiosity signal which is robust transfers across tasks. Perhaps will enable meta agents which learn explore rather forced explore mathematical trickery objectives. See appendixB explicit discussion possible future directions. Figure7:Three heuristic metrics exploration Krazy World:Fraction tile types visited test time number times killed death square test time number goal squares visited. see E-MAML is consistently diligent algorithm checking every tile type test time. Beyond things are fuzzy RL2 MAML checking majority tile types test time E-RL2 sporadic regard. number times death tile type was visited see algorithms start dying three test episodes subsequently decrease one two time have converged. mentioned RL 2 suffers finding one goal exploiting whereas algorithms regularly explore find goals. part exploratory algorithms consistently deliver best performance metrics. Performance death heuristic tile types found heuristic seem indicate meta learners are learning how to do at least system identification. Figure8:MAML right E-MAML left. look number gradient steps test time vs reward Krazy World environment. MAML E-MAML do not typically benefit seeing one gradient step test time. Hence perform one gradient step test time experiments paper.,1024,689,335,0.011,1.486,2025/11/05 17:19:04,0.01,1.413,0.4859813084112147,331.931
"We propose a new class of probabilistic neural-symbolic models for visual question answering (VQA) that provide interpretable explanations of their decision making in the form of programs, given a small annotated set of human programs. The key idea of our approach is to learn a rich latent space which effectively propagates program annotations from known questions to novel questions. We do this by formalizing prior work on VQA, called module networks (Andreas, 2016) as discrete, structured, latent variable models on the joint distribution over questions and answers given images, and devise a procedure to train the model effectively. Our results on a dataset of compositional questions about SHAPES (Andreas, 2016) show that our model generates more interpretable programs and obtains better accuracy on VQA in the low-data regime than prior work. Exciting progress has been made in recent years in deep representation learning BID19 BID32 , which has led to advances in artificial intelligence tasks such as image recognition BID30 BID18 , machine translation BID41 , visual question answering BID0 , visual dialog BID10 , and reinforcement learning BID36 , etc. While deep neural networks achieve such impressive performances, many aspects of human cognition such as compositional generalization and reasoning are harder to model with state-of-the art deep learning approaches BID6 BID5 .Symbolic approaches BID38 on the other hand provide strong compositional and reasoning capabilities which are challenging to model with neural networks BID31 . Consequently , a rich line of work in neuro-symbolic processing sought to build AI systems with both strong learning and reasoning capabilities BID46 BID12 BID4 . As we tackle higher-level tasks which involve reasoning, such as visual question answering BID0 , planning BID3 BID15 etc., it is natural to desire the ability to provide instructions to models to guide them. Symbolic instructions , by their very nature are easier to specify and more interpretable than specifying the parameters of a neural network. For such high-level tasks, a sensible approach is to specify ""what"" to do using symbols and learn how to do the task using modern representation learning techniques.For the example shown in Figure 1 , given a question ""Is a square to the left of a green shape?"", one can ask the model to reason about the answer by first applying a find [green] operator, then find [left] , then And the result together with a find [square] operator in order to predict the answer, in other words specifying ""what"" are the computations we desire to be executed, in the form of a ""program"". BID26 BID21 BID2 . The network can then learn ""how"" to execute such a program from data using deep representation learning BID26 BID21 BID2 . This paper addresses a very natural desiderata for such neuro-symbolic models, in the context of visual question answering -can we retain the intepretability of ""what the network did"" expressed in terms of the syntax and lexicon that we are interested in, while specifying minimal teaching examples of ""what to do"" given an input question? Figure 1 : An illustration of neural module networks for visual question answering. Given a question, the program generator produces a program in prefix notation which is used to construct a neural network from the specified module networks. This network operates on the image and intermediate attention maps to answer the question.We propose to approach this problem with a treatment of programs z as a latent variable, embedded into a generative model of questions x and answers a given images i as visualized in FIG0 . This model class has certain desirable properties: first, a proper treatment of z as a stochastic latent variable is helpful especially in the presence of a limited number of expert human instructions, as we model the uncertainty associated with z explicitly, leading to more interepretable latent spaces (Section 5); second, the model makes intuitive independence assumptions with regards to the question answering task -conditioned on the program z, questions x are independent of the answers a for an image, meaning that the program must be a sufficient statistic for predicting the answer given a question 1 . Third, we parameterize the p(a|i , z) term, which predicts an answer given an image and a program using a popular, related class of question answering models called neural module networks (NMNs) BID21 BID26 BID2 which previous work has shown leads to better fit between the program (or ""what the model is doing"") and the execution (or ""how it is doing what it is doing""). Given the close ties of our model to NMNs, we will refer to our model as variational neural module networks (V-NMN) for the rest of the paper.Apart from our modeling contribution of a probabilistic latent variable, neuro-symbolic model, our key technical contribution is to show how to train this model in the context of visual question answering.Optimizing such generative models with structured discrete latent variables is an intractable problem to solve in genereal -for this particular case, we formulate training into stages of grounding questions into programs (question coding), learning how to execute them and then with those initializations train the full variational objective. We demonstrate that this stage-wise optimization allows us to successfully learn a probabilistic neural-symbolic model that can answer compositional questions about shapes in an image BID2 .While the V-NMN model is instantiated for the specific problem of visual question answering, we believe the tools and techniques we develop are more generally applicable to probabilistic, structured, discrete, interpretable latent spaces for interpretable neuro-symbolic models for planning, instruction following, grounding referring expressions etc. We benchmark our model on the SHAPES BID2 dataset with compositionally novel questions and show that our model is able to provide interpretable explanations of ""what it is doing"" (measured by program correctness) for unseen questions even in the setting where it is given as few as ≈ 20 paired examples of programs and corresponding questions from the dataset, while also getting to high question answering accuracy. We find that the proposed approach outperforms a state of the art neural-symbolic model designed for VQA from BID26 , as well as deterministic ablations of our model. In this paper we presented a novel, probabilistic neural symbolic model for interpretable visual question answering, that provides explanations of ""what"" the model is doing on unseen questions given a minimal number of annotated symbolic traces or programs of ""what it should do"". We demonstrate that our formulation provides more interpretable explanations than previous work on visual question answering called neural module networks, on dataset of compositional questions about shapes BID2 .The key to our approach is a model with programs as a stochastic latent variable, which leads to better sharing of statistics across questions, yielding a latent space where program annotations for known questions propagate effectively to unknown / novel questions without annotations.In general, the model family we study is quite rich, and also supports other inference queries such as counter factual explanations of what programs could have led to particular answers for a given image. We hope our work inspires more work on applying such ideas to other tasks requiring compositional reasoning such as planning, navigation etc.",propose new class probabilistic neural-symbolic models visual question answering VQA provide interpretable explanations decision making form what programs given small annotated set human programs. key idea approach is to learn rich latent space which effectively propagates program annotations known questions novel questions. do this by formalizing prior work VQA called module networks Andreas 2016 discrete structured latent variable models joint distribution questions answers given images devise procedure train model effectively. results dataset compositional questions SHAPES Andreas 2016 show model generates interpretable programs obtains better accuracy VQA low-data regime prior work. Exciting progress has been made recent years deep representation learning BID19 BID32 which has led advances artificial intelligence tasks image recognition BID30 BID18 machine translation BID41 visual question answering BID0 visual dialog BID10 reinforcement learning BID36 etc. deep neural networks achieve impressive performances many aspects human cognition compositional generalization reasoning are harder model state-of-the art deep learning approaches BID6 BID5.Symbolic approaches BID38 hand provide strong compositional reasoning capabilities which are challenging model neural networks BID31. Consequently rich line work neuro-symbolic processing sought build AI systems strong learning reasoning capabilities BID46 BID12 BID4. tackle higher-level tasks which involve reasoning visual question answering BID0 planning BID3 BID15 etc. is natural desire ability provide instructions models guide them. Symbolic instructions nature are easier specify interpretable specifying parameters neural network. high-level tasks sensible approach is to specify what to do using symbols learn how to do the task using modern representation learning techniques.For example shown Figure1 given question Is a square left green shape? one can ask model reason answer first applying find green operator find left result together find square operator order predict answer words specifying what are the computations desire executed form program. BID26 BID21 BID2. network can then learn how to execute program data using deep representation learning BID26 BID21 BID2. paper addresses natural desiderata neuro-symbolic models context visual question answering -can retain intepretability what the network did expressed terms syntax lexicon are interested specifying minimal teaching examples what to do given input question? Figure1:illustration neural module networks visual question answering. Given question program generator produces program prefix notation which is used construct neural network specified module networks. network operates image intermediate attention maps answer question.We propose approach problem treatment what programsz latent variable embedded generative model questionsx answers given images visualized FIG0. model class has certain desirable properties:first proper treatment z stochastic latent variable is helpful especially presence limited number expert human instructions model uncertainty associated z explicitly leading interepretable latent spaces Section5 second model makes intuitive independence assumptions regards question answering task -conditioned programz questionsx are independent answers image meaning program must sufficient statistic predicting answer given question1. Third parameterize p a|i z term which predicts answer given image program using popular related class question answering models called neural module networks NMNs BID21 BID26 BID2 which previous work has shown leads better fit program what the model is doing)and execution howit is doing what it is doing). is doing what it is doing). Given close ties what the model NMNs will refer model variational neural module networks V-NMN rest paper.Apart modeling contribution probabilistic latent variable neuro-symbolic model key technical contribution is to show how to train model context visual question answering.Optimizing generative models structured discrete latent variables is an intractable problem solve genereal -for particular case formulate training stages grounding questions programs question coding learning how to execute initializations train full variational objective. demonstrate stage-wise optimization allowsus successfully learn probabilistic neural-symbolic model can answer compositional questions shapes image BID2.While V-NMN model is instantiated specific problem visual question answering believe tools techniques develop are more generally applicable probabilistic structured discrete interpretable latent spaces interpretable neuro-symbolic models planning instruction following grounding referring expressions etc. benchmark model SHAPES BID2 dataset compositionally novel questions show model is able provide interpretable explanations whatitis measured program correctness unseen questions even setting where it is given ≈ 20 paired examples what programs corresponding questions dataset also getting high question answering accuracy. find proposed approach outperforms state art neural-symbolic model designed VQA BID26 well deterministic ablations what the model. paper presented novel probabilistic neural symbolic model interpretable visual question answering provides explanations what the model is doing on unseen questions given minimal number annotated symbolic traces programs do. demonstrate formulation provides interpretable explanations previous work visual question answering called neural module networks dataset compositional questions shapes BID2.The key approach is a model programs stochastic latent variable which leads better sharing statistics across questions yielding latent space where program annotations known questions propagate effectively unknown/novel questions without annotations.In general model family study is quite rich also supports inference queries counter factual explanations what programs could have led particular answers given image. hope work inspires work applying ideas tasks requiring compositional reasoning planning navigation etc.,1441,971,470,0.016,1.484,2025/11/05 17:19:04,0.01,1.846,0.4797507788161991,464.612
"The ability to deploy neural networks in real-world, safety-critical systems is severely limited by the presence of adversarial examples: slightly perturbed inputs that are misclassified by the network. In recent years, several techniques have been proposed for training networks that are robust to such examples; and each time stronger attacks have been devised, demonstrating the shortcomings of existing defenses. This highlights a key difficulty in designing an effective defense: the inability to assess a network's robustness against future attacks. We propose to address this difficulty through formal verification techniques. We construct ground truths: adversarial examples with a provably-minimal distance from a given input point. We demonstrate how ground truths can serve to assess the effectiveness of attack techniques, by comparing the adversarial examples produced by those attacks to the ground truths; and also of defense techniques, by computing the distance to the ground truths before and after the defense is applied, and measuring the improvement. We use this technique to assess recently suggested attack and defense techniques.
 While machine learning, and in particular neural networks, have seen significant success, recent work BID20 has shown that an adversary can cause unintended behavior by performing slight modifications to the input at test-time. In neural networks used as classifiers, these adversarial examples are produced by taking some normal instance that is classified correctly, and applying a slight perturbation to cause it to be misclassified (or even misclassified as a specific target label chosen by the adversary). This phenomenon, which has been shown to affect all state-of-the-art networks, poses a significant hindrance to deploying neural networks in safety-critical settings.Many effective techniques have been proposed for generating adversarial examples BID20 ; ; BID17 ; BID1 ; BID21 ; and, conversely, several techniques have been proposed for training networks that are more robust to these examples BID8 ; BID22 BID6 ; BID7 ; BID16 ; BID21 . Unfortunately, it has proven difficult to accurately assess the robustness of any given defense by evaluating it against existing techniques for generating adversarial examples. In several cases, a defensive technique that was at first thought to produce robust networks was later shown to be susceptible to new kinds of attacks BID2 . This ongoing cycle thus cast a doubt on any newly-proposed defensive technique.In recent years, new techniques have been proposed for the formal verification of neural networks BID18 BID19 ; BID12 ; BID9 ; BID3 . These techniques take a network and a desired property, and formally prove that the network satisfies the property -or provide an input for which the property is violated, if such an input exists. Specifically, for a given input point and some allowed amount of distortion under a given metric, verification can be used for finding an adversarial example or for soundly proving that no such examples exist within the allowed distortion. While verification tends to be significantly slower in finding adversarial examples than the aforementioned heuristic-based techniques BID19 ; BID11 BID0 , it can provide the much-needed rigor for assessing the adversarial robustness of neural networks.In this paper we propose a method for using formal verification to assess the effectiveness of techniques for producing adversarial examples or defending against them. The key idea is to examine networks and apply verification to identify ground-truth adversarial examples. Formally, given a neural network F , a distance metric d, and an input x, we say that another input x is a ground-truth adversarial example for x if it is the nearest point (with respect to the metric d) such that F assigns different labels to x and x . It follows that all points whose distance to x is smaller than the distance between x and x are assigned the same label as x. The distance to the ground truth is thus an indication of how robust the network is to adversarial attacks at point x. Ground truths can serve multiple purposes: (i) if ground-truth adversarial examples are known for a set of points drawn from some meaningful distribution thought to represent real-world inputs, they can serve to estimate the robustness of a network as a whole, against any possible attack; (ii) they can be used for assessing attack techniques, by measuring the proximity of the adversarial examples that these attacks produce to the ground truths; and (iii) they can be used for assessing the effectiveness of defense techniques, by computing new ground truths for the hardened network and comparing them to the ground truths of the original network.Our contributions can thus be summarized as follows:• We suggest to use ground-truth adversarial examples, the provably closest adversarial with respect to some distance metric, as a tool for studying attacks and defenses.• We find that first-order attack algorithms often produce near-optimal results, i.e. results that are close to a ground-truth adversarial example.• We study adversarial training and find that it does increase robustness and does not overfit to a specific attack, as long as the attack is iterative.The rest of this paper is organized as follows. In Section 2 we provide some necessary background. We then describe the experiments that we conducted in Section 3, and analyze their results in Section 4. Finally , we conclude with Section 5. Neural networks hold great potential as controllers in safety-critical systems, but their susceptibility to adversarial examples poses a significant hindrance. The development of defensive techniques is difficult when they are measured only against existing attacks. The burgeoning field of neural network verification can mitigate this problem, by allowing us to obtain an absolute measurement of the usefulness of a defense, regardless of the attack to be used against it.In this paper, we introduce ground-truth adversarial examples and show how to construct them with formal verification approaches. We evaluate one recent attack BID1 and find it often produces adversarial examples whose distance is within 5.9% to 12.9% of optimal, and one defense BID16 , and find that it increases distortion to the nearest adversarial example by an average of 427% on the MNIST dataset for our tested networks. To the best of our knowledge, this is the first proof of robustness increase for a defense.Currently available verification tools afford limited scalability, which means experiments can only be conducted on small networks. However, as better verification techniques are developed, this limitation is expected to be mitigated. Orthogonally, when preparing to use a neural network in a safetycritical setting, users may choose to design their networks as to make them particularly amenable to verification techniques -e.g., by using specific activation functions or network topologies -so that strong guarantees about their correctness and robustness may be obtained.",ability deploy neural networks real-world safety-critical systems is severely limited presence adversarial examples:slightly perturbed inputs are misclassified network. recent years several techniques have been proposed training networks are are more robust examples;time stronger attacks have been devised demonstrating shortcomings existing defenses. highlights key difficulty designing effective defense:inability assess network's robustness future attacks. propose address difficulty formal verification techniques. construct ground truths:adversarial examples provably-minimal distance given input point. demonstrate how ground truths can serve assess effectiveness attack techniques comparing adversarial examples produced attacks ground truths;also defense techniques computing distance ground truths defense is applied measuring improvement. use technique assess recently suggested attack defense techniques. machine learning particular neural networks have seen significant success recent work BID20 has shown adversary can cause unintended behavior performing slight modifications input test-time neural networks used classifiers adversarial examples are produced taking normal instance is classified correctly applying slight perturbation cause misclassified even misclassified specific target label chosen adversary phenomenon which has been shown affect state-of-the-art networks poses significant hindrance deploying neural networks safety-critical settings.Many effective techniques have been proposed generating adversarial examples BID20;BID17;BID1;BID21;conversely several techniques have been proposed training networks are are more robust examples BID8;BID22 BID6;BID7;BID16;BID21. Unfortunately has proven difficult accurately assess robustness given defense evaluating existing techniques generating adversarial examples. several cases defensive technique was at first thought produce robust networks was later shown susceptible new kinds attacks BID2. ongoing cycle thus cast doubt newly-proposed defensive technique.In recent years new techniques have been proposed formal verification neural networks BID18 BID19;BID12;BID9;BID3. techniques take network desired property formally prove network satisfies property -or provide input which the property is violated if such an input exists. Specifically given input point allowed amount distortion given metric verification can be used finding adversarial example soundly proving examples exist within allowed distortion. verification tends significantly slower finding adversarial examples aforementioned heuristic-based techniques BID19;BID11 BID0 can provide much-needed rigor assessing adversarial robustness neural networks.In paper propose method using formal verification assess effectiveness techniques producing adversarial examples defending them. key idea is to examine networks apply verification identify ground-truth adversarial examples. Formally given neural networkF distance metric inputx say another inputx is a ground-truth adversarial example x if it is the nearest point respect metric F assigns different labels x x. follows points whose distance x is smaller distance x x are assigned label x. distance ground truth is thus indication how robust network is to adversarial attacks pointx. Ground truths can serve multiple purposes:if ground-truth adversarial examples are known set points drawn meaningful distribution thought represent real-world inputs can serve estimate robustness network whole possible attack;ii can be used assessing attack techniques measuring proximity adversarial examples attacks produce ground truths;iii can be used assessing effectiveness defense techniques computing new ground truths hardened network comparing ground truths original network.Our contributions can thus summarized follows:• suggest use ground-truth adversarial examples provably closest adversarial respect distance metric tool studying attacks defenses.• find first-order attack algorithms often produce near-optimal results.e results are close ground-truth adversarial example.• study adversarial training find does increase robustness does not overfit specific attack long attack is iterative.The rest paper is organized follows. Section2 provide necessary background. describe experiments conducted Section3 analyze results Section4. Finally conclude Section5. Neural networks hold great potential controllers safety-critical systems susceptibility adversarial examples poses significant hindrance. development defensive techniques is difficult when they are measured existing attacks. burgeoning field neural network verification can mitigate problem allowingus obtain absolute measurement usefulness defense regardless attack used it.In paper introduce ground-truth adversarial examples show how to construct formal verification approaches. evaluate one recent attack BID1 find often produces adversarial examples whose distance is within within 5.9 12.9 optimal one defense BID16 find increases distortion nearest adversarial example average 427% MNIST dataset tested networks. best knowledge is the first proof robustness increase defense.Currently available verification tools afford limited scalability which means experiments can only be conducted small networks. However better verification techniques are developed limitation is expected mitigated. Orthogonally when preparing use neural network safetycritical setting users may choose design networks make particularly amenable verification techniques-e.g using specific activation functions network topologies -so strong guarantees correctness robustness may obtained.,1316,896,420,0.015,1.469,2025/11/05 17:19:04,0.01,1.481,0.4330218068535826,429.619
"This paper introduces a new framework for open-domain question answering in which the retriever and the reader \emph{iteratively interact} with each other. The framework is agnostic to the architecture of the machine reading model provided it has \emph{access} to the token-level hidden representations of the reader. The retriever uses fast nearest neighbor search that allows it to scale to corpora containing millions of paragraphs. A gated recurrent unit updates the query at each step conditioned on the \emph{state} of the reader and the \emph{reformulated} query is used to re-rank the paragraphs by the retriever. We conduct analysis and show that iterative interaction helps in retrieving informative paragraphs from the corpus. Finally, we show that our multi-step-reasoning framework brings consistent improvement when applied to two widely used reader architectures (\drqa and \bidaf) on various large open-domain datasets ---\tqau, \quasart, \searchqa, and \squado\footnote{Code and pretrained models are available at \url{https://github.com/rajarshd/Multi-Step-Reasoning}}. Open-domain question answering (QA) BID40 involves a retriever for selecting relevant context from a large corpora of text (e.g. Wikipedia) and a machine reading comprehension (MRC) model for 'reasoning' on the retrieved context. A lot of effort has been put into designing sophisticated neural MRC architectures for reading short context (e.g. a single paragraph), with much success BID41 BID35 BID46 BID44 Yu et al., 2018, inter alia) . However, the performance of such systems degrades significantly when combined with a retriever in open domain settings. For example, the exact match accuracy of DrQA , on the SQUAD dataset BID33 degrades from 69.5% to 28.4% in open-domain settings. The primary reason for this degradation in performance is due to the retriever's failure to find the relevant paragraphs for the machine reading model BID18 .We propose the following two desiderata for a general purpose open-domain QA system -(a) The retriever model should be fast, since it has to find the relevant context from a very large text corpora and give it to the more sophisticated and computationally expensive MRC model (b) Secondly, the retriever and reader models should be interactive, i.e. if the reader model is unable to find the answer from the initial retrieved context, the retriever should be able to learn to provide more relevant context to the reader. Open-domain QA systems such as R 3 BID42 and DS-QA BID25 have sophisticated retriever models where the reader and retriever are jointly trained. However, their retriever computes question-dependent paragraph representation which is then encoded by running an expensive recurrent neural network over the tokens in the paragraph. Since the retriever has to rank a lot of paragraphs, this design does not scale to large corporas. One the other hand, the retriever model of QA systems such as DrQA ) is based on a tf-idf retriever, but they lack trainable parameters and are consequently unable to recover from mistakes. This paper introduces an open domain architecture in which the retriever and reader iteratively interact with each other. Our model first pre-computes and caches representation of context (paragraph). These representations are independent of the query unlike recent architectures BID42 This paper introduces a new framework for open-domain question answering in which the retriever and the reader iteratively interact with each other. The resulting framework improved performance of machine reading over the base reader model uniformly across four open-domain QA datasets. We also show that our fast retrieval method can scale upto millions of paragraphs, much beyond the current capability of existing open-domain systems with a trained retriever module. Finally, we show that our method is agnostic to the architecture of the machine reading system provided we have access to the token level hidden representations of the reader. Our method brings an increase in performance to two popular and widely used neural machine reading architectures, Dr.QA and BiDAF.",paper introduces new framework open-domain question answering which the retriever reader \emph iteratively interact other. framework is agnostic architecture machine reading model provided has \emph access token-level hidden representations reader. retriever uses fast nearest neighbor search allows scale corpora containing millions paragraphs. gated recurrent unit updates query step conditioned \emph state reader \emph reformulated query is used re-rank paragraphs retriever. conduct analysis show iterative interaction helps retrieving informative paragraphs corpus. Finally show multi-step-reasoning framework brings consistent improvement when applied two widely used reader architectures \drqa \bidaf various large open-domain datasets - \tqau \quasart \searchqa \squado\footnote Code pretrained models are available \url https://github.com/rajarshd/Multi-Step-Reasoning Open-domain question answering QA BID40 involves retriever selecting relevant context large corpora text e.g Wikipedia machine reading comprehension MRC model 'reasoning' retrieved context. lot effort has been put designing sophisticated neural MRC architectures reading short context e.g single paragraph much success BID41 BID35 BID46 BID44Yuet al. 2018 inter alia However performance systems degrades significantly when combined retriever open domain settings. example exact match accuracy DrQA SQUAD dataset BID33 degrades 69.5 28.4 open-domain settings. primary reason degradation performance is due retriever's failure find relevant paragraphs machine reading model BID18.We propose following two desiderata general purpose open-domainQA system retriever model should be fast since has to find relevant context large text corpora give sophisticated computationally expensive MRC model b Secondly retriever reader models should be interactive.e if the reader model is unable find answer initial retrieved context retriever should be able learn provide relevant context reader. Open-domain QA systems R 3 BID42 DS-QA BID25 have sophisticated retriever models where the reader retriever are jointly trained. However retriever computes question-dependent paragraph representation which is then encoded running expensive recurrent neural network tokens paragraph. Since retriever has to rank lot paragraphs design does not scale large corporas. One hand retriever model QA systems DrQA is based tf-idf retriever lack trainable parameters are consequently unable recover mistakes. paper introduces open domain architecture which the retriever reader iteratively interact other. model first pre-computes caches representation context paragraph representations are independent query unlike recent architectures BID42 paper introduces new framework open-domain question answering which the retriever reader iteratively interact other. resulting framework improved performance machine reading base reader model uniformly across four open-domainQA datasets. also show fast retrieval method can scale upto millions paragraphs much beyond current capability existing open-domain systems trained retriever module. Finally show method is agnostic architecture machine reading system provided have access token level hidden representations reader. method brings increase performance two popular widely used neural machine reading architectures Dr.QA BiDAF.,837,580,257,0.008,1.443,2025/11/05 17:19:04,0.0,1.462,0.35202492211838,274.24
"Many imaging tasks require global information about all pixels in an image. Conventional bottom-up classification networks globalize information by decreasing resolution; features are pooled and down-sampled into a single output. But for semantic segmentation and object detection tasks, a network must provide higher-resolution pixel-level outputs. To globalize information while preserving resolution, many researchers propose the inclusion of sophisticated auxiliary blocks, but these come at the cost of a considerable increase in network size and computational cost. This paper proposes stacked u-nets (SUNets), which iteratively combine features from different resolution scales while maintaining resolution. SUNets leverage the information globalization power of u-nets in a deeper net- work architectures that is capable of handling the complexity of natural images. SUNets perform extremely well on semantic segmentation tasks using a small number of parameters.",Many imaging tasks require global information pixels image. Conventional bottom-up classification networks globalize information decreasing resolution;features are pooled down-sampled single output. semantic segmentation object detection tasks network must provide higher-resolution pixel-level outputs. globalize information preserving resolution many researchers propose inclusion sophisticated auxiliary blocks come cost considerable increase network size computational cost. paper proposes stacked u-nets SUNets which iteratively combine features different resolution scales maintaining resolution. SUNets leverage information globalization power u-nets deeper net- work architectures is capable handling complexity natural images. SUNets perform extremely well semantic segmentation tasks using small number parameters.,160,117,43,0.002,1.368,2025/11/05 17:19:04,0.0,1.0,0.118380062305296,61.896
"Asking questions is an important ability for a chatbot. This paper focuses on question generation. Although there are existing works on question generation based on a piece of descriptive text, it remains to be a very challenging problem. In the paper, we propose a new question generation problem, which also requires the input of a target topic in addition to a piece of descriptive text. The key reason for proposing the new problem is that in practical applications, we found that useful questions need to be targeted toward some relevant topics. One almost never asks a random question in a conversation. Due to the fact that given a descriptive text, it is often possible to ask many types of questions, generating a question without knowing what it is about is of limited use. To solve the problem, we propose a novel neural network that is able to generate topic-specific questions. One major advantage of this model is that it can be trained directly using a question-answering corpus without requiring any additional annotations like annotating topics in the questions or answers. Experimental results show that our model outperforms the state-of-the-art baseline. The goal of question generation is to generate questions according to some given information (e.g., a sentence or a paragraph). It has been applied in many scenarios, e.g., generating questions for reading comprehension BID8 and generating data for large scale question-answering training (Serban et al., 2016; BID7 . Since questioning is an important communication skill, question generation plays an important role in both general-purpose chatbot systems and goal-oriented dialogue systems. In the context of dialogue, many researchers have studied the problem BID15 BID1 . The generated questions are mainly used to start a conversation or to obtain some specific information.Earlier approaches to question generation mainly used human-crafted rules and patterns to transform a descriptive sentence to a related question BID14 BID2 . However, human-crafted rules are limited. They cannot effectively cover a large number of question generation scenarios. Deep neural networks learned by end-to-end methods can help overcome this problem. This approach has been successfully applied to many NLP tasks, e.g., neural machine translation BID0 BID19 , summarization BID9 , etc. At the same time, some training optimization studies have further guaranteed the performance and stability of end-to-end networks BID13 BID4 . For question generation, Serban et al. (2016) applied a neural network to the knowledge base Freebase to transduce facts to questions. introduced an attention-based sequence learning model, which outperformed state-of-the-art rule-based systems. Two approaches were proposed by BID7 . One is retrieval-based, and the other is generation-based. also studied question-worthy sentences in reading comprehension.Much of the existing question generation studies mainly focused on the task of generating questions from sentences, paragraph, or structured data only. In this paper, we argue that topic-based question generation is also very important. That is, in addition to the given sentence or paragraph, it is also useful to specify a relevant topic contained in the text. The main reason is that a sentence or paragraph often involves multiple topics or concepts that questions can be generated, only arbitrarily choose one or mixing them may be of limited use because we found that in practical applications, questions need to be targeted toward some topics related to the current conversation. One almost never asks a random question in a conversation. Generating a question without knowing what it is about is not very useful. To solve the proposed problem, we propose a novel neural network that can generate topic-based questions. One major advantage of our model is that it can be trained directly using a question-answering corpus without requiring any additional annotations like annotating the topics in the questions or answers. In summary, this paper makes the following contributions:• It proposes the new problem of question generation based on a given sentence and a topic (or concept) in the sentence. To our knowledge, this topic-based question generation has not been studied before. The model can also take a question type because for the same topic, different types of questions can be asked (see section 5.3).• It proposes a novel neural network model to solve the problem. A pre-decode mechanism is also explored to improve the model performance.• The proposed model can be directly trained using a normal question-answering corpus without requiring additional labeling of topics in each input sentence.• The proposed model is evaluated using the Amazon community question-answering corpus. Experimental results show that our model is effective. In this paper, we proposed the new task of topic-based question generation, which has not been investigated before. Based on our experiences, we believe this is a more useful question generation setting than the conventional setting without a given topic because a question without the knowledge of its topic is of limited use in actual conversations. We then proposed a novel network architecture to perform the task, and discussed its generalization ability. Experimental results showed that the proposed model performed slightly better than the state-of-the-art baseline in the conventional setting (although our model not designed for this setting), and performed markedly better in the proposed new setting.","Asking questions is an important ability chatbot. paper focuses question generation. Although are existing works question generation based piece descriptive text remains challenging problem. paper propose new question generation problem which is also requires input target topic addition piece descriptive text. key reason proposing new problem is that in practical applications found useful questions need targeted toward relevant topics. One almost never asks random question conversation. Due fact given descriptive text is often possible ask many types questions generating question without knowing what it is about isof limited use. solve problem propose novel neural network is able generate topic-specific questions. One major advantage model is that it can trained directly using question-answering corpus without requiring additional annotations like annotating topics questions answers. Experimental results show model outperforms state-of-the-art baseline. goal question generation is to generate questions according given information e.g sentence paragraph has applied many scenarios e.g generating questions reading comprehension BID8 generating data large scale question-answering training Serbanetal. 2016;BID7. Since questioning is an important communication skill question generation plays important role general-purpose chatbot systems goal-oriented dialogue systems. context dialogue many researchers have studied problem BID15 BID1. generated questions are mainly used start conversation obtain specific information.Earlier approaches question generation mainly used human-crafted rules patterns transform descriptive sentence related question BID14 BID2. However human-crafted rules are limited. cannot effectively cover large number question generation scenarios. Deep neural networks learned end-to-end methods can help overcome problem. approach has been successfully applied many NLP tasks e.g neural machine translation BID0 BID19 summarization BID9 etc. time training optimization studies have further guaranteed performance stability end-to-end networks BID13 BID4. question generation Serbanetal. 2016 has applied neural network knowledge base Freebase transduce facts questions. introduced attention-based sequence learning model which outperformed state-of-the-art rule-based systems. Two approaches were proposed BID7. One is retrieval-based is generation-based generation-based also studied question-worthy sentences reading comprehension.Much existing question generation studies mainly focused task generating questions sentences paragraph structured data only. paper argue topic-based question generation is also important. is,in addition given sentence paragraph which is also useful specify relevant topic contained text. main reason is that a sentence paragraph often involves multiple topics concepts questions can be generated arbitrarily choose one mixing may limited use found practical applications questions need targeted toward topics related current conversation. One almost never asks random question conversation. Generating question without knowing what it is about is not very useful. solve proposed problem propose novel neural network can generate topic-based questions. One major advantage model is that it can trained directly using question-answering corpus without requiring additional annotations like annotating topics questions answers. summary paper makes following contributions:• proposes new problem question generation based given sentence topic concept sentence. knowledge topic-based question generation has not been studied before. model can also take question type topic different types questions can be asked see section 5.3.• proposes novel neural network model solve problem. pre-decode mechanism is also explored improve model performance.• proposed model can be directly trained using normal question-answering corpus without requiring additional labeling topics input sentence.• proposed model is evaluated using Amazon community question-answering corpus. Experimental results show model is effective. paper proposed new task topic-based question generation which has not investigated before. Based experiences believe is a more useful question generation setting conventional setting without given topic question without knowledge topic is of limited use actual conversations. proposed novel network architecture perform task discussed generalization ability. Experimental results showed proposed model performed slightly better state-of-the-art baseline conventional setting although model designed setting performed markedly better proposed new setting.",1015,717,298,0.01,1.416,2025/11/05 17:19:04,0.0,1.865,0.2679127725856693,330.508
"Brain-Machine Interfaces (BMIs) have recently emerged as a clinically viable option
 to restore voluntary movements after paralysis. These devices are based on the
 ability to extract information about movement intent from neural signals recorded
 using multi-electrode arrays chronically implanted in the motor cortices of the
 brain. However, the inherent loss and turnover of recorded neurons requires repeated
 recalibrations of the interface, which can potentially alter the day-to-day
 user experience. The resulting need for continued user adaptation interferes with
 the natural, subconscious use of the BMI. Here, we introduce a new computational
 approach that decodes movement intent from a low-dimensional latent representation
 of the neural data. We implement various domain adaptation methods
 to stabilize the interface over significantly long times. This includes Canonical
 Correlation Analysis used to align the latent variables across days; this method
 requires prior point-to-point correspondence of the time series across domains.
 Alternatively, we match the empirical probability distributions of the latent variables
 across days through the minimization of their Kullback-Leibler divergence.
 These two methods provide a significant and comparable improvement in the performance
 of the interface. However, implementation of an Adversarial Domain
 Adaptation Network trained to match the empirical probability distribution of the
 residuals of the reconstructed neural signals outperforms the two methods based
 on latent variables, while requiring remarkably few data points to solve the domain
 adaptation problem. Individuals with tetraplegia due to spinal cord injury identify restoration of hand function as their highest priority BID1 . Over 50% of respondents with a C1-C4 injury would be willing to undergo brain surgery to restore grasp . Brain-Machine Interfaces (BMIs) aim to restore motor function by extracting movement intent from neural signals. Despite its great promise, current BMI technology has significant limitations. A BMI that maps neural activity in primary motor cortex (M1) onto motor intent commands should ideally provide a stable day-to-day user experience. However, the gradual alterations of the activity recorded by chronically implanted multi-electrode arrays, due to neuron turnover or electrode movement and failure BID4 , causes considerable variation in the actions produced by the BMI. This turnover may occur within a single day BID12 , and is estimated to be on the order of 40% over two weeks BID11 ). In the face of changing neural signals, performance can be maintained by daily retraining the interface, but this is not a viable solution as it requires the user to keep on adapting to a new interface BID0 .There is a high degree of correlation across the M1 neural signals. This redundancy implies that the dimensionality of the underlying motor command is much lower than the number of M1 neurons, and even lower than the number of recorded M1 neurons BID15 . The use of dimen-sionality reduction methods is thus a common practice in BMI design, as it provides a more compact and denoised representation of neural activity, and a low-dimensional predictor of movement intent. Most of the earlier work used linear dimensionality reduction methods such as Principal Components Analysis (PCA) and Factor Analysis (FA) BID35 BID30 BID29 BID15 ; more recently, autoencoders (AEs) have been used for the nonlinear dimensionality reduction of neural signals BID27 . Here we develop a deep learning architecture to extract a low-dimensional representation of recorded M1 activity constrained to include features related to movement intent. This is achieved by the simultaneous training of a deep, nonlinear autoencoder network based on neural signals from M1, and a network that predicts movement intent from the inferred low-dimensional signals. We show that this architecture significantly improves predictions over the standard sequential approach of first extracting a low-dimensional, latent representation of neural signals, followed by training a movement predictor based on the latent signals.To stabilize the resulting BMI against continuous changes in the neural recordings, we introduce a novel approach based on the Generative Adversarial Network (GAN) architecture BID17 . This new approach, the Adversarial Domain Adaptation Network (ADAN), focuses on the probability distribution function (PDF) of the residuals of the reconstructed neural signals to align the residual's PDF at a later day to the PDF of the first day the BMI was calculated. The alignment of residual PDFs results in the alignment of the PDFs of the neural data and of their latent representation across multiple days. We show that this method results in a significantly more stable performance of the BMI over time than the stability achieved using several other domain adaptation methods. The use of an ADAN thus results in a BMI that remains stable and consistent to the user over long periods of time. A successful domain adaptation of the neural data eliminates the need for frequent recalibration of the BMI, which remains fixed. This strategy is expected to alleviate the cognitive burden on the user, who would no longer need to learn novel strategies to compensate for a changing interface. We address the problem of stabilizing a fixed Brain-Machine Interface against performance deterioration due to the loss and turnover of recorded neural signals. We introduce a new approach to extracting a low-dimensional latent representation of the neural signals while simultaneously inferring movement intent. We then implement various domain adaption methods to stabilize the latent representation over time, including Canonical Correlation Analysis and the minimization of a Kullback-Leibler divergence. These two methods provide comparable improvement in the performance of the interface. We find that an Adversarial Domain Adaptation Network trained to match the empirical probability distribution of the residuals of the reconstructed neural recordings restores the latent representation of neural trajectories and outperforms the two methods based on latent variables, while requiring remarkably little data to solve the domain adaptation problem. In addition, ADAN solves the domain adaptation problem in a manner that is not task specific, and thus is potentially applicable to unconstrained movements.Here we report on improvements in interface stability obtained offline, without a user in the loop. Online, closed-loop performance is not particularly well correlated with offline accuracy; in an online evaluation of performance, the user's ability to adapt at an unknown rate and to an unknown extent to an imperfect BMI obscures the performance improvements obtained with domain adaptation. Although the open-loop performance improvement demonstrated here is encouraging, additional experiments, both open and closed-loop, with additional animals and involving additional tasks, are required to fully validate our results and to establish that the improvements demonstrated here facilitate the sustained use of a brain-machine interface.",Brain-Machine Interfaces BMIs have recently emerged clinically viable option restore voluntary movements paralysis. devices are based ability extract information movement intent neural signals recorded using multi-electrode arrays chronically implanted motor cortices brain. However inherent loss turnover recorded neurons requires repeated recalibrations interface which can potentially alter day-to-day user experience. resulting need continued user adaptation interferes natural subconscious use BMI. introduce new computational approach decodes movement intent low-dimensional latent representation neural data. implement various domain adaptation methods stabilize interface significantly long times. includes Canonical Correlation Analysis used align latent variables across days;method requires prior point-to-point correspondence time series across domains. Alternatively match empirical probability distributions latent variables across days minimization Kullback-Leibler divergence. two methods provide significant comparable improvement performance interface. However implementation Adversarial Domain Adaptation Network trained match empirical probability distribution residuals reconstructed neural signals outperforms two methods based latent variables requiring remarkably data points solve domain adaptation problem. Individuals tetraplegia due spinal cord injury identify restoration hand function highest priority BID1. 50% respondents C1-C4 injury would willing undergo brain surgery restore grasp. Brain-Machine Interfaces BMIs aim restore motor function extracting movement intent neural signals. Despite great promise current BMI technology has significant limitations. BMI maps neural activity primary motor cortex M1 onto motor intent commands should ideally provide stable day-to-day user experience. However gradual alterations activity recorded chronically implanted multi-electrode arrays due neuron turnover electrode movement failure BID4 causes considerable variation actions produced BMI. turnover may occur within single day BID12 is estimated order 40% two weeks BID11 face changing neural signals performance can be maintained daily retraining interface is viable solution requires user keep adapting new interface BID0.There is a high degree correlation across M1 neural signals. redundancy implies dimensionality underlying motor command is much lower number M1 neurons even lower number recorded M1 neurons BID15. use dimen-sionality reduction methods is thus common practice BMI design provides compact denoised representation neural activity low-dimensional predictor movement intent. earlier work used linear dimensionality reduction methods Principal Components Analysis PCA Factor Analysis FA BID35 BID30 BID29 BID15;recently autoencoders AEs have been used nonlinear dimensionality reduction neural signals BID27. develop deep learning architecture extract low-dimensional representation recorded M1 activity constrained include features related movement intent. is achieved simultaneous training deep nonlinear autoencoder network based neural signals M1 network predicts movement intent inferred low-dimensional signals. show architecture significantly improves predictions standard sequential approach first extracting low-dimensional latent representation neural signals followed training movement predictor based latent signals.To stabilize resulting BMI continuous changes neural recordings introduce novel approach based Generative Adversarial Network GAN architecture BID17. new approach Adversarial Domain Adaptation Network ADAN focuses probability distribution function PDF residuals reconstructed neural signals align residual's PDF later day PDF first day BMI was calculated. alignment residual PDFs results alignment PDFs neural data latent representation across multiple days. show method results significantly stable performance BMI time stability achieved using several domain adaptation methods. use ADAN thus results BMI remains stable consistent user long periods time. successful domain adaptation neural data eliminates need frequent recalibration BMI which remains fixed. strategy is expected alleviate cognitive burden user would longer need learn novel strategies compensate changing interface. address problem stabilizing fixed Brain-Machine Interface performance deterioration due loss turnover recorded neural signals. introduce new approach extracting low-dimensional latent representation neural signals simultaneously inferring movement intent. implement various domain adaption methods stabilize latent representation time including Canonical Correlation Analysis minimization Kullback-Leibler divergence. two methods provide comparable improvement performance interface. find Adversarial Domain Adaptation Network trained match empirical probability distribution residuals reconstructed neural recordings restores latent representation neural trajectories outperforms two methods based latent variables requiring remarkably little data solve domain adaptation problem. addition ADAN solves domain adaptation problem manner is not task specific thus is potentially applicable unconstrained movements.Here report improvements interface stability obtained offline without user loop. Online closed-loop performance is not particularly well correlated offline accuracy;online evaluation performance user's ability adapt unknown rate unknown extent imperfect BMI obscures performance improvements obtained domain adaptation. Although open-loop performance improvement demonstrated is encouraging additional experiments open closed-loop additional animals involving additional tasks are required fully validate results establish improvements demonstrated facilitate sustained use brain-machine interface.,1292,851,441,0.013,1.518,2025/11/05 17:19:04,0.01,1.286,0.585669781931464,367.677
"Neural network-based systems can now learn to locate the referents of words and phrases in images, answer questions about visual scenes, and even execute symbolic instructions as first-person actors in partially-observable worlds. To achieve this so-called grounded language learning, models must overcome certain well-studied learning challenges that are also fundamental to infants learning their first words. While it is notable that models with no meaningful prior knowledge overcome these learning obstacles, AI researchers and practitioners currently lack a clear understanding of exactly how they do so. Here we address this question as a way of achieving a clearer general understanding of grounded language learning, both to inform future research and to improve confidence in model predictions. For maximum control and generality, we focus on a simple neural network-based language learning agent trained via policy-gradient methods to interpret synthetic linguistic instructions in a simulated 3D world. We apply experimental paradigms from developmental psychology to this agent, exploring the conditions under which established human biases and learning effects emerge. We further propose a novel way to visualise and analyse semantic representation in grounded language learning agents that yields a plausible computational account of the observed effects. The learning challenge faced by children acquiring their first words has long fascinated cognitive scientists and philosophers BID34 BID5 . To start making sense of language, an infant must induce structure in a constant stream of continuous visual input, slowly reconcile this structure with consistencies in the available linguistic observations, store this knowledge in memory, and apply it to inform decisions about how best to respond.Many neural network models also overcome a learning task that is -to varying degrees -analogous to early human word learning. Image classification tasks such as the ImageNet Challenge BID8 ) require models to induce discrete semantic classes, in many cases aligned to words, from unstructured pixel representations of large quantities of photographs BID20 . Visual question answering (VQA) systems BID0 BID41 BID42 ) must reconcile raw images with (arbitrary-length) sequences of symbols, in the form of natural language questions, in order to predict lexical or phrasal answers. Recently, situated language learning agents have been developed that learn to understand sequences of linguistic symbols not only in terms of the contemporaneous raw visual input, but also in terms of past visual input and the actions required to execute an appropriate motor response BID29 BID6 BID15 BID26 . The most advanced such agents learn to execute a range of phrasal and multi-task instructions, such as find the green object in the red room, pick up the pencil in the third room on the right or go to the small green torch, in a continous, simulated 3D world. To solve these tasks, an agent must execute sequences of hundreds of fine-grained actions, conditioned on the available sequence of language symbols and active (first-person) visual perception of the surroundings. Importantly, the knowledge acquired by such agents while mastering these tasks also permits the interpretation of familiar language in entirely novel surroundings, and the execution of novel instructions composed of combinations of familiar words BID6 BID15 .The potential impact of situated linguistic agents, VQA models and other grounded language learning systems is vast, as a basis for human users to interact with situated learning applications such as self-driving cars and domestic robotic tools. However , our understanding of how these agents learn and behave is limited. The challenges of interpreting the factors or reasoning behind the decisions and predictions of neural networks are well known. Indeed, a concerted body of research in both computer vision BID44 BID38 BID43 and natural language processing BID23 BID39 has focused on addressing this uncertainty. As grounded language learning agents become more prevalent, then, understanding their learning dynamics, representation and decision-making will become increasingly important, both to inform future research and to build confidence in users who interact with such models.We therefore aim to establish a better understanding of neural network-based models of grounded language learning, noting the parallels with research in neuroscience and psychology that aims to understand human language acquisition. Extending the approach of BID35 , we adapt various experimental techniques initially developed by experimental psychologists BID21 BID24 BID17 BID7 . In line with typical experiments on humans, our experimental simulations are conducted in a highly controlled environment: a simulated 3D world with a limited set of objects and properties, and corresponding unambiguous, symbolic linguistic stimuli (Figure 1) . However, the simplicity and generality of our architecture and the form of the inputs to the model (continuous visual plus symbolic linguistic) make the proposed methods and approach directly applicable to VQA and other tasks that combine linguistic and visual data. Using these methods, we explore how the training environment of our agent affects its learning outcomes and speed, measure the generality and robustness of its understanding of certain fundamental linguistic concepts, and test for biases in the decisions it takes once trained. Further, by applying layerwise attention , a novel tool for visualising computation in grounded language learning models, we obtain a plausible algorithmic account of some of the effects in terms of representation and processing. Our principal findings about this canonical grounded language learning architecture are the following:Shape / colour biases When the agent is trained on an equal number of shape and colour words, it develops a propensity to extend labels for ambiguous new words according to colour rather than shape (color bias). A human-like bias towards shapes can be induced in the agent, but only if it experiences many more shape terms than colour terms during training.The problem of learning negation The agent learns to execute negated instructions, but if trained on small amounts of data it tends to represent negation in an ad hoc way that does not generalise.Curriculum effects for vocabulary growth The agent learns words more quickly if the range of words to which it is exposed is limited at first and expanded gradually as its vocabulary develops.Semantic processing and representation differences The agent learns words of different semantic classes at different speeds and represents them with features that require different degrees of visual processing depth (or abstraction) to compute.Before describing the experiments that reveal these effects, we briefly outline details of the environment and agent used for the simulations. Models that are capable of grounded language learning promise to significantly advance the ways in which humans and intelligent technology can interact. In this study, we have explored how a situated language learning agent built from canonical neural-network components overcomes the challenge of early language learning. We measured the behaviour exhibited once the first words and simple phrases are acquired, tested factors that speed up this learning, explored aspects of language that pose particular problems and presented a technique, layerwise attention, for better understanding semantic and visual processing in such agents.The application of experimental paradigms from cognitive psychology to better understand deep neural nets was proposed by BID35 , who observed that convolutional architectures exhibit a shape bias when trained on the ImageNet Challenge data. The ability to control precisely both training and test stimuli in our simulated environment allowed us to isolate this effect as deriving from the training data, and indeed to reach the opposite conclusion about the architecture itself. This study also goes beyond that of BID35 in exploring more abstract linguistic operations (negation, abstract category terms) and studying curriculum effects on the dynamics of word learning. Further, we complement these behavioural observations with computatoinal analysis of representation and processing, via layerwise attention.While the control and precision afforded by the simulated environment in the present study has made these analyses and conclusions possible, in future, as our understanding of language learning agents develops, it will be essential to verify conclusions on agents trained on more naturalistic data. At first, this might involve curated sets of images, videos and naturally-occurring text etc, and, ultimately, experiments on robots trained to communicate about perceptible surroundings with human interlocutors. In a world with agents capable of learning such advanced linguistic behaviour, it would certainly be more challenging, but also even more crucial, to understand not just what they can do, but also how they learn to do it. 6 SUPPLEMENTARY MATERIAL","Neural network-based systems can now learn locate referents words phrases images answer questions visual scenes even execute symbolic instructions first-person actors partially-observable worlds. achieve so-called grounded language learning models must overcome certain well-studied learning challenges are also fundamental infants learning first words. is notable models meaningful prior knowledge overcome learning obstacles AI researchers practitioners currently lack clear understanding exactly how theydoso. address question way achieving clearer general understanding grounded language learning inform future research improve confidence model predictions. maximum control generality focus simple neural network-based language learning agent trained via policy-gradient methods interpret synthetic linguistic instructions simulated 3D world. apply experimental paradigms developmental psychology agent exploring conditions which established human biases learning effects emerge. propose novel way visualise analyse semantic representation grounded language learning agents yields plausible computational account observed effects. learning challenge faced children acquiring first words has long fascinated cognitive scientists philosophers BID34 BID5. start making sense language infant must induce structure constant stream continuous visual input slowly reconcile structure consistencies available linguistic observations store knowledge memory apply inform decisions how best respond.Many neural network models also overcome learning task is -to varying degrees -analogous early human word learning. Image classification tasks ImageNet Challenge BID8 require models induce discrete semantic classes many cases aligned words unstructured pixel representations large quantities photographs BID20. Visual question answering VQA systems BID0 BID41 BID42 must reconcile raw images arbitrary-length sequences symbols form natural language questions order predict lexical phrasal answers. Recently situated language learning agents have been developed learn understand sequences linguistic symbols terms contemporaneous raw visual input also terms past visual input actions required execute appropriate motor response BID29 BID6 BID15 BID26. advanced agents learn execute range phrasal multi-task instructions find green object red room pick pencil third room right go small green torch continous simulated 3D world. solve tasks agent must execute sequences hundreds fine-grained actions conditioned available sequence language symbols active first-person visual perception surroundings. Importantly knowledge acquired agents mastering tasks also permits interpretation familiar language entirely novel surroundings execution novel instructions composed combinations familiar words BID6 BID15.The potential impact situated linguistic agents VQA models grounded language learning systems is vast basis human users interact situated learning applications self-driving cars domestic robotic tools. However understanding how these agents learn behave is limited. challenges interpreting factors reasoning behind decisions predictions neural networks are well known. Indeed concerted body research computer vision BID44 BID38 BID43 natural language processing BID23 BID39 has focused addressing uncertainty. grounded language learning agents become prevalent understanding learning dynamics representation decision-making will become increasingly important inform future research build confidence users who interact models.We therefore aim establish better understanding neural network-based models grounded language learning noting parallels research neuroscience psychology aims understand human language acquisition. Extending approach BID35 adapt various experimental techniques initially developed experimental psychologists BID21 BID24 BID17 BID7. line typical experiments humans experimental simulations are conducted highly controlled environment:simulated 3D world limited set objects properties corresponding unambiguous symbolic linguistic stimuli Figure1 However simplicity generality architecture form inputs model continuous visual plus symbolic linguistic make proposed methods approach directly applicable VQA tasks combine linguistic visual data. Using methods explore how the training environment agent affects learning outcomes speed measure generality robustness understanding certain fundamental linguistic concepts test biases decisions takes trained. applying layerwise attention novel tool visualising computation grounded language learning models obtain plausible algorithmic account effects terms representation processing. principal findings canonical grounded language learning architecture are the following:Shape/colour biases When the agent is trained equal number shape colour words develops propensity extend labels ambiguous new words according colour rather shape color bias human-like bias towards shapes can be induced agent if experiences many shape terms colour terms training.The problem learning negation agent learns execute negated instructions if trained small amounts data tends represent negation ad hoc way does not generalise.Curriculum effects vocabulary growth agent learns words quickly if the range words which it is exposed is limited first expanded gradually vocabulary develops.Semantic processing representation differences agent learns words different semantic classes different speeds represents features require different degrees visual processing depth abstraction compute.Before describing experiments reveal effects briefly outline details environment agent used simulations. Models are capable grounded language learning promise significantly advance ways which humans intelligent technology can interact. study have explored how a situated language learning agent built canonical neural-network components overcomes challenge early language learning. measured behaviour exhibited first words simple phrases are acquired tested factors speed learning have explored aspects language pose particular problems presented technique layerwise attention better understanding semantic visual processing agents.The application experimental paradigms cognitive psychology better understand deep neural nets was proposed BID35 who observed convolutional architectures exhibit shape bias when trained ImageNet Challenge data. ability control precisely training test stimuli simulated environment allowedus isolate effect deriving training data indeed reach opposite conclusion architecture itself. study also goes beyond BID35 exploring abstract linguistic operations negation abstract category terms studying curriculum effects dynamics word learning. complement behavioural observations computatoinal analysis representation processing via layerwise attention.While control precision afforded simulated environment present study has made analyses conclusions possible future understanding language learning agents develops will be essential verify conclusions agents trained naturalistic data. first might involve curated sets images videos naturally-occurring text etc ultimately experiments robots trained communicate perceptible surroundings human interlocutors. world agents capable learning advanced linguistic behaviour would certainly challenging also even crucial understand what they can do,but also how they learn it. 6 SUPPLEMENTARY MATERIAL",1589,1050,539,0.018,1.513,2025/11/05 17:19:04,0.01,1.488,0.5700934579439247,530.736
"Humans easily recognize object parts and their hierarchical structure by watching how they move; they can then predict how each part moves in the future. In this paper, we propose a novel formulation that simultaneously learns a hierarchical, disentangled object representation and a dynamics model for object parts from unlabeled videos. Our Parts, Structure, and Dynamics (PSD) model learns to, first, recognize the object parts via a layered image representation; second, predict hierarchy via a structural descriptor that composes low-level concepts into a hierarchical structure; and third, model the system dynamics by predicting the future. Experiments on multiple real and synthetic datasets demonstrate that our PSD model works well on all three tasks: segmenting object parts, building their hierarchical structure, and capturing their motion distributions. What makes an object an object? Researchers in cognitive science have made profound investigations into this fundamental problem; results suggest that humans, even young infants, recognize objects as continuous, integrated regions that move together BID6 BID52 . Watching objects move, infants gradually build the internal notion of objects in their mind. The whole process requires little external supervision from experts.Motion gives us not only the concept of objects and parts, but also their hierarchical structure. The classic study from BID27 reveals that humans recognize the structure of a human body from a few moving dots representing the keypoints on a human skeleton. This connects to the classic Gestalt theory in psychology BID31 , which argues that human perception is holistic and generative, explaining scenes as a whole instead of in isolation. In addition to being unsupervised and hierarchical, our perception gives us concepts that are fully interpretable and disentangled. With an object-based representation, we are able to reason about object motion, predict what is going to happen in the near future, and imagine counterfactuals like ""what happens if?"" BID52 How can we build machines of such competency? Would that be possible to have an artificial system that learns an interpretable, hierarchical representation with system dynamics, purely from raw visual data with no human annotations? Recent research in unsupervised and generative deep representation learning has been making progress along this direction: there have been models that efficiently explain multiple objects in a scene BID24 , some simultaneously learning an interpretable representation BID9 . Most existing models however either do not produce a structured, hierarchical object representation, or do not characterize system dynamics.In this paper, we propose a novel formulation that learns an interpretable, hierarchical object representation and scene dynamics by predicting the future. Our model requires no human annotations, learning purely from unlabeled videos of paired frames. During training, the model sees videos of objects moving; during testing, it learns to recognize and segment each object and its parts, build their hierarchical structure, and model their motion distribution for future frame synthesis, all from a single image. Figure 1: Observing human moving, humans are able to perceive disentangled object parts, understand their hierarchical structure, and capture their corresponding motion fields (without any annotations).Our model, named Parts, Structure, and Dynamics (PSD), learns to recognize the object parts via a layered image representation. PSD learns their hierarchy via a structural descriptor that composes low-level concepts into a hierarchical structure. Formulated as a fully differentiable module, the structural descriptor can be end-to-end trained within a neural network. PSD learns to model the system dynamics by predicting the future.We evaluate our model in many possible ways. On real and synthetic datasets, we first examine its ability in learning the concept of objects and segmenting them. We then compute the likelihood that it correctly captures the hierarchical structure in the data. We finally validate how well it characterizes object motion distribution and predicts the future. Our system works well on all these tasks, with minimal input requirement (two frames during training, and one during testing). While previous state-of-the-art methods that jointly discover objects, relations, and predict future frames only work on binary images of shapes and digits, our PSD model works well on complex real-world RGB images and requires fewer input frames. We have presented a novel formulation that simultaneously discovers object parts, their hierarchical structure, and the system dynamics from unlabeled videos. Our model uses a layered image representation to discover basic concepts and a structural descriptor to compose them. Experiments suggest that it works well on both real and synthetic datasets for part segmentation, hierarchical structure recovery, and motion prediction. We hope our work will inspire future research along the direction of learning structural object representations from raw sensory inputs.",Humans easily recognize object parts hierarchical structure watching how they move;can then predict how each part moves future. paper propose novel formulation simultaneously learns hierarchical disentangled object representation dynamics model object parts unlabeled videos. Parts Structure Dynamics PSD model learns first recognize object parts via layered image representation;second predict hierarchy via structural descriptor composes low-level concepts hierarchical structure;third model system dynamics predicting future. Experiments multiple real synthetic datasets demonstrate PSD model works well three tasks:segmenting object parts building hierarchical structure capturing motion distributions. What makes object object? Researchers cognitive science have made profound investigations fundamental problem;results suggest humans even young infants recognize objects continuous integrated regions move together BID6 BID52. Watching objects move infants gradually build internal notion objects mind. whole process requires little external supervision experts.Motion givesus concept objects parts also hierarchical structure. classic study BID27 reveals humans recognize structure human body moving dots representing keypoints human skeleton. connects classic Gestalt theory psychology BID31 which argues human perception is holistic generative explaining scenes whole instead isolation. addition unsupervised hierarchical perception gives us concepts are fully interpretable disentangled. object-based representation are able reason object motion predict what is going happen near future imagine counterfactuals like what happens if? BID52 How can we build machines competency? Would possible have an artificial system learns interpretable hierarchical representation system dynamics purely raw visual data human annotations? Recent research unsupervised generative deep representation learning has been making progress along direction:have been models efficiently explain multiple objects scene BID24 simultaneously learning interpretable representation BID9. existing models however either do not produce structured hierarchical object representation do not characterize system dynamics.In paper propose novel formulation learns interpretable hierarchical object representation scene dynamics predicting future. model requires human annotations learning purely unlabeled videos paired frames. training model sees videos objects moving;testing learns recognize segment object parts build hierarchical structure model motion distribution future frame synthesis single image. Figure1:Observing human moving humans are able perceive disentangled object parts understand hierarchical structure capture corresponding motion fields without annotations.Our model named Parts Structure Dynamics PSD learns recognize object parts via layered image representation. PSD learns hierarchy via structural descriptor composes low-level concepts hierarchical structure. Formulated fully differentiable module structural descriptor can be end-to-end trained within neural network. PSD learns model system dynamics predicting future.We evaluate model many possible ways. real synthetic datasets first examine ability learning concept objects segmenting them. compute likelihood correctly captures hierarchical structure data. finally validate how well characterizes object motion distribution predicts future. system works well tasks minimal input requirement two frames training one testing previous state-of-the-art methods jointly discover objects relations predict future frames work binary images shapes digits PSD model works well complex real-world RGB images requires fewer input frames. have presented novel formulation simultaneously discovers object parts hierarchical structure system dynamics unlabeled videos. model uses layered image representation discover basic concepts structural descriptor compose them. Experiments suggest works well real synthetic datasets part segmentation hierarchical structure recovery motion prediction. hope work will inspire future research along direction learning structural object representations raw sensory inputs.,898,601,297,0.01,1.494,2025/11/05 17:19:04,0.0,1.545,0.5109034267912771,300.887
"A successful application of convolutional architectures is to increase the resolution of single low-resolution images -- a image restoration task called super-resolution (SR). Naturally, SR is of value to resource constrained devices like mobile phones, electronic photograph frames and televisions to enhance image quality. However, SR demands perhaps the most extreme amounts of memory and compute operations of any mainstream vision task known today, preventing SR from being deployed to devices that require them. In this paper, we perform a early systematic study of system resource efficiency for SR, within the context of a variety of architectural and low-precision approaches originally developed for discriminative neural networks. We present a rich set of insights, representative SR architectures, and efficiency trade-offs; for example, the prioritization of ways to compress models to reach a specific memory and computation target and techniques to compact SR models so that they are suitable for DSPs and FPGAs. As a result of doing so, we manage to achieve better and comparable performance with previous models in the existing literature, highlighting the practicality of using existing efficiency techniques in SR tasks. Collectively, we believe these results provides the foundation for further research into the little explored area of resource efficiency for SR. Rapid progress has been made in the development of convolutional networks BID10 that are capable of taking a low-resolution image and producing an image with a significant increase in resolution. This image restoration task is referred to as super-resolution (SR) and has many potential applications in devices with limited memory and compute capacity. The fundamental problem however is that the state-of-the-art networks consist of thousands of layers and are some of the most resource intensive networks currently known. Furthermore, due to the spatial dimensions of feature maps needed to maintain or up-scale the input, the number of operations are counted in the billions as opposed to millions in models for discriminative tasks. As a result, there is a need for a general systematic approach to improve the efficiency of SR models.The challenge of the system resource requirements for deep learning models for tasks other than SR have been carefully studied in previous works BID62 BID40 BID48 , achieving massive gains in size and compute with little to no loss in performance. These reductions are achieved with a wide variety of methods being developed grounded in primarily architecture-level changes and techniques grounded in the use of low precision and quantized model parameters. However, how these efficiency methods behave when applied within SR have not yet been studied in significant depth, with very few results published in the literature. Extrapolating from prior results for other tasks is problematic given that predominantly existing studies are applied to discriminative tasks with substantially different architectures and operations. Due to the up-sampling structure of SR models, these efficiency methods may therefore produce potentially stronger side-effects to image distortion.In this paper, we detail a systematic study that seeks to bridge current understanding in SR and known approaches for scaling down the consumption of system resources by deep models. By examining the impact on image distortion quality when performing various efficiency techniques, we provide the following new insights:• The effectiveness of low rank tensor decomposition and other convolution approximations, which are comparable and successful in discriminative tasks, can vary considerably in SR.(See section 4.1).• Unlike image discriminative networks, SR networks suffer from a worse trade-off between efficiency and performance as more layers are compressed. (See section 4.2)• The practicality of adopting compression techniques for other tasks to SR as our best models are better or comparable to existing literature. For instance , our best model achieves significantly better performance and 6x less compute than MemNet BID51 and VDSR BID27 . Additionally , it also performs better and is 4.1x-5.8x smaller than SRMDNF BID61 . (See section 4.3)• Successful quantization techniques used in image discriminative tasks are equally successful in SR. (See section 5)",successful application convolutional architectures is to increase resolution single low-resolution images image restoration task called super-resolution SR Naturally SR is of value resource constrained devices like mobile phones electronic photograph frames televisions enhance image quality. However SR demands perhaps extreme amounts memory compute operations mainstream vision task known today preventingSR deployed devices require them. paper perform early systematic study system resource efficiency SR within context variety architectural low-precision approaches originally developed discriminative neural networks. present rich set insights representative SR architectures how these efficiency trade-offs example prioritization ways compress models reach specific memory computation target techniques compact SR models are suitable DSPs FPGAs. result manage achieve better comparable performance previous models existing literature highlighting practicality using existing efficiency techniques SR tasks. Collectively believe results provides foundation research little explored area resource efficiency SR. Rapid progress has been made development convolutional networks BID10 are capable taking low-resolution image producing image significant increase resolution. image restoration task is referred super-resolution SR has many potential applications devices limited memory compute capacity. fundamental problem however is that the state-of-the-art networks consist thousands layers are someof resource intensive networks currently known. Furthermore due spatial dimensions feature maps needed maintain up-scale input number operations are counted billions opposed millions models discriminative tasks. result is a need general systematic approach improve efficiency SR models.The challenge system resource requirements deep learning models tasks SR have been carefully studied previous works BID62 BID40 BID48 achieving massive gains size compute little loss performance. reductions are achieved wide variety methods developed grounded primarily architecture-level changes techniques grounded use low precision quantized model parameters. However how these efficiency methods behave when applied withinSR have not yet studied significant depth results published literature. Extrapolating prior results tasks is problematic given predominantly existing studies are applied discriminative tasks substantially different architectures operations. Due up-sampling structure SR models how these efficiency methods may therefore produce potentially stronger side-effects image distortion.In paper detail systematic study seeks bridge current understanding SR known approaches scaling consumption system resources deep models. examining impact image distortion quality when performing various efficiency techniques provide following new insights:• effectiveness low rank tensor decomposition convolution approximations which are comparable successful discriminative tasks can vary considerably SR. See section 4.1.• Unlike image discriminative networks SR networks suffer worse trade-off efficiency performance layers are compressed. See section 4.2 • practicality adopting compression techniques tasks SR best models are better comparable existing literature. instance best model achieves significantly better performance 6x less compute MemNet BID51 VDSR BID27. Additionally also performs better is 4.1x-5.8x smaller SRMDNF BID61. See section 4.3 • Successful quantization techniques used image discriminative tasks are equally successful SR. See section5,779,534,245,0.008,1.459,2025/11/05 17:19:04,0.0,1.48,0.4018691588785047,279.645
"Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we show that deep ReLU networks are biased towards low frequency functions, meaning that they cannot have local fluctuations without affecting their global behavior. Intuitively, this property is in line with the observation that over-parameterized networks find simple patterns that generalize across data samples. We also investigate how the shape of the data manifold affects expressivity by showing evidence that learning high frequencies gets easier with increasing manifold complexity, and present a theoretical understanding of this behavior. Finally, we study the robustness of the frequency components with respect to parameter perturbation, to develop the intuition that the parameters must be finely tuned to express high frequency functions. While universal approximation properties of neural networks have been known since the early 90s (Hornik et al., 1989; BID6 Leshno et al., 1993; BID2 , recent research has shed light on the mechanisms underlying such expressivity (Montufar et al., 2014; Raghu et al., 2016; Poole et al., 2016) . At the same time, deep neural networks, despite being massively overparameterized, have been remarkably successful at generalizing to natural data. This fact is at odds with the traditional notions of model complexity and their empirically demonstrated ability to fit arbitrary random data to perfect accuracy (Zhang et al., 2017a; BID1 . It has prompted the recent investigations of possible implicit regularization mechanisms inherent in the learning process, inducing biases towards low complexity solutions (Soudry et al., 2017; Poggio et al., 2018; Neyshabur et al., 2017) .In this work, our main goal is to expose one such bias by taking a closer look at neural networks through the lens of Fourier analysis 1 . We focus the discussion on ReLU networks, whose piecewise linear structure enables an analytic treatment. While they can approximate arbitrary functions, we find that these networks favour low frequency ones; in other words, they exhibit a bias towards smooth functions, a phenomenon we call the spectral bias 2 . We find that this bias manifests itself not just in the process of learning, but also in the parameterization of the model itself: in fact we show that the lower frequencies of trained networks are more robust with respect to random parameter perturbations. Finally , we also exhibit and analyze a rather intricate interplay between the spectral bias and the geometry of the data manifold: we show that high frequencies get easier to learn when the data lies on a lower dimensional manifold of complex shape embedded in the input space. CONTRIBUTIONS 1. We exploit the piecewise-linear structure of ReLU networks to evaluate and bound its Fourier spectrum.2. We demonstrate the peculiar behaviour of neural networks with illustrative and minimal experiments and find evidence of a spectral bias: i.e. lower frequencies are learned first. 1 The Fourier transform affords a natural way of measuring how fast a function can change within a small neighborhood in its input of a model. See Appendix B for a brief recap of Fourier analysis.2 A similar result has been independently found and reported in Xu et al. (2018). 3. We illustrate how the manifold hypothesis adds a layer of subtlety by showing how the geometry of the data manifold attenuates the spectral bias in a non-trivial way. We present a theoretical analysis of this phenomenon and derive conditions on the manifolds that facilitate learning higher frequencies.4. Given a trained network, we investigate the relative robustness of the lower frequencies with respect to random perturbations of the network parameters.The paper is organized as follows. In Section 2, we derive the Fourier spectrum of deep ReLU networks. Section 3 presents minimal experiments that demonstrate the spectral bias of ReLU networks. In Section 4, we study and discuss the role of the geometry of the data manifold. In Section 5, we empirically illustrate and theoretically explain our robustness result. We studied deep ReLU networks through the lens of Fourier analysis. Several conclusions can be drawn from our analysis. While neural networks can approximate arbitrary functions, we find that they favour low frequency ones -hence they exhibit a bias towards smooth functions -a phenomenon that we called spectral bias. We also illustrated how the geometry of the data manifold impacts expressivity in a non-trivial way, as high frequency functions defined on complex manifolds can be expressed by lower frequency network functions defined in input space. Finally, we found that the parameters contributing towards expressing lower frequencies are more robust to random perturbations than their higher frequency counterparts.We view future work that explore the properties of neural networks in Fourier domain as promising. For example, the Fourier transform affords a natural way of measuring how fast a function can change within a small neighborhood in its input domain ; as such, it is a strong candidate for quantifying and analyzing the sensitivity of a model -which in turn provides a natural measure of complexity (Novak et al., 2018) . We hope to encourage more research in this direction. We fit a 6 layer ReLU network with 256 units per layer f θ to the target function λ, which is a superposition of sine waves with increasing frequencies: DISPLAYFORM0 where k i = (5, 10, 15, ..., 50), and ϕ i is sampled from the uniform distribution U (0, 2π). In the first setting, we set equal amplitude for all frequencies, i.e. A i = 1 ∀ i, while in the second setting we assign larger amplitudes to the higher frequencies, i.e. A i = (0.1, 0.2, ..., 1). We sample λ on 200 uniformly spaced points in [0, 1] and train the network for 80000 steps of full-batch gradient descent with Adam (Kingma & Ba, 2014) . Note that we do not use stochastic gradient descent to avoid the stochasticity in parameter updates as a confounding factor. We evaluate the network on the same 200 point grid every 100 training steps and compute the magnitude of its (single-sided) discrete fourier transform at frequencies k i which we denote with |f ki |. Finally, we plot in figure 1 the normalized magnitudes |f k i | Ai averaged over 10 runs (with different sets of sampled phases ϕ i ). We also record the spectral norms of the weights at each layer as the training progresses, which we plot in figure 1 for both settings (the spectral norm is evaluated with 10 power iterations). In FIG10 , we show an example target function and the predictions of the network trained on it (over the iterations), and in figure 7 we plot the loss curves. The above theorem provides a recursive relation for computing the Fourier transform of an arbitrary polytope. More precisely, the Fourier transform of a m-dimensional polytope is expressed as a sum of fourier transforms over the m − 1 dimensional boundaries of the said polytope (which are themselves polytopes) times a O(k −1 ) weight term (with k = k ). The recursion terminates if Proj F (k) = 0, which then yields a constant.To structure this computation, BID8 introduce a book-keeping device called the face poset of the polytope. It can be understood as a weighted tree diagram with polytopes of various dimensions as its nodes. We start at the root node which is the full dimensional polytope P (i.e. we initially set m = n). For all of the codimension-one boundary faces F of P , we then draw an edge from the root P to node F and weight it with a term given by: DISPLAYFORM0 and repeat the process iteratively for each F . Note that the weight term is O(k −1 ) where Proj F (k) = 0. This process yields tree paths T : P → F 1 → ... → F q where each F i+1 ∈ ∂F i has one dimension less than F i . For a given path and k, the terminal node for this path, F q , is the first polytope for which Proj Fq (k) = 0. The final Fourier transform is obtained by multiplying the weights along each path and summing over all tree paths: DISPLAYFORM1 where we wrote F 0 = P . Together with Lemma 1, this gives the closed form expression of the Fourier transform of ReLU networks.For a generic vector k, all paths terminate at the zero-dimensional vertices of the original polytope, i.e. dim(F q ) = 0, implying the length of the path q equals the number of dimensions d, yielding a O(k −d ) spectrum. The exceptions occur if a path terminates prematurely, because k happens to lie orthogonal to some d − r-dimensional face F r in the path, in which case we are left with a O(k −r ) term (with r < d) which dominates asymptotically. Note that all vectors orthogonal to the d − r dimensional face F r lie on a r-dimensional subspace of R d . Since a polytope has a finite number of faces (of any dimension), the k's for which the Fourier transform is O(k −r ) (instead of O(k −d )) lies on a finite union of closed subspaces of dimension r (with r < d). The Lebesgue measure of all such lower dimensional subspaces for all such r is 0, leading us to the conclusion that the spectrum decays as O(k −d ) for almost all k's. We formalize this in the following corollary.Corollary 1. Let P be a full dimensional polytope in R n . The Fourier spectrum of its indicator function1 P satisfies the following: DISPLAYFORM2 where 1 ≤ ∆ k ≤ n, and ∆ k = j for k on a finite union of j-dimensional subspaces of R n .",Neural networks are known class highly expressive functions able fit even random input-output mappings 100% accuracy. work present properties neural networks complement aspect expressivity. using tools Fourier analysis show deep ReLU networks are biased towards low frequency functions meaning cannot have local fluctuations without affecting global behavior. Intuitively property is in line observation over-parameterized networks find simple patterns generalize across data samples. also investigate how the shape data manifold affects expressivity showing evidence learning high frequencies gets easier increasing manifold complexity present theoretical understanding behavior. Finally study robustness frequency components respect parameter perturbation develop intuition parameters must finely tuned express high frequency functions. universal approximation properties neural networks have been known since early 90s Horniketal. 1989;BID6 Leshnoetal. 1993;BID2 recent research has shed light mechanisms underlying expressivity Montufaretal. 2014;Raghuetal. 2016;Pooleetal. 2016 time deep neural networks despite massively overparameterized have been remarkably successful generalizing natural data. fact is at odds traditional notions model complexity empirically demonstrated ability fit arbitrary random data perfect accuracy Zhangetal. 2017a;BID1. has prompted recent investigations possible implicit regularization mechanisms inherent learning process inducing biases towards low complexity solutions Soudryetal. 2017;Poggioetal. 2018;Neyshaburetal. 2017.In work main goal is to expose one bias taking closer look neural networks lens Fourier analysis1. focus discussion ReLU networks whose piecewise linear structure enables analytic treatment. can approximate arbitrary functions find networks favour low frequency ones;words exhibit bias towards smooth functions phenomenon call spectral bias2. find bias manifests process learning also parameterization model itself:fact show lower frequencies trained networks are more robust respect random parameter perturbations. Finally also exhibit analyze rather intricate interplay spectral bias geometry data manifold:show high frequencies get easier learn when the data lies lower dimensional manifold complex shape embedded input space. CONTRIBUTIONS1. exploit piecewise-linear structure ReLU networks evaluate bound Fourier spectrum.2 demonstrate peculiar behaviour neural networks illustrative minimal experiments find evidence spectral bias:.e lower frequencies are learned first. 1 Fourier transform affords natural way measuring how fast function can change within small neighborhood input model. See AppendixB brief recap Fourier analysis.2 similar result has been independently found reported Xuetal. 2018 3. illustrate how the manifold hypothesis adds layer subtlety showing how the geometry data manifold attenuates spectral bias non-trivial way. present theoretical analysis phenomenon derive conditions manifolds facilitate learning higher frequencies.4 Given trained network investigate relative robustness lower frequencies respect random perturbations network parameters.The paper is organized follows. Section2 derive Fourier spectrum deep ReLU networks. Section 3 presents minimal experiments demonstrate spectral bias ReLU networks. Section4 study discuss role geometry data manifold. Section5 empirically illustrate theoretically explain robustness result. studied deep ReLU networks lens Fourier analysis. Several conclusions can be drawn analysis. neural networks can approximate arbitrary functions find favour low frequency ones -hence exhibit bias towards smooth functions -a phenomenon called spectral bias. also illustrated how the geometry data manifold impacts expressivity non-trivial way high frequency functions defined complex manifolds can be expressed lower frequency network functions defined input space. Finally found parameters contributing towards expressing lower frequencies are more robust random perturbations higher frequency counterparts.We view future work explore properties neural networks Fourier domain promising. example Fourier transform affords natural way measuring how fast function can change within small neighborhood input domain;isa strong candidate quantifying analyzing sensitivity model -which turn provides natural measure complexity Novaketal. 2018 hope encourage research direction. fit 6 layer ReLU network 256 units per layer fθ target functionλ which is a superposition sine waves increasing frequencies:DISPLAYFORM0 wherek 5 10 15... 50 ϕ is sampled uniform distributionU 0 2π first setting set equal amplitude frequencies.e 1∀ second setting assign larger amplitudes higher frequencies.e 0.1 0.2... 1 sampleλ 200 uniformly spaced points 0 1 train network 80000 steps full-batch gradient descent Adam Kingma Ba 2014 Note do not use stochastic gradient descent avoid stochasticity parameter updates confounding factor. evaluate network 200 point grid every 100 training steps compute magnitude single-sided discrete fourier transform frequenciesk which we denote |f ki |. Finally which we plot figure1 normalized magnitudes|fk Ai averaged 10 runs different sets sampled phasesϕ also record spectral norms weights layer training progresses which we plot figure1 settings spectral norm is evaluated 10 power iterations FIG10 show example target function predictions network trained iterations figure7 plot loss curves. theorem provides recursive relation computing Fourier transform arbitrary polytope. precisely Fourier transform m-dimensional polytope is expressed sum fourier transforms − 1 dimensional boundaries said polytope which are themselves polytopes times k−1 weight term k k recursion terminates if ProjF k 0 which then yields constant.To structure computation BID8 introduce book-keeping device called face poset polytope. can be understood weighted tree diagram polytopes various dimensions nodes. start root node which is the full dimensional polytopeP.e initially set n codimension-one boundary facesF P draw edge rootP nodeF weight term given by:DISPLAYFORM0 repeat process iteratively F. Note weight term isO(k−1 where ProjF k 0. process yields tree paths T:P→F1 → ...→F q where eachF+1∈∂F has one dimension less F i. given path k terminal node path Fq is the first polytope which ProjFq k 0. final Fourier transform is obtained multiplying weights along path summing tree paths:DISPLAYFORM1 where we wroteF0 P. Together Lemma1 gives closed form expression Fourier transform ReLU networks.For generic vectork paths terminate zero-dimensional vertices original polytope.e dim Fq 0 implying length path q equals number dimensions yielding k−d spectrum. exceptions occur if a path terminates prematurely k happens lie orthogonal − r-dimensional faceF r path which case are left k−r term r which dominates asymptotically. Note vectors orthogonal − r dimensional face F r lie r-dimensional subspace R d. Since polytope has a finite number faces dimension k's which the Fourier transform isO(k−r instead k−d lies finite union closed subspaces dimensionr r Lebesgue measure lower dimensional subspaces r is0 leadingus conclusion spectrum decays k−d almost k's formalize following corollary.Corollary1. LetP full dimensional polytope Rn. Fourier spectrum indicator function1 P satisfies following:DISPLAYFORM2 where1≤∆k ≤n ∆k j k finite union j-dimensional subspaces Rn.,2086,1391,695,0.025,1.5,2025/11/05 17:19:04,0.01,1.611,0.5295950155763238,709.946
"Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty which can arise when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by “hedging” the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle (Alemi et al., 2016; Achille & Soatto, 2018). Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of “hedging its bets” across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure which is correlated with downstream performance. An instance embedding is a mapping f from an input x, such as an image, to a vector representation, z ∈ R D , such that ""similar"" inputs are mapped to nearby points in space. Embeddings are a versatile representation that support various downstream tasks, including image retrieval (Babenko et al., 2014) and face recognition (Schroff et al., 2015) .Instance embeddings are often treated deterministically, i.e., z = f (x) is a point in R D . We refer to this approach as a point embedding. One drawback of this representation is the difficulty of modeling aleatoric uncertainty (Kendall & Gal, 2017) , i.e. uncertainty induced by the input. In the case of images this can be caused by occlusion, blurriness, low-contrast and other factors.To illustrate this, consider the example in FIG7 . On the left , we show an image composed of two adjacent MNIST digits, the first of which is highly occluded. The right digit is clearly a 7, but the left digit could be a 1, or a 4. One way to express this uncertainty about which choice to make is to map the input to a region of space, representing the inherent uncertainty of ""where it belongs"".We propose a new method, called hedged instance embedding (HIB), which achieves this goal. Each embedding is represented as a random variable, Z ∼ p(z|x) ∈ R D . The embedding effectively spreads probability mass across locations in space, depending on the level of uncertainty. For example in Figure 1b , the corrupted image is mapped to a two-component mixture of Gaussians covering both the ""17"" and ""47"" clusters. We propose a training scheme for the HIB with a learnable-margin contrastive loss and the variational information bottleneck (VIB) principle (Alemi et al., 2016; BID1 . Figure 1: Unlike point embeddings, stochastic embeddings may hedge their bets across the space. When both ""17"" and ""47 "" are plausible, our 2-component Gaussian mixture embedding has the power to spread probability mass on clusters with clean ""17"" and ""47"" images. By contrast, the point embedding will choose to be close to one or the other of these points (or somewhere between).To evaluate our method, we propose a novel dataset, N-digit MNIST, which we will open source.Using this dataset, we show that HIB exhibits several desirable properties compared to point embeddings: (1) downstream task performance (e.g. recognition and verification) improves for uncertain inputs; (2) the embedding space exhibits enhanced structural regularity; and (3) a per-exemplar uncertainty measure that predicts when the output of the system is reliable. Hedged instance embedding is a stochastic embedding that captures the uncertainty of the mapping of an image to a latent embedding space, by spreading density across plausible locations. This results in improved performance on various tasks, such as verification and identification, especially for ambiguous corrupted input. It also allows for a simple way to estimate the uncertainty of the embedding that is correlated with performance on downstream tasks.There are many possible directions for future work, including experimenting with higherdimensional embeddings, and harder datasets. As an early look at these tasks, in the Appendix, Section C.3, we apply HIB towards cat and dog instance embedding directed towards identifying specific animals with 20D embeddings. It would also be interesting to consider the ""open world"" (or ""unknown unknowns"") scenario, in which the test set may contain examples of novel classes, such as digit combinations that were not in the training set (see e.g., Lakkaraju et al. FORMULA1 ; Günther et al. FORMULA1 ). This is likely to result in uncertainty about where to embed the input which is different from the uncertainty induced by occlusion, since uncertainty due to open world is epistemic (due to lack of knowledge of a class), whereas uncertainty due to occlusion is aleatoric (intrinsic, due to lack of information in the input), as explained in Kendall & Gal (2017) . Preliminary experiments suggest that η(x) correlates well with detecting occluded inputs, but does not work as well for novel classes. We leave more detailed modeling of epistemic uncertainty as future work.",Instance embeddings are an efficient versatile image representation facilitates applications like recognition verification retrieval clustering. Many metric learning methods represent input single point embedding space. Often distance points is used proxy match confidence. However can fail represent uncertainty which can arise when the input is ambiguous e.g due occlusion blurriness. work addresses issue explicitly models uncertainty hedging location input embedding space. introduce hedged instance embedding HIB which embeddings are modeled random variables model is trained variational information bottleneck principle Alemietal. 2016;Achille Soatto 2018 Empirical results new N-digit MNIST dataset show method leads desired behavior hedging bets across embedding space upon encountering ambiguous inputs. results improved performance image matching classification tasks structure learned embedding space ability compute per-exemplar uncertainty measure which is correlated downstream performance. instance embedding is a mappingf inputx image vector representation z∈R similar inputs are mapped nearby points space. Embeddings are a versatile representation support various downstream tasks including image retrieval Babenkoetal. 2014 face recognition Schroffetal. 2015.Instance embeddings are often treated deterministically.e z f x is a point R D. refer approach point embedding. One drawback representation is the difficulty modeling aleatoric uncertainty Kendall Gal 2017.e uncertainty induced input. case images can be caused occlusion blurriness low-contrast factors.To illustrate consider example FIG7. left show image composed two adjacent MNIST digits first which is highly occluded. right digit is clearly 7 left digit could 1 4. One way express uncertainty which choice make is to map input region space representing inherent uncertainty where it belongs.We propose new method called hedged instance embedding HIB which achieves goal. embedding is represented random variable Z∼p z|x ∈R D. embedding effectively spreads probability mass across locations space depending level uncertainty. example Figure1b corrupted image is mapped two-component mixture Gaussians covering 17 47 clusters. propose training scheme HIB learnable-margin contrastive loss variational information bottleneck VIB principle Alemietal. 2016;BID1. Figure1:Unlike point embeddings stochastic embeddings may hedge bets across space. When both17 47 are plausible 2-component Gaussian mixture embedding has the power spread probability mass clusters clean17 47 images. contrast point embedding will choose close one points somewhere.To evaluate method propose novel dataset N-digit MNIST which we will open source.Using dataset show HIB exhibits several desirable properties compared point embeddings:1 downstream task performance e.g recognition verification improves uncertain inputs;2 embedding space exhibits enhanced structural regularity;3 per-exemplar uncertainty measure predicts when the output system is reliable. Hedged instance embedding is a stochastic embedding captures uncertainty mapping image latent embedding space spreading density across plausible locations. results improved performance various tasks verification identification especially ambiguous corrupted input. also allows simple way estimate uncertainty embedding is correlated performance downstream tasks.There are many possible directions future work including experimenting higherdimensional embeddings harder datasets. early look tasks Appendix Section C.3 apply HIB towards cat dog instance embedding directed towards identifying specific animals 20D embeddings. would also interesting consider open world unknown unknowns scenario which the test set may contain examples novel classes digit combinations were notin training set seee.g Lakkarajuetal. FORMULA1;Güntheretal. FORMULA1 is likely result uncertainty where to embed input which is different uncertainty induced occlusion since uncertainty due open world is epistemic due lack knowledge class whereas uncertainty due occlusion is aleatoric intrinsic due lack information input explained Kendall Gal 2017 Preliminary experiments suggest η x correlates well detecting occluded inputs does not work well novel classes. leave detailed modeling epistemic uncertainty future work.,1123,741,382,0.012,1.516,2025/11/05 17:19:04,0.01,1.558,0.5794392523364484,345.072
"Convolution neural networks typically consist of many convolutional layers followed by several fully-connected layers.   While convolutional layers map between high-order activation tensors, the fully-connected layers operate on flattened activation vectors.   Despite its success, this approach has notable drawbacks. Flattening discards the multi-dimensional structure of the activations, and the fully-connected layers require a large number of parameters. 
 We present two new techniques to address these problems.   First, we introduce tensor contraction layers which can replace the ordinary fully-connected layers in a neural network. Second, we introduce tensor regression layers, which express the output of a neural network as a low-rank multi-linear mapping from a high-order activation tensor to the softmax layer.   Both the contraction and regression weights are learned end-to-end by backpropagation. By imposing low rank on both, we use significantly fewer parameters.   Experiments on the ImageNet dataset show that applied to the popular VGG and ResNet architectures, our methods significantly reduce the number of parameters in the fully connected layers (about 65% space savings) while negligibly impacting accuracy. Many natural datasets exhibit pronounced multi-modal structure. We represent audio spectrograms as 2nd-order tensors (matrices) with modes corresponding to frequency and time. We represent images as third-order tensors with modes corresponding to width, height and the color channels. Videos are expressed as 4th-order tensors, and the signal processed by an array of video sensors can be described as a 5th-order tensor. A broad array of multi-modal data can be naturally encoded as tensors. Tensor methods extend linear algebra to higher order tensors and are promising tools for manipulating and analyzing such data.The mathematical properties of tensors have long been the subject of theoretical study. Previously, in machine learning, data points were typically assumed to be vectors and datasets to be matrices. Hence, spectral methods, such as matrix decompositions, have been popular in machine learning. Recently, tensor methods, which generalize these techniques to higher-order tensors, have gained prominence. One class of broadly useful techniques within tensor methods are tensor decompositions, which have been studied for learning latent variables BID0 .Deep Neural Networks (DNNs) frequently manipulate high-order tensors: in a standard deep convolutional Neural Network (CNN) for image recognition, the inputs and the activations of convolutional layers are 3 rd -order tensors. And yet, to wit, most architectures output predictions by first flattening the activations tensors and then connecting to the output neurons via one or more fullyconnected layers. This approach presents several issues: we lose multi-modal information during the flattening process and the fully-connected layers require a large number of parameters.In this paper, we propose Tensor Contraction Layers (TCLs) and Tensor Regression Layers (TRLs) as end-to-end trainable components of neural networks. In doing so, we exploit multilinear structure without giving up the power and flexibility offered by modern deep learning methods. By replacing fully-connected layers with tensor contractions, we can aggregate long-range spatial information while preserving multi-modal structure. Moreover, by enforcing low rank, we can significantly reduce the number of parameters needed with minimal impact on accuracy.Our proposed TRL represent the regression weights through the factors of a low-rank tensor decomposition. The TRL obviates the need for flattening when generating output. By combining tensor regression with tensor contraction, we further increase efficiency. Augmenting the VGG and ResNet architectures, we demonstrate improved performance on the ImageNet dataset despite significantly reducing the number of parameters (almost by 65%). This is the first paper that presents an end-to-end trainable architecture that retains the multi-dimensional tensor structure throughout the network.Related work: Several recent papers apply tensor decomposition to deep learning. BID16 propose using CP decomposition to speed up convolutional layers. BID13 take a pre-trained network and apply tensor (Tucker) decomposition on the convolutional kernel tensors and then fine-tune the resulting network. BID23 propose weight sharing in multi-task learning and BID2 propose sharing residual units. These contributions are orthogonal to ours and can be applied together. BID17 use the Tensor-Train (TT) format to impose low-rank tensor structure on weights. However, they still retain the fully-connected layers for the output, while we present an end-to-end tensorized network architecture.Despite the success of DNNs, many open questions remain as to why they work so well and whether they really need so many parameters. Tensor methods have emerged as promising tools of analysis to address these questions and to better understand the success of deep neural networks. BID3 , for example, use tensor methods as tools of analysis to study the expressive power of CNNs. BID5 derive sufficient conditions for global optimality and optimization of non-convex factorization problems, including tensor factorization and deep neural network training. Other papers investigate tensor methods as tools for devising neural network learning algorithms with theoretical guarantees of convergence BID20 BID11 b) . Several prior papers address the power of tensor regression to preserve natural multi-modal structure and learn compact predictive models BID4 BID18 BID25 BID24 . However, these works typically rely on analytical solutions and require manipulating large tensors containing the data. They are usually used for small dataset or require to downsampled datasets or extract compact features prior to fitting the model, and do not scale to large datasets such as ImageNet.To our knowledge, no prior work combines tensor contraction or tensor regression with deep learning in an end-to-end trainable fashion. Unlike fully-connected layers, TCLs and TRLs obviate the need to flatten input tensors. Our experiments demonstrate that by imposing a low-rank constraint on the weights of the regression, we can learn a low-rank manifold on which both the data and the labels lie. The result is a compact network, that achieves similar accuracies with many fewer parameters. Going forward, we plan to apply the TCL and TRL to more network architectures. We also plan to leverage recent work BID21 on extending BLAS primitives to avoid transpositions needed when computing tensor contractions.",Convolution neural networks typically consist many convolutional layers followed several fully-connected layers. convolutional layers map high-order activation tensors fully-connected layers operate flattened activation vectors. Despite success approach has notable drawbacks. Flattening discards multi-dimensional structure activations fully-connected layers require large number parameters. present two new techniques address problems. First introduce tensor contraction layers which can replace ordinary fully-connected layers neural network. Second introduce tensor regression layers which express output neural network low-rank multi-linear mapping high-order activation tensor softmax layer. contraction regression weights are learned end-to-end backpropagation. imposing low rank use significantly fewer parameters. Experiments ImageNet dataset show applied popular VGG ResNet architectures methods significantly reduce number parameters fully connected layers 65% space savings negligibly impacting accuracy. Many natural datasets exhibit pronounced multi-modal structure. represent audio spectrograms 2nd-order tensors matrices modes corresponding frequency time. represent images third-order tensors modes corresponding width height color channels. Videos are expressed 4th-order tensors signal processed array video sensors can be described 5th-order tensor. broad array multi-modal data can be naturally encoded tensors. Tensor methods extend linear algebra higher order tensors are promising tools manipulating analyzing data.The mathematical properties tensors have long subject theoretical study. Previously machine learning data points were typically assumed vectors datasets matrices. Hence spectral methods matrix decompositions have been popular machine learning. Recently tensor methods which generalize techniques higher-order tensors have gained prominence. One class broadly useful techniques within tensor methods are tensor decompositions which have been studied learning latent variables BID0.Deep Neural Networks DNNs frequently manipulate high-order tensors:standard deep convolutional Neural Network CNN image recognition inputs activations convolutional layers are 3 rd -order tensors. yet wit architectures output predictions first flattening activations tensors connecting output neurons via one fullyconnected layers. approach presents several issues:lose multi-modal information flattening process fully-connected layers require large number parameters.In paper propose Tensor Contraction Layers TCLs Tensor Regression Layers TRLs end-to-end trainable components neural networks. exploit multilinear structure without giving power flexibility offered modern deep learning methods. replacing fully-connected layers tensor contractions can aggregate long-range spatial information preserving multi-modal structure. Moreover enforcing low rank can significantly reduce number parameters needed minimal impact accuracy.Our proposed TRL represent regression weights factors low-rank tensor decomposition. TRL obviates need flattening when generating output. combining tensor regression tensor contraction increase efficiency. Augmenting VGG ResNet architectures demonstrate improved performance ImageNet dataset despite significantly reducing number parameters almost 65% is first paper presents end-to-end trainable architecture retains multi-dimensional tensor structure throughout network.Related work:Several recent papers apply tensor decomposition deep learning. BID16 propose usingCP decomposition speed convolutional layers. BID13 take pre-trained network apply tensor Tucker decomposition convolutional kernel tensors fine-tune resulting network. BID23 propose weight sharing multi-task learning BID2 propose sharing residual units. contributions are orthogonal can applied together. BID17 use Tensor-Train TT format impose low-rank tensor structure weights. However still retain fully-connected layers output present end-to-end tensorized network architecture.Despite success DNNs many open questions remain why they work well whether really need many parameters. Tensor methods have emerged promising tools analysis address questions better understand success deep neural networks. BID3 example use tensor methods tools analysis study expressive power CNNs. BID5 derive sufficient conditions global optimality optimization non-convex factorization problems including tensor factorization deep neural network training. papers investigate tensor methods tools devising neural network learning algorithms theoretical guarantees convergence BID20 BID11b Several prior papers address power tensor regression preserve natural multi-modal structure learn compact predictive models BID4 BID18 BID25 BID24. However works typically rely analytical solutions require manipulating large tensors containing data. are usually used small dataset require downsampled datasets extract compact features prior fitting model do not scale large datasets ImageNet.To knowledge prior work combines tensor contraction tensor regression deep learning end-to-end trainable fashion. Unlike fully-connected layers TCLs TRLs obviate need flatten input tensors. experiments demonstrate imposing low-rank constraint weights regression can learn low-rank manifold which both the data labels lie. result is a compact network achieves similar accuracies many fewer parameters. Going forward plan apply TCL TRL network architectures. also plan leverage recent work BID21 extending BLAS primitives avoid transpositions needed when computing tensor contractions.,1229,873,356,0.011,1.408,2025/11/05 17:19:04,0.01,1.367,0.242990654205607,341.279
"We explore ways of incorporating bilingual dictionaries to enable semi-supervised
 neural machine translation. Conventional back-translation methods have shown
 success in leveraging target side monolingual data. However, since the quality of
 back-translation models is tied to the size of the available parallel corpora, this
 could adversely impact the synthetically generated sentences in a low resource
 setting. We propose a simple data augmentation technique to address both this
 shortcoming. We incorporate widely available bilingual dictionaries that yield
 word-by-word translations to generate synthetic sentences. This automatically
 expands the vocabulary of the model while maintaining high quality content. Our
 method shows an appreciable improvement in performance over strong baselines. Neural Machine Translation (NMT) methods require large amounts of parallel data to perform well. This poses a significant challenge in low-resource and out-of-domain scenarios where the amount of parallel data is usually limited. A proven way to mitigate this issue has been by leveraging the vast amounts of monolingual data in conjunction with parallel data to improve performance. Prior work in the field has explored several methods to achieve this. One of the most successful approaches has been Back-Translation (BT) BID9 , that generates artificial parallel data from target monolingual corpora by training a translation model in the reverse direction. Another approach (COPY) proposed by BID3 directly copies target monolingual data to the source, focused on capturing entities that do not change across languages.The methods mentioned above suffer from a couple of limitations. The quality of the generated source translations in the BT model are dependent on the amount of parallel data. Furthermore, the vocabulary available to the model is also limited to that of the parallel data, which increases the probability of out-of-vocabulary words. The COPY model, on the other hand, adds vocabulary, albeit only on the target side. In this paper, we propose a simple yet effective data augmentation technique that utilizes bilingual dictionaries that expands vocabulary on both source and target sides, thus significantly reducing the probability of out-of-vocabulary words. Our method also ensures that correlations between the source and target languages are modelled in the monolingual data. In particular, our contributions are as follows:• We propose the Word-on-Word (WoW) data augmentation method, that outperforms previous data augmentation methods in a low-resource setting.• We show that our method benefits from both in-domain as well as out-of-domain monolingual data and shows encouraging results for domain-adaptation.• Finally, we also apply our method over other augmentation techniques and show its effectiveness in enhancing performance. We propose a simple yet effective data augmentation technique by utilizing bilingual dictionaries for low resource NMT. In this work, we used ground truth dictionaries. A direct line of future work is to create synthetic samples using induced dictionaries and also incorporating phrase tables.",explore ways incorporating bilingual dictionaries enable semi-supervised neural machine translation. Conventional back-translation methods have shown success leveraging target side monolingual data. However since quality back-translation models is tied size available parallel corpora could adversely impact synthetically generated sentences low resource setting. propose simple data augmentation technique address shortcoming. incorporate widely available bilingual dictionaries yield word-by-word translations generate synthetic sentences. automatically expands vocabulary model maintaining high quality content. method shows appreciable improvement performance strong baselines. Neural Machine Translation NMT methods require large amounts parallel data perform well. poses significant challenge low-resource out-of-domain scenarios where the amount parallel data is usually limited. proven way mitigate issue has been by leveraging vast amounts monolingual data conjunction parallel data improve performance. Prior work field has explored several methods achieve this. One successful approaches has been Back-Translation BT BID9 generates artificial parallel data target monolingual corpora training translation model reverse direction. Another approach COPY proposed BID3 directly copies target monolingual data source focused capturing entities do not change across languages.The methods mentioned suffer couple limitations. quality generated source translations BT model are dependent amount parallel data. Furthermore vocabulary available model is also limited parallel data which increases probability out-of-vocabulary words. COPY model hand adds vocabulary albeit target side. paper propose simple yet effective data augmentation technique utilizes bilingual dictionaries expands vocabulary source target sides thus significantly reducing probability out-of-vocabulary words. method also ensures correlations source target languages are modelled monolingual data. particular contributions are as follows:• propose Word-on-Word WoW data augmentation method outperforms previous data augmentation methods low-resource setting.• show method benefits in-domain well out-of-domain monolingual data shows encouraging results domain-adaptation.• Finally also apply method augmentation techniques show effectiveness enhancing performance. propose simple yet effective data augmentation technique utilizing bilingual dictionaries low resource NMT. work used ground truth dictionaries. direct line future work is to create synthetic samples using induced dictionaries also incorporating phrase tables.,565,392,173,0.005,1.441,2025/11/05 17:19:04,0.0,1.5,0.3457943925233644,180.536
"Rewards are sparse in the real world and most of today's reinforcement learning algorithms struggle with such sparsity. One solution to this problem is to allow the agent to create rewards for itself - thus making rewards dense and more suitable for learning. In particular, inspired by curious behaviour in animals, observing something novel could be rewarded with a bonus. Such bonus is summed up with the real task reward - making it possible for RL algorithms to learn from the combined reward. We propose a new curiosity method which uses episodic memory to form the novelty bonus. To determine the bonus, the current observation is compared with the observations in memory. Crucially, the comparison is done based on how many environment steps it takes to reach the current observation from those in memory - which incorporates rich information about environment dynamics. This allows us to overcome the known ""couch-potato"" issues of prior work - when the agent finds a way to instantly gratify itself by exploiting actions which lead to hardly predictable consequences. We test our approach in visually rich 3D environments in ViZDoom, DMLab and MuJoCo. In navigational tasks from ViZDoom and DMLab, our agent outperforms the state-of-the-art curiosity method ICM. In MuJoCo, an ant equipped with our curiosity module learns locomotion out of the first-person-view curiosity only. The code is available at https://github.com/google-research/episodic-curiosity/. Many real-world tasks have sparse rewards. For example, animals searching for food may need to go many miles without any reward from the environment. Standard reinforcement learning algorithms struggle with such tasks because of reliance on simple action entropy maximization as a source of exploration behaviour.Multiple approaches were proposed to achieve better explorative policies. One way is to give a reward bonus which facilitates exploration by rewarding novel observations. The reward bonus is summed up with the original task reward and optimized by standard RL algorithms. Such an approach is motivated by neuroscience studies of animals: an animal has an ability to reward itself for something novel -the mechanism biologically built into its dopamine release system. How exactly this bonus is formed remains an open question.Many modern curiosity formulations aim at maximizing ""surprise"" -inability to predict the future. This approach makes perfect sense but, in fact, is far from perfect. To show why, let us consider a thought experiment. Imagine an agent is put into a 3D maze. There is a precious goal somewhere in the maze which would give a large reward. Now, the agent is also given a remote control to a TV and can switch the channels. Every switch shows a random image (say, from a fixed set of images). The curiosity formulations which optimize surprise would rejoice because the result of the channel switching action is unpredictable. The agent would be drawn to the TV instead of looking for a goal in the environment (this was indeed observed in BID6 ). So, should we call the channel switching behaviour curious? Maybe, but it is unproductive for the original sparsereward goal-reaching task. What would be a definition of curiosity which does not suffer from such ""couch-potato"" behaviour?We propose a new curiosity definition based on the following intuition. If the agent knew the observation after changing a TV channel is only one step away from the observation before doing that -it probably would not be so interesting to change the channel in the first place (too easy). This Our method is at the intersection of multiple topics: curiosity, episodic memory and temporal distance prediction. In the following, we discuss the relation to the prior work on those topics. In this work we propose a new model of curiosity based on episodic memory and the ideas of reachability. This allows us to overcome the known ""couch-potato"" issues of prior work and outperform the previous curiosity state-of-the-art method ICM in visually rich 3D environments from VizDoom and DMLab. Our method also allows a MuJoCo ant to learn locomotion purely out of first-personview curiosity. In the future, we want to make policy aware of memory not only in terms of receiving reward, but also in terms of acting. Can we use memory content retrieved based on reachability to guide exploration behaviour in the test time? This could open opportunities to learn exploration in new tasks in a few-shot style -which is currently a big scientific challenge.","Rewards are sparse real world today's reinforcement learning algorithms struggle sparsity. One solution problem is to allow agent create rewards - thus making rewards dense suitable learning. particular inspired curious behaviour animals observing something novel could rewarded bonus. bonus is summed real task reward making possible RL algorithms learn combined reward. propose new curiosity method which uses episodic memory form novelty bonus. determine bonus current observation is compared observations memory. Crucially comparison is done based how many environment steps takes reach current observation memory which incorporates rich information environment dynamics. allowsus overcome known couch-potato issues prior work when the agent finds way instantly gratify exploiting actions which lead hardly predictable consequences. test approach visually rich 3D environments ViZDoom DMLab MuJoCo. navigational tasks ViZDoom DMLab agent outperforms state-of-the-art curiosity method ICM. MuJoCo ant equipped curiosity module learns locomotion first-person-view curiosity only. code is available https://github.com/google-research/episodic-curiosity/. Many real-world tasks have sparse rewards. example animals searching food may need go many miles without reward environment. Standard reinforcement learning algorithms struggle tasks reliance simple action entropy maximization source exploration behaviour.Multiple approaches were proposed achieve better explorative policies. One way is to give reward bonus which facilitates exploration rewarding novel observations. reward bonus is summed original task reward optimized standard RL algorithms. approach is motivated neuroscience studies animals:animal has an ability reward something novel -the mechanism biologically built dopamine release system. How exactly bonus is formed remains open question.Many modern curiosity formulations aim maximizing surprise -inability predict future. approach makes perfect sense fact is far perfect. show why,let us consider thought experiment. Imagine agent is put 3D maze. is a precious goal somewhere maze would give large reward. agent is also given remote control TV can switch channels. Every switch shows random image say fixed set images curiosity formulations which optimize surprise would rejoice result channel switching action is unpredictable. agent would drawn TV instead looking goal environment was indeed observed BID6 shouldwe call channel switching behaviour curious? Maybe is unproductive original sparsereward goal-reaching task. would definition curiosity which does not suffer couch-potato behaviour? propose new curiosity definition based following intuition. If the agent knew observation changing TV channel is only one step away observation -it probably would interesting change channel first place easy method is at the intersection multiple topics:curiosity episodic memory temporal distance prediction. following discuss relation prior work topics. work propose new model curiosity based episodic memory ideas reachability. allowsus overcome known couch-potato issues prior work outperform previous curiosity state-of-the-art method ICM visually rich 3D environments VizDoom DMLab. method also allows MuJoCo ant learn locomotion purely first-personview curiosity. future want make policy aware memory terms receiving reward also terms acting. Can we use memory content retrieved based reachability guide exploration behaviour test time? could open opportunities learn exploration new tasks few-shot style -which is currently big scientific challenge.",882,598,284,0.008,1.475,2025/11/05 17:19:04,0.0,1.389,0.4517133956386294,293.493
"We introduce a new dataset of logical entailments for the purpose of measuring models' ability to capture and exploit the structure of logical expressions against an entailment prediction task. We use this task to compare a series of architectures which are ubiquitous in the sequence-processing literature, in addition to a new model class---PossibleWorldNets---which computes entailment as a ``convolution over possible worlds''. Results show that convolutional networks present the wrong inductive bias for this class of problems relative to LSTM RNNs, tree-structured neural networks outperform LSTM RNNs due to their enhanced ability to exploit the syntax of logic, and PossibleWorldNets outperform all benchmarks. This paper seeks to answer two questions: ""Can neural networks understand logical formulae well enough to detect entailment?"", and, more generally, ""Which architectures are best at inferring, encoding, and relating features in a purely structural sequence-based problem?"". In answering these questions, we aim to better understand the inductive biases of popular architectures with regard to structure and abstraction in sequence data. Such understanding would help pave the road to agents and classifiers that reason structurally, in addition to reasoning on the basis of essentially semantic representations. In this paper, we provide a testbed for evaluating some aspects of neural networks' ability to reason structurally and abstractly. We use it to compare a variety of popular network architectures and a new model we introduce, called PossibleWorldNet.Neural network architectures lie at the heart of a variety of applications. They are practically ubiquitous across vision tasks BID19 BID17 BID29 and natural language understanding, from machine translation BID13 BID33 BID2 to textual entailment BID3 BID27 via sentiment analysis BID31 BID14 and reading comprehension BID9 BID25 . They have been used to synthesise programs BID20 BID23 BID5 or internalise algorithms BID6 BID11 BID12 BID26 . They form the basis of reinforcement learning agents capable of playing video games BID22 , difficult perfect information games BID28 BID35 , and navigating complex environments from raw pixels BID21 ). An important question in this context is to find the inductive and generalisation properties of different neural architectures, particularly towards the ability to capture structure present in the input, an ability that might be important for many language and reasoning tasks. However, there is little work on studying these inductive biases in isolation by running these models on tasks that are primarily or purely about sequence structure, which we intend to address. The paper's contribution is three-fold. First, we introduce a new dataset for training and evaluating models. Second, we provide a thorough evaluation of the existing neural models on this dataset. Third, inspired by the semantic (model-theoretic) definition of entailment, we propose a variant of the TreeNet that evaluates the formulas in multiple different ""possible worlds"", and which significantly outperforms the benchmarks. The structure of this paper is as follows. In Section 2, we introduce the new dataset and describe a generic data generation process for entailment datasets, which offers certain guarantees against the presence of superficial exploitable biases. In Section 3, we describe a series of baseline models used to validate the dataset, benchmarks from which we will derive our analyses of popular model architectures, and also introduce our new neural model, the PossibleWorldNet. In Section 4, we describe the structure of experiments, from which we obtained the results presented and discussed in Section 5. We offer a brief survey of related work in Section 6, before making concluding remarks in Section 7. Experimental results are shown in TAB1 . The test scores of the best performing overall model are indicated in bold. The test scores of the best performing model which does not have privileged access to the syntax or semantics of the logic (i.e. excluding TreeRNN-based models) are italicised. The best benchmark test results are underlined.We observe that the baselines are doing better than random (8.2 points above for the easy test set, for the MLP BoW, and 2.6 above random for the hard test set). This indicates that there are some small number of exploitable regularities at the symbolic level in this dataset, but that they do not provide significant information.The baseline results show that convolution networks and BiDirLSTMs encoders obtain relatively mediocre results compared to other models, as do LSTM and BiDirLSTM Traversal models. LSTM encoders is the best performing model which does not have privileged access to the syntax trees. Their success relative to BiDirLSTMs Encoders could be due to their reduced number of parameters guarding against overfitting, and rendering them easier to optimise, but it is plausible BiDirLSTMs Encoders would perform similarly with a more fine-grained grid search. Both tree-based models take the lead amongst the benchmarks, with the TreeLSTM being the best performing benchmark overall on both test sets. For most models except baselines, the symbol permutation data augmentation yielded 2-3 point increase in accuracy on weaker models (BiDirLSTM encoders and traversals, an convolutional networks) and between 7-15 point increases for the Tree-based models. This indicates that this data augmentation strategy is particularly well fitted for letting structure-aware models capture, at the representational level, the arbitrariness of symbols indicating unbound variables.Overall, these results show clearly that models that exploit structure in problems where it is provided, unambiguous, and a central feature of the task, outperform models which must implicitly model the structure of sequences. LSTM-based encoders provide robust and competitive results, although bidirectionality is not necessarily always the obvious choice due to optimisation and overfitting problems. Perhaps counter-intuitively, given the results of BID27 , traversal models do not outperform encoding models in this pair-of-sequences traversal problem, indicating that they may be better at capturing the sort of long-range dependencies need to recognise textual entailment better than they are at capturing structure in general.We conclude, from these benchmark results, that tree structured networks may be a better choice for domains with unambiguous syntax, such as analysing formal languages or programs. For domains such as natural language understanding, both convolutional and recurrent network architectures have had some success, but our experiments indicate that this may be due to the fact that existing tasks favour models which capture representational or semantic regularities, and do not adequately test for structural or syntactic reasoning. In particular, the poor performance of convolutional nets on this task serves as a useful indicator that while they present the right inductive bias for capturing structure in images, where topological proximity usually indicates a joint semantic contribution (pixels close by are likely to contribute to the same ""part"" of an image, such as an edge or pattern), this inductive bias does not carry over to sequences particularly well (where dependencies may be significantly more sparse, structured, and distant) § . The results for the transformer benchmark indicate that while this architecture can capture sufficient structure for machine translation, allowing for the appropriate word order in the output, and accounting for disambiguation or relational information where it exists within sentences, it does not capture with sufficient precision the more hierarchical structure which exists in logical expressions.The best performing model overall is the PossibleWorldNet, which achieves significantly higher results than the other models, with 99.3% accuracy on test (easy), and 97.3% accuracy on test (hard). This is as to be expected, as it has the strongest inductive bias. This inductive bias has two components. First, the model has knowledge of the syntactic structure of the expression, since it is a variant of a TreeNet. Second, inspired by the definition of semantic (model-theoretic) entailment in § Related to this point, BID15 show that convolutional networks make for good character-level encoders, to produce word representations, which are in turn better exploited by RNNs. This is consistent with our interpretation of our results, since at the character level, topological distance is-like for images-a good indicator of semantic grouping (characters that are close are usually part of the same word or n-gram). general, the model evaluates the pair of formulas in lots of different situations (""possible worlds"") and combines the various results together in a product ¶ .The quality of the PossibleWorldNet depends directly on the number of ""possible worlds"" it considers (see FIG1 . As we increase the number of possible worlds, the validation error rate goes down steadily. Note that the data-efficiency also increases as we increase the number of worlds. This is because adding worlds to the model does not increase the number of model parameters-it just increases the number of different ""possibilities"" that are considered. In propositional logic, of course, if we are allowed to generate every single truth-value assignment, then it is trivial to detect entailment by checking each one. In our big test set, there are on average more than 3,000 possible truth-value assignments. In our massive test set, there are on average over 800,000 possible assignments. (See TAB0 ). The PossibleWorldNet considers at most 256 different worlds, which is only 7% of the expected total number of rows needed in the big test set, and only 0.03% of the expected number of rows needed for the massive test set.To understand this result, we sample 32, 64, 128 and 256 truth table rows (variable truth-value assignments) for each pair of formulas in Test (hard), and reject entailment if a single evaluation for the formulas amongst these finds the left hand side to be true while the right hand side is false. This gives us an estimate of the accuracy of sampling a number of truth table rows equal to the number of possible worlds in our model. We estimate that these statistical methods have 75.9%, 86.5%, 93.4% and 97.2% chance of finding a countermodel, respectively. This seems to indicate that PossibleWorldNet is capable of exploiting repeated computation across projections of random noise in order to learn, solely based on the label likelihood objective, something akin to a modelbased solution to entailment by treating the random-noise as variable valuations.6 RELATED WORK BID39 show how a neural architecture can be used to optimise matrix expressions. They generate all expressions up to a certain depth , group them into equivalence classes, and train a recursive neural network classifier to detect whether two expressions are in the same equivalence class. They use a recursive neural network BID30 to guide the search for an optimised equivalent expression. There are two major differences between this work and ours. First, the classifier is predicting whether two matrix expressions (e.g. A and (A T ) T ) compute the same values; this is an equivalence relation, while entailment is a partial order. Second, their dataset consists of matrix expressions containing at most one variable, while our formulas contain many variables. BID1 use a recursive neural network to learn whether two expressions are equivalent. They tested on two datasets: propositional logic and polynomials. There are two main differences between their approach and ours. First, we consider entailment while they consider equivalence; equivalence is a symmetric relation, while entailment is not symmetric. Second, we consider entailment as a relational classification problem: given a pair of expressions A and B, predict whether A entails B. In their paper, by contrast, they generate a set of k equivalence-classes of ¶ See Formula 2 above. This general notion of entailment as truth-in-all-worlds is not dependent on any particular formal logic, and applies to entailment in both formal logics and natural languages.formulas with the same truth-conditions, and ask the network to predict which of these k classes a single formula falls into. Their task is more specific: their network is only able to classify a formula from a new equivalence class that has not been seen during training if it has additional auxiliary information about that class (e.g. exemplar members of the class).Recognizing textual entailment (RTE) between natural language sentences is a central task in natural language processing. (See Dagan et al. (2006) ; for a recent dataset, see BID3 ). Some approaches (e.g., BID37 and BID27 ) use LSTMs with attention, while others (e.g. , BID38 ) use a convolutional neural network with attention. Of course, recognizing entailment between natural language sentences is a very different task from recognizing entailment between logical formulas. Evaluating an entailment between natural language sentences requires understanding the meaning of the non-logical terms in the sentence. For example, the inference from ""An ice skating rink placed outdoors is full of people"" to ""A lot of people are in an ice skating park"" requires knowing the non-logical semantic information that an outdoors ice skating rink is also an ice skating park.Current neural models do not always understand the structure of the sentences they are evaluating. In BID3 , all the neural models they considered wrongly claimed that ""A man wearing padded arm protection is being bitten by a German shepherd dog"" entails ""A man bit a dog"". We believe that isolating the purely structural sub-problem will be useful because only networks that can reliably predict entailment in a purely formal setting, such as propositional (or first-order) logic, will be capable of getting these sorts of examples consistently correct. In this paper, we have introduced a new process for generating datasets for the purpose of recognising logical entailment. This was used to compare benchmarks and a new model on a task which is primarily about understanding and exploiting structure. We have established two clear results on the basis of this task. First, and perhaps most intuitively, architectures which make explicit use of structure will perform significantly better than those which must implicitly capture it. Second, the best model is the one that has a strong architectural bias towards capturing the possible world semantics of entailment. In addition to these two points, experimental results also shed some light on the relative abilities of implicit structure models-namely LSTM and Convolution networkbased architectures-to capture structure, showing that convolutional networks may not present the right inductive bias to capture and exploit the heterogeneous and deeply structured syntax in certain sequence-based problems, both for formal and natural languages.This conclusion is to be expected: the most successful models are those with the most prior knowledge about the generic structure of the task at hand. But our dataset throws new light on this unsurprising thought, by providing a new data-point on which to evaluate neural models' ability to understand structural sequence problems. Logical entailment, unlike textual entailment, depends only on the meaning of the logical operators, and of the place particular arbitrarily-named variables hold within a structure. Here, we have a task in which a network's understanding of structure can be disentangled from its understanding of the meaning of words.Xiang Zhang, Junbo Zhao, and Yann LeCun. Character-level convolutional networks for text classification. In Advances in neural information processing systems, pp. 649-657, 2015.Xiaodan Zhu, Parinaz Sobihani, and Hongyu Guo. Long short-term memory over recursive structures. In International Conference on Machine Learning, pp. 1604 Learning, pp. -1612 Learning, pp. , 2015 A THE DATASET A.1 DATASET REQUIREMENTS Our dataset D is composed of triples of the form (A, B, A B) , where A B is 1 if A entails B, and 0 otherwise. For example: (p ∧ q, q, 1) (q ∨ r, r, 0)We wanted to ensure that simple baseline models are unable to exploit simple statistical regularities to perform well in this task. We define a series of baseline models which, due to their structure or the information they have access to, should not be able to solve the entailment recognition problem described in this paper. We distinguish baselines for which we believe there is little chance of them detecting entailment, from those for which there categorically cannot be true modelling of entailment. The baselines which categorically cannot detect entailment are encoding models which only observe one side of the sequent: DISPLAYFORM0 where f is a linear bag of words encoder, an MLP bag of words encoder, or a TreeNet.Because the dataset contains a roughly balanced number of positive and negative examples, it follows that we should expect any model which only sees part of the sequent to perform in line with a random classifier. If they outperform a random baseline on test, there is a structural or symbolic regularity on one side (or both) which is sufficient to identify some subset of positive or negative examples. We use these baselines to verify the soundness of the generation process.Let D + and D − be the positive and negative entailments: DISPLAYFORM1 We impose various requirements on the dataset, to rule out superficial syntactic differences between D + and D − that can be easily exploited by the simple baselines described above. We require that our classes are balanced: and , we are guaranteed to produce balanced classes. Unfortunately, this straightforward approach generates datasets that violate most of our requirements above. See TAB3 for the details. DISPLAYFORM2 In particular, the mean number of negations, conjunctions, and disjunctions at the top of the syntax tree (num at(·, 0, op)) is markedly different. A + has significantly more conjunctions at the top of the syntax tree than A − , while B + has significantly fewer than B − . Conversely, A + has significantly fewer disjunctions at the top of the syntax tree than A − , while B + has significantly more than DISPLAYFORM3 The mean number of satisfying truth-value assignments (sat(·)) is also markedly different: A + is true in on average 3.7 truth-value assignments (i.e. it is a very specific formula which is only true under very particular circumstances), while A − is true in 10.3 truth-value assignments (i.e. it is true in a wider range of circumstances). We can use these statistics to develop simple heuristic baselines that will be unreasonably effective on the dataset described above: we can estimate whether A B by comparing the lengths of A and B, or by looking at the number of variables in B that do not appear in A, or by looking at the topmost connective in A and B. In order to satisfy our requirements above, we took a different approach to dataset generation. In order to ensure that there are no crude statistical measurements that can detect differences between D + and D − , we change the generation procedure so that every formula appears in both D + and D − . We sample 4-tuples of formulas FIG1 , B 2 ) such that: DISPLAYFORM4 Here, each of the four formulas appears in one positive entailment and one negative entailment * * .Using this alternative approach, we are able to satisfy the requirements above. By construction , the mean length, number of operators at a certain level in the syntax tree, and the number of satisfying truth-value assignments is exactly the same for D + and D − . See Table 4 . DISPLAYFORM5 (r → c) → ((r → v) ∨ p) * * One consequence of this method is that it rules out A1 from being impossible (if it was impossible, we would not have A1 B2) and B1 from being a tautology (if it was a tautology, we would not have A2 B1).","introduce new dataset logical entailments purpose measuring models' ability capture exploit structure logical expressions entailment prediction task. use task compare series architectures which are ubiquitous sequence-processing literature addition new model class -PossibleWorldNets -which computes entailment convolution possible worlds. Results show convolutional networks present wrong inductive bias class problems relative LSTM RNNs tree-structured neural networks outperform LSTM RNNs due enhanced ability exploit syntax logic PossibleWorldNets outperform benchmarks. paper seeks answer two questions:Can neural networks understand logical formulae well enough detect entailment? generally Which architectures are best inferring encoding relating features purely structural sequence-based problem? answering questions aim better understand inductive biases popular architectures regard structure abstraction sequence data. understanding would help pave road agents classifiers reason structurally addition reasoning basis essentially semantic representations. paper provide testbed evaluating aspects neural networks' ability reason structurally abstractly. use compare variety popular network architectures new model introduce called PossibleWorldNet.Neural network architectures lie heart variety applications. are practically ubiquitous across vision tasks BID19 BID17 BID29 natural language understanding machine translation BID13 BID33 BID2 textual entailment BID3 BID27 via sentiment analysis BID31 BID14 reading comprehension BID9 BID25. have been used synthesise programs BID20 BID23 BID5 internalise algorithms BID6 BID11 BID12 BID26. form basis reinforcement learning agents capable playing video games BID22 difficult perfect information games BID28 BID35 navigating complex environments raw pixels BID21 important question context is to find inductive generalisation properties different neural architectures particularly towards ability capture structure present input ability might important many language reasoning tasks. However is little work studying inductive biases isolation running models tasks are primarily purely sequence structure which we intend address. paper's contribution is three-fold three-fold First introduce new dataset training evaluating models. Second provide thorough evaluation existing neural models dataset. Third inspired semantic model-theoretic definition entailment propose variant TreeNet evaluates formulas multiple different possible worlds which significantly outperforms benchmarks. structure paper is as follows. Section2 introduce new dataset describe generic data generation process entailment datasets which offers certain guarantees presence superficial exploitable biases. Section3 describe series baseline models used validate dataset benchmarks which we will derive analyses popular model architectures also introduce new neural model PossibleWorldNet. Section4 describe structure experiments which we obtained results presented discussed Section5. offer brief survey related work Section6 making concluding remarks Section7. Experimental results are shown TAB1. test scores best performing overall model are indicated bold. test scores best performing model which does not have privileged access syntax semantics logic.e excluding TreeRNN-based models are italicised. best benchmark test results are underlined.We observe baselines are doing better random 8.2 points easy test set MLP BoW 2.6 random hard test set indicates are some small number exploitable regularities symbolic level dataset do not provide significant information.The baseline results show convolution networks BiDirLSTMs encoders obtain relatively mediocre results compared models do LSTM BiDirLSTM Traversal models. LSTM encoders is the best performing model which does not have privileged access syntax trees. success relative BiDirLSTMs Encoders could due reduced number parameters guarding overfitting rendering easier optimise is plausible BiDirLSTMs Encoders would perform similarly fine-grained grid search. tree-based models take lead amongst benchmarks TreeLSTM best performing benchmark overall test sets. models except baselines symbol permutation data augmentation yielded 2-3 point increase accuracy weaker models BiDirLSTM encoders traversals convolutional networks 7-15 point increases Tree-based models. indicates data augmentation strategy is particularly well fitted letting structure-aware models capture representational level arbitrariness symbols indicating unbound variables.Overall results show clearly models exploit structure problems where it is provided unambiguous central feature task outperform models which must implicitly model structure sequences. LSTM-based encoders provide robust competitive results although bidirectionality is not necessarily always obvious choice due optimisation overfitting problems. Perhaps counter-intuitively given results BID27 traversal models do not outperform encoding models pair-of-sequences traversal problem indicating may better capturing sort long-range dependencies need recognise textual entailment better are at capturing structure general.We conclude benchmark results tree structured networks may better choice domains unambiguous syntax analysing formal languages programs. domains natural language understanding convolutional recurrent network architectures have had some success experiments indicate may due fact existing tasks favour models which capture representational semantic regularities do not adequately test structural syntactic reasoning. particular poor performance convolutional nets task serves useful indicator present right inductive bias capturing structure images where topological proximity usually indicates joint semantic contribution pixels close are likely contribute part image edge pattern inductive bias does not carry sequences particularly well where dependencies may significantly sparse structured distant § results transformer benchmark indicate architecture can capture sufficient structure machine translation allowing appropriate word order output accounting disambiguation relational information where it exists within sentences does not capture sufficient precision hierarchical structure which exists logical expressions.The best performing model overall is the PossibleWorldNet which achieves significantly higher results models 99.3 accuracy test easy 97.3 accuracy test hard is expected has strongest inductive bias. inductive bias has two components. First model has knowledge syntactic structure expression since is a variant TreeNet. Second inspired definition semantic model-theoretic entailment § Related point BID15 show convolutional networks make good character-level encoders produce word representations which are in turn better exploited RNNs. is consistent interpretation results since character level where topological distance is-like images-a good indicator semantic grouping characters are close are usually part word n-gram general model evaluates pair formulas lots different situations possible worlds combines various results together product ¶ .The quality PossibleWorldNet depends directly number possible worlds considers see FIG1. increase number possible worlds validation error rate goes steadily. Note data-efficiency also increases increase number worlds. is because adding worlds model does not increase number model parameters-it increases number different possibilities are considered. propositional logic course if we are allowed generate every single truth-value assignment is trivial detect entailment checking one. big test set are on average 3,000 possible truth-value assignments. massive test set are on average 800,000 possible assignments. See TAB0 PossibleWorldNet considers 256 different worlds which is only7% expected total number rows needed big test set 0.03 expected number rows needed massive test set.To understand result sample32 64 128 256 truth table rows variable truth-value assignments pair formulas Test hard reject entailment if a single evaluation formulas amongst finds left hand side true right hand side is false. givesus estimate accuracy sampling number truth table rows equal number possible worlds model. estimate statistical methods have 75.9 75.9 86.5 93.4 97.2 chance finding countermodel respectively. seems indicate PossibleWorldNet is capable exploiting repeated computation across projections random noise order learn solely based label likelihood objective something akin modelbased solution entailment treating random-noise variable valuations.6 RELATED WORK BID39 show how a neural architecture can be used optimise matrix expressions. generate expressions certain depth group equivalence classes train recursive neural network classifier detect whether two expressions are in the same equivalence class. use recursive neural network BID30 guide search optimised equivalent expression. are two major differences work ours. First classifier is predicting whether two matrix expressions e.g compute values;is an equivalence relation entailment is a partial order. Second dataset consists matrix expressions containing one variable formulas contain many variables. BID1 use recursive neural network learn whether two expressions are equivalent. tested two datasets:propositional logic polynomials. are two main differences approach ours. First consider entailment consider equivalence;equivalence is a is not symmetric relation entailment is a is not symmetric. Second consider entailment relational classification problem:given pair expressions B predict whether entailsB. paper contrast generate set k equivalence-classes ¶ See Formula2 above. general notion entailment truth-in-all-worlds is not dependent particular formal logic applies entailment formal logics natural languages.formulas truth-conditions ask network predict which of these k classes single formula falls into. task is more specific:network is only able classify formula new equivalence class has not been seen training if it has additional auxiliary information class e.g exemplar members class.Recognizing textual entailment RTE natural language sentences is a central task natural language processing. See Daganetal. 2006 recent dataset see BID3 approaches e.g BID37 BID27 can use LSTMs attention others e.g BID38 can use convolutional neural network attention. course recognizing entailment natural language sentences is a very different task recognizing entailment logical formulas. Evaluating entailment natural language sentences requires understanding meaning non-logical terms sentence. example inference ice skating rink placed outdoors is full people lot people are in an ice skating park requires knowing non-logical semantic information outdoors ice skating rink is also ice skating park.Current neural models do not always understand structure sentences are evaluating. BID3 neural models considered wrongly claimed man wearing padded arm protection is being bitten German shepherd dog entails man bit dog. believe isolating purely structural sub-problem will be useful networks can reliably predict entailment purely formal setting propositional first-order logic will be capable getting sorts examples consistently correct. paper have introduced new process generating datasets purpose recognising logical entailment. was used compare benchmarks new model task which is primarily understanding exploiting structure. have established two clear results basis task. First perhaps intuitively Which architectures which make explicit use structure will perform significantly better which must implicitly capture it. Second best model is the one has a strong architectural bias towards capturing possible world semantics entailment. addition two points experimental results also shed light relative abilities implicit structure models-namely LSTM Convolution networkbased architectures-to capture structure showing convolutional networks may present right inductive bias capture exploit heterogeneous deeply structured syntax certain sequence-based problems formal natural languages.This conclusion is to be expected:successful models are those with the prior knowledge generic structure task hand. dataset throws new light unsurprising thought providing new data-point which to evaluate neural models' ability understand structural sequence problems. Logical entailment unlike textual entailment depends meaning logical operators place particular arbitrarily-named variables hold within structure. have task which a network's understanding structure can be disentangled understanding meaning words.Xiang Zhang Junbo Zhao Yann LeCun. Character-level convolutional networks text classification. Advances neural information processing systems pp. 649-657 2015.Xiaodan Zhu Parinaz Sobihani Hongyu Guo. Long short-term memory recursive structures. International Conference Machine Learning pp. 1604 Learning pp. -1612 Learning pp. 2015 DATASET A.1 DATASET REQUIREMENTS dataset is composed triples form B B whereAB is1 if A entailsB 0 otherwise. example:p∧q q 1 q∨r r 0 wanted ensure simple baseline models are unable exploit simple statistical regularities perform well task. define series baseline models which,due structure information have access should not able solve entailment recognition problem described paper. distinguish baselines which we believe is little chance detecting entailment which there which categorically cannot true modelling entailment. baselines which there which categorically cannot detect entailment are encoding models which only observe one side sequent:DISPLAYFORM0 wheref is a linear bag words encoder MLP bag words encoder TreeNet.Because dataset contains roughly balanced number positive negative examples follows should expect model which only sees part sequent perform line random classifier. If they outperform random baseline test is a structural symbolic regularity one side whichis sufficient identify subset positive negative examples. use baselines verify soundness generation process.Let+− positive negative entailments:DISPLAYFORM1 impose various requirements dataset rule superficial syntactic differences+− can be easily exploited simple baselines described above. require classes are balanced:are guaranteed produce balanced classes. Unfortunately straightforward approach generates datasets violate requirements above. See TAB3 details. DISPLAYFORM2 particular mean number negations conjunctions disjunctions top syntax tree num · 0 op is markedly different.+has significantly conjunctions top syntax tree − B+has significantly fewer B − Conversely+has significantly fewer disjunctions top syntax tree − B+has significantly DISPLAYFORM3 mean number satisfying truth-value assignments sat · is also markedly different:+is true average 3.7 truth-value assignments.e is a very specific formula which is only true particular circumstances − is true 10.3 truth-value assignments.e is true wider range circumstances can use statistics develop simple heuristic baselines will be unreasonably effective dataset described above:can estimate whether B comparing lengths B looking number variables B do not appear looking topmost connective B. order satisfy requirements took different approach dataset generation. order ensure are no crude statistical measurements can detect differences+− change generation procedure every formula appears+− sample 4-tuples formulas FIG1 B2 that:DISPLAYFORM4 four formulas appears one positive entailment one negative entailment* * .Using alternative approach are able satisfy requirements above. construction mean length number operators certain level syntax tree number satisfying truth-value assignments is exactly+− See Table4. DISPLAYFORM5 r→c → r→v ∨p * * One consequence method is that it rules A1 impossible if it was impossible would haveA1B2 B1 tautology if it was tautology would haveA2B1",4001,2668,1333,0.086,1.5,2025/11/05 17:19:04,0.02,1.684,0.5295950155763238,1279.782
"Deep convolutional neural network (DCNN) based supervised learning is a widely practiced approach for large-scale image classification.   However, retraining these large networks to accommodate new, previously unseen data demands high computational time and energy requirements. Also, previously seen training samples may not be available at the time of retraining. We propose an efficient training methodology and incrementally growing a DCNN to allow new classes to be learned while sharing part of the base network. Our proposed methodology is inspired by transfer learning techniques, although it does not forget previously learned classes. An updated network for learning new set of classes is formed using previously learned convolutional layers (shared from initial part of base network) with addition of few newly added convolutional kernels included in the later layers of the network. We evaluated the proposed scheme on several recognition applications. The classification accuracy achieved by our approach is comparable to the regular incremental learning approach (where networks are updated with new training samples only, without any network sharing). Deep Convolutional Neural Networks (DCNNs) have achieved remarkable success in various cognitive applications, particularly in computer vision BID14 . They have shown human like performance on a variety of recognition, classification and inference tasks, albeit at a much higher energy consumption. One of the major challenges for convolutional networks is the computational complexity and the time needed to train large networks. Since training of DCNNs requires state-ofthe-art accelerators like GPUs BID0 , large training overhead has restricted the usage of DCNNs to clouds and servers. It is common to pre-train a DCNN on a large dataset (e.g. ImageNet, which contains 1.2 million images with 1000 categories), and then use the trained network either as an initialization or a fixed feature extractor for the specific application BID16 . A major downside of such DCNNs is the inability to learn new information since the learning process is static and only done once before it is exposed to practical applications. In real-world scenarios, classes and their associated labeled data are always collected in an incremental manner. To ensure applicability of DCNNs in such cases, the learning process needs to be continuous. However, retraining these large networks using both previously seen and unseen data to accommodate new data, is not feasible most of the time. Incremental learning plays a critical role in alleviating this issue by ensuring continuity in the learning process through regular model update based only on the new available batch of data. A system that can learn incrementally is beneficial in practical situations, since it can gradually expand its capacity to accommodate increasing number of classes. Nevertheless, incremental learning can be computationally expensive and time consuming, if the network is large enough. This paper focuses on incremental learning of deep convolutional neural network (DCNN) for image classification task. In doing so, we attempt to address the more fundamental issue: an efficient learning system must deal with new knowledge that it is exposed to, as humans do. To achieve this goal, there are two major challenges. First, as new data becomes available, we should not start learning from scratch. Rather, we leverage what we have already learned and combine them with new knowledge in a continuous manner. Second, to accommodate new data, if there is a need to increase the capacity of our network, we will have to do it in an efficient way.There have been several prior works on incremental learning of neural networks. Many of them focus on learning new classes from fewer samples BID2 BID6 ) utilizing transfer learning techniques. To avoid learning new categories from scratch, BID2 proposed a Bayesian transfer learning method using very few training samples. By introducing attribute-based classification the authors BID6 ) achieved zero-shot learning (learning a new class from zero samples). These works rely on shallow models instead of DCNN, and the category size is small in comparison. The challenge of applying incremental learning (transfer learning as well) on DCNN lies in the fact that it consists of both feature extractor and classifier in one architecture. BID13 utilized ensemble of classifiers by generating multiple hypotheses using training data sampled according to carefully tailored distributions. The outputs of the resulting classifiers are combined using a weighted majority voting procedure. Inspired form BID13 , BID8 utilized ensemble of modified convolutional neural networks as classifiers by generating multiple hypotheses. The existing classifiers are improved in BID13 BID8 ) by combining new hypothesis generated from newly available examples without compromising classification performance on old data. The new data in BID13 BID8 ) may or may not contain new classes. BID19 proposed a training algorithm that grows a network not only incrementally but also hierarchically. Classes are grouped according to similarities, and self-organized into different levels of the hierarchy. All new networks are cloned from existing ones and therefore inherit learned features. These new networks are fully retrained and connected to base network. The problem with this method is the increase of hierarchical levels as new set of classes are added over time.Our work differs in goal, as we want to grow a DCNN to accommodate new set of classes by network sharing, without forgetting the old classes. For learning new set of classes, we form a new network by reusing previously learned convolutional layers (shared from initial part of the base network) followed by new (added) trainable convolutional layers towards the later layers of the network. The shared convolutional layers work as fixed feature extractors (learning parameters are frozen) and minimize learning overhead for new set of classes. The error resilience property of neural network ensures that even if we freeze some of the learning parameters, the network will be able to adapt to it and learn. In fact, utilizing this attribute, in recent work BID15 showed the use of fixed Gabor filters as convolutional kernels in conjunction with regular trainable convolutional kernels. Since the frozen parameters are from an already learned network of similar (not same) classes, it further guarantees that the new classes can be learned smoothly without having convergence issues. By sharing initial convolutional layers of the base network, a significant fraction of the powerhungry components of the backpropagation training was eliminated, thereby achieving considerable reduction in training energy while maintaining competitive output accuracy.The novelty of this work lies in the fact that we developed an empirical mechanism to identify how much of the network can be shared as new classes are added. In this work, we also quantified the energy consumption, training time and memory storage savings associated with models trained with different amounts of sharing to emphasize the importance of network sharing from hardware point of view. In summary, the key contributions of our work are as follows:• We propose sharing of convolutional layers to reduce computational complexity while training a network to accommodate new set of classes.• We developed a methodology to identify optimal sharing of convolutional layers in order to get the best trade-off between accuracy and other parameters of interest, especially computation energy consumption, training time and memory access.• We developed an energy model for quantifying energy consumption of the network during training, based on the Multiplication and Accumulation (MAC) operations in the training algorithm.• We substantiate the scalability and robustness of the proposed methodology by applying the proposed method to different network structures trained for different benchmark datasets.We show that our proposed methodology leads to energy efficiency, reduction in storage requirements, memory access and training time, while maintaining classification accuracy. The performance of DCNNs relies greatly on the availability of a representative set of the training examples. Generally, in practical applications, data acquisition and learning process is time consuming. Also, it is very likely that the data are available in small batches over a period of time. A competent classifier should be able to support an incremental method of accommodating new data without losing ground on old data inference capability. In this paper, we introduce an incremental training methodology for DCNNs, which employs partial network sharing. This method allows us to accommodate new, previously unseen data without the need of retraining the whole network with previously seen data. It can preserve existing knowledge, and can accommodate new information. Importantly, all new networks start from an existing base network and share learning parameters. The new updated network inherit features from the base network by sharing convolutional layers, leading to improved computational effort and energy consumption during training and thus, speed up the learning process. We applied the proposed method on different DCNNs trained on real-world recognition applications. Results confirm the scalability of the proposed approach with significant improvements.",Deep convolutional neural network DCNN based supervised learning is a widely practiced approach large-scale image classification. However retraining large networks accommodate new previously unseen data demands high computational time energy requirements. Also previously seen training samples may available time retraining. propose efficient training methodology incrementally growing DCNN allow new classes learned sharing part base network. proposed methodology is inspired transfer learning techniques although does not forget previously learned classes. updated network learning new set classes is formed using previously learned convolutional layers shared initial part base network addition newly added convolutional kernels included later layers network. evaluated proposed scheme several recognition applications. classification accuracy achieved approach is comparable regular incremental learning approach where networks are updated new training samples without network sharing Deep Convolutional Neural Networks DCNNs have achieved remarkable success various cognitive applications particularly computer vision BID14. have shown human like performance variety recognition classification inference tasks albeit much higher energy consumption. One major challenges convolutional networks is the computational complexity time needed train large networks. Since training DCNNs requires state-ofthe-art accelerators like GPUs BID0 large training overhead has restricted usage DCNNs clouds servers. is common pre-train DCNN large dataset e.g ImageNet which contains 1.2 million images 1000 categories use trained network either initialization fixed feature extractor specific application BID16. major downside DCNNs is the inability learn new information since learning process is static done is exposed practical applications. real-world scenarios classes associated labeled data are always collected incremental manner. ensure applicability DCNNs cases learning process needs continuous. However retraining large networks using previously seen unseen data accommodate new data is not feasible time. Incremental learning plays critical role alleviating issue ensuring continuity learning process regular model update based new available batch data. system can learn incrementally is beneficial practical situations since can gradually expand capacity accommodate increasing number classes. Nevertheless incremental learning can be computationally expensive time consuming if the network is large enough. paper focuses incremental learning deep convolutional neural network DCNN image classification task. attempt address fundamental issue:efficient learning system must deal new knowledge is exposed humans do. achieve goal are two major challenges. First new data becomes available should not start learning scratch. Rather leverage what we have already learned combine new knowledge continuous manner. Second can accommodate new data if thereis need increase capacity network will have doitin efficient way.There have been several prior works incremental learning neural networks. Many focus learning new classes fewer samples BID2 BID6 utilizing transfer learning techniques. avoid learning new categories scratch BID2 proposed Bayesian transfer learning method using training samples. introducing attribute-based classification authors BID6 have achieved zero-shot learning learning new class zero samples works rely shallow models instead DCNN category size is small comparison. challenge applying incremental learning transfer learning well DCNN lies fact consists feature extractor classifier one architecture. BID13 utilized ensemble classifiers generating multiple hypotheses using training data sampled according carefully tailored distributions. outputs resulting classifiers are combined using weighted majority voting procedure. Inspired form BID13 BID8 utilized ensemble modified convolutional neural networks classifiers generating multiple hypotheses. existing classifiers are improved BID13 BID8 combining new hypothesis generated newly available examples without compromising classification performance old data. new data BID13 BID8 may may contain new classes. BID19 proposed training algorithm grows network incrementally also hierarchically. Classes are grouped according similarities self-organized different levels hierarchy. new networks are cloned existing ones therefore inherit learned features. new networks are fully retrained connected base network. problem method is the increase hierarchical levels new set classes are added time.Our work differs goal want grow DCNN accommodate new set classes network sharing without forgetting old classes. learning new set classes form new network reusing previously learned convolutional layers shared initial part base network followed new added trainable convolutional layers towards later layers network. shared convolutional layers work fixed feature extractors learning parameters are frozen minimize learning overhead new set classes. error resilience property neural network ensures even if we freeze learning parameters if the network will be able adapt learn. fact utilizing attribute recent work BID15 showed use fixed Gabor filters convolutional kernels conjunction regular trainable convolutional kernels. Since frozen parameters are from an already learned network similar classes guarantees new classes can be learned smoothly without convergence issues. sharing initial convolutional layers base network significant fraction powerhungry components backpropagation training was eliminated thereby achieving considerable reduction training energy maintaining competitive output accuracy.The novelty work lies fact developed empirical mechanism identify how much network can be shared new classes are added. work also quantified energy consumption training time memory storage savings associated models trained different amounts sharing emphasize importance network sharing hardware point view. summary key contributions work are as follows:• propose sharing convolutional layers reduce computational complexity training network accommodate new set classes.• developed methodology identify optimal sharing convolutional layers order get best trade-off accuracy parameters interest especially computation energy consumption training time memory access.• developed energy model quantifying energy consumption network training based Multiplication Accumulation MAC operations training algorithm.• substantiate scalability robustness proposed methodology applying proposed method different network structures trained different benchmark datasets.We show proposed methodology leads energy efficiency reduction storage requirements memory access training time maintaining classification accuracy. performance DCNNs relies greatly availability representative set training examples. Generally practical applications data acquisition learning process is time consuming. Also is very likely data are available small batches period time. competent classifier should be able support incremental method accommodating new data without losing ground old data inference capability. paper introduce incremental training methodology DCNNs which employs partial network sharing. method allowsus accommodate new previously unseen data without need retraining whole network previously seen data. can preserve existing knowledge can accommodate new information. Importantly new networks start existing base network share learning parameters. new updated network inherit features base network sharing convolutional layers leading improved computational effort energy consumption training thus speed learning process. applied proposed method different DCNNs trained real-world recognition applications. Results confirm scalability proposed approach significant improvements.,1682,1158,524,0.021,1.453,2025/11/05 17:19:04,0.01,1.464,0.383177570093458,529.872
"Recurrent neural networks (RNNs) are widely used to model sequential data but
 their non-linear dependencies between sequence elements prevent parallelizing
 training over sequence length. We show the training of RNNs with only linear
 sequential dependencies can be parallelized over the sequence length using the
 parallel scan algorithm, leading to rapid training on long sequences even with
 small minibatch size. We develop a parallel linear recurrence CUDA kernel and
 show that it can be applied to immediately speed up training and inference of
 several state of the art RNN architectures by up to 9x.  We abstract recent work
 on linear RNNs into a new framework of linear surrogate RNNs and develop a
 linear surrogate model for the long short-term memory unit, the GILR-LSTM, that
 utilizes parallel linear recurrence.  We extend sequence learning to new
 extremely long sequence regimes that were previously out of reach by
 successfully training a GILR-LSTM on a synthetic sequence classification task
 with a one million timestep dependency.
 Recurrent neural networks (RNNs) are widely used for sequence modelling tasks in domains such as natural language processing BID17 , speech recognition BID1 , and reinforcement learning BID9 . Most RNNs, including popular variants such as long short-term memories (LSTMs), introduced by BID10 , and gated recurrent units (GRUs), introduced by BID5 , contain a non-linear dependency between sequential inputs. These non-linear dependencies create a very flexible class of models but limit the feasibility of training RNNs on long sequences as each sequence element must be processed sequentially. Modelling sequences of thousands to millions of elements is important to domains such as robotics, remote sensing, control systems, speech recognition, medicine, and finance.The RNN serial evaluation inefficiency problem is usually mitigated by parallelizing the forward and backward pass over a minibatch of inputs. Without minibatches, RNN evaluation is a sequence of matrix-vector multiplications. Minibatches transform RNN computation into a sequence of more efficient matrix-matrix multiplications, but this speed-up brings several disadvantages. RNN model size is often limited by GPU memory size, and running a forward and backward pass on a minibatch requires memory linear in the minibatch size. Grouping data into minibatches increases the latency of each pass and reduces the rate of optimization steps. Finally, training with larger minibatches damages generalization ability BID12 . Given these effects, it is desirable to obtain high training throughput with small minibatches. Persistent RNNs BID6 ) use a novel implementation that can achieve high GPU utilization with very small minibatch sizes when the recurrent state is larger than 500 elements, but even persistent RNNs become limited by the serial evaluation inefficiency at smaller hidden sizes.Numerous prior works have shown strong performance from neural sequential models with only linear dependence on earlier sequence elements. BID2 investigated RNNs with only elementwise linear recurrence relations h t = α t h t−1 + (1 − α t ) x t and developed linear variants of LSTM and GRU that perform similarly to standard non-linear RNNs on text generation tasks. BID4 , , BID7 , and van den have successfully applied networks of convolutions over sequences for tasks such as machine translation, language modelling, and audio generation. These works have observed up to an order of magnitude increase in training throughput compared to RNN alternatives. Convolutional sequence models typically rely on either an attention mechanism or a (possibly linear) recurrent layer to integrate information at scales larger than the filter width. Introduction of a recurrent layer prevents full parallelization over the sequence length while attention mechanisms are expensive to apply on long sequences in online inference use cases.A linear recurrence is a specific instance of a general form of computation known as a scan. Scans and reductions are computations involving repeated application of a binary operator ⊕ over an array of data. Computing the sum or maximum of an array is an example of a reduction, while a cumulative sum is a common example of a scan operation. Throughout this work, the scan of ⊕ with initial value b is defined as DISPLAYFORM0 The reduction of ⊕ over array A and initial value b is denoted REDUCE(⊕, A, b) and is the final element of SCAN(⊕, A, b). Despite their dependent computation graph, algorithms exist to parallelize scans and reductions when ⊕ is associative BID14 . BID3 shows that first order recurrences of the form h t = (Λ t ⊗ h t−1 ) ⊕ x t can be parallelized with the parallel scan algorithm if three conditions are met: DISPLAYFORM1 Considering the familiar operations in linear algebra, we see that the associative operation of vector addition (x ⊕ y = x + y), the semiassociative operation of matrix-vector multiplication (A ⊗ x = Ax) and the associative operation of matrix-matrix multiplication (A B = AB) satisfy Blelloch's three conditions, allowing h t = Λ t h t−1 + x t to be evaluated in parallel over time steps t for vectors x t and square matrices Λ t .We investigate this idea further and deliver the following contributions:• We classify RNNs which satisfy the conditions above, and show that many RNNs used in practice such as the Quasi-RNNs (QRNNs) introduced by BID4 are contained in this class.• We provide an implementation of the parallel linear recurrence algorithm as a CUDA kernel, and show that it speeds up training of QRNN and BID19 's Simple Recurrent Unit (SRU) architectures by factors of up to 9x.• We describe how several recent linear RNNs can be described as linear surrogates for non-linear architectures. We introduce a linear surrogate for the LSTM and show that we are able to train it with a speedup of 5-10x compared to the CuDNN LSTM when we use the parallel linear recurrence algorithm. A significant portion of the success of deep learning can be attributed to access to massive amounts of computation. Most of this computation is accessed through two highly efficient and parallelizable building blocks: matrix multiplication and convolution. Recent research has demonstrated that linear RNNs can achieve similar prediction accuracy to non-linear RNNs on a wide variety of tasks in a fraction of the training time. We propose the framework of LS-RNNs as a way to tame the growing zoo of sequential neural nets. We identify linear recurrence as another parallelizable building block for current and future sequential models and we use it to obtain significant speedups on already fast models. With the power of parallel linear recurrence we are able to solve a sequential dependency problem multiple orders of magnitude larger than anything done prior. Future applications of parallel linear recurrence within neural nets could include parallel training of memory augmented models or providing a new sort of image filter on very high resolution images. We hope that parallel linear recurrence can be to large scale sequence modelling what fast convolution algorithms are to image recognition.",Recurrent neural networks RNNs are widely used model sequential data non-linear dependencies sequence elements prevent parallelizing training sequence length. show training RNNs linear sequential dependencies can be parallelized sequence length using parallel scan algorithm leading rapid training long sequences even small minibatch size. develop parallel linear recurrence CUDA kernel show can be applied immediately speed training inference several state art RNN architectures 9x. abstract recent work linear RNNs new framework linear surrogate RNNs develop linear surrogate model long short-term memory unit GILR-LSTM utilizes parallel linear recurrence. extend sequence learning new extremely long sequence regimes were previously reach successfully training GILR-LSTM synthetic sequence classification task one million timestep dependency. Recurrent neural networks RNNs are widely used sequence modelling tasks domains natural language processing BID17 speech recognition BID1 reinforcement learning BID9. RNNs including popular variants long short-term memories LSTMs introduced BID10 gated recurrent units GRUs introduced BID5 contain non-linear dependency sequential inputs. non-linear dependencies create flexible class models limit feasibility training RNNs long sequences sequence element must processed sequentially. Modelling sequences thousands millions elements is important domains robotics remote sensing control systems speech recognition medicine finance.The RNN serial evaluation inefficiency problem is usually mitigated parallelizing forward backward pass minibatch inputs. Without minibatches RNN evaluation is a sequence matrix-vector multiplications. Minibatches transform RNN computation sequence efficient matrix-matrix multiplications speed-up brings several disadvantages. RNN model size is often limited GPU memory size running forward backward pass minibatch requires memory linear minibatch size. Grouping data minibatches increases latency pass reduces rate optimization steps. Finally training larger minibatches damages generalization ability BID12. Given effects is desirable obtain high training throughput small minibatches. Persistent RNNs BID6 use novel implementation can achieve high GPU utilization small minibatch sizes when the recurrent state is larger 500 elements even persistent RNNs become limited serial evaluation inefficiency smaller hidden sizes.Numerous prior works have shown strong performance neural sequential models linear dependence earlier sequence elements. BID2 investigated RNNs elementwise linear recurrence relations h α h t−1+1−α x developed linear variants LSTM GRU perform similarly standard non-linear RNNs text generation tasks. BID4 BID7 van den have successfully applied networks convolutions sequences tasks machine translation language modelling audio generation. works have observed order magnitude increase training throughput compared RNN alternatives. Convolutional sequence models typically rely either attention mechanism possibly linear recurrent layer integrate information scales larger filter width. Introduction recurrent layer prevents full parallelization sequence length attention mechanisms are expensive apply long sequences online inference use cases.A linear recurrence is a specific instance general form computation known scan. Scans reductions are computations involving repeated application binary operator⊕ array data. Computing sum maximum array is an example reduction cumulative sum is a common example scan operation. Throughout work scan ⊕ initial valueb is defined DISPLAYFORM0 reduction ⊕ array initial valueb is denoted REDUCE ⊕ b is the final element SCAN ⊕ b Despite dependent computation graph algorithms exist parallelize scans reductions when⊕ is associative BID14. BID3 shows first order recurrences formh Λ ⊗ h t−1 ⊕x can be parallelized parallel scan algorithm if three conditions are met:DISPLAYFORM1 Considering familiar operations linear algebra see associative operation vector addition x⊕ x+semiassociative operation matrix-vector multiplication ⊗x Ax associative operation matrix-matrix multiplication B AB satisfy Blelloch's three conditions allowingh Λ h t−1+x evaluated parallel time steps vectorsx square matricesΛ.We investigate idea deliver following contributions:• classify RNNs which satisfy conditions show many RNNs used practice Quasi-RNNs QRNNs introduced BID4 are contained class.• provide implementation parallel linear recurrence algorithm CUDA kernel show speeds training QRNN BID19 's Simple Recurrent Unit SRU architectures factors 9x.• describe how several recent linear RNNs can be described linear surrogates non-linear architectures. introduce linear surrogate LSTM show are able train speedup 5-10x compared CuDNN LSTM when we use parallel linear recurrence algorithm. significant portion success deep learning can be attributed access massive amounts computation. computation is accessed two highly efficient parallelizable building blocks:matrix multiplication convolution. Recent research has demonstrated linear RNNs can achieve similar prediction accuracy non-linear RNNs wide variety tasks fraction training time. propose framework LS-RNNs way tame growing zoo sequential neural nets. identify linear recurrence another parallelizable building block current future sequential models use obtain significant speedups already fast models. power parallel linear recurrence are able solve sequential dependency problem multiple orders magnitude larger anything done prior. Future applications parallel linear recurrence within neural nets could include parallel training memory augmented models providing new sort image filter high resolution images. hope parallel linear recurrence can be to large scale sequence modelling what fast convolution algorithms are to image recognition.,1431,993,438,0.014,1.441,2025/11/05 17:19:04,0.01,1.357,0.3457943925233644,428.834
"Neural text generation models are often autoregressive language models or seq2seq models. Neural autoregressive and seq2seq models that generate text by sampling words sequentially, with each word conditioned on the previous model, are state-of-the-art for several machine translation and summarization benchmarks. These benchmarks are often defined by validation perplexity even though this is not a direct measure of sample quality. Language models are typically trained via maximum likelihood and most often with teacher forcing. Teacher forcing is well-suited to optimizing perplexity but can result in poor sample quality because generating text requires conditioning on sequences of words that were never observed at training time. We propose to improve sample quality using Generative Adversarial Network (GANs), which explicitly train the generator to produce high quality samples and have shown a lot of success in image generation. GANs were originally to designed to output differentiable values, so discrete language generation is challenging for them. We introduce an actor-critic conditional GAN that fills in missing text conditioned on the surrounding context. We show qualitatively and quantitatively, evidence that this produces more realistic text samples compared to a maximum likelihood trained model. Recurrent Neural Networks (RNNs) BID8 are the most common generative model for sequences as well as for sequence labeling tasks. They have shown impressive results in language modeling BID19 , machine translation BID32 ) and text classification BID20 . Text is typically generated from these models by sampling from a distribution that is conditioned on the previous word and a hidden state that consists of a representation of the words generated so far. These are typically trained with maximum likelihood in an approach known as teacher forcing, where ground-truth words are fed back into the model to be conditioned on for generating the following parts of the sentence. This causes problems when, during sample generation, the model is often forced to condition on sequences that were never conditioned on at training time. This leads to unpredictable dynamics in the hidden state of the RNN. Methods such as Professor Forcing BID14 and Scheduled Sampling BID1 have been proposed to solve this issue. These approaches work indirectly by either causing the hidden state dynamics to become predictable (Professor Forcing) or by randomly conditioning on sampled words at training time, however, they do not directly specify a cost function on the output of the RNN that encourages high sample quality. Our proposed method does so.Generative Adversarial Networks (GANs) BID7 are a framework for training generative models in an adversarial setup, with a generator generating images that is trying to fool a discriminator that is trained to discriminate between real and synthetic images. GANs have had a lot of success in producing more realistic images than other approaches but they have only seen limited use for text sequences. This is due to the discrete nature of text making it infeasible to propagate the gradient from the discriminator back to the generator as in standard GAN training. We overcome this by using Reinforcement Learning (RL) to train the generator while the discriminator is still trained via maximum likelihood and stochastic gradient descent. GANs also commonly suffer from issues such as training instability and mode dropping, both of which are exacerbated in a textual setting. Mode dropping occurs when certain modalities in the training set are rarely generated by the generator, for example, leading all generated images of a volcano to be multiple variants of the same volcano. This becomes a significant problem in text generation since there are many complex modes in the data, ranging from bigrams to short phrases to longer idioms. Training stability is also an issue since unlike image generation, text is generated autoregressively and thus the loss from the discriminator is only observed after a complete sentence has been generated. This problem compounds when generating longer and longer sentences.We reduce the impact of these problems by training our model on a text fill-in-the-blank or in-filling task. This is similar to the task proposed in BID3 but we use a more robust setup. In this task, portions of a body of text are deleted or redacted. The goal of the model is to then infill the missing portions of text so that it is indistinguishable from the original data. While in-filling text, the model operates autoregressively over the tokens it has thus far filled in, as in standard language modeling, while conditioning on the true known context. If the entire body of text is redacted, then this reduces to language modeling.Designing error attribution per time step has been noted to be important in prior natural language GAN research BID33 . The text infilling task naturally achieves this consideration since our discriminator will evaluate each token and thus provide a fine-grained supervision signal to the generator. Consider, for instance, if the generator produces a sequence perfectly matching the data distribution over the first t − 1 time-steps, but then produces an outlier token y t , (x 1:t−1 y t ). Despite the entire sequence now being clearly synthetic as a result of the errant token, a discriminative model that produces a high loss signal to the outlier token, but not to the others, will likely yield a more informative error signal to the generator. This research also opens further inquiry of conditional GAN models in the context of natural language.In the following sections,• We introduce a text generation model trained on in-filling (MaskGAN).• Consider the actor-critic architecture in extremely large action spaces.• Consider new evaluation metrics and the generation of synthetic training data. Our work further supports the case for matching the training and inference procedures in order to produce higher quality language samples. The MaskGAN algorithm directly achieves this through GAN-training and improved the generated samples as assessed by human evaluators.In our experiments, we generally found training where contiguous blocks of words were masked produced better samples. One conjecture is that this allows the generator an opportunity to explore longer sequences in a free-running mode; in comparison, a random mask generally has shorter sequences of blanks to fill in, so the gain of GAN-training is not as substantial. We found that policy gradient methods were effective in conjunction with a learned critic, but the highly active research on training with discrete nodes may present even more stable training procedures.We also found the use of attention was important for the in-filled words to be sufficiently conditioned on the input context. Without attention, the in-filling would fill in reasonable subsequences that became implausible in the context of the adjacent surrounding words. Given this, we suspect another promising avenue would be to consider GAN-training with attention-only models as in BID31 .In general we think the proposed contiguous in-filling task is a good approach to reduce mode collapse and help with training stability for textual GANs. We show that MaskGAN samples on a larger dataset (IMDB reviews) is significantly better than the corresponding tuned MaskMLE model as shown by human evaluation. We also show we can produce high-quality samples despite the MaskGAN model having much higher perplexity on the ground-truth test set.A TRAINING DETAILSOur model was trained with the Adam method for stochastic optimization BID13 with the default Tensorflow exponential decay rates of β 1 = 0.99 and β 2 = 0.999. Our model uses 2-layers of 650 unit LSTMs for both the generator and discriminator, 650 dimensional word embeddings, variational dropout. We used Bayesian hyperparameter tuning to tune the variational dropout rate and learning rates for the generator, discriminator and critic. We perform 3 gradient descent steps on the discriminator for every step on the generator and critic.We share the embedding and softmax weights of the generator as proposed in BID2 ; BID11 . Furthermore , to improve convergence speed, we share the embeddings of the generator and the discriminator. Additionally , as noted in our architectural section, our critic shares all of the discriminator parameters with the exception of the separate output head to estimate the value. Both our generator and discriminator use variational recurrent dropout BID6 Positive: Follow the Good Earth movie linked Vacation is a comedy that credited against the modern day era yarns which has helpful something to the modern day s best It is an interesting drama based on a story of the famed Negative: I really can t understand what this movie falls like I was seeing it I m sorry to say that the only reason I watched it was because of the casting of the Emperor I was not expecting anything as Negative: That s about so much time in time a film that persevered to become cast in a very good way I didn t realize that the book was made during the 70s The story was Manhattan the Allies were to","Neural text generation models are often autoregressive language models seq2seq models. Neural autoregressive seq2seq models generate text sampling words sequentially word conditioned previous model are state-of-the-art several machine translation summarization benchmarks. benchmarks are often defined validation perplexity even though is not a direct measure sample quality. Language models are typically trained via maximum likelihood often teacher forcing. Teacher forcing is well-suited optimizing perplexity can result poor sample quality generating text requires conditioning sequences words were never observed training time. propose improve sample quality using Generative Adversarial Network GANs which explicitly train generator produce high quality samples have shown lot success image generation. GANs were originally designed output differentiable values discrete language generation is challenging them. introduce actor-critic conditional GAN fills missing text conditioned surrounding context. show qualitatively quantitatively evidence produces realistic text samples compared maximum likelihood trained model. Recurrent Neural Networks RNNs BID8 are the most common generative model sequences well sequence labeling tasks. have shown impressive results language modeling BID19 machine translation BID32 text classification BID20. Text is typically generated models sampling distribution is conditioned previous word hidden state consists representation words generated far. are typically trained maximum likelihood approach known teacher forcing where ground-truth words are fed back model conditioned generating following parts sentence. causes problems when,during sample generation model is often forced condition sequences were never conditioned training time. leads unpredictable dynamics hidden state RNN. Methods Professor Forcing BID14 Scheduled Sampling BID1 have been proposed solve issue. approaches work indirectly either causing hidden state dynamics become predictable Professor Forcing randomly conditioning sampled words training time however do not directly specify cost function output RNN encourages high sample quality. proposed method does so.Generative Adversarial Networks GANs BID7 are a framework training generative models adversarial setup if the generator generating images is trying fool discriminator is trained discriminate real synthetic images. GANs have had a lot success producing realistic images approaches have only seen limited use text sequences. is due discrete nature text making infeasible propagate gradient discriminator back generator standard GAN training. overcome using Reinforcement Learning RL train generator discriminator is still trained via maximum likelihood stochastic gradient descent. GANs also commonly suffer issues training instability mode dropping which are exacerbated textual setting. Mode dropping occurs when certain modalities training set are rarely generated generator example leading generated images volcano multiple variants volcano. becomes significant problem text generation since are many complex modes data ranging bigrams short phrases longer idioms. Training stability is also issue since unlike image generation text is generated autoregressively thus loss discriminator is only observed complete sentence has been generated. problem compounds when generating longer longer sentences.We reduce impact problems training model text fill-in-the-blank in-filling task. is similar task proposed BID3 use robust setup. task portions body text are deleted redacted. goal model is to then infill missing portions text is indistinguishable original data. in-filling text model operates autoregressively tokens has thus far filled standard language modeling conditioning true known context. If the entire body text is redacted reduces language modeling.Designing error attribution per time step has been noted important prior natural language GAN research BID33. text infilling task naturally achieves consideration since discriminator will evaluate token thus provide fine-grained supervision signal generator. Consider instance if the generator produces sequence perfectly matching data distribution first − 1 time-steps produces outlier token x1:t−1 Despite entire sequence clearly synthetic result errant token discriminative model produces high loss signal outlier token others will likely yield informative error signal generator. research also opens inquiry conditional GAN models context natural language.In following sections • introduce text generation model trained in-filling MaskGAN.• Consider actor-critic architecture extremely large action spaces.• Consider new evaluation metrics generation synthetic training data. work supports case matching training inference procedures order produce higher quality language samples. MaskGAN algorithm directly achieves GAN-training improved generated samples assessed human evaluators.In experiments generally found training where contiguous blocks words were masked produced better samples. One conjecture is that this allows generator opportunity explore longer sequences free-running mode;comparison random mask generally has shorter sequences blanks fill gain GAN-training is not as substantial. found policy gradient methods were effective conjunction learned critic highly active research training discrete nodes may present even stable training procedures.We also found use attention was important in-filled words sufficiently conditioned input context. Without attention in-filling would fill reasonable subsequences became implausible context adjacent surrounding words. Given suspect another promising avenue would consider GAN-training attention-only models BID31.In general think proposed contiguous in-filling task is a good approach reduce mode collapse help training stability textual GANs. show MaskGAN samples larger dataset IMDB reviews is significantly better corresponding tuned MaskMLE model shown human evaluation. also show can produce high-quality samples despite MaskGAN model much higher perplexity ground-truth test set.A TRAINING DETAILSOur model was trained Adam method stochastic optimization BID13 default Tensorflow exponential decay rates β1 0.99 β2 0.999 model uses 2-layers 650 unit LSTMs generator discriminator 650 dimensional word embeddings variational dropout. used Bayesian hyperparameter tuning tune variational dropout rate learning rates generator discriminator critic. perform 3 gradient descent steps discriminator every step generator critic.We share embedding softmax weights generator proposed BID2;BID11. Furthermore improve convergence speed share embeddings generator discriminator. Additionally noted architectural section critic shares discriminator parameters exception separate output head estimate value. generator discriminator use variational recurrent dropout BID6 Positive:Follow Good Earth movie linked Vacation is a comedy credited modern day era yarns which has helpful something modern day best is an interesting drama based story famed Negative:really can t understand what this movie falls like was seeing sorry say reason watched was becauseof casting Emperor was not expecting anything Negative:much time time film persevered become cast good way realize book was made 70s story was Manhattan Allies",1722,1164,558,0.019,1.479,2025/11/05 17:19:04,0.01,1.444,0.4641744548286605,552.723
"Parametric texture models have been applied successfully to synthesize artificial images. Psychophysical studies show that under defined conditions observers are unable to differentiate between model-generated and original natural textures. In industrial applications the reverse case is of interest: a texture analysis system should decide if human observers are able to discriminate between a reference and a novel texture. For example, in case of inspecting decorative surfaces the de- tection of visible texture anomalies without any prior knowledge is required. Here, we implemented a human-vision-inspired novelty detection approach. Assuming that the features used for texture synthesis are important for human texture percep- tion, we compare psychophysical as well as learnt texture representations based on activations of a pretrained CNN in a novelty detection scenario. Additionally, we introduce a novel objective function to train one-class neural networks for novelty detection and compare the results to standard one-class SVM approaches. Our experiments clearly show the differences between human-vision-inspired texture representations and learnt features in detecting visual anomalies. Based on a dig- ital print inspection scenario we show that psychophysical texture representations are able to outperform CNN-encoded features. The idea of describing the appearance of textures using statistics goes back to the early work by Gibson BID0 BID5 and by Julesz BID10 BID11 BID12 . Since then, a number of Markov random field texture models for modelling and characterizing textures using the statistical description of local neighbourhoods were introduced by BID1 and BID4 . Another category of models tries to find a plausible texture representation for the early visual system of humans BID7 BID14 BID16 . These human-vision-inspired models are based on a decomposition of the texture to frequency and orientation bands. The well-known texture model by BID14 (PS-model) and the recently published image-computable spatial vision model by (SW-model) are two representatives of such psychophysical models. The PSmodel is based on joint statistics of complex wavelet coefficients BID21 and focuses on synthesizing realistic textures. The SW-model is based on a log-Gabor decomposition followed by an accelerating nonlinearity and normalization. In contrast to these psychophysically motivated models (assuming a plausible image representation for the early visual system), BID2 introduced a texture model based on features of a pretrained deep convolutional neural network (CNN). Using these CNN-encoded features, the model shows impressive results in generating artificial textures BID3 BID24 .Specific texture representations are required in industrial applications, e.g. for pattern recognition tasks or modelling human perception. In this work we focus on representing textures in such a way that visual anomalies can be detected when comparing reference and novel examples. This is particularly required whenever a reference texture should be reproduced visually indistinguishable. In general , the task of identifying data that differs from a reference is known as novelty detection. In contrast to classification tasks, only one class of labelled data (reference texture) is available. As an example of application, we use images of artificial wood textures which we digitised using line-scanner cameras, installed in an industrial digital printer for laminate flooring. Here, the reference texture is only available digitally as a scanned image of the initially produced reference decor. From a machine learning point of view, there are no labelled training samples available to train a supervised classifier. Another critical point is the interdependency of the surrounding texture and the visibility of specific anomalies. Hence, isolated anomaly consideration is not feasible (cf. FIG0 . In decorative surfaces , e.g. , a wallpaper of a printed brick wall or a cupboard with an artificial wood texture, each print should be indistinguishable from any other. Since humans perceive small variations in a texture when comparing two examples, the detection of visual anomalies perceived by a human observer is an open challenge in computer vision and a continuous problem in industrial applications.To learn the model of a reference texture and detect visual anomalies in novel examples, we present an unsupervised one-class neural network approach using a parametric texture representation. We summarize our main contributions as follows:• We introduce a novel objective function (MinMax-loss) to train one-class neural networks for novelty detection in textures.• We introduce psychophysically motivated texture models -PS-model and SW-model -for novelty detection using one-class classifiers and provide a comparison with deep CNN texture features.• We show texture dependent differences between the models which are of interest in visual surface inspection applications. In this paper, we evaluated the performance of novelty detection in digital print inspection using psychophysical and learnt texture representations. First we introduced state-of-the art methods for statistical and early vision based modelling of textures. While the model by BID14 focuses on synthesizing realistic textures, the model by focuses on modelling the human early vision system in an image-computable way. Another branch of texture modelling uses learnt representations based on features of a pretrained CNN BID2 . Based on the aforementioned features we learnt the reference model of a texture and detected visual anomalies in novel examples. Therefore, we introduced a novel objective for training neural network based one-class classifiers for novelty detection (OC-NN). Additionally, we compared our OC-NN approach with an OC-SVM based classifier and showed superior results in our application scenario.All texture representations achieve reasonable results, when being evaluated with our OC-NN approach on a quasi-periodic texture (cf. red-bricks). However, when being evaluated by an OC-SVM based classifier, anomalies cannot be detected using SW-as well as VGG-19-features. This might be due to the lack of preprocessing, such as z-normalisation or whitening, but this is referred to future work. Altogether the learnt texture representations provide a set of features for detecting novelties, that performs well, whether or not they are perceived by a human observer. Furthermore, PS-features provide a texture-dependent descriptor, that achieves reasonable results on quasi-periodic textures.Finally the SW-features outperform the PS-and VGG-19-features for small anomalies on aperiodic textures, which is great from the application point of view. However, when anomalies dominate (fixed patch size and increasing anomaly size), the detection rate decreases.As a part of the work for this paper, we evaluated our one-class model for novelty detection on a broad range of industrial printed decors, but more work using psychophysical data from experiments is needed. We plan to validate selected anomalies in psychophysical experiments. Further work will also include evaluating different pooling and averaging methods for SW-features. Finally, we plan to fine-tune an OC-SVM for being able to use SW-features.",Parametric texture models have been applied successfully synthesize artificial images. Psychophysical studies show defined conditions observers are unable differentiate model-generated original natural textures. industrial applications reverse case is of interest:texture analysis system should decide if human observers are able discriminate reference novel texture. example case inspecting decorative surfaces de- tection visible texture anomalies without prior knowledge is required. implemented human-vision-inspired novelty detection approach. Assuming features used texture synthesis are important human texture percep- tion compare psychophysical well learnt texture representations based activations pretrained CNN novelty detection scenario. Additionally introduce novel objective function train one-class neural networks novelty detection compare results standard one-class SVM approaches. experiments clearly show differences human-vision-inspired texture representations learnt features detecting visual anomalies. Based dig- ital print inspection scenario show psychophysical texture representations are able outperform CNN-encoded features. idea describing appearance textures using statistics goes back early work Gibson BID0 BID5 Julesz BID10 BID11 BID12. Since number Markov random field texture models modelling characterizing textures using statistical description local neighbourhoods were introduced BID1 BID4. Another category models tries find plausible texture representation early visual system humans BID7 BID14 BID16. human-vision-inspired models are based decomposition texture frequency orientation bands. well-known texture model BID14 PS-model recently published image-computable spatial vision model SW-model are two representatives psychophysical models. PSmodel is based joint statistics complex wavelet coefficients BID21 focuses synthesizing realistic textures. SW-model is based log-Gabor decomposition followed accelerating nonlinearity normalization. contrast psychophysically motivated models assuming plausible image representation early visual system BID2 introduced texture model based features pretrained deep convolutional neural network CNN Using CNN-encoded features model shows impressive results generating artificial textures BID3 BID24.Specific texture representations are required industrial applications e.g pattern recognition tasks modelling human perception. work focus representing textures way visual anomalies can be detected when comparing reference novel examples. is particularly required whenever reference texture should be reproduced visually indistinguishable. general task identifying data differs reference is known novelty detection. contrast classification tasks one class labelled data reference texture is available. example application use images artificial wood textures which we digitised using line-scanner cameras installed industrial digital printer laminate flooring. reference texture is only available digitally scanned image initially produced reference decor. machine learning point view are no labelled training samples available train supervised classifier. Another critical point is the interdependency surrounding texture visibility specific anomalies. Hence isolated anomaly consideration is not feasible cf. FIG0. decorative surfaces e.g wallpaper printed brick wall cupboard artificial wood texture print should be indistinguishable other. Since humans perceive small variations texture when comparing two examples detection visual anomalies perceived human observer is an open challenge computer vision continuous problem industrial applications.To learn model reference texture detect visual anomalies novel examples present unsupervised one-class neural network approach using parametric texture representation. summarize main contributions follows:• introduce novel objective function MinMax-loss train one-class neural networks novelty detection textures.• introduce psychophysically motivated texture models -PS-model SW-model -for novelty detection using one-class classifiers provide comparison deep CNN texture features.• show texture dependent differences models which are of interest visual surface inspection applications. paper when being evaluated performance novelty detection digital print inspection using psychophysical learnt texture representations. First introduced state-of-the art methods statistical early vision based modelling textures. model BID14 focuses synthesizing realistic textures model focuses modelling human early vision system image-computable way. Another branch texture modelling uses learnt representations based features pretrained CNN BID2. Based aforementioned features learnt reference model texture detected visual anomalies novel examples. Therefore introduced novel objective training neural network based one-class classifiers novelty detection OC-NN Additionally compared OC-NN approach OC-SVM based classifier showed superior results application scenario.All texture representations achieve reasonable results when being evaluated OC-NN approach quasi-periodic texture cf. red-bricks However when being evaluated OC-SVM based classifier when anomalies cannot detected using SW-as well VGG-19-features might due lack preprocessing z-normalisation whitening is referred future work. Altogether learnt texture representations provide set features detecting novelties performs well whether are perceived human observer. Furthermore PS-features provide texture-dependent descriptor achieves reasonable results quasi-periodic textures.Finally SW-features outperform PS-and VGG-19-features small anomalies aperiodic textures which is great application point view. However when anomalies dominate fixed patch size increasing anomaly size detection rate decreases.As part work paper when being evaluated one-class model novelty detection broad range industrial printed decors work using psychophysical data experiments is needed. plan validate selected anomalies psychophysical experiments. work will also include evaluating different pooling averaging methods SW-features Finally plan fine-tune OC-SVM able use SW-features,1308,931,377,0.013,1.405,2025/11/05 17:19:04,0.01,1.441,0.233644859813084,400.187
"In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regularization approach that encourages the supports of weight vectors in RL models to have small overlap, by simultaneously promoting near-orthogonality among vectors and sparsity of each vector. We apply the proposed regularizer to two models: neural networks (NNs) and sparse coding (SC), and develop an efficient ADMM-based algorithm for regularized SC. Experiments on various datasets demonstrate that weight vectors learned under our regularizer are more interpretable and have better generalization performance. In representation learning (RL), two critical issues need to be considered. First, how to make the learned representations more interpretable? Interpretability is a must in many applications. For instance, in a clinical setting, when applying deep learning (DL) and machine learning (ML) models to learn representations for patients and use the representations to assist clinical decision-making, we need to explain the representations to physicians such that the decision-making process is transparent, rather than being black-box. Second, how to avoid overfitting? It is often the case that the learned representations yield good performance on the training data, but perform less well on the testing data. How to improve the generalization performance on previously unseen data is important.In this paper, we make an attempt towards addressing these two issues, via a unified approach. DL/ML models designed for representation learning are typically parameterized with a collection of weight vectors, each aiming at capturing a certain latent feature. For example, neural networks are equipped with multiple layers of hidden units where each unit is parameterized by a weight vector. In another representation learning model -sparse coding BID74 , a dictionary of basis vectors are utilized to reconstruct the data. In the interpretation of RL models, a major part is to interpret the learned weight vectors. Typically, elements of a weight vector have one-to-one correspondence with observed features and a weight vector is oftentimes interpreted by examining the top observed-features that correspond to the largest weights in this vector. For instance, when applying SC to reconstruct documents that are represented with bag-of-words feature vectors, each dimension of a basis vector corresponds to one word in the vocabulary. To visualize/interpret a basis vector, one can inspect the words corresponding to the large values in this vector. To achieve better interpretability, various constraints have been imposed on the weight vectors. Some notable ones are: (1) Sparsity BID80 -which encourages most weights to be zero. Observed features that have zeros weights are considered to be irrelevant and one can focus on interpreting a few non-zero weights. (2) Diversity BID81 -which encourages different weight vectors to be mutually ""different"" (e.g., having larger angles ). By doing this, the redundancy among weight vectors is reduced and cognitively one can map each weight vector to a physical concept in a more unambiguous way. (3) Non-negativeness BID66 -which encourages the weights to be nonnegative since in certain scenarios (e.g., bag of words representation of documents), it is difficult to make sense of negative weights. In this paper, we propose a new perspective of interpretability: less-overlapness, which encourages the weight vectors to have small overlap in supports 1 . By doing this, each weight vector is anchored on a unique subset of observed features without being redundant with other vectors, which greatly facilitates interpretation. For example, if topic models BID47 are learned in such a way, each topic will be characterized by a few representative words and the representative words of different topics are different. Such topics are more amenable for interpretation. Besides improving interpretability, less-overlapness helps alleviate overfitting. It imposes a structural constraint over the weight vectors, thus can effectively shrink the complexity of the function class induced by the RL models and improve the generalization performance on unseen data.To encourage less-overlapness, we propose a regularizer that simultaneously encourages different weight vectors to be close to being orthogonal and each vector to be sparse, which jointly encourage vectors' supports to have small overlap. The major contributions of this work include:• We propose a new type of regularization approach which encourages less-overlapness, for the sake of improving interpretability and reducing overfitting.• We apply the proposed regularizer to two models: neural networks and sparse coding (SC), and derive an efficient ADMM-based algorithm for the regularized SC problem.• In experiments, we demonstrate the empirical effectiveness of this regularizer. In this paper, we propose a new type of regularization approach that encourages the weight vectors to have less-overlapped supports. The proposed LDD-L1 regularizer simultaneously encourages the weight vectors to be sparse and close to being orthogonal, which jointly produces the effects of less overlap. We apply this regularizer to two models: neural networks and sparse coding (SC), and derive an efficient ADMM-based algorithm for solving the regularized SC problem. Experiments on various datasets demonstrate the effectiveness of this regularizer in alleviating overfitting and improving interpretability.",representation learning RL how to make learned representations easy interpret less overfitted training data are two important challenging issues. address problems study new type regularization approach encourages supports weight vectors RL models have small overlap simultaneously promoting near-orthogonality among vectors sparsity vector. apply proposed regularizer two models:neural networks NNs sparse coding SC develop efficient ADMM-based algorithm regularizedSC. Experiments various datasets demonstrate weight vectors learned regularizer are more interpretable have better generalization performance. representation learning RL two critical issues need considered. First how to make learned representations interpretable? Interpretability is a must many applications. instance clinical setting when applying deep learning DL machine learning ML models learn representations patients use representations assist clinical decision-making need explain representations physicians decision-making process is transparent rather black-box Second how to avoid overfitting? is often case learned representations yield good performance training data perform less well testing data. How to improve generalization performance previously unseen data is important.In paper how to make attempt towards addressing two issues via unified approach. DL/ML models designed representation learning are typically parameterized collection weight vectors aiming capturing certain latent feature. example neural networks are equipped multiple layers hidden units where each unit is parameterized weight vector. another representation learning model -sparse coding BID74 dictionary basis vectors are utilized reconstruct data. interpretation RL models major part is to interpret learned weight vectors. Typically elements weight vector have one-to-one correspondence observed features weight vector is oftentimes interpreted examining top observed-features correspond largest weights vector. instance when applyingSC reconstruct documents are represented bag-of-words feature vectors dimension basis vector corresponds one word vocabulary. visualize/interpret basis vector one can inspect words corresponding large values vector. achieve better interpretability various constraints have been imposed weight vectors. notable ones are:1 Sparsity BID80 -which encourages weights zero. Observed features have zeros weights are considered irrelevant one can focus interpreting non-zero weights. 2 Diversity BID81 -which encourages different weight vectors mutually different e.g larger angles redundancy among weight vectors is reduced cognitively one can map weight vector physical concept unambiguous way. 3 Non-negativeness BID66 -which encourages weights nonnegative since certain scenarios e.g bag words representation documents is difficult make sense negative weights. paper propose new perspective interpretability:less-overlapness which encourages weight vectors have small overlap supports1. weight vector is anchored unique subset observed features without redundant vectors which greatly facilitates interpretation. example if topic models BID47 are learned way if topic will be characterized representative words representative words different topics are different. topics are more amenable interpretation. Besides improving interpretability less-overlapness helps alleviate overfitting. imposes structural constraint weight vectors thus can effectively shrink complexity function class induced RL models improve generalization performance unseen data.To encourage less-overlapness propose regularizer simultaneously encourages different weight vectors close orthogonal vector sparse which jointly encourage vectors' supports have small overlap. major contributions work include:• propose new type regularization approach which encourages less-overlapness sake improving interpretability reducing overfitting.• apply proposed regularizer two models:neural networks sparse coding SC derive efficient ADMM-based algorithm regularized SC problem.• experiments demonstrate empirical effectiveness regularizer. paper propose new type regularization approach encourages weight vectors have less-overlapped supports. proposed LDD-L1 regularizer simultaneously encourages weight vectors sparse close orthogonal which jointly produces effects less overlap. apply regularizer two models:neural networks sparse coding SC derive efficient ADMM-based algorithm solving regularized SC problem. Experiments various datasets demonstrate effectiveness regularizer alleviating overfitting improving interpretability.,1046,718,328,0.011,1.457,2025/11/05 17:19:04,0.0,1.262,0.3956386292834891,336.411
"Successful recurrent models such as long short-term memories (LSTMs) and gated recurrent units (GRUs) use \emph{ad hoc} gating mechanisms.   Empirically these models have been found to improve the learning of medium to long term temporal dependencies and to help with vanishing gradient issues.
	
 We prove that learnable gates in a recurrent model formally provide \emph{quasi-invariance to general time transformations} in the input data. We recover part of the LSTM architecture from a simple axiomatic approach.
	
 This result leads to a new way of initializing gate biases in LSTMs and GRUs. Experimentally, this new \emph{chrono initialization} is shown to greatly improve learning of long term dependencies, with minimal implementation effort.

 The self loop feedback gating mechanism of recurrent networks has been derived from first principles via a postulate of invariance to time warpings. Gated connections appear to regulate the local time constants in recurrent models. With this in mind, the chrono initialization, a principled way of initializing gate biases in LSTMs, has been introduced. Experimentally, chrono initialization is shown to bring notable benefits when facing long term dependencies.A ADDITIONAL EXPERIMENTS On the generalization capacity of recurrent architectures. We proceeded to test the generalization properties of RNNs, leaky RNNs and chrono RNNs on the pure warping experiments presented in Section 3. For each of the architectures, a recurrent network with 64 recurrent units is trained for 3 epochs on a variable warping task with warps between 1 and 50. Each network is then tested on warped sequences, with warps between 100 and an increasingly big maximum warping. Results are summarized in Figure 5 .All networks display reasonably good, but not perfect, generalization. Even with warps 10 times longer than the training set warps, the networks still have decent accuracy, decreasing from 100% to around 75%.Interestingly , plain RNNs and gated RNNs display a different pattern: overall, gated RNNs perform better but their generalization performance decreases faster with warps eight to ten times longer than those seen during training, while plain RNN never have perfect accuracy, below 80% even within the training set range, but have a flatter performance when going beyond the training set warp range.Pixel level classification: MNIST and pMNIST. This task, introduced in BID15 , consists in classifying images using a recurrent model. The model is fed pixels one by one, from top to bottom, left to right, and has to output a probability distribution for the class of the object in the image.We evaluate standard and chrono initialization on two image datasets: MNIST (LeCun et al., 1999) and permuted MNIST, that is, MNIST where all images have undergone the same pixel permutation.LSTMs with 512 hidden units are used. Once again, standard initialization sets forget biases to 1, and the chrono initialization parameter is set to the length of the input sequences, max = 784. Results on the validation set are provided in Figure 6 . On non-permuted MNIST, there is no clear difference , even though the best validation error is obtained with chrono initialization. On permuted MNIST, chrono initialization performs better, with a best validation result of 96.3%, while standard initialization obtains a best validation result of 95.4%.Next character prediction on text8. Chrono initialization is benchmarked against standard initialization on the character level text8 dataset BID17 . Text8 is a 100M character formatted text sample from Wikipedia. BID21 's train-valid-test split is used: the first 90M characters are used as training set, the next 5M as validation set and the last 5M as test set.The exact same setup as in BID3 ) is used, with the code directly taken from there. Namely: LSTMs with 2000 units, trained with Adam BID13 with learning rate 10 −3 , batches of size 128 made of non-overlapping sequences of length 180, and gradient clipping at 1.0. Weights are orthogonally initialized, and recurrent batch normalization BID3 ) is used.Chrono initialization with max = 8 is compared to standard = 1 initialization. Results are presented in FIG4 . On the validation set, chrono initialization uniformly outperforms standard initialization by a small margin. On the test set, the compression rate is 1.37 with chrono initialization, versus 1.38 for standard initialization.8 This same slight difference is observed on two independent runs.Our guess is that , on next character prediction, with moderately sized networks, short term dependencies dominate, making the difference between standard and chrono initialization relatively small.Next word prediction on Penn Treebank. To attest for the resilience of chrono initialization to more complex models than simple LSTMs, we train on word level Penn Treebank BID21 using the best deep RHN network from BID25 . All hyperparameters are taken from of BID25 . For the chrono bias initialization, a single bias vector is sampled according to ∼ log( (1, max )), the carry gate bias vectors of all layers are initialized to − , and the transform gate biases to . max is chosen to be 11 (because this gives an average bias initialization close to the value 2 from (Zilly et al., 2016)).9 . Without further hyperparameter search and with a single run, we obtain test results similar to BID25 , with a test perplexity of 6.54.","Successful recurrent models long short-term memories LSTMs gated recurrent units GRUs use \emph ad hoc gating mechanisms. Empirically models have been found improve learning medium long term temporal dependencies help vanishing gradient issues. prove learnable gates recurrent model formally provide \emph quasi-invariance general time transformations input data. recover part LSTM architecture simple axiomatic approach. result leads new way initializing gate biases LSTMs GRUs. Experimentally new \emph chrono initialization is shown greatly improve learning long term dependencies minimal implementation effort. self loop feedback gating mechanism recurrent networks has been derived first principles via postulate invariance time warpings. Gated connections appear regulate local time constants recurrent models. mind chrono initialization principled way initializing gate biases LSTMs has been introduced. Experimentally chrono initialization is shown bring notable benefits when facing long term dependencies.A ADDITIONAL EXPERIMENTS generalization capacity recurrent architectures. proceeded test generalization properties RNNs leaky RNNs chrono RNNs pure warping experiments presented Section3. architectures recurrent network 64 recurrent units is trained 3 epochs variable warping task warps 1 50. network is then tested warped sequences warps 100 increasingly big maximum warping. Results are summarized Figure 5.All networks display reasonably good perfect generalization. Even warps 10 times longer training set warps networks still have decent accuracy decreasing 100% around 75%.Interestingly plain RNNs gated RNNs display different pattern:overall gated RNNs perform better generalization performance decreases faster warps eight ten times longer seen training plain RNN never have perfect accuracy 80% even within training set range have a flatter performance when going beyond training set warp range.Pixel level classification:MNIST pMNIST. task has been introduced BID15 consists classifying images using recurrent model. model is fed pixels one one top bottom left right has to output probability distribution class object image.We evaluate standard chrono initialization two image datasets:MNIST LeCunetal. 1999 permuted MNIST MNIST where all images have undergone pixel permutation.LSTMs 512 hidden units are used. standard initialization sets forget biases 1 chrono initialization parameter is set length input sequences max 784. Results validation set are provided Figure6. non-permuted MNIST is no clear difference even though best validation error is obtained chrono initialization. permuted MNIST chrono initialization performs better best validation result 96.3 standard initialization obtains best validation result 95.4%.Next character prediction text8. Chrono initialization is benchmarked standard initialization character level text8 dataset BID17. Text8 is a 100M character formatted text sample Wikipedia. BID21 's train-valid-test split is used:first 90M characters are used training set next5M validation set last5M test set.The exact setup BID3 is used code directly taken there. Namely:LSTMs 2000 units trained Adam BID13 learning rate10−3 batches size 128 made non-overlapping sequences length 180 gradient clipping 1.0 Weights are orthogonally initialized recurrent batch normalization BID3 is used.Chrono initialization max 8 is compared standard 1 initialization. Results are presented FIG4. validation set chrono initialization uniformly outperforms standard initialization small margin. test set compression rate is 1.37 chrono initialization versus 1.38 standard initialization.8 slight difference is observed two independent runs.Our guess is that,on next character prediction moderately sized networks short term dependencies dominate making difference standard chrono initialization relatively small.Next word prediction Penn Treebank. attest resilience chrono initialization complex models simple LSTMs train word level Penn Treebank BID21 using best deep RHN network BID25. hyperparameters are taken BID25. chrono bias initialization single bias vector is sampled according ∼ log 1 max carry gate bias vectors layers are initialized − transform gate biases to. max is chosen 11 gives average bias initialization close value2 Zillyetal. 2016 .9 Without hyperparameter search single run obtain test results similar BID25 test perplexity 6.54",1147,818,329,0.011,1.402,2025/11/05 17:19:05,0.0,1.324,0.2242990654205602,322.914
"Teaching plays a very important role in our society, by spreading human knowledge and educating our next generations. A good teacher will select appropriate teaching materials, impact suitable methodologies, and set up targeted examinations, according to the learning behaviors of the students. In the field of artificial intelligence, however, one has not fully explored the role of teaching, and pays most attention to machine \emph{learning}. In this paper, we argue that equal attention, if not more, should be paid to teaching, and furthermore, an optimization framework (instead of heuristics) should be used to obtain good teaching strategies. We call this approach ``learning to teach''. In the approach, two intelligent agents interact with each other: a student model (which corresponds to the learner in traditional machine learning algorithms), and a teacher model (which determines the appropriate data, loss function, and hypothesis space to facilitate the training of the student model). The teacher model leverages the feedback from the student model to optimize its own teaching strategies by means of reinforcement learning, so as to achieve teacher-student co-evolution. To demonstrate the practical value of our proposed approach, we take the training of deep neural networks (DNN) as an example, and show that by using the learning to teach techniques, we are able to use much less training data and fewer iterations to achieve almost the same accuracy for different kinds of DNN models (e.g., multi-layer perceptron, convolutional neural networks and recurrent neural networks) under various machine learning tasks (e.g., image classification and text understanding). The evolution of modern human society heavily depends on its advanced education system. The goal of education is to equip the students with necessary knowledge and skills, so as to empower them to further deepen the understanding of the world, and push the frontier of our humanity. In general, the growth of a student will be influenced by two factors: his/her own learning ability and the teaching ability of his/her teacher. Among these two, the teacher plays a critical role: an experienced teacher enables faster learning of a student through elaborated strategies such as selecting appropriate teaching materials, imparting suitable methodologies, and setting up targeted examinations.The training of an agent in artificial intelligence (e.g., an image classification model) is very similar to the growth of a student in human society. However, after carefully revisiting the literature of artificial intelligence (AI), we find that the importance role of the teacher has not been fully realized. Researchers put most of their efforts on the student, e.g., designing various optimization algorithms to enhance the learning ability of intelligent agents. In contrast, there are very limited attempts on building good teaching strategies, as briefly summarized below. Machine teaching BID41 BID42 BID21 BID22 studies the problem of how to identify the smallest training set to push the machine learning model towards a pre-defined oracle model. Curriculum learning (CL) BID2 BID31 BID8 and self-paced learning (SPL) BID18 BID19 BID15 heuristically define the scheduling of training data in a from-easy-to-hard order. Graduated optimization BID9 heuristically refines the non-convex loss function in a from-smooth-to-sharp manner, in order to make the machine learning process more robust. These attempts are either based on task-specific heuristic rules, or the strong assumption of a pre-known oracle model. In this regard, these works have not reflected the nature of education and the best practices in human society, where a good teacher is able to adaptively adopt different teaching strategies for different students under different circumstances, and is good at constantly improving his/her own teaching skills based on the feedback from the students.In this paper, we argue that a formal study on the role of 'teaching' in artificial intelligence is sorely needed. Actually, there could be a natural analogy between teaching in artificial intelligence and teaching in human society. For example, selecting training data corresponds to choosing right teaching materials (e.g. textbooks); designing the loss functions corresponds to setting up targeted examinations; defining the hypothesis space corresponds to imparting the proper methodologies. Furthermore, an optimization framework (instead of heuristics) should be used to update the teaching skills based on the feedback from the students, so as to achieve teacher-student co-evolution. Just as French essayist Joseph Joubert said -""To teach is to learn twice"", we call this new approach ""learning to teach"" (L2T).In the L2T framework, there are two intelligent agents: a student model/agent, corresponding to the learner in traditional machine learning algorithms, and a teacher model/agent, determining the appropriate data, loss function, and hypothesis space to facilitate the learning of the student model. The training phase of L2T contains several episodes of sequential interactions between the teacher model and the student model. Based on the state information in each step, the teacher model updates the teaching actions so as to refine the machine learning problem of the student model. The student model then performs its learning process based on the inputs from the teacher model, and provides reward signals (e.g., the accuracy on the held-out development set) back to the teacher afterwards. The teacher model then utilizes such rewards to update its parameters via policy gradient methods (e.g., REINFORCE BID39 ). This interactive process is end-to-end trainable, exempt from the limitations of human-defined heuristics. Once converged, the teacher model could be applied to new learning scenarios and even new students, without extra efforts on re-training.To demonstrate the practical value of our proposed approach, we take a specific problem, training data scheduling, as an example. We show that by using our method to adaptively select the most suitable training data, we can significantly improve the accuracy and convergence speed of various neural networks including multi-layer perceptron (MLP), convolutional neural networks (CNNs) and recurrent neural networks (RNNs), for different applications including image classification and text understanding. Furthermore, the teacher model obtained by our method from one task can be smoothly transferred to other tasks. For example, with the teacher model trained on MNIST with the MLP learner, one can achieve a satisfactory performance on CIFAR-10 only using roughly half of the training data to train a ResNet model as the student. Inspired by the education systems in human society, we have proposed the framework of learning to teach, an end-to-end trainable method to automate the teaching process. Comprehensive experiments on several real-world tasks have demonstrated the effectiveness of the framework.There are many directions to explore for learning to teach in future. First, we have studied the application of L2T to image classification and sentiment analysis. We will study more applications such as machine translation and speech recognition. Second, we have focused on data teaching in this work. As stated in Subsection 3.1, we plan to investigate other teaching problems such as loss function teaching and hypothesis space teaching. Third, we have empirically verified the L2T framework through experiments. It is interesting to build theoretical foundations for learning to teach, such as the consistence and generalization of the teacher model.",Teaching plays important role society spreading human knowledge educating next generations. good teacher will select appropriate teaching materials impact suitable methodologies set targeted examinations according learning behaviors students. field artificial intelligence however one has not has not been fully explored role teaching pays attention machine \emph learning paper argue equal attention if not more shouldbe if not more shouldbe paid teaching furthermore optimization framework instead heuristics should be used obtain good teaching strategies. call approach learning teach. approach are two intelligent agents interact other:student model which corresponds learner traditional machine learning algorithms teacher model which determines appropriate data loss function hypothesis space facilitate training student model teacher model leverages feedback student model optimize teaching strategies means reinforcement learning achieve teacher-student co-evolution demonstrate practical value proposed approach take training deep neural networks DNN example show using learning teach techniques are able use much less training data fewer iterations achieve almost accuracy different kinds DNN models e.g multi-layer perceptron convolutional neural networks recurrent neural networks various machine learning tasks e.g image classification text understanding evolution modern human society heavily depends advanced education system. goal education is to equip students necessary knowledge skills empower deepen understanding world push frontier humanity. general growth student will be influenced two factors:/learning ability teaching ability/teacher. Among two teacher plays critical role:experienced teacher enables faster learning student elaborated strategies selecting appropriate teaching materials imparting suitable methodologies setting targeted examinations.The training agent artificial intelligence e.g image classification model is very similar growth student human society. However carefully revisiting literature artificial intelligence AI find importance role teacher has not has not been fully realized. Researchers put efforts student e.g designing various optimization algorithms enhance learning ability intelligent agents. contrast are very limited attempts building good teaching strategies briefly summarized below. Machine teaching BID41 BID42 BID21 BID22 studies problem how to identify smallest training set push machine learning model towards pre-defined oracle model. Curriculum learning CL BID2 BID31 BID8 self-paced learning SPL BID18 BID19 BID15 heuristically define scheduling training data from-easy-to-hard order. Graduated optimization BID9 heuristically refines non-convex loss function from-smooth-to-sharp manner order make machine learning process robust. attempts are either based task-specific heuristic rules strong assumption pre-known oracle model. regard works have not reflected nature education best practices human society where a is good teacher is able adaptively adopt different teaching strategies different students different circumstances where a is good constantly improving/teaching skills based feedback students.In paper argue formal study role 'teaching' artificial intelligence is sorely needed. Actually could natural analogy teaching artificial intelligence teaching human society. example selecting training data corresponds choosing right teaching materials e.g textbooks designing loss functions corresponds setting targeted examinations;defining hypothesis space corresponds imparting proper methodologies. Furthermore optimization framework instead heuristics should be used update teaching skills based feedback students achieve teacher-student co-evolution French essayist Joseph Joubert said -To teach is to learn twice call new approach learning teach L2T.In L2T framework are two intelligent agents:student model/agent corresponding learner traditional machine learning algorithms teacher model/agent determining appropriate data loss function hypothesis space facilitate learning student model. training phase L2T contains several episodes sequential interactions teacher model student model. Based state information step teacher model updates teaching actions refine machine learning problem student model. student model performs learning process based inputs teacher model provides reward signals e.g accuracy held-out development set back teacher afterwards. teacher model utilizes rewards update parameters via policy gradient methods e.g REINFORCE BID39 interactive process is end-to-end trainable exempt limitations human-defined heuristics. converged teacher model could applied new learning scenarios even new students without extra efforts re-training.To demonstrate practical value proposed approach take specific problem training data scheduling example. show using method adaptively select suitable training data can significantly improve accuracy convergence speed various neural networks including multi-layer perceptron MLP convolutional neural networks CNNs recurrent neural networks RNNs different applications including image classification text understanding. Furthermore teacher model obtained method one task can be smoothly transferred tasks. example teacher model trained MNIST MLP learner one can achieve satisfactory performance CIFAR-10 using roughly half training data train ResNet model student. Inspired education systems human society have proposed framework learning teach end-to-end trainable method automate teaching process. Comprehensive experiments several real-world tasks have demonstrated effectiveness framework.There are many directions explore learning teach future. First have studied application L2T image classification sentiment analysis. will study applications machine translation speech recognition. Second have focused data teaching work. stated Subsection 3.1 plan investigate teaching problems loss function teaching hypothesis space teaching. Third have empirically verified L2T framework experiments. is interesting build theoretical foundations learning teach consistence generalization teacher model.,1431,931,500,0.017,1.537,2025/11/05 17:19:05,0.01,1.471,0.6448598130841118,471.179
"We present DL2, a system for training and querying neural networks with logical constraints. The key idea is to translate these constraints into a differentiable loss with desirable mathematical properties and to then either train with this loss in an iterative manner or to use the loss for querying the network for inputs subject to the constraints. We empirically demonstrate that DL2 is effective in both training and querying scenarios, across a range of constraints and data sets. With the success of neural networks across a wide range of important application domains, a key challenge that has emerged is that of making neural networks more reliable. Promising directions to address this challenge are incorporating constraints during training BID14 BID16 and inspecting already trained networks by posing specific queries BID7 BID21 BID27 ). While useful, these approaches are described and hardcoded to particular kinds of constraints, making their application to other settings difficult.Inspired by prior work (e.g., BID3 ; BID5 ; BID10 ; BID0 ), we introduce a new method and system, called DL2 (acronym for Deep Learning with Differentiable Logic), which can be used to: (i) query networks for inputs meeting constraints, and (ii) train networks to meet logical specifications, all in a declarative fashion. Our constraint language can express rich combinations of arithmetic comparisons over inputs, neurons and outputs of neural networks using negations, conjunctions, and disjunctions. Thanks to its expressiveness, DL2 enables users to enforce domain knowledge during training or interact with the network in order to learn about its behavior via querying. DL2 works by translating logical constraints into non-negative loss functions with two key properties: (P1) a value where the loss is zero is guaranteed to satisfy the constraints, and (P2) the resulting loss is differentiable almost everywhere. Combined, these properties enable us to solve the problem of querying or training with constraints by minimizing a loss with off-the-shelf optimizers.Training with DL2 To make optimization tractable, we exclude constraints on inputs that capture convex sets and include them as constraints to the optimization goal. We then optimize with projected gradient descent (PGD), shown successful for training with robustness constraints BID14 . The expressiveness of DL2 along with tractable optimization through PGD enables us to train with new, interesting constraints. For example, we can express constraints over probabilities which are not explicitly computed by the network. Consider the following:∀x. p θ people (x) < ∨ p θ people (x) > 1 − This constraint, in the context of CIFAR-100, says that for any network input x (network is parameterized by θ), the probability of people (p people ) is either very small or very large. However, CIFAR-100 does not have the class people, and thus we define it as a function of other probabilities, in particular: p people = p baby + p boy + p girl + p man + p woman . We show that with a similar constraint (but with 20 classes), DL2 increases the prediction accuracy of CIFAR-100 networks in the semi-supervised setting, outperforming prior work whose expressiveness is more restricted. DL2 can capture constraints arising in both, classification and regression tasks. For example, GalaxyGAN BID22 , a generator of galaxy images, requires the network to respect constraints imposed by the underlying physical systems, e.g., flux: the sum of input pixels should equal the sum of output pixels. Instead of hardcoding such a constraint into the network in an ad hoc way, with DL2, this can now be expressed declaratively: sum(x) = sum(GalaxyGAN(x)).Global training A prominent feature of DL2 is its ability to train with constraints that place restrictions on inputs outside the training set. Prior work on training with constraints (e.g., BID27 ) focus on the given training set to locally train the network to meet the constraints. With DL2, we can, for the first time, query for inputs which are outside the training set, and use them to globally train the network. Previous methods that trained on examples outside the training set were either tailored to a specific task BID14 or types of networks BID16 . Our approach splits the task of global training between: (i) the optimizer , which trains the network to meet the constraints for the given inputs, and (ii) the oracle, which provides the optimizer with new inputs that aim to violate the constraints. To illustrate, consider the following Lipshcitz condition: DISPLAYFORM0 Here, for two inputs from the training set (x 1 , x 2 ), any point in their -neighborhood (z 1 , z 2 ) must satisfy the condition. This constraint is inspired by recent works (e.g., BID8 ; BID1 ) which showed that neural networks are more stable if satisfying the Lipschitz condition.Querying with DL2 We also designed an SQL-like language which enables users to interact with the model by posing declarative queries. For example, consider the scenarios studied by a recent work BID23 where authors show how to generate adversarial examples with ACGANs BID17 . The generator is used to create images from a certain class (e.g., 1) which fools a classifier (to classify as, e.g., 7). With DL2, this can be phrased as: DISPLAYFORM1 where n i n [-1, 1], c l a s s (M_NN1(M_ACGAN_G(n, 1))) = 7 r e t u r n M_ACGAN_G (n, 1) This query aims to find an input n ∈ R 100 to the generator satisfying two constraints: its entries are between −1 and 1 (enforcing a domain constraint) and it results in the generator producing an image, which it believes to be classified as 1 (enforced by M_ACGAN_G(n, 1)) but is classified by the network (M_NN1) as 7. DL2 automatically translates this query to a DL2 loss and optimizes it with an off-the-shelf optimizer (L-BFGS-B) to find solutions, in this case, the image to the right. Our language can naturally capture many prior works at the declarative level, including finding neurons responsible for a given prediction BID18 , inputs that differentiate two networks BID21 , and adversarial example generation (e.g., BID24 ). We presented DL2, a system for training and querying neural networks. DL2 supports an expressive logical fragment and provides translation rules into a differentiable (almost everywhere) loss, which is zero only for inputs satisfying the constraints. To make training tractable, we handle input constraints which capture convex sets through PGD. We also introduce a declarative language for querying networks which uses the logic and the translated loss. Experimental results indicate that DL2 is effective in both, training and querying neural networks. DISPLAYFORM0 We start by giving a proof for the if direction of the Theorem 1, i.e. if L(ϕ)(x) = 0, thenx satisfies ϕ. The proof is by induction on the formula structure (we assume ϕ is negation-free as negations can be eliminated as described in the text).As a base case, we consider formulas consisting of a single atomic constraint.• DISPLAYFORM1 , and ϕ is satisfied.• DISPLAYFORM2 and ϕ is satisfied.• DISPLAYFORM3 , and since ξ > 0, we get t 1 (x) < t 2 (x). Thus, ϕ is satisfied .As an induction step, we consider combination of formulas using single logical and or logical or operation.• DISPLAYFORM4 By the induction hypothesis, either ϕ is satisfied or ψ is satisfied, implying that ϕ ∨ ψ is satisfied. DISPLAYFORM5 By the induction hypothesis, ϕ and ψ are satisfied, implying that ϕ ∧ ψ is satisfied.","present DL2 system training querying neural networks logical constraints. key idea is to translate constraints differentiable loss desirable mathematical properties either train loss iterative manner use loss querying network inputs subject constraints. empirically demonstrate DL2 is effective training querying scenarios across range constraints data sets. success neural networks across wide range important application domains key challenge has emerged is that of making neural networks reliable. Promising directions address challenge are incorporating constraints training BID14 BID16 inspecting already trained networks posing specific queries BID7 BID21 BID27 useful approaches are described hardcoded particular kinds constraints making application settings difficult.Inspired prior work e.g BID3;BID5;BID10;BID0 introduce new method system called DL2 acronym Deep Learning Differentiable Logic which can used to:query networks inputs meeting constraints ii train networks meet logical specifications declarative fashion. constraint language can express rich combinations arithmetic comparisons inputs neurons outputs neural networks using negations conjunctions disjunctions. Thanks expressiveness DL2 enables users enforce domain knowledge training interact network order learn behavior via querying. DL2 works translating logical constraints non-negative loss functions two key properties:P1 value where the loss is zero is guaranteed satisfy constraints P2 resulting loss is differentiable almost everywhere. Combined properties enableus solve problem querying training constraints minimizing loss off-the-shelf optimizers.Training DL2 make optimization tractable exclude constraints inputs capture convex sets include constraints optimization goal. optimize projected gradient descent PGD shown successful training robustness constraints BID14. expressiveness DL2 along tractable optimization PGD enablesus train new interesting constraints. example can express constraints probabilities which are not explicitly computed network. Consider following:∀x p θ people x ∨ p θ people x 1− constraint context CIFAR-100 says network inputx network is parameterized θ probability people p people is either small large. However CIFAR-100 does not have the class people thus define function probabilities particular:p people p baby+p boy+p girl+p man+p woman. show similar constraint 20 classes DL2 increases prediction accuracy CIFAR-100 networks semi-supervised setting outperforming prior work whose expressiveness is more restricted. DL2 can capture constraints arising classification regression tasks. example GalaxyGAN BID22 generator galaxy images requires network respect constraints imposed underlying physical systems e.g flux:sum input pixels should equal sum output pixels. Instead hardcoding constraint network ad hoc way DL2 can now expressed declaratively:sum x sum GalaxyGAN x.Global training prominent feature DL2 is its ability train constraints place restrictions inputs outside training set. Prior work training constraints e.g BID27 focus given training set locally train network meet constraints. DL2 can,first time query inputs which are outside training set use globally train network. Previous methods trained examples outside training set were either tailored specific task BID14 types networks BID16. approach splits task global training between:optimizer which trains network meet constraints given inputs ii oracle which provides optimizer new inputs aim violate constraints. illustrate consider following Lipshcitz condition:DISPLAYFORM0 two inputs training set x1 x2 point -neighborhood z1 z2 must satisfy condition. constraint is inspired recent works e.g BID8;BID1 which showed neural networks are more stable if satisfying Lipschitz condition.Querying DL2 also designed SQL-like language which enables users interact model posing declarative queries. example consider scenarios studied recent work BID23 where authors show how to generate adversarial examples ACGANs BID17. generator is used create images certain class e.g 1 which fools classifier classify e.g 7 DL2 can be phrased as:DISPLAYFORM1 wheren n -1 1 cl M_NN1 M_ACGAN_G n 1 7re u r n M_ACGAN_G n 1 query aims find inputn∈R 100 generator satisfying two constraints:entries are between−1 1 enforcing domain constraint results generator producing image which it believes classified 1 enforced M_ACGAN_G n 1 is classified network M_NN1 7. DL2 automatically translates query DL2 loss optimizes off-the-shelf optimizer L-BFGS-B find solutions case image right. language can naturally capture many prior works declarative level including finding neurons responsible given prediction BID18 inputs differentiate two networks BID21 adversarial example generation e.g BID24 presented DL2 system training querying neural networks. DL2 supports expressive logical fragment provides translation rules differentiable almost everywhere loss which is zero inputs satisfying constraints. make training tractable handle input constraints which capture convex sets PGD. also introduce declarative language querying networks which uses logic translated loss. Experimental results indicate DL2 is effective training querying neural networks. DISPLAYFORM0 start giving proof if direction Theorem1.e ifL ϕ x 0 thenx satisfiesϕ. proof is by induction formula structure assumeϕ is negation-free negations can be eliminated described text.As base case consider formulas consisting single atomic constraint.• DISPLAYFORM1 ϕ is satisfied.• DISPLAYFORM2 ϕ is satisfied.• DISPLAYFORM3 sinceξ 0 get 1 x 2 x Thus ϕ is satisfied.As induction step consider combination formulas using single logical logical operation.• DISPLAYFORM4 induction hypothesis eitherϕ is satisfied ψ is satisfied implying ϕ∨ψ is satisfied. DISPLAYFORM5 induction hypothesis ϕ ψ are satisfied implying ϕ∧ψ is satisfied.",1627,1075,552,0.023,1.513,2025/11/05 17:19:05,0.01,1.442,0.5700934579439247,516.97
"Genetic algorithms have been widely used in many practical optimization problems.
 Inspired by natural selection, operators, including mutation, crossover
 and selection, provide effective heuristics for search and black-box optimization.
 However, they have not been shown useful for deep reinforcement learning, possibly
 due to the catastrophic consequence of parameter crossovers of neural networks.
 Here, we present Genetic Policy Optimization (GPO), a new genetic algorithm
 for sample-efficient deep policy optimization. GPO uses imitation learning
 for policy crossover in the state space and applies policy gradient methods for mutation.
 Our experiments on MuJoCo tasks show that GPO as a genetic algorithm
 is able to provide superior performance over the state-of-the-art policy gradient
 methods and achieves comparable or higher sample efficiency. Reinforcement learning (RL) has recently demonstrated significant progress and achieves state-ofthe-art performance in games BID14 , locomotion control BID12 , visual-navigation BID29 , and robotics BID11 . Among these successes, deep neural networks (DNNs) are widely used as powerful functional approximators to enable signal perception, feature extraction and complex decision making. For example, in continuous control tasks, the policy that determines which action to take is often parameterized by a deep neural network that takes the current state observation or sensor measurements as input. In order to optimize such policies, various policy gradient methods BID15 BID19 BID7 have been proposed to estimate gradients approximately from rollout trajectories. The core idea of these policy gradient methods is to take advantage of the temporal structure in the rollout trajectories to construct a Monte Carlo estimator of the gradient of the expected return.In addition to the popular policy gradient methods, other alternative solutions, such as those for black-box optimization or stochastic optimization, have been recently studied for policy optimization. Evolution strategies (ES) is a class of stochastic optimization techniques that can search the policy space without relying on the backpropagation of gradients. At each iteration, ES samples a candidate population of parameter vectors (""genotypes"") from a probability distribution over the parameter space, evaluates the objective function (""fitness"") on these candidates, and constructs a new probability distribution over the parameter space using the candidates with the high fitness. This process is repeated iteratively until the objective is maximized. Covariance matrix adaptation evolution strategy (CMA-ES; BID5 ) and recent work from BID18 are examples of this procedure. These ES algorithms have also shown promising results on continuous control tasks and Atari games, but their sample efficiency is often not comparable to the advanced policy gradient methods, because ES is black-box and thus does not fully exploit the policy network architectures or the temporal structure of the RL problems.Very similar to ES, genetic algorithms (GAs) are a heuristic search technique for search and optimization. Inspired by the process of natural selection, GAs evolve an initial population of genotypes by repeated application of three genetic operators -mutation, crossover and selection. One of the main differences between GA and ES is the use of the crossover operator in GA, which is able to provide higher diversity of good candidates in the population. However, the crossover operator is often performed on the parameter representations of two parents, thus making it unsuitable for nonlinear neural networks. The straightforward crossover of two neural networks by exchanging their parameters can often destroy the hierarchical relationship of the networks and thus cause a catastrophic drop in performance. NeuroEvolution of Augmenting Topologies (NEAT; BID24 a) ), which evolves neural networks through evolutionary algorithms such as GA, provides a solution to exchange and augment neurons but has found limited success when used as a method of policy search in deep RL for high-dimensional tasks. A major challenge to making GAs work for policy optimization is to design a good crossover operator which efficiently combines two parent policies represented by neural networks and generates an offspring that takes advantage of both parents. In addition, a good mutation operator is needed as random perturbations are often inefficient for high-dimensional policies.In this paper, we present Genetic Policy Optimization (GPO), a new genetic algorithm for sampleefficient deep policy optimization. There are two major technical advances in GPO. First, instead of using parameter crossover, GPO applies imitation learning for policy crossovers in the state space. The state-space crossover effectively combines two parent policies into an offspring or child policy that tries to mimic its best parent in generating similar state visitation distributions. Second, GPO applies advanced policy gradient methods for mutation. By randomly rolling out trajectories and performing gradient descent updates, this mutation operator is more efficient than random parameter perturbations and also maintains sufficient genetic diversity. Our experiments on several continuous control tasks show that GPO as a genetic algorithm is able to provide superior performance over the state-of-the-art policy gradient methods and achieves comparable or higher sample efficiency. We presented Genetic Policy Optimization (GPO), a new approach to deep policy optimization which combines ideas from evolutionary algorithms and reinforcement learning. First, GPO does efficient policy crossover in state space using imitation learning. Our experiments show the benefits of crossover in state-space over parameter-space for deep neural network policies. Second, GPO mutates the policy weights by using advanced policy gradient algorithms instead of random perturbations. We conjecture that the noisy gradient estimates used by policy gradient methods offer sufficient genetic diversity, while providing a strong learning signal. Our experiments on several MuJoCo locomotion tasks show that GPO has superior performance over the state-of-the-art policy gradient methods and achieves comparable or higher sample efficiency. Future advances in policy gradient methods and imitation learning will also likely improve the performance of GPO for challenging RL tasks. Table 2 : Mean and standard-error for final performance of GPO and baselines using A2C.",Genetic algorithms have been widely used many practical optimization problems. Inspired natural selection operators including mutation crossover selection provide effective heuristics search black-box optimization. However have not shown useful deep reinforcement learning possibly due catastrophic consequence parameter crossovers neural networks. present Genetic Policy Optimization GPO new genetic algorithm sample-efficient deep policy optimization. GPO uses imitation learning policy crossover state space applies policy gradient methods mutation. experiments MuJoCo tasks show GPO genetic algorithm is able provide superior performance state-of-the-art policy gradient methods achieves comparable higher sample efficiency. Reinforcement learning RL has recently demonstrated significant progress achieves state-ofthe-art performance games BID14 locomotion control BID12 visual-navigation BID29 robotics BID11. Among successes deep neural networks DNNs are widely used powerful functional approximators enable signal perception feature extraction complex decision making. example continuous control tasks policy determines which action take is often parameterized deep neural network takes current state observation sensor measurements input. order optimize policies various policy gradient methods BID15 BID19 BID7 have been proposed estimate gradients approximately rollout trajectories. core idea policy gradient methods is to take advantage temporal structure rollout trajectories construct Monte Carlo estimator gradient expected return.In addition popular policy gradient methods alternative solutions black-box optimization stochastic optimization have been recently studied policy optimization. Evolution strategies ES is a class stochastic optimization techniques can search policy space without relying backpropagation gradients. iteration ES samples candidate population parameter vectors genotypes probability distribution parameter space evaluates objective function fitness candidates constructs new probability distribution parameter space using candidates high fitness. process is repeated iteratively objective is maximized. Covariance matrix adaptation evolution strategy CMA-ES BID5 recent work BID18 are examples procedure. ES algorithms have also shown promising results continuous control tasks Atari games sample efficiency is often comparable advanced policy gradient methods ES is black-box thus does not fully exploit policy network architectures temporal structure RL problems.Very similar ES genetic algorithms GAs are a heuristic search technique search optimization. Inspired process natural selection GAs evolve initial population genotypes repeated application three genetic operators -mutation crossover selection. One main differences GA ES is the use crossover operator GA which is able provide higher diversity good candidates population. However crossover operator is often performed parameter representations two parents thus making unsuitable nonlinear neural networks. straightforward crossover two neural networks exchanging parameters can often destroy hierarchical relationship networks thus cause catastrophic drop performance. NeuroEvolution Augmenting Topologies NEAT;BID24 which evolves neural networks evolutionary algorithms GA provides solution exchange augment neurons has found limited success when used method policy search deepRL high-dimensional tasks. major challenge making GAs work policy optimization is to design good crossover operator which efficiently combines two parent policies represented neural networks generates offspring takes advantage parents. addition good mutation operator is needed random perturbations are often inefficient high-dimensional policies.In paper present Genetic Policy Optimization GPO new genetic algorithm sampleefficient deep policy optimization. are two major technical advances GPO. First instead using parameter crossover GPO applies imitation learning policy crossovers state space. state-space crossover effectively combines two parent policies offspring child policy tries mimic best parent generating similar state visitation distributions. Second GPO applies advanced policy gradient methods mutation. randomly rolling trajectories performing gradient descent updates mutation operator is more efficient random parameter perturbations also maintains sufficient genetic diversity. experiments several continuous control tasks show GPO genetic algorithm is able provide superior performance state-of-the-art policy gradient methods achieves comparable higher sample efficiency. presented Genetic Policy Optimization GPO new approach deep policy optimization which combines ideas evolutionary algorithms reinforcement learning. First GPO does efficient policy crossover state space using imitation learning. experiments show benefits crossover state-space parameter-space deep neural network policies. Second GPO mutates policy weights using advanced policy gradient algorithms instead random perturbations. conjecture noisy gradient estimates used policy gradient methods offer sufficient genetic diversity providing strong learning signal. experiments several MuJoCo locomotion tasks show GPO has superior performance state-of-the-art policy gradient methods achieves comparable higher sample efficiency. Future advances policy gradient methods imitation learning will also likely improve performance GPO challenging RL tasks. Table2:Mean standard-error final performance GPO baselines using A2C.,1134,804,330,0.011,1.41,2025/11/05 17:19:05,0.0,1.343,0.2492211838006226,347.332
"To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the straight-through gradient method, which enables back-propagation through the quantization mapping. Despite its empirical success, little is understood about why the straight-through gradient method works.
 Building upon a novel observation that the straight-through gradient method is in fact identical to the well-known Nesterov’s dual-averaging algorithm on a quantization constrained optimization problem, we propose a more principled alternative approach, called ProxQuant , that formulates quantized network training as a regularized learning problem instead and optimizes it via the prox-gradient method. ProxQuant does back-propagation on the underlying full-precision vector and applies an efficient prox-operator in between stochastic gradient steps to encourage quantizedness. For quantizing ResNets and LSTMs, ProxQuant outperforms state-of-the-art results on binary quantization and is on par with state-of-the-art on multi-bit quantization. We further perform theoretical analyses showing that ProxQuant converges to stationary points under mild smoothness assumptions, whereas variants such as lazy prox-gradient method can fail to converge in the same setting. Deep neural networks (DNNs) have achieved impressive results in various machine learning tasks BID6 . High-performance DNNs typically have over tens of layers and millions of parameters, resulting in a high memory usage and a high computational cost at inference time. However, these networks are often desired in environments with limited memory and computational power (such as mobile devices), in which case we would like to compress the network into a smaller, faster network with comparable performance.A popular way of achieving such compression is through quantization -training networks with lowprecision weights and/or activation functions. In a quantized neural network, each weight and/or activation can be representable in k bits, with a possible codebook of negligible additional size compared to the network itself. For example, in a binary neural network (k = 1), the weights are restricted to be in {±1}. Compared with a 32-bit single precision float, a quantized net reduces the memory usage to k/32 of a full-precision net with the same architecture BID7 BID4 BID19 BID13 BID26 BID27 . In addition, the structuredness of the quantized weight matrix can often enable faster matrixvector product, thereby also accelerating inference BID13 .Typically , training a quantized network involves (1) the design of a quantizer q that maps a full-precision parameter to a k-bit quantized parameter, and (2) the straight-through gradient method BID4 that enables back-propagation from the quantized parameter back onto the original full-precision parameter, which is critical to the success of quantized network training. With quantizer q, an iterate of the straight-through gradient method (see FIG7 proceeds Code available at https://github.com/allenbai01/ProxQuant. as θ t+1 = θ t − η t ∇L(θ)| θ=q(θt) , and q( θ) (for the converged θ) is taken as the output model. For training binary networks, choosing q(·) = sign(·) gives the BinaryConnect method BID4 .Though appealingly simple and empirically effective, it is information-theoretically rather mysterious why the straight-through gradient method works well, at least in the binary case: while the goal is to find a parameter θ ∈ {±1} d with low loss, the algorithm only has access to stochastic gradients at {±1} d . As this is a discrete set , a priori, gradients in this set do not necessarily contain any information about the function values. Indeed, a simple one-dimensional example (Figure 1b) shows that BinaryConnect fails to find the minimizer of fairly simple convex Lipschitz functions in {±1}, due to a lack of gradient information in between.rL(q(✓t)) DISPLAYFORM0 0 B N 6 N u 6 N R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" k 8 o W Y E M 4 F 9 J U h g q 5 4 4 1 T N Q W 4 X m E = "" > A A A B / n i c d V D L S g M x F M 3 U V 6 2 v U X H l J l g E V 2 W m t e 1 0 V 3 D j s o J 9 Q K e U T C Z t Q z M P k j t C G Q r + i h s X i r j 1 O 9 z 5 N 2 b a C i p 6 I O R w z r 3 k 5 H i x 4 A o s 6 8 P I r a 1 v b G 7 l t w s 7 u 3 v 7 DISPLAYFORM1 0 B N 6 N u 6 N R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" k 8 o W Y E M 4 F 9 J U h g q 5 4 4 1 T N Q W 4 X m E = "" > A A A B / n i c d V D L S g M x F M 3 U V 6 2 v U X H l J l g E V 2 W m t e 1 0 V 3 D j s o J 9 Q K e U T C Z t Q z M P k j t C G Q r + i h s X i r j 1 O 9 z 5 N 2 b a C i p 6 I O R w z r 3 k 5 H i x 4 A o s 6 8 P I r a 1 v b G 7 l t w s 7 u 3 v 7 DISPLAYFORM2 0 B N 6 N u 6 N R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" k 8 o W Y E M 4 F 9 J U h g q 5 4 4 1 T N Q W 4 X m E = "" > A A A B / n i c d V D L S g M x F M 3 U V 6 2 v U X H l J l g E V 2 W m t e 1 0 V 3 D j s o J 9 Q K e U T C Z t Q z M P k j t C G Q r + i h s X i r j 1 O 9 z 5 N 2 b a C i p 6 I O R w z r 3 k 5 H i x 4 A o s 6 8 P I r a 1 v b G 7 l t w s 7 u 3 v 7 DISPLAYFORM3 0 B N 6 N u 6 N R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > q(✓t) DISPLAYFORM4 a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" DISPLAYFORM5 a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" DISPLAYFORM6 a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" DISPLAYFORM7 a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e x i t > rL(✓t) < l a t e x i t s h a 1 _ b a s e 6 4 = "" k M y 6 L o 8 X P y through method computes the gradient at the quantized vector and performs the update at the original real vector; PROXQUANT performs a gradient update at the current real vector followed by a prox step which encourages quantizedness. (b) A two-function toy failure case for BinaryConnect. The two functions are f1(x) = |x + 0.5| − 0.5 (blue) and f−1(x) = |x − 0.5| − 0.5 (orange). The derivatives of f1 and f−1 coincide at {−1, 1}, so any algorithm that only uses this information will have identical behaviors on these two functions. However, the minimizers in {±1} are x 1 = −1 and x −1 = 1, so the algorithm must fail on one of them. DISPLAYFORM8 DISPLAYFORM9 DISPLAYFORM10 DISPLAYFORM11 DISPLAYFORM12 DISPLAYFORM13 In this paper, we formulate the problem of model quantization as a regularized learning problem and propose to solve it with a proximal gradient method. Our contributions are summarized as follows.• We present a unified framework for defining regularization functionals that encourage binary, ternary, and multi-bit quantized parameters, through penalizing the distance to quantized sets (see Section 3.1). For binary quantization, the resulting regularizer is a W -shaped non-smooth regularizer, which shrinks parameters towards either −1 or 1 in the same way that the L 1 norm regularization shrinks parameters towards 0.• We propose training quantized networks using PROXQUANT (Algorithm 1) -a stochastic proximal gradient method with a homotopy scheme. Compared with the straightthrough gradient method, PROXQUANT has access to additional gradient information at non-quantized points, which avoids the problem in FIG7 and its homotopy scheme prevents potential overshoot early in the training (Section 3.2).• We demonstrate the effectiveness and flexibility of PROXQUANT through systematic experiments on (1) image classification with ResNets (Section 4.1); (2) language modeling with LSTMs (Section 4.2). The PROXQUANT method outperforms the state-of-the-art results on binary quantization and is comparable with the state-of-the-art on ternary and multi-bit quantization.• We perform a systematic theoretical study of quantization algorithms , showing that our PROXQUANT (standard prox-gradient method) converges to stataionary points under mild smoothness assumptions (Section 5.1), where as lazy prox-gradient method such as BinaryRelax BID25 fails to converge in general (Section 5.2). Further, we show that BinaryConnect has a very stringent condition to converge to any fixed point (Section 5.3), which we verify through a sign change experiment (Appendix C). In this paper, we propose and experiment with the PROXQUANT method for training quantized networks. Our results demonstrate that PROXQUANT offers a powerful alternative to the straightthrough gradient method and has theoretically better convergence properties. For future work, it would be of interest to propose alternative regularizers for ternary and multi-bit PROXQUANT and experiment with our method on larger tasks.",make deep neural networks feasible resource-constrained environments mobile devices is beneficial quantize models using low-precision weights. One common technique quantizing neural networks is the straight-through gradient method which enables back-propagation quantization mapping. Despite empirical success little is understood why the straight-through gradient method works. Building upon novel observation straight-through gradient method is in fact identical well-known Nesterovs dual-averaging algorithm quantization constrained optimization problem propose principled alternative approach called ProxQuant formulates quantized network training regularized learning problem instead optimizes via prox-gradient method. ProxQuant does back-propagation underlying full-precision vector applies efficient prox-operator stochastic gradient steps encourage quantizedness. quantizing ResNets LSTMs ProxQuant outperforms state-of-the-art results binary quantization is on par state-of-the-art multi-bit quantization. perform theoretical analyses showing ProxQuant converges stationary points mild smoothness assumptions whereas variants lazy prox-gradient method can fail converge setting. Deep neural networks DNNs have achieved impressive results various machine learning tasks BID6. High-performance DNNs typically have over tens layers millions parameters resulting high memory usage high computational cost inference time. However networks are often desired environments limited memory computational power mobile devices which case would like compress network smaller faster network comparable performance.A popular way achieving compression is through quantization -training networks lowprecision weights/activation functions. quantized neural network weight/activation can be representable k bits possible codebook negligible additional size compared network itself. example binary neural network k 1 weights are restricted ±1 Compared 32-bit single precision float quantized net reduces memory usage k/32 full-precision net architecture BID7 BID4 BID19 BID13 BID26 BID27. addition structuredness quantized weight matrix can often enable faster matrixvector product thereby also accelerating inference BID13.Typically training quantized network involves 1 design quantizerq maps full-precision parameter k-bit quantized parameter 2 straight-through gradient method BID4 enables back-propagation quantized parameter back onto original full-precision parameter which is critical success quantized network training. quantizerq iterate straight-through gradient method see FIG7 proceeds Code available https://github.com/allenbai01/ProxQuant. θ+1 θ −η ∇L θ θ=q θt q θ convergedθ is taken output model. training binary networks choosingq · sign · gives BinaryConnect method BID4.Though appealingly simple empirically effective is information-theoretically rather mysterious why the straight-through gradient method works well least binary case:goal is to find parameterθ∈ ±1 low loss algorithm has access stochastic gradients ±1 d. is a discrete set priori gradients set do not necessarily contain information function values. Indeed simple one-dimensional example Figure1b shows BinaryConnect fails find minimizer fairly simple convex Lipschitz functions ±1 due lack gradient information between.rL q ✓t DISPLAYFORM00BN 6Nu6 NR+P FeF2 5 zVzj H6 eP E7ve lpc/l ex l ex h 1 b e64 k8 W E 4F9J Uhgq 5441 NQW4 X E B/n c V L g xF 3UV6 2vUX HlJl gEV2 W e10V 3 j J9QK eU CZ Qz Pkj CGQr+h X rj1 9z5N 2b C p6 Rwzr 3k5H x4 68P r 1vbG 7l w 7u3v 7 DISPLAYFORM10B N6Nu 6NR+PFeF 2 5 zVzj H6 eP E7ve lpc/l ex l ex h 1 b e64 k8 W E 4F9J Uhgq 5441 NQW4 X E B/n c V L g xF 3UV6 2vUX HlJl gEV2 W e10V 3 j J9QK eU CZ Qz Pkj CGQr+h X rj1 9z5N 2b C p6 Rwzr 3k5H x4 68P r 1vbG 7l w 7u3v 7 DISPLAYFORM20B N6Nu 6NR+PFeF 2 5 zVzj H6 eP E7ve lpc/l ex l ex h 1 b e64 k8 W E 4F9J Uhgq 5441 NQW4 X E B/n c V L g xF 3UV6 2vUX HlJl gEV2 W e10V 3 j J9QK eU CZ Qz Pkj CGQr+h X rj1 9z5N 2b C p6 Rwzr 3k5H x4 68P r 1vbG 7l w 7u3v 7 DISPLAYFORM30B N6Nu 6NR+PFeF 2 5 zVzj H6 eP E7ve lpc/l ex q ✓t DISPLAYFORM4 EH9 ejXv j0Xg xXhe lK8 5wj9 gPH2 C n U/l ex l ex h 1 b e64 DISPLAYFORM5 EH9 ejXv j0Xg xXhe lK8 5wj9 gPH2 C n U/l ex l ex h 1 b e64 DISPLAYFORM6 EH9 ejXv j0Xg xXhe lK8 5wj9 gPH2 C n U/l ex l ex h 1 b e64 DISPLAYFORM7 EH9 ejXv j0Xg xXhe lK8 5wj9 gPH2 C n U/l ex rL ✓t l ex h 1 b e64 k 6L 8XP method computes gradient quantized vector performs update original real vector;PROXQUANT performs gradient update current real vector followed prox step which encourages quantizedness. b two-function toy failure case BinaryConnect. two functions aref1 x |x+0.5|− 0.5 blue f−1 x |x − 0.5|− 0.5 orange derivatives f1 f−1 coincide −1 1 algorithm uses information will have identical behaviors two functions. However minimizers ±1 arex1 −1 x−1 1 algorithm must fail one them. DISPLAYFORM8 DISPLAYFORM9 DISPLAYFORM10 DISPLAYFORM11 DISPLAYFORM12 DISPLAYFORM13 paper formulate problem model quantization regularized learning problem propose solve proximal gradient method. contributions are summarized follows.• present unified framework defining regularization functionals encourage binary ternary multi-bit quantized parameters penalizing distance quantized sets see Section 3.1 binary quantization resulting regularizer is a W -shaped non-smooth regularizer which shrinks parameters towards either −1 1 way L 1 norm regularization shrinks parameters towards0.• propose training quantized networks using PROXQUANT Algorithm1 -a stochastic proximal gradient method homotopy scheme. Compared straightthrough gradient method PROXQUANT has access additional gradient information non-quantized points which avoids problem FIG7 homotopy scheme prevents potential overshoot early training Section 3.2.• demonstrate effectiveness flexibility PROXQUANT systematic experiments 1 image classification ResNets Section 4.1 2 language modeling LSTMs Section 4.2 PROXQUANT method outperforms state-of-the-art results binary quantization is comparable state-of-the-art ternary multi-bit quantization.• perform systematic theoretical study quantization algorithms showing PROXQUANT standard prox-gradient method converges stataionary points mild smoothness assumptions Section 5.1 where as lazy prox-gradient method BinaryRelax BID25 fails converge general Section 5.2 show BinaryConnect has a very stringent condition converge fixed point Section 5.3 which we verify sign change experiment AppendixC paper propose experiment PROXQUANT method training quantized networks. results demonstrate PROXQUANT offers powerful alternative straightthrough gradient method has theoretically better convergence properties. future work would interest propose alternative regularizers ternary multi-bit PROXQUANT experiment method larger tasks.,2704,1703,1001,0.035,1.588,2025/11/05 17:19:05,0.02,1.462,0.8037383177570094,717.041
"Background: Statistical mechanics results (Dauphin et al. (2014); Choromanska et al. (2015)) suggest that local minima with high error are exponentially rare in high dimensions. However, to prove low error guarantees for Multilayer Neural Networks (MNNs), previous works so far required either a heavily modified MNN model or training method, strong assumptions on the labels (e.g., “near” linear separability), or an unrealistically wide hidden layer with \Omega\(N) units. 

 Results: We examine a MNN with one hidden layer of piecewise linear units, a single output, and a quadratic loss. We prove that, with high probability in the limit of N\rightarrow\infty datapoints, the volume of differentiable regions of the empiric loss containing sub-optimal differentiable local minima is exponentially vanishing in comparison with the same volume of global minima, given standard normal input of dimension d_0=\tilde{\Omega}(\sqrt{N}), and a more realistic number of d_1=\tilde{\Omega}(N/d_0) hidden units. We demonstrate our results numerically: for example, 0% binary classification training error on CIFAR with only N/d_0 = 16 hidden neurons. Motivation. Multilayer Neural Networks (MNNs), trained with simple variants of stochastic gradient descent (SGD), have achieved state-of-the-art performances in many areas of machine learning . However, theoretical explanations seem to lag far behind this empirical success (though many hardness results exist, e.g., BID44 BID42 ). For example, as a common rule-of-the-thumb, a MNN should have at least as many parameters as training samples. However, it is unclear why such over-parameterized MNNs often exhibit remarkably small generalization error (i.e., difference between ""training error"" and ""test error""), even without explicit regularization BID54 .Moreover , it has long been a mystery why MNNs often achieve low training error BID10 . SGD is only guaranteed to converge to critical points in which the gradient of the expected loss is zero BID3 , and, specifically, to local minima BID35 ) (this is true also for regular gradient descent BID29 ). Since loss functions parameterized by MNN weights are non-convex, it is unclear why does SGD often work well -rather than converging to sub-optimal local minima with high training error, which are known to exist BID16 BID50 . Understanding this behavior is especially relevant in important cases where SGD does get stuck BID20 ) -where training error may be a bottleneck in further improving performance.Ideally, we would like to quantify the probability to converge to a local minimum as a function of the error at this minimum, where the probability is taken with the respect to the randomness of the initialization of the weights, the data and SGD. Specifically, we would like to know, under which conditions this probability is very small if the error is high, as was observed empirically (e.g., BID10 BID17 ). However, this seems to be a daunting task for realistic MNNs, since it requires a characterization of the sizes and distributions of the basins of attraction for all local minima.Previous works BID10 BID7 , based on statistical physics analogies, suggested a simpler property of MNNs: that with high probability, local minima with high error diminish exponentially with the number of parameters. Though proving such a geometric property with realistic assumptions would not guarantee convergence to global minima, it appears to be a necessary first step in this direction (see discussion on section 6). It was therefore pointed out as an open problem at the Conference of Learning Theory (COLT) 2015. However, one has to be careful and use realistic MMN architectures, or this problem becomes ""too easy"".For example, one can easily achieve zero training error (Nilsson, 1965; BID2 -if the MNN's last hidden layer has more neurons than training samples. Such extremely wide MNNs are easy to optimize (Yu, 1992; BID23 BID31 BID19 BID43 Nguyen & Hein, 2017) . In this case, the hidden layer becomes linearly separable in classification tasks, with high probability over the random initialization of the weights. Thus, by training the last layer we get to a global minimum (zero training error). However, such extremely wide layers are not very useful, since they result in a huge number of weights, and serious overfitting issues. Also, training only the last layer seems to take little advantage of the inherently non-linear nature of MNNs.Therefore, in this paper we are interested to understand the properties of local and global minima, but at a more practical number of parameters -and when at least two weight layers are trained. For example, Alexnet BID27 is trained using about 1.2 million ImageNet examples, and has about 60 million parameters -16 million of these in the two last weight layers. Suppose we now train the last two weight layers in such an over-parameterized MNN. When do the sub-optimal local minima become exponentially rare in comparison to the global minima?Main contributions. We focus on MNNs with a single hidden layer and piecewise linear units, optimized using the Mean Square Error (MSE) in a supervised binary classification task (Section 2). We define N as the number of training samples, d l as the width of the l-th activation layer, and g (x)<h (x) as an asymptotic inequality in the leading order (formally: lim x→∞ log g(x)log h(x) < 1). We examine Differentiable Local Minima (DLMs) of the MSE: sub-optimal DLMs where at least a fraction of > 0 of the training samples are classified incorrectly, and global minima where all samples are classified correctly.Our main result, Theorem 10, states that, with high probability, the total volume of the differentiable regions of the MSE containing sub-optimal DLMs is exponentially vanishing in comparison to the same volume of global minima, given that: Assumption 1. The datapoints (MNN inputs) are sampled from a standard normal distribution. 4 N neurons. This improves over previously known results (Yu, 1992; BID23 BID31 BID43 Nguyen & Hein, 2017 ) -which require an extremely wide hidden layer with d 1 ≥ N neurons (and thus N d 0 parameters) to remove sub-optimal local minima with high probability.In section 5 we validate our results numerically. We show that indeed the training error becomes low when the number of parameters is close to N . For example, with binary classification on CIFAR and ImageNet, with only 16 and 105 hidden neurons (about N/d 0 ), respectively, we obtain less then 0.1% training error. Additionally, we find that convergence to non-differentiable critical points does not appear to be very common.Lastly, in section 6 we discuss our results might be extended, such as how to apply them to ""mildly"" non-differentiable critical points.Plausibility of assumptions. Assumption 1 is common in this type of analysis (Andoni et al. , 2014; BID7 BID53 BID51 BID4 . At first it may appear rather unrealistic, especially since the inputs are correlated in typical datasets. However, this no-correlation part of the assumption may seem more justified if we recall that datasets are many times whitened before being used as inputs. Alternatively, if, as in our motivating question, we consider the input to the our simple MNN to be the output of the previous layers of a deep MNN with fixed random weights, this also tends to de-correlate inputs (Poole et al., 2016, Figure 3) . The remaining part of assumption 1, that the distribution is normal , is indeed strong, but might be relaxed in the future, e.g. using central limit theorem type arguments.In assumption 2 we use this asymptotic limit to simplify our proofs and final results. Multiplicative constants and finite (yet large) N results can be found by inspection of the proofs. We assume a constant error since typically the limit → 0 is avoided to prevent overfitting.In assumption 3, for simplicity we have d 0≤ N , since in the case d 0 ≥ N the input is generically linearly separable, and sub-optimal local minima are not a problem BID18 BID39 . Additionally, we have √ N<d 0 , which seems very reasonable, since for example, d 0 /N ≈ 0.016, 0.061 and 0.055 MNIST, CIFAR and ImageNet, respectively.In assumption 4, for simplicity we have d 1< N , since, as mentioned earlier, if d 1 ≥ N the hidden layer is linearly separable with high probability, which removes sub-optimal local minima. The other bound N log 4 N<d 0 d 1 is our main innovation -a large over-parameterization which is nevertheless asymptotically mild and improves previous results.Previous work. So far, general low (training or test) error guarantees for MNNs could not be found -unless the underlying model (MNN) or learning method (SGD or its variants) have been significantly modified. For example, BID10 made an analogy with high-dimensional random Gaussian functions, local minima with high error are exponentially rare in high dimensions; BID7 BID25 replaced the units (activation functions) with independent random variables; BID36 replaces the weights and error residuals with independent random variables; (Baldi, 1989; BID40 BID20 BID32 BID57 used linear units; BID55 used unconventional units (e.g., polynomials) and very large hidden layers (d 1 = poly (d 0 ), typically N ); BID4 BID11 BID41 used a modified convnet model with less then d 0 parameters (therefore, not a universal approximator BID9 BID22 ); BID51 BID47 BID30 assume the weights are initialized very close to those of the teacher generating the labels; and BID24 BID56 ) use a non-standard tensor method during training. Such approaches fall short of explaining the widespread success of standard MNN models and training practices.Other works placed strong assumptions on the target functions. For example, to prove convergence of the training error near the global minimum, BID18 assumed linearly separable datasets, while BID39 assumed strong clustering of the targets (""near"" linear-separability). Also, (Andoni et al., 2014) showed a p-degree polynomial is learnable by a MNN, if the hidden layer is very large ( DISPLAYFORM0 , typically N ) so learning the last weight layer is sufficient. However, these are not the typical regimes in which MNNs are required or used. In contrast, we make no assumption on the target function. Other closely related results BID48 BID53 ) also used unrealistic assumptions, are discussed in section 6, in regards to the details of our main results. Therefore, in contrast to previous works, the assumptions in this paper are applicable in some situations (e.g., Gaussian input) where a MNN trained using SGD might be used and be useful (e.g., have a lower test error then a linear classier). In this paper we examine Differentiable Local Minima (DLMs) of the empiric loss of Multilayer Neural Networks (MNNs) with one hidden layer, scalar output, and LReLU nonlinearities (section 2). We prove (Theorem 10) that with high probability the angular volume (definition 3) of sub-optimal DLMs is exponentially vanishing in comparison to the angular volume of global minima (definition 4), under assumptions 1-4. This results from an upper bound on sub-optimal DLMs (Theorem 6) and a lower bound on global minima (Theorem 9). 2 /5 for 1000 epochs, then decreased the learning rate exponentially for another 1000 epochs. This was repeated 30 times. For all d and repeats, we see that (left) the final absolute value of the minimal neural input (i.e., min i,n w i x (n) ) in the range of 10 −3 − 10 0 , which is much larger then (right) the final MSE error for all d and all repeats -in the range 10 −31 − 10 −7 .Convergence of SGD to DLMs. These results suggest a mechanism through which low training error is obtained in such MNNs. However, they do not guarantee it. One issue is that sub-optimal DLMs may have exponentially large basins of attraction. We see two possible paths that might address this issue in future work, using additional assumptions on y. One approach is to show that, with high probability, no sub optimal DLM falls within the vanishingly small differentiable regions we bounded in Theorem 6. Another approach would be to bound the size of these basins of attraction, by showing that sufficiently large of number of differentiable regions near the DLM are also vanishingly small (other methods might also help here BID15 ). Another issue is that SGD might get stuck near differentiable saddle points, if their Hessian does not have strictly negative eigenvalues (i.e., the strict saddle property ). It should be straightforward to show that such points also have exponentially vanishing angular volume, similar to sub-optimal DLMs. Lastly, SGD might also converge to non-differentiable critical points, which we discuss next.Non-differentiable critical points. The proof of Theorem 6 stems from a first order necessary condition (Lemma 2): (A • X) e = 0, which is true for any DLM. However, non-differentiable critical points, in which some neural inputs are exactly zero, may also exist (though, numerically, they don't seem very common -see FIG1 .2). In this case, to derive a similar bound , we can replace the condition with P (A • X) e = 0, where P is a projection matrix to the subspace orthogonal to the non-differentiable directions. As long as there are not too many zero neural inputs, we should be able to obtain similar results. For example, if only a constant ratio r of the neural inputs are zero, we can simply choose P to remove all rows of (A • X) corresponding to those neurons, and proceed with exactly the same proof as before, with d 1 replaced with (1 − r) d 1 . It remains a theoretical challenge to find reasonable assumptions under which the number of non-differentiable directions (i.e., zero neural inputs) does not become too large.Related results. Two works have also derived related results using the (A • X) e = 0 condition from Lemma 2. In BID48 , it was noticed that an infinitesimal perturbation of A makes the matrix A • X full rank with probability 1 (Allman et al., 2009, Lemma 13 ) -which entails that e = 0 at all DLMs. Though a simple and intuitive approach, such an infinitesimal perturbation is problematic: from continuity, it cannot change the original MSE at sub-optimal DLMs -unless the weights go to infinity, or the DLM becomes non-differentiable -which are both undesirable results. An extension of this analysis was also done to constrain e using the singular values of A•X BID53 , deriving bounds that are easier to combine with generalization bounds. Though a promising approach, the size of the sub-optimal regions (where the error is high) does not vanish exponentially in the derived bounds. More importantly, these bounds require assumptions on the activation kernel spectrum γ m , which do not appear to hold in practice (e.g., BID53 , Theorems 1,3) require mγ m 1 to hold with high probability, while mγ m < 10 −2 in BID53 , FIG9 ).Modifications and extensions. There are many relatively simple extensions of these results: the Gaussian assumption could be relaxed to other near-isotropic distributions (e.g., sparse-land model, (Elad, 2010, Section 9 .2)) and other convex loss functions are possible instead of the quadratic loss. More challenging directions are extending our results to MNNs with multi-output and multiple hidden layers, or combining our training error results with novel generalization bounds which might be better suited for MNNs (e.g., BID14 BID46 BID12 ) than previous approaches BID54 .","Background:Statistical mechanics results Dauphinetal. 2014 Choromanskaetal. 2015 suggest local minima high error are exponentially rare high dimensions. However prove low error guarantees Multilayer Neural Networks MNNs previous works far required either heavily modified MNN model training method strong assumptions labels e.g near linear separability unrealistically wide hidden layer \Omega\ N units. Results:examine MNN one hidden layer piecewise linear units single output quadratic loss. prove high probability limit N\rightarrow\infty datapoints volume differentiable regions empiric loss containing sub-optimal differentiable local minima is exponentially vanishing comparison volume global minima given standard normal input dimension d_0=\tilde \Omega \sqrt N realistic number d_1=\tilde \Omega N/d_0 hidden units. demonstrate results numerically:example 0% binary classification training error CIFAR N/d_0 16 hidden neurons. Motivation. Multilayer Neural Networks MNNs trained simple variants stochastic gradient descent SGD have achieved state-of-the-art performances many areas machine learning. However theoretical explanations seem lag far behind empirical success though many hardness results exist e.g BID44 BID42 example common rule-of-the-thumb MNN should have at least are not many parameters training samples. However is unclear why such over-parameterized MNNs often exhibit remarkably small generalization error.e difference training error test error even without explicit regularization BID54.Moreover has long mystery why MNNs often achieve low training error BID10. SGD is only guaranteed converge critical points which the gradient expected loss is zero BID3 specifically local minima BID35 is true also regular gradient descent BID29 Since loss functions parameterized MNN weights are non-convex is unclear why does SGD often work well -rather converging sub-optimal local minima high training error which are known exist BID16 BID50. Understanding behavior is especially relevant important cases where SGD does get stuck BID20 -where training error may bottleneck improving performance.Ideally would like quantify probability converge local minimum function error minimum where the probability is taken respect randomness initialization weights data SGD. Specifically would like know which conditions probability is very small if the error is high was observed empirically e.g BID10 BID17 However which seems daunting task realistic MNNs since requires characterization sizes distributions basins attraction local minima.Previous works BID10 BID7 based statistical physics analogies suggested simpler property MNNs:high probability local minima high error diminish exponentially number parameters. Though proving geometric property realistic assumptions would guarantee convergence global minima appears necessary first step direction see discussion section6 was therefore pointed open problem Conference Learning Theory COLT 2015. However one has to be careful use realistic MMN architectures problem becomes easy.For example one can easily achieve zero training error Nilsson 1965;BID2 -if MNN's last hidden layer has more neurons training samples. extremely wide MNNs are easy optimize Yu 1992;BID23 BID31 BID19 BID43 Nguyen Hein 2017 case if the hidden layer becomes linearly separable classification tasks high probability random initialization weights. Thus training last layer get global minimum zero training error However extremely wide layers are not very useful since result huge number weights serious overfitting issues. Also training last layer seems take little advantage inherently non-linear nature MNNs.Therefore paper are interested understand properties local global minima practical number parameters -and when at least two weight layers are trained. example Alexnet BID27 is trained using 1.2 million ImageNet examples has about 60 million parameters -16 million two last weight layers. Suppose train last two weight layers over-parameterized MNN. When do the sub-optimal local minima become exponentially rare comparison global minima? Main contributions. focus MNNs single hidden layer piecewise linear units optimized using Mean Square Error MSE supervised binary classification task Section2 defineN number training samples l width l-th activation layer g x h x asymptotic inequality leading order formally:lim x→∞ logg x logh x 1 examine Differentiable Local Minima DLMs MSE:sub-optimal DLMs where at least fraction 0 training samples are classified incorrectly global minima where all samples are classified correctly.Our main result Theorem10 states high probability total volume differentiable regions MSE containing sub-optimal DLMs is exponentially vanishing comparison volume global minima given that:Assumption1. datapoints MNN inputs are sampled standard normal distribution. 4 N neurons. improves previously known results Yu 1992;BID23 BID31 BID43 Nguyen Hein 2017 -which require extremely wide hidden layer 1 ≥ N neurons thusN 0 parameters remove sub-optimal local minima high probability.In section5 validate results numerically. show indeed training error becomes low when the number parameters is close N. example binary classification CIFAR ImageNet 16 105 hidden neurons N/0 respectively obtain less 0.1 training error. Additionally find convergence non-differentiable critical points does not appear common.Lastly section6 discuss results might extended how apply mildly non-differentiable critical points.Plausibility assumptions. Assumption1 is common type analysis Andonietal. 2014;BID7 BID53 BID51 BID4. first may appear rather unrealistic especially since inputs are correlated typical datasets. However no-correlation part assumption may seem justified if we recall datasets are many times whitened used inputs. Alternatively if,as motivating question consider input simple MNN output previous layers deep MNN fixed random weights also tends de-correlate inputs Pooleetal. 2016 Figure3 remaining part assumption1 distribution is normal is indeed strong might relaxed future e.g using central limit theorem type arguments.In assumption2 use asymptotic limit simplify proofs final results. Multiplicative constants finite yet large N results can be found inspection proofs. assume constant error since typically limit→0 is avoided prevent overfitting.In assumption3 simplicity haved0≤N since case 0≥N input is generically linearly separable sub-optimal local minima are not a problem BID18 BID39. Additionally have√N 0 which seems reasonable since example 0/N≈ 0.016 0.061 0.055 MNIST CIFAR ImageNet respectively.In assumption4 simplicity haved1 N since mentioned earlier ifd1≥N hidden layer is linearly separable high probability which removes sub-optimal local minima. bound N log4 N 0 1 is our main innovation -a large over-parameterization which is nevertheless asymptotically mild improves previous results.Previous work. far general low training test error guarantees MNNs could found -unless underlying model MNN learning method SGD variants have been significantly modified. example BID10 made analogy high-dimensional random Gaussian functions local minima high error are exponentially rare high dimensions;BID7 BID25 replaced units activation functions independent random variables;BID36 replaces weights error residuals independent random variables;Baldi 1989;BID40 BID20 BID32 BID57 used linear units;BID55 used unconventional units e.g polynomials large hidden layers 1 poly 0 typicallyN BID4 BID11 BID41 used modified convnet model less 0 parameters therefore universal approximator BID9 BID22 BID51 BID47 BID30 assume weights are initialized close teacher generating labels;BID24 BID56 use non-standard tensor method training. approaches fall short explaining widespread success standard MNN models training practices.Other works placed strong assumptions target functions. example prove convergence training error near global minimum BID18 assumed linearly separable datasets BID39 assumed strong clustering targets near linear-separability Also Andonietal. 2014 showed p-degree polynomial is learnable MNN if the hidden layer is very large DISPLAYFORM0 typicallyN learning last weight layer is sufficient. However are not typical regimes which MNNs are required used. contrast make assumption target function. closely related results BID48 BID53 also used unrealistic assumptions are discussed section6 regards details main results. Therefore contrast previous works assumptions paper are applicable situations e.g Gaussian input where a MNN trained using SGD might used useful e.g have a lower test error linear classier paper examine Differentiable Local Minima DLMs empiric loss Multilayer Neural Networks MNNs one hidden layer scalar output LReLU nonlinearities section2 prove Theorem10 high probability angular volume definition3 sub-optimal DLMs is exponentially vanishing comparison angular volume global minima definition4 assumptions 1-4 results upper bound sub-optimal DLMs Theorem6 lower bound global minima Theorem9 2/5 1000 epochs decreased learning rate exponentially another 1000 epochs. was repeated 30 times. repeats see left final absolute value minimal neural input.e min nw x n range 10−3−10 0 which is much larger right final MSE error repeats -in range 10 −31− 10 −7.Convergence SGD DLMs. results suggest mechanism which low training error is obtained which MNNs. However do not guarantee it. One issue is that sub-optimal DLMs may have exponentially large basins attraction. see two possible paths might address issue future work using additional assumptions y. One approach is to show high probability sub optimal DLM falls within vanishingly small differentiable regions bounded Theorem6. Another approach would bound size basins attraction showing sufficiently large number differentiable regions near DLM are also vanishingly small methods might also help BID15 Another issue is that SGD might get stuck near differentiable saddle points if their Hessian does not have strictly negative eigenvalues.e strict saddle property should straightforward show points also have exponentially vanishing angular volume similar sub-optimal DLMs. Lastly SGD might also converge non-differentiable critical points which we discuss next.Non-differentiable critical points. proof Theorem 6 stems first order necessary condition Lemma2 •X e 0 which is true DLM. However non-differentiable critical points which some neural inputs are exactly zero may also exist though numerically seem common -see FIG1.2 case derive similar bound can replace condition P •X e 0 whereP is a projection matrix subspace orthogonal non-differentiable directions. long are not many zero neural inputs should be able obtain similar results. example if only a constant ratior neural inputs are zero can simply chooseP remove rows •X corresponding neurons proceed exactly proof 1 replaced 1−r 1. remains theoretical challenge find reasonable assumptions which the number non-differentiable directions.e zero neural inputs does not become large.Related results. Two works have also derived related results using •X e 0 condition Lemma2. BID48 was noticed infinitesimal perturbation makes matrix • X full rank probability1 Allmanetal. 2009 Lemma13 -which entails e 0 DLMs. Though simple intuitive approach infinitesimal perturbation is problematic:continuity cannot change original MSE sub-optimal DLMs -unless weightsgo infinity DLM becomes non-differentiable -which are both undesirable results. extension analysis was also done constrain e using singular values A•X BID53 deriving bounds are easier combine generalization bounds. Though promising approach size sub-optimal regions where the error is high does not vanish exponentially derived bounds. importantly bounds require assumptions activation kernel spectrumγ whichdo appear hold practice e.g BID53 Theorems 1,3 requiremγ 1 hold high probability mγ 10−2 BID53 FIG9.Modifications extensions. are many relatively simple extensions results:Gaussian assumption could relaxed near-isotropic distributions e.g sparse-land model Elad 2010 Section9.2 convex loss functions are possible instead quadratic loss. challenging directions are extending results MNNs multi-output multiple hidden layers combining training error results novel generalization bounds might better suited MNNs e.g BID14 BID46 BID12 previous approaches BID54.",3484,2414,1070,0.065,1.443,2025/11/05 17:19:05,0.02,1.53,0.35202492211838,1078.527
"Deep neural networks are vulnerable to adversarial examples, which can mislead classifiers by adding imperceptible perturbations. An intriguing property of adversarial examples is their good transferability, making black-box attacks feasible in real-world applications. Due to the threat of adversarial attacks, many methods have been proposed to improve the robustness, and several state-of-the-art defenses are shown to be robust against transferable adversarial examples. In this paper, we identify the attention shift phenomenon, which may hinder the transferability of adversarial examples to the defense models. It indicates that the defenses rely on different discriminative regions to make predictions compared with normally trained models. Therefore, we propose an attention-invariant attack method to generate more transferable adversarial examples. Extensive experiments on the ImageNet dataset validate the effectiveness of the proposed method. Our best attack fools eight state-of-the-art defenses at an 82% success rate on average based only on the transferability, demonstrating the insecurity of the defense techniques. Recent progress in machine learning and deep neural networks has led to substantial improvements in various pattern recognition tasks such as image understanding BID21 BID9 , speech recognition BID7 , and machine translation . However, deep neural networks are highly vulnerable to adversarial examples BID2 BID24 BID6 . They are maliciously generated by adding small perturbations to legitimate examples, but make deep neural networks produce unreasonable predictions. The existence of adversarial examples, even in the physical world BID11 BID5 BID1 , has raised concerns in security-sensitive applications, e.g., self-driving cars, healthcare and finance.Attacking deep neural networks has drawn an increasing attention since the generated adversarial examples can serve as a surrogate to evaluate the robustness of different models BID3 and help to improve the robustness BID6 BID16 . Several methods have been proposed to generate adversarial examples with the knowledge of the gradient information of a given model, such as fast gradient sign method BID6 , basic iterative method BID11 , and BID3 's method, which are known as white-box attacks. Moreover, it is shown that adversarial examples have cross-model transferability BID15 , i.e., the adversarial examples crafted for one model can fool a different model with a high probability. The transferability of adversarial examples enables practical black-box attacks to real-world applications and induces serious security issues.The threat of adversarial examples has motivated extensive research on building robust models or techniques to defend against adversarial attacks. These include training with adversarial examples BID6 BID12 BID27 BID16 , image denoising/transformation BID29 BID8 , leveraging generative models to move adversarial examples towards data manifold BID20 , and theoretically-certified defenses BID19 BID28 . Although the non-certified defenses have demonstrated robustness against common attacks, they do so by causing obfuscated gradients, which can be easily circumvented by new attacks BID0 . However, some of the defenses BID27 BID29 ; BID8 Figure 1: Demonstration of the attention shift phenomenon of the defense models compared with normally trained models. We adopt class activation mapping (Zhou et al., 2016) to visualize the attentive regions of three normally trained models-Inception v3 BID25 , Inception ResNet v2 BID26 , ResNet 152 BID9 and four defense models BID27 BID29 BID8 . These defense models focus their attention on slightly different regions compared with normally trained models, which may affect the transferability of adversarial examples. BID8 claim to be resistant to transferable adversarial examples, making black-box attacks difficult to evade these defenses.In this paper, we identify attention shift, that the defenses make predictions based on slightly different discriminative regions compared with normally trained models, as a phenomenon which may hinder the transferability of adversarial examples to the defense models. For example, we show the attention maps of several normally trained models and defense models in Fig. 1 , to represent the discriminative regions for their predictions. It is apparent that the normally trained models have similar attention maps while the defenses induce shifting attention maps. The attention shift of the defenses is caused by either training under different data distributions BID27 or transforming the inputs before classification BID29 BID8 . Therefore, the transferability of adversarial examples is largely reduced to the defenses since the structure information hidden in adversarial perturbations may be easily overlooked if a model focuses its attention on different regions.To mitigate the effect of attention shift and evade the defenses by transferable adversarial examples, we propose an attention-invariant attack method. In particular, we generate an adversarial example for an ensemble of examples composed of an legitimate one and its shifted versions. Therefore the resultant adversarial example is less sensitive to the attentive region of the white-box model being attacked and may have a bigger chance to fool another black-box model with a defense mechanism based on attention shift. We further show that this method can be simply implemented by convolving the gradient with a pre-defined kernel under a mild assumption. The proposed method can be integrated into any gradient-based attack methods such as fast gradient sign method and basic iterative method. Extensive experiments demonstrate that the proposed attention-invariant attack method helps to improve the success rates of black-box attacks against the defense models by a large margin. Our best attack reaches an average success rate of 82% to evade eight state-of-the-art defenses based only on the transferability, thus demonstrating the insecurity of the current defenses. In this paper, we propose an attention-invariant attack method to mitigate the attention shift phenomenon and generate more transferable adversarial examples against the defense models. Our method optimizes an adversarial image by using a set of shifted images. Based on an assumption, our method is simply implemented by convolving the gradient with a pre-defined kernel, and can be integrated into any gradient-based attack methods. We conduct experiments to validate the effectiveness of the proposed method. Our best attack A-DIM, the combination of the proposed attentioninvariant method and diverse input iterative method BID30 , can fool eight state-of-the-art defenses at an 82% success rate on average, where the adversarial examples are generated against four normally trained models. The results identify the vulnerability of the current defenses, which raises security issues for the development of more robust deep learning models.",Deep neural networks are vulnerable adversarial examples which can mislead classifiers adding imperceptible perturbations. intriguing property adversarial examples is their good transferability making black-box attacks feasible real-world applications. Due threat adversarial attacks many methods have been proposed improve robustness several state-of-the-art defenses are shown robust transferable adversarial examples. paper identify attention shift phenomenon may hinder transferability adversarial examples defense models. indicates defenses rely different discriminative regions make predictions compared normally trained models. Therefore propose attention-invariant attack method generate transferable adversarial examples. Extensive experiments ImageNet dataset validate effectiveness proposed method. best attack fools eight state-of-the-art defenses 82% success rate average based transferability demonstrating insecurity defense techniques. Recent progress machine learning deep neural networks has led substantial improvements various pattern recognition tasks image understanding BID21 BID9 speech recognition BID7 machine translation. However deep neural networks are highly vulnerable adversarial examples BID2 BID24 BID6. are maliciously generated adding small perturbations legitimate examples make deep neural networks produce unreasonable predictions. existence adversarial examples even physical world BID11 BID5 BID1 has raised concerns security-sensitive applications e.g self-driving cars healthcare finance.Attacking deep neural networks has drawn increasing attention since generated adversarial examples can serve surrogate evaluate robustness different models BID3 help improve robustness BID6 BID16. Several methods have been proposed generate adversarial examples knowledge gradient information given model fast gradient sign method BID6 basic iterative method BID11 BID3 's method which are known white-box attacks. Moreover is shown adversarial examples have cross-model transferability BID15.e where the adversarial examples crafted one model can fool different model high probability. transferability adversarial examples enables practical black-box attacks real-world applications induces serious security issues.The threat adversarial examples has motivated extensive research building robust models techniques defend adversarial attacks. include training adversarial examples BID6 BID12 BID27 BID16 image denoising/transformation BID29 BID8 leveraging generative models move adversarial examples towards data manifold BID20 theoretically-certified defenses BID19 BID28. Although non-certified defenses have demonstrated robustness common attacks doso causing obfuscated gradients which can be easily circumvented new attacks BID0. However defenses BID27 BID29;BID8 Figure1:Demonstration attention shift phenomenon defense models compared normally trained models. adopt class activation mapping Zhouetal. 2016 visualize attentive regions three normally trained models-Inception v3 BID25 Inception ResNet v2 BID26 ResNet 152 BID9 four defense models BID27 BID29 BID8. defense models focus attention slightly different regions compared normally trained models may affect transferability adversarial examples. BID8 claim resistant transferable adversarial examples making black-box attacks difficult evade defenses.In paper identify attention shift defenses make predictions based slightly different discriminative regions compared normally trained models phenomenon may hinder transferability adversarial examples defense models. example show attention maps several normally trained models defense models Fig. 1 represent discriminative regions predictions. is apparent normally trained models have similar attention maps defenses induce shifting attention maps. attention shift defenses is caused either training different data distributions BID27 transforming inputs classification BID29 BID8. Therefore transferability adversarial examples is largely reduced defenses since structure information hidden adversarial perturbations may easily overlooked if a model focuses attention different regions.To mitigate effect attention shift evade defenses transferable adversarial examples propose attention-invariant attack method. particular generate adversarial example ensemble examples composed legitimate one shifted versions. Therefore resultant adversarial example is less sensitive attentive region white-box model attacked may have a bigger chance fool another black-box model defense mechanism based attention shift. show method can be simply implemented convolving gradient pre-defined kernel mild assumption. proposed method can be integrated gradient-based attack methods fast gradient sign method basic iterative method. Extensive experiments demonstrate proposed attention-invariant attack method helps improve success rates black-box attacks defense models large margin. best attack reaches average success rate 82% evade eight state-of-the-art defenses based transferability thus demonstrating insecurity current defenses. paper propose attention-invariant attack method mitigate attention shift phenomenon generate transferable adversarial examples defense models. method optimizes adversarial image using set shifted images. Based assumption method is simply implemented convolving gradient pre-defined kernel can be integrated gradient-based attack methods. conduct experiments validate effectiveness proposed method. best attack A-DIM combination proposed attentioninvariant method diverse input iterative method BID30 can fool eight state-of-the-art defenses 82% success rate average where the adversarial examples are generated four normally trained models. results identify vulnerability current defenses which raises security issues development robust deep learning models.,1248,904,344,0.012,1.381,2025/11/05 17:19:05,0.01,1.382,0.158878504672897,351.488
"We present Merged-Averaged Classifiers via Hashing (MACH) for $K$-classification with large $K$. Compared to traditional one-vs-all classifiers that require $O(Kd)$ memory and inference cost, MACH only need $O(d\log{K})$ memory while only requiring $O(K\log{K} + d\log{K})$ operation for inference. MACH is the first generic $K$-classification algorithm, with provably theoretical guarantees, which requires $O(\log{K})$ memory without any assumption on the relationship between classes. MACH uses universal hashing to reduce classification with a large number of classes to few independent classification task with very small (constant) number of classes. We provide theoretical quantification of accuracy-memory tradeoff by showing the first connection between extreme classification and heavy hitters. With MACH we can train ODP dataset with 100,000 classes and 400,000 features on a single Titan X GPU (12GB), with the classification accuracy of 19.28\%, which is the best-reported accuracy on this dataset. Before this work, the best performing baseline is a one-vs-all classifier that requires 40 billion parameters (320 GB model size) and achieves 9\% accuracy.   In contrast, MACH can achieve 9\% accuracy with 480x reduction in the model size (of mere 0.6GB). With MACH, we also demonstrate complete training of fine-grained imagenet dataset (compressed size 104GB), with 21,000 classes, on a single GPU. We run MACH on these two datasets varying B and R. B and R are two knobs in MACH to balance resource and accuracy. We used plain logistic regression classifier, i.e., cross entropy loss without any regularization, in the Tensorflow environment BID0 . We plot the accuracy as a function of different values of B and R in FIG1 .The plots show that for ODP dataset MACH can even surpass OAA achieving 18% accuracy while the best-known accuracy on this partition is only 9%. LOMtree and Recall Tree can only achieve 6-6.5% accuracy. It should be noted that with 100,000 classes, a random accuracy is 10 −5 . Thus, the improvements are staggering with MACH. Even with B = 32 and R = 25, we can obtain more than 15% accuracy with 105,000 32×25 = 120 times reduction in the model size. Thus, OAA needs 160GB model size, while we only need around 1.2GB. To get the same accuracy as OAA, we only need R = 50 and B = 4, which is a 480x reduction in model size requiring mere 0.3GB model file.We believe that randomization and averaging in MACH cancel the noise and lead to better generalization. Another reason for the poor accuracy of other baselines could be due to the use of VW BID10 platforms. VW platform inherently uses feature hashing that may lose some information in features, which is critical for high dimensional datasets such as ODP.On Imagenet dataset, MACH can achieve around 11% which is roughly the same accuracy of LOMTree and Recall Tree while using R = 20 and B = 512. With R = 20 and B = 512 , the memory requirement is 21841 512×20 = 2 times less than that of OAA. On the contrary, Recall Tree and LOMTree use 2x more memory than OAA. OAA achieves the best result of 17%. With MACH, we can run at any memory budget.","present Merged-Averaged Classifiers via Hashing MACH $K $-classification large $K $. Compared traditional one-vs-all classifiers require$O Kd memory inference cost MACH need$O d\log K memory requiring$O K\log K+d\log K operation inference. MACH is the first generic $K $-classification algorithm provably theoretical guarantees which requires$O \log K memory without assumption relationship classes. MACH uses universal hashing reduce classification large number classes independent classification task small constant number classes. provide theoretical quantification accuracy-memory tradeoff showing first connection extreme classification heavy hitters. MACH can train ODP dataset 100,000 classes 400,000 features single Titan X GPU 12GB classification accuracy 19.28\ which is the best-reported accuracy dataset. work best performing baseline is a one-vs-all classifier requires 40 billion parameters 320 GB model size achieves 9\ accuracy. contrast MACH can achieve can only achieve can achieve 9\ accuracy 480x reduction model size mere 0.6GB MACH also demonstrate complete training fine-grained imagenet dataset compressed size 104GB 21,000 classes single GPU. run MACH two datasets varyingB R. B R are two knobs MACH balance resource accuracy. used plain logistic regression classifier.e cross entropy loss without regularization Tensorflow environment BID0. plot accuracy function different values B R FIG1.The plots show ODP dataset MACH can even surpass OAA achieving 18% accuracy best-known accuracy partition is only 9%. LOMtree Recall Tree can achieve can only achieve can achieve 6-6.5 accuracy. should be noted 100,000 classes random accuracy is 10 10 −5 Thus improvements are staggering MACH. Even B 32 R 25 can obtain 15% accuracy 105,000 32×25 120 times reduction model size. Thus OAA needs 160GB model size need around 1.2GB get accuracy OAA needR 50 B 4 which is a 480x reduction model size requiring mere 0.3GB model file.We believe randomization averaging MACH cancel noise lead better generalization. Another reason poor accuracy baselines could due use VW BID10 platforms. VW platform inherently uses feature hashing may lose information features which is critical high dimensional datasets ODP.On Imagenet dataset MACH can achieve can only achieve can achieve around11% which is roughly accuracy LOMTree Recall Tree usingR 20 B 512. R 20 B 512 memory requirement is 21841 512×20 2 times less OAA. contrary Recall Tree LOMTree use2x memory OAA. OAA achieves best result 17%. MACH can run memory budget.",752,549,203,0.007,1.37,2025/11/05 17:19:05,0.0,1.7,0.1246105919003116,237.271
"Gradient-based optimization is the foundation of deep learning and reinforcement learning.
 Even when the mechanism being optimized is unknown or not differentiable, optimization using high-variance or biased gradient estimates is still often the best strategy. We introduce a general framework for learning low-variance, unbiased gradient estimators for black-box functions of random variables, based on gradients of a learned function.
 These estimators can be jointly trained with model parameters or policies, and are applicable in both discrete and continuous settings. We give unbiased, adaptive analogs of state-of-the-art reinforcement learning methods such as advantage actor-critic. We also demonstrate this framework for training discrete latent-variable models. Gradient-based optimization has been key to most recent advances in machine learning and reinforcement learning. The back-propagation algorithm BID21 , also known as reverse-mode automatic differentiation BID25 BID16 computes exact gradients of deterministic, differentiable objective functions. The reparameterization trick BID33 BID7 BID17 allows backpropagation to give unbiased, lowvariance estimates of gradients of expectations of continuous random variables. This has allowed effective stochastic optimization of large probabilistic latent-variable models.Unfortunately, there are many objective functions relevant to the machine learning community for which backpropagation cannot be applied. In reinforcement learning, for example, the function being optimized is unknown to the agent and is treated as a black box BID23 . Similarly, when fitting probabilistic models with discrete latent variables, discrete sampling operations create discontinuities giving the objective function zero gradient with respect to its parameters. Much recent work has been devoted to constructing gradient estimators for these situations. In reinforcement learning, advantage actor-critic methods BID27 give unbiased gradient estimates with reduced variance obtained by jointly optimizing the policy parameters with an estimate of the value function. In discrete latent-variable models, low-variance but biased gradient estimates can be given by continuous relaxations of discrete variables BID10 BID4 .A recent advance by BID30 used a continuous relaxation of discrete random variables to build an unbiased and lower-variance gradient estimator, and showed how to tune the free parameters of these relaxations to minimize the estimator's variance during training. We generalize the method of BID30 to learn a free-form control variate parameterized by a neural network. This gives a lower-variance, unbiased gradient estimator which can be applied to a wider variety of problems. Most notably, our method is applicable even when no continuous relaxation is available, as in reinforcement learning or black-box function optimization. In this work we synthesized and generalized several standard approaches for constructing gradient estimators. We proposed a generic gradient estimator that can be applied to expectations of known or black-box functions of discrete or continuous random variables, and adds little computational overhead. We also derived a simple extension to reinforcement learning in both discrete and continuous-action domains.Future applications of this method could include training models with hard attention or memory indexing BID36 . One could also apply our estimators to continuous latentvariable models whose likelihood is non-differentiable, such as a 3D rendering engine. Extensions to the reparameterization gradient estimator BID20 BID14 could also be applied to increase the scope of distributions that can be modeled.In the reinforcement learning setting, our method could be combined with other variance-reduction techniques such as generalized advantage estimation BID5 BID24 , or other optimization methods, such as KFAC BID35 . One could also train our control variate off-policy, as in Q-prop .",Gradient-based optimization is the foundation deep learning reinforcement learning. Even when the mechanism optimized is unknown differentiable optimization using high-variance biased gradient estimates is still often best strategy. introduce general framework learning low-variance unbiased gradient estimators black-box functions random variables based gradients learned function. estimators can be jointly trained model parameters policies are applicable discrete continuous settings. give unbiased adaptive analogs state-of-the-art reinforcement learning methods advantage actor-critic also demonstrate framework training discrete latent-variable models. Gradient-based optimization has been key recent advances machine learning reinforcement learning. back-propagation algorithm BID21 also known reverse-mode automatic differentiation BID25 BID16 computes exact gradients deterministic differentiable objective functions. reparameterization trick BID33 BID7 BID17 allows backpropagation give unbiased lowvariance estimates gradients expectations continuous random variables. has allowed effective stochastic optimization large probabilistic latent-variable models.Unfortunately are many objective functions relevant machine learning community which backpropagation cannot applied. reinforcement learning example function optimized is unknown agent is treated black box BID23. Similarly when fitting probabilistic models discrete latent variables discrete sampling operations create discontinuities giving objective function zero gradient respect parameters. Much recent work has been devoted constructing gradient estimators situations. reinforcement learning advantage actor-critic methods BID27 give unbiased gradient estimates reduced variance obtained jointly optimizing policy parameters estimate value function. discrete latent-variable models low-variance biased gradient estimates can be given continuous relaxations discrete variables BID10 BID4.A recent advance BID30 used continuous relaxation discrete random variables build unbiased lower-variance gradient estimator showed how to tune free parameters relaxations minimize estimator's variance training. generalize method BID30 learn free-form control variate parameterized neural network. gives lower-variance unbiased gradient estimator which can be applied wider variety problems. notably method is applicable even when no continuous relaxation is available reinforcement learning black-box function optimization. work synthesized generalized several standard approaches constructing gradient estimators. proposed generic gradient estimator can be applied expectations known black-box functions discrete continuous random variables adds little computational overhead. also derived simple extension reinforcement learning discrete continuous-action domains.Future applications method could include training models hard attention memory indexing BID36. One could also apply estimators continuous latentvariable models whose likelihood is non-differentiable 3D rendering engine. Extensions reparameterization gradient estimator BID20 BID14 could also applied increase scope distributions can be modeled.In reinforcement learning setting method could combined variance-reduction techniques generalized advantage estimation BID5 BID24 optimization methods KFAC BID35. One could also train control variate off-policy Q-prop,685,500,185,0.006,1.37,2025/11/05 17:19:05,0.0,1.545,0.1246105919003116,218.614
"Do GANS (Generative Adversarial Nets) actually learn the target distribution? The foundational paper of Goodfellow et al. (2014) suggested they do, if they were given sufficiently large deep nets, sample size, and computation time. A recent theoretical analysis in Arora et al. (2017) raised doubts whether the same holds when discriminator has bounded size. It showed that the training objective can approach its optimum value even if the generated distribution has very low support. In other words, the training objective is unable to prevent mode collapse. The current paper makes two contributions. (1) It proposes a novel test for estimating support size using the birthday paradox of discrete probability. Using this  evidence is presented that well-known GANs approaches do learn distributions of fairly low support.   (2) It theoretically studies encoder-decoder GANs architectures (e.g., BiGAN/ALI), which were proposed to learn more meaningful features via GANs, and consequently to also solve the mode-collapse issue. Our result shows that such encoder-decoder training objectives also cannot guarantee learning of the full distribution because they cannot prevent serious mode collapse. More seriously, they cannot prevent learning meaningless codes for data, contrary to usual intuition. From the earliest papers on Generative Adversarial Networks the question has been raised whether or not they actually come close to learning the distribution they are trained with (henceforth refered to as the target distribution)? These methods train a generator deep net that converts a random seed into a realistic-looking image. Concurrently they train a discriminator deep net to discriminate between its output and real images, which in turn is used to produce gradient feedback to improve the generator net. In practice the generator deep net starts producing realistic outputs by the end, and the objective approaches its optimal value. But does this mean the deep net has learnt the target distribution of real images? Standard analysis introduced in BID3 shows that given ""sufficiently large"" generator and discriminator, sample size, and computation time the training does succeed in learning the underlying distribution arbitrarily closely (measured in JensenShannon divergence). But this does not settle the question of what happens with realistic sample and net sizes.Note that GANs differ from many previous methods for learning distributions in that they do not provide an estimate of a measure of distributional fit -e.g., perplexity score. Therefore researchers have probed their performance using surrogate qualitative tests, which were usually designed to rule out the most obvious failure mode of the training, namely, that the GAN has simply memorized the training data. One test checks the similarity of each generated image to the nearest images in the training set. Another takes two random seeds s 1 , s 2 that produced realistic images and checks the images produced using seeds lying on the line joining s 1 , s 2 . If such ""interpolating"" images are reasonable and original as well, then this may be taken as evidence that the generated distribution has many novel images. Yet other tests check for existence of semantically meaningful directions in the latent space, meaning that varying the seed along these directions leads to predictable changes e.g., (in case of images of human faces) changes in facial hair, or pose. A recent test proposed by BID12 checks the log-likelihoods of GANs using Annealed Importance Sampling, whose results indicate the mismatch between generator's distribution and the target distribution. BID8 proposed a method to trade-off between sample quality and sample diversity but they don't provide a clear definition or a quantitative metric of sample diversity.Recently a new theoretical analysis of GANs with finite sample sizes and finite discriminator size revealed the possibility that training objective can sometimes approach optimality even if the generator is far from having actually learnt the distribution. Specifically, if the discriminator has size p, then the training objective could be close to optimal even though the output distribution is supported on only O(p log p/ 2 ) images. By contrast one imagines that the target distribution usually must have very large support. For example, the set of all possible images of human faces (a frequent setting in GANs work) must involve all combinations of hair color/style, facial features, complexion, expression, pose, lighting, race, etc., and thus the possible set of images of faces approaches infinity. The above paper raises the possibility that the discriminator may be unable to meaningfully distinguish such a diverse target distribution from a trained distribution with fairly small support. Furthermore, the paper notes that this failure mode is different from the one usually feared, namely the generator memorizing training samples. The analysis of raises the possibility that the trained distribution has small support, and yet all its samples could be completely disjoint from the training samples.However, the above analysis was only a theoretical one, exhibiting a particular near-equilibrium solution that can happen from certain hyper-parameter combinations. It left open the possibility that real-life GANs training avoids such solutions thanks to some not-as-yet-understood property of SGD, or hyper-parameter choices. Thus further experimental investigation seems necessary. And yet it seems difficult at first sight to do such an empirical evaluation of the support size of a distribution: it is not humanly possible to go through hundreds of thousands of images, whereas automated tests of image similarity can be thrown off by small changes in lighting, pose etc.The current paper makes two important contributions. On the empirical side it introduces a new test for the support size of the trained distribution, and uses it to find that unfortunately these mode collapse problems do arise in many well-regarded GAN training methods. On the theoretical side we prove the limitations of encoder-decoder frameworks like BiGAN BID1 and Adversarially Learned Inference or ALI BID2 , which, inspired by autoencoder models, require the setup to learn an inference mechanism as well as a generative mechanism. The result of applies only to standard GAN training objectives (including JS and Wasserstein), but not to encoder-decoder setups. The clear hope in defining encoder-decoder setups is that the encoding mechanism ""inverts"" the generator and thus forces the generator to learn meaningful featurizations of data that are useful in downstream applications. In fact it has often been proposed that this need to learn meaningful featurizations will also solve the mode collapse problem: BID2 provide experiments on 2-dimensional mixtures of Gaussians suggesting this phenomenon. Our analysis shows not only that encoder-decoder training objectives cannot avoid mode collapse, but that they also cannot enforce learning of meaningful codes/features. The paper reveals gaps in current thinking about GANs, and hopes to stimulate further theoretical and empirical study. GANs research has always struggled with the issue of mode collapse, and recent theoretical analysis of shows that the GANs training objective is not capable of preventing mode collapse. This exhibits the existence of bad solutions in the optimization landscape. This in itself is not definitive, since existence of bad solutions is also known for the more traditional classification tasks , where heldout sets can nevertheless prove that a good solution has been reached. The difference in case of GANs is lack of an obvious way to establish that training succeeded.Our new Birthday Paradox test gives a new benchmark for testing the support size (i.e., diversity of images) in a distribution. Though it may appear weak, experiments using this test suggest that current GANs approaches, specifically, the ones that produce images of higher visual quality, do suffer mode collapse. Our rough experiments also suggest -again in line with the previous theoretical analysis-that the size of the distribution's support scales near-linearly with discriminator capacity.Researchers have raised the possibility that the best use of GANs is not distribution learning but feature learning. Encoder-decoder GAN architectures seem promising since they try to force the generator to use ""meaningful"" encodings of the image. While such architectures do exhibit slightly better diversity in our experiments, our theoretical result suggest that the the encoder-decoder objective is also unable to avoid mode collapse, furthermore, also fails to guarantee meaningful codes.","Do GANS Generative Adversarial Nets actually learn target distribution? foundational paper Goodfellowetal. 2014 suggested do,if were do,if were given sufficiently large deep nets sample size computation time. recent theoretical analysis Aroraetal. 2017 raised doubts whether holds when discriminator has bounded size. showed training objective can approach optimum value even if the generated distribution has very low support. words training objective is unable prevent mode collapse. current paper makes two contributions. 1 proposes novel test estimating support size using birthday paradox discrete probability. Using evidence is presented well-known GANs approaches do learn distributions fairly low support. 2 theoretically studies encoder-decoder GANs architectures e.g BiGAN/ALI which were proposed learn meaningful features via GANs consequently also solve mode-collapse issue. result shows encoder-decoder training objectives also cannot guarantee learning full distribution cannot prevent serious mode collapse. seriously cannot prevent learning meaningless codes data contrary usual intuition. earliest papers Generative Adversarial Networks question has been raised whether actually come close learning distribution are trained henceforth refered target distribution methods train generator deep net converts random seed realistic-looking image. Concurrently train discriminator deep net discriminate output real images which in turn is used produce gradient feedback improve generator net. practice generator deep net starts producing realistic outputs end objective approaches optimal value. does this mean deep net has learnt target distribution real images? Standard analysis introduced BID3 shows given sufficiently large generator discriminator sample size computation time training does succeed learning underlying distribution arbitrarily closely measured JensenShannon divergence does not settle question what happens realistic sample net sizes.Note GANs differ many previous methods learning distributions do provide estimate measure distributional fit-e.g perplexity score. Therefore researchers have probed performance using surrogate qualitative tests which were usually designed rule obvious failure mode training namely GAN has simply memorized training data. One test checks similarity generated image nearest images training set. Another takes two random seeds 1 2 produced realistic images checks images produced using seeds lying line joining 1 2. If such interpolating images are reasonable original well may taken evidence generated distribution has many novel images. Yet tests check existence semantically meaningful directions latent space meaning varying seed along directions leads predictable changese.g case images human faces changes facial hair pose. recent test proposed BID12 checks log-likelihoods GANs using Annealed Importance Sampling whose results indicate mismatch generator's distribution target distribution. BID8 proposed method trade-off sample quality sample diversity provide clear definition quantitative metric sample diversity.Recently new theoretical analysis GANs finite sample sizes finite discriminator size revealed possibility training objective can sometimes approach optimality even if the generator is far actually learnt distribution. Specifically if the discriminator has sizep training objective could close optimal even though output distribution is supported p logp/2 images. contrast one imagines target distribution usually must have very large support. example set possible images human faces frequent setting GANs work must involve combinations hair color/style facial features complexion expression pose lighting race etc. thus possible set images faces approaches infinity. paper raises possibility discriminator may unable meaningfully distinguish diverse target distribution trained distribution fairly small support. Furthermore paper notes failure mode is different one usually feared namely generator memorizing training samples. analysis raises possibility trained distribution has small support yet samples could completely disjoint training samples.However analysis was only a theoretical one exhibiting particular near-equilibrium solution can happen certain hyper-parameter combinations. left open possibility real-life GANs training avoids solutions thanks not-as-yet-understood property SGD hyper-parameter choices. Thus experimental investigation seems necessary. yet seems difficult first sight do such an empirical evaluation support size distribution:is not humanly possible go hundreds thousands images whereas automated tests image similarity can be thrown small changes lighting pose etc.The current paper makes two important contributions. empirical side introduces new test support size trained distribution uses find unfortunately mode collapse problems do arise many well-regarded GAN training methods. theoretical side prove limitations encoder-decoder frameworks like BiGAN BID1 Adversarially Learned Inference ALI BID2 inspired autoencoder models require setup learn inference mechanism well generative mechanism. result applies standard GAN training objectives includingJS Wasserstein encoder-decoder setups. clear hope defining encoder-decoder setups is that the encoding mechanism inverts generator thus forces generator learn meaningful featurizations data are useful downstream applications. fact has often proposed need learn meaningful featurizations will also solve mode collapse problem:BID2 provide experiments 2-dimensional mixtures Gaussians suggesting phenomenon. analysis shows encoder-decoder training objectives cannot avoid mode collapse also cannot enforce learning meaningful codes/features. paper reveals gaps current thinking GANs hopes stimulate theoretical empirical study. GANs research has always struggled issue mode collapse recent theoretical analysis shows GANs training objective is not capable preventing mode collapse. exhibits existence bad solutions optimization landscape. is definitive since existence bad solutions is also known traditional classification tasks where heldout sets can nevertheless prove good solution has been reached. difference case GANs is lack obvious way establish training succeeded.Our new Birthday Paradox test gives new benchmark testing support size.e diversity images distribution. Though may appear weak experiments using test suggest current GANs approaches specifically ones produce images higher visual quality do suffer mode collapse. rough experiments also suggest -again line previous theoretical analysis-that size distribution's support scales near-linearly discriminator capacity.Researchers have raised possibility best use GANs is not distribution learning feature learning. Encoder-decoder GAN architectures seem promising since try force generator use meaningful encodings image. architectures do exhibit slightly better diversity experiments theoretical result suggest encoder-decoder objective is also unable avoid mode collapse furthermore also fails guarantee meaningful codes.",1608,1101,507,0.019,1.46,2025/11/05 17:19:05,0.01,1.424,0.4049844236760122,525.921
"Due to their complex nature, it is hard to characterize the ways in which machine learning models can misbehave or be exploited when deployed. Recent work on adversarial examples, i.e. inputs with minor perturbations that result in substantially different model predictions, is helpful in evaluating the robustness of these models by exposing the adversarial scenarios where they fail. However, these malicious perturbations are often unnatural, not semantically meaningful, and not applicable to complicated domains such as language. In this paper, we propose a framework to generate natural and legible adversarial examples that lie on the data manifold, by searching in semantic space of dense and continuous data representation, utilizing the recent advances in generative adversarial networks. We present generated adversaries to demonstrate the potential of the proposed approach for black-box classifiers for a wide range of applications such as image classification, textual entailment, and machine translation. We include experiments to show that the generated adversaries are natural, legible to humans, and useful in evaluating and analyzing black-box classifiers. With the impressive success and extensive use of machine learning models in various securitysensitive applications, it has become crucial to study vulnerabilities in these systems. BID7 show that adversarial manipulations of input data often result in incorrect predictions from classifiers. This raises serious concerns regarding the security and integrity of existing machine learning algorithms, especially when even state-of-the-art models including deep neural networks have been shown to be highly vulnerable to adversarial attacks with intentionally worst-case perturbations to the input BID28 BID10 BID16 BID22 BID17 . These adversaries are generated effectively with access to the gradients of target models, resulting in much higher successful attack rates than data perturbed by random noise of even larger magnitude. Further, training models by including such adversaries can provide machine learning models with additional regularization benefits BID10 .Although these adversarial examples expose ""blind spots"" in machine learning models, they are unnatural, i.e. these worst-case perturbed instances are not ones the classifier is likely to face when deployed. Due to this , it is difficult to gain helpful insights into the fundamental decision behavior inside the black-box classifier: why is the decision different for the adversary, what can we change in order to prevent this behavior, and is the classifier robust to natural variations in the data when not in an adversarial scenario? Moreover, there is often a mismatch between the input space and the semantic space that we can understand. Changes to the input we may not think meaningful, like slight rotation or translation in images, often lead to substantial differences in the input instance. For example , BID24 show that minimal changes in the lighting conditions can fool automated-driving systems, a behavior adversarial examples are unable to discover. Due to the unnatural perturbations, these approaches cannot be applied to complex domains such as language, in which enforcing grammar and semantic similarity is difficult when perturbing instances. Therefore, existing approaches that find adversarial examples for text often result in ungrammatical sentences, as in the examples generated by BID19 , or require manual intervention, as in BID14 .In this paper , we introduce a framework to generate natural adversarial examples, i.e. instances that are meaningfully similar, valid/legible, and helpful for interpretation. The primary intuition Given an instance (a), existing FGSM approach BID10 adds small perturbations in (b) , that change the prediction of the model (to be ""2"", in this case).Instead of such random-looking noise, our framework generates natural adversarial examples, such as in (e), where the differences, shown in (d) (with blue/+, red/-), are meaningful changes to the strokes.behind our proposed approach is to perform the search for adversaries in a dense and continuous representation of the data instead of searching in the input data space directly. We use generative adversarial networks (GANs) to learn a projection to map normally distributed fixed-length vectors to data instances. Given an input instance, we search for adversaries in the neighborhood of its corresponding representation in latent space by sampling within a range that is recursively tightened. FIG0 provides an example of adversaries for digit recognition. Given a multi-layer perceptron (MLP) for MNIST and an image from test data FIG0 ), our approach generates a natural adversarial example ( FIG0 ) which is classified incorrectly as ""2"" by the classifier. Compared to the adversary generated by the existing Fast Gradient Sign Method (FGSM) BID10 that adds gradient-based noise FIG0 , our adversary ( FIG0 ) looks like a hand-written digit similar to the original input. Further, the difference ( FIG0 ) provides some insight into the classifier's behavior, such as the fact that slightly thickening (blue) the bottom stroke and thinning (red) the one above it, fools the classifier.We apply our approach to both image and text domains, and generate adversaries that are more natural and grammatical, semantically close to the input, and helpful to interpret the local behavior of black-box models. We present examples of natural adversaries for image classification, textual entailment, and machine translation. Experiments and human evaluation also demonstrate that our approach can help evaluate the robustness of black-box classifiers, even without labeled training data. Our framework builds upon GANs as the generative models, and thus the capabilities of GANs directly effects the quality of generated examples. In visual domains, although there have been lots of appealing results produced by GANs, the training is well known to be brittle. Many recent approaches address how to improve the training stability and the objective function of GANs BID27 . BID11 further improve the training of WGAN with regularization of gradient penalty instead of weight clipping. In our practice, we observe that we need to carefully balance the capacities of the generator, the critic, and the inverter that we introduced, to avoid situations such as model collapse. For natural languages, because of the discrete nature and non-differentiability, applications related to text generation have been relatively less studied. BID31 propose to incorporate a discrete structure autoencoder with continuous code space regularized by WGAN for text generation. Given that there are some concerns about whether GANs actually learn the distribution BID3 , it is worth noting that we can also incorporate other generative models such as Variational Auto-Encoders (VAEs) (Kingma & Welling, 2014) into our framework, as used in BID13 to generate text with controllable attributes, which we will explore in the future. We focus on GANs because adversarial training often results in higher quality images, while VAEs tend to produce blurrier ones BID8 . We also plan to apply the fusion and variant of VAEs and GANs such as α-GAN in BID26 and Wasserstein Auto-Encoders in BID29 . Note that as more advanced GANs are introduced to address these issues, they can be directly incorporated into our framework.Our iterative stochastic search algorithm for identifying adversaries is computationally expensive since it is based on naive sampling and local-search. Search based on gradients such as FGSM are not applicable to our setup because of black-box classifiers and discrete domain applications. We improve the efficiency with hybrid shrinking search by using a coarse-to-fine strategy that finds the upper-bounds by using fewer samples, and then performs finer search in the restricted range. We observe around 4× speedup with this search while achieving similar results as the iterative search. The accuracy of our inverter mapping the input to its corresponding dense vector in latent space is also important for searching adversaries in the right neighborhood. In our experiments, we find that fine-tuning the latent vector produced by the inverter with a fixed GAN can further refine the generated adversarial examples, and we will investigate other such extensions of the search in future.There is an implicit assumption in this work that the generated samples are within the same class if the added perturbations are small enough, and the generated samples look as if they belong to different classes when the perturbations are large. However, note that it is also the case for FGSM and other such approaches: when their is small, the noise is imperceptible; but with a large , one often finds noisy instances that might be in a different class (see TAB0 , digit 8 for an example). While we do observe this behavior in some cases, the corresponding classifiers require much more substantial changes to the input, which is why we can utilize our approach to evaluate black-box classifiers. In this paper, we propose a framework for generating natural adversaries against black-box classifiers, and apply the same approach to both visual and textual domains. We obtain adversaries that are legible, grammatical, and meaningfully similar to the input. We show that these natural adversaries can help in interpreting the decision behavior and evaluating the accuracy of black-box classifiers even in absence of labeled training data. We use our approach, built upon recent work in GANs, to generate adversaries for a wide range of applications including image classification, textual entailment, and machine translation (via the Google Translate API). Code used to generate such natural adversaries is available at https://github.com/zhengliz/natural-adversary.",Due complex nature is hard characterize ways which machine learning models can misbehave exploited when deployed. Recent work adversarial examples.e inputs minor perturbations result substantially different model predictions is helpful evaluating robustness models exposing adversarial scenarios where they fail. However malicious perturbations are often unnatural semantically meaningful applicable complicated domains language. paper propose framework generate natural legible adversarial examples lie data manifold searching semantic space dense continuous data representation utilizing recent advances generative adversarial networks. present generated adversaries demonstrate potential proposed approach black-box classifiers wide range applications image classification textual entailment machine translation. include experiments show generated adversaries are natural legible humans useful evaluating analyzing black-box classifiers. impressive success extensive use machine learning models various securitysensitive applications has become crucial study vulnerabilities systems. BID7 show adversarial manipulations input data often result incorrect predictions classifiers. raises serious concerns regarding security integrity existing machine learning algorithms especially when even state-of-the-art models including deep neural networks have been shown highly vulnerable adversarial attacks intentionally worst-case perturbations input BID28 BID10 BID16 BID22 BID17. adversaries are generated effectively access gradients target models resulting much higher successful attack rates data perturbed random noise even larger magnitude. training models including adversaries can provide machine learning models additional regularization benefits BID10.Although adversarial examples expose blind spots which machine learning models are unnatural.e worst-case perturbed instances are not ones classifier is likely face when deployed. Due is difficult gain helpful insights fundamental decision behavior inside black-box classifier:why is the decision different adversary what can we change order prevent behavior is the classifier robust natural variations data when not in an adversarial scenario? Moreover is often mismatch input space semantic space can understand. Changes input may think meaningful like slight rotation translation images is often lead substantial differences input instance. example BID24 show minimal changes lighting conditions can fool automated-driving systems behavior adversarial examples are unable discover. Due unnatural perturbations approaches cannot applied complex domains language which enforcing grammar semantic similarity is difficult when perturbing instances. Therefore existing approaches find adversarial examples text often result ungrammatical sentences examples generated BID19 require manual intervention BID14.In paper introduce framework generate natural adversarial examples.e instances are meaningfully similar valid/legible is helpful interpretation. primary intuition Given instance existing FGSM approach BID10 adds small perturbations b change prediction model 2 case.Instead random-looking noise framework generates natural adversarial examples e where the differences shown blue/+red/are meaningful changes strokes.behind proposed approach is to perform search adversaries dense continuous representation data instead searching input data space directly. use generative adversarial networks GANs learn projection map normally distributed fixed-length vectors data instances. Given input instance search adversaries neighborhood corresponding representation latent space sampling within range is recursively tightened. FIG0 provides example adversaries digit recognition. Given multi-layer perceptron MLP MNIST image test data FIG0 approach generates natural adversarial example FIG0 which is classified incorrectly 2 classifier. Compared adversary generated existing Fast Gradient Sign Method FGSM BID10 adds gradient-based noise FIG0 adversary FIG0 looks like hand-written digit similar original input. difference FIG0 provides insight classifier's behavior fact slightly thickening blue bottom stroke thinning red one fools classifier.We apply approach image text domains generate adversaries are more natural grammatical semantically close input is helpful interpret local behavior black-box models. present examples natural adversaries image classification textual entailment machine translation. Experiments human evaluation also demonstrate approach can help evaluate robustness black-box classifiers even without labeled training data. framework builds upon GANs generative models thus capabilities GANs directly effects quality generated examples. visual domains although have been lots appealing results produced GANs training is well known brittle. Many recent approaches address how to improve training stability objective function GANs BID27. BID11 improve training WGAN regularization gradient penalty instead weight clipping. practice observe need carefully balance capacities generator critic inverter introduced avoid situations model collapse. natural languages discrete nature non-differentiability applications related text generation have been relatively less studied. BID31 propose incorporate discrete structure autoencoder continuous code space regularized WGAN text generation. Given are some concerns whether GANs actually learn distribution BID3 is worth noting can is also incorporate generative models Variational Auto-Encoders VAEs Kingma Welling 2014 framework used BID13 generate text controllable attributes which we will explore future. focus GANs adversarial training often results higher quality images VAEs tend produce blurrier ones BID8. also plan apply fusion variant VAEs GANs α-GAN BID26 Wasserstein Auto-Encoders BID29. Note advanced GANs are introduced address issues can be directly incorporated framework.Our iterative stochastic search algorithm identifying adversaries is computationally expensive since is based naive sampling local-search Search based gradients FGSM are not applicable setup black-box classifiers discrete domain applications. improve efficiency hybrid shrinking search using coarse-to-fine strategy finds upper-bounds using fewer samples performs finer search restricted range. observe around 4× speedup search achieving similar results iterative search. accuracy inverter mapping input corresponding dense vector latent space is also important searching adversaries right neighborhood. experiments find fine-tuning latent vector produced inverter fixed GAN can further refine generated adversarial examples will investigate extensions search future.There is an implicit assumption work generated samples are within class if the added perturbations are small enough generated samples look if they belong different classes when the perturbations are large. However note can is also case FGSM approaches:when their is small noise is imperceptible;large one often finds noisy instances might different class see TAB0 digit8 example do observe behavior cases corresponding classifiers require much substantial changes input which is why can utilize approach evaluate black-box classifiers. paper propose framework generating natural adversaries black-box classifiers apply approach visual textual domains. obtain adversaries are legible grammatical meaningfully similar input. show are more natural adversaries can help interpreting decision behavior evaluating accuracy black-box classifiers even absence labeled training data. use approach built upon recent work GANs generate adversaries wide range applications including image classification textual entailment machine translation via Google Translate API Code used generate natural adversaries is available https://github.com/zhengliz/natural-adversary.,1862,1227,635,0.024,1.518,2025/11/05 17:19:05,0.01,1.485,0.585669781931464,676.653
"Kronecker-factor Approximate Curvature (Martens & Grosse, 2015) (K-FAC) is a 2nd-order optimization method which has been shown to give state-of-the-art performance on large-scale neural network optimization tasks (Ba et al., 2017).   It is based on an approximation to the Fisher information matrix (FIM) that makes assumptions about the particular structure of the network and the way it is parameterized. The original K-FAC method was applicable only to fully-connected networks, although it has been recently extended by Grosse & Martens (2016) to handle convolutional networks as well. In this work we extend the method to handle RNNs by introducing a novel approximation to the FIM for RNNs. This approximation works by modelling the covariance structure between the gradient contributions at different time-steps using a chain-structured linear Gaussian graphical model, summing the various cross-covariances, and computing the inverse in closed form. We demonstrate in experiments that our method significantly outperforms general purpose state-of-the-art optimizers like SGD with momentum and Adam on several challenging RNN training tasks. As neural networks have become ubiquitous in both research and applications the need to efficiently train has never been greater. The main workhorses for neural net optimization are stochastic gradient descent (SGD) with momentum and various 2nd-order optimizers that use diagonal curvature-matrix approximations, such as RMSprop BID32 and Adam BID1 . While the latter are typically easier to tune and work better out of the box, they unfortunately only offer marginal performance improvements over well-tuned SGD on most problems.Because modern neural networks have many millions of parameters it is computationally too expensive to compute and invert an entire curvature matrix and so approximations are required. While early work on non-diagonal curvature matrix approximations such as TONGA BID17 and the Hessian-free (HF) approach BID20 BID21 BID4 BID30 demonstrated the potential of such methods, they never achieved wide adoption due to issues of scalability (to large models in the case of the former, and large datasets in the case of the latter).Motivated in part by these older results and by the more recent success of centering and normalization methods (e.g. BID31 BID34 BID15 a new family of methods has emerged that are based on non-diagonal curvature matrix approximations the rely on the special structure of neural networks. Such methods , which include Kronecker-factored approximated curvature (K-FAC) BID24 , Natural Neural Nets BID5 , Practical Riemannian Neural Networks BID18 , and others BID29 , have achieved state-of-the-art optimization performance on various challenging neural network training tasks and benchmarks.While the original K-FAC method is applicable only to standard feed-forward networks with fully connected layers, it has recently been extended to handle convolutional networks BID8 through the introduction of the ""Kronecker Factors for Convolution"" (KFC) approximation. BID2 later developed a distributed asynchronous version which proposed additional approximations to handle very large hidden layers.In this work we develop a new family of curvature matrix approximations for recurrent neural networks (RNNs) within the same design space. As in the original K-FAC approximation and the KFC approximation, we focus on the Fisher information matrix (a popular choice of curvature matrix), and show how it can be approximated in different ways through the adoption of various approximating assumptions on the statistics of the network's gradients. Our main novel technical contribution is an approximation which uses a chain-structured linear Gaussian graphical model to describe the statistical relationship between gradient contributions coming from different time-steps. Somewhat remarkably, it is possible to sum the required cross-moments to obtain a Fisher approximations which has enough special algebraic structure that it can still be efficiently inverted. In experiments we demonstrate the usefulness of our approximations on several challenging RNN training tasks. We have presented a new family of approximations to the Fisher information matrix of recurrent neural networks (RNNs), extending previous work on Kronecker-factored approximations. With this contribution, recurrent networks can now finally be trained with the K-FAC optimization method. We have demonstrated that our new approximations substantially reduce the required number of iterations for convergence vs standard baseline optimizers on several realistic tasks. And we have also shown that in a modern distributed training setup this results in a substantial savings in wallclock time as well.Jason Weston, Sumit Chopra, and Antoine Bordes. A SUPPLEMENTARY COMPUTATIONS A.1 PROOFS FOR SECTION 3.5.1Proposition 1 GivenF DISPLAYFORM0 , which can be seen as follows: DISPLAYFORM1 And using DISPLAYFORM2 Setting d = 1 and multiplying both sides by V 0 (which is assumed to be invertible) one can also derive the following simple formula for Ψ: DISPLAYFORM3 To proceed from here we define a ""transformed"" version of the original chain-structured linearGaussian graphical model whose variables areŵ t = V −1/2 0 w t . (Here we assume that V 0 is invertible -it is symmetric by definition.) All quantities related to the original model have their analogues in the transformed model, which we indicate with the hat symbol·.In the transformed model the 2nd-order moments of theŵ t 's are given bŷ DISPLAYFORM4 We observe thatV 0 = I.Analogously to the original model, the transformed version obeyŝ DISPLAYFORM5 =V 1 (usingV 0 = I). This can be seen by noting that DISPLAYFORM6 It also remains true that the spectral radius ofΨ is less than 1, which can be seen in at least one of two ways: by noticing that the transformed model is well-defined in the infinite limit if and only if the original one is, or thatΨ DISPLAYFORM7 is a similar matrix to Ψ (in the technical sense) and hence has the same eigenvalues.As the transformed model is isomorphic to the original one, all of the previously derived relationships which held for it also hold here, simply by replacing each quantity with its transformed version (denoted by the hat symbol·).Given these relations (included the transformed analogue of equation 5) we can expressF T aŝ DISPLAYFORM8 It is a well-known fact that one can evaluate rational functions, and functions that are the limiting values of sequences of rational functions, with matrix arguments. This is done by replacing scalar multiplication with matrix multiplication, division with matrix inversion, and scalar constants with scalar multiples of the identity matrix, etc. Note that because sums of powers and inverses of matrices are co-diagonalizable/commutative when the matrices themselves are, there is no issue of ambiguity caused by mixing commutative and non-commutative algebra in this way.Moreover, the value of some such function f (x), given a matrix argument B, is DISPLAYFORM9 DISPLAYFORM10 undefined from some i, either because of a division by zero, or because the limit which defines f (x) doesn't converge for x = [b] i , then f (B) doesn't exist for that particular B (and otherwise it does).We observe that our above expression for F T can be rewritten aŝ DISPLAYFORM11 By Proposition 3 in Appendix B.1, we have for x = 1 that DISPLAYFORM12 Let U diag(ψ)U −1 =Ψ be the eigendecomposition ofΨ. BecauseΨ has a spectral radius less than 1, we have |[ψ] i | < 1 for each i (so that in particular [ψ] i = 1), and thus we can evaluate ζ T (Ψ) and ζ T (Ψ ) according to the above formula for ζ T (x).","Kronecker-factor Approximate Curvature Martens Grosse 2015 K-FAC is a 2nd-order optimization method which has been shown give state-of-the-art performance large-scale neural network optimization tasks Baetal. 2017 is based approximation Fisher information matrix FIM makes assumptions particular structure network way is parameterized. original K-FAC method was applicable fully-connected networks although has been recently extended Grosse Martens 2016 handle convolutional networks well. work extend method handle RNNs introducing novel approximation FIM RNNs. approximation works modelling covariance structure gradient contributions different time-steps using chain-structured linear Gaussian graphical model summing various cross-covariances computing inverse closed form. demonstrate experiments method significantly outperforms general purpose state-of-the-art optimizers like SGD momentum Adam several challenging RNN training tasks. neural networks have become ubiquitous research applications need efficiently train has never greater. main workhorses neural net optimization are stochastic gradient descent SGD momentum various 2nd-order optimizers use diagonal curvature-matrix approximations RMSprop BID32 Adam BID1. latter are typically easier tune work better box unfortunately offer marginal performance improvements well-tuned SGD problems.Because modern neural networks have many millions parameters is computationally expensive compute invert entire curvature matrix approximations are required. early work non-diagonal curvature matrix approximations TONGA BID17 Hessian-free HF approach BID20 BID21 BID4 BID30 demonstrated potential methods never achieved wide adoption due issues scalability large models case former large datasets case latter.Motivated part older results recent success centering normalization methods e.g BID31 BID34 BID15 new family methods has emerged are based non-diagonal curvature matrix approximations rely special structure neural networks. methods which include Kronecker-factored approximated curvature K-FAC BID24 Natural Neural Nets BID5 Practical Riemannian Neural Networks BID18 others BID29 have achieved state-of-the-art optimization performance various challenging neural network training tasks benchmarks.While original K-FAC method is applicable standard feed-forward networks fully connected layers has recently extended handle convolutional networks BID8 introduction Kronecker Factors Convolution KFC approximation. BID2 later developed distributed asynchronous version which proposed additional approximations handle large hidden layers.In work develop new family curvature matrix approximations recurrent neural networks RNNs within design space. original K-FAC approximation KFC approximation focus Fisher information matrix popular choice curvature matrix show how it can be approximated different ways adoption various approximating assumptions statistics network's gradients. main novel technical contribution is an approximation which uses chain-structured linear Gaussian graphical model describe statistical relationship gradient contributions coming different time-steps Somewhat remarkably is possible sum required cross-moments obtain Fisher approximations which has enough special algebraic structure can still efficiently inverted. experiments demonstrate usefulness approximations several challenging RNN training tasks. have presented new family approximations Fisher information matrix recurrent neural networks RNNs extending previous work Kronecker-factored approximations. contribution recurrent networks can now finally trained K-FAC optimization method. have demonstrated new approximations substantially reduce required number iterations convergence vs standard baseline optimizers several realistic tasks. have also shown modern distributed training setup results substantial savings wallclock time well.Jason Weston Sumit Chopra Antoine Bordes. SUPPLEMENTARY COMPUTATIONS A.1 PROOFS SECTION 3.5.1Proposition 1 GivenF DISPLAYFORM0 which can be seen follows:DISPLAYFORM1 using DISPLAYFORM2 Setting 1 multiplying sides V0 which is assumed invertible one can also derive following simple formula Ψ:DISPLAYFORM3 proceed define transformed version original chain-structured linearGaussian graphical model whose variables areŵ V−1/2 0w t. assume V0 is invertible -it is symmetric definition. quantities related original model have their analogues transformed model which we indicate hat symbol·.In transformed model 2nd-order moments theŵ 's are given bŷ DISPLAYFORM4 observe thatV0 I.Analogously original model transformed version obeyŝ DISPLAYFORM5 =V1 usingV0 canbe seen noting DISPLAYFORM6 also remains true spectral radius ofΨ is less 1 which can be seen least one two ways:noticing transformed model is well-defined infinite limit if and onlyif original one is,or thatΨ DISPLAYFORM7 is a similar matrix Ψ technical sense hence has the same eigenvalues.As transformed model is isomorphic original one previously derived relationships which held also hold simply replacing quantity transformed version denoted hat symbol· .Given relations included transformed analogue equation5 can expressF aŝ DISPLAYFORM8 is a well-known fact one can evaluate rational functions functions are the limiting values sequences rational functions matrix arguments. is done replacing scalar multiplication matrix multiplication division matrix inversion scalar constants scalar multiples identity matrix etc. Note sums powers inverses matrices are co-diagonalizable/commutative when the matrices are,there isno issue ambiguity caused mixing commutative non-commutative algebra way.Moreover value functionf x given matrix argumentB is DISPLAYFORM9 DISPLAYFORM10 undefined either division zero limit which definesf x converge x b f B exist particularB otherwise does).We observe expression F can be rewritten aŝ DISPLAYFORM11 Proposition3 Appendix B.1 have forx 1 DISPLAYFORM12 Let U diag ψ U−1=Ψ eigendecomposition ofΨ. BecauseΨ has a spectral radius less 1 have| ψ 1 particular ψ 1 thus can evaluateζ Ψ ζ Ψ according formula ζ x",1600,1098,502,0.016,1.457,2025/11/05 17:19:05,0.01,1.547,0.3956386292834891,493.624
"Bayesian inference is known to provide a general framework for incorporating prior knowledge or specific properties into machine learning models via carefully choosing a prior distribution. In this work, we propose a new type of prior distributions for convolutional neural networks, deep weight prior (DWP), that exploit generative models to encourage a specific structure of trained convolutional filters e.g., spatial correlations of weights. We define DWP in the form of an implicit distribution and propose a method for variational inference with such type of implicit priors. In experiments, we show that DWP improves the performance of Bayesian neural networks when training data are limited, and initialization of weights with samples from DWP accelerates training of conventional convolutional neural networks.
 Bayesian inference is a tool that, after observing training data, allows to transforms a prior distribution over parameters of a machine learning model to a posterior distribution. Recently, stochastic variational inference (Hoffman et al., 2013 ) -a method for approximate Bayesian inference -has been successfully adopted to obtain a variational approximation of a posterior distribution over weights of a deep neural network . Currently, there are two major directions for the development of Bayesian deep learning. The first direction can be summarized as the improvement of approximate inference with richer variational approximations and tighter variational bounds BID4 . The second direction is the design of probabilistic models, in particular, prior distributions, that widen the scope of applicability of the Bayesian approach.Prior distributions play an important role for sparsification BID25 , quantization and compression BID6 of deep learning models. Although these prior distributions proved to be helpful, they are limited to fully-factorized structure. Thus, the often observed spatial structure of convolutional filters cannot be enforced with such priors. Convolutional neural networks are an example of the model family, where a correlation of the weights plays an important role, thus it may benefit from more flexible prior distributions.Convolutional neural networks are known to learn similar convolutional kernels on different datasets from similar domains BID31 BID39 . Based on this fact, within a specific data domain, we consider a distribution of convolution kernels of trained convolutional networks. In the rest of the paper, we refer to this distribution as the source kernel distribution. Our main assumption is that within a specific domain the source kernel distribution can be efficiently approximated with convolutional kernels of models that were trained on a small subset of problems from this domain. For example, given a specific architecture, we expect that kernels of a model trained on notMNIST dataset -a dataset of grayscale images -come from the same distribution as kernels of the model trained on MNIST dataset. In this work, we propose a method that estimates the source kernel distribution in an implicit form and allows us to perform variational inference with the specific type of implicit priors.Our contributions can be summarized as follows:1. We propose deep weight prior, a framework that approximates the source kernel distribution and incorporates prior knowledge about the structure of convolutional filters into the prior distribution. We also propose to use an implicit form of this prior (Section 3.1).2. We develop a method for variational inference with the proposed type of implicit priors (Section 3.2).3. In experiments (Section 4), we show that variational inference with deep weight prior significantly improves classification performance upon a number of popular prior distributions in the case of limited training data. We also find that initialization of conventional convolution networks with samples from a deep weight prior leads to faster convergence and better feature extraction without training i.e., using random weights. In this work we propose deep weight prior -a framework for designing a prior distribution for convolutional neural networks, that exploits prior knowledge about the structure of learned convolutional filters. This framework opens a new direction for applications of Bayesian deep learning, in particular to transfer learning.Factorization. The factorization of deep weight prior does not take into account inter-layer dependencies of the weights. Although a more complex factorization might be a better fit for CNNs. Accounting inter-layer dependencies may give us an opportunity to recover a distribution in the space of trained networks rather than in the space of trained kernels. However, estimating prior distributions of more complex factorization may require significantly more data and computational budget, thus the topic needs an additional investigation.Inference. An alternative to variational inference with auxiliary variables is semi-implicit variational inference BID38 . The method was developed only for semiimplicit variational approximations, and only the recent work on doubly semi-implicit variational inference generalized it for implicit prior distributions . These algorithms might provide a better way for variational inference with a deep weight prior, however, the topic needs further investigation. DISPLAYFORM0 is a transition operator, and z = (z 0 , . . . , z T ) . Unfortunately, gradients of L cannot be efficiently estimated, but we construct a tractable lower bound L aux for L: DISPLAYFORM1 Inequality 13 has a very natural interpretation. The lower bound L aux is tight if and only if the KLdivergence between the auxiliary reverse model and the posterior intractable distribution p(z | w) is zero.The deep weight prior (Section 3) is a special of Markov chain prior for T = 0 and p(w) = p(w | z)p(z)dz. The auxiliary variational bound has the following form: DISPLAYFORM2 where the gradients in equation 14 can be efficiently estimated in case q(w), for explicit distributions q(w), p φ (w | z), r(z | w) that can be reparametrized. During variational inference with deep weight prior (Algorithm 1) we optimize a new auxiliary lower bound L aux (θ, ψ) on the evidence lower bound L(θ). However, the quality of such inference depends on the gap G(θ, ψ) between the original variational lower bound L(θ) and the variational lower bound in auxiliary space L aux (θ, ψ):",Bayesian inference is known provide general framework incorporating prior knowledge specific properties machine learning models via carefully choosing prior distribution. work propose new type prior distributions convolutional neural networks deep weight prior DWP exploit generative models encourage specific structure trained convolutional filterse.g spatial correlations weights. define DWP form implicit distribution propose method variational inference type implicit priors. experiments show DWP improves performance Bayesian neural networks when training data are limited initialization weights samples DWP accelerates training conventional convolutional neural networks. Bayesian inference is a tool observing training data allows transforms prior distribution parameters machine learning model posterior distribution. Recently stochastic variational inference Hoffmanetal. 2013 -a method approximate Bayesian inference -has successfully adopted obtain variational approximation posterior distribution weights deep neural network. Currently are two major directions development Bayesian deep learning. first direction can be summarized improvement approximate inference richer variational approximations tighter variational bounds BID4. second direction is the design probabilistic models particular prior distributions widen scope applicability Bayesian approach.Prior distributions play important role sparsification BID25 quantization compression BID6 deep learning models. Although prior distributions proved helpful are limited fully-factorized structure. Thus often observed spatial structure convolutional filters cannot enforced priors. Convolutional neural networks are an example model family where a correlation weights plays important role thus may benefit flexible prior distributions.Convolutional neural networks are known learn similar convolutional kernels different datasets similar domains BID31 BID39. Based fact within specific data domain consider distribution convolution kernels trained convolutional networks. rest paper refer distribution source kernel distribution. main assumption is that within specific domain source kernel distribution can be efficiently approximated convolutional kernels models were trained small subset problems domain. example given specific architecture expect kernels model trained notMNIST dataset -a dataset grayscale images -come distribution kernels model trained MNIST dataset. work propose method estimates source kernel distribution implicit form allowsus perform variational inference specific type implicit priors.Our contributions can be summarized follows:1 propose deep weight prior framework approximates source kernel distribution incorporates prior knowledge structure convolutional filters prior distribution. also propose use implicit form prior Section 3.1 .2 develop method variational inference proposed type implicit priors Section 3.2 .3 experiments Section4 show variational inference deep weight prior significantly improves classification performance upon number popular prior distributions case limited training data. also find initialization conventional convolution networks samples deep weight prior leads faster convergence better feature extraction without training.e using random weights. work propose deep weight prior -a framework designing prior distribution convolutional neural networks exploits prior knowledge structure learned convolutional filters. framework opens new direction applications Bayesian deep learning particular transfer learning.Factorization. factorization deep weight prior does not take account inter-layer dependencies weights. Although complex factorization might better fit CNNs. Accounting inter-layer dependencies may giveus opportunity recover distribution space trained networks rather space trained kernels. However estimating prior distributions complex factorization may require significantly data computational budget thus topic needs additional investigation.Inference. alternative variational inference auxiliary variables is semi-implicit variational inference BID38. method was developed semiimplicit variational approximations recent work doubly semi-implicit variational inference generalized implicit prior distributions. algorithms might provide better way variational inference deep weight prior however topic needs investigation. DISPLAYFORM0 is a transition operator z z0 z Unfortunately gradients L cannot efficiently estimated construct tractable lower boundL aux L:DISPLAYFORM1 Inequality13 has a very natural interpretation. lower bound L aux is tight if and onlyif KLdivergence auxiliary reverse model posterior intractable distributionp z w is zero.The deep weight prior Section3 is a special Markov chain prior 0 p w p w z p z dz. auxiliary variational bound has the following form:DISPLAYFORM2 where the gradients equation14 can be efficiently estimated caseq w explicit distributionsq w pφ w z r z w can be reparametrized. variational inference deep weight prior Algorithm1 optimize new auxiliary lower bound L aux θ ψ evidence lower boundL θ However quality inference depends gapG θ ψ original variational lower bound L θ variational lower bound auxiliary space L aux θ ψ,1210,820,390,0.013,1.476,2025/11/05 17:19:05,0.01,1.692,0.4548286604361368,364.606
"The high dimensionality of hyperspectral imaging forces unique challenges in scope, size and processing requirements.   Motivated by the potential for an in-the-field cell sorting detector, we examine a Synechocystis sp. PCC 6803 dataset wherein cells are grown alternatively in nitrogen rich or deplete cultures.   We use deep learning techniques to both successfully classify cells and generate a mask segmenting the cells/condition from the background. Further, we use the classification accuracy to guide a data-driven, iterative feature selection method, allowing the design neural networks requiring 90% fewer input features with little accuracy degradation. Hyperspectral confocal fluorescence microscopy and hyperspectral imaging are powerful tools for the biological sciences, allowing high-content views of multiple pigments and proteins in individual cells within larger populations. As the technology has advanced in speed and ease of use, it is has become practical to think of applications such as high-throughput screening, or understanding heterogeneous cell response to changing environmental conditions, where one might want to identify cells of certain characteristics including phenotype, pigment content, protein expression, as determined by their spatially resolved fluorescence emission for subsequent analysis. Although a few researchers have used classification techniques such as support vector machines BID13 to identify cells of that exhibit similar spectral emission characteristics, the majority of the analysis of hyperspectral images has been exploratory-developing spectral models for identifying the underlying spectral components BID15 BID11 .In this work, we employ deep artificial neural network algorithms to classify individual cyanobacterial cells based on their hyperspectral fluorescence emission signatures. Such deep learning methods have increasingly seen extensive use in conventional image processing tasks with relatively low numbers of channels (such as processing RGB images) BID8 , however their utility in tasks with larger numbers of sensors, such as hyperspectral systems, remains an area of active research. In particular , in biological systems, non-trivial processes may yield complex interactions that can be detected through hyperspectral imaging that are in addition to the long-acknowledged challenges of automated data processing of spatial structure.In addition to classifying the experimental effects on individual cells, we show how this method can help identify which spectral wavelengths are most useful for the classification. Importantly, the feature selection information could allow customized sensors to be designed for specific applications. This work demonstrates that this technique is suitable for real-time image analysis and high-throughput screening of heterogeneous populations of cyanobacterial cells for differentiating environmental response. The method can be further extended to other cell populations or complex tissue containing multiple cell types. In this study, we demonstrate that modern deep artificial neural network approaches can be used to perform rapid classification of biological data sampled by hyperspectral imaging. Both the pixelbased and whole image-based classification results demonstrate that these approaches are highly effective with the class of data represented by this experimental data and suggest that deep neural network approaches are well suited for hyperspectral imaging analysis even in non-trivial application domains such as biological tissue.We believe that the sampling reduction technique we describe here is a unique use of a neural network's classification ability to guide the identification of which particular sensors-in this case wavelengths-are necessary to measure. Most dimensionality reduction methods, such as PCA and non-linear variants such as local linear embedding (LLE), are focused primarily on reducing the size. While they can identify channels that are not used at all, they are more directed towards storing and communicating data in fewer dimensions which still leverage information sampled across the original cadre of sensors. Thus these dimensionality reduction do not necessarily reduce the demands on the sensor side, even though they do often compress and describe data quite effectively.The methods described here share some similarities to existing techniques for hyperspectral imaging using techniques such as deep stacked autoencoders or principal components analysis coupled with a deep convolutional network that extract high-level features which can then be fed into a simple classifier BID2 BID17 . In contrast, our approach is focused on directly going from the data to the classification of either pixels or whole regions (in our case, cells). This allows us to better leverage the structure of the dimensionality of the data, which for hyperspectral scenarios is often sparser in absolute numbers of images but is proportionally richer in terms of dimensionality.Given deep neural networks' history of broad applicability in other domains, we fully expect that these methods will be generalizable to other, similar datasets and anticipate subsequent analysis of a variety of cell types under experimental conditions. Further refinement of our convolutional neural network should provide effective and efficient sub-cellular segmentation via embedded computing platforms, and ultimately we aim to extend the use of these neural network algorithms to inform experimental results.",high dimensionality hyperspectral imaging forces unique challenges scope size processing requirements. Motivated potential in-the-field cell sorting detector examine Synechocystissp. PCC 6803 dataset wherein cells are grown alternatively nitrogen rich deplete cultures. use deep learning techniques successfully classify cells generate mask segmenting cells/condition background. use classification accuracy guide data-driven iterative feature selection method allowing design neural networks requiring 90% fewer input features little accuracy degradation. Hyperspectral confocal fluorescence microscopy hyperspectral imaging are powerful tools biological sciences allowing high-content views multiple pigments proteins individual cells within larger populations. technology has advanced speed ease use is has become practical think applications high-throughput screening understanding heterogeneous cell response changing environmental conditions where one might want identify cells certain characteristics including phenotype pigment content protein expression determined spatially resolved fluorescence emission subsequent analysis. Although researchers have used classification techniques support vector machines BID13 identify cells exhibit similar spectral emission characteristics majority analysis hyperspectral images has been exploratory-developing spectral models identifying underlying spectral components BID15 BID11.In work employ deep artificial neural network algorithms classify individual cyanobacterial cells based hyperspectral fluorescence emission signatures. deep learning methods have increasingly seen extensive use conventional image processing tasks relatively low numbers channels processing RGB images BID8 however utility tasks larger numbers sensors which for hyperspectral systems remains area active research. particular biological systems non-trivial processes may yield complex interactions can be detected hyperspectral imaging are in addition long-acknowledged challenges automated data processing spatial structure.In addition classifying experimental effects individual cells show how this method can help identify which spectral wavelengths are most useful classification. Importantly feature selection information could allow customized sensors designed specific applications. work demonstrates technique is suitable real-time image analysis high-throughput screening heterogeneous populations cyanobacterial cells differentiating environmental response. method can be further extended cell populations complex tissue containing multiple cell types. study demonstrate modern deep artificial neural network approaches can be used perform rapid classification biological data sampled hyperspectral imaging. pixelbased whole image-based classification results demonstrate approaches are highly effective class data represented experimental data suggest deep neural network approaches are well suited hyperspectral imaging analysis even non-trivial application domains biological tissue.We believe sampling reduction technique describe is a unique use neural network's classification ability guide identification which particular sensors-in case wavelengths-are necessary measure. dimensionality reduction methods PCA non-linear variants local linear embedding LLE are focused primarily reducing size. can identify channels are not used are more directed towards storing communicating data fewer dimensions which still leverage information sampled across original cadre sensors. Thus dimensionality reduction do not necessarily reduce demands sensor side even though do often compress describe data quite effectively.The methods described share similarities existing techniques hyperspectral imaging using techniques deep stacked autoencoders principal components analysis coupled deep convolutional network extract high-level features which can then be fed simple classifier BID2 BID17. contrast approach is focused directly going data classification either pixels whole regions case cells allowsus better leverage structure dimensionality data which for hyperspectral scenarios is often sparser absolute numbers images is proportionally richer terms dimensionality.Given deep neural networks' history broad applicability domains fully expect methods will be generalizable similar datasets anticipate subsequent analysis variety cell types experimental conditions. refinement convolutional neural network should provide effective efficient sub-cellular segmentation via embedded computing platforms ultimately aim extend use neural network algorithms inform experimental results.,922,653,269,0.009,1.412,2025/11/05 17:19:05,0.0,1.514,0.2554517133956382,299.276
"Data Interpretation is an important part of Quantitative Aptitude exams and requires an individual to answer questions grounded in plots such as bar charts, line graphs, scatter plots, \textit{etc}. Recently, there has been an increasing interest in building models which can perform this task by learning from datasets containing triplets of the form \{plot, question, answer\}. Two such datasets have been proposed in the recent past which contain plots generated from synthetic data with limited (i) $x-y$ axes variables (ii) question templates and (iii) answer vocabulary and hence do not adequately capture the challenges posed by this task. To overcome these limitations of existing datasets, we introduce a new dataset containing $9.7$ million question-answer pairs grounded over $270,000$ plots with three main differentiators. First, the plots in our dataset contain a wide variety of realistic $x$-$y$ variables such as CO2 emission, fertility rate, \textit{etc. } extracted from  real word data sources such as World Bank, government sites, \textit{etc}. Second, the questions in our dataset are more complex as they are based on templates extracted from interesting questions asked by a crowd of workers using a fraction of these plots. Lastly, the answers in our dataset are not restricted to a small vocabulary and a large fraction of the answers seen at test time are not present in the training vocabulary. As a result, existing models for Visual Question Answering which largely use end-to-end models in a multi-class classification framework cannot be used for this task. We establish initial results on this dataset and emphasize the complexity of the task using a multi-staged modular pipeline with various sub-components to (i) extract relevant data from the plot and convert it to a semi-structured table (ii) combine the question with this table and use compositional semantic parsing to arrive at a logical form from which the answer can be derived. We believe that such a modular framework is the best way to go forward as it would enable the research community to independently make progress on all the sub-tasks involved in plot question answering. Data plots such as bar charts, line graphs, scatter plots, etc. provide an efficient way of summarizing numeric information and are frequently encountered in textbooks, research papers, professional reports, newspaper articles, etc. Machine comprehension of these plots with the aim of answering questions grounded in them is an interesting research problem which lies at the intersection of Language and Vision and has widespread applications. For example, such a system could enable financial analysts to use natural language questions to access the information locked in a collection of data plots within financial reports, journals, etc. Such a system could also serve as an important educational assistant for the visually impaired by helping them understand the information summarized in a plot by asking a series of questions.Recently, two datasets , viz., FigureQA BID6 and DVQA BID5 have been released for this task which contain triplets of the form {plots, questions, answers}. These datasets clearly show that despite its apparent similarity to Visual Question Answering (VQA), this task has several additional challenges due to which existing state of the art VQA methods do not perform well on this task. However, both FigureQA and DVQA themselves have some limitations which warrants the creation of more challenging datasets which adequately capture a wider range of Figure 1 shows a sample triplet from FigureQA, DVQA and DIP (our dataset). First, we note that FigureQA and DVQA contain plots created from synthetic data. In particular, note that the label names (either x-axis or y-axis or legend names) in FigureQA and DVQA come from a limited vocabulary (color names and top-1000 nouns from Brown corpus respectively). This clearly reduces the vocabulary that a model needs to deal with. Further, the label names are not really meaningful in the context of the plot leading to unnatural questions. In contrast, the plots in our dataset are based on World Bank Open Data which contains realistic variable names such as mortality rate, crop yield, country names, etc. The values associated with each plot are also realistic with different scales including floating point numbers as opposed to DVQA which contains only integers in a fixed range. Secondly, the questions in FigureQA and DVQA are based on a smaller number of templates (15 and 25). Instead of hand designing a small number of templates, we first show a fraction of the plots to crowdsourced workers and ask them to create natural language questions which can be answered from these plots. We then analyze these questions and extract templates from them which results in a richer question repository with more templates (74) and more complex questions. Lastly, unlike FigureQA and DVQA the answers in our dataset do not come from a small fixed set of vocabulary. For example, the answer to the question shown in FIG0 is 60.49, which is not present in the training data. More specifically, the answer vocabulary for the test data is 248, 878 words of which 187, 688 are not seen in the training data. This is quite natural and expected when the plots and questions are extracted from real world data. In addition to the above differentiators, we also include an extra novel test set which contains plots based on data extracted from Open Government Data as opposed to World Bank Data. This test set contains additional variable and legend names which are not seen in the World Bank Data.Given the large answer vocabulary, it is infeasible to use any of the existing VQA models on our dataset as they largely treat VQA as a multi-class classification problem where the task is to select the right answer from a fixed vocabulary. Even the recent models proposed on DVQA take a similar multi-class classification approach. Further, we believe that given the various sub-tasks involved in this problem it is not prudent to use a single end-to-end system which simply takes the plot and question as input and generates as answer. Instead, as a baseline we propose a modular multi-staged pipeline wherein the first stage in the pipeline extracts (i) data objects in the plot such as bars, lines, etc.(ii ) text objects in the plot such as titles, legend names, x-y axes names, etc. (iii ) the numeric objects in the plot such as tick values, scales, etc. At the end of this stage, the plot is converted to a semi-structured table. We then use a method BID13 which combines the question with this table and uses compositional semantic parsing to arrive at a logical form from which the answer can be derived. The key point here is that the output is neither selected from a fixed vocabulary nor generated using a decoder but it is derived from a logical form. Our experiments using this model suggest that this dataset is indeed very challenging and requires the community to look beyond existing end-to-end models. We introduced the DIP dataset for Data Interpretation over Plots which contains scientific plots created from real world data sources such as World Bank, stock market, etc. Further, the questions in our dataset are based on templates which were manually extracted from realistic questions created by crowd-workers. One of the primary challenges of this dataset is that it has a large vocabulary because of which existing VQA models which treat this as a multi-class classification model cannot be applied. Instead we propose a modular pipeline which first converts the plot to a semi-structured table and then learns to answer questions from this table using compositional semantic parsing. Our experiments suggest that this is a very challenging dataset and requires significant progress on multiple sub-tasks. In particular, we need improved models for reasoning over structured data.Ray Smith. TAB7 presents the detailed statistics of the number of plots present in each of our data splits according to plot type. Note that the plot type k-multi means that the number of lines/bars on each tick is k. In the above mentioned samples, the horizontal bar graph is 3-multi and so on. (e) In how many <plural form of X label>, is the <Y label> of/in <legend label> greater than <N> <units>? (f) What is the ratio of the <Y label> of/in <legend label1> in < i th x tick> to that in < j th x tick>? (g) Is the <Y label> of/in <legend label> in < i th x tick> less than that in < j th x tick> ? 5. Compound : (a) Is the difference between the <Y label> in < i th x tick> and < j th x tick> greater than the difference between any two <plural form of X label> ? (b) What is the difference between the highest and the second highest <Y label> ? (c) Is the sum of the <Y label> in < i th x tick> and < (i + 1) th x tick> greater than the maximum <Y label> across all <plural form of X label> ? (d) What is the difference between the highest and the lowest <Y label> ? (e) In how many <plural form of X label>, is the <Y label> greater than the average <Y label> taken over all <plural form of X label> ? (f) Is the difference between the <Y label> of/in <legend label1> in < i th x tick> and < j th x tick> greater than the difference between the <Y label> of/in <legend label2> in < i th x tick> and < j th x tick> ? (g) What is the difference between the highest and the second highest <Y label> of/in <legend label> ? (h) What is the difference between the highest and the lowest <Y label> of/in <legend label> ? (i) In how many <plural form of X label>, is the <Y label> of/in <legend label> greater than the average <Y label> of/in <legend label> taken over all <plural form of X label> ? (j) Is it the case that in every <singular form of X label>, the sum of the <Y label> of/in <legend label1> and <legend label2> is greater than the <Y label> of/in <legend label3> ? (k) Is the sum of the <Y label> of/in <legend label1> in < i th x tick> and < j th x tick> greater than the maximum <Y label> of/in <legend label2> across all <plural form of X label>? (l) Is it the case that in every <singular form of X label>, the sum of the <Y label> of/in <legend label1> and <legend label2> is greater than the sum of <Y label> of <legend label3> and <Y label> of <legend label4> ? D. QUESTION TYPES TAB8 presents the distribution of the number of questions, categorized by their template type, that are present in each of the data splits.","Data Interpretation is an important part Quantitative Aptitude exams requires individual answer questions grounded plots bar charts line graphs scatter plots \textit etc Recently has been increasing interest building models which can perform task learning datasets containing triplets form plot question answer\ Two datasets have been proposed recent past which contain plots generated synthetic data limited $x-y axes variables ii question templates iii answer vocabulary hence do not adequately capture challenges posed task. overcome limitations existing datasets introduce new dataset containing $9.7 million question-answer pairs grounded $270,000 plots three main differentiators. First plots dataset contain wide variety realistic$x$y variables CO2 emission fertility rate \textit etc. extracted real word data sources World Bank government sites \textit etc Second questions dataset are more complex are based templates extracted interesting questions asked crowd workers using fraction plots. Lastly answers dataset are not restricted small vocabulary large fraction answers seen test time are not present training vocabulary. result existing models Visual Question Answering which largely use end-to-end models multi-class classification framework cannot used task. establish initial results dataset emphasize complexity task using multi-staged modular pipeline various sub-components extract relevant data plot convert semi-structured table ii combine question table use compositional semantic parsing arrive logical form which the answer can be derived. believe modular framework is the best way go forward would enable research community independently make progress sub-tasks involved plot question answering. Data plots bar charts line graphs scatter plots etc. provide efficient way summarizing numeric information are frequently encountered textbooks research papers professional reports newspaper articles etc. Machine comprehension plots aim answering questions grounded is an interesting research problem which lies intersection Language Vision has widespread applications. example system could enable financial analysts use natural language questions access information locked collection data plots within financial reports journals etc. system could also serve important educational assistant visually impaired helping understand information summarized plot asking series questions.Recently two datasets viz. FigureQA BID6 DVQA BID5 have been released task which contain triplets form plots questions answers datasets clearly show despite apparent similarity Visual Question Answering VQA task has several additional challenges due which existing state art VQA methods do not perform well task. However FigureQA DVQA have some limitations which warrants creation challenging datasets which adequately capture wider range Figure 1 shows sample triplet FigureQA DVQA DIP dataset First note FigureQA DVQA contain plots created synthetic data. particular note label names either x-axis y-axis legend names FigureQA DVQA come limited vocabulary color names top-1000 nouns Brown corpus respectively clearly reduces vocabulary model needs deal with. label names are not really meaningful context plot leading unnatural questions. contrast plots dataset are based World Bank Open Data which contains realistic variable names mortality rate crop yield country names etc. values associated plot are also realistic different scales including floating point numbers opposed DVQA which contains integers fixed range. Secondly questions FigureQA DVQA are based smaller number templates 15 25 Instead hand designing small number templates first show fraction plots crowdsourced workers ask create natural language questions which can be answered plots. analyze questions extract templates which results richer question repository templates 74 complex questions. Lastly unlike FigureQA DVQA answers dataset do not come small fixed set vocabulary. example answer question shown FIG0 is 60.49 which is not are present training data. specifically answer vocabulary test data is 248 878 words which 187 688 are not seen training data. is quite natural expected when the plots questions are extracted real world data. addition differentiators also include extra novel test set which contains plots based data extracted Open Government Data opposed World Bank Data. test set contains additional variable legend names which are not seen World Bank Data.Given large answer vocabulary is infeasible use existing VQA models dataset largely treat VQA multi-class classification problem where the task is to select right answer fixed vocabulary. Even recent models proposed DVQA take similar multi-class classification approach. believe given various sub-tasks involved problem is not prudent use single end-to-end system which simply takes plot question input generates answer. Instead baseline propose modular multi-staged pipeline wherein first stage pipeline extracts data objects plot bars lines etc. ii text objects plot titles legend names x-y axes names etc. iii numeric objects plot tick values scales etc. end stage plot is converted semi-structured table. use method BID13 which combines question table uses compositional semantic parsing arrive logical form which the answer can be derived. key point is that the output is neither selected fixed vocabulary generated using decoder is derived logical form. experiments using model suggest dataset is indeed challenging requires community look beyond existing end-to-end models. introduced DIP dataset Data Interpretation Plots which contains scientific plots created real world data sources World Bank stock market etc. questions dataset are based templates which were manually extracted realistic questions created crowd-workers One primary challenges dataset is that it has large vocabulary which existing VQA models which treat multi-class classification model cannot applied. Instead propose modular pipeline which first converts plot semi-structured table learns answer questions table using compositional semantic parsing. experiments suggest isa challenging dataset requires significant progress multiple sub-tasks particular need improved models reasoning structured data.Ray Smith. TAB7 presents detailed statistics number plots present data splits according plot type. Note plot type k-multi means number lines/bars tick isk. mentioned samples horizontal bar graph is 3-multi on. e how many plural form X label is the label/legend label is greater N units f What is the ratio label/legend label1 th x tick j th x tick g Is the<label/legend label th x tick less j th x tick 5. Compound:Is difference label th x tick j th x tick is greater difference two plural form X label b What is the Is the difference highest second highest label c Is the sum label th x tick+1 th x tick is greater maximum label across plural form X label What is the Is the difference highest lowest label e how many plural form X label is the label is greater average label taken plural form X label f What is the Is the difference label/legend label1 th x tick j th x tick is greater difference label/legend label2 th x tick j th x tick g What is the Is the difference highest second highest label/legend label h What is the Is the difference highest lowest label/legend label how many plural form X label is the label/legend label is greater average label/legend label taken plural form X label j Is it the case every singular form X label sum label/legend label1 legend label2 is greater label/legend label3 k Is the sum label/legend label1 th x tick j th x tick is greater maximum label/legend label2 across plural form X label l Is it the case every singular form X label sum label/legend label1 legend label2 is greater sum label legend label3 is the label legend label4 D. QUESTION TYPES TAB8 presents distribution number questions categorized template type which is not are present data splits.",2251,1369,882,0.044,1.644,2025/11/05 17:19:05,0.01,1.648,0.978193146417445,825.914
"Learning to predict complex time-series data is a fundamental challenge in a range of disciplines including Machine Learning, Robotics, and Natural Language Processing. Predictive State Recurrent Neural Networks (PSRNNs) (Downey et al.) are a state-of-the-art approach for modeling time-series data which combine the benefits of probabilistic filters and Recurrent Neural Networks into a single model. PSRNNs leverage the concept of Hilbert Space Embeddings of distributions (Smola et al.) to embed predictive states into a Reproducing Kernel Hilbert Space, then estimate, predict, and update these embedded states using Kernel Bayes Rule. Practical implementations of PSRNNs are made possible by the machinery of Random Features, where input features are mapped into a new space where dot products approximate the kernel well. Unfortunately PSRNNs often require a large number of RFs to obtain good results, resulting in large models which are slow to execute and slow to train. Orthogonal Random Features (ORFs) (Choromanski et al.) is an improvement on RFs which has been shown to decrease the number of RFs required for pointwise kernel approximation. Unfortunately, it is not clear that ORFs can be applied to PSRNNs, as PSRNNs rely on Kernel Ridge Regression as a core component of their learning algorithm, and the theoretical guarantees of ORF do not apply in this setting. In this paper, we extend the theory of ORFs to Kernel Ridge Regression and show that ORFs can be used to obtain Orthogonal PSRNNs (OPSRNNs), which are smaller and faster than PSRNNs. In particular, we show that OPSRNN models clearly outperform LSTMs and furthermore, can achieve accuracy similar to PSRNNs with an order of magnitude smaller number of features needed. Learning to predict temporal sequences of observations is a fundamental challenge in a range of disciplines including machine learning, robotics, and natural language processing. There exist a wide variety of approaches to modeling time series data, however recurrent neural networks (RNNs) have emerged as the clear frontrunner, achieving state-of-the-art performance in applications such as speech recognition (Heigold et al., 2016) , language modeling BID5 , translation (Cho et al., 2014b) , and image captioning BID13 .Predictive State Recurrent Neural Networks (PSRNNs) are a state-of-the-art RNN architecture recently introduced by Downey et al. (2017) that combine the strengths of probabilistic models and RNNs in a single model. Specifically PSRNNs offer strong statistical theory, globally consistent model initializations, and a rich functional form which is none-the-less amenable to refinement via backpropogation through time (BPTT). Despite consisting of a simple bi-linear operations, PSRNNs have been shown to significantly outperform more complex RNN architectures (Downey et al., 2017) , such as the widely used LSTMs BID3 and GRUs (Cho et al., 2014a) .PSRNNs leverage the concept of Hilbert Space embeddings of distributions BID10 to embed predictive states into a Reproducing Kernel Hilbert Space (RKHS), then estimate, predict, and update these embedded states using Kernel Bayes Rule (KBR) BID10 . Because PSRNNs directly manipulate (kernel embeddings of) distributions over observations, they can be initialized via a globally consistent method-of-moments algorithm which reduces to a series of linear ridge regressions.Practical implementations of PSRNNs are made possible by the machinery of Random Features (RFs): input features are mapped into a new space where dot products approximate the kernel well BID7 . RFs are crucial to the success of PSRNNs, however PSRNNs often require a significant number of RFs in order to obtain good results. And, unfortunately, the number of required RFs grows with the dimensionality of the input, resulting in models which can be large, slow to execute, and slow to train.One technique that has proven to be effective for reducing the required number of RFs for kernel machines is Orthogonal Random Features (ORFs) BID14 . When using ORFs, the matrix of RFs is replaced by a properly scaled random orthogonal matrix, resulting in significantly decreased kernel approximation error. A particularly nice feature of ORFs is that BID14 Choromanski et al., 2017) prove that using ORFs results in a guaranteed improvement in pointwise kernel approximation error when compared with RFs.Unfortunately the guarantees in BID14 are not directly applicable to the PSRNN setting. PSRNNs first obtain a set of model parameters via ridge regression, then use these model parameters to calculate inner products in RF space. This ""downstream"" application of RFs goes beyond the results proven in BID14 and Choromanski et al. (2017) . Hence it is not clear whether or not ORF can be applied to obtain an improvement in the PSRNN setting.In this work, we show that ORFs can be used to obtain OPSRNNs: PSRNNs initialized using ORFs which are smaller, faster to execute and train than PSRNNs initialized using conventional unstructured RFs. We theoretically analyze the orthogonal version of the KRR algorithm that is used to initialize OPSRNNs. We show that orthogonal RNNs lead to kernel algorithms with strictly better spectral properties and explain how this translates to strictly smaller upper bounds on failure probabilities regarding KRR empirical risk. We compare the performance of OPSRNNs with that of LSTMs as well as conventional PSRNNs on a number of robotics tasks, and show that OPSRRNs are consistently superior on all tasks. In particular, we show that OPSRNN models can achieve accuracy similar to PSRNNs with an order of magnitude smaller number of features needed. We showed how structured orthogonal constructions can be effectively integrated with recurrent neural network based architectures to provide models that consistently achieve performance superior to the baselines. They also provide significant compression, achieving similar accuracy as PSRNNs with an order of magnitude smaller number of features needed. Furthermore, we gave the first theoretical guarantees showing that orthogonal random features lead to exponentially small bounds on the failure probability regarding empirical risk of the kernel ridge regression model. The latter one is an important component of the RNN based architectures for state prediction that we consider in this paper. Finally, we proved that these bounds are strictly better than for the standard nonorthogonal random feature map mechanism. Exhaustive experiments conducted on several robotics task confirm our theoretical findings.",Learning predict complex time-series data is a fundamental challenge range disciplines including Machine Learning Robotics Natural Language Processing. Predictive State Recurrent Neural Networks PSRNNs Downeyetal. are a state-of-the-art approach modeling time-series data which combine benefits probabilistic filters Recurrent Neural Networks single model. PSRNNs leverage concept Hilbert Space Embeddings distributions Smolaetal. embed predictive states Reproducing Kernel Hilbert Space estimate predict update embedded states using Kernel Bayes Rule. Practical implementations PSRNNs are made possible machinery Random Features where input features are mapped new space where dot products approximate kernel well. Unfortunately PSRNNs often require large number RFs obtain good results resulting large models which are slow execute slow train. Orthogonal Random Features ORFs Choromanskietal. is an improvement RFs which has been shown decrease number RFs required pointwise kernel approximation. Unfortunately is not clear ORFs can be applied PSRNNs PSRNNs rely Kernel Ridge Regression core component learning algorithm theoretical guarantees ORF do not apply setting. paper extend theory ORFs Kernel Ridge Regression show ORFs can be used obtain Orthogonal PSRNNs OPSRNNs which are smaller faster PSRNNs. particular show OPSRNN models clearly outperform LSTMs furthermore can achieve accuracy similar PSRNNs order magnitude smaller number features needed. Learning predict temporal sequences observations is a fundamental challenge range disciplines including machine learning robotics natural language processing. exist wide variety approaches modeling time series data however recurrent neural networks RNNs have emerged clear frontrunner achieving state-of-the-art performance applications speech recognition Heigoldetal. 2016 language modeling BID5 translation Choetal. 2014b image captioning BID13.Predictive State Recurrent Neural Networks PSRNNs are a state-of-the-art RNN architecture recently introduced Downeyetal. 2017 combine strengths probabilistic models RNNs single model. Specifically PSRNNs offer strong statistical theory globally consistent model initializations rich functional form which is none-the-less amenable refinement via backpropogation time BPTT Despite consisting simple bi-linear operations PSRNNs have been shown significantly outperform complex RNN architectures Downeyetal. 2017 widely used LSTMs BID3 GRUs Choetal. 2014a.PSRNNs leverage concept Hilbert Space embeddings distributions BID10 embed predictive states Reproducing Kernel Hilbert Space RKHS estimate predict update embedded states using Kernel Bayes Rule KBR BID10. PSRNNs directly manipulate kernel embeddings distributions observations can be initialized via globally consistent method-of-moments algorithm which reduces series linear ridge regressions.Practical implementations PSRNNs are made possible machinery Random Features RFs input features are mapped new space where dot products approximate kernel well BID7. RFs are crucial success PSRNNs however PSRNNs often require significant number RFs order obtain good results. unfortunately number required RFs grows dimensionality input resulting models which can be large slow execute slow train.One technique has proven effective reducing required number RFs kernel machines is Orthogonal Random Features ORFs BID14. When using ORFs matrix RFs is replaced properly scaled random orthogonal matrix resulting significantly decreased kernel approximation error. particularly nice feature ORFs is that BID14 Choromanskietal. 2017 prove using ORFs results guaranteed improvement pointwise kernel approximation error when compared RFs.Unfortunately guarantees BID14 are not directly applicable PSRNN setting. PSRNNs first obtain set model parameters via ridge regression use model parameters calculate inner products RF space. downstream application RFs goes beyond results proven BID14 Choromanskietal. 2017 Hence is not clear whether ORF can be applied obtain improvement PSRNN setting.In work show ORFs can be used obtain OPSRNNs:PSRNNs initialized using ORFs which are smaller faster execute train PSRNNs initialized using conventional unstructured RFs. theoretically analyze orthogonal version KRR algorithm is used initialize OPSRNNs. show orthogonal RNNs lead kernel algorithms strictly better spectral properties explain how this translates strictly smaller upper bounds failure probabilities regarding KRR empirical risk. compare performance OPSRNNs LSTMs well conventional PSRNNs number robotics tasks show OPSRRNs are consistently superior tasks. particular show OPSRNN models can achieve accuracy similar PSRNNs order magnitude smaller number features needed. showed how structured orthogonal constructions can be effectively integrated recurrent neural network based architectures provide models consistently achieve performance superior baselines. also provide significant compression achieving similar accuracy PSRNNs order magnitude smaller number features needed. Furthermore gave first theoretical guarantees showing orthogonal random features lead exponentially small bounds failure probability regarding empirical risk kernel ridge regression model. latter one is an important component RNN based architectures state prediction consider paper. Finally proved bounds are strictly better standard nonorthogonal random feature map mechanism. Exhaustive experiments conducted several robotics task confirm theoretical findings.,1356,994,362,0.013,1.364,2025/11/05 17:19:05,0.01,1.575,0.1059190031152649,407.842
"Training deep neural networks requires many training samples, but in practice training labels are expensive to obtain and may be of varying quality, as some may be from trusted expert labelers while others might be from heuristics or other sources of weak supervision such as crowd-sourcing. This creates a fundamental quality- versus-quantity trade-off in the learning process. Do we learn from the small amount of high-quality data or the potentially large amount of weakly-labeled data? We argue that if the learner could somehow know and take the label-quality into account when learning the data representation, we could get the best of both worlds. To this end, we propose “fidelity-weighted learning” (FWL), a semi-supervised student- teacher approach for training deep neural networks using weakly-labeled data. FWL modulates the parameter updates to a student network (trained on the task we care about) on a per-sample basis according to the posterior confidence of its label-quality estimated by a teacher (who has access to the high-quality labels). Both student and teacher are learned from the data. We evaluate FWL on two tasks in information retrieval and natural language processing where we outperform state-of-the-art alternative semi-supervised methods, indicating that our approach makes better use of strong and weak labels, and leads to better task-dependent data representations. The success of deep neural networks to date depends strongly on the availability of labeled data which is costly and not always easy to obtain. Usually it is much easier to obtain small quantities of high-quality labeled data and large quantities of unlabeled data. The problem of how to best integrate these two different sources of information during training is an active pursuit in the field of semi-supervised learning BID6 . However, for a large class of tasks it is also easy to define one or more so-called ""weak annotators"", additional (albeit noisy) sources of weak supervision based on heuristics or ""weaker"", biased classifiers trained on e.g. non-expert crowd-sourced data or data from different domains that are related. While easy and cheap to generate, it is not immediately clear if and how these additional weakly-labeled data can be used to train a stronger classifier for the task we care about. More generally, in almost all practical applications machine learning systems have to deal with data samples of variable quality. For example, in a large dataset of images only a small fraction of samples may be labeled by experts and the rest may be crowd-sourced using e.g. Amazon Mechanical Turk BID68 . In addition, in some applications, labels are intentionally perturbed due to privacy issues BID69 Papernot et al., 2017 ).Assuming we can obtain a large set of weakly-labeled data in addition to a much smaller training set of ""strong"" labels, the simplest approach is to expand the training set by including the weakly-supervised samples (all samples are equal). Alternatively , one may pretrain on the weak data and then fine-tune on observations from the true function or distribution (which we call strong data). Indeed, it has recently been shown that a small amount of expert-labeled data can be augmented in such a way by a large set of raw data, with labels coming from a heuristic function, to train a more accurate neural ranking model BID12 . The downside is that such approaches are oblivious to the amount or source of noise in the labels. Step 1: Pre-train student on weak data, Step 2: Fit teacher to observations from the true function, and Step 3: Fine-tune student on labels generated by teacher, taking the confidence into account. Red dotted borders and blue solid borders depict components with trainable and non-trainable parameters, respectively.In this paper, we argue that treating weakly-labeled samples uniformly (i.e. each weak sample contributes equally to the final classifier) ignores potentially valuable information of the label quality. Instead, we propose Fidelity-Weighted Learning (FWL), a Bayesian semi-supervised approach that leverages a small amount of data with true labels to generate a larger training set with confidence-weighted weakly-labeled samples, which can then be used to modulate the fine-tuning process based on the fidelity (or quality) of each weak sample. By directly modeling the inaccuracies introduced by the weak annotator in this way, we can control the extent to which we make use of this additional source of weak supervision: more for confidently-labeled weak samples close to the true observed data, and less for uncertain samples further away from the observed data.We propose a setting consisting of two main modules. One is called the student and is in charge of learning a suitable data representation and performing the main prediction task, the other is the teacher which modulates the learning process by modeling the inaccuracies in the labels. We explain our approach in much more detail in Section 2, but at a high level it works as follows (see FIG0 ): We pretrain the student network on weak data to learn an initial task-dependent data representation which we pass to the teacher along with the strong data. The teacher then learns to predict the strong data, but crucially, based on the student's learned representation. This then allows the teacher to generate new labeled training data from unlabeled data, and in the process correct the student's mistakes, leading to a better final data representation and better final predictor.We introduce the proposed FWL approach in more detail in Section 2. We then present our experimental setup in Section 3 where we evaluate FWL on a toy task and two real-world tasks, namely document ranking and sentence sentiment classification. In all cases, FWL outperforms competitive baselines and yields state-of-the-art results, indicating that FWL makes better use of the limited true labeled data and is thereby able to learn a better and more meaningful task-specific representation of the data. Section 4 provides analysis of the bias-variance trade-off and the learning rate, suggesting also to view FWL from the perspective of Vapnik's learning with privileged information (LUPI) framework BID64 . Section 5 situates FWL relative to related work, and we end the paper by drawing the main conclusions in Section 6. We conducted k-fold cross validation on D s (the strong data) and report two standard evaluation metrics for ranking: mean average precision (MAP) of the top-ranked 1,000 documents and normalized discounted cumulative gain calculated for the top 20 retrieved documents (nDCG@20). TAB0 shows the performance on both datasets. As can be seen, FWL provides a significant boost on the performance over all datasets. In the ranking task, the student is designed in particular to be trained on weak annotations BID12 , hence training the network only on weak supervision, i.e. NN W performs better than NN S . This can be due to the fact that ranking is a complex task requiring many training samples, while relatively few data with true labels are available.Alternating between strong and weak data during training, i.e. NN S + /W seems to bring little (but statistically significant) improvement. However, we can gain better results by the typical fine-tuning strategy, NN W→S . Comparing the performance of FWL unsuprep to FWL indicates that, first of all learning the representation of the input data downstream of the main task leads to better results compared to a task-independent unsupervised or self-supervised way. Also the dramatic drop in the performance compared to the FWL, emphasizes the importance of the preretraining the student on weakly labeled data. We can gain improvement by fine-tuning the NN W using labels generated by the teacher without considering their confidence score, i.e. FWL \Σ. This means we just augmented the fine-tuning process by generating a fine-tuning set using teacher which is better than D s in terms of quantity and D w in terms of quality. This baseline is equivalent to setting β = 0 in Equation 1. However, we see a big jump in performance when we use FWL to include the estimated label quality from the teacher, leading to the best overall results. We report Macro-F1, the official SemEval metric, in TAB1 . We see that the proposed FWL is the best performing approach.For this task, since the amount of data with true labels are larger compared to the ranking task, the performance of NN S is acceptable. Alternately sampling from weak and strong data gives better results. Pretraining on weak labels then fine-tuning the network on true labels, further improves the performance. Weighting the gradient updates from weak labels during pretraining and fine-tuning the network with true labels, i.e. NN W ω →S seems to work quite well in this task. For this task, like ranking task, learning the representation in an unsupervised task independent fashion, i.e. FWL unsuprep , does not lead to good results compared to the FWL. Similar to the ranking task, fine-tuning NN S based on labels generated by GP instead of data with true labels, regardless of the confidence score, works better than standard fine-tuning.Besides the baselines, we also report the best performing systems which are also convolution-based models (Rouvier & Favre 2016 on SemEval-14; Deriu et al. 2016 on SemEval-15) . Using FWL and taking the confidence into consideration outperforms the best systems and leads to the highest reported results on both datasets. Training neural networks using large amounts of weakly annotated data is an attractive approach in scenarios where an adequate amount of data with true labels is not available, a situation which often arises in practice. In this paper, we introduced fidelity-weighted learning (FWL), a new student-teacher framework for semi-supervised learning in the presence of weakly labeled data. We applied FWL to document ranking and sentiment classification, and empirically verified that FWL speeds up the training process and improves over state-of-the-art semi-supervised alternatives.","Training deep neural networks requires many training samples practice training labels are expensive obtain may varying quality may trusted expert labelers others might heuristics sources weak supervision crowd-sourcing creates fundamental quality- versus-quantity trade-off learning process. Do we learn small amount high-quality data potentially large amount weakly-labeled data? argue if the learner could somehow know take label-quality account when learning data representation could get best worlds. end propose fidelity-weighted learning FWL semi-supervised student- teacher approach training deep neural networks using weakly-labeled data. FWL modulates parameter updates student network trained task care per-sample basis according posterior confidence label-quality estimated teacher who has access high-quality labels student teacher are learned data. evaluate FWL two tasks information retrieval natural language processing where we outperform state-of-the-art alternative semi-supervised methods indicating approach makes better use strong weak labels leads better task-dependent data representations. success deep neural networks date depends strongly availability labeled data which is costly always easy obtain. Usually is much easier obtain small quantities high-quality labeled data large quantities unlabeled data. problem how to best integrate two different sources information training is an active pursuit field semi-supervised learning BID6. However large class tasks is also easy define one so-called weak annotators additional albeit noisy sources weak supervision based heuristics weaker biased classifiers trained e.g non-expert crowd-sourced data data different domains are related. easy cheap generate is not immediately clear if and how these additional weakly-labeled data can be used train stronger classifier task care about. generally almost practical applications machine learning systems have to deal data samples variable quality. example large dataset images small fraction samples may labeled experts rest may crowd-sourced usinge.g Amazon Mechanical Turk BID68. addition applications labels are intentionally perturbed due privacy issues BID69 Papernot etal. 2017.Assuming can obtain large set weakly-labeled data addition much smaller training set strong labels simplest approach is to expand training set including weakly-supervised samples samples are equal Alternatively one may pretrain weak data fine-tune observations true function distribution which we call strong data Indeed has recently shown small amount expert-labeled data can be augmented way large set raw data labels coming heuristic function train accurate neural ranking model BID12. downside is that such approaches are oblivious amount source noise labels. Step1:Pre-train student weak data Step2:Fit teacher observations true function Step3:Fine-tune student labels generated teacher taking confidence account. Red dotted borders blue solid borders depict components trainable non-trainable parameters respectively.In paper argue treating weakly-labeled samples uniformly.e weak sample contributes equally final classifier ignores potentially valuable information label quality. Instead propose Fidelity-Weighted Learning FWL Bayesian semi-supervised approach leverages small amount data true labels generate larger training set confidence-weighted weakly-labeled samples which can then used modulate fine-tuning process based fidelity quality weak sample. directly modeling inaccuracies introduced weak annotator way can control extent which we make use additional source weak supervision:confidently-labeled weak samples close true observed data less uncertain samples away observed data.We propose setting consisting two main modules. One is called student is in charge learning suitable data representation performing main prediction task is teacher which modulates learning process modeling inaccuracies labels. explain approach much detail Section2 high level works follows see FIG0 pretrain student network weak data learn initial task-dependent data representation which we pass teacher along strong data. teacher learns predict strong data crucially based student's learned representation. allows teacher generate new labeled training data unlabeled data process correct student's mistakes leading better final data representation better final predictor.We introduce proposed FWL approach detail Section2. present experimental setup Section3 where we evaluate FWL toy task two real-world tasks namely document ranking sentence sentiment classification. cases FWL outperforms competitive baselines yields state-of-the-art results indicating FWL makes better use limited true labeled data is thereby able learn better meaningful task-specific representation data. Section 4 provides analysis bias-variance trade-off learning rate suggesting also view FWL perspective Vapnik's learning privileged information LUPI framework BID64. Section 5 situates FWL relative related work end paper drawing main conclusions Section6. conducted k-fold cross validation strong data report two standard evaluation metrics ranking:mean average precision MAP top-ranked 1,000 documents normalized discounted cumulative gain calculated top 20 retrieved documents nDCG@20 TAB0 shows performance datasets. can be seen FWL provides significant boost performance datasets. ranking task student is designed particular trained weak annotations BID12 hence training network weak supervision.e NN W performs better NN S. can be due fact ranking is a complex task requiring many training samples relatively data true labels are available.Alternating strong weak data training.eNN+/W seems bring little statistically significant improvement. However can gain better results typical fine-tuning strategy NN W→S Comparing performance FWL unsuprep FWL indicates first learning representation input data downstream main task leads better results compared task-independent unsupervised self-supervised way. Also dramatic drop performance compared FWL emphasizes importance preretraining student weakly labeled data. can gain improvement fine-tuning NN W using labels generated teacher without considering confidence score.e FWL\Σ means augmented fine-tuning process generating fine-tuning set using teacher which is better terms quantity w terms quality. baseline is equivalent settingβ 0 Equation1. However see big jump performance when we use FWL include estimated label quality teacher leading best overall results. report Macro-F1 official SemEval metric TAB1. see proposed FWL is the best performing approach.For task since amount data true labels are larger compared ranking task performance NN is acceptable. Alternately sampling weak strong data gives better results. Pretraining weak labels fine-tuning network true labels improves performance. Weighting gradient updates weak labels pretraining fine-tuning network true labels.eNNWω →S seems work quite well task. task like ranking task learning representation unsupervised task independent fashion.e FWL unsuprep does not lead good results compared FWL. Similar ranking task fine-tuningNN based labels generated GP instead data true labels regardless confidence score works better standard fine-tuning.Besides baselines also report best performing systems which are also convolution-based models Rouvier Favre 2016 SemEval-14 Deriuetal. 2016 SemEval-15 Using FWL taking confidence consideration outperforms best systems leads highest reported results datasets. Training neural networks using large amounts weakly annotated data is an attractive approach scenarios where an adequate amount data true labels is not available situation which often arises practice. paper introduced fidelity-weighted learning FWL new student-teacher framework semi-supervised learning presence weakly labeled data. applied FWL document ranking sentiment classification empirically verified FWL speeds training process improves state-of-the-art semi-supervised alternatives.",2033,1361,672,0.025,1.494,2025/11/05 17:19:05,0.01,1.636,0.5109034267912771,699.34
" Online learning has attracted great attention due to the increasing demand for systems that have the ability of learning and evolving. When the data to be processed is also high dimensional and dimension reduction is necessary for visualization or prediction enhancement, online dimension reduction will play an essential role. The purpose of this paper is to propose new online learning approaches for supervised dimension reduction. Our first algorithm is motivated by adapting the sliced inverse regression (SIR), a pioneer and effective algorithm for supervised dimension reduction, and making it implementable in an incremental manner. The new algorithm, called incremental sliced inverse regression (ISIR), is able to update the subspace of significant factors with intrinsic lower dimensionality fast and efficiently when new observations come in. We also refine the algorithm by using an overlapping technique  and develop an incremental overlapping sliced inverse regression (IOSIR) algorithm. We verify the effectiveness and efficiency of both algorithms by simulations and real data applications. Dimension reduction aims to explore low dimensional representation for high dimensional data. It helps to promote our understanding of the data structure through visualization and enhance the predictive performance of machine learning algorithms by preventing the ""curse of dimensionality"". Therefore, as high dimensional data become ubiquitous in modern sciences, dimension reduction methods are playing more and more important roles in data analysis. Dimension reduction algorithms can be either unsupervised or supervised. Principle component analysis (PCA) might be the most popular unsupervised dimension reduction method. Other unsupervised dimension reduction methods include the kernel PCA, multidimensional scaling, and manifold learning based methods such as isometric mapping and local linear embedding. Unlike unsupervised dimension reduction, supervised dimension reduction involves a response variable. It finds the intrinsic lower-dimensional representations that are relevant to the prediction of the response values. Supervised dimension reduction methods can date back to the well known linear discriminant analysis (LDA) while its blossom occurred in the last twenty years. Many approaches have been proposed and successfully applied in various scientific domains; see BID21 ; BID9 ; BID22 ; BID35 ; BID31 ; BID14 ; BID24 ; BID33 ; BID34 ; BID10 and the references therein.We are in a big data era and facing the challenges of big data processing, thanks to the fast development of modern information technology. Among others, two primary challenges are the big volume and fast velocity of the data. When a data set is too big to be stored in a single machine or when the data arrives in real time and information update is needed frequently, analysis of the data in an online manner is necessary and efficient. If the data is simultaneously big and high dimensional, it becomes necessary to develop online learning approaches for dimension reduction. As PCA and LDA are the most wildly used dimension reduction techniques, a bunch of PCA-based and LDA-based online dimension reduction algorithms has been proposed. Incremental PCA have been described in BID17 BID18 ; BID32 ; BID43 ; BID29 . Incremental LDA have been developed in BID27 ; BID42 ; BID20 ; BID7 . Other strategies like QR decomposition or SVD have also been used in BID6 ; BID36 ; BID28 .In this paper, our purpose is to propose a new online learning approach for supervised dimension reduction. Our motivation is to implement the sliced inverse regression (SIR) in an incremental manner. SIR was proposed in BID21 and has become one of the most efficient supervised dimension reduction method. SIR and its refined versions have been found successful in many scientific areas such as bioinformatics, hyperspectral image analysis, and physics; see BID8 BID4 ; BID3 ; BID12 ; BID15 ; BID19 ; BID0 ; BID23 BID11 ; BID41 . SIR can be implemented by solving an generalized eigen-decomposition problem, Γβ = λΣβ, where Γ is a matrix depending on the response variable (whose definition is described in the next section) and Σ is the covariance matrix. To make it implementable in an online manner we rewrite it as standard eigendecomposition problem Σ − 1 2 ΓΣ − 1 2 η = λη where η = Σ 1 2 β and adopt the ideas from incremental PCA. We need to overcome two main challenges in this process. First , how do we transform the data so that they are appropriate for the transformed PCA problem? Note that simply normalizing the data does not work. Second , online update of Σ − 1 2 , if not impossible, seems very difficult. The first contribution of this paper is to overcome these difficulties and design a workable incremental SIR method. Our second contribution will be to refine the method by an overlapping technique and design an incremental overlapping SIR algorithm.The rest of this paper is arranged as follows. We review SIR algorithm in Section 2 and the incremental PCA algorithm in Section 3. We propose the incremental SIR algorithm in Section 4 and refine it in Section 5. Simulations are done in Section 6. We close with discussions in Section 7. We proposed two online learning approaches for supervised dimension reduction, namely, ISIR and IOSIR. They are motivated by standardizing the data and reformulate the SIR algorithm to a PCA problem. However, data standardization is only used to motivate the algorithm while not explicitly calculated in the algorithms. We proposed to use Sherman Morrison formula to online update Σ −1 and some approximated calculations to circumvent explicit data standardization. This novel idea played a key role in our algorithm design. Both algorithms are shown effective and efficient. While IOSIR does not apply to classification problems, it is usually superior over ISIR in regression problems.We remark that the purpose of ISIR and IOSIR is to keep the dimension reduction accuracy in the situation that a batch learning is not suitable. This is especially the case for streaming data where information update and system involving is necessary whenever new data becomes available. When the whole data set is given and one only needs the EDR space from batch learning, ISIR or IOSIR is not necessarily more efficient than SIR because their complexity to run over the whole sample path is O(p 2 N ), comparable to the complexity O(p 3 + p 2 N ) of SIR.There are two open problems worth further investigation. First, the need to store and use Σ −1 during the updating process is the main bottleneck for ISIR and IOSIR when the dimensionality of the data is ultrahigh. Second, for SIR and other batch dimension reduction methods, many methods have been proposed to determine the intrinsic dimension K; see e.g. BID21 ; Schott (1994); BID5 ; BID1 ; BID2 ; Nkiet (2008) . They depend on all p eigenvalues of the generalized eigen-decomposition problem and are impractical for incremental learning. We do not have obvious solutions to these problems at this moment and would like to leave them for future research.",Online learning has attracted great attention due increasing demand systems have the ability learning evolving. When the When a data processed is also high dimensional dimension reduction is necessary visualization prediction enhancement online dimension reduction will play essential role. purpose paper is to propose new online learning approaches supervised dimension reduction. first algorithm is motivated adapting sliced inverse regression SIR pioneer effective algorithm supervised dimension reduction making implementable incremental manner. new algorithm called incremental sliced inverse regression ISIR is able update subspace significant factors intrinsic lower dimensionality fast efficiently when new observations come in. also refine algorithm using overlapping technique develop incremental overlapping sliced inverse regression IOSIR algorithm. verify effectiveness efficiency algorithms simulations real data applications. Dimension reduction aims explore low dimensional representation high dimensional data. helps promote understanding data structure visualization enhance predictive performance machine learning algorithms preventing curse dimensionality. Therefore high dimensional data become ubiquitous modern sciences dimension reduction methods are playing important roles data analysis. Dimension reduction algorithms can be either unsupervised supervised. Principle component analysis PCA might popular unsupervised dimension reduction method. unsupervised dimension reduction methods include kernel PCA multidimensional scaling manifold learning based methods isometric mapping local linear embedding. Unlike unsupervised dimension reduction supervised dimension reduction involves response variable. finds intrinsic lower-dimensional representations are relevant prediction response values. Supervised dimension reduction methods can date back well known linear discriminant analysis LDA blossom occurred last twenty years. Many approaches have been proposed successfully applied various scientific domains;see BID21;BID9;BID22;BID35;BID31;BID14;BID24;BID33;BID34;BID10 references therein.We are in a are the big data era facing challenges big data processing thanks fast development modern information technology. Among others two primary challenges are in a are the big volume fast velocity data. When the When a data set is too big stored single machine when the data arrives real time information update is needed frequently analysis data online manner is necessary efficient. If the data is simultaneously big high dimensional becomes necessary develop online learning approaches dimension reduction. PCA LDA are the most wildly used dimension reduction techniques bunch PCA-based LDA-based online dimension reduction algorithms has been proposed. Incremental PCA have been described BID17 BID18;BID32;BID43;BID29. Incremental LDA have been developed BID27;BID42;BID20;BID7. strategies like QR decomposition SVD have also used BID6;BID36;BID28.In paper purpose is to propose new online learning approach supervised dimension reduction. motivation is to implement sliced inverse regression SIR incremental manner. SIR was proposed BID21 has become one efficient supervised dimension reduction method. SIR refined versions have been found successful many scientific areas bioinformatics hyperspectral image analysis physics;see BID8 BID4;BID3;BID12;BID15;BID19;BID0;BID23 BID11;BID41. SIR can be implemented solving generalized eigen-decomposition problem Γβ λΣβ whereΓ is a matrix depending response variable whose definition is described next section Σ is the covariance matrix. make implementable online manner rewrite standard eigendecomposition problemΣ −12ΓΣ −12η λη whereη Σ12β adopt ideas incremental PCA. need overcome two main challenges process. First how do we transform data are appropriate transformed PCA problem? Note simply normalizing data does not work. Second online update Σ−12 if not impossible seems difficult. first contribution paper is to overcome difficulties design workable incremental SIR method. second contribution will be to refine method overlapping technique design incremental overlapping SIR algorithm.The rest paper is arranged follows. review SIR algorithm Section2 incremental PCA algorithm Section3. propose incremental SIR algorithm Section4 refine Section5. Simulations are done Section6. close discussions Section7. proposed two online learning approaches supervised dimension reduction namely ISIR IOSIR. are motivated standardizing data reformulate SIR algorithm PCA problem. However data standardization is only used motivate algorithm explicitly calculated algorithms. proposed use Sherman Morrison formula online updateΣ−1 approximated calculations circumvent explicit data standardization. novel idea played key role algorithm design. algorithms are shown effective efficient. IOSIR does not apply classification problems is usually superior ISIR regression problems.We remark purpose ISIR IOSIR is to keep dimension reduction accuracy situation batch learning is not suitable. is especially case streaming data where information update system involving is necessary whenever new data becomes available. When the whole data set is given one needs EDR space batch learning ISIR IOSIR is not necessarily efficient SIR complexity run whole sample path isO(p2N comparable complexity p3+p 2N SIR.There are two open problems worth investigation. First need store useΣ−1 updating process is the main bottleneck ISIR IOSIR when the dimensionality data is ultrahigh. Second SIR batch dimension reduction methods many methods have been proposed determine intrinsic dimensionK;see e.g BID21;Schott 1994 BID5;BID1;BID2;Nkiet 2008 depend p eigenvalues generalized eigen-decomposition problem are impractical incremental learning. do not have obvious solutions problems moment would like leave future research.,1390,1045,345,0.014,1.33,2025/11/05 17:19:05,0.01,1.631,0.0,438.573
"This paper presents a storage-efficient learning model titled Recursive Binary Neural Networks for embedded and mobile devices having a limited amount of on-chip data storage such as hundreds of kilo-Bytes. The main idea of the proposed model is to recursively recycle data storage of weights (parameters) during training. This enables a device with a given storage constraint to train and instantiate a neural network classifier with a larger number of weights on a chip, achieving better classification accuracy. Such efficient use of on-chip storage reduces off-chip storage accesses, improving energy-efficiency and speed of training. We verified the proposed training model with deep and convolutional neural network classifiers on the MNIST and voice activity detection benchmarks. For the deep neural network, our model achieves data storage requirement of as low as 2 bits/weight, whereas the conventional binary neural network learning models require data storage of 8 to 32 bits/weight. With the same amount of data storage, our model can train a bigger network having more weights, achieving 1% less test error than the conventional binary neural network learning model. To achieve the similar classification error, the conventional binary neural network model requires 4× more data storage for weights than our proposed model. For the convolution neural network classifier, the proposed model achieves 2.4% less test error for the same on-chip storage or 6× storage savings to achieve the similar accuracy.
 Deep Neural Networks (DNN) have demonstrated the state-of-the-art results in a wide range of cognitive workloads such as computer vision BID10 and speech recognition ), achieving better-than-human performance for the tasks often considered too complex for machines. The success of DNNs has indeed motivated scientists and engineers to implement a DNN in mobile and embedded devices, dubbed as Internet of Smart Things BID9 ). The recent works in this area, however, mostly implement the inference function of DNN, rather than training, while training is performed in cloud computers and posttraining weights are downloaded to mobile and embedded devices BID11 ).On-device learning, however, becomes increasingly important for the mobile and embedded devices for the following three reasons. First, an intelligent device benefits to have the model that is custombuilt for the device itself, its end user, and environment. This is because the model tends to be more accurate and effective if constructed with the consideration of those factors. Second, the training data from mobile and embedded devices can contain security-sensitive information, e.g., personal health data from wearable medical devices. At the risk of being leaked, users typically do not want to upload such data onto cloud computers. Finally, in the era of Internet of Things (IoT), we anticipate a drastic increase in the number of deployed devices, which can proportionally increase the number of learning tasks to be done in the cloud. Coupled with the complexity of training, even for powerful cloud computers, this can be a computationally challenging task.On-device learning, however, entails various challenges in algorithms, data, and systems BID15 ; BID18 ). The most eminent challenge regarding computing systems is high energy consumption caused by dense computation and data access, which is considered prohibitive for the limited resources of embedded devices. The high overhead of data access is caused by fetching DNN weights from DRAM (or FLASH) external to a computing chip on an embedded device. Since the data storage size is limited for such computing chip, the parameters of a DNN have to be stored in external DRAM and FLASH during training. For example, ARM Cortex M3 processor, a processor widely used in commercial wearable devices such as FitBit, has only 64 kilo-Byte (kB) on-chip data storage. This can only store very small size of DNN especially if each weight is 32-bit float point number. Compared to accessing on-chip SRAM, accessing off-chip DRAM incurs 3 to 4 orders of magnitudes more energy and delay overhead. Therefore, fetching weights every time for each data makes training prohibitive to be implemented on a mobile and embedded device BID5 ).Recently several techniques such as pruning, distilling, and binarizing weights have been proposed to compress the parameters of a DNN. This makes it more feasible to fit weights in on-chip SRAM BID5 ; BID2 ; BID14 ; BID8 ). These techniques can also reduce computation overhead. However, these works focused on weight size compression after training is finished. The data storage requirement during training remains the same.Similarly, several learning models, which belong to so-called Binary Neural Networks (BNN), have been proposed BID2 ; BID14 ). These model uses sign bits (or binary information ) of weights in several parts of the learning model notably the part of multiplying and accumulating weights with inputs/activations. Although this greatly reduces computational complexity , each weight still needs to be represented in high precision number with multiple bits (e.g. 32 bits in BID2 ; BID14 ) during the end-to-end training process. This is because weights have to be fine-tuned in the weight update part. Therefore, this so-called BNN models have not demonstrated to scale storage requirement for training below 32 bits/weight.Our goal is, therefore, to efficiently use the limited amount of on-chip data storage during training. We also aim to scale computational complexity. Toward this goal, we propose a new learning model, Recursive Binary Neural Network (RBNN). This model is based on the process of weight training, weight binarization, recycling storage of the non-sign-bit portion of weights to add more weights to enlarge the neural network for accuracy improvement. We recursively perform this process until either accuracy stops improving or we use up all the storage on a chip.We verified the proposed RBNN model on a Multi-Layer Perceptron (MLP)-like and a convolutional neural network classifier on the MNIST and Voice Activity Detection (VAD) benchmark. We considered typical storage constraints of embedded sensing devices in the order of hundreds of kB. The experiment in the MLP-like classifier on MNIST confirms that the proposed model (i) demonstrates 1% less test error over the conventional BNN learning model specifically following BID2 for the same storage constraints or (ii) scales on-chip data storage requirement by 4× for the same classification test error rate(∼2%), marking the storage requirement of 2 bits/weight. The conventional BNN models in BID2 ; BID14 exhibit a significantly larger storage requirements of 8 to 32 bits/weight. The experiment of the CNN classifier for MNIST confirms up to 6× reduction of data storage requirement and 2.4% less test error. For the VAD benchmark, the proposed RBNN achieves 9× savings in data storage requirement .The remainder of the paper is as follow. In Sec. 2 we will introduce the works related to this paper, including comparison to existing works on distillation, compression, BNNs, and low-precision weights. In Sec. 3 we will describe our proposed model. Sec. 4 will present the experimental results and comparisons to the conventional BNN model. Finally , in Sec. 5, we will conclude the paper. The paper includes Appendix A to D to describe additional experiments and analysis.2 RELATED WORK 2.1 DISTILLATION AND COMPRESSION OF DNN PARAMETERS Knowledge distillation BID8 ) is a technique to compress knowledge of an ensemble of DNNs into one small DNN while maintaining the accuracy. Although this technique can scale the number of weights for deployment systems post-training, it cannot scale data storage requirement Under review as a conference paper at ICLR 2018 for training. Specifically, during training, each of weights is represented in high-precision number, which needs to be stored in multi-bit data storage.Another technique is to compress the data size of weights by exploiting redundancies in them. In BID5 , the authors combine four sub-techniques, namely weight pruning, quantization, sharing, and compression coding to reduce the data size of weights. Similar to the knowledge distillation, this technique can be applied to the weights that are already trained, and cannot scale data storage requirement of weights during training. This paper presents a new learning model for on-device training with limited data storage. The proposed RBNN model efficiently uses limited on-chip data storage resources by recycling the part of data storage that would have been wasted in conventional BNN model, to add and train more weights to a neural network classifier. We verified the proposed model with MLP-like DNN and CNN classifiers on the MNIST and VAD benchmark under the typical embedded device storage constraints. The results of MLP-like DNNs on MNIST show that the proposed model achieves 2 bits/weight storage requirement while achieving 1% less test error as compared to the conventional BNN model for the same storage constraint. Our proposed model also achieves 4× less data storage than the conventional model for the same classification error. The similar to greater savings are verified with the CNN classifiers and the VAD benchmarks. We expect the future work of further reduce computation complexity, such as binarization of activation function of BNN BID3 ). We also expect to apply the RBNN model to the ensembles of neural networks BID20 , and the mixture of experts BID16 ).","paper presents storage-efficient learning model titled Recursive Binary Neural Networks embedded mobile devices limited amount on-chip data storage hundreds kilo-Bytes main idea proposed model is to recursively recycle data storage weights parameters training. enables device given storage constraint train instantiate neural network classifier larger number weights chip achieving better classification accuracy. efficient use on-chip storage reduces off-chip storage accesses improving energy-efficiency speed training. verified proposed training model deep convolutional neural network classifiers MNIST voice activity detection benchmarks. deep neural network model achieves data storage requirement low 2 bits/weight whereas conventional binary neural network learning models require data storage 8 32 bits/weight. amount data storage model can train bigger network weights achieving1% less test error conventional binary neural network learning model. achieve similar classification error conventional binary neural network model requires4× data storage weights proposed model. convolution neural network classifier proposed model achieves 2.4 less test error on-chip storage 6× storage savings achieve similar accuracy. Deep Neural Networks DNN have demonstrated state-of-the-art results wide range cognitive workloads computer vision BID10 speech recognition achieving better-than-human performance tasks often considered complex machines. success DNNs has indeed motivated scientists engineers implement DNN mobile embedded devices dubbed Internet Smart Things BID9 recent works area however mostly implement inference function DNN rather training training is performed cloud computers posttraining weights are downloaded mobile embedded devices BID11.On-device learning however becomes increasingly important mobile embedded devices following three reasons. First intelligent device benefits have the model is custombuilt device end user environment. is because the model tends accurate effective if constructed consideration factors. Second training data mobile embedded devices can contain security-sensitive information e.g personal health data wearable medical devices. risk leaked users typically do not want upload data onto cloud computers. Finally era Internet Things IoT anticipate drastic increase number deployed devices which can proportionally increase number learning tasks done cloud. Coupled complexity training even powerful cloud computers canbe computationally challenging task.On-device learning however entails various challenges algorithms data systems BID15;BID18 eminent challenge regarding computing systems is high energy consumption caused dense computation data access which is considered prohibitive limited resources embedded devices. high overhead data access is caused fetching DNN weights DRAM FLASH external computing chip embedded device. Since data storage size is limited computing chip parameters DNN have to be stored external DRAM FLASH training. example ARM Cortex M3 processor processor widely used commercial wearable devices FitBit has only 64 kilo-Byte kB on-chip data storage. can only store small size DNN especially if each weight is 32-bit float point number. Compared accessing on-chip SRAM accessing off-chip DRAM incurs 3 4 orders magnitudes energy delay overhead. Therefore fetching weights every time data makes training prohibitive implemented mobile embedded device BID5.Recently several techniques pruning distilling binarizing weights have been proposed compress parameters DNN. makes feasible fit weights on-chip SRAM BID5;BID2;BID14;BID8 techniques can also reduce computation overhead. However works focused weight size compression training is finished. data storage requirement training remains same.Similarly several learning models which belong so-called Binary Neural Networks BNN have been proposed BID2;BID14 model uses sign bits binary information weights several parts learning model notably part multiplying accumulating weights inputs/activations. Although greatly reduces computational complexity weight still needs represented high precision number multiple bits e.g 32 bits BID2;BID14 end-to-end training process. is because weights have to be fine-tuned weight update part. Therefore so-called BNN models have not demonstrated scale storage requirement training 32 bits/weight.Our goal is,therefore efficiently use limited amount on-chip data storage training. also aim scale computational complexity. Toward goal propose new learning model Recursive Binary Neural Network RBNN model is based process weight training weight binarization recycling storage non-sign-bit portion weights add weights enlarge neural network accuracy improvement. recursively perform process either accuracy stops improving use storage chip.We verified proposed RBNN model Multi-Layer Perceptron MLP -like convolutional neural network classifier MNIST Voice Activity Detection VAD benchmark. considered typical storage constraints embedded sensing devices order hundreds kB. experiment MLP-like classifier MNIST confirms proposed model demonstrates1% less test error conventional BNN learning model specifically following BID2 storage constraints ii scales on-chip data storage requirement 4× classification test error rate ∼2 marking storage requirement 2 bits/weight. conventional BNN models BID2;BID14 exhibit significantly larger storage requirements 8 32 bits/weight. experiment CNN classifier MNIST confirms 6× reduction data storage requirement 2.4 less test error. VAD benchmark proposed RBNN achieves9× savings data storage requirement.The remainder paper is as follow. Sec. 2 will introduce works related paper including comparison existing works distillation compression BNNs low-precision weights. Sec. 3 will describe proposed model. Sec. 4 will present experimental results comparisons conventional BNN model. Finally Sec. 5 will conclude paper. paper includes Appendix describe additional experiments analysis.2 RELATED WORK 2.1 DISTILLATION COMPRESSION DNN PARAMETERS Knowledge distillation BID8 is a technique compress knowledge ensemble DNNs one small DNN maintaining accuracy. Although technique can scale number weights deployment systems post-training cannot scale data storage requirement review conference paper ICLR 2018 training. Specifically training weights is represented high-precision number which needs stored multi-bit data storage.Another technique is to compress data size weights exploiting redundancies them. BID5 authors combine four sub-techniques namely weight pruning quantization sharing compression coding reduce data size weights. Similar knowledge distillation technique can be applied weights are already trained cannot scale data storage requirement weights training. paper presents new learning model on-device training limited data storage. proposed RBNN model efficiently uses limited on-chip data storage resources recycling part data storage would have been wasted conventional BNN model add train weights neural network classifier. verified proposed model MLP-like DNN CNN classifiers MNIST VAD benchmark typical embedded device storage constraints. results MLP-like DNNs MNIST show proposed model achieves2 bits/weight storage requirement achieving1% less test error compared conventional BNN model storage constraint. proposed model also achieves 4× less data storage conventional model classification error. similar greater savings are verified CNN classifiers VAD benchmarks. expect future work reduce computation complexity binarization activation function BNN BID3 also expect apply RBNN model ensembles neural networks BID20 mixture experts BID16",1876,1301,575,0.021,1.442,2025/11/05 17:19:05,0.01,1.532,0.3489096573208719,544.374
"Within-class variation in a high-dimensional dataset can be modeled as being on a low-dimensional manifold due to the constraints of the physical processes producing that variation (e.g., translation, illumination, etc.). We desire a method for learning a representation of the manifolds induced by identity-preserving transformations that can be used to increase robustness, reduce the training burden, and encourage interpretability in machine learning tasks. In particular, what is needed is a representation of the transformation manifold that can robustly capture the shape of the manifold from the input data, generate new points on the manifold, and extend transformations outside of the training domain without significantly increasing the error. Previous work has proposed algorithms to efficiently learn analytic operators (called transport operators) that define the process of transporting one data point on a manifold to another.   The main contribution of this paper is to define two transfer learning methods that use this generative manifold representation to learn natural transformations and incorporate them into new data. The first method uses this representation in a novel randomized approach to transfer learning that employs the learned generative model to map out unseen regions of the data space. These results are shown through demonstrations of transfer learning in a data augmentation task for few-shot image classification. The second method use of transport operators for injecting specific transformations into new data examples which allows for realistic image animation and informed data augmentation.   These results are shown on stylized constructions using the classic swiss roll data structure and in demonstrations of transfer learning in a data augmentation task for few-shot image classification. We also propose the use of transport operators for injecting transformations into new data examples which allows for realistic image animation. While significant progress has been made in training classifiers that can effectively discriminate between thousands of classes, the increasing classifier complexity obfuscates the reasoning behind class selection and requires large training datasets to capture variations within each class. In many settings, the within-class variation in a high-dimensional dataset can be modeled as being lowdimensional due to the constraints of the physical processes producing that variation (e.g., translation, illumination, etc.). When these variations are within a linear subspace, classic techniques such as principal component analysis (PCA) can be used to efficiently capture the transformations within the data. However, the manifold hypothesis states that in many cases of interest (e.g., images, sounds, text), the within-class variations lie on or near a low-dimensional nonlinear manifold BID5 . In the neuroscience literature there is a hypothesis that the manifold nature of these variations is explicitly exploited by hierarchical processing stages to untangle the representations of different objects undergoing the same physical transformations (e.g., pose) BID7 .By learning manifold representations of identity-preserving transformations on a subset of classes or data points, we gain the ability to transfer these natural variations to previously unseen data. A generative model of the transformation manifold trained on a dataset rich in variation can be used to transfer knowledge of those variations to previously unseen domains. This can increase robustness and reduce the training burden for machine learning tasks as well as enable the generation of novel examples. Additionally , an explicit understanding of the transformations occuring within a dataset provides interpretibility of machine learning tasks that is typically unavailable. One can view this approach as a variant of pattern theory that seeks transformations that operate on representational primitives BID15 , but with an explicit unsupervised learning of the low-dimensional manifold structure of many real-world datasets.There are a large number of ""manifold learning"" algorithms that have been introduced in the literature to discover manifold structure from data. The most common approach to this task is to perform an embedding of the original data points after performing a transformation to preserve either local or global properties of the manifold (e.g., local neighborhood relationships, global geodesic distances, etc.) BID32 BID29 BID37 BID1 . Unfortunately, such approaches capture manifold structure through a transformation of the data points themselves into a lower dimensional space and therefore are not suitable for the desired tasks. Specifically, there is no generative model of the data in the original high-dimensional space, meaning that the inferred manifold structure is not transferable to other data classes, is not amenable to strong interpolation/extrapolation, and does not provide a probabilistic model that can be used in machine learning tasks. More recently , there there are a number of methods that have been introduced that capture manifold structure through a variety of approaches that involve estimating local tangent planes BID9 a; BID3 BID26 . While these methods can admit representations that have some of the above advantages of generative models, the linear approximations can cause challenges when trying to perform transfer learning by extrapolating to out-of-sample points in manifold locations not well-represented in the training data.As an alternative to the above, previous work has proposed unsupervised learning algorithms to efficiently learn Lie group operators that capture the structure of low-dimensional manifolds BID6 BID33 BID24 BID28 . The manifold representation that is described by analytic operators (called transport operators) defines the process of transporting one data point to another, thereby providing a probabilistic generative model for the manifold structure BID6 ). The main contribution of this paper is to define two transfer learning methods that use this generative manifold representation to learn natural transformations and incorporate them into new data. The first method uses this representation in a novel randomized approach to transfer learning that employs the learned generative model to map out unseen regions of the data space. These results are shown through demonstrations of transfer learning in a data augmentation task for few-shot image classification. The second method use of transport operators for injecting specific transformations into new data examples which allows for realistic image animation and informed data augmentation. We have shown that we can transfer meaninful transformation information between classes and examples using manifold transport operators which provide accurate and robust characterization of manifold data in the context of a probabilistic generative model. We have demonstrated that the learned transformations can be transferred accurately to other portions of the manifold (including out-of-sample extensions) through applying the generative model with both randomized and structured coefficients. The transfer learning potential was shown in the context of data generation and augmentation applications by animating individuals with new facial expression and providing examples of few-shot learning on digit and facial expression classification. These results constitute some Classification Accuracy Figure 9 : The boxes represent the classification accuracy distribution when the classifier is trained using the transport operator-augmented dataset (transport operator), using only one example per expression without data augmentation (single example), and using landmarks from the expression frames in all of the training sequences from the CK+ database (CK+).of the first demonstrations that transport operators can form the basis of a learned representation for manifold data that has utility in applications and transfer learning tasks. The presented simulations are proof-of-concept simulations that allow us to fully explore and visualize the results in a way that is impossible with larger or more complex datasets.While successful in these demonstrations, as with any algorithm the results depend on the data characteristics being sufficiently captured by the model family. Though there is evidence in the literature that Lie group operators can capture complex transformations in images BID6 , it is unknown if the transport operator approach will be sufficient to represent the rich variations in more complex datasets. Future work will be required to determine the complexity of manifold models that can be captured successfully by the proposed manifold transport operator approach, including demonstrations of similar tasks on more complex image classification tasks. Additionally , the current model only captures local transformations between points, but it will likely be beneficial to develop the model further to capture more regularity in the coefficient behavior across multiple pairs of points.",Within-class variation high-dimensional dataset can be modeled low-dimensional manifold due constraints physical processes producing variation e.g translation illumination etc. desire method learning representation manifolds induced identity-preserving transformations can be used increase robustness reduce training burden encourage interpretability machine learning tasks. particular what is needed is a representation transformation manifold can robustly capture shape manifold input data generate new points manifold extend transformations outside training domain without significantly increasing error. Previous work has proposed algorithms efficiently learn analytic operators called transport operators define process transporting one data point manifold another. main contribution paper is to define two transfer learning methods use generative manifold representation learn natural transformations incorporate new data. first method uses representation novel randomized approach transfer learning employs learned generative model map unseen regions data space. results are shown demonstrations transfer learning data augmentation task few-shot image classification. second method use transport operators injecting specific transformations new data examples which allows realistic image animation informed data augmentation. results are shown stylized constructions using classic swiss roll data structure demonstrations transfer learning data augmentation task few-shot image classification. also propose use transport operators injecting transformations new data examples which allows realistic image animation. significant progress has been made training classifiers can effectively discriminate thousands classes increasing classifier complexity obfuscates reasoning behind class selection requires large training datasets capture variations within class. many settings within-class variation high-dimensional dataset can be modeled lowdimensional due constraints physical processes producing variation e.g translation illumination etc. When these variations are within linear subspace classic techniques principal component analysis PCA can be used efficiently capture transformations within data. However manifold hypothesis states many cases interest e.g images sounds text within-class variations lie near low-dimensional nonlinear manifold BID5. neuroscience literature is a hypothesis manifold nature variations is explicitly exploited hierarchical processing stages untangle representations different objects undergoing physical transformations e.g pose BID7.By learning manifold representations identity-preserving transformations subset classes data points gain ability transfer natural variations previously unseen data. generative model transformation manifold trained dataset rich variation can be used transfer knowledge variations previously unseen domains. can increase robustness reduce training burden machine learning tasks well enable generation novel examples. Additionally explicit understanding transformations occuring within dataset provides interpretibility machine learning tasks is typically unavailable. One can view approach variant pattern theory seeks transformations operate representational primitives BID15 explicit unsupervised learning low-dimensional manifold structure many real-world datasets.There are a large number manifold learning algorithms have been introduced literature discover manifold structure data. common approach task is to perform embedding original data points performing transformation preserve either local global properties manifold e.g local neighborhood relationships global geodesic distances etc. BID32 BID29 BID37 BID1. Unfortunately approaches capture manifold structure transformation data points lower dimensional space therefore are not suitable desired tasks. Specifically is no generative model data original high-dimensional space meaning inferred manifold structure is not transferable data classes is not amenable strong interpolation/extrapolation does not provide probabilistic model can be used machine learning tasks. recently are number methods have been introduced capture manifold structure variety approaches involve estimating local tangent planes BID9 a;BID3 BID26. methods can admit representations have someof advantages generative models linear approximations can cause challenges when trying perform transfer learning extrapolating out-of-sample points manifold locations well-represented training data.As alternative previous work has proposed unsupervised learning algorithms efficiently learn Lie group operators capture structure low-dimensional manifolds BID6 BID33 BID24 BID28. manifold representation is described analytic operators called transport operators defines process transporting one data point another thereby providing probabilistic generative model manifold structure BID6 main contribution paper is to define two transfer learning methods use generative manifold representation learn natural transformations incorporate new data. first method uses representation novel randomized approach transfer learning employs learned generative model map unseen regions data space. results are shown demonstrations transfer learning data augmentation task few-shot image classification. second method use transport operators injecting specific transformations new data examples which allows realistic image animation informed data augmentation. have shown can transfer meaninful transformation information classes examples using manifold transport operators which provide accurate robust characterization manifold data context probabilistic generative model. have demonstrated learned transformations can be transferred accurately portions manifold including out-of-sample extensions applying generative model randomized structured coefficients. transfer learning potential was shown context data generation augmentation applications animating individuals new facial expression providing examples few-shot learning digit facial expression classification. results constitute Classification Accuracy Figure9:boxes represent classification accuracy distribution when the classifier is trained using transport operator-augmented dataset transport operator using one example per expression without data augmentation single example using landmarks expression frames training sequences CK+database CK+.of first demonstrations transport operators can form basis learned representation manifold data has utility applications transfer learning tasks. presented simulations are proof-of-concept simulations allowus fully explore visualize results way is impossible larger complex datasets.While successful demonstrations algorithm results depend data characteristics sufficiently captured model family. Though is evidence literature Lie group operators can capture complex transformations images BID6 is unknown if the transport operator approach will be sufficient represent rich variations complex datasets. Future work will be required determine complexity manifold models can be captured successfully proposed manifold transport operator approach including demonstrations similar tasks complex image classification tasks. Additionally current model captures local transformations points will likely beneficial develop model capture regularity coefficient behavior across multiple pairs points.,1508,1022,486,0.017,1.476,2025/11/05 17:19:05,0.01,1.481,0.4548286604361368,497.46
"The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such representations are compositional and hierarchical, they can be recombined into an exponentially large set of new concepts. This paper describes SCAN (Symbol-Concept Association Network), a new framework for learning such abstractions in the visual domain. SCAN learns concepts through fast symbol association, grounding them in disentangled visual primitives that are discovered in an unsupervised manner. Unlike state of the art multimodal generative model baselines, our approach requires very few pairings between symbols and images and makes no assumptions about the form of symbol representations. Once trained, SCAN is capable of multimodal bi-directional inference, generating a diverse set of image samples from symbolic descriptions and vice versa. It also allows for traversal and manipulation of the implicit hierarchy of visual concepts through symbolic instructions and learnt logical recombination operations. Such manipulations enable SCAN to break away from its training data distribution and imagine novel visual concepts through symbolically instructed recombination of previously learnt concepts. State of the art deep learning approaches to machine learning have achieved impressive results in many problem domains, including classification BID7 BID33 , density modelling BID6 Oord et al., 2016a; , and reinforcement learning BID17 BID10 BID28 . They are still, however, far from possessing many traits characteristic of human intelligence. Such deep learning techniques tend to be overly data hungry, often rely on significant human supervision and tend to overfit to the training data distribution BID14 BID5 ). An important step towards bridging the gap between human and artificial intelligence is endowing algorithms with compositional concepts BID14 BID5 . Compositionality allows for reuse of a finite set of primitives (addressing the data efficiency and human supervision issues) across many scenarios by recombining them to produce an exponentially large number of novel yet coherent and potentially useful concepts (addressing the overfitting problem). Compositionality is at the core of such human abilities as creativity, imagination and language-based communication.We propose that concepts are abstractions over a set of primitives. For example, consider a toy hierarchy of visual concepts shown in Fig. 1 . Each node in this hierarchy is defined as a subset of visual primitives that make up the scene in the input image. These visual primitives might include factors like object identity, object colour, floor colour and wall colour. As one traverses the hierarchy from the subordinate over basic to superordinate levels of abstraction BID27 (i.e. from the more specific to the more general concepts corresponding to the same visual scene), the number of concept-defining visual primitives decreases. Hence, each parent concept in such a hierarchy is an Figure 1 : Schematic of an implicit concept hierarchy built upon a subset of four visual primitives: object identity (I), object colour (O), floor colour (F ) and wall colour (W ) (other visual primitives necessary to generate the scene are ignored in this example). Concepts form an implicit hierarchy, where each parent is an abstraction over its children and over the original set of visual primitives (the values of the concept-defining sets of visual primitives are indicated by the bold capital letters). In order to generate an image that corresponds to a concept, one has to fill in values for the factors that got abstracted away (represented as ""_""), e.g. by sampling from their respective priors. Given certain nodes in the concept hierarchy, one can traverse the other nodes using logical operations. See Sec.3 for our formal definition of concepts. abstraction (i.e. a subset) over its children and over the original set of visual primitives. A more formal definition of concepts is provided in Sec. 3.Intelligent agents are able to discover and learn abstract compositional concepts using little supervision BID1 BID31 BID2 BID29 . Think of human word learning -we acquire the meaning of words through a combination of a continual stream of unsupervised visual data occasionally paired with a corresponding word label. This paper describes SCAN (Symbol-Concept Association Network, see Fig. 2A ), a neural network model capable of learning grounded visual concepts in a largely unsupervised manner through fast symbol association. First, we use the β-VAE BID8 to learn a set of independent representational primitives through unsupervised exposure to the visual data. This is equivalent to learning a disentangled (factorised and interpretable) representation of the independent ground truth ""generative factors"" of the data BID3 . Next, we allow SCAN to discover meaningful abstractions over these disentangled primitives by exposing it to a small number of symbol-image pairs that apply to a particular concept (e.g. a few example images of an apple paired with the symbol ""apple""). SCAN learns the meaning of the concept by identifying the set of visual primitives that all the visual examples have in common (e.g. all observed apples are small, round and red). The corresponding symbol (""apple"") then becomes a ""pointer"" to the newly acquired concept {small, round, red} -a way to access and manipulate the concept without having to know its exact representational form. Our approach does not make any assumptions about how these symbols are encoded, which also allows SCAN to learn multiple referents to the same concept, i.e. synonyms.Once a concept is acquired, it should be possible to use it for bi-directional inference: the model should be able to generate diverse visual samples that correspond to a particular concept (sym2img) and vice versa (img2sym). Since the projection from the space of visual primitives to the space of concepts (img2sym, red dash arrow in Fig. 1 ) involves abstraction and hence a loss of information, one then needs to add compatible information back in when moving from the space of concepts to that of visual primitives (sym2img, blue dot arrow in Fig. 1 ). In our setup, concepts are defined in terms of a set of relevant visual primitives (e.g. colour, shape and size for ""apple""). This leaves a set of irrelevant visual attributes (e.g. lighting, position, background) to be ""filled in"". We do so by defaulting them to their respective priors, which ensures high diversity of samples (in both image or symbol space) for each concept during img2sym and sym2img inferences.The structured nature of learnt concepts acquired by SCAN allows for sample efficient learning of logical recombination operators: AND (corresponding to a set union of relevant primitives), IN COMMON (corresponding to set intersection) and IGNORE (corresponding to set difference), by pairing a small number of valid visual examples of recombined concepts with the respective operator names. Once the meaning of the operators has been successfully learned, SCAN can exploit the compositionality of the acquired concepts, and traverse previously unexplored parts of the implicit underlying concept hierarchy by manipulating and recombining existing concepts in novel ways. For example, a new node corresponding to the concept {blue, small} can be reached through the following instructions: ""blue"" AND ""small"" (going down the hierarchy from more general to more specific), ""blueberry"" IN COMMON ""bluebell"" (going up the hierarchy from more specific to more general) or ""blueberry"" IGNORE ""round"" (also going up the hierarchy). DISPLAYFORM0 To summarise, our paper 1) presents SCAN, a neural network model capable of learning compositional and hierarchical representations of visual concepts; 2) demonstrates that SCAN can be successfully trained with very little supervised data; 3) shows that after training, SCAN can perform multimodal (visual and symbolic) bi-directional inference and generation with high accuracy and diversity, outperforming all baselines; 4) shows that the addition of logical recombination operations allows SCAN to break out of its limited training data distribution and reach new nodes within the implicit hierarchy of concepts. This paper introduced a new approach to learning grounded visual concepts. We defined concepts as abstractions over independent (and often interpretable) visual primitives, where each concept is given by learned distributions over a set of relevant visual factors. We proposed that all other (irrelevant) visual factors should default to their prior in order to produce a diverse set of samples corresponding to a concept. We then proposed SCAN, a neural network implementation of such an approach, which was able to discover and learn an implicit hierarchy of abstract concepts from as few as five symbolimage pairs per concept and no assumptions on the nature of symbolic representations. SCAN was then capable of bi-directional inference, generating diverse and accurate image samples from symbolic instructions, and vice versa, qualitatively and quantitatively outperforming all baselines, including on a realistic CelebA dataset with noisy attribute labels. The structure of the learnt concepts allowed us to train an extension to SCAN that could perform logical recombination operators. We demonstrated how such operators could be used to traverse the implicit concept hierarchy, including imagining completely new concepts. Due to the sample efficiency and the limited number of assumptions in our approach, the representations learnt by SCAN should be immediately applicable within a large set of broader problem domains, including reinforcement learning, classification, control and planning.",seemingly infinite diversity natural world arises relatively small set coherent rules laws physics chemistry. conjecture rules give rise regularities can be are discovered primarily unsupervised experiences represented abstract concepts. If such representations are compositional hierarchical can be recombined exponentially large set new concepts. paper describes SCAN Symbol-Concept Association Network new framework learning abstractions visual domain. SCAN learns concepts fast symbol association grounding disentangled visual primitives can be are discovered unsupervised manner. Unlike state art multimodal generative model baselines approach requires pairings symbols images makes assumptions form symbol representations. trained SCAN is capable multimodal bi-directional inference generating diverse set image samples symbolic descriptions vice versa. also allows traversal manipulation implicit hierarchy visual concepts symbolic instructions learnt logical recombination operations. manipulations enable SCAN break away training data distribution imagine novel visual concepts symbolically instructed recombination previously learnt concepts. State art deep learning approaches machine learning have achieved impressive results many problem domains including classification BID7 BID33 density modelling BID6 Oord etal. 2016a;reinforcement learning BID17 BID10 BID28. are still however far possessing many traits characteristic human intelligence. deep learning techniques tend overly data hungry often rely significant human supervision tend overfit training data distribution BID14 BID5 important step towards bridging gap human artificial intelligence is endowing algorithms compositional concepts BID14 BID5. Compositionality allows reuse finite set primitives addressing data efficiency human supervision issues across many scenarios recombining produce exponentially large number novel yet coherent potentially useful concepts addressing overfitting problem Compositionality is at the core human abilities creativity imagination language-based communication.We propose concepts are abstractions set primitives. example consider toy hierarchy visual concepts shown Fig. 1. node hierarchy is defined subset visual primitives make scene input image. visual primitives might include factors like object identity object colour floor colour wall colour. one traverses hierarchy subordinate basic superordinate levels abstraction BID27.e specific general concepts corresponding visual scene number concept-defining visual primitives decreases. Hence where each parent concept hierarchy is an Figure1:Schematic implicit concept hierarchy built upon subset four visual primitives:object identity object colour floor colour F wall colour W visual primitives necessary generate scene are ignored example Concepts form implicit hierarchy where each parent is an abstraction children original set visual primitives values concept-defining sets visual primitives are indicated bold capital letters order generate image corresponds concept one has to fill values factors got abstracted away represented e.g sampling respective priors. Given certain nodes concept hierarchy one can traverse nodes using logical operations. See Sec.3 formal definition concepts. abstraction.e subset children original set visual primitives. formal definition concepts is provided Sec. 3.Intelligent agents are able discover learn abstract compositional concepts using little supervision BID1 BID31 BID2 BID29. Think human word learning -we acquire meaning words combination continual stream unsupervised visual data occasionally paired corresponding word label. paper describes SCAN Symbol-Concept Association Network see Fig. 2A neural network model capable learning grounded visual concepts largely unsupervised manner fast symbol association. First use β-VAE BID8 learn set independent representational primitives unsupervised exposure visual data. is equivalent learning disentangled factorised interpretable representation independent ground truth generative factors data BID3. Next allow SCAN discover meaningful abstractions disentangled primitives exposing small number symbol-image pairs apply particular concept e.g example images apple paired symbol apple SCAN learns meaning concept identifying set visual primitives visual examples have in common e.g observed apples are small round red corresponding symbol apple becomes pointer newly acquired concept small round red -a way access manipulate concept without know exact representational form. approach does not make assumptions how these symbols are encoded which also allows SCAN learn multiple referents concept.e synonyms.Once concept is acquired should be possible use bi-directional inference:model should be able generate diverse visual samples correspond particular concept sym2img vice versa img2sym Since projection space visual primitives space concepts img2sym red dash arrow Fig. 1 involves abstraction hence loss information one needs add compatible information back when moving space concepts visual primitives sym2img blue dot arrow Fig. 1 setup concepts are defined terms set relevant visual primitives e.g colour shape size apple leaves set irrelevant visual attributes e.g lighting position background filled in. do so by defaulting respective priors which ensures high diversity samples image symbol space concept img2sym sym2img inferences.The structured nature learnt concepts acquired SCAN allows sample efficient learning logical recombination operators:corresponding set union relevant primitives COMMON corresponding set intersection IGNORE corresponding set difference pairing small number valid visual examples recombined concepts respective operator names. meaning operators has been successfully learned SCAN can exploit compositionality acquired concepts traverse previously unexplored parts implicit underlying concept hierarchy manipulating recombining existing concepts novel ways. example new node corresponding concept blue small can be reached following instructions:blue small going hierarchy general specific blueberry COMMON bluebell going hierarchy specific general blueberry IGNORE round also going hierarchy DISPLAYFORM0 summarise paper1 presents SCAN neural network model capable learning compositional hierarchical representations visual concepts;2 demonstrates SCAN can be successfully trained little supervised data;3 shows training SCAN can perform multimodal visual symbolic bi-directional inference generation high accuracy diversity outperforming baselines;4 shows addition logical recombination operations allows SCAN break limited training data distribution reach new nodes within implicit hierarchy concepts. paper introduced new approach learning grounded visual concepts. defined concepts abstractions independent often interpretable visual primitives where each concept is given learned distributions set relevant visual factors. proposed irrelevant visual factors should default prior order produce diverse set samples corresponding concept. proposed SCAN neural network implementation approach which was able discover learn implicit hierarchy abstract concepts five symbolimage pairs per concept assumptions nature symbolic representations. SCAN was then capable bi-directional inference generating diverse accurate image samples symbolic instructions vice versa qualitatively quantitatively outperforming baselines including realistic CelebA dataset noisy attribute labels. structure learnt concepts allowedus train extension SCAN could perform logical recombination operators. demonstrated how such operators could used traverse implicit concept hierarchy including imagining completely new concepts. Due sample efficiency limited number assumptions approach representations learnt SCAN should be immediately applicable within large set broader problem domains including reinforcement learning classification control planning.,1901,1231,670,0.022,1.544,2025/11/05 17:19:05,0.01,1.511,0.6666666666666666,692.634
"Despite much success in many large-scale language tasks, sequence-to-sequence (seq2seq) models have not been an ideal choice for conversational modeling as they tend to generate generic and repetitive responses. In this paper, we propose a Latent Topic Conversational Model (LTCM) that augments the seq2seq model with a neural topic component to better model human-human conversations. The neural topic component encodes information from the source sentence to build a global “topic” distribution over words, which is then consulted by the seq2seq model to improve generation at each time step. The experimental results show that the proposed LTCM can generate more diverse and interesting responses by sampling from its learnt latent representations. In a subjective human evaluation, the judges also confirm that LTCM is the preferred option comparing to competitive baseline models.
 Sequence-to-Sequence model (seq2seq) BID35 , as a data-driven approach to mapping between two arbitrary length sequences, has attracted much attention and been widely applied to many natural language processing tasks such as machine translation BID20 , syntactic parsing , and summarisation BID28 . Neural conversational models BID32 BID30 are the latest development in open-domain conversational modelling, where seq2seq-based models are employed for learning dialogue decisions in an end-to-end fashion. Despite promising results, the lack of explicit knowledge representations (or the inability to learn them from data) impedes the model from generating causal or even rational responses. This leads to many problems discussed in previous literature such as generic responses BID17 , inconsistency BID18 , and redundancy and contradiction BID33 .On the other hand, goal-oriented dialogues BID45 use the notion of dialogue ontology to constrain the scope of conversation and facilitate rational system behaviour within the domain. Neural network-based task-oriented dialogue systems usually retrieve knowledge from a pre-defined database either by discrete accessing BID41 BID3 or through an attention mechanism BID8 . The provision of this database offers a proxy for language grounding, which is crucial to guide the generation or selection of the system responses. As shown in BID40 , a stochastic neural dialogue model can generate diverse yet rational responses mainly because they are heavily driven by the knowledge the model is conditioned on.Despite the need for explicit knowledge representations, building a general-purpose knowledge base and actually making use of it have been proven difficult BID22 BID25 . Therefore, progress has been made in conditioning the seq2seq model on coarse-grained knowledge representations, such as a fuzzily-matched retrieval result via attention BID10 or a set of pre-organised topic or scenario labels . In this work, we propose a hybrid of a seq2seq conversational model and a neural topic model -Latent Topic Conversational Model (LTCM) -to jointly learn the useful latent representations and the way to make use of them in a conversation. LTCM uses its underlying seq2seq model to capture the local dynamics of a sentence while extracts and represents its global semantics by a mixture of topic components like topic models BID2 . This separation of global semantics and local dynamics turns out to be crucial to the success of LTCM.Recent advances in neural variational inference BID27 BID23 have sparked a series of latent variable models applied to conversational modeling BID31 BID5 . The majority of the work passes a Gaussian random variable to the hidden state of the LSTM decoder and employs the reparameterisation trick BID15 to build an unbiased and low-variance gradient estimator for updating the model parameters. However, studies have shown that training this type of models for language generation tasks is tough because the effect of the latent variable tends to vanish and the language model would take over the entire generation process over time BID4 . This results in several workarounds such as KL annealing BID4 BID5 , word dropout and historyless decoding BID4 , as well as auxiliary bag-of-word signals . Unlike previous approaches, LTCM is similar to TopicRNN (Dieng et al., 2017) where it passes the latent variable to the output layer of the decoder and only back-propagates the gradient of the topic words to the latent variable.In summary, the contribution of this paper is two-fold: first and most importantly, we show that LTCM can learn to generate more diverse and interesting responses by sampling from the learnt topic representations. The results were confirmed by a corpus-based evaluation and a human assessment; secondly, we conducted a series of experiments to understand the properties of seq2seq-based latent variables models better, which may serve as rules of thumb for future model development. In this paper, we have proposed the Latent Topic Conversational Model (LTCM) for general-purpose conversational modeling. We have shown that LTCM can generate more interesting and diverse responses by combining the seq2seq model and neural topic model so that global semantic representations and local word transitions can be modeled separately but learned jointly. Both a corpus-based evaluation and a human assessment confirm this finding. Future work would be to study the learned representations and use them to control the meaning of the generated responses.",Despite much success many large-scale language tasks sequence-to-sequence seq2seq models have not been an ideal choice conversational modeling tend generate generic repetitive responses. paper propose Latent Topic Conversational Model LTCM augments seq2seq model neural topic component better model human-human conversations. neural topic component encodes information source sentence build global topic distribution words which is then consulted seq2seq model improve generation time step. experimental results show proposed LTCM can generate diverse interesting responses sampling learnt latent representations. subjective human evaluation judges also confirm LTCM is the preferred option comparing competitive baseline models. Sequence-to-Sequence model seq2seq BID35 data-driven approach mapping two arbitrary length sequences has attracted much attention widely applied many natural language processing tasks machine translation BID20 syntactic parsing summarisation BID28. Neural conversational models BID32 BID30 are the latest development open-domain conversational modelling where seq2seq-based models are employed learning dialogue decisions end-to-end fashion. Despite promising results lack explicit knowledge representations inability learn data impedes model generating causal even rational responses. leads many problems discussed previous literature generic responses BID17 inconsistency BID18 redundancy contradiction BID33.On hand goal-oriented dialogues BID45 use notion dialogue ontology constrain scope conversation facilitate rational system behaviour within domain. Neural network-based task-oriented dialogue systems usually retrieve knowledge pre-defined database either discrete accessing BID41 BID3 attention mechanism BID8. provision database offers proxy language grounding which is crucial guide generation selection system responses. shown BID40 stochastic neural dialogue model can generate diverse yet rational responses mainly are heavily driven knowledge model is conditioned on.Despite need explicit knowledge representations building general-purpose knowledge base actually making use have been proven difficult BID22 BID25. Therefore progress has been made conditioning seq2seq model coarse-grained knowledge representations fuzzily-matched retrieval result via attention BID10 set pre-organised topic scenario labels. work propose hybrid seq2seq conversational model neural topic model -Latent Topic Conversational Model LTCM -to jointly learn useful latent representations way make use conversation. LTCM uses underlying seq2seq model capture local dynamics sentence extracts represents global semantics mixture topic components like topic models BID2. separation global semantics local dynamics turns crucial success LTCM.Recent advances neural variational inference BID27 BID23 have sparked series latent variable models applied conversational modeling BID31 BID5. majority work passes Gaussian random variable hidden state LSTM decoder employs reparameterisation trick BID15 build unbiased low-variance gradient estimator updating model parameters. However studies have shown training type models language generation tasks is tough effect latent variable tends vanish language model would take entire generation process time BID4. results several workarounds KL annealing BID4 BID5 word dropout historyless decoding BID4 well auxiliary bag-of-word signals. Unlike previous approaches LTCM is similar TopicRNN Diengetal. 2017 where it passes latent variable output layer decoder back-propagates gradient topic words latent variable.In summary contribution paper is two-fold two-fold first importantly show LTCM can learn generate diverse interesting responses sampling learnt topic representations. results were confirmed corpus-based evaluation human assessment;secondly conducted series experiments understand properties seq2seq-based latent variables models better may serve rules thumb future model development. paper have proposed Latent Topic Conversational Model LTCM general-purpose conversational modeling. have shown LTCM can generate interesting diverse responses combining seq2seq model neural topic model global semantic representations local word transitions can be modeled separately learned jointly. corpus-based evaluation human assessment confirm finding. Future work would study learned representations use control meaning generated responses.,1008,694,314,0.01,1.452,2025/11/05 17:19:05,0.0,1.542,0.3800623052959498,307.045
"Most of the existing Graph Neural Networks (GNNs) are the mere extension of the Convolutional Neural Networks (CNNs) to graphs. Generally, they consist of several steps of message passing between the nodes followed by a global indiscriminate feature pooling function. In many data-sets, however, the nodes are unlabeled or their labels provide no information about the similarity between the nodes and the locations of the nodes in the graph. Accordingly, message passing may not propagate helpful information throughout the graph. We show that this conventional approach can fail to learn to perform even simple graph classification tasks. We alleviate this serious shortcoming of the GNNs by making them a two step method. In the first of the proposed approach, a graph embedding algorithm is utilized to obtain a continuous feature vector for each node of the graph. The embedding algorithm represents the graph as a point-cloud in the embedding space. In the second step, the GNN is applied to the point-cloud representation of the graph provided by the embedding method. The GNN learns to perform the given task by inferring the topological structure of the graph encoded in the spatial distribution of the embedded vectors. In addition, we extend the proposed approach to the graph clustering problem and a new architecture for graph clustering is proposed. Moreover, the spatial representation of the graph is utilized to design a graph pooling algorithm. We turn the problem of graph down-sampling into a column sampling problem, i.e., the sampling algorithm selects a subset of the nodes whose feature vectors preserve the spatial distribution of all the feature vectors. We apply the proposed approach to several popular benchmark data-sets and it is shown that the proposed geometrical approach strongly improves the state-of-the-art result for several data-sets. For instance, for the PTC data-set, we improve the state-of-the-art result for more than 22 %. Many of the modern data/signals are naturally represented by graphs BID2 BID5 BID4 BID31 and it is of great interest to design data analysis algorithms which can work directly with graphs. Due to the remarkable success of deep learning based methods in many machine learning applications, it is an attractive research problem to design new neural network architectures which can make the deep networks able to work with graphs. The adjacency matrix of a graph exhibits the local connectivity of the nodes. Thus, it is straightforward to extend the local feature aggregation in the Convolutional Neural Networks (CNNs) to the Graph Neural Networks (GNNs) BID34 BID38 BID0 BID28 BID3 BID11 . The local feature aggregation in the graphs is equivalent to message passing between the nodes BID38 BID12 . However, if the graph is not labeled (the nodes/edges do not have feature vectors) or the feature vectors of the nodes do not carry information about the similarities between the nodes or any information about their structural role, the message passing may not propagate informative features throughout the graph. Thus, the GNN can fail to infer the topological structure of the graph. Another limitation of the current GNN architectures is that they are mostly unable to do the hierarchical feature learning employed in the CNNs BID26 BID19 . The main reason is that graphs lack the tensor representation and it is hard to measure how accurate a subset of nodes represent the topological structure of the given graph. In this paper, we address these two shortcomings of the GNNs.In the proposed approach, we provide a spatial representation of the graph to the GNN. The spatial representation makes the network aware of the similarity/difference between the nodes and also the location of the nodes in the graph. Accordingly, the local feature aggregation can propagate informative messages throughout the graph. In addition, we propose a down-sampling method to perform graph pooling. The proposed node sampling approach measures the similarities between the nodes in the spatial domain and merges the closest pairs of nodes. The main contributions of the proposed approach can be summarized as follows:• It is shown that the existing GNNs lack the important embedding step. The proposed approach enhances the capability of the GNNs in inferring the topological structure of the graphs.• A new graph pooling method is proposed which can be implemented in any GNN. The proposed pooling method preserves the spatial representation of the graph by merging the closest pairs of nodes in the spatial domain.• To the best of our knowledge, the proposed approach advances the state-of-the-art results for 5 established benchmark data-sets. For instance, the improvement in accuracy with the PTC data-set is more than 22 %.• An architecture for graph clustering is presented. In contrary to the conventional GNNs which can not be trained to cluster unlabeled graphs, the proposed approach utilizes the geometrical representation of the graph to infer the structure of the graph. We pointed this important fact out that the GNNs which are the mere extension of the CNNs to graphs may not be able to infer the structure of the graphs. In the proposed approach, the GNN analyzes a spatial representation of the graph provided by the embedding step. In other word, the graph data analysis problem is translated into a point-cloud data analysis problem. We also extended the proposed approach to a graph clustering method. In addition, we addressed one of the challenges of extending the architecture of the CNNs to graphs by proposing a graph pooling method. The proposed pooling method merges the closest pairs of nodes in the spatial domain. We showed that the proposed approach outperforms most of the existing graph classification methods. For instance, for the PTC data-set the proposed approach advances the state-of-the-art result for more than 22 %.",existing Graph Neural Networks GNNs are the mere extension Convolutional Neural Networks CNNs graphs. Generally consist several steps message passing nodes followed global indiscriminate feature pooling function. many data-sets however nodes are unlabeled labels provide information similarity nodes locations nodes graph. Accordingly message passing may propagate helpful information throughout graph. show conventional approach can fail learn perform even simple graph classification tasks. alleviate serious shortcoming GNNs making two step method. first proposed approach if the graph embedding algorithm is utilized obtain continuous feature vector node graph. embedding algorithm represents graph point-cloud embedding space. second step GNN is applied point-cloud representation graph provided embedding method. GNN learns perform given task inferring topological structure graph encoded spatial distribution embedded vectors. addition extend proposed approach graph clustering problem new architecture graph clustering is proposed. Moreover spatial representation graph is utilized design graph pooling algorithm. turn problem graph down-sampling column sampling problem.e sampling algorithm selects subset nodes whose feature vectors preserve spatial distribution feature vectors. apply proposed approach several popular benchmark data-sets is shown proposed geometrical approach strongly improves state-of-the-art result several data-sets instance PTC data-set improve state-of-the-art result 22%. Many modern data/signals are naturally represented graphs BID2 BID5 BID4 BID31 is of great interest design data analysis algorithms which can work directly graphs. Due remarkable success deep learning based methods many machine learning applications is an attractive research problem design new neural network architectures which can make deep networks able work graphs. adjacency matrix graph exhibits local connectivity nodes. Thus is straightforward extend local feature aggregation Convolutional Neural Networks CNNs Graph Neural Networks GNNs BID34 BID38 BID0 BID28 BID3 BID11. local feature aggregation graphs is equivalent message passing nodes BID38 BID12. However if the graph is not labeled nodes/edges do not have feature vectors feature vectors nodes do not carry information similarities nodes information structural role message passing may propagate informative features throughout graph. Thus GNN can fail infer topological structure graph. Another limitation current GNN architectures is that they are mostly unable do the hierarchical feature learning employed CNNs BID26 BID19. main reason is that graphs lack tensor representation is hard measure how accurate subset nodes represent topological structure given graph. paper address two shortcomings GNNs.In proposed approach provide spatial representation graph GNN. spatial representation makes network aware similarity/difference nodes also location nodes graph. Accordingly local feature aggregation can propagate informative messages throughout graph. addition propose down-sampling method perform graph pooling. proposed node sampling approach measures similarities nodes spatial domain merges closest pairs nodes. main contributions proposed approach can be summarized follows:• is shown existing GNNs lack important embedding step. proposed approach enhances capability GNNs inferring topological structure graphs.• new graph pooling method is proposed which can be implemented GNN. proposed pooling method preserves spatial representation graph merging closest pairs nodes spatial domain.• best knowledge proposed approach advances state-of-the-art results 5 established benchmark data-sets instance improvement accuracy PTC data-set is more than 22%.• architecture graph clustering is presented. contrary conventional GNNs which can not be trained cluster unlabeled graphs proposed approach utilizes geometrical representation graph infer structure graph. pointed important fact GNNs which are the mere extension CNNs graphs may able infer structure graphs. proposed approach GNN analyzes spatial representation graph provided embedding step. word if the graph data analysis problem is translated point-cloud data analysis problem. also extended proposed approach graph clustering method. addition addressed one challenges extending architecture CNNs graphs proposing graph pooling method. proposed pooling method merges closest pairs nodes spatial domain. showed proposed approach outperforms existing graph classification methods. instance PTC data-set proposed approach advances state-of-the-art result 22%,1127,742,385,0.013,1.519,2025/11/05 17:19:05,0.01,1.781,0.5887850467289715,352.992
"Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results.
 Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. 
 In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. 
 For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses.  
 We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly.
 Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack  has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge. Deep Neural Networks (DNNs) have achieved great successes in a variety of applications ranging from image recognition BID19 BID12 to speech processing and from robotics training BID23 to medical diagnostics BID7 . However, recent work has demonstrated that DNNs are vulnerable to adversarial perturbations BID32 BID10 . An adversary can add small-magnitude perturbations to inputs and generate adversarial examples to mislead DNNs. Such maliciously perturbed instances can cause the learning system to misclassify them into either a maliciously-chosen target class (in a targeted attack) or classes that are different from the ground truth (in an untargeted attack). Different algorithms have been proposed for generating such adversarial examples, such as the fast gradient sign method (FGSM) BID10 and optimization-based methods (Opt.) BID4 BID24 .Most of the the current attack algorithms BID4 BID24 rely on optimization schemes with simple pixel space metrics, such as L ∞ distance from a benign image, to encourage visual realism. To generate more perceptually realistic adversarial examples, in this paper, we propose to train a feed-forward network to generate perturbations such that the resulting example must be realistic according to a discriminator network. We apply generative adversarial networks (GANs) to produce adversarial examples in both the semi-whitebox and black-box settings. As conditional GANs are capable of producing high-quality images BID16 , we apply a similar paradigm to produce perceptually realistic adversarial instances. We name our method AdvGAN.Note that in the previous white-box attacks, such as FGSM and optimization methods, the adversary needs to have white-box access to the architecture and parameters of the model all the time. However, by deploying AdvGAN, once the feed-forward network is trained, it can instantly pro-duce adversarial perturbations for any input instances without requiring access to the model itself anymore. We name this attack setting semi-whitebox.To evaluate the effectiveness of our attack strategy AdvGAN, we first generate adversarial instances based on AdvGAN and other attack strategies on different target models. We then apply the stateof-the-art defenses to defend against these generated adversarial examples BID10 BID33 BID27 . We evaluate these attack strategies in both semi-whitebox and black-box settings. We show that adversarial examples generated by AdvGAN can achieve a high attack success rate, potentially due to the fact that these adversarial instances appear closer to real instances compared to other recent attack strategies.Our contributions are listed as follows.• Different from the previous optimization-based methods, we train a conditional adversarial network to directly produce adversarial examples, which are both perceptually realistic and achieve state-of-the-art attack success rate against different target models.• We show that AdvGAN can attack black-box models by training a distilled model. We propose to dynamically train the distilled model with query information and achieve high black-box attack success rate and targeted black-box attack, which is difficult to achieve for transferability-based black-box attacks.• We use the state-of-the-art defense methods to defend against adversarial examples and show that AdvGAN achieves much higher attack success rate under current defenses.• We apply AdvGAN on Mądry et al.'s MNIST challenge (2017a ) and achieve 88.93% accuracy on the published robust model in the semi-whitebox setting and 92.76% in the blackbox setting, which wins the top position in the challenge BID28 . In this paper, we propose AdvGAN to generate adversarial examples using generative adversarial networks (GANs). In our AdvGAN framework, once trained, the feed-forward generator can produce adversarial perturbations efficiently. It can also perform both semi-whitebox and black-box attacks with high attack success rate. In addition, when we apply AdvGAN to generate adversarial instances on different models without knowledge of the defenses in place, the generated adversarial examples can attack the state-of-the-art defenses with higher attack success rate than examples generated by the competing methods. This property makes AdvGAN a promising candidate for improving adversarial training defense methods. The generated adversarial examples produced by AdvGAN preserve high perceptual quality due to GANs' distribution approximation property.A ARCHITECTURE OF MODELS BID16 . Let c3s1-k denotes 3 × 3 Convolution-InstanceNorm-ReLU layer with k filter and stride 1. Rk means residual block that contains two 3 × 3 convolution layers with the same numbers of filters. dk denotes the 3 × 3 Convolution-InstanceNorm-ReLU layer with k filters and stride 2. uk denotes a 3 × 3 fractional-strided-ConvolutionInstanceNorm-ReLU layer with k filters, and stride c3s1-8, d16, d32, r32, r32, r32, r32, u16, u8, c3s1-3 Discriminator architecture We use CNNs as our discriminator network BID31 . Let Ck denote a 4 × 4 Convolution-InstanceNorm-LeakyReLU layer with k filters and stride 2. After the last conv layer, we apply a FC layer to produce a 1 dimensional output. We do not use InstanceNorm for the first C8 layer. We use leaky ReLUs with slope 0.2. c7s1-8, d16, d32, d64, d64, d64, d64, r64, r64, r64, r64, u64, u64, u64, u64, u32, u16, u8, c7s1-3 The architecture of discriminator for ImageNet is: C8, C16, C32, FC",Deep neural networks DNNs have been found vulnerable adversarial examples resulting adding small-magnitude perturbations inputs. adversarial examples can mislead DNNs produce adversary-selected results. Different attack strategies have been proposed generate adversarial examples how to produce high perceptual quality efficiently requires research efforts. paper propose AdvGAN generate adversarial examples generative adversarial networks GANs which can learn approximate distribution original instances. AdvGAN generator is trained can generate adversarial perturbations efficiently instance potentially accelerate adversarial training defenses. apply AdvGAN semi-whitebox black-box attack settings. semi-whitebox attacks is no need access original target model generator is trained contrast traditional white-box attacks. black-box attacks dynamically train distilled model black-box model optimize generator accordingly. Adversarial examples generated AdvGAN different target models have high attack success rate state-of-the-art defenses compared attacks. attack has placed first 92.76 accuracy public MNIST black-box attack challenge. Deep Neural Networks DNNs have achieved great successes variety applications ranging image recognition BID19 BID12 speech processing robotics training BID23 medical diagnostics BID7. However recent work has demonstrated DNNs are vulnerable adversarial perturbations BID32 BID10. adversary can add small-magnitude perturbations inputs generate adversarial examples mislead DNNs. maliciously perturbed instances can cause learning system misclassify either maliciously-chosen target class targeted attack classes are different ground truth untargeted attack Different algorithms have been proposed generating adversarial examples fast gradient sign method FGSM BID10 optimization-based methods Opt. BID4 BID24.Most current attack algorithms BID4 BID24 rely optimization schemes simple pixel space metrics L ∞ distance benign image encourage visual realism. generate perceptually realistic adversarial examples paper propose train feed-forward network generate perturbations resulting example must realistic according discriminator network. apply generative adversarial networks GANs produce adversarial examples semi-whitebox black-box settings. conditional GANs are capable producing high-quality images BID16 when we apply similar paradigm produce perceptually realistic adversarial instances. name method AdvGAN.Note previous white-box attacks FGSM optimization methods adversary needs have white-box access architecture parameters model time. However deploying AdvGAN feed-forward network is trained can instantly pro-duce adversarial perturbations input instances without requiring access model anymore. name attack setting semi-whitebox.To evaluate effectiveness attack strategy AdvGAN first generate adversarial instances based AdvGAN attack strategies different target models. apply stateof-the-art defenses defend generated adversarial examples BID10 BID33 BID27. evaluate attack strategies semi-whitebox black-box settings. show adversarial examples generated AdvGAN can achieve high attack success rate potentially due fact adversarial instances appear closer real instances compared recent attack strategies.Our contributions are listed follows.• Different previous optimization-based methods train conditional adversarial network directly produce adversarial examples which are both perceptually realistic achieve state-of-the-art attack success rate different target models.• show AdvGAN can attack black-box models training distilled model. propose dynamically train distilled model query information achieve high black-box attack success rate targeted black-box attack which is difficult achieve transferability-based black-box attacks.• do not use state-of-the-art defense methods defend adversarial examples show AdvGAN achieves much higher attack success rate current defenses.• apply AdvGAN Mądry et al.'s MNIST challenge 2017a achieve 88.93 accuracy published robust model semi-whitebox setting 92.76 blackbox setting which wins top position challenge BID28. paper propose AdvGAN generate adversarial examples using generative adversarial networks GANs AdvGAN framework trained feed-forward generator can produce adversarial perturbations efficiently. can also perform semi-whitebox black-box attacks high attack success rate. addition when we apply AdvGAN generate adversarial instances different models without knowledge defenses place generated adversarial examples can attack state-of-the-art defenses higher attack success rate examples generated competing methods. property makes AdvGAN promising candidate improving adversarial training defense methods. generated adversarial examples produced AdvGAN preserve high perceptual quality due GANs' distribution approximation property.A ARCHITECTURE MODELS BID16. Let c3s1-k denotes3 × 3 Convolution-InstanceNorm-ReLU layer k filter stride1. Rk means residual block contains two3× 3 convolution layers numbers filters. dk denotes 3 × 3 Convolution-InstanceNorm-ReLU layer k filters stride2. uk denotes 3 × 3 fractional-strided-ConvolutionInstanceNorm-ReLU layer k filters stride c3s1-8 d16 d32 r32 r32 r32 r32 u16 u8 c3s1-3 Discriminator architecture do not use CNNs discriminator network BID31. Let Ck denote 4 × 4 Convolution-InstanceNorm-LeakyReLU layer k filters stride2. last conv layer when we apply FC layer produce 1 dimensional output. do not use InstanceNorm first C8 layer. do not use leaky ReLUs slope 0.2 c7s1-8 d16 d32 d64 d64 d64 d64 r64 r64 r64 r64 u64 u64 u64 u64 u32 u16 u8 c7s1-3 architecture discriminator ImageNet is:C8 C16 C32 FC,1428,1051,377,0.013,1.359,2025/11/05 17:19:05,0.01,1.345,0.0903426791277256,364.362
"This paper proposes a new model for the rating prediction task in recommender systems which significantly outperforms previous state-of-the art models on a time-split Netflix data set. Our model is based on deep autoencoder with 6 layers and is trained end-to-end without any layer-wise pre-training. We empirically demonstrate that: a) deep autoencoder models generalize much better than the shallow ones, b) non-linear activation functions with negative parts are crucial for training deep models, and c) heavy use of regularization techniques such as dropout is necessary to prevent over-fitting. We also propose a new training algorithm based on iterative output re-feeding to overcome natural sparseness of collaborate filtering. The new algorithm significantly speeds up training and improves model performance. Our code is publicly available. Sites like Amazon, Netflix and Spotify use recommender systems to suggest items to users. Recommender systems can be divided into two categories: context-based and personalized recommendations.Context based recommendations take into account contextual factors such as location, date and time BID0 . Personalized recommendations typically suggest items to users using the collaborative filtering (CF) approach. In this approach the user's interests are predicted based on the analysis of tastes and preference of other users in the system and implicitly inferring ""similarity"" between them. The underlying assumption is that two people who have similar tastes, have a higher likelihood of having the same opinion on an item than two randomly chosen people.In designing recommender systems, the goal is to improve the accuracy of predictions. The Netflix Prize contest provides the most famous example of this problem BID1 : Netflix held the Netflix Prize to substantially improve the accuracy of the algorithm to predict user ratings for films. This is a classic CF problem: Infer the missing entries in an mxn matrix, R, whose (i, j) entry describes the ratings given by the ith user to the jth item. The performance is then measured using Root Mean Squared Error (RMSE).Training very deep autoencoders is non trivial both from optimization and regularization points of view. Early works on training auto-enocoders adapted layer-wise pre-training to solve optimization issues BID5 . In this work , we empirically show that optimization difficulties of training deep autoencoders can be solved by using scaled exponential linear units (SELUs) BID9 . This enables training without any layer-wise pre-training or residual connections. Since publicly available data sets for CF are relatively small, sufficiently large models can easily overfit. To prevent overfitting we employ heavy dropout with drop probability as high as 0.8. We also introduce a new output re-feeding training algorithm which helps to bypass the natural sparseness of updates in collaborative filtering and helps to further improve the model performance. Deep learning has revolutionized many areas of machine learning, and it is poised do so with recommender systems as well. In this paper we demonstrated how very deep autoencoders can be successfully trained even on relatively small amounts of data by using both well established (dropout) and relatively recent (""scaled exponential linear units"") deep learning techniques. Further, we introduced iterative output re-feeding -a technique which allowed us to perform dense updates in collaborative filtering, increase learning rate and further improve generalization performance of our model. On the task of future rating prediction, our model outperforms other approaches even without using additional temporal signals.While our code supports item-based model (such as I-AutoRec) we argue that this approach is less practical than user-based model (U-AutoRec). This is because in real-world recommender systems, there are usually much more users then items. Finally, when building personalized recommender system and faced with scaling problems, it can be acceptable to sample items but not users.",paper proposes new model rating prediction task recommender systems which significantly outperforms previous state-of-the art models time-split Netflix data set. model is based deep autoencoder 6 layers is trained end-to-end without layer-wise pre-training empirically demonstrate that:deep autoencoder models generalize much better shallow ones b non-linear activation functions negative parts are crucial training deep models c heavy use regularization techniques dropout is necessary prevent over-fitting also propose new training algorithm based iterative output re-feeding overcome natural sparseness collaborate filtering. new algorithm significantly speeds training improves model performance. code is publicly available. Sites like Amazon Netflix Spotify use recommender systems suggest items users. Recommender systems can be divided two categories:context-based personalized recommendations.Context based recommendations take account contextual factors location date time BID0. Personalized recommendations typically suggest items users using collaborative filtering CF approach. approach user's interests are predicted based analysis tastes preference users system implicitly inferring similarity them. underlying assumption is that two people who have similar tastes have a higher likelihood opinion item two randomly chosen people.In designing recommender systems goal is to improve accuracy predictions. Netflix Prize contest provides famous example problem BID1:Netflix held Netflix Prize substantially improve accuracy algorithm predict user ratings films. is a classic CF problem:Infer missing entries mxn matrix R whose j entry describes ratings given ith user jth item. performance is then measured using Root Mean Squared Error RMSE.Training deep autoencoders is non trivial optimization regularization points view. Early works training auto-enocoders adapted layer-wise pre-training solve optimization issues BID5. work empirically show optimization difficulties training deep autoencoders can be solved using scaled exponential linear units SELUs BID9. enables training without layer-wise pre-training residual connections. Since publicly available data sets CF are relatively small sufficiently large models can easily overfit. prevent overfitting employ heavy dropout drop probability high 0.8 also introduce new output re-feeding training algorithm which helps bypass natural sparseness updates collaborative filtering helps improve model performance. Deep learning has revolutionized many areas machine learning is poised do so with recommender systems well. paper demonstrated how very deep autoencoders can be successfully trained even relatively small amounts data using well established dropout relatively recent scaled exponential linear units deep learning techniques. introduced iterative output re-feeding -a technique which allowedus perform dense updates collaborative filtering increase learning rate improve generalization performance model. task future rating prediction model outperforms approaches even without using additional temporal signals.While code supports item-based model I-AutoRec argue approach is less practical user-based model U-AutoRec is real-world recommender systems are usually much users items. Finally when building personalized recommender system faced scaling problems can be acceptable sample items users.,754,545,209,0.007,1.383,2025/11/05 17:19:05,0.0,1.433,0.1651090342679126,256.337
"Recurrent neural networks (RNNs) sequentially process data by updating their state with each new data point, and have long been the de facto choice for sequence modeling tasks. However, their inherently sequential computation makes them slow to train. Feed-forward and convolutional architectures have recently been shown to achieve superior results on some sequence modeling tasks such as machine translation, with the added advantage that they concurrently process all inputs in the sequence, leading to easy parallelization and faster training times. Despite these successes, however, popular feed-forward sequence models like the Transformer fail to generalize in many simple tasks that recurrent models handle with ease, e.g. copying strings or even simple logical inference when the string or formula lengths exceed those observed at training time. We propose the Universal Transformer (UT), a parallel-in-time self-attentive recurrent sequence model which can be cast as a generalization of the Transformer model and which addresses these issues. UTs combine the parallelizability and global receptive field of feed-forward sequence models like the Transformer with the recurrent inductive bias of RNNs. We also add a dynamic per-position halting mechanism and find that it improves accuracy on several tasks. In contrast to the standard Transformer, under certain assumptions UTs can be shown to be Turing-complete. Our experiments show that UTs outperform standard Transformers on a wide range of algorithmic and language understanding tasks, including the challenging LAMBADA language modeling task where UTs achieve a new state of the art, and machine translation where UTs achieve a 0.9 BLEU improvement over Transformers on the WMT14 En-De dataset. Convolutional and fully-attentional feed-forward architectures like the Transformer have recently emerged as viable alternatives to recurrent neural networks (RNNs) for a range of sequence modeling tasks, notably machine translation BID8 Vaswani et al., 2017) . These parallel-in-time architectures address a significant shortcoming of RNNs, namely their inherently sequential computation which prevents parallelization across elements of the input sequence, whilst still addressing the vanishing gradients problem as the sequence length gets longer BID15 . The Transformer model in particular relies entirely on a self-attention mechanism BID23 BID20 to compute a series of context-informed vector-space representations of the symbols in its input and output, which are then used to predict distributions over subsequent symbols as the model predicts the output sequence symbol-by-symbol. Not only is this mechanism straightforward to parallelize, but as each symbol's representation is also directly informed by all other symbols' representations, this results in an effectively global receptive field across the whole sequence. This stands in contrast to e.g. convolutional architectures which typically only have a limited receptive field.Notably, however, the Transformer with its fixed stack of distinct layers foregoes RNNs' inductive bias towards learning iterative or recursive transformations. Our experiments indicate that this inductive The Universal Transformer repeatedly refines a series of vector representations for each position of the sequence in parallel, by combining information from different positions using self-attention (see Eqn 2) and applying a recurrent transition function (see Eqn 4) across all time steps 1 ≤ t ≤ T . We show this process over two recurrent time-steps. Arrows denote dependencies between operations. Initially, h 0 is initialized with the embedding for each symbol in the sequence. h t i represents the representation for input symbol 1 ≤ i ≤ m at recurrent time-step t. With dynamic halting, T is dynamically determined for each position (Section 2.2).bias may be crucial for several algorithmic and language understanding tasks of varying complexity: in contrast to models such as the Neural Turing Machine BID12 , the Neural GPU BID17 or Stack RNNs , the Transformer does not generalize well to input lengths not encountered during training.In this paper, we introduce the Universal Transformer (UT), a parallel-in-time recurrent self-attentive sequence model which can be cast as a generalization of the Transformer model, yielding increased theoretical capabilities and improved results on a wide range of challenging sequence-to-sequence tasks. UTs combine the parallelizability and global receptive field of feed-forward sequence models like the Transformer with the recurrent inductive bias of RNNs, which seems to be better suited to a range of algorithmic and natural language understanding sequence-to-sequence problems. As the name implies, and in contrast to the standard Transformer, under certain assumptions UTs can be shown to be Turing-complete (or ""computationally universal"", as shown in Section 4).In each recurrent step, the Universal Transformer iteratively refines its representations for all symbols in the sequence in parallel using a self-attention mechanism BID23 BID20 , followed by a transformation (shared across all positions and time-steps) consisting of a depth-wise separable convolution BID4 BID18 or a position-wise fully-connected layer (see FIG0 . We also add a dynamic per-position halting mechanism BID11 , allowing the model to choose the required number of refinement steps for each symbol dynamically, and show for the first time that such a conditional computation mechanism can in fact improve accuracy on several smaller, structured algorithmic and linguistic inference tasks (although it marginally degraded results on MT).Our strong experimental results show that UTs outperform Transformers and LSTMs across a wide range of tasks. The added recurrence yields improved results in machine translation where UTs outperform the standard Transformer. In experiments on several algorithmic tasks and the bAbI language understanding task, UTs also consistently and significantly improve over LSTMs and the standard Transformer. Furthermore , on the challenging LAMBADA text understanding data set UTs with dynamic halting achieve a new state of the art. When running for a fixed number of steps, the Universal Transformer is equivalent to a multi-layer Transformer with tied parameters across all its layers. This is partly similar to the Recursive Transformer, which ties the weights of its self-attention layers across depth BID13 5 . However, as the per-symbol recurrent transition functions can be applied any number of times, another and possibly more informative way of characterizing the UT is as a block of parallel RNNs (one for each symbol, with shared parameters) evolving per-symbol hidden states concurrently, generated at each step by attending to the sequence of hidden states at the previous step. In this way, it is related to architectures such as the Neural GPU BID17 and the Neural Turing Machine BID12 . UTs thereby retain the attractive computational efficiency of the original feedforward Transformer model, but with the added recurrent inductive bias of RNNs. Furthermore, using a dynamic halting mechanism, UTs can choose the number of processing steps based on the input data.The connection between the Universal Transformer and other sequence models is apparent from the architecture: if we limited the recurrent steps to one, it would be a Transformer. But it is more interesting to consider the relationship between the Universal Transformer and RNNs and other networks where recurrence happens over the time dimension. Superficially these models may seem closely related since they are recurrent as well. But there is a crucial difference: time-recurrent models like RNNs cannot access memory in the recurrent steps. This makes them computationally more similar to automata, since the only memory available in the recurrent part is a fixed-size state vector. UTs on the other hand can attend to the whole previous layer, allowing it to access memory in the recurrent step.Given sufficient memory the Universal Transformer is computationally universal -i.e. it belongs to the class of models that can be used to simulate any Turing machine, thereby addressing a shortcoming of the standard Transformer model 6 . In addition to being theoretically appealing, our results show that this added expressivity also leads to improved accuracy on several challenging sequence modeling tasks. This closes the gap between practical sequence models competitive on large-scale tasks such as machine translation, and computationally universal models such as the Neural Turing Machine or the Neural GPU BID12 BID17 , which can be trained using gradient descent to perform algorithmic tasks.To show this, we can reduce a Neural GPU to a Universal Transformer. Ignoring the decoder and parameterizing the self-attention module, i.e. self-attention with the residual connection, to be the identity function, we assume the transition function to be a convolution. If we now set the total number of recurrent steps T to be equal to the input length, we obtain exactly a Neural GPU. Note that the last step is where the Universal Transformer crucially differs from the vanilla Transformer whose depth cannot scale dynamically with the size of the input. A similar relationship exists between the Universal Transformer and the Neural Turing Machine, whose single read/write operations per step can be expressed by the global, parallel representation revisions of the Universal Transformer. In contrast to these models, however, which only perform well on algorithmic tasks, the Universal Transformer also achieves competitive results on realistic natural language tasks such as LAMBADA and machine translation.Another related model architecture is that of end-to-end Memory Networks BID27 . In contrast to end-to-end memory networks, however, the Universal Transformer uses memory corresponding to states aligned to individual positions of its inputs or outputs. Furthermore, the Universal Transformer follows the encoder-decoder configuration and achieves competitive performance in large-scale sequence-to-sequence tasks. This paper introduces the Universal Transformer, a generalization of the Transformer model that extends its theoretical capabilities and produces state-of-the-art results on a wide range of challenging sequence modeling tasks, such as language understanding but also a variety of algorithmic tasks, thereby addressing a key shortcoming of the standard Transformer. The Universal Transformer combines the following key properties into one model:Weight sharing: Following intuitions behind weight sharing found in CNNs and RNNs, we extend the Transformer with a simple form of weight sharing that strikes an effective balance between inductive bias and model expressivity, which we show extensively on both small and large-scale experiments.Conditional computation: In our goal to build a computationally universal machine, we equipped the Universal Transformer with the ability to halt or continue computation through a recently introduced mechanism, which shows stronger results compared to the fixed-depth Universal Transformer.We are enthusiastic about the recent developments on parallel-in-time sequence models. By adding computational capacity and recurrence in processing depth, we hope that further improvements beyond the basic Universal Transformer presented here will help us build learning algorithms that are both more powerful, data efficient, and generalize beyond the current state-of-the-art.The code used to train and evaluate Universal Transformers is available at https: //github.com/tensorflow/tensor2tensor BID31 .",Recurrent neural networks RNNs sequentially process data updating state new data point have long de facto choice sequence modeling tasks. However inherently sequential computation makes slow train. Feed-forward convolutional architectures have recently shown achieve superior results sequence modeling tasks machine translation added advantage concurrently process inputs sequence leading easy parallelization faster training times. Despite successes however popular feed-forward sequence models like Transformer fail generalize many simple tasks recurrent models handle ease e.g copying strings even simple logical inference when the string formula lengths exceed observed training time. propose Universal Transformer UT parallel-in-time self-attentive recurrent sequence model which can be cast generalization Transformer model which addresses issues. UTs combine parallelizability global receptive field feed-forward sequence models like Transformer recurrent inductive bias RNNs. also add dynamic per-position halting mechanism find improves accuracy several tasks. contrast standard Transformer certain assumptions UTs can be shown Turing-complete experiments show UTs outperform standard Transformers wide range algorithmic language understanding tasks including challenging LAMBADA language modeling task where UTs achieve new state art machine translation where UTs achieve 0.9 BLEU improvement Transformers WMT14 En-De dataset. Convolutional fully-attentional feed-forward architectures like Transformer have recently emerged viable alternatives recurrent neural networks RNNs range sequence modeling tasks notably machine translation BID8 Vaswanietal. 2017 parallel-in-time architectures address significant shortcoming RNNs namely inherently sequential computation which prevents parallelization across elements input sequence whilst still addressing vanishing gradients problem sequence length gets longer BID15. Transformer model particular relies entirely self-attention mechanism BID23 BID20 compute series context-informed vector-space representations symbols input output which are then used predict distributions subsequent symbols model predicts output sequence symbol-by-symbol is this mechanism straightforward parallelize symbol's representation is also directly informed symbols' representations results effectively global receptive field across whole sequence. stands contrast e.g convolutional architectures which typically have a limited receptive field.Notably however Transformer fixed stack distinct layers foregoes RNNs' inductive bias towards learning iterative recursive transformations. experiments indicate inductive Universal Transformer repeatedly refines series vector representations position sequence parallel combining information different positions using self-attention see Eqn2 applying recurrent transition function see Eqn4 across time steps1≤ ≤ T. show process two recurrent time-steps Arrows denote dependencies operations. Initially h0 is initialized embedding symbol sequence. h represents representation input symbol1≤ ≤ recurrent time-step t. dynamic halting is dynamically determined position Section 2.2.bias may crucial several algorithmic language understanding tasks varying complexity:contrast models Neural Turing Machine BID12 Neural GPU BID17 Stack RNNs Transformer does not generalize well input lengths encountered training.In paper introduce Universal Transformer UT parallel-in-time recurrent self-attentive sequence model which can be cast generalization Transformer model yielding increased theoretical capabilities improved results wide range challenging sequence-to-sequence tasks. UTs combine parallelizability global receptive field feed-forward sequence models like Transformer recurrent inductive bias RNNs which seems better suited range algorithmic natural language understanding sequence-to-sequence problems. name implies contrast standard Transformer certain assumptions UTs can be shown Turing-complete computationally universal shown Section4.In recurrent step Universal Transformer iteratively refines representations symbols sequence parallel using self-attention mechanism BID23 BID20 followed transformation shared across positions time-steps consisting depth-wise separable convolution BID4 BID18 position-wise fully-connected layer see FIG0. also add dynamic per-position halting mechanism BID11 allowing model choose required number refinement steps symbol dynamically which we show first time conditional computation mechanism can in fact improve accuracy several smaller structured algorithmic linguistic inference tasks although marginally degraded results MT.Our strong experimental results show UTs outperform Transformers LSTMs across wide range tasks. added recurrence yields improved results machine translation where UTs outperform standard Transformer. experiments several algorithmic tasks bAbI language understanding task UTs also consistently significantly improve LSTMs standard Transformer. Furthermore challenging LAMBADA text understanding data set UTs dynamic halting achieve new state art. When running fixed number steps Universal Transformer is equivalent multi-layer Transformer tied parameters across layers. is partly similar Recursive Transformer which ties weights self-attention layers across depth BID135. However per-symbol recurrent transition functions can be applied number times another possibly informative way characterizing UT is as a block parallel RNNs one symbol shared parameters evolving per-symbol hidden states concurrently generated step attending sequence hidden states previous step. way is related architectures Neural GPU BID17 Neural Turing Machine BID12. UTs thereby retain attractive computational efficiency original feedforward Transformer model added recurrent inductive bias RNNs. Furthermore using dynamic halting mechanism UTs can choose number processing steps based input data.The connection Universal Transformer sequence models is apparent architecture:if we limited recurrent steps one would Transformer. is more interesting consider relationship Universal Transformer RNNs networks where recurrence happens time dimension. Superficially models may seem closely related since are recurrent well. is a crucial difference:time-recurrent models like RNNs cannot access memory recurrent steps. makes computationally similar automata since memory available recurrent part is a fixed-size state vector. UTs hand can attend whole previous layer allowing access memory recurrent step.Given sufficient memory Universal Transformer is computationally computationally universal-i.e belongs class models can be used simulate Turing machine thereby addressing shortcoming standard Transformer model6. addition theoretically appealing results show added expressivity also leads improved accuracy several challenging sequence modeling tasks. closes gap practical sequence models competitive large-scale tasks machine translation computationally universal models Neural Turing Machine Neural GPU BID12 BID17 which can be trained using gradient descent perform algorithmic tasks.To show can reduce Neural GPU Universal Transformer. Ignoring decoder parameterizing self-attention module.e self-attention residual connection identity function assume transition function convolution. If we now set total number recurrent steps equal input length obtain exactly Neural GPU. Note last step is where the Universal Transformer crucially differs vanilla Transformer whose depth cannot scale dynamically size input. similar relationship exists Universal Transformer Neural Turing Machine whose single read/write operations per step can be expressed global parallel representation revisions Universal Transformer. contrast models however which only perform well algorithmic tasks Universal Transformer also achieves competitive results realistic natural language tasks LAMBADA machine translation.Another related model architecture is that of end-to-end Memory Networks BID27. contrast end-to-end memory networks however Universal Transformer uses memory corresponding states aligned individual positions inputs outputs. Furthermore Universal Transformer follows encoder-decoder configuration achieves competitive performance large-scale sequence-to-sequence tasks. paper introduces Universal Transformer generalization Transformer model extends theoretical capabilities produces state-of-the-art results wide range challenging sequence modeling tasks language understanding also variety algorithmic tasks thereby addressing key shortcoming standard Transformer. Universal Transformer combines following key properties one model:Weight sharing:Following intuitions behind weight sharing found CNNs RNNs extend Transformer simple form weight sharing strikes effective balance inductive bias model expressivity which we show extensively small large-scale experiments.Conditional computation:goal build computationally universal machine equipped Universal Transformer ability halt continue computation recently introduced mechanism which shows stronger results compared fixed-depth Universal Transformer.We are enthusiastic recent developments parallel-in-time sequence models. adding computational capacity recurrence processing depth hope improvements beyond basic Universal Transformer presented will help us build learning algorithms are both more powerful data efficient generalize beyond current state-of-the-art.The code used train evaluate Universal Transformers is available https://github.com/tensorflow/tensor2tensor BID31.,2137,1472,665,0.023,1.452,2025/11/05 17:19:05,0.01,1.653,0.3800623052959498,709.354
"We present a framework for interpretable continual learning (ICL). We show that explanations of previously performed tasks can be used to improve performance on future tasks. ICL generates a good explanation of a finished task, then uses this to focus attention on what is important when facing a new task. The ICL idea is general and may be applied to many continual learning approaches. Here we focus on the variational continual learning framework to take advantage of its flexibility and efficacy in overcoming catastrophic forgetting. We use saliency maps to provide explanations of performed tasks and propose a new metric to assess their quality. Experiments show that ICL achieves state-of-the-art results in terms of overall continual learning performance as measured by average classification accuracy, and also in terms of its explanations, which are assessed qualitatively and quantitatively using the proposed metric. Continual learning, also called lifelong learning, refers to frameworks where knowledge acquired from past tasks is accumulated for use on future tasks, i.e. where learning continually proceeds in an online fashion. Data belonging to different tasks might be non i.i.d. BID17 BID20 BID25 BID24 BID29 . Crucially, a continual learner must be able to learn a new task without forgetting how to perform previous tasks BID19 BID27 . Continual learning frameworks need to continually adapt to the domain shift occurring across tasks, without revisiting data from previous tasks. An appropriate balance is required between stability and adapting to new tasks and data, since excessive adaptation might lead to dramatic degradation in performance of earlier tasks, known as catastrophic forgetting BID6 BID7 BID16 BID18 .Several approaches have been introduced to address catastrophic forgetting. One approach is based on regularisation where stability is maintained by restricting the change of parameters with high influence while allowing the other parameters to vary freely BID14 BID17 BID11 BID30 BID35 . Another approach divides the network architecture into reusable parts that are less prone to changes, and parts devoted to individual tasks BID4 BID23 a; BID34 . The framework in BID33 constructs the neural network architecture via designed reinforcement learning (RL) strategies. The framework in BID13 bases its solution on moment matching. Another RL based framework is presented in BID9 where catastrophic forgetting is mitigated at multiple time scales by using RL agents with a synaptic model. BID15 propose a framework where multiple agents jointly learn to achieve multiple goals at once in a parallel offpolicy setup. The work in BID3 proposes experimental evaluations of continual learning as well as a variational Bayesian loss, via which they categorise a few previous works into either prior-focused or likelihood-focused. Attention mechanisms have been developed in rather similar problems before, e.g. in BID10 BID28 BID31 BID8 . Other saliency metrics have been introduced in BID2 BID0 . To the best of our knowledge , our framework is the first piece of work to pursue a comprehensive interpretability approach in the continual learning setting.Our work is based on the idea of imitating some aspects of how humans learn continually. We suggest that humans are quite successful in achieving goals and performing tasks sequentially, partly because we manage to understand and explain to ourselves certain aspects of the tasks we have already accomplished. This provides a contribution to our performance on similar tasks in the future.When given a task, we typically not only accomplish it, but also often (perhaps unconsciously) gain a useful interpretable concept. For instance, when a child tries to grasp an object, the progress in the child's skill is accompanied by improvements in similar tasks, e.g. grasping other objects which the child has never seen before. The development of the child's cognitive abilities shows an understanding of the concepts of gravity, geometric characteristics of the object, etc BID26 . We suggest that this development may be established by the consolidation of interpretable information from past experience. With this motivation, here we consider and analyse the impact of interpretable methods on continual learning. While there can be a tradeoff between performance and interpretability when considering just one task, here we show that interpretability can help performance when a learner faces consecutive tasks over time, as in continual learning.We propose a continual learning framework where the training phase of each task is followed by an explanation stage, which provides insights to be utilised along with the established training platform in learning the subsequent tasks. We focus on image classification tasks where training of the first task proceeds normally, before providing a saliency map for each test data point (image). By highlighting the most relevant areas of the test image w.r.t. the classification prediction, an understanding of the individual decisions taken by the classifier is attained. Afterwards, we compute a saliency map representing a summary (or average) of the saliency maps of test images per class, i.e. a summary of the classifier's decisions on the test data. This represents a summarised belief of the relevant areas of the input for each class. After completing the current task, we can use the explanation , depicted by the average saliency map, to achieve two goals:i Assessing how good the developed continual learning framework is at eradicating catastrophic forgetting. This evaluation is typically performed by measuring the difference in the classification performance on a certain task when it is the most recently encountered vs. when other tasks subsequently followed. Here we propose a new measure by adding a test which compares the saliency map resulting from testing a task right after finishing the corresponding training phase, with the saliency map of the same test on the same task after having other tasks subsequently trained by our continual learner. Degradation of the provided explanations provides a measure of the level of catastrophic forgetting induced in the continual learning framework. ii Providing interpretable attention information for subsequent tasks by involving the obtained saliency maps of the current task in the optimisation for the future tasks.To achieve the first goal, we need a metric to assess the quality of the extracted saliency maps. We propose a new metric for evaluating saliency maps resulting from the classification decisions on test data. Measuring the quality of a saliency map is not a straightforward task. Saliency maps typically aim at explaining the classification decision taken by a classifier. In other words, a saliency map seeks the subset of features that are the most influential in the resulting prediction of the classifier. As such, the explanation provided by a saliency map comes out in the form of a summary of the significant parts (features) of the input data, from the classifier's point of view. We propose a metric to assess the quality of an explanation resulting from a saliency map.To achieve the second goal, we need to involve the saliency maps in the learning procedure, not just during the test phase. We propose an attention mechanism that exploits the feature relevance values learnt in the latest task to focus the attention of the new learner on what is believed to be the most important parts of the input as per the latest task, which (w.r.t. continual learning) is assumed to be similar. Thus, an explanation of a task evolving over time is utilised to help the emerging tasks.Note that there is a difference in the nature of the two proposed goals described above. The optimisation needed to achieve the second goal does not guarantee that the first goal is automatically achieved, since the first goal addresses explanations (saliency maps) related to the same task at different time steps, whereas the second goal is concerned with exchanging interpretable information among different tasks. Hence, the assessment involved in the first goal is still needed regardless of the level of perfection of the second goal.In this work we perform experiments for the classification case illustrated above, but the same paradigm could be applied in future work to tasks other than classification, where the personalisation or notion of the explanation will need to be adapted to the nature of the task, i.e. saliency maps should be replaced with something more suitable to the task.We highlight the following contributions of our framework: 1) the interpretable continual learning (ICL) framework where, in addition to the ordinary understanding benefits of interpretable frame-works, explanations of the finished tasks are used to enhance the attention of the learner during the future tasks. Although we focus on performing within the variational continual learning framework BID17 , our proposed methodology is flexible and can be deployed with other continual learning frameworks, and also with other saliency detection methods. To the best of our knowledge, ICL represents a novel direction in the continual learning literature that focuses on interpretability; 2) introducing a new metric for saliency maps that aims at robustly assessing their quality without significant engineering required, i.e. no need to construct bounding rectangles of the relevant zones or similar; 3) learning from past experiences using an attention mechanism based on explanations (saliency maps) from the latest task; 4) Our quantitative and qualitative state-of-the-art results in four experiments on three datasets demonstrate the efficacy of the proposed framework. We introduced a continual learning framework incorporating interpretability, where saliency based explanations of previously learnt tasks are used to enhance the attention of the learner during future tasks. This framework demonstrates that interpretability is not only useful for increasing the understanding of the obtained results, but can also improve the performance of a sequential learning procedure. The proposed framework is flexible and can enhance both the interpretability and performance of continual learning methods, especially in terms of mitigating catastrophic forgetting. We proposed a new metric for saliency maps. We believe that adopting a Bayesian attention mechanism could be a fruitful direction for future work, especially when integrated with fully Bayesian variational continual learning.","present framework interpretable continual learning ICL show explanations previously performed tasks can be used improve performance future tasks. ICL generates good explanation finished task uses focus attention what is important when facing new task. ICL idea is general may applied many continual learning approaches. focus variational continual learning framework take advantage flexibility efficacy overcoming catastrophic forgetting. use saliency maps provide explanations performed tasks propose new metric assess quality. Experiments show ICL achieves state-of-the-art results terms overall continual learning performance measured average classification accuracy can also terms explanations which are assessed qualitatively quantitatively using proposed metric. Continual learning can also called lifelong learning refers frameworks where knowledge acquired past tasks is accumulated use future tasks.e where learning continually proceeds online fashion. Data belonging different tasks might non.i.d BID17 BID20 BID25 BID24 BID29. Crucially continual learner must able learn new task without forgetting how to perform previous tasks BID19 BID27. Continual learning frameworks need continually adapt domain shift occurring across tasks without revisiting data previous tasks. appropriate balance is required stability adapting new tasks data since excessive adaptation might lead dramatic degradation performance earlier tasks known catastrophic forgetting BID6 BID7 BID16 BID18.Several approaches have been introduced address catastrophic forgetting. One approach is based regularisation where stability is maintained restricting change parameters high influence allowing parameters vary freely BID14 BID17 BID11 BID30 BID35. Another approach divides network architecture reusable parts are less prone changes parts devoted individual tasks BID4 BID23 a;BID34. framework BID33 constructs neural network architecture via designed reinforcement learning RL strategies. framework BID13 bases solution moment matching. Another RL based framework is presented BID9 where catastrophic forgetting is mitigated multiple time scales using RL agents synaptic model. BID15 propose framework where multiple agents jointly learn achieve multiple goals parallel offpolicy setup. work BID3 proposes experimental evaluations continual learning well variational Bayesian loss via which they categorise previous works either prior-focused likelihood-focused Attention mechanisms have been developed rather similar problems e.g BID10 BID28 BID31 BID8. saliency metrics have been introduced BID2 BID0. best knowledge framework is the first piece work pursue comprehensive interpretability approach continual learning setting.Our work is based idea imitating aspects how humans learn continually. suggest humans are quite successful achieving goals performing tasks sequentially partly manage understand explain certain aspects tasks have already accomplished. provides contribution performance similar tasks future.When given task typically accomplish also often perhaps unconsciously gain useful interpretable concept. instance when a child tries grasp object progress child's skill is accompanied improvements similar tasks e.g grasping objects which the child has never seen before. development child's cognitive abilities shows understanding concepts gravity geometric characteristics object etc BID26. suggest development may established consolidation interpretable information past experience. motivation consider analyse impact interpretable methods continual learning. canbe tradeoff performance interpretability when considering one task show interpretability can help performance when a learner faces consecutive tasks time continual learning.We propose continual learning framework where the where training phase task is followed explanation stage which provides insights utilised along established training platform learning subsequent tasks. focus image classification tasks where the where training first task proceeds normally providing saliency map test data point image highlighting relevant areas test imagew.r.t classification prediction understanding individual decisions taken classifier is attained. Afterwards compute saliency map representing summary average saliency maps test images per class.e summary classifier's decisions test data. represents summarised belief relevant areas input class. completing current task can use explanation depicted average saliency map achieve two goals:Assessing how good developed continual learning framework is at eradicating catastrophic forgetting. evaluation is typically performed measuring difference classification performance certain task when it is the recently encounteredvs. when other tasks subsequently followed. propose new measure adding test which compares saliency map resulting testing task right finishing corresponding training phase where saliency map test task tasks subsequently trained continual learner. Degradation provided explanations provides measure level catastrophic forgetting induced continual learning framework. ii Providing interpretable attention information subsequent tasks involving obtained saliency maps current task optimisation future tasks.To achieve first goal need metric assess quality extracted saliency maps. propose new metric evaluating saliency maps resulting classification decisions test data. Measuring quality saliency map is not a straightforward task. Saliency maps typically aim explaining classification decision taken classifier. words where saliency map seeks subset features are the most influential resulting prediction classifier. explanation provided saliency map comes form summary significant parts features input data classifier's point view. propose metric assess quality explanation resulting saliency map.To achieve second goal need involve saliency maps learning procedure test phase. propose attention mechanism exploits feature relevance values learnt latest task focus attention new learner what is believed important parts input per latest task which(w w.r.t continual learning is assumed similar. Thus explanation task evolving time is utilised help emerging tasks.Note is a difference nature two proposed goals described above. optimisation needed achieve second goal does not guarantee first goal is automatically achieved since first goal addresses explanations saliency maps related task different time steps whereas second goal is concerned exchanging interpretable information among different tasks. Hence assessment involved first goal is still needed regardless level perfection second goal.In work perform experiments classification case illustrated paradigm could applied future work tasks classification where the personalisation notion explanation will need adapted nature task.e saliency maps should be replaced something suitable task.We highlight following contributions framework:1 interpretable continual learning ICL framework where,in addition ordinary understanding benefits interpretable frame-works explanations finished tasks are used enhance attention learner future tasks. Although focus performing within variational continual learning framework BID17 proposed methodology is flexible can be deployed continual learning frameworks can also saliency detection methods. best knowledge ICL represents novel direction continual learning literature focuses interpretability;2 introducing new metric saliency maps aims robustly assessing quality without significant engineering required.e need construct bounding rectangles relevant zones similar;3 learning past experiences using attention mechanism based explanations saliency maps latest task;4 quantitative qualitative state-of-the-art results four experiments three datasets demonstrate efficacy proposed framework. introduced continual learning framework incorporating interpretability where saliency based explanations previously learnt tasks are used enhance attention learner future tasks. framework demonstrates interpretability is not only useful increasing understanding obtained results can also improve performance sequential learning procedure. proposed framework is flexible can enhance interpretability performance continual learning methods especially terms mitigating catastrophic forgetting. proposed new metric saliency maps. believe adopting Bayesian attention mechanism could fruitful direction future work especially when integrated fully Bayesian variational continual learning.",1903,1262,641,0.022,1.508,2025/11/05 17:19:06,0.01,1.5,0.5545171339563861,711.479
"The state-of-the-art (SOTA) for mixed precision training is dominated by variants of low precision floating point operations, and in particular, FP16 accumulating into FP32 Micikevicius et al. (2017). On the other hand, while a lot of research has also happened in the domain of low and mixed-precision Integer training, these works either present results for non-SOTA networks (for instance only AlexNet for ImageNet-1K), or relatively small datasets (like CIFAR-10). In this work, we train state-of-the-art visual understanding neural networks on the ImageNet-1K dataset, with Integer operations on General Purpose (GP) hardware. In particular, we focus on Integer Fused-Multiply-and-Accumulate (FMA) operations which take two pairs of INT16 operands and accumulate results into an INT32 output.We propose a shared exponent representation of tensors and develop a Dynamic Fixed Point (DFP) scheme suitable for common neural network operations. The nuances of developing an efficient integer convolution kernel is examined, including methods to handle overflow of the INT32 accumulator. We implement CNN training for ResNet-50, GoogLeNet-v1, VGG-16 and AlexNet; and these networks achieve or exceed SOTA accuracy within the same number of iterations as their FP32 counterparts without any change in hyper-parameters and with a 1.8X improvement in end-to-end training throughput. To the best of our knowledge these results represent the first INT16 training results on GP hardware for ImageNet-1K dataset using SOTA CNNs and achieve highest reported accuracy using half precision While single precision floating point (FP32) representation has been the mainstay for deep learning training, half-precision and sub-half-precision arithmetic has recently captured interest of the academic and industrial research community. Primarily this interest stems from the ability to attain potentially upto 2X or more speedup of training as compared to FP32, when using half-precision fused-multiply and accumulate operations. For instance NVIDIA Volta NVIDIA (2017) provides 8X more half-precision Flops as compared to FP32.Unlike single precision floating point, which is a unanimous choice for 32b training, half-precision training can either use half-precision floating point (FP16), or integers (INT16). These two options offer varying degrees of precision and range; with INT16 having higher precision but lower dynamic range as compared to FP16. This also leads to residues between half-precision representation and single precision to be fundamentally different -with integer representations contributing lower residual errors for larger (and possibly more important) elements of a tensor. Beyond this first order distinction in data types, there are multiple algorithmic and semantic differences (for example FP16 multiply-and-accumulate operation accumulating into FP32 results) for each of these data types. Hence, when discussing half-precision training, the whole gamut of tensor representation, semantics of multiply-and-accumulate operation, down-conversion scheme (if the accumulation is to a higher precision), scaling and normalization techniques, and overflow management methods must be considered in totality to achieve SOTA accuracy. Indeed, unless the right combination of the aforesaid vectors are selected, half precision training is likely to fail. Conversely, drawing conclusions on the efficacy of a method by not selecting all vectors properly can lead to inaccurate conclusions.In this work we describe a mixed-precision training setup which uses:• INT16 tensors with shared tensor-wide exponent, with a potential to extend to sub-tensor wide exponents.• An instruction which multiplies two INT16 numbers and stores the output into a INT32 accumulator.• A down-convert scheme based on the maximum value of the output tensor in the current iteration using multiple rounding methods like nearest, stochastic, and biased rounding.• An overflow management scheme which accumulates partial INT32 results into FP32, along with trading off input precision with length of accumulate chain to gain performance.The compute for neural network training is dominated by GEMM-like, convolution, or dot-product operations. These are amenable to speedup via specialized low-precision instructions for fusedmultiply-and-accumulate (FMA), like AVX512_4VNNI 1 . However , this does not necessarily mean using half-precision representation for all tensors, or using only half-precision operations. In fact , performance speedups by migrating the compute intensive operations in both forward and back prorogation (FPROP, BPROP and WTGRAD) is often close to the maximum achievable speedup obtained by replacing all operations (for instance SGD) in half-precision. In cases where it is not, performance degradation typically happens due to limitations of memory bandwidth, and other architectural reasons.Hence on a balanced general purpose machine, a mixed-precision strategy of keeping precision critical operations (like SGD and some normalizations) in single precision and compute intensive operations in half precision can be employed. The proposed integer-16 based mixed-precision training follows this template.Using the aforesaid method, we train multiple visual understanding CNNs and achieve Top-1 accuracies BID16 on the ImageNet-1K dataset BID2 which match or exceed single precision results. These results are obtained without changing any hyper-parameters, and in as many iterations as the baseline FP32 training. We achieve 75.77 % Top-1 accuracy for ResNet-50 which, to the best of our knowledge, significantly exceeds any result published for halfprecision training, for example ; . Further, we also demonstrate our methodology achieves state-of-the-art accuracy (comparable to FP32 baseline) with int16 training on GoogLeNet-v1, VGG-16 and AlexNet networks. To the best of our knowledge, these are first such results using int16 training.The rest of the paper is organized as follows: Section 2 discusses the literature pertaining to various aspects of half-precision training. The dynamic fixed point format for representing half-precision tensors is described in Section 3. Dynamic fixed point kernels and neural network training operations are described in Section 4, and experimental results are presented in Section 5. Finally, we conclude this work in Section 6. We demonstrate industry-first reduced precision INT-based training result on large networks/data-sets. Showing on-par or better than FP32 baseline accuracies and potentially 2× savings in computation, communication and storage. Further, we propose a general dynamic fixed point representation scheme, with associated compute primitives and algorithm for the shared exponent management. This DFP solution can be used with general purpose hardware, leveraging the integer compute pipeline. We demonstrate this with implementation of CNN training for ResNet-50, GoogLeNet-v1, VGG-16 and AlexNet; training these networks with mixed precision DFP16 for the ImageNet-1K classification task. While this work focuses on visual understanding CNNs, in future we plan to demonstrate the efficacy of this method for other types of networks like RNNs, LSTMs, GANs and extend this to wider set of applications.","state-of-the-art SOTA mixed precision training is dominated variants low precision floating point operations particular FP16 accumulating FP32 Micikeviciusetal. 2017 hand lot research has also happened domain low mixed-precision Integer training works either present results non-SOTA networks instance AlexNet ImageNet-1K relatively small datasets like CIFAR-10 work train state-of-the-art visual understanding neural networks ImageNet-1K dataset Integer operations General Purpose GP hardware. particular focus Integer Fused-Multiply-and-Accumulate FMA operations which take two pairs INT16 operands accumulate results INT32 output.We propose shared exponent representation tensors develop Dynamic Fixed Point DFP scheme suitable common neural network operations. nuances developing efficient integer convolution kernel is examined including methods handle overflow INT32 accumulator. implement CNN training ResNet-50 GoogLeNet-v1 VGG-16 AlexNet;networks achieve exceed SOTA accuracy within number iterations FP32 counterparts without change hyper-parameters 1.8X improvement end-to-end training throughput. best knowledge results represent first INT16 training results GP hardware ImageNet-1K dataset using SOTA CNNs achieve highest reported accuracy using half precision single precision floating point FP32 representation has been the mainstay deep learning training half-precision sub-half-precision arithmetic has recently captured interest academic industrial research community. Primarily interest stems ability attain potentially upto2X speedup training compared FP32 when using half-precision fused-multiply accumulate operations. instance NVIDIA Volta NVIDIA 2017 provides8X half-precision Flops compared FP32.Unlike single precision floating point which is a unanimous choice 32b training half-precision training can either use half-precision floating point FP16 integers INT16 two options offer varying degrees precision range;INT16 higher precision lower dynamic range compared FP16. also leads residues half-precision representation single precision fundamentally different -with integer representations contributing lower residual errors larger possibly important elements tensor. Beyond first order distinction data types are multiple algorithmic semantic differences example FP16 multiply-and-accumulate operation accumulating FP32 results data types. Hence when discussing half-precision training whole gamut tensor representation semantics multiply-and-accumulate operation down-conversion scheme if the accumulation is to a higher precision scaling normalization techniques overflow management methods must considered totality achieve SOTA accuracy. Indeed unless right combination aforesaid vectors are selected half precision training is likely fail. Conversely drawing conclusions efficacy method selecting vectors properly can lead inaccurate conclusions.In work describe mixed-precision training setup which uses:• INT16 tensors shared tensor-wide exponent potential extend sub-tensor wide exponents.• instruction which multiplies two INT16 numbers stores output INT32 accumulator.• down-convert scheme based maximum value output tensor current iteration using multiple rounding methods like nearest stochastic biased rounding.• overflow management scheme which accumulates partial INT32 results FP32 along trading input precision length accumulate chain gain performance.The compute neural network training is dominated GEMM-like convolution dot-product operations. are amenable speedup via specialized low-precision instructions fusedmultiply-and-accumulate FMA like AVX512_4VNNI1. However does not necessarily mean using half-precision representation tensors when using half-precision operations. fact performance speedups migrating compute intensive operations forward back prorogation FPROP BPROP WTGRAD is often close maximum achievable speedup obtained replacing operations instance SGD half-precision cases where it is not performance degradation typically happens due limitations memory bandwidth architectural reasons.Hence balanced general purpose machine mixed-precision strategy keeping precision critical operations like SGD normalizations single precision compute intensive operations half precision can be employed. proposed integer-16 based mixed-precision training follows template.Using aforesaid method train multiple visual understanding CNNs achieve Top-1 accuracies BID16 ImageNet-1K dataset BID2 which match exceed single precision results. results are obtained without changing hyper-parameters many iterations baseline FP32 training. achieve 75.77 Top-1 accuracy ResNet-50 which,to the best knowledge significantly exceeds result published halfprecision training example;also demonstrate methodology achieves state-of-the-art accuracy comparable FP32 baseline int16 training GoogLeNet-v1 VGG-16 AlexNet networks. best knowledge are first results using int16 training.The rest paper is organized follows:Section 2 discusses literature pertaining various aspects half-precision training. dynamic fixed point format representing half-precision tensors is described Section3. Dynamic fixed point kernels neural network training operations are described Section4 experimental results are presented Section5. Finally conclude work Section6. demonstrate industry-first reduced precision INT-based training result large networks/data-sets Showing on-par better FP32 baseline accuracies potentially 2× savings computation communication storage. propose general dynamic fixed point representation scheme associated compute primitives algorithm shared exponent management. DFP solution can be used general purpose hardware leveraging integer compute pipeline. demonstrate implementation CNN training ResNet-50 GoogLeNet-v1 VGG-16 AlexNet;training networks mixed precision DFP16 ImageNet-1K classification task. work focuses visual understanding CNNs future plan demonstrate efficacy method types networks like RNNs LSTMs GANs extend wider set applications.",1429,1022,407,0.014,1.398,2025/11/05 17:19:06,0.01,1.485,0.2118380062305291,414.385
"In this paper we introduce a new speech recognition system, leveraging a simple letter-based ConvNet acoustic model. The acoustic model requires only audio transcription for training -- no alignment annotations, nor any forced alignment step is needed. At inference, our decoder takes only a word list and a language model, and is fed with letter scores from the acoustic model -- no phonetic word lexicon is needed. Key ingredients for the acoustic model are Gated Linear Units and high dropout. We show near state-of-the-art results in word error rate on the LibriSpeech corpus with MFSC features, both on the clean and other configurations.
 Top speech recognition systems are either complicated pipelines or using more data that is publicly available. We set out to show that it is possible to train a nearly state of the art speech recognition system for read speech, with a public dataset (LibriSpeech), on a GPU-equipped workstation. Thus, we present an end-to-end system for speech recognition, going from Mel-Frequency Spectral Coefficients (MFSCs) to the transcription in words. The acoustic model is trained using letters (graphemes) directly, which take out the need for an intermediate (human or automatic) phonetic transcription.The classical pipeline to build state of the art systems for speech recognition consists in first training an HMM/GMM model to force align the units on which the final acoustic model operates (most often context-dependent phone states). This approach takes its roots in HMM/GMM training BID31 . The improvements brought by deep neural networks (DNNs) and convolutional neural networks (CNNs) BID26 BID27 for acoustic modeling only extend this training pipeline. The current state of the art on LibriSpeech belongs to this approach too BID16 BID19 , with an additional step of speaker adaptation BID22 BID18 . Recently, BID25 proposed GMM-free training, but the approach still requires to generate a forced alignment.An approach that cut ties with the HMM/GMM pipeline (and with forced alignment) was to train with a recurrent neural network (RNN) BID7 ) for phoneme transcription. There are now competitive end-to-end approaches of acoustic models toppled with RNNs layers as in BID9 BID14 BID23 BID0 , trained with a sequence criterion BID8 . However these models are computationally expensive, and thus often take a long time to train. On conversational speech (that is not the topic of this paper), the state of the art is still held by complex ConvNets+RNNs acoustic models, coupled to domain-adapted language models BID32 BID24 .Compared to classical approaches that need phonetic annotation (often derived from a phonetic dictionary, rules, and generative training), we propose to train the model end-to-end, using graphemes directly. Compared to sequence criterion based approaches that train directly from speech signal to graphemes BID14 , we propose an RNN-free architecture based on convolutional networks for the acoustic model, toppled with a simple sequence-level variant of CTC.We reach the clean speech performance of BID19 , but without performing speaker adaptation. Our word-error-rate on clean speech is better than BID0 , while being worse on noisy speech, but they train on 11,900 hours while we only train on the 960h available in LibriSpeech's train set. The rest of the paper is structured as follows: the next section presents the convolutional networks used for acoustic modeling, along with the automatic segmentation criterion and decoding approaches. The last section shows experimental results on LibriSpeech. Figure 1: Overview of our acoustic model, which computes MFSC features which are fed to a Gated ConvNet. The ConvNet output one score for each letter in the dictionary, and for each MFSC frame. At inference time, theses scores are fed to a decoder (see Section 2.4) to form the most likely sequence of words. At training time, the scores are fed to the ASG criterion (see FIG1 ) which promotes sequences of letters leading to the transcrition sequence (here ""c a t""). We have introduced a simple end-to-end automatic speech recognition system, which combines a large (208M parameters) but efficient ConvNet acoustic model, an easy sequence criterion which can infer the segmentation, and a simple beam-search decoder. The decoding results are competitive on the LibriSpeech corpus (4.8% WER dev-clean). Our approach breaks free from HMM/GMM pre-training and forced alignment, as well as not being as computationally intensive as RNN-based approaches BID0 . We based all our work on a publicly available (free) dataset, all of which should make it easier to reproduce. Further work should include leveraging speaker identity, training from the raw waveform, data augmentation, training with more data, better language models.","paper introduce new speech recognition system leveraging simple letter-based ConvNet acoustic model. acoustic model requires audio transcription training alignment annotations forced alignment step is needed. inference decoder takes word list language model is fed letter scores acoustic model phonetic word lexicon is needed. Key ingredients acoustic model are Gated Linear Units high dropout. show near state-of-the-art results word error rate LibriSpeech corpus MFSC features clean configurations. Top speech recognition systems are either complicated pipelines using data is publicly available. set show is possible train nearly state art speech recognition system read speech public dataset LibriSpeech GPU-equipped workstation. Thus present end-to-end system speech recognition going Mel-Frequency Spectral Coefficients MFSCs transcription words. acoustic model is trained using letters graphemes directly which take need intermediate human automatic phonetic transcription.The classical pipeline build state art systems speech recognition consists first training HMM/GMM model force align units which the final acoustic model operates often context-dependent phone states approach takes roots HMM/GMM training BID31. improvements brought deep neural networks DNNs convolutional neural networks CNNs BID26 BID27 acoustic modeling extend training pipeline. current state art LibriSpeech belongs approach BID16 BID19 additional step speaker adaptation BID22 BID18. Recently BID25 proposed GMM-free training approach still requires generate forced alignment.An approach cut ties HMM/GMM pipeline forced alignment was to train recurrent neural network RNN BID7 phoneme transcription. are now competitive end-to-end approaches acoustic models toppled RNNs layers BID9 BID14 BID23 BID0 trained sequence criterion BID8. However models are computationally expensive thus often take long time train. conversational speech is not topic paper state art is still held complex ConvNets+RNNs acoustic models coupled domain-adapted language models BID32 BID24.Compared classical approaches need phonetic annotation often derived phonetic dictionary rules generative training propose train model end-to-end using graphemes directly. Compared sequence criterion based approaches train directly speech signal graphemes BID14 propose RNN-free architecture based convolutional networks acoustic model toppled simple sequence-level variant CTC.We reach clean speech performance BID19 without performing speaker adaptation. word-error-rate clean speech is better BID0 worse noisy speech train 11,900 hours train 960h available LibriSpeech's train set. rest paper is structured follows:next section presents convolutional networks used acoustic modeling along automatic segmentation criterion decoding approaches. last section shows experimental results LibriSpeech. Figure1:Overview acoustic model which computes MFSC features which are fed Gated ConvNet. ConvNet output one score letter dictionary MFSC frame. inference time theses scores are fed decoder see Section 2.4 form likely sequence words. training time scores are fed ASG criterion see FIG1 which promotes sequences letters leading transcrition sequence c have introduced simple end-to-end automatic speech recognition system which combines large 208M parameters efficient ConvNet acoustic model easy sequence criterion which can infer segmentation simple beam-search decoder. decoding results are competitive LibriSpeech corpus 4.8 WER dev-clean approach breaks free HMM/GMM pre-training forced alignment well computationally intensive RNN-based approaches BID0. based work publicly available free dataset which should make easier reproduce. work should include leveraging speaker identity training raw waveform data augmentation training data better language models.",980,665,315,0.009,1.474,2025/11/05 17:19:06,0.0,1.222,0.4485981308411212,301.958
"Generative adversarial networks (GANs) are a powerful framework for generative tasks. However, they are difficult to train and tend to miss modes of the true data generation process. Although GANs can learn a rich representation of the covered modes of the data in their latent space, the framework misses an inverse mapping from data to this latent space. We propose Invariant Encoding Generative Adversarial Networks (IVE-GANs), a novel GAN framework that introduces such a mapping for individual samples from the data by utilizing features in the data which are invariant to certain transformations. Since the model maps individual samples to the latent space, it naturally encourages the generator to cover all modes. We demonstrate the effectiveness of our approach in terms of generative performance and learning rich representations on several datasets including common benchmark image generation tasks. Generative Adversarial Networks (GANs) BID4 emerged as a powerful framework for training generative models in the recent years. GANs consist of two competing (adversarial) networks: a generative model that tries to capture the distribution of a given dataset to map from an arbitrary latent space (usually drawn from a multi-variate Gaussian) to new synthetic data points, and a discriminative model that tries to distinguish between samples from the generator and the true data. Iterative training of both models ideally results in a discriminator capturing features from the true data that the generator does not synthesize, while the generator learns to include these features in the generative process, until real and synthesized data are no longer distinguishable. Experiments by BID10 showed that a GAN can learn rich representation of the data in the latent space in which interpolations produce semantic variations and shifts in certain directions correspond to variations of specific features of the generated data. However, due to the lack of an inverse mapping from data to the latent space, GANs cannot be used to encode individual data points in the latent space BID2 . Moreover, although GANs show promising results in various tasks, such as the generation of realistic looking images BID9 BID0 BID11 or 3D objects BID13 , training a GAN in the aforementioned ideal way is difficult to set up and sensitive to hyper-parameter selection BID10 . Additionally, GANs tend to restrict themselves on generating only a few major modes of the true data distribution, since such a so-called mode collapse is not penalized in the GAN objective, while resulting in more realistic samples from these modes BID1 . Hence, the majority of the latent space only maps to a few regions in the target space resulting in poor representation of the true data. We propose a novel GAN framework, Invariant-Encoding Generative Adversarial Networks (IVE-GAN), which extends the classical GAN architecture by an additional encoding unit E to map samples from the true data x to the latent space z (compare FIG0 ). To encourage the encoder to learn a rich representation of the data in the latent space, the discriminator D is asked to distinguish between different predefined transformations T(x) of the input sample and generated samples G(E(x)) by taking the the original input as condition into account. While the discriminator has to learn what the different variations have in common with the original input, the encoder is forced to encode the necessary information in the latent space so that the generator can fool the discriminator by generating samples which are similar to the original samples. Since the discriminator is invariant to the predefined transformations, the encoder can ignore these variations in the input space and learn a rich and to such transformations invariant representation of the data. The variations of the generated samples are modeled by an additional latent vector z (drawn from a multi-variate Gaussian). Thus, the encoded samples condition the generator G(z , E(x)). Moreover, since the discriminator learns to distinguish between generated samples and variations of the original for each individual sample x in the data, the latent space can not collapse to a few modes of the true data distribution since it will be easy for the discriminator to distinguish generated samples from original ones if the mode is not covered by the generator. Thus, the proposed IVE-GAN learns a rich and to certain transformations invariant representation of a dataset and naturally encourages the generator to cover all modes of the data distribution.To generate novel samples, the generator G(z) can be fed with an arbitrary latent representation z ∼ P noise .In summary, we make the following contributions:• We derive a novel GAN framework for learning rich and transformation invariant representation of the data in the latent space.• We show that our GANs reproduce samples from a data distribution without mode collapsing issues.• We demonstrate robust GAN training across various data sets and showcase that our GAN produces very realistic samples. With this work we proposed a novel GAN framework that includes a encoding unit that maps data to a latent representation by utilizing features in the data which are invariant to certain transformations.We evaluate the proposed model on three different dataset and show the IVE-GAN can generate visually appealing images of high variance while learning a rich representation of the dataset also covering subtle features. B NETWORK ARCHITECTURE AND HYPERPARAMETERS",Generative adversarial networks GANs are a powerful framework generative tasks. However are difficult train tend miss modes true data generation process. Although GANs can learn rich representation covered modes data latent space framework misses inverse mapping data latent space. propose Invariant Encoding Generative Adversarial Networks IVE-GANs novel GAN framework introduces mapping individual samples data utilizing features data which are invariant certain transformations. Since model maps individual samples latent space naturally encourages generator cover modes. demonstrate effectiveness approach terms generative performance learning rich representations several datasets including common benchmark image generation tasks. Generative Adversarial Networks GANs BID4 emerged powerful framework training generative models recent years. GANs consist two competing adversarial networks:generative model tries capture distribution given dataset map arbitrary latent space usually drawn multi-variate Gaussian new synthetic data points discriminative model tries distinguish samples generator true data. Iterative training models ideally results discriminator capturing features true data generator does not synthesize generator learns include features generative process real synthesized data are no longer distinguishable. Experiments BID10 showed GAN can learn rich representation data latent space which interpolations produce semantic variations shifts certain directions correspond variations specific features generated data. However due lack inverse mapping data latent space GANs cannot used encode individual data points latent space BID2. Moreover although GANs show promising results various tasks generation realistic looking images BID9 BID0 BID11 3D objects BID13 training GAN aforementioned ideal way is difficult set sensitive hyper-parameter selection BID10. Additionally GANs tend restrict generating major modes true data distribution since so-called mode collapse is not penalized GAN objective resulting realistic samples modes BID1. Hence majority latent space maps regions target space resulting poor representation true data. propose novel GAN framework Invariant-Encoding Generative Adversarial Networks IVE-GAN which extends classical GAN architecture additional encoding unitE map samples true datax latent spacez compare FIG0 encourage encoder learn rich representation data latent space discriminator is asked distinguish different predefined transformations x input sample generated samplesG E x taking original input condition account. discriminator has to learn what the different variations have in common original input encoder is forced encode necessary information latent space generator can fool discriminator generating samples which are similar original samples. Since discriminator is invariant predefined transformations encoder can ignore variations input space learn rich transformations invariant representation data. variations generated samples are modeled additional latent vectorz drawn multi-variate Gaussian Thus encoded samples condition generatorG z E x Moreover since discriminator learns distinguish generated samples variations original individual samplex data latent space can not collapse modes true data distribution since will be easy discriminator distinguish generated samples original ones if the mode is not covered generator. Thus proposed IVE-GAN learns rich certain transformations invariant representation dataset naturally encourages generator cover modes data distribution.To generate novel samples generatorG z can be fed arbitrary latent representationz ∼ P noise.In summary make following contributions:• derive novel GAN framework learning rich transformation invariant representation data latent space.• show GANs reproduce samples data distribution without mode collapsing issues.• demonstrate robust GAN training across various data sets showcase GAN produces realistic samples. work proposed novel GAN framework includes encoding unit maps data latent representation utilizing features data which are invariant certain transformations.We evaluate proposed model three different dataset show IVE-GAN can generate visually appealing images high variance learning rich representation dataset also covering subtle features. B NETWORK ARCHITECTURE HYPERPARAMETERS,1016,662,354,0.011,1.535,2025/11/05 17:19:06,0.01,1.538,0.6386292834890962,329.889
"We propose a method for learning the dependency structure between latent variables in deep latent variable models.   Our general modeling and inference framework combines the complementary strengths of deep generative models and probabilistic graphical models. In particular, we express the latent variable space of a variational autoencoder (VAE) in terms of a Bayesian network with a learned, flexible dependency structure.   The network parameters, variational parameters as well as the latent topology are optimized simultaneously with a single objective.   Inference is formulated via a sampling procedure that produces expectations over latent variable structures and incorporates top-down and bottom-up reasoning over latent variable values.   We validate our framework in extensive experiments on MNIST, Omniglot, and CIFAR-10. Comparisons to state-of-the-art structured variational autoencoder baselines show improvements in terms of the expressiveness of the learned model.",propose method learning dependency structure latent variables deep latent variable models. general modeling inference framework combines complementary strengths deep generative models probabilistic graphical models. particular express latent variable space variational autoencoder VAE terms Bayesian network learned flexible dependency structure. network parameters variational parameters well latent topology are optimized simultaneously single objective. Inference is formulated via sampling procedure produces expectations latent variable structures incorporates top-down bottom-up reasoning latent variable values. validate framework extensive experiments MNIST Omniglot CIFAR-10 Comparisons state-of-the-art structured variational autoencoder baselines show improvements terms expressiveness learned model.,174,119,55,0.002,1.462,2025/11/05 17:19:06,0.0,1.0,0.4112149532710277,71.102
"Many real-world time series, such as in activity recognition, finance, or climate science, have changepoints where the system's structure or parameters change. Detecting changes is important as they may indicate critical events. However, existing methods for changepoint detection face challenges when (1) the patterns of change cannot be modeled using simple and predefined metrics, and (2) changes can occur gradually, at multiple time-scales. To address this, we show how changepoint detection can be treated as a supervised learning problem, and propose a new deep neural network architecture that can efficiently identify both abrupt and gradual changes at multiple scales. Our proposed method, pyramid recurrent neural network (PRNN), is designed to be scale-invariant, by incorporating wavelets and pyramid analysis techniques from multi-scale signal processing. Through experiments on synthetic and real-world datasets, we show that PRNN can detect abrupt and gradual changes with higher accuracy than the state of the art and can extrapolate to detect changepoints at novel timescales that have not been seen in training. Changepoints, when the structure or parameters of a system change, are critical to detect in many domains. In medicine, finance, climate science and other fields, these changes can indicate that important events have occurred (e.g. onset of illness or a financial crisis), or changed in important ways (e.g. increasing illness severity). In both cases, these affect decision-making. Changepoint detection (CPD) aims to find these critical times. However, changes may result in complex patterns across multiple observed variables, and can be hard to recognize, especially in multivariate timeseries where interdependencies exist among variables. Further, not all changepoints lead to a sudden transition, many occur over a duration of time (e.g. weightloss, transition between activities) and are harder to identify.Various methods have been proposed for CPD including parametric methods BID0 BID49 BID34 , which make strong assumptions about data distributions, and nonparametric methods BID12 BID39 , which are based on engineered divergence metrics or kernel functions. Most parametric methods are highly context specific, and face difficulty when changes result in complex temporal patterns that are hard to model manually. For nonparametic methods, the main drawback is that these methods rely heavily on the choice of parameters or kernels. To handle data from different domains, BID8 proposed a nonparametric CPD method. However, like many other CPD methods, it can only detect abrupt changes. Yet in real-world applications, the effect of a change may be gradual and may happen over different durations. Some methods have been explicitly designed for detecting gradual changepoints BID2 BID20 , but cannot handle changes occurring at arbitrary timescales. In some applications, like detecting changes in activity, how quickly someone transitions from sitting to standing should not affect accuracy at detecting the transition.In contrast, Deep Neural Networks (DNN) have been used for time series forecasting BID43 and classification as they can learn functions automatically. These can be more easily adapted to new tasks if there is sufficient training data. However, DNNs typically need enough examples of all possible ways a pattern can appear, and thus all possible transition speeds, to reliably detect it in test data. Since this data is costly and may be infeasible to collect in some cases, it is ideal to have a scale-invariant approach that can generalize beyond observed timescales.We propose a novel DNN architecture for CPD using supervised learning. Our approach makes two key contributions to neural network architecture: a trainable wavelet layer that transforms input into a pyramid of multiscale feature maps; and Pyramid recurrent neural networks (PRNN), which build a multi-scale Recurrent Neural Network (RNN) on top of a multi-channel Convolutional Neural Network (CNN) processing the wavelet layer. Finally, we use a binary classifier on the PRNN output to detect changepoints. On both simulated and real-world data, we show that the proposed model can encode short-term and long-term temporal patterns and detect from abrupt to extremely gradual changepoints. The model is scale invariant, and can detect changes at any timescale, regardless of those seen in training. We focus on the task of CPD, but this architecture may have more general applications in time series analysis. We propose a new class of DNNs that are scale-invariant, and show they can detect from abrupt to gradual changepoints in multimodality time series. The core is 1) augmenting CNNs with trainable Wavelet layers to recognize short-term multi-scale patterns; and 2) building a pyramid-shaped RNN on top of the multi-scale feature maps to simultaneously model long-term patterns and fuse multiscale information. The final model can detect events involving short-and long-term patterns at various scales, which is a difficult task for conventional DNNs. Although this reduces the amount of training data required to learn from changes, the proposed method still requires clean labels. Experiments show our approach detects changes quickly, with lower sensitivity to the tolerance parameter than other approaches. For real-world applications, this leads to much higher reliability. In future work we will real-world challenges (e.g. noisy data, missing/noisy labels) by incorporating robustness, semi-supervised learning methods, and multi-view learning techniques. TAB0 -3 show the AUC (Area Under the ROC Curve) results for synthetic data. To detect changepoints, we apply non-maximum suppression with a sliding window of length ω and filter the maximum values with a threshold. We evaluate AUC by iterating over this threshold. Since changepoints may not exactly match the true changepoints, we use a tolerance parameter η that sets how close a detected change must be to a true change to be considered a correct detection. We match detected changepoints to the closest true changepoint within η time step. TAB0 shows the results for the experiment of ""train abrupt and test gradual"" for synthetic data. TAB1 shows the results for the experiment of ""train gradual and test abrupt"" for synthetic data. TAB2 shows the results for the experiment of ""train all and test all"" for synthetic data. TAB3 shows the results for Opportunity data. TAB4 shows the results for Bee Waggle Dance data.",Many real-world time series activity recognition finance climate science have changepoints where the system's structure parameters change. Detecting changes is important may indicate critical events. However existing methods changepoint detection face challenges when(1 patterns change cannot modeled using simple predefined metrics 2 changes can occur gradually multiple time-scales address show how changepoint detection can be treated supervised learning problem propose new deep neural network architecture can efficiently identify abrupt gradual changes multiple scales. proposed method pyramid recurrent neural network PRNN is designed have a scale-invariant incorporating wavelets pyramid analysis techniques multi-scale signal processing. experiments synthetic real-world datasets show PRNN can detect abrupt gradual changes higher accuracy state art can extrapolate detect changepoints novel timescales have not been seen training. Changepoints when the structure parameters system change are critical detect many domains. medicine finance climate science fields changes can indicate important events have occurred e.g onset illness financial crisis changed important ways e.g increasing illness severity cases affect decision-making Changepoint detection CPD aims find critical times. However changes may result complex patterns across multiple observed variables can be hard recognize especially multivariate timeseries where interdependencies exist among variables. changepoints lead sudden transition many occur duration time e.g weightloss transition activities are harder identify.Various methods have been proposed CPD including parametric methods BID0 BID49 BID34 which make strong assumptions data distributions nonparametric methods BID12 BID39 which are based engineered divergence metrics kernel functions. parametric methods are highly context specific face difficulty when changes result complex temporal patterns are hard model manually. nonparametic methods main drawback is that these methods rely heavily choice parameters kernels. handle data different domains BID8 proposed nonparametric CPD method. However like many CPD methods can only can detect abrupt changes. Yet real-world applications effect change may gradual may happen different durations. methods have been explicitly designed detecting gradual changepoints BID2 BID20 cannot handle changes occurring arbitrary timescales. applications like detecting changes activity how quickly someone transitions sitting standing should not affect accuracy detecting transition.In contrast Deep Neural Networks DNN have been used time series forecasting BID43 classification can learn functions automatically. can be more easily adapted new tasks if there is sufficient training data. However DNNs typically need enough examples possible ways pattern can appear thus possible transition speeds reliably detect test data. Since data is costly may infeasible collect cases is ideal have a scale-invariant approach can generalize beyond observed timescales.We propose novel DNN architecture CPD using supervised learning. approach makes two key contributions neural network architecture:trainable wavelet layer transforms input pyramid multiscale feature maps;Pyramid recurrent neural networks PRNN which build multi-scale Recurrent Neural Network RNN top multi-channel Convolutional Neural Network CNN processing wavelet layer. Finally use binary classifier PRNN output detect changepoints. simulated real-world data show proposed model can encode short-term long-term temporal patterns detect abrupt extremely gradual changepoints. model is scale invariant can only can detect changes timescale regardless seen training. focus task CPD architecture may have more general applications time series analysis. propose new class DNNs are scale-invariant show can detect abrupt gradual changepoints multimodality time series. core is1 augmenting CNNs trainable Wavelet layers recognize short-term multi-scale patterns;2 building pyramid-shaped RNN top multi-scale feature maps simultaneously model long-term patterns fuse multiscale information. final model can detect events involving short-and long-term patterns various scales which is a difficult task conventional DNNs. Although reduces amount training data required learn changes proposed method still requires clean labels. Experiments show approach detects changes quickly lower sensitivity tolerance parameter approaches. real-world applications leads much higher reliability. future work will real-world challenges e.g noisy data missing/noisy labels incorporating robustness semi-supervised learning methods multi-view learning techniques. TAB0 -3 show AUC Area ROC Curve results synthetic data. detect changepoints apply non-maximum suppression sliding window lengthω filter maximum values threshold. evaluate AUC iterating threshold. Since changepoints may exactly match true changepoints use tolerance parameterη sets how close detected change must true change considered correct detection. match detected changepoints closest true changepoint within η time step. TAB0 shows results experiment train abrupt test gradual synthetic data. TAB1 shows results experiment train gradual test abrupt synthetic data. TAB2 shows results experiment train test synthetic data. TAB3 shows results Opportunity data. TAB4 shows results Bee Waggle Dance data.,1277,902,375,0.012,1.416,2025/11/05 17:19:06,0.01,1.46,0.2679127725856693,373.928
"We demonstrate how to learn efficient heuristics for automated reasoning algorithms through deep reinforcement learning. We focus on backtracking search algorithms for quantified Boolean logics, which already can solve formulas of impressive size - up to 100s of thousands of variables. The main challenge is to find a representation of these formulas that lends itself to making predictions in a scalable way. For challenging problems, the heuristic learned through our approach reduces execution time by a factor of 10 compared to the existing handwritten heuristics. Automated reasoning and machine learning have both made tremendous progress over the last decades. Automated reasoning algorithms are now able to solve challenging logical problems that once seemed intractable, and today are used in industry for the verification of hardware and software systems. At the core of this progress are logic solvers for Boolean Satisfiability (SAT), Satisfiability Modulo Theories (SMT), and recently also Quantified Boolean Formulas (QBF). These solvers rely on advanced backtracking search algorithms, such as conflict-driven clause learning (CDCL) BID30 , to solve formulas with thousands or even millions of variables. Many automated reasoning algorithms are not only able to answer challenging queries, but also to explain their answer by providing detailed mathematical proofs. However, when problems lack a formal semantics automated reasoning algorithms are hard to apply, and they tend to scale poorly for problems involving uncertainty (e.g. in form of probabilities).Machine learning, on the other hand, recently experienced several breakthroughs in object recognition, machine translation, board games, and language understanding. At the heart of the recent progress in machine learning lie optimization algorithms that train deep and overparameterized models on large amounts of data. The resulting models generalize to unseen inputs and can generally deal well with uncertainty. However, the predictions made by learned models are often hard to explain and hard to restrict to safe behaviors.The complementary strengths of machine learning and automated reasoning raise the question how the methods of the two fields can be combined. In this paper we study how neural networks can be employed within automated reasoning algorithms. We discuss the unique challenges that arise in applying neural networks to vast logical formulas and how reinforcement learning can be used to learn better heuristics for backtracking search algorithms.Backtracking search algorithms in automated reasoning are highly nondeterministic: at many points in their execution there are multiple options for how to proceed. These choices have a big impact on performance; in fact we often see that some problems cannot be solved within hours of computation that under different heuristics are solved within milliseconds. The most prominent heuristic choice in CDCL-style search algorithms is the variable selection heuristic, which is to select a variable (and which value to assign to that variable). Until today, Variable State Independent Decaying Sum (VSIDS) BID33 and its variants are used as the variable selection heuristic in some of the most competitive SAT solvers BID4 Soos, 2014; BID2 and QBF solvers BID28 BID36 . Even small improvements over VSIDS, such as the recent introduction of learning rate branching BID27 , are highly interesting for the automated reasoning community.Designing heuristics for backtracking search algorithms is often counter-intuitive: For example, it is well-known that heuristics that aim to find a correct solution perform worse than heuristics that aim to quickly cause a conflict (i.e. reach a dead-end in the search tree). This is because running into a conflict allows us to apply clause learning, a process that (deductively) derives a new constraint that prevents running into the similar conflicts again. This can cut off an exponential number of branches and can therefore save a lot of computation time in the future. Heuristics for search algorithms are an interesting target for machine learning with immediate impact in verification.The Problem We want to learn a heuristic for a backtracking search algorithm such that it solves more formulas in less time. We view this as a reinforcement learning problem where we are given a formula from some distribution of formulas, and we run the backtracking search algorithm until it reaches a decision point and then query the neural network to predict an action. We iterate this process until termination (at which point the formula is proven or refuted) or a time limit is reached. The input to the neural network is thus the current state of the algorithm, including the formula, and we reward it for reaching termination quickly.In this work, we focus on learning heuristics for the solver CADET BID36 BID38 . CADET is a competitive solver for QBF formulas with the quantifier prefix ∀X ∃Y , which covers most of the known applications of QBF. For all purposes of this work, we can assume the algorithm works exactly like a SAT solver. The heuristic we address in this work is the variable selection heuristic.Challenges The setting comes with several unique challenges:Size: While typical reinforcement learning settings have a small, fixed-size input (a Go board or an Atari screen), the formulas that we consider have hundreds of variables and thousands of clauses, each with several data points. All variables appear both as part of the state and as actions in the reinforcement learning environment. At the same time, the size of the formulas varies dramatically (from tens of variables up to 700k variables) and is hardly correlated with their 'difficulty' -while some of the largest formulas can be solved with little effort, some of the formulas with only 100 variables cannot be solved by any modern QBF solver. We presented an approach to improve the heuristics of a backtracking search algorithm for Boolean logic through deep reinforcement learning. The setting is new and challenging to reinforcement learning, featuring an unbounded input-size and action space, a connection between the length of episodes and rewards. We demonstrate that these problems can be overcome, and learn a heuristic that reduces the overall execution time of a competitive QBF solver by a factor of 10 after training on similar formulas.We believe that this work motivates more aggressive research efforts in the area and will lead to a significant improvement in the performance of logic solvers. Our experiments uncover particu-lar challenges to be addressed in the future. The transfer of the learned insights between different sets of formulas is still limited, learning from long episodes seems to be challenging, andcounterintuitively-it does not seem to help to consider multiple iterations of the GNN.14. Number of successful propagation steps indicates whether the variable is universally quantified, DISPLAYFORM0 indicates whether the variable is existentially quantified, y 2 ∈ {0, 1}indicates whether the variable has a Skolem function already, y 3 ∈ {0, 1} indicates whether the variable was assigned constant True, y 4 ∈ {0, 1} indicates whether the variable was assigned constant False, DISPLAYFORM1 indicates whether the variable was decided positive, y 6 ∈ {0, 1} indicates whether the variable was decided negative, and DISPLAYFORM2 indicates the activity level of the variable. There is no way to assign variables strings as names. The reasoning behind this decision is that this format is only meant to be used for the computational backend.",demonstrate how to learn efficient heuristics automated reasoning algorithms deep reinforcement learning. focus backtracking search algorithms quantified Boolean logics which already can solve formulas impressive size 100s thousands variables. main challenge is to find representation formulas lends making predictions scalable way. challenging problems heuristic learned approach reduces execution time factor 10 compared existing handwritten heuristics. Automated reasoning machine learning have both made tremendous progress last decades. Automated reasoning algorithms are now are not only able solve challenging logical problems seemed intractable today are used industry verification hardware software systems. core progress are logic solvers Boolean Satisfiability SAT Satisfiability Modulo Theories SMT recently also Quantified Boolean Formulas QBF solvers rely advanced backtracking search algorithms conflict-driven clause learning CDCL BID30 solve formulas thousands even millions variables. Many automated reasoning algorithms are now are not only able answer challenging queries also explain answer providing detailed mathematical proofs. However when problems lack formal semantics automated reasoning algorithms are hard apply tend scale poorly problems involving uncertainty e.g form probabilities.Machine learning hand recently experienced several breakthroughs object recognition machine translation board games language understanding. heart recent progress machine learning lie optimization algorithms train deep overparameterized models large amounts data. resulting models generalize unseen inputs can generally deal well uncertainty. However predictions made learned models are often hard explain hard restrict safe behaviors.The complementary strengths machine learning automated reasoning raise question how the methods two fields can be combined. paper study how neural networks can be employed within automated reasoning algorithms. discuss unique challenges arise applying neural networks vast logical formulas how reinforcement learning can be used learn better heuristics backtracking search algorithms.Backtracking search algorithms automated reasoning are highly nondeterministic:many points execution are multiple options how to proceed. choices have a big impact performance;fact often see problems cannot solved within hours computation different heuristics are solved within milliseconds. prominent heuristic choice CDCL-style search algorithms is the variable selection heuristic which is to select variable which value assign variable today Variable State Independent Decaying Sum VSIDS BID33 variants are used variable selection heuristic competitive SAT solvers BID4 Soos 2014;BID2 QBF solvers BID28 BID36. Even small improvements VSIDS recent introduction learning rate branching BID27 are highly interesting automated reasoning community.Designing heuristics backtracking search algorithms is often often counter-intuitive example is well-known heuristics aim find correct solution perform worse heuristics aim quickly cause conflict.e reach dead-end search tree is running conflict allowsus apply clause learning process deductively derives new constraint prevents running similar conflicts again. can cut exponential number branches can therefore save lot computation time future. Heuristics search algorithms are an interesting target machine learning immediate impact verification.The Problem want learn heuristic backtracking search algorithm solves formulas less time. view reinforcement learning problem where we are given formula distribution formulas run backtracking search algorithm reaches decision point query neural network predict action. iterate process termination which point formula is proven refuted time limit is reached. input neural network is thus current state algorithm including formula reward reaching termination quickly.In work focus learning heuristics solver CADET BID36 BID38. CADET is a competitive solver QBF formulas quantifier prefix∀X∃Y which covers known applications QBF. purposes work can assume algorithm works exactly like SAT solver. heuristic address work is the variable selection heuristic.Challenges setting comes several unique challenges:Size:typical reinforcement learning settings have a small fixed-size input Go board Atari screen formulas consider have hundreds variables thousands clauses several data points. variables appear part state actions reinforcement learning environment. time size formulas varies dramatically tens variables 700k variables is hardly correlated 'difficulty' -while largest formulas can be solved little effort formulas 100 variables cannot solved modern QBF solver. presented approach improve heuristics backtracking search algorithm Boolean logic deep reinforcement learning. setting is new challenging reinforcement learning featuring unbounded input-size action space connection length episodes rewards. demonstrate problems can be overcome learn heuristic reduces overall execution time competitive QBF solver factor 10 training similar formulas.We believe work motivates aggressive research efforts area will lead significant improvement performance logic solvers. experiments uncover particu-lar challenges addressed future. transfer learned insights different sets formulas is still limited learning long episodes seems challenging andcounterintuitively-it does not seem help consider multiple iterations GNN.14 Number successful propagation steps indicates whether variable is universally quantified DISPLAYFORM0 indicates whether variable is existentially quantified 2∈ 0 1 indicates whether variable has a Skolem function already 3∈ 0 1 indicates whether variable was assigned constant True 4∈ 0 1 indicates whether variable was assigned constant False DISPLAYFORM1 indicates whether variable was decided positive 6∈ 0 1 indicates whether variable was decided negative DISPLAYFORM2 indicates activity level variable. is no way assign variables strings names. reasoning behind decision is that this format is only meant used computational backend.,1434,968,466,0.017,1.481,2025/11/05 17:19:06,0.01,1.492,0.4704049844236761,495.791
"We consider the question of how to assess generative adversarial networks, in particular with respect to whether or not they generalise beyond memorising the training data. We propose a simple procedure for assessing generative adversarial network performance based on a principled consideration of what the actual goal of generalisation is. Our approach involves using a test set to estimate the Wasserstein distance between the generative distribution produced by our procedure, and the underlying data distribution. We use this procedure to assess the performance of several modern generative adversarial network architectures. We find that this procedure is sensitive to the choice of ground metric on the underlying data space, and suggest a choice of ground metric that substantially improves performance.   We finally suggest that attending to the ground metric used in Wasserstein generative adversarial network training may be fruitful, and outline a concrete pathway towards doing so. Generative adversarial networks (GANs) BID6 have attracted significant interest as a means for generative modelling. However, recently concerns have been raised about their ability to generalise from training data and their capacity to overfit . Moreover, techniques for evaluating the quality of GAN output are either ad hoc, lack theoretical rigor, or are not suitably objective -often times ""visual inspection"" of samples is the main tool of choice for the practitioner. More fundamentally, it is sometimes unclear exactly what we want a GAN to do: what is the learning task that we are trying to achieve?In this paper, we provide a simple formulation of the GAN training framework, which consists of using a finite dataset to estimate an underlying data distribution. The quality of GAN output is measured precisely in terms of a statistical distance D between the estimated and true distribution. Within this context, we propose an intuitive notion of what it means for a GAN to generalise.We also show how our notion of performance can be measured empirically for any GAN architecture when D is chosen to be a Wasserstein distance, which -unlike other methods such as the inception score BID14 ) -requires no density assumptions about the data-generating distribution. We investigate this choice of D empirically, finding that its performance is heavily dependent on the choice of ground metric underlying the Wasserstein distance. We suggest a novel choice of ground metric that we show performs well, and also discuss how we might otherwise use this observation to improve the design of Wasserstein GANs (WGANs) . We believe our work reveals two promising avenues of future inquiry. First, we suggest that W L p •η is an appealing choice of D, both due to its nice theoretical properties -it metricises weak convergence, and does not require us to make any density assumptions about π -and due to its sound empirical performance demonstrated above. It would be very interesting to use this D to produce a systematic and objective comparison of the performance of all current major GAN implementations, and indeed to use this as a metric for guiding future GAN design. We also view the test (5) as potentially useful for determining whether our algorithms are overfitting. This would be particularly so if applied via a cross-validation procedure: if we consistently observe that (5) holds when training a GAN according to many different X and Y partitions of our total π samples, then it seems reasonable to infer that α(X) has indeed learnt something useful about π.We also believe that the empirical inadequacy of W L 2 that we observed suggests a path towards a better WGAN architecture. At present, WGAN implementations implicitly use W L 2 for their choice of D Γ . We suspect that altering this to our suggested W L 2 •η may yield better quality samples. We briefly give here one possible way to do so that is largely compatible with existing WGAN setups. In particular, following , we take DISPLAYFORM0 for a class F of functions f : X → R that are all (L 2 • η, d R )-Lipschitz for some fixed Lipschitz constant K. Here d R denotes the usual distance on R. To optimise over such an F in practice, we can require our discriminator f : X → R to have the form f (x) := h(η(x)), where h : Y → R is (d Y , d R )-Lipschitz, which entails that f is Lipschitz provided η is (which is almost always the case in practice). In other words, we compute DISPLAYFORM1 where F is a class of (d Y , d R )-Lipschitz functions. Optimising over this objective may now proceed as usual via weight-clipping like , or via a gradient penalty like BID8 . Note that this suggestion may be understood as training a standard WGAN with the initial layers of the discriminator fixed to the embedding η; our analysis here shows that this is equivalent to optimising with respect to W L 2 •η instead of W L 2 . We have begun some experimentation in this area but leave a more detailed empirical inquiry to future work.It is also clearly important to establish better theoretical guarantees for our method. At present, we have no guarantee that the number of samples in A and Y are enough to ensure that DISPLAYFORM2 (perhaps with some fixed bias that is fairly independent of α, so that it is valid to use the value of D(Â,Ŷ ) to compare different choices of α), or that (5) entails (2) with high probability. We do however note that some recent theoretical work on the convergence rate of empirical Wasserstein estimations BID18 does suggest that it is plausible to hope for fast convergence of D(Â,Ŷ ) to D(α(X),Ŷ ). We also believe that the convincing empirical behaviour of W L 2 •η does suggest that it is possible to say something more substantial about our approach, which we leave to future work.",consider question how to assess generative adversarial networks particular respect whether generalise beyond memorising training data. propose simple procedure assessing generative adversarial network performance based principled consideration what the actual goal generalisation is. approach involves using test set estimate Wasserstein distance generative distribution produced procedure underlying data distribution. use procedure assess performance several modern generative adversarial network architectures. find procedure is sensitive choice ground metric underlying data space suggest choice ground metric substantially improves performance. finally suggest attending ground metric used Wasserstein generative adversarial network training may fruitful outline concrete pathway towards so. Generative adversarial networks GANs BID6 have attracted significant interest means generative modelling. However recently concerns have been raised ability generalise training data capacity overfit. Moreover techniques evaluating quality GAN output are either ad hoc lack theoretical rigor are not suitably objective -often times visual inspection samples is the main tool choice practitioner. fundamentally is sometimes unclear exactly what we want GAN do:what is the learning task are trying achieve? paper provide simple formulation GAN training framework which consists using finite dataset estimate underlying data distribution. quality GAN output is measured precisely terms statistical distance estimated true distribution. Within context propose intuitive notion what it means GAN generalise.We also show how our notion performance can be measured empirically GAN architecture when D is chosen Wasserstein distance which -unlike methods inception score BID14 -requires density assumptions data-generating distribution. investigate choice empirically finding performance is heavily dependent choice ground metric underlying Wasserstein distance. suggest novel choice ground metric show performs well also discuss might otherwise use observation improve design Wasserstein GANs WGANs believe work reveals two promising avenues future inquiry. First suggest WLp•η is an appealing choice due nice theoretical properties -it metricises weak convergence does not can requireus make density assumptions π -and due sound empirical performance demonstrated above. would interesting use produce systematic objective comparison performance current major GAN implementations indeed use metric guiding future GAN design. also view test 5 potentially useful determining whether algorithms are overfitting. would particularly if applied via cross-validation procedure:if we consistently observe 5 holds when training GAN according many differentX partitions total π samples seems reasonable infer α X has indeed learnt something useful π.We also believe empirical inadequacy WL2 observed suggests path towards better WGAN architecture. present WGAN implementations implicitly use WL2 choice Γ. suspect altering suggestedWL2 •η may yield better quality samples. briefly give one possible way do so that is largely compatible existing WGAN setups. particular following take DISPLAYFORM0 classF functionsf:X→R are all(L2•η R -Lipschitz fixed Lipschitz constantK. R denotes usual distance R. optimise F practice does not can require discriminatorf:X→R have the formf x whereh η x whereh:→R is(dY R -Lipschitz which entails f is Lipschitz providedη is almost always case practice words compute DISPLAYFORM1 whereF is a class R -Lipschitz functions. Optimising objective may proceed usual via weight-clipping like via gradient penalty like BID8. Note suggestion may understood training standard WGAN initial layers discriminator fixed embeddingη;analysis shows is equivalent optimising respect WL2•η instead WL2. have begun experimentation area leave detailed empirical inquiry future work.It is also clearly important establish better theoretical guarantees method. present have no guarantee number samples are enough ensure DISPLAYFORM2 perhaps fixed bias is fairly independent α is valid use value  Ŷ compare different choices α 5 entails 2 high probability. do however note recent theoretical work convergence rate empirical Wasserstein estimations BID18 does suggest is plausible hope fast convergence  Ŷ α X Ŷ also believe convincing empirical behaviour WL2•η does suggest is possible say something substantial approach which we leave future work.,1180,758,422,0.013,1.557,2025/11/05 17:19:06,0.01,1.529,0.7071651090342675,363.862
"The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although various hand-designed alternatives to ReLU have been proposed, none have managed to replace it due to inconsistent gains. In this work, we propose to leverage automatic search techniques to discover new activation functions. Using a combination of exhaustive and reinforcement learning-based search, we discover multiple novel activation functions. We verify the effectiveness of the searches by conducting an empirical evaluation with the best discovered activation function. Our experiments show that the best discovered activation function, f(x) = x * sigmoid(beta * x), which we name Swish, tends to work better than ReLU on deeper models across a number of challenging datasets. For example, simply replacing ReLUs with Swish units improves top-1 classification accuracy on ImageNet by 0.9% for Mobile NASNet-A and 0.6% for Inception-ResNet-v2. The simplicity of Swish and its similarity to ReLU make it easy for practitioners to replace ReLUs with Swish units in any neural network. At the heart of every deep network lies a linear transformation followed by an activation function f (·). The activation function plays a major role in the success of training deep neural networks. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU) BID12 BID21 BID29 , defined as f (x) = max(x, 0). The use of ReLUs was a breakthrough that enabled the fully supervised training of state-of-the-art deep networks BID25 . Deep networks with ReLUs are more easily optimized than networks with sigmoid or tanh units, because gradients are able to flow when the input to the ReLU function is positive. Thanks to its simplicity and effectiveness, ReLU has become the default activation function used across the deep learning community.While numerous activation functions have been proposed to replace ReLU (Maas et al., 2013; BID13 BID5 BID23 , none have managed to gain the widespread adoption that ReLU enjoys. Many practitioners have favored the simplicity and reliability of ReLU because the performance improvements of the other activation functions tend to be inconsistent across different models and datasets.The activation functions proposed to replace ReLU were hand-designed to fit properties deemed to be important. However, the use of search techniques to automate the discovery of traditionally human-designed components has recently shown to be extremely effective BID51 BID3 . For example, used reinforcement learningbased search to find a replicable convolutional cell that outperforms human-designed architectures on ImageNet.In this work, we use automated search techniques to discover novel activation functions. We focus on finding new scalar activation functions, which take in as input a scalar and output a scalar, because scalar activation functions can be used to replace the ReLU function without changing the network architecture. Using a combination of exhaustive and reinforcement learning-based search, we find a number of novel activation functions that show promising performance. To further validate the effectiveness of using searches to discover scalar activation functions, we empirically evaluate the best discovered activation function. The best discovered activation function, which we call Swish, is f (x) = x · sigmoid(βx), where β is a constant or trainable parameter. Our extensive experiments show that Swish consistently matches or outperforms ReLU on deep networks applied to a variety of challenging domains such as image classification and machine translation. On ImageNet, replacing ReLUs with Swish units improves top-1 classification accuracy by 0.9% on Mobile NASNet-A and 0.6% on Inception-ResNet-v2 BID40 . These accuracy gains are significant given that one year of architectural tuning and enlarging yielded 1.3% accuracy improvement going from Inception V3 BID39 to Inception-ResNet-v2 BID40 . In this work, we utilized automatic search techniques to discover novel activation functions that have strong empirical performance. We then empirically validated the best discovered activation function, which we call Swish and is defined as f (x) = x · sigmoid(βx). Our experiments used models and hyperparameters that were designed for ReLU and just replaced the ReLU activation function with Swish; even this simple, suboptimal procedure resulted in Swish consistently outperforming ReLU and other activation functions. We expect additional gains to be made when these models and hyperparameters are specifically designed with Swish in mind. The simplicity of Swish and its similarity to ReLU means that replacing ReLUs in any network is just a simple one line code change.",choice activation functions deep networks has a significant effect training dynamics task performance. Currently successful widely-used activation function is the Rectified Linear Unit ReLU Although various hand-designed alternatives ReLU have been proposed none have managed replace due inconsistent gains. work propose leverage automatic search techniques discover new activation functions. Using combination exhaustive reinforcement learning-based search discover multiple novel activation functions. verify effectiveness searches conducting empirical evaluation best discovered activation function. experiments show best discovered activation function isf x x * sigmoid beta*x which we name Swish tends work better ReLU deeper models across number challenging datasets. example simply replacing ReLUs Swish units improves top-1 classification accuracy ImageNet 0.9 Mobile NASNet-A 0.6 Inception-ResNet-v2 simplicity Swish similarity ReLU make easy practitioners replace ReLUs Swish units neural network. heart every deep network lies linear transformation followed activation functionf · activation function plays major role success training deep neural networks. Currently successful widely-used activation function is the Rectified Linear Unit ReLU BID12 BID21 BID29 defined f x max x 0 use ReLUs was a breakthrough enabled fully supervised training state-of-the-art deep networks BID25. Deep networks ReLUs are more easily optimized networks sigmoid tanh units gradients are able flow when the input ReLU function is positive. Thanks simplicity effectiveness ReLU has become default activation function used across deep learning community.While numerous activation functions have been proposed replace ReLU Maasetal. 2013;BID13 BID5 BID23 none have managed gain widespread adoption ReLU enjoys. Many practitioners have favored simplicity reliability ReLU performance improvements activation functions tend inconsistent across different models datasets.The activation functions proposed replace ReLU were hand-designed fit properties deemed important. However use search techniques automate discovery traditionally human-designed components has recently shown extremely effective BID51 BID3. example used reinforcement learningbased search find replicable convolutional cell outperforms human-designed architectures ImageNet.In work use automated search techniques discover novel activation functions. focus finding new scalar activation functions which take input scalar output scalar scalar activation functions can be used replace ReLU function without changing network architecture. Using combination exhaustive reinforcement learning-based search find number novel activation functions show promising performance. validate effectiveness using searches discover scalar activation functions empirically evaluate best discovered activation function. best discovered activation function which we call Swish isf x x · sigmoid βx whereβ is a constant trainable parameter. extensive experiments show Swish consistently matches outperforms ReLU deep networks applied variety challenging domains image classification machine translation. ImageNet replacing ReLUs Swish units improves top-1 classification accuracy 0.9 Mobile NASNet-A 0.6 Inception-ResNet-v2 BID40. accuracy gains are significant given one year architectural tuning enlarging yielded 1.3 accuracy improvement going Inception V3 BID39 Inception-ResNet-v2 BID40. work utilized automatic search techniques discover novel activation functions have strong empirical performance. empirically validated best discovered activation function which we call Swish is defined f x x · sigmoid βx experiments used models hyperparameters were designed ReLU replaced ReLU activation function Swish;even simple suboptimal procedure resulted Swish consistently outperforming ReLU activation functions. expect additional gains made when these models hyperparameters are specifically designed Swish mind. simplicity Swish similarity ReLU means replacing ReLUs network is just a simple one line code change.,948,683,265,0.009,1.388,2025/11/05 17:19:06,0.0,1.481,0.1806853582554512,298.568
"Successful training of convolutional neural networks is often associated with suffi-
 ciently deep architectures composed of high amounts of features. These networks
 typically rely on a variety of regularization and pruning techniques to converge
 to less redundant states. We introduce a novel bottom-up approach to expand
 representations in fixed-depth architectures. These architectures start from just a
 single feature per layer and greedily increase width of individual layers to attain
 effective representational capacities needed for a specific task. While network
 growth can rely on a family of metrics, we propose a computationally efficient
 version based on feature time evolution and demonstrate its potency in determin-
 ing feature importance and a networks’ effective capacity. We demonstrate how
 automatically expanded architectures converge to similar topologies that benefit
 from lesser amount of parameters or improved accuracy and exhibit systematic
 correspondence in representational complexity with the specified task. In contrast
 to conventional design patterns with a typical monotonic increase in the amount of
 features with increased depth, we observe that CNNs perform better when there is
 more learnable parameters in intermediate, with falloffs to earlier and later layers. Estimating and consequently adequately setting representational capacity in deep neural networks for any given task has been a long standing challenge. Fundamental understanding still seems to be insufficient to rapidly decide on suitable network sizes and architecture topologies. While widely adopted convolutional neural networks (CNNs) such as proposed by BID17 ; BID27 ; BID12 ; Zagoruyko & Komodakis (2016) demonstrate high accuracies on a variety of problems, the memory footprint and computational complexity vary. An increasing amount of recent work is already providing valuable insights and proposing new methodology to address these points. For instance, the authors of BID2 propose a reinforcement learning based meta-learning approach to have an agent select potential CNN layers in a greedy, yet iterative fashion. Other suggested architecture selection algorithms draw their inspiration from evolutionary synthesis concepts BID25 BID22 . Although the former methods are capable of evolving architectures that rival those crafted by human design, it is currently only achievable at the cost of navigating large search spaces and hence excessive computation and time. As a trade-off in present deep neural network design processes it thus seems plausible to consider layer types or depth of a network to be selected by an experienced engineer based on prior knowledge and former research. A variety of techniques therefore focus on improving already well established architectures. Procedures ranging from distillation of one network's knowledge into another , compressing and encoding learned representations BID8 , pruning alongside potential re-training of networks BID7 BID26 BID10 , small capacity increases on trained networks in transfer-learning scenarios (WardeFarley et al., 2014) and the employment of different regularization terms during training BID11 BID15 BID23 BID0 , are just a fraction of recent efforts in pursuit of reducing representational complexity while attempting to retain accuracy. Underlying mechanisms rely on a multitude of criteria such as activation magnitudes BID26 and small weight values BID7 that are used as pruning metrics for either single neurons or complete feature maps, in addition to further combination with regularization and penalty terms.Common to these approaches is the necessity of training networks with large parameter quantities for maximum representational capacity to full convergence and the lack of early identification of insufficient capacity. In contrast, this work proposes a bottom-up approach with the following contributions:• We introduce a computationally efficient, intuitive metric to evaluate feature importance at any point of training a neural network. The measure is based on feature time evolution, specifically the normalized cross-correlation of each feature with its initialization state.• We propose a bottom-up greedy algorithm to automatically expand fixed-depth networks that start with one feature per layer until adequate representational capacity is reached. We base addition of features on our newly introduced metric due to its computationally efficient nature, while in principle a family of similarly constructed metrics is imaginable.• We revisit popular CNN architectures and compare them to automatically expanded networks. We show how our architectures systematically scale in terms of complexity of different datasets and either maintain their reference accuracy at reduced amount of parameters or achieve better results through increased network capacity.• We provide insights on how evolved network topologies differ from their reference counterparts where conventional design commonly increases the amount of features monotonically with increasing network depth. We observe that expanded architectures exhibit increased feature counts at early to intermediate layers and then proceed to decrease in complexity. In this work we have introduced a novel bottom-up algorithm to start neural network architectures with one feature per layer and widen them until a task depending suitable representational capacity is achieved. For the use in this framework we have presented one potential computationally efficient and intuitive metric to gauge feature importance. The proposed algorithm is capable of expanding architectures that provide either reduced amount of parameters or improved accuracies through higher amount of representations. This advantage seems to be gained through alternative network topologies with respect to commonly applied designs in current literature. Instead of increasing the amount of features monotonically with increasing depth of the network, we empirically observe that expanded neural network topologies have high amount of representations in early to intermediate layers.Future work could include a re-evaluation of plainly stacked deep architectures with new insights on network topologies and extended evaluation on different domain data. We have furthermore started to replace the currently present re-initialization step in the proposed expansion algorithm by keeping learned filters. In principle this approach looks promising but does need further systematic analysis of new feature initialization with respect to the already learned feature subset and accompanied investigation of orthogonality to avoid falling into local minima.",Successful training convolutional neural networks is often associated suffi- ciently deep architectures composed high amounts features. networks typically rely variety regularization pruning techniques converge less redundant states. introduce novel bottom-up approach expand representations fixed-depth architectures. architectures start single feature per layer greedily increase width individual layers attain effective representational capacities needed specific task. network growth can rely family metrics propose computationally efficient version based feature time evolution demonstrate potency determin- ing feature importance networks effective capacity. demonstrate how automatically expanded architectures converge similar topologies benefit lesser amount parameters improved accuracy exhibit systematic correspondence representational complexity specified task. contrast conventional design patterns typical monotonic increase amount features increased depth observe CNNs perform better when there is more learnable parameters intermediate falloffs earlier later layers. Estimating consequently adequately setting representational capacity deep neural networks given task has been a long standing challenge. Fundamental understanding still seems insufficient rapidly decide suitable network sizes architecture topologies. widely adopted convolutional neural networks CNNs proposed BID17;BID27;BID12;Zagoruyko Komodakis 2016 demonstrate high accuracies variety problems memory footprint computational complexity vary. increasing amount recent work is already providing valuable insights proposing new methodology address points. instance authors BID2 propose reinforcement learning based meta-learning approach have an agent select potential CNN layers greedy yet iterative fashion. suggested architecture selection algorithms draw inspiration evolutionary synthesis concepts BID25 BID22. Although former methods are capable evolving architectures rival crafted human design is currently achievable cost navigating large search spaces hence excessive computation time. trade-off present deep neural network design processes thus seems plausible consider layer types depth network selected experienced engineer based prior knowledge former research. variety techniques therefore focus improving already well established architectures. Procedures ranging distillation one network's knowledge another compressing encoding learned representations BID8 pruning alongside potential re-training networks BID7 BID26 BID10 small capacity increases trained networks transfer-learning scenarios WardeFarleyetal. 2014 employment different regularization terms training BID11 BID15 BID23 BID0 are just a fraction recent efforts pursuit reducing representational complexity attempting retain accuracy. Underlying mechanisms rely multitude criteria activation magnitudes BID26 small weight values BID7 are used pruning metrics either single neurons complete feature maps addition combination regularization penalty terms.Common approaches is the necessity training networks large parameter quantities maximum representational capacity full convergence lack early identification insufficient capacity. contrast work proposes bottom-up approach following contributions:• introduce computationally efficient intuitive metric evaluate feature importance point training neural network. measure is based feature time evolution specifically normalized cross-correlation feature initialization state.• propose bottom-up greedy algorithm automatically expand fixed-depth networks start one feature per layer adequate representational capacity is reached. base addition features newly introduced metric due computationally efficient nature principle family similarly constructed metrics is imaginable.• revisit popular CNN architectures compare automatically expanded networks. show how our architectures systematically scale terms complexity different datasets either maintain reference accuracy reduced amount parameters achieve better results increased network capacity.• provide insights how evolved network topologies differ reference counterparts where conventional design commonly increases amount features monotonically increasing network depth. observe expanded architectures exhibit increased feature counts early intermediate layers proceed decrease complexity. work have introduced novel bottom-up algorithm start neural network architectures one feature per layer widen task depending suitable representational capacity is achieved. use framework have presented one potential computationally efficient intuitive metric gauge feature importance. proposed algorithm is capable expanding architectures provide either reduced amount parameters improved accuracies higher amount representations. advantage seems gained alternative network topologies respect commonly applied designs current literature. Instead increasing amount features monotonically increasing depth network empirically observe expanded neural network topologies have high amount representations early intermediate layers.Future work could include re-evaluation plainly stacked deep architectures new insights network topologies extended evaluation different domain data. have furthermore started replace currently present re-initialization step proposed expansion algorithm keeping learned filters. principle approach looks promising does need systematic analysis new feature initialization respect already learned feature subset accompanied investigation orthogonality avoid falling local minima.,1104,776,328,0.01,1.423,2025/11/05 17:19:06,0.0,1.4,0.2897196261682242,333.745
"Deep neural networks are almost universally trained with reverse-mode automatic differentiation (a.k.a. backpropagation). Biological networks, on the other hand, appear to lack any mechanism for sending gradients back to their input neurons, and thus cannot be learning in this way. In response to this, Scellier & Bengio (2017) proposed Equilibrium Propagation - a method for gradient-based train- ing of neural networks which uses only local learning rules and, crucially, does not rely on neurons having a mechanism for back-propagating an error gradient. Equilibrium propagation, however, has a major practical limitation: inference involves doing an iterative optimization of neural activations to find a fixed-point, and the number of steps required to closely approximate this fixed point scales poorly with the depth of the network. In response to this problem, we propose Initialized Equilibrium Propagation, which trains a feedforward network to initialize the iterative inference procedure for Equilibrium propagation. This feed-forward network learns to approximate the state of the fixed-point using a local learning rule. After training, we can simply use this initializing network for inference, resulting in a learned feedforward network. Our experiments show that this network appears to work as well or better than the original version of Equilibrium propagation. This shows how we might go about training deep networks without using backpropagation. Deep neural networks are almost always trained with gradient descent, and gradients are almost always computed with backpropagation. For those interested in understanding the working of the brain in the context of machine learning, it is therefore distressing that biological neurons appear not to send signals backwards.Biological neurons communicate by sending a sequence of pulses to downstream neurons along a one-way signaling pathway called an ""axon"". If neurons were doing backpropagation, one would expect a secondary signalling pathway wherein gradient signals travel backwards along axons. This appears not to exist, so it seems that biological neurons cannot be doing backpropagation.Moreover, backpropagation may not be the ideal learning algorithm for efficient implementation in hardware, because it involves buffering activations for each layer until an error gradient returns. This requirement becomes especially onerous when we wish to backpropagate through many steps of time, or through many layers of depth. For these reasons, researchers are looking into other means of neural credit assignment -mechanisms for generating useful learning signals without doing backpropagation.Recently, BID19 proposed a novel algorithm called Equilibrium Propagation, which enables the computation of parameter gradients in a deep neural network without backpropagation. Equilibrium Propagation defines a neural network as a dynamical system, whose dynamics follow the negative-gradient of an energy function. The ""prediction"" of this network is the fixedpoint of the dynamics -the point at which the system settles to a local minimum energy given the input, and ceases to change. Because of this inference scheme, Equilibrium Propagation is impractically slow for large networks -the network has to iteratively converge to a fixed point at every training iteration.In this work, we take inspiration from BID6 and distill knowledge from a slow, energy based equilibrating network into a fast feedforward network by training the feedforward network to predict the fixed-points of the equilibrating network with a local loss. At the end of training, we can then discard the equilibrating network and simply use our feedforward network for testtime inference. We thus have a way to train a feedforward network without backpropagation. The resulting architecture loosely resembles a Conditional Generative Adversarial Network BID17 , where the feedforward network produces a network state which is evaluated by the energy-based equilibrating network.To aid the reader, this paper contains a glossary of symbols in Appendix A. In this paper we describe how to use a recurrent, energy-based model to provide layerwise targets with which to train a feedforward network without backpropagation. This work helps us understand how the brain might be training fast inference networks. In this view, neurons in the inference network learn to predict local targets, which correspond to the minimal energy states, which are found by the iterative settling of a separate, recurrently connected equilibrating network.More immediately perhaps, this could lead towards efficient analog neural network designs in hardware. As pointed out by BID19 , it is much easier to design an analog circuit to minimize some (possibly unknown) energy function than it is to design a feedforward circuit and a parallel backwards circuit which exactly computes its gradients. However it is very undesirable for the function of a network to depend on peculiarities of a particular piece of analog hardware, because then the network cannot be easily replicated. We could imagine using a hybrid circuit to train a digital, copy-able feedforward network, which is updated by gradients computed in the analog hardware. Without the constraint of having to backpropagate through the feedforward network, designs could be simplified, for example to do away with the need for differentiable activation functions or to use feedforward architectures which would otherwise suffer from vanishing/exploding gradient effects.",Deep neural networks are almost universally trained reverse-mode automatic differentiation.k.a backpropagation Biological networks hand appear lack mechanism sending gradients back input neurons thus cannot learning way. response Scellier Bengio 2017 proposed Equilibrium Propagation method gradient-based train- ing neural networks which uses local learning rules crucially does not rely neurons mechanism back-propagating error gradient. Equilibrium propagation however has a major practical limitation:inference involves iterative optimization neural activations find fixed-point number steps required closely approximate fixed point scales poorly depth network. response problem propose Initialized Equilibrium Propagation which trains feedforward network initialize iterative inference procedure Equilibrium propagation. feed-forward network learns approximate state fixed-point using local learning rule. training can simply use initializing network inference resulting learned feedforward network. experiments show network appears work well better original version Equilibrium propagation. shows mightgo training deep networks without using backpropagation. Deep neural networks are almost always trained gradient descent gradients are almost always computed backpropagation. interested understanding working brain context machine learning is therefore distressing biological neurons appear send signals backwards.Biological neurons communicate sending sequence pulses downstream neurons along one-way signaling pathway called axon. If neurons were doing backpropagation one would expect secondary signalling pathway wherein gradient signals travel backwards along axons. appears exist seems biological neurons cannot backpropagation.Moreover backpropagation may ideal learning algorithm efficient implementation hardware involves buffering activations layer error gradient returns. requirement becomes especially onerous when we wish backpropagate many steps time many layers depth. reasons researchers are looking means neural credit assignment -mechanisms generating useful learning signals without backpropagation.Recently BID19 proposed novel algorithm called Equilibrium Propagation which enables computation parameter gradients deep neural network without backpropagation. Equilibrium Propagation defines neural network dynamical system whose dynamics follow negative-gradient energy function. prediction network is the fixedpoint dynamics -the point which the system settles local minimum energy given input ceases change. inference scheme Equilibrium Propagation is impractically slow large networks -the network has to iteratively converge fixed point every training iteration.In work take inspiration BID6 distill knowledge slow energy based equilibrating network fast feedforward network training feedforward network predict fixed-points equilibrating network local loss. end training can then discard equilibrating network simply use feedforward network testtime inference. thus have a way train feedforward network without backpropagation. resulting architecture loosely resembles Conditional Generative Adversarial Network BID17 where the feedforward network produces network state which is evaluated energy-based equilibrating network.To aid reader paper contains glossary symbols Appendix A. paper describe how to use recurrent energy-based model provide layerwise targets which to train feedforward network without backpropagation. work helps us understand how the brain might training fast inference networks. view neurons inference network learn predict local targets which correspond minimal energy states which are found iterative settling separate recurrently connected equilibrating network.More immediately perhaps could lead towards efficient analog neural network designs hardware. pointed BID19 is much easier design analog circuit minimize possibly unknown energy function is to design feedforward circuit parallel backwards circuit which exactly computes gradients. However is very undesirable function network depend peculiarities particular piece analog hardware network cannot easily replicated. could imagine using hybrid circuit train digital copy-able feedforward network which is updated gradients computed analog hardware. Without constraint backpropagate feedforward network designs could simplified example do away need differentiable activation functions use feedforward architectures would otherwise suffer vanishing/exploding gradient effects.,1012,691,321,0.01,1.465,2025/11/05 17:19:06,0.0,1.581,0.4205607476635514,309.319
"We propose a novel generative model architecture designed to learn representations for images that factor out a single attribute from the rest of the representation. A single object may have many attributes which when altered do not change the identity of the object itself. Consider the human face; the identity of a particular person is independent of whether or not they happen to be wearing glasses. The attribute of wearing glasses can be changed without changing the identity of the person. However, the ability to manipulate and alter image attributes without altering the object identity is not a trivial task. Here, we are interested in learning a representation of the image that separates the identity of an object (such as a human face) from an attribute (such as 'wearing glasses'). We demonstrate the success of our factorization approach by using the learned representation to synthesize the same face with and without a chosen attribute. We refer to this specific synthesis process as image attribute manipulation. We further demonstrate that our model achieves competitive scores, with state of the art, on a facial attribute classification task. Latent space generative models, such as generative adversarial networks (GANs) BID11 BID27 and variational autoencoders (VAEs) BID28 BID14 , learn a mapping from a latent encoding space to a data space, for example, the space of natural images. It has been shown that the latent space learned by these models is often organized in a near-linear fashion BID27 BID14 , whereby neighbouring points in latent space map to similar images in data space. Certain ""directions"" in latent space correspond to changes in the intensity of certain attributes. In the context of faces, for example, directions in latent space would correspond to the extent to which someone is smiling. This may be useful for image synthesis where one can use the latent space to develop new design concepts BID9 Zhu et al., 2016) , edit an existing image (Zhu et al., 2016) or synthesize avatars BID35 BID32 . This is because semantically meaningful changes may be made to images by manipulating the latent space BID27 Zhu et al., 2016; BID17 .One avenue of research for latent space generative models has been class conditional image synthesis BID25 BID24 , where an image of a particular object category is synthesized. Often , object categories may be sub-divided into fine-grain subcategories. For example, the category ""dog"" may be split into further sub-categories of different dog breeds. Work by BID3 propose latent space generative models for synthesizing images from fine-grained categories, in particular for synthesizing different celebrities' faces conditional on the identity of the celebrity.Rather than considering fine-grain categories, we propose to take steps towards solving the different, but related problem of image attribute manipulation. To solve this problem we want to be able to synthesize images and only change one element or attribute of its content. For example , if we are synthesizing faces we would like to edit whether or not a person is smiling. This is a different problem to fine-grain synthesis; we want to be able to synthesize two faces that are similar, with only a single chosen attribute changed, rather than synthesizing two different faces. The need to synthesis two faces that are similar makes the problem of image attribute manipulation more difficult than the fine-grain image synthesis problem; we need to learn a latent space representation that separates an object category from its attributes.In this paper, we propose a new model that learns a factored representation for faces, separating attribute information from the rest of the facial representation. We apply our model to the CelebA BID21 dataset of faces and control several facial attributes.Our contributions are as follows:1. Our core contribution is the novel cost function for training a VAE encoder to learn a latent representation which factorizes binary facial attribute information from a continuous identity representation (Section 3.2). 2. We provide an extensive quantitative analysis of the contributions of each of the many loss components in our model (Section 4.2). 3. We obtain classification scores that are competitive with state of the art (Zhuang et al., 2018) using the classifier that is already incorporated into the encoder of the VAE (Section 4.3). 4. We provide qualitative results demonstrating that our latent variable, generative model may be used to successfully edit the 'Smiling' attribute in more than 90% of the test cases (Section 4.4). 5. We discuss and clarify the distinction between conditional image synthesis and image attribute editing (Section 5). 6. We present code to reproduce experiments shown in this paper: (provided after review). We have proposed a novel perspective and approach to learning representations of images which subsequently allows elements, or attributes, of the image to be modified. We have demonstrated our approach on images of the human face, however, the method is generalisable to other objects. We modelled a human face in two parts, with a continuous latent vector that captures the identity of a person and a binary unit vector that captures a facial attribute, such as whether or not a person is smiling. By modelling an image with two separate representations, one for the object and the other for the object's attribute, we are able to change attributes without affecting the identity of the object. To learn this factored representation we have proposed a novel model aptly named Information Factorization conditional VAE-GAN. The model encourages the attribute information to be factored out of the identity representation via an adversarial learning process. Crucially, the representation learned by our model both captures identity faithfully and facilitates accurate and easy attribute editing without affecting identity. We have demonstrated that our model performs better than pre-existing models intended for category conditional image synthesis (Section 4.4), and have performed a detailed ablation study TAB0 which confirms the importance and relevance of our proposed method. Indeed, our model is highly effective as a classifier, achieving state of the art accuracy on facial attribute classification for several attributes (Figure 2 ). Our approach to learning factored representations for images is both a novel and important contribution to the general field of representation learning.",propose novel generative model architecture designed learn representations images factor single attribute rest representation. single object may have many attributes which when altered do not change identity object itself. Consider human face;identity particular person is independent whether happen wearing glasses. attribute wearing glasses can be changed without changing identity person. However ability manipulate alter image attributes without altering object identity is not a trivial task. are interested learning representation image separates identity object human face attribute 'wearing glasses' demonstrate success factorization approach using learned representation synthesize face without chosen attribute. refer specific synthesis process image attribute manipulation. demonstrate model achieves competitive scores state art facial attribute classification task. Latent space generative models generative adversarial networks GANs BID11 BID27 variational autoencoders VAEs BID28 BID14 learn mapping latent encoding space data space example space natural images. has been shown latent space learned models is often organized near-linear fashion BID27 BID14 whereby neighbouring points latent space map similar images data space. Certain directions latent space correspond changes intensity certain attributes. context faces example directions latent space would correspond extent which someone is smiling. may useful image synthesis where one can use latent space develop new design concepts BID9 Zhuetal. 2016 edit existing image Zhuetal. 2016 synthesize avatars BID35 BID32. is because semantically meaningful changes may made images manipulating latent space BID27 Zhu etal. 2016;BID17.One avenue research latent space generative models has been class conditional image synthesis BID25 BID24 where an image particular object category is synthesized. Often object categories may sub-divided fine-grain subcategories. example category dog may split sub-categories different dog breeds. Work BID3 propose latent space generative models synthesizing images fine-grained categories particular synthesizing different celebrities' faces conditional identity celebrity.Rather considering fine-grain categories propose take steps towards solving different related problem image attribute manipulation. solve problem want able synthesize images change one element attribute content. example if we are synthesizing faces would like edit whether person is smiling. is a different problem fine-grain synthesis;want able synthesize two faces are similar single chosen attribute changed rather synthesizing two different faces. need synthesis two faces are similar makes problem image attribute manipulation difficult fine-grain image synthesis problem;need learn latent space representation separates object category attributes.In paper propose new model learns factored representation faces separating attribute information rest facial representation. apply model CelebA BID21 dataset faces control several facial attributes.Our contributions are as follows:1 follows:1 core contribution is the is both a novel cost function training VAE encoder learn latent representation which factorizes binary facial attribute information continuous identity representation Section 3.2 2. provide extensive quantitative analysis contributions many loss components model Section 4.2 3. obtain classification scores are competitive state art Zhuangetal. 2018 using classifier is already incorporated encoder VAE Section 4.3 4. provide qualitative results demonstrating latent variable generative model may used successfully edit 'Smiling' attribute 90% test cases Section 4.4 5. discuss clarify distinction conditional image synthesis image attribute editing Section5 6. present code reproduce experiments shown paper:provided review have proposed novel perspective approach learning representations images which subsequently allows elements attributes where an image modified. have demonstrated approach images human face however method is generalisable objects. modelled human face two parts continuous latent vector captures identity person binary unit vector captures facial attribute whether person is smiling. modelling image two separate representations one object object's attribute are able change attributes without affecting identity object. learn factored representation have proposed novel model aptly named Information Factorization conditional VAE-GAN model encourages attribute information factored identity representation via adversarial learning process. Crucially representation learned model captures identity faithfully facilitates accurate easy attribute editing without affecting identity. have demonstrated model performs better pre-existing models intended category conditional image synthesis Section 4.4 have performed detailed ablation study TAB0 which confirms importance relevance proposed method. Indeed model is highly effective classifier achieving state art accuracy facial attribute classification several attributes Figure2 approach learning factored representations images is the is both a novel important contribution general field representation learning.,1244,828,416,0.013,1.502,2025/11/05 17:19:06,0.01,1.486,0.5358255451713394,401.007
"Stochastic video prediction models take in a sequence of image frames, and generate a sequence of consecutive future image frames. These models typically generate future frames in an autoregressive fashion, which is slow and requires the input and output frames to be consecutive. We introduce a model that overcomes these drawbacks by generating a latent representation from an arbitrary set of frames that can then be used to simultaneously and efficiently sample temporally consistent frames at arbitrary time-points. For example, our model can ""jump"" and directly sample frames at the end of the video, without sampling intermediate frames. Synthetic video evaluations confirm substantial gains in speed and functionality without loss in fidelity. We also apply our framework to a 3D scene reconstruction dataset. Here, our model is conditioned on camera location and can sample consistent sets of images for what an occluded region of a 3D scene might look like, even if there are multiple possibilities for what that region might contain. Reconstructions and videos are available at https://bit.ly/2O4Pc4R.
 The ability to fill in the gaps in high-dimensional data is a fundamental cognitive skill. Suppose you glance out of the window and see a person in uniform approaching your gate carrying a letter. You can easily imagine what will (probably) happen a few seconds later. The person will walk up the path and push the letter through your door. Now suppose you glance out of the window the following day and see a person in the same uniform walking down the path, away from the house. You can easily imagine what (probably) happened a few seconds earlier. The person came through your gate, walked up the path, and delivered a letter. Moreover, in both instances, you can visualize the scene from different viewpoints. From your vantage point at the window, you can imagine how things might look from the gate, or from the front door, or even from your neighbour's roof. Essentially, you have learned from your past experience of unfolding visual scenes how to flexibly extrapolate and interpolate in both time and space. Replicating this ability is a significant challenge for AI.To make this more precise, let's first consider the traditional video prediction setup. Video prediction is typically framed as a sequential forward prediction task. Given a sequence of frames f 1 , ..., f t , a model is tasked to generate future frames that follow, f t+1 , ..., f T . Existing models BID0 BID7 carry out the prediction in an autoregressive manner, by sequentially sampling frame f t+n from p(f t+n |f 1 , ..., f t+n−1 ).This traditional setup is often limiting -in many cases, we are interested in what happens a few seconds after the input sequence. For example, in model based planning tasks, we might want to predict what frame f T is, but might not care what intermediate frames f t+1 , ..., f T −1 are. Existing models must still produce the intermediate frames, which is inefficient. Instead, our model is ""jumpy"" -it can directly sample frames in the future, bypassing intermediate frames. For example , in a 40-frame video, our model can sample the final frame 12 times faster than an autoregressive model like SV2P BID0 .More generally , existing forward video prediction models are not flexible at filling in gaps in data. Instead, our model can sample frames at arbitrary time points of a video, given a set of frames at arbitrary time points as context. So it can, for example, be used to infer backwards or interpolate between frames, as easily as forwards. Our model is also not autoregressive on input or output frames -it takes in each input frame in parallel, and samples each output frame in parallel.In our setup of ""jumpy"" video prediction, a model is given frames f 1 , ..., f n from a single video along with the arbitrary time-points t 1 , ..., t n at which those frames occurred. To be clear, t 1 , ..., t n need not be consecutive or even in increasing order. The model is then asked to sample plausible frames at arbitrary time points t 1 , ..., t k . In many cases there are multiple possible predicted frames given the context, making the problem stochastic. For example, a car moving towards an intersection could turn left or turn right. Although our model is not autoregressive, each set of k sampled frames is consistent with a single coherent possibility, while maintaining diversity across sets of samples. That is, in each sampled set all k sampled frames correspond to the car moving left, or all correspond to the car moving right.At a high level, our model, JUMP, takes in the input frames and samples a stochastic latent that models the stochasticity in the video. Given an arbitrary query time-point, the model uses the sampled latent to render the frame at that time-point. The model is not autoregressive on input or output frames, but still captures correlations over multiple target frames. Our method is not restricted to video prediction. When conditioned on camera position , our model can sample consistent sets of images for an occluded region of a scene, even if there are multiple possibilities for what that region might contain.We test JUMP on multiple synthetic datasets. To summarize our results: on a synthetic video prediction task involving five shapes, we show that JUMP produces frames of a similar image quality to modern video prediction methods. Moreover, JUMP converges more reliably, and can do jumpy predictions. To showcase the flexibility of our model we also apply it to stochastic 3D reconstruction, where our model is conditioned on camera location instead of time. For this, we introduce a dataset that consists of images of 3D scenes containing a cube with random MNIST digits engraved on each of its faces. JUMP outperforms GQN (Eslami et al., 2018) on this dataset, as GQN is unable to capture several correlated frames of occluded regions of the scene. We focus on synthetic datasets so that we can quantify how each model deals with stochasticity. For example, in our 3D reconstruction dataset we can control when models are asked to sample image frames for occluded regions of the scene, to quantify the consistency of these samples. We strongly encourage the reader to check the project website https://bit.ly/2O4Pc4R to view videos of our experiments.To summarize, our key contributions are as follows.1. We motivate and formulate the problem of jumpy stochastic video prediction, where a model has to predict consistent target frames at arbitrary time points, given context frames at arbitrary time points. We observe close connections with consistent stochastic 3D reconstruction tasks, and abstract both problems in a common framework.2. We present a model for consistent jumpy predictions in videos and scenes. Unlike existing video prediction models, our model consumes input frames and samples output frames entirely in parallel. It enforces consistency of the sampled frames by training on multiple correlated targets, sampling a global latent, and using a deterministic rendering network.3. We show strong experimental results for our model. Unlike existing sequential video prediction models, our model can also do jumpy video predictions. We show that our model also produces images of similar quality while converging more reliably. Our model is not limited to video prediction -we develop a dataset for stochastic 3D reconstruction. Here, we show that our model significantly outperforms GQN. We have presented an architecture for learning generative models in the visual domain that can be conditioned on arbitrary points in time or space. Our models can extrapolate forwards or backwards in time, without needing to generate intermediate frames. Moreover, given a small set of contextual frames they can be used to render 3D scenes from arbitrary camera positions. In both cases, they generate consistent sets of frames for a given context, even in the presence of stochasticity. One limitation of our method is that the stochastic latent representation is of a fixed size, which may limit its expressivity in more complicated applications -fixing this limitation and testing on more complex datasets are good avenues for future work. Among other applications, video prediction can be used to improve the performance of reinforcement learning agents on tasks that require lookahead BID21 . In this context, the ability to perform jumpy predictions that look many frames ahead in one go is an important step towards agents that can explore a search space of possible futures, as it effectively divides time into discrete periods. This is an avenue we will be exploring in future work.","Stochastic video prediction models take sequence image frames generate sequence consecutive future image frames. models typically generate future frames autoregressive fashion which is slow requires input output frames consecutive. introduce model overcomes drawbacks generating latent representation arbitrary set frames can then be used simultaneously efficiently sample temporally consistent frames arbitrary time-points example where our where a model can jump directly sample frames end video without sampling intermediate frames. Synthetic video evaluations confirm substantial gains speed functionality without loss fidelity. also apply framework 3D scene reconstruction dataset. model is conditioned camera location can sample consistent sets images what an occluded region 3D scene might look like even if there are multiple possibilities what that region might contain. Reconstructions videos are available https://bit.ly/2O4Pc4R. ability fill gaps high-dimensional data is a fundamental cognitive skill. Suppose glance window see person uniform approaching gate carrying letter. can easily imagine what will(what(probably happen seconds later. person will walk path push letter door. suppose glance window following day see person uniform walking path away house. can easily imagine what will(what(probably happened seconds earlier. person came gate walked path delivered letter. Moreover instances can visualize scene different viewpoints. vantage point window can imagine how things might look gate front door even neighbour's roof. Essentially have learned past experience unfolding visual scenes how to flexibly extrapolate interpolate time space. Replicating ability is a significant challenge AI.To make precise let's first consider traditional video prediction setup. Video prediction is typically framed sequential forward prediction task. Given sequence framesf1... f model is tasked generate future frames follow f+1... f T. Existing models BID0 BID7 carry prediction autoregressive manner sequentially sampling framef+n p f+n|f1... f+n−1.This traditional setup is often limiting -in many cases are interested what happens seconds input sequence. example where our where a model based planning tasks might want predict what framef might care what intermediate framesf+1... f −1 are. Existing models must still produce intermediate frames which is inefficient. Instead where our where a model is jumpy -it can directly sample frames future bypassing intermediate frames. example 40-frame video where our where a model can sample final frame 12 times faster autoregressive model like SV2P BID0.More generally existing forward video prediction models are not flexible filling gaps data. Instead where our where a model can sample frames arbitrary time points video given set frames arbitrary time points context. can,example used infer backwards interpolate frames easily forwards. model is also autoregressive input output frames -it takes input frame parallel samples output frame parallel.In setup jumpy video prediction where our where a model is given framesf1... fn single video along arbitrary time-points 1... n which those frames occurred. clear 1... n need consecutive even increasing order. model is then asked sample plausible frames arbitrary time points 1... k. many cases are multiple possible predicted frames given context making problem stochastic. example car moving towards intersection could turn left turn right. Although model is not autoregressive set k sampled frames is consistent single coherent possibility maintaining diversity across sets samples. is,in sampled set k sampled frames correspond car moving left correspond car moving right.At high level where our where a model JUMP takes input frames samples stochastic latent models stochasticity video. Given arbitrary query time-point where our where a model uses sampled latent render frame time-point model is not autoregressive input output frames still captures correlations multiple target frames. method is not restricted video prediction. When conditioned camera position where our where a model can sample consistent sets images what an occluded region scene even if there are multiple possibilities what that region might contain.We test JUMP multiple synthetic datasets. summarize results:synthetic video prediction task involving five shapes show JUMP produces frames similar image quality modern video prediction methods. Moreover JUMP converges reliably can do jumpy predictions. showcase flexibility model also apply stochastic 3D reconstruction where our where a model is conditioned camera location instead time. introduce dataset consists images 3D scenes containing cube random MNIST digits engraved faces. JUMP outperforms GQN Eslamietal. 2018 dataset GQN is unable capture several correlated frames occluded regions scene. focus synthetic datasets can quantify how each model deals stochasticity. example 3D reconstruction dataset can control when models are asked sample image frames what an occluded regions scene quantify consistency samples. strongly encourage reader check project website https://bit.ly/2O4Pc4R view videos experiments.To summarize key contributions are as follows.1 follows.1 motivate formulate problem jumpy stochastic video prediction where our where a model has to predict consistent target frames arbitrary time points given context frames arbitrary time points. observe close connections consistent stochastic 3D reconstruction tasks abstract problems common framework.2 present model consistent jumpy predictions videos scenes. Unlike existing video prediction models where our where a model consumes input frames samples output frames entirely parallel. enforces consistency sampled frames training multiple correlated targets sampling global latent using deterministic rendering network.3 show strong experimental results model. Unlike existing sequential video prediction models where our where a model can also do jumpy video predictions. show model also produces images similar quality converging reliably. model is not limited video prediction -we develop dataset stochastic 3D reconstruction. show model significantly outperforms GQN. have presented architecture learning generative models visual domain can be conditioned arbitrary points time space. models can extrapolate forwards backwards time without needing generate intermediate frames. Moreover given small set contextual frames can be used render 3D scenes arbitrary camera positions. cases generate consistent sets frames given context even presence stochasticity. One limitation method is that the stochastic latent representation is of a fixed size may limit expressivity complicated applications -fixing limitation testing complex datasets are good avenues future work. Among applications video prediction can be used improve performance reinforcement learning agents tasks require lookahead BID21. context ability perform jumpy predictions look many frames ahead onego is an important step towards agents can explore search space possible futures effectively divides time discrete periods. is an avenue will be exploring future work.",1716,1215,501,0.021,1.412,2025/11/05 17:19:06,0.01,1.58,0.2554517133956382,548.889
"The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn’t. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the sign of the stochastic gradient, whereas the update magnitude is solely determined by an estimate of its relative variance. We  disentangle these two aspects and analyze them in isolation, shedding light on ADAM ’s inner workings. Transferring the ""variance adaptation” to momentum- SGD gives rise to a novel method, completing the practitioner’s toolbox for problems where ADAM fails. Many prominent machine learning models pose empirical risk minimization problems of the form DISPLAYFORM0 where θ ∈ R d is a vector of parameters, {x 1 , . . . , x M } a training set, and (θ; x) is a loss quantifying the performance of parameter vector θ on example x. Computing the exact gradient in each step of an iterative optimization algorithm becomes inefficient for large M . Instead, we construct a minibatch B ⊂ {1, . . . , M } of |B| M data points sampled uniformly and independently from the training set and compute an approximate stochastic gradient DISPLAYFORM1 which is an unbiased estimate, E[g(θ)] = ∇L(θ). We will denote by σ(θ) The basic stochastic optimizer is stochastic gradient descent (SGD, Robbins & Monro, 1951) and its momentum variants (Polyak, 1964; Nesterov, 1983) . A number of methods, widely-used in the deep learning community, choose per-element update magnitudes based on the history of stochastic gradient observations. Among these are ADAGRAD (Duchi et al., 2011) , RMSPROP (Tieleman & Hinton, 2012) , ADADELTA (Zeiler, 2012) and ADAM (Kingma & Ba, 2015) . We have argued that ADAM combines two aspects: taking signs and variance adaptation. Our separate analysis of both aspects provides some insight into the inner workings of this method. Taking the sign can be beneficial, but does not need to be. Our theoretical analysis suggests that it depends on the interplay of stochasticity, the conditioning of the problem, and its ""axis-alignment"". Our experiments confirm that sign-based methods work well on some, but not all problems.Variance adaptation can be applied to any stochastic update direction. In our experiments it was beneficial in all cases, but its effect can sometimes be minuscule. M-SVAG, a variance-adapted variant of momentum-SGD, is a useful addition to the practitioner's toolbox for problems where sign-based methods like ADAM fail. Its memory and computation cost are identical to ADAM and it has two hyper-parameters, the momentum constant µ and the global step size α. Our TensorFlow (Abadi et al., 2015) implementation of this method will be made available upon publication. MNIST We train a simple fully-connected neural network with three hidden layers of 1000, 500 and 100 units with ReLU activation. The output layer has 10 units with softmax activation. We use the cross-entropy loss function and apply L 2 -regularization on all weights, but not the biases. We use a batch size of 128. The global learning rate α stays constant.",ADAM optimizer is exceedingly popular deep learning community. Often works well sometimes doesnt. Why? interpret ADAM combination two aspects:weight update direction is determined sign stochastic gradient whereas update magnitude is solely determined estimate relative variance. disentangle two aspects analyze isolation shedding light ADAM inner workings. Transferring variance adaptation momentum- SGD gives rise novel method completing practitioners toolbox problems where ADAM fails. Many prominent machine learning models pose empirical risk minimization problems form DISPLAYFORM0 whereθ∈R is a vector parameters x1 x training set θ;x is a loss quantifying performance parameter vectorθ examplex. Computing exact gradient step iterative optimization algorithm becomes inefficient large M. Instead construct minibatchB⊂ 1 |B| data points sampled uniformly independently training set compute approximate stochastic gradient DISPLAYFORM1 which is an unbiased estimate E g θ ∇L θ will denote σ θ basic stochastic optimizer is stochastic gradient descent SGD Robbins Monro 1951 momentum variants Polyak 1964;Nesterov 1983 number methods widely-used deep learning community choose per-element update magnitudes based history stochastic gradient observations. Among are ADAGRAD Duchietal. 2011 RMSPROP Tieleman Hinton 2012 ADADELTA Zeiler 2012 ADAM Kingma Ba 2015 have argued ADAM combines two aspects:taking signs variance adaptation. separate analysis aspects provides insight inner workings method. Taking sign can be beneficial does not need be. theoretical analysis suggests depends interplay stochasticity conditioning problem axis-alignment experiments confirm sign-based methods work well problems.Variance adaptation can be applied stochastic update direction. experiments was beneficial cases effect can sometimes minuscule. M-SVAG variance-adapted variant momentum-SGD is a useful addition practitioner's toolbox problems where sign-based methods like ADAM fail. memory computation cost are identical ADAM has two hyper-parameters momentum constantµ global step sizeα. TensorFlow Abadietal. 2015 implementation method will be made available upon publication. MNIST train simple fully-connected neural network three hidden layers 1000 500 100 units ReLU activation. output layer has 10 units softmax activation. use cross-entropy loss function apply L 2 -regularization weights biases. use batch size 128. global learning rateα stays constant.,699,462,237,0.006,1.513,2025/11/05 17:19:06,0.0,1.391,0.5700934579439247,234.537
"We propose a novel framework to adaptively adjust the dropout rates for the deep neural network based on a Rademacher complexity bound. The state-of-the-art deep learning algorithms impose dropout strategy to prevent feature co-adaptation. However, choosing the dropout rates remains an art of heuristics or relies on empirical grid-search over some hyperparameter space. In this work, we show the network Rademacher complexity is bounded by a function related to the dropout rate vectors and the weight coefficient matrices. Subsequently, we impose this bound as a regularizer and provide a theoretical justified way to trade-off between model complexity and representation power. Therefore, the dropout rates and the empirical loss are unified into the same objective function, which is then optimized using the block coordinate descent algorithm. We discover that the adaptively adjusted dropout rates converge to some interesting distributions that reveal meaningful patterns.Experiments on the task of image and document classification also show our method achieves better performance compared to the state-of the-art dropout algorithms. Dropout training BID19 has been proposed to regularize deep neural networks for classification tasks. It has been shown to work well in reducing co-adaptation of neurons-and hence, preventing model overfitting. The idea of dropout is to stochastically set a neuron's output to zero according to Bernoulli random variables. It has been a crucial component in the winning solution to visual object recognition on ImageNet BID7 . Ever since, there have been many follow-ups on novel learning algorithms (Goodfellow et al., 2013; BID1 , regularization techniques BID23 , and fast approximations BID25 .However , the classical dropout model has a few limitations. First, the model requires to specify the retain rates, i.e., the probabilities of keeping a neuron's output, a priori to model training. Subsequently , these retain rates are kept fixed throughout the training process thereafter. It is often not clear how to choose the retain rates in an optimal way. They are usually set via grid-search over hyper-parameter space or simply according to some rule-of-thumb. Another limitation is that all neurons in the same layer share the same retain rate. This exponentially reduces the search space of hyper-parameter optimization. For example, BID19 use a fixed retain probability throughout training for all dropout variables in each layer.In this paper, we propose a novel regularizer based on the Rademacher complexity of a neural network BID16 . Without loss of generality , we use multilayer perceptron with dropout as our example and prove its Rademacher complexity is bounded by a term related to the dropout probabilities. This enables us to explicitly incorporate the model complexity term as a regularizer into the objective function.This Rademacher complexity bound regularizer provides us a lot of flexibility and advantage in modeling and optimization. First, it combines the model complexity and the loss function in an unified objective. This offers a viable way to trade-off the model complexity and representation power through the regularizer weighting coefficient. Second, since this bound is a function of dropout probabilities, we are able to incorporate them explictly into the computation graph of the optimization procedure. We can then adaptively optimize the objective and adjust the dropout probabilities throughout training in a way similar to ridge regression and the lasso BID4 . Third, our proposed regularizer assumes a neuron-wise dropout manner and models different neurons to have different retain rates during the optimization. Our empirical results demonstrate interesting trend on the changes in histograms of dropout probabilities for both hidden and input layers. We also discover that the distribution over retain rates upon model convergence reveals meaningful pattern on the input features.To the best of our knowledge, this is the first ever effort of using the Rademacher complexity bound to adaptively adjust the dropout probabilities for the neural networks. We organize the rest of the paper as following . Section 2 reviews some past approaches well aligned with our motivation, and highlight some major difference to our proposed approach. We subsequently detail our proposed approach in Section 3. In Section 4, we present our thorough empirical evaluations on the task of image and document classification on several benchmark datasets. Finally, Section 5 concludes this paper and summarizes some possible future research ideas. Imposing regularizaiton for a better model generalization is not a new topic. However we tackle the problem for the dropout neural network regularization in a different way. The theoretical upper bound we proved on the Rademacher complexity facilitates us to directly incorporate the dropout rates into the objective function. In this way the dropout rate can be optimized by block coordinate descent procedure with one consistent objective. Our empirical evaluation demonstrates promising results and interesting patterns on adapted retain rates.In the future, we would like to investigate the sparsity property of the learnt retain rates to encourage a sparse representation of the data and the neural network structure BID26 , similar to the sparse Bayesian models and relevance vector machine BID21 . We would also like to explore the applications of deep network compression (Han et al., 2015a; BID5 BID13 BID9 . In addition, one other possible research direction is to dynamically adjust the architecture of the deep neural networks BID17 BID3 Guo et al., 2016) , and hence reduce the model complexity via dropout rates. Features include words associated with the 20 largest and smallest retain rates, as well as a collection of movie related entities, e.g., actor, director, etc. From our model, words like ""love"", ""great"", ""terribl(e)"", ""perfect"", ""uniqu(e)"", ""fine(st)"", ""supris(e)"", and ""silli(y)"" yield large retain rates and hence are indicative feature for predication (in the top half). On the other hand, words like ""say"", ""pretti(y)"", ""young"", ""review"", ""role"", ""anim(ation)"" and ""actual"" have near zero retain rates upon model convergence, which are less informative. For named entities that are relevant to movie industry, we also observe some interesting pattern. Some actors (e.g., ""baldwin"" and ""kidman"", etc.) and directors (e.g., ""kurosawa"" and ""eastwood"" etc.), yield high retain rates shortly after initialization. The retain rates of actors like ""downey"" or ""spacey"", and directors like ""spielberg"" or ""cameron"" slightly increase or remain similar throughout optimization. Note that higher retain rate means the corresponding features are more indicative in classifying IMDB reviews into positive or negative labels, i.e., no explicit association with the label itself. Proof. In the analysis of Rademacher complexity, we treat the functions fed into the neurons of the l th layer as one function class F l = f l (x; w :l ). Here again we are using the notation w :l = {w 1 , . . . , w l }, and w = w :L . As a consequence ∀j, f DISPLAYFORM0 Note here f L (x; W ) used in section 3 is a vector, but f L (x; w) used in this subsection is a scalar. The connection between f L (x; W ) and f L (x; w) is that each dimension of f L (x; W ) is viewed as one instance coming from the same function classs f L (x; w). Similar ways of proof have been adopted in BID24 .To simplify our analysis, we follow BID24 and reformulate the cross-entropy loss on top of the softmax into a single logistic function DISPLAYFORM1 .The function class fed into the neurons of the l th layer f l (x; w :l ) admits a recursive expression DISPLAYFORM2 Given the neural network function (1) and the logistic loss function l is 1 Lipschitz, by Contraction lemma (a variant of the lemma 26.9 on page 381, Chapter 26 of BID16 ), the empirical Rademacher complexity of the loss function is bounded by DISPLAYFORM3 Note the empirical Rademacher complexity of the function class of the L th layer, i.e., the last output layer, is DISPLAYFORM4 To prove the bound in a recursive way, let's also define a variant of the Rademacher complexity with absolute value inside the supremum: DISPLAYFORM5 Note hereR S (f ) is not exactly the same as the Rademacher complexity defined before in this paper. And we have DISPLAYFORM6 Now we start the recursive proof. The empirical Rademacher complexity (with absolute value inside supremum) of the function class of the l th layer is DISPLAYFORM7 DISPLAYFORM8 By the calculous of Rademacher complexity, DISPLAYFORM9 Now we havê DISPLAYFORM10 Let g DISPLAYFORM11 Combining the inequalities (6), FORMULA22 , FORMULA5 , FORMULA5 , and (19), we have DISPLAYFORM12",propose novel framework adaptively adjust dropout rates deep neural network based Rademacher complexity bound. state-of-the-art deep learning algorithms impose dropout strategy prevent feature co-adaptation However choosing dropout rates remains art heuristics relies empirical grid-search hyperparameter space. work show network Rademacher complexity is bounded function related dropout rate vectors weight coefficient matrices. Subsequently impose bound regularizer provide theoretical justified way trade-off model complexity representation power. Therefore dropout rates empirical loss are unified objective function which is then optimized using block coordinate descent algorithm. discover adaptively adjusted dropout rates converge interesting distributions reveal meaningful patterns.Experiments task image document classification also show method achieves better performance compared state-of the-art dropout algorithms. Dropout training BID19 has been proposed regularize deep neural networks classification tasks. has been shown work well reducing co-adaptation neurons-and hence preventing model overfitting. idea dropout is to stochastically set neuron's output zero according Bernoulli random variables. has been a crucial component winning solution visual object recognition ImageNet BID7. Ever since have been many follow-ups novel learning algorithms Goodfellowetal. 2013;BID1 regularization techniques BID23 fast approximations BID25.However classical dropout model has a few limitations. First model requires specify retain rates.e probabilities keeping neuron's output priori model training. Subsequently retain rates are kept fixed throughout training process thereafter. is often clear how to choose retain rates optimal way. are usually set via grid-search hyper-parameter space simply according rule-of-thumb Another limitation is that all neurons layer share retain rate. exponentially reduces search space hyper-parameter optimization. example BID19 use fixed retain probability throughout training dropout variables layer.In paper propose novel regularizer based Rademacher complexity neural network BID16. Without loss generality use multilayer perceptron dropout example prove Rademacher complexity is bounded term related dropout probabilities. enablesus explicitly incorporate model complexity term regularizer objective function.This Rademacher complexity bound regularizer providesus lot flexibility advantage modeling optimization. First combines model complexity loss function unified objective. offers viable way trade-off model complexity representation power regularizer weighting coefficient. Second since bound is a function dropout probabilities are able incorporate explictly computation graph optimization procedure. can then adaptively optimize objective adjust dropout probabilities throughout training way similar ridge regression lasso BID4. Third proposed regularizer assumes neuron-wise dropout manner models different neurons have different retain rates optimization. empirical results demonstrate interesting trend changes histograms dropout probabilities hidden input layers. also discover distribution retain rates upon model convergence reveals meaningful pattern input features.To best knowledge is the first ever effort using Rademacher complexity bound adaptively adjust dropout probabilities neural networks. organize rest paper following. Section 2 reviews past approaches well aligned motivation highlight major difference proposed approach. subsequently detail proposed approach Section3. Section4 present thorough empirical evaluations task image document classification several benchmark datasets. Finally Section 5 concludes paper summarizes possible future research ideas. Imposing regularizaiton better model generalization is not a new topic. However tackle problem dropout neural network regularization different way. theoretical upper bound proved Rademacher complexity facilitatesus directly incorporate dropout rates objective function. way dropout rate can be optimized block coordinate descent procedure one consistent objective. empirical evaluation demonstrates promising results interesting patterns adapted retain rates.In future would like investigate sparsity property learnt retain rates encourage sparse representation data neural network structure BID26 similar sparse Bayesian models relevance vector machine BID21. would also like explore applications deep network compression Hanetal. 2015a;BID5 BID13 BID9. addition one possible research direction is to dynamically adjust architecture deep neural networks BID17 BID3 Guoetal. 2016 hence reduce model complexity via dropout rates. Features include words associated 20 largest smallest retain rates well collection movie related entities e.g actor director etc. model words like love great terribl e perfect uniqu e fine st supris e silli yield large retain rates hence are are more indicative feature predication top half hand words like say pretti young review role anim ation actual have near zero retain rates upon model convergence which are less informative. named entities are relevant movie industry also observe interesting pattern. actors e.g baldwin kidman etc. directors e.g kurosawa eastwood etc. yield high retain rates shortly initialization. retain rates actors like downey spacey directors like spielberg cameron slightly increase remain similar throughout optimization. Note higher retain rate means corresponding features are are more indicative classifying IMDB reviews positive negative labels.e explicit association label itself. Proof. analysis Rademacher complexity treat functions fed neurons l th layer one function classF l fl x;w:l are using notationw:l w1 wl w w:L. consequence∀j f DISPLAYFORM0 Note fL x;W used section3 is a vector fL x;w used subsection is a scalar. connection fL x;W fL x;w is that each dimension fL x;W is viewed one instance coming function classsfL x;w Similar ways proof have been adopted BID24.To simplify analysis follow BID24 reformulate cross-entropy loss top softmax single logistic function DISPLAYFORM1.The function class fed neurons l th layerf l x;w:l admits recursive expression DISPLAYFORM2 Given neural network function 1 logistic loss functionl is 1 Lipschitz Contraction lemma variant lemma 26.9 page 381 Chapter26 BID16 empirical Rademacher complexity loss function is bounded DISPLAYFORM3 Note empirical Rademacher complexity function class L th layer.e last output layer is DISPLAYFORM4 prove bound recursive way let's also define variant Rademacher complexity absolute value inside supremum:DISPLAYFORM5 Note hereR f is not exactly Rademacher complexity defined paper. have DISPLAYFORM6 start recursive proof. empirical Rademacher complexity absolute value inside supremum function class l th layer is DISPLAYFORM7 DISPLAYFORM8 calculous Rademacher complexity DISPLAYFORM9 havê DISPLAYFORM10 Letg DISPLAYFORM11 Combining inequalities 6 FORMULA22 FORMULA5 FORMULA5 19 have DISPLAYFORM12,1797,1210,587,0.02,1.485,2025/11/05 17:19:06,0.01,1.718,0.4828660436137073,532.403
"Sensor fusion is a key technology that integrates various sensory inputs to allow for robust decision making in many applications such as autonomous driving and robot control. Deep neural networks have been adopted for sensor fusion in a body of recent studies. Among these, the so-called netgated architecture was proposed, which has demonstrated improved performances over the conventional convolu- tional neural networks (CNN). In this paper, we address several limitations of the baseline negated architecture by proposing two further optimized architectures: a coarser-grained gated architecture employing (feature) group-level fusion weights and a two-stage gated architectures leveraging both the group-level and feature- level fusion weights. Using driving mode prediction and human activity recogni- tion datasets, we demonstrate the significant performance improvements brought by the proposed gated architectures and also their robustness in the presence of sensor noise and failures.
 Sensor fusion is an essential technology to autonomous systems such as self-driving cars and mobile robots. In advanced driver-assistance systems (ADAS), many sensors such as cameras, ultrasonic sensors, and LiDARs are utilized for enhanced safety and driving experience. Sensor fusion based vehicle and robot control technologies have been explored BID9 BID7 BID4 BID2 BID8 . In addition, devices like smartphones and smartwatches typically integrate a number of sensors, making these devices a suitable platform for running sensor fusion applications such as activity recognition. Several sensor fusion techniques for activity recognition have been proposed BID10 BID3 BID11 BID5 .More specifically, in BID2 , a deep reinforcement learning based sensor fusion algorithm is discussed for robot control. A Kuka YouBot is used with multiple LiDAR sensors for simulations. In terms of sensor fusion, early fusion which concatenates all inputs as feature planes is compared with three other fusion techniques: concatenating convolution layer outputs, reducing the concatenated features with a 1x1 convolution, and accumulating convolution outputs. However, sensor noise and failures are not considered in this work. In addition , due to the fact that only the same type of sensory inputs is used in the experiments, the performance of sensor fusion based on different kinds of sensory inputs is unclear.Among sensor fusion techniques employed in automobiles, BID9 exploit neural networks with a Kalman filter for vehicle roll angle estimation, and show the advantage of using an inertial measurement unit (IMU) without additional suspension deflection sensors. BID7 consider a sensor-rich platform with a learning algorithm for maneuver prediction. Long short-term memory (LSTM) networks, which are a type of recurrent neural networks (RNN) are used with sensory inputs from cameras, GPS, and speedometers. BID4 propose joint probabilistic data fusion for road environments. However, neither a multiplicity of sensory inputs nor sensory noise and failures are considered. The adopted architecture is simplistic where input data are only fused in one layer.In the field of wearable devices, BID10 utilize early fusion, which concatenates sensory inputs. With this simple fusion approach, classical supervised learning methods such as Bayesian classifiers, k-nearest-neighbors, support vector machines, and artificial neural networks are compared. BID3 use deep convolutional neural networks with IMU data. BID11 use a CNN with angle embedded gate dynamic images, which are pre-processed inputs for gait recognition. BID5 summarize three fusion methods, namely, data, feature, and decision level fusion. However, effective sensor fusion network architectures for coping with sensor failures are not deeply investigated.In terms of sensor fusion architectures, BID8 propose a so-called netgated architecture in which the information flow in a given convolutional neural network (CNN) is gated by fusion weights extracted from camera and LiDAR inputs. These fusion weights are used for computing a weighted sum of the sensory inputs. The weighted sum passes through fully connected layers to create a steering command. The gated networks (netgated) is shown to be robust to sensor failures, comparing to basic CNNs. However, a deep understanding of the relationships between sensory inputs, fusion weights, network architecture, and the resulting performances are not examined.The main objective of this paper is to propose optimized gated architectures that can address three limitations of the baseline netgated architecture of BID8 and investigate how different fusion architectures operate under clean sensory data and in the presence of snesor noise and failures. Our main contributions are:• Propose a new coarser-grained gated architecture which learns robustly a set of fusion weights at the (feature) group level;• Further propose a two-stage gating architecture which exploits both the feature-level and group-level fusion weights, leading to further performance improvements.• Analyze the characteristics of the proposed architectures and show how they may address the limitations of the negated architecture in terms of inconsistency of fusion weights, overfitting, and lack of diverse fusion mechanisms.By utilizing driving mode prediction and human activity recognition datasets, we demonstrate the significant performance improvements brought by the proposed architectures over the conventional CNN and netgated architectures under various settings including cases where random sensor noise and failures are presented. Empirical evidence is also analyzed to help shed light on the underlying causes that may be responsible for the observed improvements of the two proposed architectures.",Sensor fusion is a key technology integrates various sensory inputs allow robust decision making many applications autonomous driving robot control. Deep neural networks have been adopted sensor fusion body recent studies. Among so-called netgated architecture was proposed which has demonstrated improved performances conventional convolu- tional neural networks CNN paper address several limitations baseline negated architecture proposing two optimized architectures:coarser-grained gated architecture employing feature group-level fusion weights two-stage gated architectures leveraging group-level feature- level fusion weights. Using driving mode prediction human activity recogni- tion datasets demonstrate significant performance improvements brought proposed gated architectures also robustness presence sensor noise failures. Sensor fusion is an essential technology autonomous systems self-driving cars mobile robots. advanced driver-assistance systems ADAS many sensors cameras ultrasonic sensors LiDARs are utilized enhanced safety driving experience. Sensor fusion based vehicle robot control technologies have been explored BID9 BID7 BID4 BID2 BID8. addition devices like smartphones smartwatches typically integrate number sensors making devices suitable platform running sensor fusion applications activity recognition. Several sensor fusion techniques activity recognition have been proposed BID10 BID3 BID11 BID5.More specifically BID2 deep reinforcement learning based sensor fusion algorithm is discussed robot control. Kuka YouBot is used multiple LiDAR sensors simulations. terms sensor fusion early fusion which concatenates inputs feature planes is compared three fusion techniques:concatenating convolution layer outputs reducing concatenated features 1x1 convolution accumulating convolution outputs. However sensor noise failures are not are considered work. addition due fact type sensory inputs is used experiments performance sensor fusion based different kinds sensory inputs is unclear.Among sensor fusion techniques employed automobiles BID9 exploit neural networks Kalman filter vehicle roll angle estimation show advantage using inertial measurement unit IMU without additional suspension deflection sensors. BID7 consider sensor-rich platform learning algorithm maneuver prediction. Long short-term memory LSTM networks which are a type recurrent neural networks RNN are used sensory inputs cameras GPS speedometers. BID4 propose joint probabilistic data fusion road environments. However neither multiplicity sensory inputs sensory noise failures are not are considered. adopted architecture is simplistic where input data are only fused one layer.In field wearable devices BID10 utilize early fusion which concatenates sensory inputs. simple fusion approach classical supervised learning methods Bayesian classifiers k-nearest-neighbors support vector machines artificial neural networks are compared. BID3 use deep convolutional neural networks IMU data. BID11 use CNN angle embedded gate dynamic images which are pre-processed inputs gait recognition. BID5 summarize three fusion methods namely data feature decision level fusion. However effective sensor fusion network architectures coping sensor failures are not deeply investigated.In terms sensor fusion architectures BID8 propose so-called netgated architecture which the information flow given convolutional neural network CNN is gated fusion weights extracted camera LiDAR inputs. fusion weights are used computing weighted sum sensory inputs. weighted sum passes fully connected layers create steering command. gated networks netgated is shown robust sensor failures comparing basic CNNs. However deep understanding relationships sensory inputs fusion weights network architecture resulting performances are not examined.The main objective paper is to propose optimized gated architectures can address three limitations baseline netgated architecture BID8 investigate how different fusion architectures operate clean sensory data presence snesor noise failures. main contributions are:• Propose new coarser-grained gated architecture which learns robustly set fusion weights feature group level;• propose two-stage gating architecture which exploits feature-level group-level fusion weights leading performance improvements.• Analyze characteristics proposed architectures show may address limitations negated architecture terms inconsistency fusion weights overfitting lack diverse fusion mechanisms.By utilizing driving mode prediction human activity recognition datasets demonstrate significant performance improvements brought proposed architectures conventional CNN netgated architectures various settings including cases where random sensor noise failures are presented. Empirical evidence is also analyzed help shed light underlying causes may responsible observed improvements two proposed architectures.,1027,752,275,0.009,1.366,2025/11/05 17:19:06,0.0,1.405,0.1121495327102804,314.839
"We develop a mean field theory for batch normalization in fully-connected feedforward neural networks. In so doing, we provide a precise characterization of signal propagation and gradient backpropagation in wide batch-normalized networks at initialization. Our theory shows that gradient signals grow exponentially in depth and that these exploding gradients cannot be eliminated by tuning the initial weight variances or by adjusting the nonlinear activation function. Indeed, batch normalization itself is the cause of gradient explosion. As a result, vanilla batch-normalized networks without skip connections are not trainable at large depths for common initialization schemes, a prediction that we verify with a variety of empirical simulations. While gradient explosion cannot be eliminated, it can be reduced by tuning the network close to the linear regime, which improves the trainability of deep batch-normalized networks without residual connections. Finally, we investigate the learning dynamics of batch-normalized networks and observe that after a single step of optimization the networks achieve a relatively stable equilibrium in which gradients have dramatically smaller dynamic range. Our theory leverages Laplace, Fourier, and Gegenbauer transforms and we derive new identities that may be of independent interest. Deep neural networks have been enormously successful across a broad range of disciplines. These successes are often driven by architectural innovations. For example, the combination of convolutions BID15 , residual connections BID12 , and batch normalization BID13 has allowed for the training of very deep networks and these components have become essential parts of models in vision (Zoph et al.) , language BID4 , and reinforcement learning (Silver et al., 2017) . However, a fundamental problem that has accompanied this rapid progress is a lack of theoretical clarity. An important consequence of this gap between theory and experiment is that two important issues become conflated. In particular, it is generally unclear whether novel neural network components improve generalization or whether they merely increase the fraction of hyperparameter configurations where good generalization can be achieved. Resolving this confusion has the promise of allowing researchers to more effectively and deliberately design neural networks.Recently, progress has been made (Poole et al., 2016; Schoenholz et al., 2016; BID6 BID16 BID11 in this direction by considering neural networks at initialization, before any training has occurred. In this case, the parameters of the network are random variables which induces a distribution of the activations of the network as well as the gradients. Studying these distributions is equivalent to understanding the prior over functions that these random neural networks compute. Picking hyperparameters that correspond to well-conditioned priors ensures that the neural network will be trainable and this fact has been extensively verified experimentally. However, to fulfill its promise of making neural network design less of a black box, these techniques must be applied to neural network architectures that are used in practice. Over the past year, this gap has closed significantly and theory for networks with skip connections (Yang & Schoenholz, 2017; , convolutional networks (Xiao et al., 2018) , and gated recurrent networks BID3 BID9 have been developed. More recently, Yang (2019) devised a formalism that extends this approach to include an even wider range of architectures.Before state-of-the-art models can be analyzed in this framework, a slowly-decreasing number of architectural innovations must be studied. One particularly important component that has thus-far remained elusive is batch normalization.Our Contributions. In this paper, we develop a theory of fully-connected networks with batch normalization whose weights and biases are randomly distributed. A significant complication in the case of batch normalization (compared to e.g. layer normalization or weight normalization) is that the statistics of the network depend non-locally on the entire batch. Thus, our first main result is to recast the theory for random fully-connected networks so that it can be applied to batches of data. We then extend the theory to include batch normalization explicitly and validate this theory against Monte-Carlo simulations. We show that as in previous cases we can leverage our theory to predict valid hyperparameter configurations.In the process of our investigation, we identify a number of previously unknown properties of batch normalization that make training unstable. In particular, for most nonlinearities used in practice, batchnorm in a deep, randomly initialized network induces high degree of symmetry in the embeddings of the samples in the batch (Thm 3.4) . Whenever this symmetry takes hold, we show that for any choice of nonlinearity, gradients of fully-connected networks with batch normalization explode exponentially in the depth of the network (Thm 3.9) . This imposes strong limits on the maximum trainable depth of batch normalized networks. This limit can be lifted partially but not completely by pushing activation functions to be more linear at initialization. It might seem that such gradient explosion ought to lead to learning dynamics that are unfavorable. However, we show that networks with batch normalization causes the scale of the gradients to naturally equilibrate after a single step of gradient descent (provided the initial gradients are not so large as to cause numerical instabilities). For shallower networks, this equilibrating effect is sufficient to allow adequate training.Finally, we note that there is a related vein of research that has emerged that leverages the prior over functions induced by random networks to perform exact Bayesian inference BID16 BID7 BID18 BID8 . One of the natural consequences of this work is that the prior for networks with batch normalization can be computed exactly in the wide network limit. As such, it is now possible to perform exact Bayesian inference in the case of wide neural networks with batch normalization. In this work we have presented a theory for neural networks with batch normalization at initialization. In the process of doing so, we have uncovered a number of counterintuitive aspects of batch normalization and -in particular -the fact that at initialization it unavoidably causes gradients to explode with depth. We have introduced several methods to reduce the degree of gradient explosion, enabling the training of significantly deeper networks in the presence of batch normalization. Finally, this work paves the way for future work on more advanced, state-of-the-art, network architectures and topologies. : Batch norm leads to a chaotic input-output map with increasing depth. A linear network with batch norm is shown acting on two minibatches of size 64 after random orthogonal initialization. The datapoints in the minibatch are chosen to form a 2d circle in input space, except for one datapoint that is perturbed separately in each minibatch (leftmost datapoint at input layer 0). Because the network is linear, for a given minibatch it performs an affine transformation on its inputs -a circle in input space remains an ellipse throughout the network. However, due to batch norm the coefficients of that affine transformation change nonlinearly as the datapoints in the minibatch are changed. (a) Each pane shows a scatterplot of activations at a given layer for all datapoints in the minibatch, projected onto the top two PCA directions. PCA directions are computed using the concatenation of the two minibatches. Due to the batch norm nonlinearity, minibatches that are nearly identical in input space grow increasingly dissimilar with depth. Intuitively, this chaotic input-output map can be understood as the source of exploding gradients when batch norm is applied to very deep networks, since very small changes in an input correspond to very large movements in network outputs. (b) The correlation between the two minibatches, as a function of layer, for the same network. Despite having a correlation near one at the input layer, the two minibatches rapidly decorrelate with depth. See Appendix H for a theoretical treatment.A VGG19 WITH BATCHNORM ON CIFAR100Even though at initialization time batchnorm causes gradient explosion, after the first few epochs, the relative gradient norms ∇ θ L / θ for weight parameters θ = W or BN scale parameter θ = γ, equilibrate to about the same magnitude. See Fig. 7 . with batchnorm on CIFAR100 with data augmentation. We use 8 random seeds for each combination, and assign to each combination the median training/validation accuracy over all runs. We then aggregate these scores here. In the first row we look at training accuracy with different learning rate vs β initialization at different epochs of training, presenting the max over . In the second row we do the same for validation accuracy. In the third row, we look at the matrix of training accuracy for learning rate vs , taking max over β. In the fourth row, we do the same for validation accuracy.",develop mean field theory batch normalization fully-connected feedforward neural networks. provide precise characterization signal propagation gradient backpropagation wide batch-normalized networks initialization. theory shows gradient signals grow exponentially depth exploding gradients cannot eliminated tuning initial weight variances adjusting nonlinear activation function. Indeed batch normalization is the cause gradient explosion. result vanilla batch-normalized networks without skip connections are not trainable large depths common initialization schemes prediction verify variety empirical simulations. gradient explosion cannot eliminated can be reduced tuning network close linear regime which improves trainability deep batch-normalized networks without residual connections. Finally investigate learning dynamics batch-normalized networks observe single step optimization networks achieve relatively stable equilibrium which gradients have dramatically smaller dynamic range. theory leverages Laplace Fourier Gegenbauer transforms derive new identities may independent interest. Deep neural networks have been enormously successful across broad range disciplines. successes are often driven architectural innovations. example combination convolutions BID15 residual connections BID12 batch normalization BID13 has allowed training deep networks components have become essential parts models vision Zophetal. language BID4 reinforcement learning Silveretal. 2017 However fundamental problem has accompanied rapid progress is a lack theoretical clarity. important consequence gap theory experiment is that two important issues become conflated. particular is generally unclear whether novel neural network components improve generalization whether merely increase fraction hyperparameter configurations where good generalization can be achieved. Resolving confusion has the promise allowing researchers effectively deliberately design neural networks.Recently progress has been made Pooleetal. 2016;Schoenholzetal. 2016;BID6 BID16 BID11 direction considering neural networks initialization training has occurred. case parameters network are random variables which induces distribution activations network well gradients. Studying distributions is equivalent understanding prior functions random neural networks compute. Picking hyperparameters correspond well-conditioned priors ensures neural network will be trainable fact has been extensively verified experimentally. However fulfill promise making neural network design less black box techniques must applied neural network architectures are used practice. past year gap has closed significantly theory networks skip connections Yang Schoenholz 2017;convolutional networks Xiaoetal. 2018 gated recurrent networks BID3 BID9 have been developed. recently Yang 2019 devised formalism extends approach include even wider range architectures.Before state-of-the-art models can be analyzed framework slowly-decreasing number architectural innovations must studied. One particularly important component has thus-far remained elusive is batch normalization.Our Contributions. paper develop theory fully-connected networks batch normalization whose weights biases are randomly distributed. significant complication case batch normalization compared e.g layer normalization weight normalization is that the statistics network depend non-locally entire batch. Thus first main result is to recast theory random fully-connected networks can applied batches data. extend theory include batch normalization explicitly validate theory Monte-Carlo simulations. show previous cases can leverage theory predict valid hyperparameter configurations.In process investigation identify number previously unknown properties batch normalization make training unstable. particular nonlinearities used practice batchnorm deep randomly initialized network induces high degree symmetry embeddings samples batch Thm 3.4 Whenever symmetry takes hold show choice nonlinearity gradients fully-connected networks batch normalization explode exponentially depth network Thm 3.9 imposes strong limits maximum trainable depth batch normalized networks. limit can be lifted partially completely pushing activation functions linear initialization. might seem gradient explosion ought lead learning dynamics are unfavorable. However show networks batch normalization causes scale gradients naturally equilibrate single step gradient descent provided initial gradients are not so large cause numerical instabilities shallower networks equilibrating effect is sufficient allow adequate training.Finally note is a related vein research has emerged leverages prior functions induced random networks perform exact Bayesian inference BID16 BID7 BID18 BID8. One natural consequences work is that the prior networks batch normalization can be computed exactly wide network limit. is now possible perform exact Bayesian inference case wide neural networks batch normalization. work have presented theory neural networks batch normalization initialization. process have uncovered number counterintuitive aspects batch normalization -in particular -the fact initialization unavoidably causes gradients explode depth. have introduced several methods reduce degree gradient explosion enabling training significantly deeper networks presence batch normalization. Finally work paves way future work advanced state-of-the-art network architectures topologies. Batch norm leads chaotic input-output map increasing depth. linear network batch norm is shown acting two minibatches size64 random orthogonal initialization. datapoints minibatch are chosen form 2d circle input space except one datapoint is perturbed separately minibatch leftmost datapoint input layer0 network is linear given minibatch performs affine transformation inputs -a circle input space remains ellipse throughout network. However due batch norm coefficients affine transformation change nonlinearly datapoints minibatch are changed. pane shows scatterplot activations given layer datapoints minibatch projected onto top two PCA directions. PCA directions are computed using concatenation two minibatches. Due batch norm nonlinearity minibatches are nearly identical input space grow increasingly dissimilar depth. Intuitively chaotic input-output map can be understood source exploding gradients when batch norm is applied deep networks since small changes input correspond large movements network outputs. b correlation two minibatches function layer network. Despite correlation near one input layer two minibatches rapidly decorrelate depth. See AppendixH theoretical treatment.A VGG19 BATCHNORM CIFAR100Even though initialization time batchnorm causes gradient explosion first epochs relative gradient norms∇ θL/θ weight parametersθ W BN scale parameterθ γ equilibrate magnitude. See Fig. 7. batchnorm CIFAR100 data augmentation. use 8 random seeds combination assign combination median training/validation accuracy runs. aggregate scores here. first row look training accuracy different learning ratevs β initialization different epochs training presenting max over. second row do the same validation accuracy. third row look matrix training accuracy learning ratevs taking max β. fourth row do the validation accuracy.,1720,1153,567,0.022,1.492,2025/11/05 17:19:06,0.01,1.475,0.5046728971962615,545.513
"We present NeuroSAT, a message passing neural network that learns to solve SAT problems after only being trained as a classifier to predict satisfiability.   Although it is not competitive with state-of-the-art SAT solvers, NeuroSAT can solve problems that are substantially larger and more difficult than it ever saw during training by simply running for more iterations. Moreover, NeuroSAT generalizes to novel distributions; after training only on random SAT problems, at test time it can solve SAT problems encoding graph coloring, clique detection, dominating set, and vertex cover problems, all on a range of distributions over small random graphs. The propositional satisfiability problem (SAT) is one of the most fundamental problems of computer science. BID4 showed that the problem is NP-complete, which means that searching for any kind of efficiently-checkable certificate in any context can be reduced to finding a satisfying assignment of a propositional formula. In practice, search problems arising from a wide range of domains such as hardware and software verification, test pattern generation, planning, scheduling, and combinatorics are all routinely solved by constructing an appropriate SAT problem and then calling a SAT solver BID9 . Modern SAT solvers based on backtracking search are extremely well-engineered and have been able to solve problems of practical interest with millions of variables BID2 ).We consider the question: can a neural network learn to solve SAT problems? To answer, we develop a novel message passing neural network (MPNN) BID21 BID16 BID8 , NeuroSAT, and train it as a classifier to predict satisfiability on a dataset of random SAT problems. We provide NeuroSAT with only a single bit of supervision for each SAT problem that indicates whether or not the problem is satisfiable. When making a prediction about a new SAT problem, we find that NeuroSAT guesses unsatisfiable with low confidence until it finds a solution, at which point it converges and guesses satisfiable with very high confidence. The solution itself can almost always be automatically decoded from the network's activations, making NeuroSAT an end-to-end SAT solver. See Figure 1 for an illustration of the train and test regimes.Although it is not competitive with state-of-the-art SAT solvers, NeuroSAT can solve SAT problems that are substantially larger and more difficult than it ever saw during training by simply performing more iterations of message passing. Despite only running for a few dozen iterations during training, at test time NeuroSAT continues to find solutions to harder problems after hundreds and even thousands of iterations. The learning process has yielded not a traditional classifier but rather a procedure that can be run indefinitely to search for solutions to problems of varying difficulty. Our main motivation has been scientific: to better understand the extent to which neural networks are capable of precise, logical reasoning. Our work has definitively established that neural networks can learn to perform discrete search on their own without the help of hard-coded search procedures, even after only end-to-end training with minimal supervision. We found this result surprising and think it constitutes an important contribution to the community's evolving understanding of the capabilities and limitations of neural networks.Although not our primary concern, we also hope that our findings eventually lead to improvements in practical SAT solving. As we stressed early on, as an end-to-end SAT solver the trained NeuroSAT system discussed in this paper is still vastly less reliable than the state-of-the-art. We concede that we see no obvious path to beating existing SAT solvers. One approach might be to continue to train NeuroSAT as an end-to-end solver on increasingly difficult problems. A second approach might be to use a system like NeuroSAT to help guide decisions within a more traditional SAT solver, though it is not clear that NeuroSAT provides any useful information before it finds a satisfying assignment. However, as we discussed in §8, when we trained our architecture on different data it learned an entirely different procedure. In a separate experiment omitted for space reasons, we also trained our architecture to predict whether there is a satisfying assignment involving each individual literal in the problem and found that it was able to predict these bits with high accuracy as well. Unlike NeuroSAT, it made both type I and type II errors, had no discernable phase transition, and could make reasonable predictions within only a few rounds. We believe that architectures descended from NeuroSAT will be able to learn very different mechanisms and heuristics depending on the data they are trained on and the details of their objective functions. We are cautiously optimistic that a descendant of NeuroSAT will one day lead to improvements to the state-of-the-art.",present NeuroSAT message passing neural network learns solve SAT problems trained classifier predict satisfiability. Although is not competitive state-of-the-art SAT solvers NeuroSAT can solve problems are substantially larger difficult ever saw training simply running iterations. Moreover NeuroSAT generalizes novel distributions;training random SAT problems test time can solve SAT problems encoding graph coloring clique detection dominating set vertex cover problems range distributions small random graphs. propositional satisfiability problem SAT is one fundamental problems computer science. BID4 showed problem is NP-complete which means searching kind efficiently-checkable certificate context can be reduced finding satisfying assignment propositional formula. practice search problems arising wide range domains hardware software verification test pattern generation planning scheduling combinatorics are all routinely solved constructing appropriate SAT problem calling SAT solver BID9. Modern SAT solvers based backtracking search are extremely well-engineered have been able solve problems practical interest millions variables BID2.We consider question:can a neural network learn solve SAT problems? answer develop novel message passing neural network MPNN BID21 BID16 BID8 NeuroSAT train classifier predict satisfiability dataset random SAT problems. provide NeuroSAT single bit supervision SAT problem indicates whether problem is satisfiable. When making prediction new SAT problem find NeuroSAT guesses unsatisfiable low confidence finds solution which point converges guesses satisfiable high confidence. solution can almost always automatically decoded network's activations making NeuroSAT end-to-end SAT solver. See Figure1 illustration train test regimes.Although is not competitive state-of-the-art SAT solvers NeuroSAT can solve SAT problems are substantially larger difficult ever saw training simply performing iterations message passing. Despite running dozen iterations training test time NeuroSAT continues find solutions harder problems hundreds even thousands iterations. learning process has yielded traditional classifier rather procedure can be run indefinitely search solutions problems varying difficulty. main motivation has been scientific:better understand extent which neural networks are capable precise logical reasoning. work has definitively established neural networks can learn perform discrete search without help hard-coded search procedures even end-to-end training minimal supervision. found result surprising think constitutes important contribution community's evolving understanding capabilities limitations neural networks.Although primary concern also hope findings eventually lead improvements practical SAT solving. stressed early end-to-end SAT solver trained NeuroSAT system discussed paper is still vastly less reliable state-of-the-art concede see obvious path beating existing SAT solvers. One approach might continue train NeuroSAT end-to-end solver increasingly difficult problems. second approach might use system like NeuroSAT help guide decisions within traditional SAT solver though is not clear NeuroSAT provides useful information finds satisfying assignment. However discussed §8 when we trained architecture different data learned entirely different procedure. separate experiment omitted space reasons also trained architecture predict whether is a satisfying assignment involving individual literal problem found was able predict bits high accuracy well. Unlike NeuroSAT made type type II errors had no discernable phase transition could make reasonable predictions within rounds. believe architectures descended NeuroSAT will be able learn different mechanisms heuristics depending data are trained details objective functions. are cautiously optimistic descendant NeuroSAT will one day lead improvements state-of-the-art,913,601,312,0.009,1.519,2025/11/05 17:19:06,0.0,1.364,0.5887850467289715,302.135
"Spatiotemporal forecasting has various applications in neuroscience, climate and transportation domain. Traffic forecasting is one canonical example of such learning task. The task is challenging due to (1) complex spatial dependency on road networks, (2) non-linear temporal dynamics with changing road conditions and (3) inherent difficulty of long-term forecasting. To address these challenges, we propose to model the traffic flow as a diffusion process on a directed graph and introduce Diffusion Convolutional Recurrent Neural Network (DCRNN), a deep learning framework for traffic forecasting that incorporates both spatial and temporal dependency in the traffic flow. Specifically, DCRNN captures the spatial dependency using bidirectional random walks on the graph, and the temporal dependency using the encoder-decoder architecture with scheduled sampling. We evaluate the framework on two real-world large-scale road network traffic datasets and observe consistent improvement of 12% - 15% over state-of-the-art baselines Spatiotemporal forecasting is a crucial task for a learning system that operates in a dynamic environment. It has a wide range of applications from autonomous vehicles operations, to energy and smart grid optimization, to logistics and supply chain management. In this paper, we study one important task: traffic forecasting on road networks, the core component of the intelligent transportation systems. The goal of traffic forecasting is to predict the future traffic speeds of a sensor network given historic traffic speeds and the underlying road networks. This task is challenging mainly due to the complex spatiotemporal dependencies and inherent difficulty in the long term forecasting. On the one hand, traffic time series demonstrate strong temporal dynamics. Recurring incidents such as rush hours or accidents can cause nonstationarity, making it difficult to forecast longterm. On the other hand, sensors on the road network contain complex yet unique spatial correlations. FIG0 illustrates an example. Road 1 and road 2 are correlated, while road 1 and road 3 are not. Although road 1 and road 3 are close in the Euclidean space, they demonstrate very different behaviors. Moreover, the future traffic speed is influenced more by the downstream traffic than the upstream one. This means that the spatial structure in traffic is nonEuclidean and directional.Traffic forecasting has been studied for decades, falling into two main categories: knowledgedriven approach and data-driven approach. In transportation and operational research, knowledgedriven methods usually apply queuing theory and simulate user behaviors in traffic BID6 . In time series community, data-driven methods such as Auto-Regressive Integrated Moving Average (ARIMA) model and Kalman filtering remain popular BID22 BID21 . However, simple time series models usually rely on the stationarity assumption, which is often violated by the traffic data. Most recently, deep learning models for traffic forecasting have been developed in BID23 ; BID35 , but without considering the spatial structure. BID31 and BID24 model the spatial correlation with Convolutional Neural Networks (CNN), but the spatial structure is in the Euclidean space (e.g., 2D images). BID4 , studied graph convolution, but only for undirected graphs.In this work, we represent the pair-wise spatial correlations between traffic sensors using a directed graph whose nodes are sensors and edge weights denote proximity between the sensor pairs measured by the road network distance. We model the dynamics of the traffic flow as a diffusion process and propose the diffusion convolution operation to capture the spatial dependency. We further propose Diffusion Convolutional Recurrent Neural Network (DCRNN) that integrates diffusion convolution, the sequence to sequence architecture and the scheduled sampling technique. When evaluated on realworld traffic datasets, DCRNN consistently outperforms state-of-the-art traffic forecasting baselines by a large margin. In summary:• We study the traffic forecasting problem and model the spatial dependency of traffic as a diffusion process on a directed graph. We propose diffusion convolution, which has an intuitive interpretation and can be computed efficiently.• We propose Diffusion Convolutional Recurrent Neural Network (DCRNN), a holistic approach that captures both spatial and temporal dependencies among time series using diffusion convolution and the sequence to sequence learning framework together with scheduled sampling. DCRNN is not limited to transportation and is readily applicable to other spatiotemporal forecasting tasks.• We conducted extensive experiments on two large-scale real-world datasets, and the proposed approach obtains significant improvement over state-of-the-art baseline methods. In this paper, we formulated the traffic prediction on road network as a spatiotemporal forecasting problem, and proposed the diffusion convolutional recurrent neural network that captures the spatiotemporal dependencies. Specifically, we use bidirectional graph random walk to model spatial dependency and recurrent neural network to capture the temporal dynamics. We further integrated the encoder-decoder architecture and the scheduled sampling technique to improve the performance for long-term forecasting. When evaluated on two large-scale real-world traffic datasets, our approach obtained significantly better prediction than baselines. For future work, we will investigate the following two aspects (1) applying the proposed model to other spatial-temporal forecasting tasks; (2) modeling the spatiotemporal dependency when the underlying graph structure is evolving, e.g., the K nearest neighbor graph for moving objects.",Spatiotemporal forecasting has various applications neuroscience climate transportation domain. Traffic forecasting is one canonical example learning task. task is challenging due 1 complex spatial dependency road networks 2 non-linear temporal dynamics changing road conditions 3 inherent difficulty long-term forecasting. address challenges propose model traffic flow diffusion process directed graph introduce Diffusion Convolutional Recurrent Neural Network DCRNN deep learning framework traffic forecasting incorporates spatial temporal dependency traffic flow. Specifically DCRNN captures spatial dependency using bidirectional random walks graph temporal dependency using encoder-decoder architecture scheduled sampling. evaluate framework two real-world large-scale road network traffic datasets observe consistent improvement 12% -15% state-of-the-art baselines Spatiotemporal forecasting is a crucial task learning system operates dynamic environment. has a wide range applications autonomous vehicles operations energy smart grid optimization logistics supply chain management. paper study one important task:traffic forecasting road networks core component intelligent transportation systems. goal traffic forecasting is to predict future traffic speeds sensor network given historic traffic speeds underlying road networks. task is challenging mainly due complex spatiotemporal dependencies inherent difficulty long term forecasting. one hand traffic time series demonstrate strong temporal dynamics. Recurring incidents rush hours accidents can cause nonstationarity making difficult forecast longterm. hand sensors road network contain complex yet unique spatial correlations. FIG0 illustrates example. Road1 road2 are correlated road1 road3 are not. Although road1 road3 are close Euclidean space demonstrate different behaviors. Moreover future traffic speed is influenced downstream traffic upstream one. means spatial structure traffic is nonEuclidean directional.Traffic forecasting has been studied decades falling two main categories:knowledgedriven approach data-driven approach. transportation operational research knowledgedriven methods usually apply queuing theory simulate user behaviors traffic BID6. time series community data-driven methods Auto-Regressive Integrated Moving Average ARIMA model Kalman filtering remain popular BID22 BID21. However simple time series models usually rely stationarity assumption which is often violated traffic data. recently deep learning models traffic forecasting have been developed BID23;BID35 without considering spatial structure. BID31 BID24 model spatial correlation Convolutional Neural Networks CNN spatial structure is in the Euclidean space e.g 2D images BID4 studied graph convolution undirected graphs.In work represent pair-wise spatial correlations traffic sensors using directed graph whose nodes are sensors edge weights denote proximity sensor pairs measured road network distance. model dynamics traffic flow diffusion process propose diffusion convolution operation capture spatial dependency. propose Diffusion Convolutional Recurrent Neural Network DCRNN integrates diffusion convolution sequence sequence architecture scheduled sampling technique. When evaluated realworld traffic datasets DCRNN consistently outperforms state-of-the-art traffic forecasting baselines large margin. summary:• study traffic forecasting problem model spatial dependency traffic diffusion process directed graph. propose diffusion convolution which has an intuitive interpretation can be computed efficiently.• propose Diffusion Convolutional Recurrent Neural Network DCRNN holistic approach captures spatial temporal dependencies among time series using diffusion convolution sequence sequence learning framework together scheduled sampling. DCRNN is not limited transportation is readily applicable spatiotemporal forecasting tasks.• conducted extensive experiments two large-scale real-world datasets proposed approach obtains significant improvement state-of-the-art baseline methods. paper formulated traffic prediction road network spatiotemporal forecasting problem proposed diffusion convolutional recurrent neural network captures spatiotemporal dependencies. Specifically use bidirectional graph random walk model spatial dependency recurrent neural network capture temporal dynamics. integrated encoder-decoder architecture scheduled sampling technique improve performance long-term forecasting. When evaluated two large-scale real-world traffic datasets approach obtained significantly better prediction baselines. future work will investigate following two aspects 1 applying proposed model spatial-temporal forecasting tasks;2 modeling spatiotemporal dependency when the underlying graph structure is evolving e.g K nearest neighbor graph moving objects.,1039,750,289,0.01,1.385,2025/11/05 17:19:06,0.0,1.52,0.1713395638629281,309.41
"Obtaining reliable uncertainty estimates of neural network predictions is a long standing challenge. Bayesian neural networks have been proposed as a solution, but it remains open how to specify their prior. In particular, the common practice of a standard normal prior in weight space imposes only weak regularities, causing the function posterior to possibly generalize in unforeseen ways on inputs outside of the training distribution. We propose noise contrastive priors (NCPs) to obtain reliable uncertainty estimates. The key idea is to train the model to output high uncertainty for data points outside of the training distribution. NCPs do so using an input prior, which adds noise to the inputs of the current mini batch, and an output prior, which is a wide distribution given these inputs. NCPs are compatible with any model that can output uncertainty estimates, are easy to scale, and yield reliable uncertainty estimates throughout training. Empirically, we show that NCPs prevent overfitting outside of the training distribution and result in uncertainty estimates that are useful for active learning. We demonstrate the scalability of our method on the flight delays data set, where we significantly improve upon previously published results. Many successful applications of neural networks BID25 BID53 BID57 are in restricted settings where predictions are only made for inputs similar to the training distribution. In real-world scenarios, neural networks can face truly novel data points during inference, and in these settings it can be valuable to have good estimates of the model's uncertainty. For example, in healthcare, reliable uncertainty estimates can prevent overconfident decisions for rare or novel patient conditions BID49 . Similarly, autonomous agents that actively explore their environment can use uncertainty estimates to decide what data points will be most informative.Epistemic uncertainty describes the amount of missing knowledge about the data generating function. Uncertainty can in principle be completely reduced by observing more data points at the right locations and training on them. In contrast, the data generating function may also have inherent randomness, which we call aleatoric noise. This noise can be captured by models outputting a distribution rather than a point prediction. Obtaining more data points allows the noise estimate to move closer to the true value, which is usually different from zero. For active learning, it is crucial to separate the two types of randomness: we want to acquire labels in regions of high uncertainty but low noise BID36 .Bayesian analysis provides a principled approach to modeling uncertainty in neural networks BID8 BID37 . Namely, one places a prior over the network's weights and biases. This effectively places a distribution over the functions that the network represents, capturing uncertainty about which function best fits the data. Specifying this prior remains an open challenge. Common practice is to use a standard normal prior in weight space, which imposes weak shrinkage regularities analogous to weight decay. It is neither informative about the induced function class nor the data (e.g., it is sensitive to parameterization). This can cause the induced function posterior to generalize in unforeseen ways on out-of-distribution (OOD) inputs, which are inputs outside of the distribution that generated the training data.Motivated by these challenges, we introduce noise contrastive priors (NCPs), which encourage uncertainty outside of the training distribution through a loss in data space. NCPs are compatible with any model that represents functional uncertainty as a random variable, are easy to scale, and yield reliable uncertainty estimates that show significantly improved active learning performance.",Obtaining reliable uncertainty estimates neural network predictions is a long standing challenge. Bayesian neural networks have been proposed solution remains open how to specify prior. particular common practice standard normal prior weight space imposes weak regularities causing function posterior possibly generalize unforeseen ways inputs outside training distribution. propose noise contrastive priors NCPs obtain reliable uncertainty estimates. key idea is to train model output high uncertainty data points outside training distribution. NCPs do so using input prior which adds noise inputs current mini batch output prior which is a wide distribution given inputs. NCPs are compatible model can output uncertainty estimates are easy scale yield reliable uncertainty estimates throughout training. Empirically show NCPs prevent overfitting outside training distribution result uncertainty estimates are useful active learning. demonstrate scalability method flight delays data set where we significantly improve upon previously published results. Many successful applications neural networks BID25 BID53 BID57 are in restricted settings where predictions are only made inputs similar training distribution. real-world scenarios neural networks can face truly novel data points inference settings can be valuable have good estimates model's uncertainty. example healthcare reliable uncertainty estimates can prevent overconfident decisions rare novel patient conditions BID49. Similarly autonomous agents actively explore environment can use uncertainty estimates decide what data points will be most informative.Epistemic uncertainty describes amount missing knowledge data generating function. Uncertainty can in principle completely reduced observing data points right locations training them. contrast data generating function may also have inherent randomness which we call aleatoric noise. noise can be captured models outputting distribution rather point prediction. Obtaining data points allows noise estimate move closer true value which is usually different zero. active learning is crucial separate two types randomness:want acquire labels regions high uncertainty low noise BID36.Bayesian analysis provides principled approach modeling uncertainty neural networks BID8 BID37. Namely one places prior network's weights biases. effectively places distribution functions network represents capturing uncertainty which function best fits data. Specifying prior remains open challenge. Common practice is to use standard normal prior weight space which imposes weak shrinkage regularities analogous weight decay. is neither informative induced function class data e.g is sensitive parameterization can cause induced function posterior generalize unforeseen ways out-of-distribution OOD inputs which are inputs outside distribution generated training data.Motivated challenges introduce noise contrastive priors NCPs which encourage uncertainty outside training distribution loss data space. NCPs are compatible model represents functional uncertainty random variable are easy scale yield reliable uncertainty estimates show significantly improved active learning performance.,691,498,193,0.007,1.388,2025/11/05 17:19:06,0.0,1.528,0.1806853582554512,244.153
"Convolutional neural networks (CNNs) were inspired by human vision and, in some settings, achieve a performance comparable to human object recognition. This has lead to the speculation that both systems use similar mechanisms to perform recognition. In this study, we conducted a series of simulations that indicate that there is a fundamental difference between human vision and CNNs: while object recognition in humans relies on analysing shape, CNNs do not have such a shape-bias. We teased apart the type of features selected by the model by modifying the CIFAR-10 dataset so that, in addition to containing objects with shape, the images concurrently contained non-shape features, such as a noise-like mask. When trained on these modified set of images, the model did not show any bias towards selecting shapes as features. Instead it relied on whichever feature allowed it to perform the best prediction -- even when this feature was a noise-like mask or a single predictive pixel amongst 50176 pixels. We also found that regularisation methods, such as batch normalisation or Dropout, did not change this behaviour and neither did past or concurrent experience with images from other datasets. Object recognition in humans is largely a function of analyzing shape BID1 BID6 . A wealth of data from psychological experiments show that shape plays a privileged role in object recognition compared to other diagnostic features such as size, colour, luminance or texture. For example, BID2 showed that error rates and reaction times are virtually identical in a recognition task when full coloured photographs of objects are replaced by their line drawings even when colour was a diagnostic feature. This indicates that shape-based representations mediate recognition. Similarly, BID11 found that, for patients with an object recognition deficit (visual agnosia), surface colour played minimal role in aiding object recognition unless the shape of the object was ambiguous, indicating that shape is instrumental to recognition, whereas surface characteristics such as colour and texture play only a secondary role. More recently, BID0 have shown that participants extract shape information automatically from arrays of dot patterns within the first 100ms of stimulus onset, even for tasks where extracting this information may be detrimental to performance on a task. Experiments from developmental psychology show that this privileged status of shape starts early in life and becomes stronger with age. For example, BID10 found that 2-3-year-old children as well as adults weight shape more heavily than size or texture when generalising the name of a learnt object to novel instances. They also found that the weight placed on shape increases in strength and generality from early childhood to adulthood. Following BID10 , we will call this privileged status of shape in performing recognition a ""shape bias"".By contrast, it is unclear whether shape plays a privileged role in how convolutional neural networks (CNNs) categorise objects. It is often claimed that CNNs learn representations of objects that are similar to the representations that monkeys and humans use when identifying objects BID14 , and that CNNs largely rely on learning shape representations in order to categorise objects BID9 BID15 BID7 . On the other hand, there are a growing number of studies that show that CNNs often categorise images on the basis on nonshape attributes of images. This is demonstrated by the existence of adversarial images that are confidently classified as a familiar category despite the lack of any shape information in the input BID13 , adversarial images that contain the correct shape but altered colours that are confidently misclassified (e.g., categorizing an image of an airplane as a dog when only the colour of the plane has been manipulated), and large reductions in performance when trained coloured images are converted to greyscale BID3 or the colours are inverted BID5 . In addition , there are demonstrations that CNNs can easily learn to categorise random patterns of pixels that have no shape BID4 . All of these findings suggest that shape may not play a privileged role in CNN's object categorisation, or that the relevant role of shape and non-shape features depends on the specific model or training conditions.Here we systematically explore the impact of non-shape features in the categorisation performance of convolutional neural networks on CIFAR-10 images. We introduced non-shape features to images by adding informative noise-like masks to the training set. We tried several types of masks and an extreme version where the non-shape feature consisted of just a single pixel with a location correlated to the image category (see FIG0 and Appendix B). We show that CNNs often learn and depend on non-shape features that are highly diagnostic of object categories and often fails to learn anything about shape under these conditions. This highlights that CNNs simply picks up whatever statistical structure is most relevant to learning the training set, with shape playing no special role. Note that this does not imply that CNNs do not encode shape information under any circumstance, but that shape does not seem to be weighted more than other diagnostic features, even when these features are noise-like masks or the luminance of a single pixel. Importantly, this behaviour contrasts with humans, for whom shape plays a privileged role in performing recognition, even in the presence of much more salient diagnostic features such as size, colour or texture. If the models are to more closely capture human performance, these results suggest that additional machinery needs to be added to networks in order to prioritize the role of learning shape-based representations while performing the object categorisations. This might also reduce the model's susceptibility to being fooled by non-shape features of images, and being more robust to various forms of non-shape noise that currently reduce performance. The non-shape features used in the experiments above have all been completely invariant from one image to another within a category. It can be argued that these features are selected by the model over other shape-based features because they provide a very strong predictive signal and consequently suppress the selection of any shape-based features. It is possible that if these features contained larger variance, the model would be more likely to rely on shape-based features while performing categorisation. In a series of experiments where we increased the variability of the non-shape (noiselike) features, we noticed that this was generally not the case -the model still relied a lot more on these features than on any shape-based features to perform categorisation.The first type of variability we introduced was to sample the noise mask independently from a distribution for each training and test image within a category. In order to make these noise masks diagnostic of an image's category, a parameter of this distribution correlated with an image's category. For the salt-and-pepper noise, this meant that the probability, p, of changing a pixel to black or white was different for each category. Thus, the parameter, p, became diagnostic of the category. However, the masks now varied from image to image and were independently sampled with the (category-dependent) probability, p. Similarly, for the additive uniform noise, masks could vary from one image to other within a category but the mean of the distribution depended on each category (see Appendix A for details). For the single diagnostic pixel, the inserted pixel could vary in location from one image to the other, but was generated from a Gaussian distribution with a mean determined by the category of the image and a fixed standard deviation. Similarly the colour of the pixel was sampled from a Gaussian distribution with a mean determined by the category of the image and a fixed standard deviation. FIG1 ). Performance in the NoPix condition was somewhat better for ResNet, however the pattern of result remained the same -performance dropped substantially from the Same to NoPix condition. Similarly, introducing variability in the salt-and-pepper masks lead to only a minor change in behaviour of the model, with accuracy in 'Diff' condition dropping to chance, rather than 0%. The most intriguing change in behaviour occurred when variability was introduced to the additive uniform noise mask FIG4 ). While the VGG and ResNet networks differed quantitatively in these results, the pattern of results remained the same: when the noise mask was completely removed (NoPix condition) the model performed worse than when the images contained a noise mask from a different category (Diff condition). In other words, removing the mask makes the image less informative for the model, not only compared to images with the correct category-correlated (Same) mask, but also compared to images with the incorrect (Diff) maskthe model seems to rely on the presence of noise to make an inference.Next, we examined how the model changes it's behaviour when only a subset of images contain a diagnostic non-shape feature. We restricted this experiment to the case of a single diagnostic pixel. The location and colour of this pixel were fixed across all images of a category, but we introduced stochasticity in the presence of this pixel within a training image. FIG5 shows the change in accuracy for the 'NoPix' condition with an decrease in the probability with which a pixel is present in a training image. We specifically focus on the 'NoPix' condition as the accuracy on this condition is inversely correlated with how much the network relies on this pixel to predict the output category. It can be seen from this figure that accuracy increases smoothly, rising sharply at first and then slowing down as the probability of the pixel being present in a training image decreases. This smooth increase is consistent with the hypothesis that the learning algorithm selects the feature based on the predictive power of the feature; as the single pixel becomes less predictive, the network starts relying on other features to choose the output category. This smooth increase also indicates that the model is able to combine information from this diagnostic pixel with other features that it uses to predict the output category. For example, when the pixel is present in only 90% of the images, the model is able to correctly categorise an image containing no diagnostic pixel 70% of the time, indicating that it simultaneously represents both the diagnostic pixel as well as other features that it uses to perform categorisation.The figure also shows that a single pixel present in training images adversely affects the performance of the network even when it is present on only a fraction of the images. When the network is trained on images from the original CIFAR-10 dataset, it's accuracy is close to 90% (dotted black line); inserting a single pixel on 70% of the images meant that the performance decreased by more than 10%. This reduction in performance could be due to one of two reasons: (a) the network mistakes a pixel value in one of the original images as a predictive pixel and performs an incorrect classification based on this pixel, or (b) adding a mask to a subset of training images means that the network has to learn the correct classification function on a fraction of the original dataset. This decrease in the size of the dataset may be affecting its performance. Further testing will be needed to correctly establish which of these reasons is responsible for a reduction in performance. Lastly, we also observed that L2 regularisation made the performance of the network worse on the original images when a diagnostic pixel was inserted on a fraction of the images. While L2 regularisation should help the network learn a more general solution, in this case it lead to the opposite effect. In a series of simulations we found that the VGG network trained to categorise CIFAR-10 images that included noise-like masks diagnostic of the output categories often learned to categorise on the basis of these masks rather than the CIFAR images themselves. Indeed, the models often entirely relied on the masks, and performed at floor when the noise was removed from the images. Even though we specifically engineered our dataset to contain non-shape features, it is well-known that popular datasets such as CIFAR and ImageNet contain various biases due to conditions under which the images were captured as well as the different motivations for construction of the datasets (Torralba & Efros, 2011) . Our results suggest that CNNs may be relying too heavily on non-shape features when categorising images and therefore may be extremely susceptible to non-shape biases present within datasets. This, in turn, could be the source of various idiosyncratic behaviours such as being confounded by fooling images BID13 or being overly sensitive to colour BID5 , noise BID3 or even single pixels in images BID18 . This contrasts with human visual object recognition that is largely based on shape BID1 . It will be important to introduce shape biases to CNNs if they are to mirror human object recognition performance more closely. The introduction of shape biases may also prove useful in making CNNs more robust to various non-shape manipulations of images (e.g., changes in colour or the introduction of noise) that often impair performance. We used a method similar to BID3 to transform images from the CIFAR-10 dataset (https://www.cs.toronto.edu/˜kriz/cifar.html). All transformations were performed using the Pillow fork of the Python Imaging Library (https://pillow. readthedocs.io). Each 32x32 pixel image was rescaled to 224x224 pixels using the PIL.Image.LANCZOS method. For the salt-and-pepper and additive noise masks, each image was transformed from RGB to greyscale using PIL.Image.convert() method. For the extreme case of single pixel, the images were not colour transformed (we obtained qualitatively similar results if images were transformed to greyscale). When images were transformed to greyscale, their contrast was adjusted to 80% by scaling the value of each pixel using the formula: DISPLAYFORM0 × 128, where v was the original value of the pixel in the range [0, 255] .The salt-and-pepper mask was created by taking the transformed greyscale image and setting each pixel to either black or white with a probability p. When the mask was fixed for a category, all images had the exact same set of pixels that were turned either black or white and the p was set to 0.05. When the mask varied from image to image within a category, the pixels were sampled independently for each image and the probability p was fixed for each category but varied between categories in the range [0.03, 0.06].The additive uniform noise mask was created by taking the transformed greyscale image and adding a value sampled from the uniform distribution [−w, w] to this image, where 2w was the width of the uniform distribution and was set to 8. When the noise mask was fixed, this sampling was done only once per category and the same mask was added to each image. When the mask was variable, it was sampled independently for each image from a distribution [µ − w, µ + w], where µ was the mean that depended on the category and varied in the range [−50, 50] .The single pixel mask was created by choosing a random location, (x, y), (sampled from a uniform distribution on the interval [0, 224]) on the image and changing the colour of the pixel to a value c (sampled from a uniform distribution on the interval [0, 255] ). When the mask was fixed for each category, (x, y, c) remained constant for all images in a category, but varied between categories. In other words, the pixel was inserted at different locations and was of different colours for different categories, but all images within a category had the pixel at the same location and of same colour. When the mask was variable , each of x, y and c were sampled independently for each image from a Gaussian distribution with a constant variance and a mean that depended on the category of the image. If any value in a sampled set of (x, y, c) values fell out of their respective range, that value was re-sampled.All simulations reported in this study (except for the Conv Drop simulation in FIG2 were carried out using a pre-trained 16-layer VGG network BID17 provided by the torchvision package of Pytorch. This network had been pre-trained on the ImageNet dataset. We replaced the fully-connected layers of this pre-trained model with three fully-connected layers with Dropout after the first two layers. This model was then trained on the modified training set using the RMSProp gradient descent optimization algorithm (see BID16 with learning rate of 1e−5, a momentum of 0.9 and a cross-entropy loss function. We also experimented with Adam (Kingma & Ba , 2014) and results remained qualitatively same. For testing the effect of Dropout in the early layers, we constructed a six-layer convolutional neural network with three convolutional layers and three fully connected layers and dropout after every convolutional layer. The same learning rule and parameters were used as for the VGG network and we experimented with several model architectures with most architectures giving similar results. This network was able to achieve an accuracy of 70% on categorising the CIFAR-10 dataset. The input to both types of networks was a 3-channel RGB image. For greyscale images, all three channels were set to the same value. Figure 8 : Examples of images used for training and testing. The columns show the condition under which the image was used and the rows show the type of noise-like mask inserted. These noise masks are, respectively, (row 1) salt-and-pepper noise with a fixed mask, (row 2) salt-and-pepper noise with a variable mask, (row 3) additive uniform noise with fixed mask, (row 4) additive uniform noise with a variable mask, (row 5) single diagnostic pixel, fixed location and colour and (row 6) single diagnostic pixel with variable location and colour.","Convolutional neural networks CNNs were inspired human vision settings achieve performance comparable human object recognition. has lead speculation systems use similar mechanisms perform recognition. study conducted series simulations indicate is a fundamental difference human vision CNNs:object recognition humans relies analysing shape CNNs do not have such shape-bias teased apart type features selected model modifying CIFAR-10 dataset addition containing objects shape images concurrently contained non-shape features noise-like mask. When trained modified set images model did not show bias towards selecting shapes features. Instead relied whichever feature allowed perform best prediction even when this feature was a noise-like mask single predictive pixel amongst 50176 pixels. also found regularisation methods batch normalisation Dropout did not change behaviour neither did past concurrent experience images datasets. Object recognition humans is largely function analyzing shape BID1 BID6. wealth data psychological experiments show have no shape plays privileged role object recognition compared diagnostic features size colour luminance texture. example BID2 showed error rates reaction times are virtually identical recognition task when full coloured photographs objects are replaced line drawings even when when only the colour was a diagnostic feature. indicates shape-based representations mediate recognition. Similarly BID11 found patients object recognition deficit visual agnosia surface colour played minimal role aiding object recognition unless shape object was ambiguous indicating have no shape is instrumental recognition whereas surface characteristics colour texture play secondary role. recently BID0 have shown participants extract shape information automatically arrays dot patterns within first 100ms stimulus onset even tasks where extracting information may detrimental performance task. Experiments developmental psychology show privileged status shape starts early life becomes stronger age. example BID10 found 2-3-year-old children well adults weight shape heavily size texture when generalising name learnt object novel instances. also found weight placed shape increases strength generality early childhood adulthood. Following BID10 will call privileged status shape performing recognition shape bias.By contrast is unclear whether shape plays privileged role how convolutional neural networks CNNs categorise objects. is often claimed CNNs learn representations objects are similar representations monkeys humans use when identifying objects BID14 CNNs largely rely learning shape representations order categorise objects BID9 BID15 BID7. hand are a growing number studies show CNNs often categorise images basis nonshape attributes images. is demonstrated existence adversarial images are confidently classified familiar category despite lack shape information input BID13 adversarial images contain correct shape altered colours are confidently misclassified e.g categorizing image airplane dog when when only the colour plane has been manipulated large reductions performance when trained coloured images are converted greyscale BID3 colours are inverted BID5. addition are demonstrations CNNs can easily learn categorise random patterns pixels have no shape BID4. findings suggest have no shape may play privileged role CNN's object categorisation relevant role shape non-shape features depends specific model training conditions.Here systematically explore impact non-shape features categorisation performance convolutional neural networks CIFAR-10 images. introduced non-shape features images adding informative noise-like masks training set. tried several types masks extreme version where the non-shape feature consisted single pixel location correlated image category see FIG0 AppendixB show CNNs often learn depend non-shape features are highly diagnostic object categories often fails learn anything shape conditions. highlights CNNs simply picks whatever statistical structure is most relevant learning training set shape playing special role. Note does not imply CNNs do not encode shape information circumstance shape does not seem weighted diagnostic features even when these features are noise-like masks luminance single pixel. Importantly behaviour contrasts humans shape plays privileged role performing recognition even presence much salient diagnostic features size colour texture. If the models are to more closely capture human performance results suggest additional machinery needs added networks order prioritize role learning shape-based representations performing object categorisations. might also reduce model's susceptibility fooled non-shape features images robust various forms non-shape noise currently reduce performance. non-shape features used experiments have all been completely invariant one image another within category. can be argued if these features are selected model shape-based features provide strong predictive signal consequently suppress selection shape-based features. is possible if these features contained larger variance model would likely rely shape-based features performing categorisation. series experiments where we increased variability non-shape noiselike features noticed was generally case -the model still relied lot features shape-based features perform categorisation.The first type variability introduced was to sample noise mask independently distribution training test image within category. order make noise masks diagnostic image's category parameter distribution correlated image's category. salt-and-pepper noise meant probability p changing pixel black white was different category. Thus parameter p became diagnostic category. However masks varied image image were independently sampled category-dependent probability p. Similarly additive uniform noise masks could vary one image within category mean distribution depended category see Appendix details single diagnostic pixel inserted pixel could vary location one image was generated Gaussian distribution mean determined category image fixed standard deviation. Similarly colour pixel was sampled Gaussian distribution mean determined category image fixed standard deviation. FIG1 Performance NoPix condition was somewhat better ResNet however pattern result remained -performance dropped substantially NoPix condition. Similarly introducing variability salt-and-pepper masks lead minor change behaviour model accuracy 'Diff' condition dropping chance rather 0%. intriguing change behaviour occurred when variability was introduced additive uniform noise mask FIG4 VGG ResNet networks differed quantitatively results pattern results remained same:when the noise mask was completely removed NoPix condition model performed worse when the images contained noise mask different category Diff condition words removing mask makes image less informative model compared images correct category-correlated mask also compared images incorrect Diff maskthe model seems rely presence noise make inference.Next examined how the model changes behaviour when only a subset images contain diagnostic non-shape feature. restricted experiment case single diagnostic pixel. location colour pixel were fixed across images category introduced stochasticity presence pixel within training image. FIG5 shows change accuracy 'NoPix' condition decrease probability which a pixel is present training image. specifically focus 'NoPix' condition accuracy condition is inversely correlated how much network relies pixel predict output category. can be seen figure accuracy increases smoothly rising sharply first slowing probability pixel present training image decreases. smooth increase is consistent hypothesis learning algorithm selects feature based predictive power feature;single pixel becomes less predictive network starts relying features choose output category. smooth increase also indicates model is able combine information diagnostic pixel features uses predict output category. example when the pixel is present 90% images model is able correctly categorise image containing diagnostic pixel70% time indicating simultaneously represents diagnostic pixel well features uses perform categorisation.The figure also shows single pixel present training images adversely affects performance network even when it is present fraction images. When the network is trained images original CIFAR-10 dataset accuracy is close 90% dotted black line inserting single pixel 70% images meant performance decreased 10%. reduction performance could due one two reasons:network mistakes pixel value one original images predictive pixel performs incorrect classification based pixel b adding mask subset training images means network has to learn correct classification function fraction original dataset. decrease size dataset may affecting performance. testing will be needed correctly establish which of these reasons is responsible reduction performance. Lastly also observed L2 regularisation made performance network worse original images when a diagnostic pixel was inserted fraction images. L2 regularisation should help network learn general solution case lead opposite effect. series simulations found VGG network trained categorise CIFAR-10 images included noise-like masks diagnostic output categories often learned categorise basis masks rather CIFAR images themselves. Indeed models often entirely relied masks performed floor when the noise was removed images. Even though specifically engineered dataset contain non-shape features is well-known popular datasets CIFAR ImageNet contain various biases due conditions which the images were captured well different motivations construction datasets Torralba Efros 2011 results suggest CNNs may relying heavily non-shape features when categorising images therefore may extremely susceptible non-shape biases present within datasets. turn could source various idiosyncratic behaviours confounded fooling images BID13 overly sensitive colour BID5 noise BID3 even single pixels images BID18. contrasts human visual object recognition is largely based shape BID1. will be important introduce shape biases CNNs if they are to mirror human object recognition performance closely. introduction shape biases may also prove useful making CNNs robust various non-shape manipulations images e.g changes colour introduction noise often impair performance. used method similar BID3 transform images CIFAR-10 dataset https://www.cs.toronto.edu/˜kriz/cifar.html transformations were performed using Pillow fork Python Imaging Library https://pillow. readthedocs.io 32x32 pixel image was rescaled 224x224 pixels using PIL.Image.LANCZOS method. salt-and-pepper additive noise masks image was transformed RGB greyscale using PIL.Image.convert method. extreme case single pixel images were not colour transformed obtained qualitatively similar results if images were transformed greyscale When images were transformed greyscale contrast was adjusted 80% scaling value pixel using formula:DISPLAYFORM0 × 128 wherev was the original value pixel range 0 255.The salt-and-pepper mask was created taking transformed greyscale image setting pixel either black white probabilityp. When the mask was fixed category images had the exact set pixels were turned either black white p was set 0.05 When the mask varied image image within category pixels were sampled independently image probabilityp was fixed category varied categories range 0.03 0.06.The additive uniform noise mask was created taking transformed greyscale image adding value sampled uniform distribution −w w image where2w was the width uniform distribution was set 8. When the noise mask was fixed sampling was done per category mask was added image. When the mask was variable was sampled independently image distribution µ−w µ+w whereµ was the mean depended category varied range −50 50.The single pixel mask was created choosing random location x was sampled uniform distribution interval 0 224 image changing colour pixel valuec sampled uniform distribution interval 0 255 When mask was fixed category x c remained constant images category varied categories. words when the pixel was inserted different locations was of different colours different categories images within category had the pixel location colour. When the mask was variable x c were sampled independently image Gaussian distribution constant variance mean depended category image. If any value sampled set x c values fell respective range value was re-sampled.All simulations reported study except Conv Drop simulation FIG2 were carried using pre-trained 16-layer VGG network BID17 provided torchvision package Pytorch. network had been pre-trained ImageNet dataset. replaced fully-connected layers pre-trained model three fully-connected layers Dropout first two layers. model was then trained modified training set using RMSProp gradient descent optimization algorithm see BID16 learning rate 1e−5 momentum 0.9 cross-entropy loss function. also experimented Adam Kingma Ba 2014 results remained qualitatively same. testing effect Dropout early layers constructed six-layer convolutional neural network three convolutional layers three fully connected layers dropout every convolutional layer. learning rule parameters were used VGG network experimented several model architectures architectures giving similar results. network was able achieve accuracy 70% categorising CIFAR-10 dataset. input types networks was a 3-channel RGB image. greyscale images three channels were set value. Figure8:Examples images used training testing. columns show condition which the image was used rows show type noise-like mask inserted. noise masks are,respectively row1 salt-and-pepper noise fixed mask row2 salt-and-pepper noise variable mask row3 additive uniform noise fixed mask row4 additive uniform noise variable mask row5 single diagnostic pixel fixed location colour row6 single diagnostic pixel variable location colour.",3572,2311,1261,0.076,1.546,2025/11/05 17:19:06,0.02,1.471,0.6728971962616822,1215.163
"The development of high-dimensional generative models has recently gained a great surge of interest with the introduction of variational auto-encoders and generative adversarial neural networks. Different variants have been proposed where the underlying latent space is structured, for example, based on attributes describing the data to generate. We focus on a particular problem where one aims at generating samples corresponding to a number of objects under various views. We assume that the distribution of the data is driven by two independent latent factors: the content, which represents the intrinsic features of an object, and the view, which stands for the settings of a particular observation of that object. Therefore, we propose a generative model and a conditional variant built on such a disentangled latent space. This approach allows us to generate realistic samples corresponding to various objects in a high variety of views. Unlike many multi-view approaches, our model doesn't need any supervision on the views but only on the content. Compared to other conditional generation approaches that are mostly based on binary or categorical attributes, we make no such assumption about the factors of variations. Our model can be used on problems with a huge, potentially infinite, number of categories. We experiment it on four images datasets on which we demonstrate the effectiveness of the model and its ability to generalize. Multi-view learning aims at developing models that are trained over datasets composed of multiple views over different objects. The problem of handling multi-view inputs has mainly been studied from the predictive point of view where one wants, for example, to learn a model able to predict/classify over multiple views of the same object BID25 ; BID23 ). For example, using deep learning approaches, different strategies have been explored to aggregate multiple views but a common general idea is based on the (early or late) fusion of the different views at a particular level of a deep architecture. Few other studies have proposed to predict missing views from one or multiple remaining views as in Arsalan BID0 .Recent research has focused on identifying factors of variations from multiview datasets. The underlying idea is to consider that a particular data sample may be thought as the mix of a content information (e.g. related to its class label like a given person in a face dataset) and of a side information, the view, which accounts for factors of variability (e.g. exposure, viewpoint, with/wo glasses...). All samples of a given class share the same content information while they differ on the view information. A number of approaches have been proposed to disentangle the content from the view, also referred as the style in some papers BID19 ; BID4 ). For instance, different models have been built to extract from a single photo of any object both the characteristics of the object but also the camera position. Once such a disentanglement is learned, one may build various applications like predicting how an object looks like under different viewpoints BID19 ; BID28 ). In the generative domain, models with a disentangled latent space BID18 ; BID5 ) have been recently proposed with applications to image editing, where one wants to modify an input sample by preserving its content while changing its view BID13 ; BID10 ) (see Section 6).Yet most existing controlled generative approaches have two strong limitations: (i) they usually consider discrete views that are characterized by a domain or a set of discrete (binary/categorical) attributes (e.g. face with/wo glasses, the color of the hair, etc.) and could not easily scale to a large number of attributes or to continuous views. (ii) most models are trained using view supervision (e.g. the view attributes), which of course greatly helps learning such model, yet prevents their use on many datasets where this information is not available. Recently, some attempts have been made to learn such models without any supervision ; BID7 ), but they cannot disentangle high level concepts as only simple features can be reliably captured without any guidance.In this paper, we are interested in learning generative models that build and make use of a disentangled latent space where the content and the view are encoded separately. We propose to take an original approach by learning such models from multi-view datasets, where (i) samples are labeled based on their content, and without any view information, and (ii) where the generated views are not restricted to be one view in a subset of possible views. Following with our same example above, it means first, learning from a face dataset including multiple photos of multiple persons taken in various conditions related to exposure, viewpoint etc. and second, being able to generate an infinity of views of an imaginary person (or the same views of an infinity of imaginary persons) -see FIG0 . This contrast with most current approaches that use information about the style, and cannot generate multiple possible outputs.More precisely, we propose two models to tackle this particularly difficult setting: a generative model (GMV -Generative Multi-view Model) that generates objects under various views (multiview generation), and a conditional extension (C-GMV) of this model that generates a large number of views of any input object (conditional multi-view generation). These two models are based on the adversarial training schema of Generative Adversarial Networks (GAN) proposed in BID6 ). The simple but strong idea is to focus on distributions over pairs of examples (e.g. images representing a same object in different views) rather than distribution on single examples as we will explain later.Our contributions are the following: (i) We propose a new generative model able to generate data with various content and high view diversity using a supervision on the content information only.(ii) We extend the model to a conditional model that allows generating new views over any input sample. (iii) We report experimental results on four different images datasets that show the ability of our models to generate realistic samples and to capture (and generate with) the diversity of views.The paper is organized as follows. We first remind useful background on GANs and their conditional variant (Section 2). Then we successively detail our proposal for a generative multiview model (Section 3.2) and for its conditional extension (Section 4). Finally, we report experimental results on the various generative tasks allowed by our models in Section 5.2. We have proposed a generative model operating on a disentangled latent space which may be learned from multiview data without any view supervision, allowing its application to many multiview dataset. Our model allows generating realistic data with a rich view diversity. We also proposed a conditional version of this model which allows generating new views of an input image which may again be learned without view supervision. Our experimental results show the quality of the produced outputs, and the ability of the model to capture content and view factors. They also illustrate the ability of GMV and CGMV to capture the diversity over the CelebA dataset, and to generate more realistic samples than baseline models. In a near future, we plan to investigate the use of such an approach for data augmentation. Indeed, when only a few training data are available, one elegant solution for learning a model could be to generate new views of the existing data in order to increase the size of the training set. This solution will be explored in both semi-supervised and one-shot/few-shot learning settings. APPENDIX Figure 9 : Additional results on GMV: All images in a row have been generated with the same content vector, and all images in a column have been generated with the same view vector TAB7 : Distribution of the different attributes over generated samples. For example, 3.8 % of the samples generated by the GMV model exhibit the ""Eyeglasses"" attribute. 23",development high-dimensional generative models has recently gained great surge interest introduction variational auto-encoders generative adversarial neural networks. Different variants have been have proposed where the underlying latent space is structured example based attributes describing data generate. focus particular problem where one aims generating samples corresponding number objects various views. assume distribution data is driven two independent latent factors:content which represents intrinsic features object view which stands settings particular observation object. Therefore propose generative model conditional variant built disentangled latent space. approach allowsus generate realistic samples corresponding various objects high variety views. Unlike many multi-view approaches model need supervision views content. Compared conditional generation approaches are mostly based binary categorical attributes make assumption factors variations. model can be used problems huge potentially infinite number categories. experiment four images datasets which we demonstrate effectiveness model ability generalize. Multi-view learning aims developing models are trained datasets composed multiple views different objects. problem handling multi-view inputs has mainly studied predictive point view where one wants example learn model able predict/classify multiple views object BID25;BID23 example using deep learning approaches different strategies have been explored aggregate multiple views common general idea is based early late fusion different views particular level deep architecture. studies have been have proposed predict missing views one multiple remaining views Arsalan BID0.Recent research has focused identifying factors variations multiview datasets. underlying idea is to consider particular data sample may thought mix content information e.g related class label like given person face dataset side information view which accounts factors variability e.g exposure viewpoint/wo glasses... samples given class share content information differ view information. number approaches have been have proposed disentangle content view also referred style papers BID19;BID4 instance different models have been built extract single photo object characteristics object also camera position. disentanglement is learned where one may build various applications like predicting how an object looks like different viewpoints BID19;BID28 generative domain models disentangled latent space BID18;BID5 have been recently proposed applications image editing where one wants modify input sample preserving content changing view BID13;BID10 see Section6.Yet existing controlled generative approaches have two strong limitations:usually consider discrete views are characterized domain set discrete binary/categorical attributes e.g face/wo glasses color hair etc. could easily scale large number attributes continuous views. ii models are trained using view supervision e.g view attributes which of course greatly helps learning model yet prevents use many datasets where this information is not available. Recently attempts have been made learn models without supervision;BID7 cannot disentangle high level concepts simple features can be reliably captured without guidance.In paper are interested learning generative models build make use disentangled latent space where the content view are encoded separately. propose take original approach learning models multi-view datasets where(i samples are labeled based content without view information ii where the generated views are not restricted one view subset possible views. Following example means first learning face dataset including multiple photos multiple persons taken various conditions related exposure viewpoint etc. second able generate infinity views imaginary person views infinity imaginary persons -see FIG0. contrast current approaches use information style cannot generate multiple possible outputs.More precisely propose two models tackle particularly difficult setting:generative model GMV -Generative Multi-view Model generates objects various views multiview generation conditional extension C-GMV model generates large number views input object conditional multi-view generation two models are based adversarial training schema Generative Adversarial Networks GAN proposed BID6 simple strong idea is to focus distributions pairs examples e.g images representing object different views rather distribution single examples will explain later.Our contributions are the following:propose new generative model able generate data various content high view diversity using supervision content information only. ii extend model conditional model allows generating new views input sample. iii report experimental results four different images datasets show ability models generate realistic samples capture generate diversity views.The paper is organized follows. first remind useful background GANs conditional variant Section2 successively detail proposal generative multiview model Section 3.2 conditional extension Section4 Finally report experimental results various generative tasks allowed models Section 5.2 have proposed generative model operating disentangled latent space may learned multiview data without view supervision allowing application many multiview dataset. model allows generating realistic data rich view diversity. also proposed conditional version model which allows generating new views input image may learned without view supervision. experimental results show quality produced outputs ability model capture content view factors. also illustrate ability GMV CGMV capture diversity CelebA dataset generate realistic samples baseline models. near future plan investigate use approach data augmentation. Indeed when onlya training data are available where one elegant solution learning model could generate new views existing data order increase size training set. solution will be explored semi-supervised one-shot/few-shot learning settings. APPENDIX Figure9:Additional results GMV:images row have been generated content vector images column have been generated view vector TAB7:Distribution different attributes generated samples. example 3.8 samples generated GMV model exhibit Eyeglasses attribute. 23,1551,996,555,0.018,1.557,2025/11/05 17:19:06,0.01,1.5,0.7071651090342675,510.521
"The huge size of deep networks hinders their use in small computing devices. In this paper, we consider compressing the network by weight quantization. We extend a recently proposed loss-aware weight binarization scheme to ternarization, with possibly different scaling parameters for the positive and negative weights, and m-bit (where m > 2) quantization. Experiments on feedforward and recurrent neural networks show that the proposed scheme outperforms state-of-the-art weight quantization algorithms, and is as accurate (or even more accurate) than the full-precision network. The last decade has witnessed huge success of deep neural networks in various domains. Examples include computer vision, speech recognition, and natural language processing BID16 . However, their huge size often hinders deployment to small computing devices such as cell phones and the internet of things. Many attempts have been recently made to reduce the model size. One common approach is to prune a trained dense network BID5 BID29 . However, most of the pruned weights may come from the fully-connected layers where computations are cheap, and the resultant time reduction is insignificant. BID21 and Molchanov et al. (2017) proposed to prune filters in the convolutional neural networks based on their magnitudes or significance to the loss. However, the pruned network has to be retrained, which is again expensive.Another direction is to use more compact models. GoogleNet (Szegedy et al., 2015) and ResNet BID7 replace the fully-connected layers with simpler global average pooling. However, they are also deeper. SqueezeNet BID11 reduces the model size by replacing most of the 3 × 3 filters with 1 × 1 filters. This is less efficient on smaller networks because the dense 1 × 1 convolutions are costly. MobileNet BID10 compresses the model using separable depth-wise convolution. ShuffleNet (Zhang et al., 2017) utilizes pointwise group convolution and channel shuffle to reduce the computation cost while maintaining accuracy. However, highly optimized group convolution and depth-wise convolution implementations are required. Alternatively, Novikov et al. (2015) compressed the model by using a compact multilinear format to represent the dense weight matrix. The CP and Tucker decompositions have also been used on the kernel tensor in CNNs BID15 BID13 . However, they often need expensive fine-tuning.Another effective approach to compress the network and accelerate training is by quantizing each full-precision weight to a small number of bits. This can be further divided to two sub-categories, depending on whether pre-trained models are used BID22 BID24 or the quantized model is trained from scratch BID1 BID20 . Some of these also directly learn with low-precision weights, but they usually suffer from severe accuracy deterioration BID20 BID26 . By keeping the full-precision weights during learning, BID1 pioneered the BinaryConnect algorithm, which uses only one bit for each weight while still achieving state-of-the-art classification results. Rastegari et al. (2016) further incorporated weight scaling, and obtained better results. Instead of simply finding the closest binary approximation of the full-precision weights, a loss-aware scheme is proposed in . Beyond binarization, TernaryConnect BID23 quantizes each weight to {−1, 0, 1}. BID19 and added scaling to the ternarized weights, and DoReFa-Net (Zhou et al., 2016) further extended quantization to more than three levels. However, these methods do not consider the effect of quantization on the loss, and rely on heuristics in their procedures (Zhou et al., 2016; . Recently, a loss-aware low-bit quantized neural network is proposed in BID18 . However, it uses full-precision weights in the forward pass and the extra-gradient method (Vasilyev et al., 2010) for update, both of which are expensive.In this paper, we propose an efficient and disciplined ternarization scheme for network compression. Inspired by , we explicitly consider the effect of ternarization on the loss. This is formulated as an optimization problem which is then solved efficiently by the proximal Newton algorithm. When the loss surface's curvature is ignored, the proposed method reduces to that of BID19 , and is also related to the projection step of BID18 . Next, we extend it to (i) allow the use of different scaling parameters for the positive and negative weights; and (ii) the use of m bits (where m > 2) for weight quantization. Experiments on both feedforward and recurrent neural networks show that the proposed quantization scheme outperforms state-of-the-art algorithms.Notations: For a vector x, √ x denotes the element-wise square root (i.e., [ DISPLAYFORM0 p is its p-norm, and Diag(x) returns a diagonal matrix with x on the diagonal. For two vectors x and y, x y denotes the element-wise multiplication and x y the element-wise division. Given a threshold ∆, I ∆ (x) returns a vector such DISPLAYFORM1 In this paper, we proposed a loss-aware weight quantization algorithm that directly considers the effect of quantization on the loss. The problem is solved using the proximal Newton algorithm. Each iteration consists of a preconditioned gradient descent step and a quantization step that projects fullprecision weights onto a set of quantized values. For ternarization, an exact solution and an efficient approximate solution are provided. The procedure is also extended to the use of different scaling parameters for the positive and negative weights, and to m-bit (where m > 2) quantization. Experiments on both feedforward and recurrent networks show that the proposed quantization scheme outperforms the current state-of-the-art.",huge size deep networks hinders use small computing devices. paper consider compressing network weight quantization. extend recently proposed loss-aware weight binarization scheme ternarization possibly different scaling parameters positive negative weights m-bit wherem>2 quantization. Experiments feedforward recurrent neural networks show proposed scheme outperforms state-of-the-art weight quantization algorithms is as accurate even accurate full-precision network. last decade has witnessed huge success deep neural networks various domains. Examples include computer vision speech recognition natural language processing BID16. However huge size often hinders deployment small computing devices cell phones internet things. Many attempts have been recently made reduce model size. One common approach is to prune trained dense network BID5 BID29. However pruned weights may come fully-connected layers where computations are cheap resultant time reduction is insignificant. BID21 Molchanovetal. 2017 proposed prune filters convolutional neural networks based magnitudes significance loss. However pruned network has to be retrained which is again expensive.Another direction is to use compact models. GoogleNet Szegedyetal. 2015 ResNet BID7 replace fully-connected layers simpler global average pooling. However are is also deeper. SqueezeNet BID11 reduces model size replacing 3 × 3 filters 1 × 1 filters. is less efficient smaller networks dense1×1 convolutions are costly. MobileNet BID10 compresses model using separable depth-wise convolution. ShuffleNet Zhangetal. 2017 utilizes pointwise group convolution channel shuffle reduce computation cost maintaining accuracy. However highly optimized group convolution depth-wise convolution implementations are required. Alternatively Novikovetal. 2015 compressed model using compact multilinear format represent dense weight matrix. CP Tucker decompositions have also used kernel tensor CNNs BID15 BID13. However often need expensive fine-tuning.Another effective approach compress network accelerate training is by quantizing full-precision weight small number bits. can be further divided two sub-categories depending whether pre-trained models are used BID22 BID24 quantized model is trained scratch BID1 BID20. also directly learn low-precision weights usually suffer severe accuracy deterioration BID20 BID26. keeping full-precision weights learning BID1 pioneered BinaryConnect algorithm which uses one bit weight still achieving state-of-the-art classification results. Rastegarietal. 2016 incorporated weight scaling obtained better results. Instead simply finding closest binary approximation full-precision weights loss-aware scheme is proposed in. Beyond binarization TernaryConnect BID23 quantizes weight −1 0 1 BID19 added scaling ternarized weights DoReFa-Net Zhouetal. 2016 extended quantization three levels. However methods do not consider effect quantization loss rely heuristics procedures Zhouetal. 2016;Recently loss-aware low-bit quantized neural network is proposed BID18. However which uses full-precision weights forward pass extra-gradient method Vasilyevetal. 2010 update which are expensive.In paper propose efficient disciplined ternarization scheme network compression. Inspired explicitly consider effect ternarization loss. is formulated optimization problem which is then solved efficiently proximal Newton algorithm. When the loss surface's curvature is ignored proposed method reduces BID19 are is also related projection step BID18. Next extend allow use different scaling parameters positive negative weights;ii use bits wherem>2 weight quantization. Experiments feedforward recurrent neural networks show proposed quantization scheme outperforms state-of-the-art algorithms.Notations:vectorx √ x denotes element-wise square root.e DISPLAYFORM0p is its p-norm Diag x returns diagonal matrix x diagonal. two vectorsx x denotes element-wise multiplication x element-wise division. Given threshold∆ ∆ x returns vector DISPLAYFORM1 paper proposed loss-aware weight quantization algorithm directly considers effect quantization loss. problem is solved using proximal Newton algorithm. iteration consists preconditioned gradient descent step quantization step projects fullprecision weights onto set quantized values. ternarization exact solution efficient approximate solution are provided. procedure is also extended use different scaling parameters positive negative weights m-bit wherem>2 quantization. Experiments feedforward recurrent networks show proposed quantization scheme outperforms current state-of-the-art,1182,840,342,0.011,1.407,2025/11/05 17:19:06,0.01,1.529,0.2398753894080995,331.916
"In the pursuit of increasingly intelligent learning systems, abstraction plays a vital role in enabling sophisticated decisions to be made in complex environments. The options framework provides formalism for such abstraction over sequences of decisions.   However most models require that options be given a priori, presumably specified by hand, which is neither efficient, nor scalable. Indeed, it is preferable to learn options directly from interaction with the environment. Despite several efforts, this remains a difficult problem: many approaches require access to a model of the environmental dynamics, and inferred options are often not interpretable, which limits our ability to explain the system behavior for verification or debugging purposes.   In this work we develop a novel policy gradient method for the automatic learning of policies with options.   This algorithm uses inference methods to simultaneously improve all of the options available to an agent, and thus can be employed in an off-policy manner, without observing option labels. Experimental results show that the options learned can be interpreted. Further, we find that the method presented here is more sample efficient than existing methods, leading to faster and more stable learning of policies with options. Recent developments in reinforcement learning (RL) methods have enabled agents to solve problems in increasingly complicated domains BID14 . However, in order for agents to solve more difficult and realistic environments-potentially involving long sequences of decisions-more sample efficient techniques are needed. One way to improve on existing agents is to leverage abstraction. By reasoning at various levels of abstraction, it is possible to infer, learn and plan much more efficiently. Recent developments have lead to breakthroughs in terms of learning rich representations for perceptual information BID2 . In RL domains, however, while efficient methods exist to plan and learn when abstraction over sequences of actions is provided a priori, it has proven more difficult to learn this type of temporal abstraction from interaction data.Many frameworks for formalizing temporal abstraction have been proposed; most recent developments build on the Options framework BID21 BID16 , which offers a flexible parameterization, potentially amenable to learning. The majority of prior work on learning options has centered around the idea of discovering subgoals in state space, and constructing a set of options such that each option represents a policy leading to that subgoal BID11 BID12 BID20 ). These methods can lead to useful abstraction, however, they often require access to a model of the environment dynamics, which is not always available, and can be infeasible to learn. Our contributions instead build on the work of BID1 , and exploits a careful parameterization of the policy of the agent, in order to simultaneously learn a set of options, while directly optimizing returns. We relax a few key assumptions of this previous work, including the expectation that only options that were actually executed during training can be learned, and the focus on executing options in an on-policy manner, with option labels available. By relaxing these, we can improve sample efficiency and practical applicability, including the possibility to seed control policies from expert demonstrations. In this paper, we have introduced a new algorithm for learning hierarchical policies within the options framework, called inferred option policy gradients. This algorithm treats options as latent variables. Gradients are propagated through a differentiable inference step that allows end-to-end learning of option policies, as well as option selection and termination probabilities.In our algorithms policies take responsibility for state-actions pairs they could have generated. In contrast, in learning algorithms for hierarchical policies that use an augmented state space, option policies are updated using only those state-action pairs the actually generated. As a result, in our algorithm options do not tend to become 'responsible' for unlikely states or actions they generated. Thus, options are stimulated more strongly to specialize in a part of the state space. We conjecture that this specialization caused the discussed increase in the interpretability of options.(a ) Performance in the Walker2d environment as a function of available options. We see that in this environment, having several options available to the agent leads to an improved policy.(b) In the Walker2d environment, initially option selection is uniform. After training only 3 options tend to be selected, even when more are available. Selection frequencies are averaged over 100 sampled states.(c) As the options improve during training, the probability of remaining in the active option increases, plateauing at around 0.85. This suggests that the options learned here exhibit temporal extension. Furthermore, in our experiments learning with inferred options was significantly faster than learning with an option-augmented state space. In fact, learning with inferred options proved equally fast, or sometimes even faster, than using a comparable non-hierarchical policy gradient method despite IOPG having many more parameters. We conjecture that option inference encourages intra-option learning, thus allowing multiple options to improve as the result of a single learning experience, causing this speed-up.In future work, we want to quantify the suitability of the learned options for transfer between tasks. Our experiments so far were in the episodic setting. We want to investigate an on-line, actor-critic version of learning with inferred options to learn continuously in infinite-horizon problems.",pursuit increasingly intelligent learning systems abstraction plays vital role enabling sophisticated decisions made complex environments. options framework provides formalism abstraction sequences decisions. However models require options given priori presumably specified hand which is neither efficient scalable. Indeed is preferable learn options directly interaction environment. Despite several efforts remains difficult problem:many approaches require access model environmental dynamics inferred options are often interpretable which limits ability explain system behavior verification debugging purposes. work develop novel policy gradient method automatic learning policies options. algorithm uses inference methods simultaneously improve options available agent thus can be employed off-policy manner without observing option labels. Experimental results show options learned can be interpreted. find method presented is more sample efficient existing methods leading faster stable learning policies options. Recent developments reinforcement learning RL methods have enabled agents solve problems increasingly complicated domains BID14. However order agents solve difficult realistic environments-potentially involving long sequences decisions-more sample efficient techniques are needed. One way improve existing agents is to leverage abstraction. reasoning various levels abstraction is possible infer learn plan much efficiently. Recent developments have lead breakthroughs terms learning rich representations perceptual information BID2. RL domains however efficient methods exist plan learn when abstraction sequences actions is provided priori has proven difficult learn type temporal abstraction interaction data.Many frameworks formalizing temporal abstraction have been proposed;recent developments build Options framework BID21 BID16 which offers flexible parameterization potentially amenable learning. majority prior work learning options has centered around idea discovering subgoals state space constructing set options option represents policy leading subgoal BID11 BID12 BID20 methods can lead useful abstraction however often require access model environment dynamics which is not always available can be infeasible learn. contributions instead build work BID1 exploits careful parameterization policy agent order simultaneously learn set options directly optimizing returns. relax key assumptions previous work including expectation options were actually executed training can be learned focus executing options on-policy manner option labels available. relaxing can improve sample efficiency practical applicability including possibility seed control policies expert demonstrations. paper have introduced new algorithm learning hierarchical policies within options framework called inferred option policy gradients. algorithm treats options latent variables. Gradients are propagated differentiable inference step allows end-to-end learning option policies well option selection termination probabilities.In algorithms policies take responsibility state-actions pairs could have generated. contrast learning algorithms hierarchical policies use augmented state space option policies are updated using state-action pairs actually generated. result algorithm options do not tend become 'responsible' unlikely states actions generated. Thus options are stimulated strongly specialize part state space. conjecture specialization caused discussed increase interpretability options. Performance Walker2d environment function available options. see environment several options available agent leads improved policy. b Walker2d environment initially option selection is uniform. training 3 options tend selected even when more are available. Selection frequencies are averaged 100 sampled states. c options improve training probability remaining active option increases plateauing around 0.85 suggests options learned exhibit temporal extension. Furthermore experiments learning inferred options was significantly faster learning option-augmented state space. fact learning inferred options proved equally fast sometimes even faster using comparable non-hierarchical policy gradient method despite IOPG many parameters. conjecture option inference encourages intra-option learning thus allowing multiple options improve result single learning experience causing speed-up.In future work want quantify suitability learned options transfer tasks. experiments far were in the episodic setting. want investigate on-line actor-critic version learning inferred options learn continuously infinite-horizon problems.,1015,665,350,0.011,1.526,2025/11/05 17:19:06,0.01,1.429,0.6105919003115264,333.185
"The paper, interested in unsupervised feature selection, aims to retain the features best accounting for the local patterns in the data. The proposed approach, called Locally Linear Unsupervised Feature Selection, relies on a dimensionality reduction method to characterize such patterns; each feature is thereafter assessed according to its compliance w.r.t. the local patterns, taking inspiration from Locally Linear Embedding (Roweis and Saul, 2000). The experimental validation of the approach on the scikit-feature benchmark suite demonstrates its effectiveness compared to the state of the art. Machine Learning faces statistical and computational challenges due to the increasing dimension of modern datasets. Dimensionality reduction aims at addressing such challenges through embedding the data in a lower dimensionality space, in an unsupervised BID17 BID28 BID34 BID41 or supervised BID9 BID8 BID25 way.The requirement for understandable Machine Learning BID36 BID5 however makes it desirable to achieve interpretable dimensionality reduction. In order to do so, the simplest way is to select a subset of the initial features, i.e. to achieve feature selection (FS), as opposed to generating compound new features from the initial ones, a.k.a. feature construction. For instance, determining the genes most important w.r.t. a given disease or the underlying generative model of the data can be viewed as the mother goal in bioinformatics BID13 BID23 .In the supervised ML setting, features are assessed and selected based on their relevance to the prediction goal BID11 BID31 BID3 . Unsupervised learning, aimed at making sense of the data, however constitutes a primary and most important task of ML, as emphasized by BID20 , while supervised ML intervenes at a later stage of the data exploitation process.Unsupervised FS approaches BID14 BID47 BID2 BID22 BID48 ) (more in section 2) essentially rely on the assumption that the data samples are structured in clusters, and use the cluster partition in lieu of labels, making it possible to fall down on supervised FS, and select the features most amenable to characterize and separate the clusters. A main limitation of this methodology is that clusters are bound to rely on some metric defined from the initial features (with the notable exception of BID22 ), although this metric can be arbitrarily corrupted based on irrelevant or random features. On the other hand , as far as one considers the unsupervised setting, a feature can hardly be considered irrelevant per se.The main contribution of the paper is to address both limitations: the proposed approach, called Locally Linear Unsupervised Feature Selection (LLUFS) jointly determines patterns in the data, and features relevant to characterize these patterns. LLUFS is a 2-step process (Sec. 3): In a first step, a compressed representation of the data is built using Auto-Encoders BID37 BID7 . In a second step, viewing the initial dataset as a high-dimensional embedding of the compressed dataset, each feature is scored according to its contribution to the reconstruction error of the embedding, taking inspiration from Locally Linear Embedding BID28 BID29 BID40 .After describing the goals of experiments and the experimental setting used to validate the approach, extensively relying on the scikit-feature project BID21 SKf, 2018) (Sec. 4) , the empirical validation is presented and discussed (Sec. 5), establishing the merits and discussing the weaknesses of the approach. The paper concludes with a discussion and some perspectives for further research. One weakness of the method is that the distorsion scores depend on the latent representation produced by the auto-encoder, which might be biased due to the redundancy of the initial features; typically, duplicating an initial feature will entail that the latent representation is more able to express this feature, mechanically reducing its distorsion score. For this reason, a preliminary step is to detect and reduce the redundancy of the initial features.In order to do so, LLUFS i) normalizes the initial features (with zero mean and unit variance); ii) uses Agglomerative Hierarchical feature clustering BID18 BID35 , using a high number of clusters n c (n c = 3 4 D in the experiments); iii) selects one feature per cluster (the nearest one to the cluster mean); iv) apply the auto-encoder on the pruned data.Further work is concerned with taking into account the feature redundancy within the AE loss.A second limitation is due to the sensitivity of the distorsion score to the feature distribution. Typically, while a constant feature carries no information, its distorsion is null. Likewise, the distorsion of discrete features depends on their being balanced. In order to alleviate this issue, the reliability of the distorsion associated to each feature is measured through an empirical p-value BID33 . Given a p-value threshold τ , 1/τ copies of each feature are generated and independently shuffled. The feature distorsion is deemed relevant iff it is lower than the distorsion of all shuffled copies. A novel approach to unsupervised feature selection has been proposed in this paper, with a proof of concept of its empirical merits. The core idea is to find an ""oracle"" representation of the data, and to consider the actual data as an inflated and corrupted image of the oracle data. The quality of each feature is thereafter assessed depending on how it contributes to the loss of information between the ""oracle"" and the actual data.A first perspective for further research, taking inspiration from NDFS, is to allow a feature to be partially relevant, e.g. through considering the quantiles of its distorsion. A second perspective is to integrate the feature redundancy in the auto-encoder loss, to decrease the bias in favor of redundant features. The approach will also be extended to supervised feature selection.","paper interested unsupervised feature selection aims retain features best accounting local patterns data. proposed approach called Locally Linear Unsupervised Feature Selection relies dimensionality reduction method characterize patterns;feature is thereafter assessed according compliancew.r.t local patterns taking inspiration Locally Linear Embedding Roweis Saul 2000 experimental validation approach scikit-feature benchmark suite demonstrates effectiveness compared state art. Machine Learning faces statistical computational challenges due increasing dimension modern datasets. Dimensionality reduction aims addressing challenges embedding data lower dimensionality space unsupervised BID17 BID28 BID34 BID41 supervised BID9 BID8 BID25 way.The requirement understandable Machine Learning BID36 BID5 however makes desirable achieve interpretable dimensionality reduction. order doso,simplest way is to select subset initial features.e achieve feature selection FS opposed generating compound new features initial ones.k.a feature construction. instance determining genes importantw.r.t given disease underlying generative model data can be viewed mother goal bioinformatics BID13 BID23.In supervised ML setting features are assessed selected based relevance prediction goal BID11 BID31 BID3. Unsupervised learning aimed making sense data however constitutes primary important task ML emphasized BID20 supervised ML intervenes later stage data exploitation process.UnsupervisedFS approaches BID14 BID47 BID2 BID22 BID48 section2 essentially rely assumption data samples are structured clusters use cluster partition lieu labels making possible fall supervisedFS select features amenable characterize separate clusters. main limitation methodology is that clusters are bound rely metric defined initial features notable exception BID22 although metric can be arbitrarily corrupted based irrelevant random features. hand far one considers unsupervised setting feature can hardly considered irrelevant per se.The main contribution paper is to address limitations:proposed approach called Locally Linear Unsupervised Feature Selection LLUFS jointly determines patterns data features relevant characterize patterns. LLUFS is a 2-step process Sec. 3 first step compressed representation data is built using Auto-Encoders BID37 BID7. second step viewing initial dataset high-dimensional embedding compressed dataset feature is scored according contribution reconstruction error embedding taking inspiration Locally Linear Embedding BID28 BID29 BID40.After describing goals experiments experimental setting used validate approach extensively relying scikit-feature project BID21 SKf 2018 Sec. 4 empirical validation is presented discussed Sec. 5 establishing merits discussing weaknesses approach. paper concludes discussion perspectives research. One weakness method is that the distorsion scores depend latent representation produced auto-encoder might biased due redundancy initial features;typically duplicating initial feature will entail latent representation is more able express feature mechanically reducing distorsion score. reason preliminary step is to detect reduce redundancy initial features.In order do so,LLUFS normalizes initial features zero mean unit variance ii uses Agglomerative Hierarchical feature clustering BID18 BID35 using high number clustersnc nc 34 experiments iii selects one feature per cluster nearest one cluster mean iv apply auto-encoder pruned data.Further work is concerned taking account feature redundancy within AE loss.A second limitation is due sensitivity distorsion score feature distribution. Typically constant feature carries information distorsion is null. Likewise distorsion discrete features depends balanced. order alleviate issue reliability distorsion associated feature is measured empirical p-value BID33. Given p-value thresholdτ 1/τ copies feature are generated independently shuffled. feature distorsion is deemed relevant iff is lower distorsion shuffled copies. novel approach unsupervised feature selection has been proposed paper proof concept empirical merits. core idea is to find oracle representation data consider actual data inflated corrupted image oracle data. quality feature is thereafter assessed depending how it contributes loss information oracle actual data.A first perspective research taking inspiration NDFS is to allow feature partially relevant e.g considering quantiles distorsion. second perspective is to integrate feature redundancy auto-encoder loss decrease bias favor redundant features. approach will also extended supervised feature selection.",1168,764,404,0.012,1.529,2025/11/05 17:19:06,0.01,1.576,0.6199376947040495,353.591
"Humans can understand and produce new utterances effortlessly, thanks to their systematic compositional skills. Once a person learns the meaning of a new verb ""dax,"" he or she can immediately understand the meaning of ""dax twice"" or ""sing and dax."" In this paper, we introduce the SCAN domain, consisting of a set of simple compositional navigation commands paired with the corresponding action sequences. We then test the zero-shot generalization capabilities of a variety of recurrent neural networks (RNNs) trained on SCAN with sequence-to-sequence methods. We find that RNNs can generalize well when the differences between training and test commands are small, so that they can apply ""mix-and-match"" strategies to solve the task. However, when generalization requires systematic compositional skills (as in the ""dax"" example above), RNNs fail spectacularly. We conclude with a proof-of-concept experiment in neural machine translation, supporting the conjecture that lack of systematicity is an important factor explaining why neural networks need very large training sets. Human language and thought are characterized by systematic compositionality, the algebraic capacity to understand and produce a potentially infinite number of novel combinations from known components. For example, if a person knows the meaning and usage of words such as ""twice,"" ""and,"" and ""again,"" once she learns a new verb such as ""to dax"" she can immediately understand or produce instructions such as ""dax twice and then dax again."" This type of compositionality is central to the human ability to make strong generalizations from very limited data. In a set of influential and controversial papers, Jerry Fodor and other researchers have argued that neural networks are not plausible models of the mind because they are associative devices that cannot capture systematic compositionality BID11 BID22 BID10 BID23 Calvo & Symons, 2014, a.o.) .In the last few years, neural network research has made astounding progress in practical domains where success crucially depends on the generalization capabilities of a system. Perhaps most strikingly, end-to-end recurrent neural networks currently dominate the state-of-the-art in machine translation BID2 BID30 . 1 Since the overwhelming majority of sentences or even word sequences in a language only occur once, even in a large corpus BID1 , this points to strong generalization abilities. Still, it is commonly observed that neural networks are extremely sample inefficient, requiring very large training sets, which suggests they may lack the same algebraic compositionality that humans exploit, and they might only be sensitive to broad patterns over lots of accumulated statistics BID21 .In this paper, we introduce a grounded navigation environment where the learner must translate commands given in a limited form of natural language into a sequence of actions. This problem is naturally framed as a sequence-to-sequence task, and, due to its simplicity, it is ideal to study the systematic generalization capabilities of computational systems to novel examples in a controlled setup. We thus use it to test a wide range of modern recurrent network architectures in terms of their compositional skills. Our results suggest that, although standard architectures such as LSTMs with attention BID0 do generalize when novel examples feature a mixture of constructions that have been observed in training, the models are catastrophically affected by systematic differences between training and test sentences, of the sort that would be trivial for an agent equipped with an ""algebraic mind"" BID23 . In the thirty years since the inception of the systematicity debate, many authors on both sides have tested the ability of neural networks to solve tasks requiring compositional generalization, with mixed results (e.g., BID6 BID22 BID25 BID5 BID27 BID29 BID3 BID12 . However, to the best of our knowledge, ours is the first study testing systematicity in modern seq2seq models, and our results confirm the mixed picture. On the one hand, standard recurrent models can reach very high zero-shot accuracy from relatively few training examples, as long as the latter are generally representative of the test data (Experiment 1). However, the same networks fail spectacularly when there are systematic differences between training and testing. Crucially, the training data of the relevant experiments provide enough evidence to learn composition rules affording the correct generalizations. In Experiment 2, the training data contain examples of all modifiers and connectives that are needed at test time for producing longer action sequences. In Experiment 3, the usage of modifiers and connectives is illustrated at training time by their application to some primitive commands, and, at test time, the model should apply them to a new command it encountered in isolation during training. Nonetheless, this evidence was not sufficient for each of the networks we tested. Generalization only occurs when the networks are also exposed to the target command (or the corresponding action) in a fair number of composed contexts during training.Given the astounding successes of seq2seq models in challenging tasks such as machine translation, one might argue that failure to generalize by systematic composition indicates that neural networks are poor models of some aspects of human cognition, but it is of little practical import. However, systematicity is an extremely efficient way to generalize. Once a person learns the new English adjective ""daxy"", he or she can immediately produce and understand an infinity of sentences containing it. The SCAN experiments and a proof-of-concept machine translation experiment (Experiment 4) suggest that this ability is still beyond the grasp of state-of-the-art networks, likely contributing to their striking sample-inefficiency. These results give us hope that a model capable of systematic compositionality could greatly benefit machine translation and other applications.A natural way of achieving stronger compositionality is through learning more structured representations. Recently, neural networks with external memories have shown promise for extracting algorithm-like representations from input/output examples BID19 BID15 ; for instance, these networks can outperform standard RNNs on generalizing to longer sequences. Future work will explore these approaches on SCAN and other tests of zero-shot compositional generalization. Ultimately, we see systematic compositionality as key both to developing more powerful algorithms and to enriching our computational understanding of the human mind.",Humans can understand produce new utterances effortlessly thanks systematic compositional skills. person learns meaning new verb dax can immediately understand meaning dax twice sing dax. paper introduce SCAN domain consisting set simple compositional navigation commands paired corresponding action sequences. test zero-shot generalization capabilities variety recurrent neural networks RNNs trained SCAN sequence-to-sequence methods. find RNNs can generalize well when the differences training test commands are small can apply mix-and-match strategies solve task. However when generalization requires systematic compositional skills dax example RNNs fail spectacularly. conclude proof-of-concept experiment neural machine translation supporting conjecture lack systematicity is an important factor explaining why neural networks need large training sets. Human language thought are characterized systematic compositionality algebraic capacity understand produce potentially infinite number novel combinations known components. example if a person knows meaning usage words twice learns new verb dax can immediately understand produce instructions dax twice dax again. type compositionality is central human ability make strong generalizations limited data. set influential controversial papers Jerry Fodor researchers have argued neural networks are not plausible models mind are associative devices cannot capture systematic compositionality BID11 BID22 BID10 BID23 Calvo Symons 2014.o.In last years neural network research has made astounding progress practical domains where success crucially depends generalization capabilities system. Perhaps strikingly end-to-end recurrent neural networks currently dominate state-of-the-art machine translation BID2 BID30. 1 Since overwhelming majority sentences even word sequences language occur even large corpus BID1 points strong generalization abilities. Still is commonly observed neural networks are extremely sample inefficient requiring large training sets which suggests may lack algebraic compositionality humans exploit might sensitive broad patterns lots accumulated statistics BID21.In paper introduce grounded navigation environment where the learner must translate commands given limited form natural language sequence actions. problem is naturally framed sequence-to-sequence task due simplicity is ideal study systematic generalization capabilities computational systems novel examples controlled setup. thus use test wide range modern recurrent network architectures terms compositional skills. results suggest although standard architectures LSTMs attention BID0 do generalize when novel examples feature mixture constructions have been observed training models are catastrophically affected systematic differences training test sentences sort would trivial agent equipped algebraic mind BID23. thirty years since inception systematicity debate many authors sides have tested ability neural networks solve tasks requiring compositional generalization mixed results e.g BID6 BID22 BID25 BID5 BID27 BID29 BID3 BID12. However best knowledge is the first study testing systematicity modern seq2seq models results confirm mixed picture. one hand standard recurrent models can reach high zero-shot accuracy relatively training examples long latter are generally representative test data Experiment1 However networks fail spectacularly when there are systematic differences training testing. Crucially training data relevant experiments provide enough evidence learn composition rules affording correct generalizations. Experiment2 training data contain examples modifiers connectives are needed test time producing longer action sequences. Experiment3 usage modifiers connectives is illustrated training time application primitive commands test time model should apply new command encountered isolation training. Nonetheless evidence was not sufficient networks tested. Generalization occurs when the networks are also exposed target command corresponding action fair number composed contexts training.Given astounding successes seq2seq models challenging tasks machine translation one might argue failure generalize systematic composition indicates neural networks are poor models aspects human cognition is little practical import. However systematicity is an extremely efficient way generalize. person learns new English adjective daxy can immediately produce understand infinity sentences containing it. SCAN experiments proof-of-concept machine translation experiment Experiment4 suggest ability is still beyond grasp state-of-the-art networks likely contributing striking sample-inefficiency results give us hope model capable systematic compositionality could greatly benefit machine translation applications.A natural way achieving stronger compositionality is through learning structured representations. Recently neural networks external memories have shown promise extracting algorithm-like representations input/output examples BID19 BID15;instance networks can outperform standard RNNs generalizing longer sequences. Future work will explore approaches SCAN tests zero-shot compositional generalization. Ultimately see systematic compositionality key developing powerful algorithms enriching computational understanding human mind.,1246,817,429,0.013,1.525,2025/11/05 17:19:06,0.01,1.277,0.6074766355140183,365.08
"This paper addresses the challenging problem of retrieval and matching of graph structured objects, and makes two key contributions. First, we demonstrate how  Graph Neural Networks (GNN), which have emerged as an effective model for various supervised prediction problems defined on structured data, can be trained to produce embedding of graphs in vector spaces that enables efficient similarity reasoning. Second, we propose a novel Graph Matching Network model that, given a pair of graphs as input, computes a similarity score between them by jointly reasoning on the pair through a new cross-graph attention-based matching mechanism. We demonstrate the effectiveness of our models on different domains including the challenging problem of control-flow-graph based function similarity search that plays an important role in the detection of vulnerabilities in software systems. The experimental analysis demonstrates that our models are not only able to exploit structure in the context of similarity learning but they can also outperform domain-specific baseline systems that have been carefully hand-engineered for these problems. Graphs are natural representations for encoding relational structures that are encountered in many domains. Expectedly, computations defined over graph structured data are employed in a wide variety of fields, from the analysis of molecules for computational biology and chemistry BID22 BID38 , to the analysis of knowledge graphs or graph structured parses for natural language understanding.In the past few years graph neural networks (GNNs) have emerged as an effective class of models for learning representations of structured data and for solving various supervised prediction problems on graphs. Such models are invariant to permutations of graph elements by design and compute graph node representations through a propagation process which iteratively aggregates local structural information (Scarselli et al., 2009; BID31 BID22 ). These node representations are then used directly for node classification, or pooled into a graph vector for graph classification. Problems beyond supervised classification or regression are relatively less well-studied for GNNs.In this paper we study the problem of similarity learning for graph structured objects, which appears in many important real world applications, in particular similarity based retrieval in graph databases. One motivating application is the computer security problem of binary function similarity search, where given a binary which may or may not contain code with known vulnerabilities, we wish to check whether any control-flow-graph in this binary is sufficiently similar to a database of known-vulnerable functions. This helps identify vulnerable statically linked libraries in closed-source software, a recurring problem (CVE, 2010; BID16 for which no good solutions are currently available. Figure 1 shows one example from this application, where the binary functions are represented as control flow graphs annotated with assembly instructions. This similarity learning problem is very challenging as subtle differences can make two graphs be semantically very different, while graphs with different structures can still be similar. A successful model for this problem should therefore (1) exploit the graph structures, and (2) be able to reason about the similarity of graphs both from the graph structures as well as from learned semantics. Figure 1 : The binary function similarity learning problem. Checking whether two graphs are similar requires reasoning about both the structure as well as the semantics of the graphs. Here the left two control flow graphs correspond to the same function compiled with different compilers (and therefore similar), while the graph on the right corresponds to a different function.In order to solve the graph similarity learning problem, we investigate the use of GNNs in this context, explore how they can be used to embed graphs into a vector space, and learn this embedding model to make similar graphs close in the vector space, and dissimilar graphs far apart. One important property of this model is that, it maps each graph independently to an embedding vector, and then all the similarity computation happens in the vector space. Therefore, the embeddings of graphs in a large database can be precomputed and indexed, which enables efficient retrieval with fast nearest neighbor search data structures like k-d trees BID4 or locality sensitive hashing BID23 .We further propose an extension to GNNs which we call Graph Matching Networks (GMNs) for similarity learning. Instead of computing graph representations independently for each graph, the GMNs compute a similarity score through a cross-graph attention mechanism to associate nodes across graphs and identify differences. By making the graph representation computation dependent on the pair, this matching model is more powerful than the embedding model, providing a nice accuracy-computation trade-off.We evaluate the proposed models and baselines on three tasks: a synthetic graph edit-distance learning task which captures structural similarity only, and two real world tasks -binary function similarity search and mesh retrieval, which require reasoning about both the structural and semantic similarity. On all tasks , the proposed approaches outperform established baselines and structure agnostic models; in more detailed ablation studies, we found that the Graph Matching Networks consistently outperform the graph embedding model and Siamese networks.To summarize, the contributions of this paper are:(1) we demonstrate how GNNs can be used to produce graph embeddings for similarity learning; (2) we propose the new Graph Matching Networks that computes similarity through cross-graph attention-based matching; (3) empirically we show that the proposed graph similarity learning models achieve good performance across a range of applications, outperforming structure agnostic models and established hand-engineered baselines. In this paper we studied the problem of graph similarity learning using graph neural networks. Compared to standard prediction problems for graphs, similarity learning poses a unique set of challenges and potential benefits. For example, the graph embedding models can be learned through a classification setting when we do have a set of classes in the dataset, but formulating it as a similarity learning problem can handle cases where we have a very large number of classes and only very few examples for each class. The representations learned from the similarity learning setting can also easily generalize to data from classes unseen during training (zero-shot generalization).We proposed the new graph matching networks as a stronger alternative to the graph embedding models. The added power for the graph matching models comes from the fact that they are not independently mapping each graph to an embedding, but rather doing comparisons at all levels across the pair of graphs, in addition to the embedding computation. The model can then learn to properly allocate capacity toward the embedding part or the matching part. The price to pay for this expressivity is the added computation cost in two aspects: (1) since each cross-graph matching step requires the computation of the full attention matrices, which requires at least O(|V 1 ||V 2 |) time, this may be expensive for large graphs; (2) the matching models operate on pairs, and cannot directly be used for indexing and searching through large graph databases. Therefore it is best to use the graph matching networks when we (1) only care about the similarity between individual pairs, or (2) use them in a retrieval setting together with a faster filtering model like the graph embedding model or standard graph similarity search methods, to narrow down the search to a smaller candidate set, and then use the more expensive matching model to rerank the candidates to improve precision.Developing neural models for graph similarity learning is an important research direction with many applications. There are still many interesting challenges to resolve, for example to improve the efficiency of the matching models, study different matching architectures, adapt the GNN capacity to graphs of different sizes, and applying these models to new application domains. We hope our work can spur further research in this direction.","paper addresses challenging problem retrieval matching graph structured objects makes two key contributions. First demonstrate how Graph Neural Networks GNN which have have emerged effective model various supervised prediction problems defined structured data can be trained produce embedding graphs vector spaces enables efficient similarity reasoning. Second propose novel Graph Matching Network model given pair graphs input computes similarity score jointly reasoning pair new cross-graph attention-based matching mechanism. demonstrate effectiveness models different domains including challenging problem control-flow-graph based function similarity search plays important role detection vulnerabilities software systems. experimental analysis demonstrates models are not only able exploit structure context similarity learning can also outperform domain-specific baseline systems have been carefully hand-engineered problems. Graphs are natural representations encoding relational structures are encountered many domains. Expectedly computations defined graph structured data are employed wide variety fields analysis molecules computational biology chemistry BID22 BID38 analysis knowledge graphs graph structured parses natural language understanding.In past years graph neural networks GNNs which have have emerged effective class models learning representations structured data solving various supervised prediction problems graphs. models are invariant permutations graph elements design compute graph node representations propagation process which iteratively aggregates local structural information Scarsellietal. 2009;BID31 BID22 node representations are then used directly node classification pooled graph vector graph classification. Problems beyond supervised classification regression are relatively less well-studied GNNs.In paper study problem similarity learning graph structured objects which appears many important real world applications particular similarity based retrieval graph databases. One motivating application is the computer security problem binary function similarity search where given binary may may contain code known vulnerabilities wish check whether control-flow-graph binary is sufficiently similar database known-vulnerable functions. helps identify vulnerable statically linked libraries closed-source software recurring problem CVE 2010;BID16 which no good solutions are currently available. Figure 1 shows one example application where the binary functions are represented control flow graphs annotated assembly instructions. similarity learning problem is very challenging subtle differences can make two graphs semantically different graphs different structures can still similar. successful model problem should therefore 1 exploit graph structures 2 able reason similarity graphs graph structures well learned semantics. Figure1:binary function similarity learning problem. Checking whether two graphs are similar requires reasoning structure well semantics graphs. left two control flow graphs correspond function compiled different compilers therefore similar graph right corresponds different function.In order solve graph similarity learning problem investigate use GNNs context explore how they can be used embed graphs vector space learn embedding model make similar graphs close vector space dissimilar graphs far apart. One important property model is that,it maps graph independently embedding vector similarity computation happens vector space. Therefore embeddings graphs large database can be precomputed indexed which enables efficient retrieval fast nearest neighbor search data structures like k-d trees BID4 locality sensitive hashing BID23.We propose extension GNNs which we call Graph Matching Networks GMNs similarity learning. Instead computing graph representations independently graph GMNs compute similarity score cross-graph attention mechanism associate nodes across graphs identify differences. making graph representation computation dependent pair matching model is more powerful embedding model providing nice accuracy-computation trade-off.We evaluate proposed models baselines three tasks:synthetic graph edit-distance learning task which captures structural similarity two real world tasks -binary function similarity search mesh retrieval which require reasoning structural semantic similarity. tasks proposed approaches outperform established baselines structure agnostic models;detailed ablation studies found Graph Matching Networks consistently outperform graph embedding model Siamese networks.To summarize contributions paper are:1 demonstrate how GNNs can be used produce graph embeddings similarity learning;2 propose new Graph Matching Networks computes similarity cross-graph attention-based matching;3 empirically show proposed graph similarity learning models achieve good performance across range applications outperforming structure agnostic models established hand-engineered baselines. paper studied problem graph similarity learning using graph neural networks. Compared standard prediction problems graphs similarity learning poses unique set challenges potential benefits. example graph embedding models can be learned classification setting when we do have set classes dataset formulating similarity learning problem can handle cases where we havea large number classes examples class. representations learned similarity learning setting can also easily generalize data classes unseen training zero-shot generalization.We proposed new graph matching networks stronger alternative graph embedding models. added power graph matching models comes fact are not independently mapping graph embedding rather comparisons levels across pair graphs addition embedding computation. model can then learn properly allocate capacity toward embedding part matching part. price pay expressivity is the added computation cost two aspects:1 since cross-graph matching step requires computation full attention matrices which requires least |V 1 ||V2 time may expensive large graphs;2 matching models operate pairs cannot directly used indexing searching large graph databases. Therefore is best use graph matching networks whenwe(1 care similarity individual pairs 2 use retrieval setting together faster filtering model like graph embedding model standard graph similarity search methods narrow search smaller candidate set use expensive matching model rerank candidates improve precision.Developing neural models graph similarity learning is an important research direction many applications. are still many interesting challenges resolve example improve efficiency matching models study different matching architectures adapt GNN capacity graphs different sizes applying models new application domains. hope work can spur research direction.",1483,1010,473,0.015,1.468,2025/11/05 17:19:06,0.01,1.647,0.4299065420560745,484.484
"Context information plays an important role in human language understanding, and it is also useful for machines to learn vector representations of language. In this paper, we explore an asymmetric encoder-decoder structure for unsupervised context-based sentence representation learning. As a result, we build an encoder-decoder architecture with an RNN encoder and a CNN decoder, and we show that neither an autoregressive decoder nor an RNN decoder is required.   We further combine a suite of effective designs to significantly improve model efficiency while also achieving better performance. Our model is trained on two different large unlabeled corpora, and in both cases transferability is evaluated on a set of downstream language understanding tasks. We empirically show that our model is simple and fast while producing rich sentence representations that excel in downstream tasks. Learning distributed representations of sentences is an important and hard topic in both the deep learning and natural language processing communities, since it requires machines to encode a sentence with rich language content into a fixed-dimension vector filled with continuous values. We are interested in learning to build a distributed sentence encoder in an unsupervised fashion by exploiting the structure and relationship in a large unlabeled corpus. Since humans interpret sentences by composing from the meanings of the words, we decompose the task of learning a sentence encoder into two essential components: learning distributed word representations, and learning how to compose a sentence representation from the representations of words in the given sentence.Numerous studies in human language processing have claimed that the context in which words and sentences are understood plays an important role in human language understanding BID1 BID4 . The idea of learning from the context information BID35 was recently successfully applied to vector representation learning for words in ; BID30 . BID8 proposed a unified framework for learning language representation from the unlabeled data, and it is able to generalize to various NLP tasks. Inspired by the prior work on incorporating context information into representation learning, proposed the Skipthought model, which is an encoder-decoder model for unsupervised sentence representation learning. The paper exploits the semantic similarity within a tuple of adjacent sentences as supervision, and successfully built a generic, distributed sentence encoder. Rather than applying the conventional autoencoder model, the skip-thought model tries to reconstruct the surrounding 2 sentences instead of the input sentence. The learned sentence representation encoder outperforms previous unsupervised pretrained models on the evaluation tasks with no finetuning, and the results are comparable to the models which were trained directly on the datasets in a supervised fashion.The usage of 2 independent decoders in Skip-thought model matches our intuition that, given the current sentence, inferring the previous sentence and inferring the next one should be different.Figure 1: Our proposed model is composed of an RNN encoder, and a CNN decoder. During training, a batch of sentences are sent to the model, and the RNN encoder computes a vector representation for each of sentences; then the CNN decoder needs to reconstruct the paired target sequence, which contains 30 contiguous words right after the input sentence, given the vector representation. 300 is the dimension of word vectors. D is the dimension of sentence representation, and it varies along with the change of the RNN encoder size. (Better view in color.) DISPLAYFORM0 Representation: We aim to provide a model with faster training speed with better transferability than existing algorithms, thus we choose to apply a parameter-free composition function, which is a concatenation of the outputs from a global mean pooling over time and a global max pooling over time, on the computed sequence of hidden states. The composition function can be represented as DISPLAYFORM1 where max H d· is the max operation on the d-th row of the matrix H, which outputs a scalar. Thus the representation z has a dimension of 2d.Decoder: The decoder is a 3-layer CNN to reconstruct the paired target sequence t, which needs to expand z from length 1 to the length of t. Intuitively, the decoder could be a stack of deconvolution layers. For fast training speed, we optimized the architecture to make it plausible to use fullyconnected layers and convolution layers in the decoder, since generally, convolution layers run faster than deconvolution layers in modern deep learning frameworks.Suppose that the target sequence t has N words, the first layer of deconvolution will expand z, which could be considered as a sequence with length 1, into a feature map with length N . It can be easily implemented as a concatenation of outputs from N linear transformations in parallel. Then the second and third layer are 1D-convolution layers with kernel size 3 and 1, respectively. The output feature DISPLAYFORM2 , where v ∈ R e , and e is dimension of the word vectors.Note that our decoder is not an autoregressive model, and it brings us high training efficiency. We will discuss the reason of choosing this decoder which we call a predict-all-words CNN decoder.Objective: A softmax layer is applied after the decoder to produce a probability distribution over words at each position, softmax(Ev n ), and the training objective is to minimize the sum of the negative log-likelihood over all positions in the target sequence t: DISPLAYFORM3 The loss function L is summed over all sentences in the training corpus. Inspired by learning to exploit the contextual information present in adjacent sentences, we proposed an asymmetric encoder-decoder model with a suite of techniques for improving context-based unsupervised sentence representation learning. Since we believe that a simple model will be faster in training and easier to analyze, we opt to use simple techniques in our proposed model, including 1) an RNN as the encoder, and a predict-all-words CNN as the decoder, 2) learning by inferring next contiguous words, 3) mean+max pooling, and 4) tying word vectors with word prediction. With thorough discussion and extensive evaluation, we justify our decision making for each component in our RNN-CNN model. In terms of the performance and the efficiency of training, we justify that our model is a fast and simple algorithm for learning generic sentence representations from unlabeled corpora. Further research will focus on how to maximize the utility of the context information, and how to design simple architectures to best make use of it. 9 , and 12) works better than other asymmetric models (CNN-LSTM, row 11), and models with symmetric structure (RNN-RNN, row 5 and 10). In addition, with larger encoder size, our model demonstrates stronger transferability. The default setting for our CNN decoder is that it learns to reconstruct 30 words right next to every input sentence. ""CNN(10)"" represents a CNN decoder with the length of outputs as 10, and ""CNN(50)"" represents it with the length of outputs as 50. "" †"" indicates that the CNN decoder learns to reconstruct next sentence. "" ‡"" indicates the results reported in Gan et al. as future predictor. The CNN encoder in our experiment, noted as "" §"", was based on AdaSent in Zhao et al. and Conneau et al.. Bold numbers are best results among models at same dimension, and underlined numbers are best results among all models. For STS14, the performance measures are Pearson's and Spearman's score. For MSRP, the performance measures are accuracy and F1 score.",Context information plays important role human language understanding is also useful machines learn vector representations language. paper explore asymmetric encoder-decoder structure unsupervised context-based sentence representation learning. result build encoder-decoder architecture RNN encoder CNN decoder show neither autoregressive decoder RNN decoder is required. combine suite effective designs significantly improve model efficiency also achieving better performance. model is trained two different large unlabeled corpora cases transferability is evaluated set downstream language understanding tasks. empirically show model is simple fast producing rich sentence representations excel downstream tasks. Learning distributed representations sentences is an important hard topic deep learning natural language processing communities since requires machines encode sentence rich language content fixed-dimension vector filled continuous values. are interested learning build distributed sentence encoder unsupervised fashion exploiting structure relationship large unlabeled corpus. Since humans interpret sentences composing meanings words decompose task learning sentence encoder two essential components:learning distributed word representations learning how to compose sentence representation representations words given sentence.Numerous studies human language processing have claimed context which words sentences are understood plays important role human language understanding BID1 BID4. idea learning context information BID35 was recently successfully applied vector representation learning words in;BID30. BID8 proposed unified framework learning language representation unlabeled data is able generalize various NLP tasks. Inspired prior work incorporating context information representation learning proposed Skipthought model which is an encoder-decoder model unsupervised sentence representation learning. paper exploits semantic similarity within tuple adjacent sentences supervision successfully built generic distributed sentence encoder. Rather applying conventional autoencoder model skip-thought model tries reconstruct surrounding 2 sentences instead input sentence. learned sentence representation encoder outperforms previous unsupervised pretrained models evaluation tasks finetuning results are comparable models which were trained directly datasets supervised fashion.The usage 2 independent decoders Skip-thought model matches intuition given current sentence inferring previous sentence inferring next one should be different.Figure1:proposed model is composed RNN encoder CNN decoder. training batch sentences are sent model RNN encoder computes vector representation sentences;CNN decoder needs reconstruct paired target sequence which contains 30 contiguous words right input sentence given vector representation. 300 is the is dimension word vectors. is the dimension sentence representation varies along change RNN encoder size. Better view color. DISPLAYFORM0 Representation:aim provide model faster training speed better transferability existing algorithms thus choose apply parameter-free composition function which is a concatenation outputs global mean pooling time global max pooling time computed sequence hidden states. composition function can be represented DISPLAYFORM1 where maxHd· is the max operation d-th row matrixH which outputs scalar. Thus representationz has a dimension 2d.Decoder:decoder is a 3-layer CNN reconstruct paired target sequence which needs expandz length1 length t. Intuitively decoder could stack deconvolution layers. fast training speed optimized architecture make plausible use fullyconnected layers convolution layers decoder since generally convolution layers run faster deconvolution layers modern deep learning frameworks.Suppose target sequence has N words first layer deconvolution will expandz could considered sequence length1 feature map lengthN. can be easily implemented concatenation outputs N linear transformations parallel. second third layer are 1D-convolution layers kernel size3 1 respectively. output feature DISPLAYFORM2 wherev∈Re e is the is dimension word vectors.Note decoder is not an autoregressive model brings us high training efficiency. will discuss reason choosing decoder which we call predict-all-words CNN decoder.Objective:softmax layer is applied decoder produce probability distribution words position softmax Evn training objective is to minimize sum negative log-likelihood positions target sequence t:DISPLAYFORM3 loss functionL is summed sentences training corpus. Inspired learning exploit contextual information present adjacent sentences proposed asymmetric encoder-decoder model suite techniques improving context-based unsupervised sentence representation learning. Since believe simple model will be faster training easier analyze opt use simple techniques proposed model including1 RNN encoder predict-all-words CNN decoder 2 learning inferring next contiguous words 3 mean+max pooling 4 tying word vectors word prediction. thorough discussion extensive evaluation justify decision making component RNN-CNN model. terms performance efficiency training justify model is a fast simple algorithm learning generic sentence representations unlabeled corpora. research will focus how to maximize utility context information how to design simple architectures best make use it. 9 12 works better asymmetric models CNN-LSTM row11 models symmetric structure RNN-RNN row5 10 addition larger encoder size model demonstrates stronger transferability. default setting CNN decoder is that it learns reconstruct 30 words right next every input sentence. CNN 10 represents CNN decoder length outputs 10 CNN 50 represents length outputs 50. † indicates CNN decoder learns reconstruct next sentence. ‡ indicates results reported Ganetal. future predictor. CNN encoder experiment noted § was based AdaSent Zhaoetal. Conneauetal.. Bold numbers are best results among models dimension underlined numbers are best results among models. STS14 performance measures are Pearson's Spearman's score. MSRP performance measures are accuracy F1 score.,1491,1000,491,0.016,1.491,2025/11/05 17:19:06,0.01,1.481,0.5015576323987541,479.187
"Building on the success of deep learning, two modern approaches to learn a probability model of the observed data are Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs). VAEs consider an explicit probability model for the data and compute a generative distribution by maximizing a variational lower-bound on the log-likelihood function. GANs, however, compute a generative model by minimizing a distance between observed and generated probability distributions without considering an explicit model for the observed data. The lack of having explicit probability models in GANs prohibits computation of sample likelihoods in their frameworks and limits their use in statistical inference problems. In this work, we show that an optimal transport GAN with the entropy regularization can be viewed as a generative model that maximizes a lower-bound on average sample likelihoods, an approach that VAEs are based on. In particular, our proof constructs an explicit probability model for GANs that can be used to compute likelihood statistics within GAN's framework. Our numerical results on several datasets demonstrate consistent trends with the proposed theory. Learning generative models is becoming an increasingly important problem in machine learning and statistics with a wide range of applications in self-driving cars BID26 , robotics BID10 , natural language processing BID14 , domain-transfer BID25 , computational biology BID6 , etc. Two modern approaches to deal with this problem are Generative Adversarial Networks (GANs) BID7 and Variational AutoEncoders (VAEs) BID13 BID15 BID23 BID28 BID17 .VAEs BID13 ) compute a generative model by maximizing a variational lowerbound on average sample likelihoods using an explicit probability distribution for the data. GANs , however, learn a generative model by minimizing a distance between observed and generated distributions without considering an explicit probability model for the data. Empirically , GANs have been shown to produce higher-quality generative samples than that of VAEs BID12 . However, since GANs do not consider an explicit probability model for the data, we are unable to compute sample likelihoods using their generative models. Computations of sample likelihoods and posterior distributions of latent variables are critical in several statistical inference. Inability to obtain such statistics within GAN's framework severely limits their applications in such statistical inference problems.In this paper, we resolve these issues for a general formulation of GANs by providing a theoreticallyjustified approach to compute sample likelihoods using GAN's generative model. Our results can open new directions to use GANs in massive-data applications such as model selection, sample selection, hypothesis-testing, etc (see more details in Section 5). Now, we state our main results informally without going into technical conditions while precise statements of our results are presented in Section 2. Let Y andŶ ∶= G(X) represent observed (i.e. real) and generative (i.e. fake or synthetic) variables, respectively. X (i.e. the latent variable) is the randomness used as the input to the generator G(.). Consider the following explicit probability By training a GAN model, we first compute optimal generator G * and optimal coupling between the observed variable Y and the latent variable X. The likelihood of a test sample y test can then be lower-bounded using a combination of three terms: (1) the expected distance of y test to the distribution learnt by the generative model, (2) the entropy of the coupled latent variable given y test and (3) the likelihood of the coupled latent variable with y test .model of the data given a latent sample X = x: f Y X=x (y) ∝ exp(− (y, G(x))), (1.1)where (., .) is a loss function. f Y X=x (y) is the model that we are considering for the underlying data distribution. This is a reasonable model for the data as the function G can be a complex function. Similar data models have been used in VAEs . Under this explicit probability model, we show that minimizing the objective of an optimal transport GAN (e.g. Wasserstein BID0 ) with the cost function (., .) and an entropy regularization BID2 BID27 ) maximizes a variational lower-bound on average sample likelihoods. I.e.average sample likelihoods ≥ − (entropic GAN objective) + constants.(1.2)If (y,ŷ) = y −ŷ 2 , the optimal transport (OT) GAN simplifies to WGAN while if (y,ŷ) = y −ŷ 2 2 , the OT GAN simplifies to the quadratic GAN (or, W2GAN) BID3 ). The precise statement of this result can be found in Theorem 1. This result provides a statistical justification for GAN's optimization and puts it in par with VAEs whose goal is to maximize a lower bound on sample likelihoods. We note that the entropy regularization has been proposed primarily to improve computational aspects of GANs BID5 . Our results provide an additional statistical justification for this regularization term. Moreover, using GAN's training, we obtain a coupling between the observed variable Y and the latent variable X. This coupling provides the conditional distribution of the latent variable X given an observed sample Y = y. The explicit model of equation 1.1 acts similar to the decoder in the VAE framework, while the coupling computed using GANs acts as an encoder.Connections between GANs and VAEs have been investigated in some of the recent works as well BID11 BID16 . In BID11 , GANs are interpreted as methods performing variational inference on a generative model in the label space. In their framework, observed data samples are treated as latent variables while the generative variable is the indicator of whether data is real or fake. The method in BID16 , on the other hand, uses an auxiliary discriminator network to rephrase the maximum-likelihood objective of a VAE as a twoplayer game similar to the objective of a GAN. Our method is different from both these approaches as we consider an explicit probability model for the data, and show that the entropic GAN objective maximizes a variational lower bound under this probability model, thus allowing sample likelihood computation in GANs similar to VAEs.Of relevance to our work is BID30 , in which annealed importance sampling (AIS) is used to evaluate the approximate likelihood of decoder-based generative models. More specifically, a Gaussian observation model with a fixed variance is used as the generative distribution for GANbased models on which the AIS is computed. Gaussian observation models may not be proper specially in high-dimensional spaces . Our approach, on the other hand, makes a connection between GANs and VAEs by constructing a theoretically-motivated model for the data distribution in GANs. We then leverage this approach in computing sample likelihood estimates in GANs.Another key question that we address here is how to estimate the likelihood of a new sample y test given the generative model trained using GANs. For instance, if we train a GAN on stop-sign images, upon receiving a new image, one may wish to compute the likelihood of the new sample y test according to the trained generative model. In standard GAN formulations, the support of the generative distribution lies on the range of the optimal generator function. Thus, if the observed sample y test does not lie on that range (which is very likely in practice ), there is no way to assign a sensible likelihood score to that sample. Below, we show that using the explicit probability model of equation 1.1, we can lower-bound the likelihood of this sample y test . This is similar to the variational lower-bound on sample likelihoods used in VAEs. Our numerical results show that this lower-bound well-reflect the expected trends of the true sample likelihoods.Let G * and P * Y,X be the optimal generator and the optimal coupling between real and latent variables, respectively. The optimal coupling P * Y,X can be computed efficiently for entropic GANs as we explain in Section 3. For other GAN architectures, one may approximate such couplings as we explain in Section 4. The log likelihood of a new test sample y test can be lower-bounded as DISPLAYFORM0 distance to the generative model DISPLAYFORM1 We present the precise statement of this result in Corollary 2. This result combines three components in order to approximate the likelihood of a sample given a trained generative model:• The distance between y test to the generative model. If this distance is large, the likelihood of observing y test from the generative model is small.• The entropy of the coupled latent variable. If the entropy term is large, the coupled latent variable has a large randomness. This contributes positively to the sample likelihood.• The likelihood of the coupled latent variable. If latent samples have large likelihoods, the likelihood of the observed test sample will be large as well. FIG2 provides a pictorial illustration of these components. In what follows, we explain the technical ingredients of our main results. In Section 3, we present computational methods for GANs and entropic GANs, while in Section 4, we provide numerical experiments on benchmark datasets. In this paper, we have provided a statistical framework for a family of GANs. Our main result shows that the entropic GAN optimization can be viewed as maximization of a variational lower-bound on average log-likelihoods, an approach that VAEs are based upon. This result makes a connection between two most-popular generative models, namely GANs and VAEs. More importantly, our result constructs an explicit probability model for GANs that can be used to compute a lower-bound on sample likelihoods. Our experimental results on various datasets demonstrate that this likelihood surrogate can be a good approximation of the true likelihood function. Although in this paper we mainly focus on understanding the behavior of the sample likelihood surrogate in different datasets, the proposed statistical framework of GANs can be used in various statistical inference applications. For example, our proposed likelihood surrogate can be used as a quantitative measure to evaluate the performance of different GAN architectures, it can be used to quantify the domain shifts, it can be used to select a proper generator class by balancing the bias term vs. variance, it can be used to detect outlier samples, it can be used in statistical tests such as hypothesis testing, etc. We leave exploring these directions for future work. APPENDIX A PROOF OF THEOREM 1Using the Baye's rule, one can compute the log-likelihood of an observed sample y as follows: DISPLAYFORM0 where the second step follows from equation 2.4.Consider a joint density function P X,Y such that its marginal distributions match P X and P Y . Note that the equation A.1 is true for every x. Thus, we can take the expectation of both sides with respect to a distribution P X Y =y . This leads to the following equation: DISPLAYFORM1 where H(.) is the Shannon-entropy function.Next we take the expectation of both sides with respect to P Y : DISPLAYFORM2 Here, we replaced the expectation over P X with the expectation over f X since one can generate an arbitrarily large number of samples from the generator. Since the KL divergence is always nonnegative, we have DISPLAYFORM3 Moreover, using the data processing inequality, we have BID1 . Thus, DISPLAYFORM4 DISPLAYFORM5 GAN objective with entropy regularizer DISPLAYFORM6 This inequality is true for every P X,Y satisfying the marginal conditions. Thus, similar to VAEs, we can pick P X,Y to maximize the lower bound on average sample log-likelihoods. This leads to the entropic GAN optimization 2.3.",Building success deep learning two modern approaches learn probability model observed data are Generative Adversarial Networks GANs Variational AutoEncoders VAEs VAEs consider explicit probability model data compute generative distribution maximizing variational lower-bound log-likelihood function. GANs however compute generative model minimizing distance observed generated probability distributions without considering explicit model observed data. lack explicit probability models GANs prohibits computation sample likelihoods frameworks limits use statistical inference problems. work show optimal transport GAN entropy regularization can be viewed generative model maximizes lower-bound average sample likelihoods approach VAEs are based on. particular proof constructs explicit probability model GANs can be used compute likelihood statistics within GAN's framework. numerical results several datasets demonstrate consistent trends proposed theory. Learning generative models is becoming increasingly important problem machine learning statistics wide range applications self-driving cars BID26 robotics BID10 natural language processing BID14 domain-transfer BID25 computational biology BID6 etc. Two modern approaches deal problem are Generative Adversarial Networks GANs BID7 Variational AutoEncoders VAEs BID13 BID15 BID23 BID28 BID17.VAEs BID13 compute generative model maximizing variational lowerbound average sample likelihoods using explicit probability distribution data. GANs however learn generative model minimizing distance observed generated distributions without considering explicit probability model data. Empirically GANs have been shown produce higher-quality generative samples VAEs BID12. However since GANs do not consider explicit probability model data are unable compute sample likelihoods using generative models. Computations sample likelihoods posterior distributions latent variables are critical several statistical inference. Inability obtain statistics within GAN's framework severely limits applications statistical inference problems.In paper resolve issues general formulation GANs providing theoreticallyjustified approach compute sample likelihoods using GAN's generative model. results can open new directions use GANs massive-data applications model selection sample selection hypothesis-testing etc see details Section5 state main results informally without going technical conditions precise statements results are presented Section2. Let andŶ∶=G X represent observed.e real generative.e fake synthetic variables respectively. X.e latent variable is the randomness used input generatorG Consider following explicit probability training GAN model first compute optimal generator G* optimal coupling observed variable latent variableX. likelihood test sample test can then be can be lower-bounded using combination three terms:1 expected distance test distribution learnt generative model 2 entropy coupled latent variable given test 3 likelihood coupled latent variable test.model data given latent sampleX x:f X=x ∝ exp − G x 1.1 where(. is loss function. f X=x is model are considering underlying data distribution. is a reasonable model data functionG can be a complex function. Similar data models have been used VAEs. explicit probability model show minimizing objective optimal transport GAN e.g Wasserstein BID0 cost function entropy regularization BID2 BID27 maximizes variational lower-bound average sample likelihoods. I. e.average sample likelihoods≥ − entropic GAN objective+constants. 1.2 If(y ŷ −ŷ2 optimal transport OT GAN simplifies WGAN if(y ŷ −ŷ22 OT GAN simplifies quadratic GAN W2GAN BID3 precise statement result can be found Theorem1. result provides statistical justification GAN's optimization puts par VAEs whose goal is to maximize lower bound sample likelihoods. note entropy regularization has been proposed primarily improve computational aspects GANs BID5. results provide additional statistical justification regularization term. Moreover using GAN's training obtain coupling observed variable latent variableX. coupling provides conditional distribution latent variable X given observed sample y. explicit model equation 1.1 acts similar decoder VAE framework coupling computed using GANs acts encoder.Connections GANs VAEs have been investigated recent works well BID11 BID16. BID11 GANs are interpreted methods performing variational inference generative model label space. framework if the observed data samples are treated latent variables generative variable is the indicator whether data is real fake. method BID16 hand uses auxiliary discriminator network rephrase maximum-likelihood objective VAE twoplayer game similar objective GAN. method is different approaches consider explicit probability model data show entropic GAN objective maximizes variational lower bound probability model thus allowing sample likelihood computation GANs similar VAEs.Of relevance work is BID30 which annealed importance sampling AIS is used evaluate approximate likelihood decoder-based generative models. specifically Gaussian observation model fixed variance is used generative distribution GANbased models which the AIS is computed. Gaussian observation models may proper specially high-dimensional spaces. approach hand makes connection GANs VAEs constructing theoretically-motivated model data distribution GANs. leverage approach computing sample likelihood estimates GANs.Another key question address is how to estimate likelihood new sample test given generative model trained using GANs. instance if we train GAN stop-sign images upon receiving new image one may wish compute likelihood new sample test according trained generative model. standard GAN formulations support generative distribution lies range optimal generator function. Thus if the observed sample test does not lie range which is very likely practice is way assign sensible likelihood score sample. show using explicit probability model equation 1.1 can lower-bound likelihood sample test. is similar variational lower-bound sample likelihoods used VAEs. numerical results show lower-bound well-reflect expected trends true sample likelihoods.LetG * P* X optimal generator optimal coupling real latent variables respectively. optimal couplingP* X can be computed efficiently entropic GANs explain Section3. GAN architectures one may approximate couplings explain Section4. log likelihood new test sample test can then be can be lower-bounded DISPLAYFORM0 distance generative model DISPLAYFORM1 present precise statement result Corollary2. result combines three components order approximate likelihood sample given trained generative model:• distance test generative model. If this distance is large likelihood observing test generative model is small.• entropy coupled latent variable. If the entropy term is large coupled latent variable has a large randomness. contributes positively sample likelihood.• likelihood coupled latent variable. If latent samples have large likelihoods likelihood observed test sample will be large well. FIG2 provides pictorial illustration components. what follows explain technical ingredients main results. Section3 present computational methods GANs entropic GANs Section4 provide numerical experiments benchmark datasets. paper have provided statistical framework family GANs. main result shows entropic GAN optimization can be viewed maximization variational lower-bound average log-likelihoods approach VAEs are based upon. result makes connection two most-popular generative models namely GANs VAEs. importantly result constructs explicit probability model GANs can be used compute lower-bound sample likelihoods. experimental results various datasets demonstrate likelihood surrogate can be a good approximation true likelihood function. Although paper mainly focus understanding behavior sample likelihood surrogate different datasets proposed statistical framework GANs can be used various statistical inference applications. example proposed likelihood surrogate can be used quantitative measure evaluate performance different GAN architectures can be used quantify domain shifts can be used select proper generator class balancing bias termvs. variance can be used detect outlier samples can be used statistical tests hypothesis testing etc. leave exploring directions future work. APPENDIX PROOF THEOREM 1Using Baye's rule one can compute log-likelihood observed sample follows:DISPLAYFORM0 where the second step follows equation2. 4.Consider joint density functionP X marginal distributions matchP X P Y. Note equation A.1 is true everyx. Thus can take expectation sides respect distributionPX =y leads following equation:DISPLAYFORM1 whereH is Shannon-entropy function.Next take expectation sides respect P Y:DISPLAYFORM2 replaced expectation PX expectation f X since one can generate arbitrarily large number samples generator. Since KL divergence is always nonnegative have DISPLAYFORM3 Moreover using data processing inequality have BID1. Thus DISPLAYFORM4 DISPLAYFORM5 GAN objective entropy regularizer DISPLAYFORM6 inequality is true everyPX satisfying marginal conditions. Thus similar VAEs can pickPX maximize lower bound average sample log-likelihoods leads entropic GAN optimization 2.3,2368,1594,774,0.034,1.486,2025/11/05 17:19:06,0.01,1.577,0.4859813084112147,786.068
"We introduce geomstats, a Python package for Riemannian modelization and optimization over manifolds such as hyperspheres, hyperbolic spaces, SPD matrices or Lie groups of transformations. Our contribution is threefold. First, geomstats allows the flexible modeling of many a machine learning problem through an efficient and extensively unit-tested implementations of these manifolds, as well as the set of useful Riemannian metrics, exponential and logarithm maps that we provide. Moreover, the wide choice of loss functions and our implementation of the corresponding gradients allow fast and easy optimization over manifolds. Finally, geomstats is the only package to provide a unified framework for Riemannian geometry, as the operations implemented in geomstats are available with different computing backends (numpy,tensorflow and keras), as well as with a GPU-enabled mode–-thus considerably facilitating the application of Riemannian geometry in machine learning. In this paper, we present geomstats through a review of the utility and advantages of manifolds in machine learning, using the concrete examples that they span to show the efficiency and practicality of their implementation using our package From soft-classification to image recognition, Riemannian manifolds provide a natural framework to many a machine learning problem. Consider the following standard supervised learning problem: given an input X, the goal is to predict an output Y . The relation between X and Y is typically modeled by a function f θ : X → Y , characterized by a set of parameters θ. Riemannian geometry often naturally arises at each of the three different stages of the modelization: through the input X, the output Y , or the parameters θ. For instance, the input X might belong to a Riemannian manifold. This is typically the case in image processing, where images X are frequently modeled as elements of a low-dimensional manifold (17; 57; 61; 67; 18; 6) . Such is the case in BID61 , in which the authors consider spherical images as elements of the orthogonal rotation group SO BID2 . In some cases, X can even be a manifold itself-in BID7 for instance, the authors propose to model images as a function of a 2D smooth surface representing a shape such as a human pose. Similarly, the output Y often belongs to a Riemannian manifold (42; 47) . Such is the case in problems where the output is a member of the set of doubly stochastic matrices -as for instance in some neurosciences applications (48; 11)-. or when the optimization is carried on a given manifold (2; 44; 27) . In BID27 for example, the authors use a neural network to predict the pose of a camera Y , which is defined as an element of the Lie group SE(3). Finally, the parameter θ of a model can be constrained on a Riemannian manifold, such as in the work of BID28 which constrains the weights of a neural network on multiple dependent Stiefel manifolds.Manifolds offer intuitive and practical advantages for modeling inputs, outputs and parameters. When applied to the input, they constitute lower dimensional spaces with fewer degrees of freedom, thus potentially allowing faster computations and less substantial memory allocation costs. Moreover, the non-linear degrees of freedom in these manifolds are often more intuitive and benefit from more expressive power. For instance, the geolocation of points of interest on Earth is more efficiently achieved through their longitude and latitude-i.e., their 2D manifold coordinates-rather than through their position (x, y, z) in the 3D Cartesian space. Most current machine learning problems make little use of this underlying manifold structure -rather viewing their optimization task as a constrained optimization over Euclidean space. Riemannian geometry, on the other hand, attempts to leverage the manifold structure to solve the corresponding optimization problem, replacing lines by geodesics, partial differential by covariate differentiation (59)-thus potentially reducing the dimension of the prblem space and the memory allocation costs.Yet, the adoption of Riemannian geometry by the machine learning community has been largely hindered by the lack of a modular framework for implementing such methods. Code sequences are often custom tailored for specific problems and/or computing backends, and are thus not easily re-usable: . To address this issue, some packages have been written to perform computations on manifolds. The theanogeometry package BID38 provides an implementation of differential geometric tensors on manifolds where closed forms do not necessarily exist, using the automatic differentiation tool theano to integrate differential equations that define the geometric tensors. The pygeometry package (10) offers an implementation primarily focused on the Lie groups SO(3) and SE(3) for robotics applications. However, no implementation of non-canonical metrics on these Lie groups is provided. The pymanopt package BID62 , originally implemented in Matlab as manopt, provides a very comprehensive toolbox for optimization on a extensive list of manifolds. However, not only is the choice of metrics on these manifolds rather restricted, the manifolds themselves are often implemented using canonical embeddings in higher-dimensional euclidean spaces, with high computational costs. This paper presents geomstats, a package specifically targeted at the machine learning community to perform computations on Riemannian manifolds with a flexible choice of Riemannian metrics. The geomstats package makes three contributions. First, geomstats is the first Riemannian geometry package to be extensively unit-tested with more than 90 % code coverage. Second, geomstats implements numpy (51) and tensorflow (1) backends, providing vectorized, intuitive computations, and available for GPU implementation. We also provide an updated version of the deep learning framework,keras, equipped with Riemannian gradient descent on manifolds. Finally, geomstats strives to be a user-friendly and educational a tool, presenting Riemannian geometry to computer scientists and facilitating its use as a complement to theoretical papers or books. We refer to BID54 for the theory and expect the reader to have a high-level understanding of Riemannian geometry.Our paper is organized as follows. We begin by providing an overview of geomstats in Section 2. We then present concrete use cases of geomstats for machine learning on manifolds of increasing geometric complexity, starting with manifolds embedded in flat spaces in Section 3, to a manifold embedded in a Lie group with a Lie group action in Section 4, to the Lie groups SO(n) and SE(n) in Section 5. Along the way, we present a review of the occurrences of each manifold in the machine learning literature, some educational visualizations of the Riemannian geometry as well as implementations of machine learning models where the inputs, the outputs and the parameters successively belong to manifolds. We introduce the open-source package geomstats to democratize the use of Riemannian geometry in machine learning for a wide range of applications. Regarding the geometry, we have presented manifolds of increasing complexity: manifolds embedded in flat Riemannian spaces, then the case of the SPD matrices space and lastly Lie groups with invariant Riemannian metrics. This provides an educational tool for users who want to delve into Riemannian geometry through a hands-on approach, with intuitive visualizations for example in subsections 3.4 and 5.2.In regard to machine learning, we have presented concrete use cases where inputs, outputs and parameters belong to manifolds, in the respective examples of subsection 4.2, subsection 5.3 and subsection 3.2. They demonstrate the usability of geomstats package for efficient and userfriendly Riemannian geometry. Regarding the machine learning applications, we have reviewed the occurrences of each manifold in the literature across many different fields. We kept the range of applications very wide to show the many new research avenues that open at the cross-roads of Riemannian geometry and machine learning.geomstats implements manifolds where closed-forms for the Exponential and the Logarithm maps of the Riemannian metrics exist. Future work will involve implementing manifolds where these closed forms do not necessarily exist. We will also provide the pytorch backend.",introduce geomstats Python package Riemannian modelization optimization manifolds hyperspheres hyperbolic spaces SPD matrices Lie groups transformations. contribution is threefold. First geomstats allows flexible modeling many machine learning problem efficient extensively unit-tested implementations manifolds well set useful Riemannian metrics exponential logarithm maps provide. Moreover wide choice loss functions implementation corresponding gradients allow fast easy optimization manifolds. Finally geomstats is the only package provide unified framework Riemannian geometry operations implemented geomstats are available different computing backends numpy tensorflow keras well GPU-enabled mode–-thus considerably facilitating application Riemannian geometry machine learning. paper present geomstats review utility advantages manifolds machine learning using concrete examples span show efficiency practicality implementation using package soft-classification image recognition Riemannian manifolds provide natural framework many machine learning problem. Consider following standard supervised learning problem:given inputX goal is to predict output Y. relation X is typically modeled functionfθ:X→ characterized set parametersθ. Riemannian geometry often naturally arises three different stages modelization:inputX output parametersθ. instance input X might belong Riemannian manifold. is typically case image processing where imagesX are frequently modeled elements low-dimensional manifold 17;57;61;67;18;6 is case BID61 which the authors consider spherical images elements orthogonal rotation group BID2. cases X can even manifold itself-in BID7 instance which the authors propose model images function 2D smooth surface representing shape human pose. Similarly output often belongs Riemannian manifold 42;47 is case problems where the output is a member set doubly stochastic matrices -as instance neurosciences applications 48;11 -. when the optimization is carried given manifold 2;44;27 BID27 example which the authors use neural network predict pose camera which is defined element Lie groupSE 3 Finally parameterθ model can be constrained Riemannian manifold work BID28 which constrains weights neural network multiple dependent Stiefel manifolds.Manifolds offer intuitive practical advantages modeling inputs outputs parameters. When applied input constitute lower dimensional spaces fewer degrees freedom are thus potentially allowing faster computations less substantial memory allocation costs. Moreover non-linear degrees freedom manifolds are often intuitive benefit expressive power. instance geolocation points interest Earth is more efficiently achieved longitude latitude-i.e 2D manifold coordinates-rather position x z 3D Cartesian space. current machine learning problems make little use underlying manifold structure -rather viewing optimization task constrained optimization Euclidean space. Riemannian geometry hand attempts leverage manifold structure solve corresponding optimization problem replacing lines geodesics partial differential covariate differentiation 59 -thus potentially reducing dimension prblem space memory allocation costs.Yet adoption Riemannian geometry machine learning community has been largely hindered lack modular framework implementing methods. Code sequences are often custom tailored specific problems/computing backends are thus easily re-usable address issue packages have been written perform computations manifolds. theanogeometry package BID38 provides implementation differential geometric tensors manifolds where where these closed forms do not necessarily exist using automatic differentiation tool theano integrate differential equations define geometric tensors. pygeometry package 10 offers implementation primarily focused Lie groups 3 SE 3 robotics applications. However implementation non-canonical metrics Lie groups is provided. pymanopt package BID62 originally implemented Matlab manopt provides comprehensive toolbox optimization extensive list manifolds. However is choice metrics manifolds rather restricted manifolds are often implemented using canonical embeddings higher-dimensional euclidean spaces high computational costs. paper presents geomstats package specifically targeted machine learning community perform computations Riemannian manifolds flexible choice Riemannian metrics. geomstats package makes three contributions. First geomstats is the first Riemannian geometry package extensively unit-tested 90% code coverage. Second geomstats implements numpy 51 tensorflow 1 backends providing vectorized intuitive computations available GPU implementation. will also provide updated version deep learning framework keras equipped Riemannian gradient descent manifolds. Finally geomstats strives user-friendly educational tool presenting Riemannian geometry computer scientists facilitating use complement theoretical papers books. refer BID54 theory expect reader have a high-level understanding Riemannian geometry.Our paper is organized follows. begin providing overview geomstats Section2. present concrete use cases geomstats machine learning manifolds increasing geometric complexity starting manifolds embedded flat spaces Section3 manifold embedded Lie group Lie group action Section4 Lie groups n SE n Section5. Along way present review occurrences manifold machine learning literature educational visualizations Riemannian geometry well implementations machine learning models where the where inputs outputs parameters successively belong manifolds. introduce open-source package geomstats democratize use Riemannian geometry machine learning wide range applications. Regarding geometry have presented manifolds increasing complexity:manifolds embedded flat Riemannian spaces case SPD matrices space lastly Lie groups invariant Riemannian metrics. provides educational tool users who want delve Riemannian geometry hands-on approach intuitive visualizations example subsections 3.4 5. 2.In regard machine learning have presented concrete use cases where the where inputs outputs parameters belong manifolds respective examples subsection 4.2 subsection 5.3 subsection 3.2 demonstrate usability geomstats package efficient userfriendly Riemannian geometry. Regarding machine learning applications have reviewed occurrences manifold literature across many different fields. kept range applications wide show many new research avenues open cross-roads Riemannian geometry machine learning.geomstats implements manifolds where closed-forms Exponential Logarithm maps Riemannian metrics exist. Future work will involve implementing manifolds where where these closed forms do not necessarily exist. will also provide pytorch backend.,1667,1130,537,0.02,1.475,2025/11/05 17:19:06,0.01,1.415,0.4517133956386294,507.316
"We propose to execute deep neural networks (DNNs) with dynamic and sparse graph (DSG) structure for compressive memory and accelerative execution during both training and inference. The great success of DNNs motivates the pursuing of lightweight models for the deployment onto embedded devices. However, most of the previous studies optimize for inference while neglect training or even complicate it. Training is far more intractable, since (i) the neurons dominate the memory cost rather than the weights in inference; (ii) the dynamic activation makes previous sparse acceleration via one-off optimization on fixed weight invalid; (iii) batch normalization (BN) is critical for maintaining accuracy while its activation reorganization damages the sparsity. To address these issues, DSG activates only a small amount of neurons with high selectivity at each iteration via a dimensionreduction search and obtains the BN compatibility via a double-mask selection. Experiments show significant memory saving (1.7-4.5x) and operation reduction (2.3-4.4x) with little accuracy loss on various benchmarks. Deep Neural Networks (DNNs) BID23 have been achieving impressive progress in a wide spectrum of domains (Simonyan & Zisserman, 2014; BID0 Redmon & Farhadi, 2016; , while the models are extremely memory-and compute-intensive. The high representational and computational costs motivate many researchers to investigate approaches on improving the execution performance, including matrix or tensor decomposition BID44 Novikov et al., 2015; Garipov et al., 2016; BID47 BID3 , data quantization (Courbariaux et al., 2016; BID51 BID27 BID24 BID39 BID33 , and network pruning BID4 BID8 a; BID30 BID13 Molchanov et al., 2016; BID13 Spring & Shrivastava, 2017; BID28 BID49 BID12 Chin et al., 2018; BID31 BID14 . However, most of the previous work aim at inference while the challenges for reducing the representational and computational costs of training are not well-studied. Although some works demonstrate acceleration in the distributed training BID29 BID6 BID47 , we target at the single-node optimization, and our method can also boost training in a distributed fashion. DNN training, which demands much more hardware resources in terms of both memory capacity and computation volume, is far more challenging than inference. Firstly, activation data in training will be stored for backpropagation, significantly increasing the memory consumption. Secondly, training iteratively updates model parameters using mini-batched stochastic gradient descent. We almost always expect larger mini-batches for higher throughput FIG0 ), faster convergence, and better accuracy (Smith et al., 2017) . However, memory capacity is often the limitation factor FIG0 Upper and lower one are the feature maps before and after BN, respectively. However, using BN damages the sparsity through information fusion; (f) There exists such great representational redundancy that more than 80% of activations are close to zero.that may cause performance degradation or even make large models with deep structures or targeting high-resolution vision tasks hard to train BID42 .It is difficult to apply existing sparsity techniques towards inference phase to training phase because of the following reasons: 1) Prior arts mainly compress the pre-trained and fixed weight parameters to reduce the off-chip memory access in inference BID9 , while instead, the dynamic neuronal activations turn out to be the crucial bottleneck in training BID17 , making the prior inference-oriented methods inefficient. Besides , during training we need to stash a vast batched activation space for the backward gradient calculation. Therefore , neuron activations creates a new memory bottleneck (Figure 1(c) ). In this paper, we will sparsify the neuron activations for training compression.2) The existing inference accelerations usually add extra optimization problems onto the critical path Molchanov et al., 2016; BID30 BID27 BID49 BID31 , i.e., 'complicated training ⇒ simplified inference', which embarrassingly complicates the training phase. 3) Moreover , previous studies reveal that batch normalization (BN) is crucial for improving accuracy and robustness FIG0 ) through activation fusion across different samples within one mini-batch for better representation (Morcos et al., 2018; BID16 . BN almost becomes a standard training configuration; however, inference-oriented methods seldom discuss BN and treat BN parameters as scaling and shift factors in the forward pass. We further find that BN will damage the sparsity due to the activation reorganization FIG0 ). Since this work targets both training and inference, the BN compatibility problem should be addressed.From the view of information representation, the activation of each neuron reflects its selectivity to the current stimulus sample (Morcos et al., 2018) , and this selectivity dataflow propagates layer by layer forming different representation levels. Fortunately , there is much representational redundancy, for example, lots of neuron activations for each stimulus sample are so small and can be removed FIG0 ). Motivated by above comprehensive analysis regarding memory and compute, we propose to search critical neurons for constructing a sparse graph at every iteration. By activating only a small amount of neurons with a high selectivity, we can significantly save memory and simplify computation with tolerable accuracy degradation. Because the neuron response dynamically changes under different stimulus samples, the sparse graph is variable. The neuronaware dynamic and sparse graph (DSG) is fundamentally distinct from the static one in previous work on permanent weight pruning since we never prune the graph but activate part of them each time. Therefore, we maintain the model expressive power as much as possible. A graph selection method , dimension-reduction search, is designed for both compressible activations with elementwise unstructured sparsity and accelerative vector-matrix multiplication (VMM) with vector-wise structured sparsity. Through double-mask selection design, it is also compatible with BN. We can use the same selection pattern and extend our method to inference. In a nutshell, we propose a compressible and accelerative DSG approach supported by dimension-reduction search and doublemask selection. It can achieve 1.7-4.5x memory compression and 2.3-4.4x computation reduction with minimal accuracy loss. This work simultaneously pioneers the approach towards efficient online training and offline inference, which can benefit the deep learning in both the cloud and the edge. In this work, we propose DSG (dynamic and sparse graph) structure for efficient DNN training and inference through a dimension-reduction search based sparsity forecast for compressive memory and accelerative execution and a double-mask selection for BN compatibility without sacrificing model's expressive power. It can be easily extended to the inference by using the same selection pattern after training. Our experiments over various benchmarks demonstrate significant memory saving (up to 4.5x for training and 1.7x for inference) and computation reduction (up to 2.3x for training and 4.4x for inference). Through significantly boosting both forward and backward passes in training, as well as in inference, DSG promises efficient deep learning in both the cloud and edge. DISPLAYFORM0 Further recalling the norm preservation in equation (3) of the main text: there exist a linear map f : R d ⇒ R k and a 0 ∈ (0, 1), for 0 < ≤ 0 we have DISPLAYFORM1 Substituting the equation FORMULA0 into equation FORMULA0 yields DISPLAYFORM2 Combining equation FORMULA0 and FORMULA0 , finally we have DISPLAYFORM3 It can be seen that, for any given X i and W j pair, the inner product can be preserved if the is sufficiently small. Actually, previous work BID1 BID5 BID36 discussed a lot on the random projection for various big data applications, here we re-organize these supporting materials to form a systematic proof. We hope this could help readers to follow this paper. In practical experiments, there exists a trade-off between the dimension reduction degree and the recognition accuracy. Smaller usually brings more accurate inner product estimation and better recognition accuracy while at the cost of higher computational complexity with larger k, and vice versa. Because the X i 2 and W j 2 are not strictly bounded, the approximation may suffer from some noises. Anyway, from the abundant experiments in this work, the effectiveness of our approach for training dynamic and sparse neural networks has been validated.",propose execute deep neural networks DNNs dynamic sparse graph DSG structure compressive memory accelerative execution training inference. great success DNNs motivates pursuing lightweight models deployment onto embedded devices. However previous studies optimize inference neglect training even complicate it. Training is far intractable since neurons dominate memory cost rather weights inference;ii dynamic activation makes previous sparse acceleration via one-off optimization fixed weight invalid;iii batch normalization BN is critical maintaining accuracy activation reorganization damages sparsity. address issues DSG activates small amount neurons high selectivity iteration via dimensionreduction search obtains BN compatibility via double-mask selection. Experiments show significant memory saving 1.7-4.5x operation reduction 2.3-4.4x little accuracy loss various benchmarks. Deep Neural Networks DNNs BID23 have been achieving impressive progress wide spectrum domains Simonyan Zisserman 2014;BID0 Redmon Farhadi 2016;models are extremely extremely memory-and compute-intensive high representational computational costs motivate many researchers investigate approaches improving execution performance including matrix tensor decomposition BID44 Novikov etal. 2015;Garipovetal. 2016;BID47 BID3 data quantization Courbariauxetal. 2016;BID51 BID27 BID24 BID39 BID33 network pruning BID4 BID8 a;BID30 BID13 Molchanovet al. 2016;BID13 Spring Shrivastava 2017;BID28 BID49 BID12 Chin etal. 2018;BID31 BID14. However previous work aim inference challenges reducing representational computational costs training are not well-studied well-studied Although works demonstrate acceleration distributed training BID29 BID6 BID47 target single-node optimization method can also boost training distributed fashion. DNN training which demands much hardware resources terms memory capacity computation volume is far challenging inference. Firstly activation data training will be stored backpropagation can significantly increasing memory consumption. Secondly training iteratively updates model parameters using mini-batched stochastic gradient descent. almost always expect larger mini-batches higher throughput FIG0 faster convergence better accuracy Smithetal. 2017 However memory capacity is often limitation factor FIG0 Upper lower one are the feature maps BN respectively. However using BN damages sparsity information fusion;f exists great representational redundancy 80% activations are close zero.that may cause performance degradation even make large models deep structures targeting high-resolution vision tasks hard train BID42.It is difficult apply existing sparsity techniques towards inference phase training phase following reasons:1 Prior arts mainly compress pre-trained fixed weight parameters reduce off-chip memory access inference BID9 instead dynamic neuronal activations turn crucial bottleneck training BID17 making prior inference-oriented methods inefficient. Besides training need stash vast batched activation space backward gradient calculation. Therefore neuron activations creates new memory bottleneck Figure1 c paper will sparsify neuron activations training compression.2 existing inference accelerations usually add extra optimization problems onto critical path Molchanovet al. 2016;BID30 BID27 BID49 BID31.e 'complicated training ⇒ simplified inference' which embarrassingly complicates training phase. 3 Moreover previous studies reveal batch normalization BN is crucial improving accuracy robustness FIG0 activation fusion across different samples within one mini-batch better representation Morcosetal. 2018;BID16. BN almost becomes standard training configuration;however inference-oriented methods seldom discuss BN treat BN parameters scaling shift factors forward pass. find BN will damage sparsity due activation reorganization FIG0 Since work targets training inference BN compatibility problem should be addressed.From view information representation activation neuron reflects selectivity current stimulus sample Morcosetal. 2018 selectivity dataflow propagates layer layer forming different representation levels. Fortunately is much representational redundancy example lots neuron activations stimulus sample are so small can be removed FIG0 Motivated comprehensive analysis regarding memory compute propose search critical neurons constructing sparse graph every iteration. activating small amount neurons high selectivity can significantly save memory simplify computation tolerable accuracy degradation. neuron response dynamically changes different stimulus samples sparse graph is variable. neuronaware dynamic sparse graph DSG is fundamentally distinct static one previous work permanent weight pruning since never prune graph activate part time. Therefore maintain model expressive power much possible. graph selection method dimension-reduction search is designed compressible activations elementwise unstructured sparsity accelerative vector-matrix multiplication VMM vector-wise structured sparsity. double-mask selection design is also compatible BN. can use selection pattern extend method inference. nutshell propose compressible accelerative DSG approach supported dimension-reduction search doublemask selection. can achieve 1.7-4.5x memory compression 2.3-4.4x computation reduction minimal accuracy loss. work simultaneously pioneers approach towards efficient online training offline inference which can benefit deep learning cloud edge. work propose DSG dynamic sparse graph structure efficient DNN training inference dimension-reduction search based sparsity forecast compressive memory accelerative execution double-mask selection BN compatibility without sacrificing model's expressive power. can be easily extended inference using selection pattern training. experiments various benchmarks demonstrate significant memory saving 4.5x training 1.7x inference computation reduction 2.3x training 4.4x inference significantly boosting forward backward passes training well inference DSG promises efficient deep learning cloud edge. DISPLAYFORM0 recalling norm preservation equation 3 main text:exist linear mapf:R ⇒Rk 0∈ 0 1 0 ≤0 have DISPLAYFORM1 Substituting equation FORMULA0 equation FORMULA0 yields DISPLAYFORM2 Combining equation FORMULA0 FORMULA0 finally have DISPLAYFORM3 can be seen givenX W j pair inner product can be preserved if the is sufficiently small. Actually previous work BID1 BID5 BID36 discussed lot random projection various big data applications re-organize supporting materials form systematic proof. hope could help readers follow paper. practical experiments exists trade-off dimension reduction degree recognition accuracy. Smaller usually brings accurate inner product estimation better recognition accuracy cost higher computational complexity largerk vice versa. X 2 Wj2 are not strictly bounded approximation may suffer noises. Anyway abundant experiments work effectiveness approach training dynamic sparse neural networks has been validated.,1718,1240,478,0.018,1.385,2025/11/05 17:19:07,0.01,1.459,0.1713395638629281,486.935
"Efficient exploration remains a major challenge for reinforcement learning. One reason is that the variability of the returns often depends on the current state and action, and is therefore heteroscedastic. Classical exploration strategies such as upper confidence bound algorithms and Thompson sampling fail to appropriately account for heteroscedasticity, even in the bandit setting. Motivated by recent findings that address this issue in bandits, we propose to use Information-Directed Sampling (IDS) for exploration in reinforcement learning. As our main contribution, we build on recent advances in distributional reinforcement learning and propose a novel, tractable approximation of IDS for deep Q-learning. The resulting exploration strategy explicitly accounts for both parametric uncertainty and heteroscedastic observation noise. We evaluate our method on Atari games and demonstrate a significant improvement over alternative approaches. In Reinforcement Learning (RL), an agent seeks to maximize the cumulative rewards obtained from interactions with an unknown environment. Given only knowledge based on previously observed trajectories, the agent faces the exploration-exploitation dilemma: Should the agent take actions that maximize rewards based on its current knowledge or instead investigate poorly understood states and actions to potentially improve future performance. Thus, in order to find the optimal policy the agent needs to use an appropriate exploration strategy.Popular exploration strategies, such as -greedy BID37 , rely on random perturbations of the agent's policy, which leads to undirected exploration. The theoretical RL literature offers a variety of statistically-efficient methods that are based on a measure of uncertainty in the agent's model. Examples include upper confidence bound (UCB) BID0 and Thompson sampling (TS) BID40 . In recent years, these have been extended to practical exploration algorithms for large state-spaces and shown to improve performance BID27 O'Donoghue et al., 2018; BID15 . However, these methods assume that the observation noise distribution is independent of the evaluation point, while in practice heteroscedastic observation noise is omnipresent in RL. This means that the noise depends on the evaluation point, rather than being identically distributed (homoscedastic). For instance, the return distribution typically depends on a sequence of interactions and, potentially, on hidden states or inherently heteroscedastic reward observations. BID20 recently demonstrated that, even in the simpler bandit setting, classical approaches such as UCB and TS fail to efficiently account for heteroscedastic noise.In this work, we propose to use Information-Directed Sampling (IDS) BID31 BID20 for efficient exploration in RL. The IDS framework can be used to design exploration-exploitation strategies that balance the estimated instantaneous regret and the expected information gain. Importantly, through the choice of an appropriate information-gain function, IDS is able to account for parametric uncertainty and heteroscedastic observation noise during exploration.As our main contribution, we propose a novel, tractable RL algorithm based on the IDS principle. We combine recent advances in distributional RL BID4 BID12 and approximate parameter uncertainty methods in order to develop both homoscedastic and heteroscedastic variants of an agent that is similar to DQN BID25 , but uses informationdirected exploration. Our evaluation on Atari 2600 games shows the importance of accounting for heteroscedastic noise and indicates that at our approach can substantially outperform alternative state-of-the-art algorithms that focus on modeling either only epistemic or only aleatoric uncertainty. To the best of our knowledge, we are the first to develop a tractable IDS algorithm for RL in large state spaces. We extended the idea of frequentist Information-Directed Sampling to a practical RL exploration algorithm that can account for heteroscedastic noise. To the best of our knowledge, we are the first to propose a tractable IDS algorithm for RL in large state spaces. Our method suggests a new way to use the return distribution in combination with parametric uncertainty for efficient deep exploration and demonstrates substantial gains on Atari games. We also identified several sources of heteroscedasticity in RL and demonstrated the importance of accounting for heteroscedastic noise for efficient exploration. Additionally, our evaluation results demonstrated that similarly to the bandit setting, IDS has the potential to outperform alternative strategies such as TS in RL.There remain promising directions for future work. Our preliminary results show that similar improvements can be observed when IDS is combined with continuous control RL methods such as the Deep Deterministic Policy Gradient (DDPG) BID23 . Developing a computationally efficient approximation of the randomized IDS version, which minimizes the regret-information ratio over the set of stochastic policies, is another idea to investigate. Additionally, as indicated by BID31 , IDS should be seen as a design principle rather than a specific algorithm, and thus alternative information gain functions are an important direction for future research.",Efficient exploration remains major challenge reinforcement learning. One reason is that the variability returns often depends current state action is therefore heteroscedastic. Classical exploration strategies upper confidence bound algorithms Thompson sampling fail appropriately account heteroscedasticity even bandit setting. Motivated recent findings address issue bandits propose use Information-Directed Sampling IDS exploration reinforcement learning. main contribution build recent advances distributional reinforcement learning propose novel tractable approximation IDS deep Q-learning resulting exploration strategy explicitly accounts parametric uncertainty heteroscedastic observation noise. evaluate method Atari games demonstrate significant improvement alternative approaches. Reinforcement Learning RL agent seeks maximize cumulative rewards obtained interactions unknown environment. Given knowledge based previously observed trajectories agent faces exploration-exploitation dilemma:Should the agent take actions maximize rewards based current knowledge instead investigate poorly understood states actions potentially improve future performance. Thus order find optimal policy agent needs use appropriate exploration strategy.Popular exploration strategies -greedy BID37 rely random perturbations agent's policy which leads undirected exploration. theoretical RL literature offers variety statistically-efficient methods are based measure uncertainty agent's model. Examples include upper confidence bound UCB BID0 Thompson sampling TS BID40. recent years have been extended practical exploration algorithms large state-spaces shown improve performance BID27 Donoghueetal. 2018;BID15. However methods assume observation noise distribution is independent evaluation point practice heteroscedastic observation noise is omnipresent RL. means noise depends evaluation point rather identically distributed homoscedastic instance return distribution typically depends sequence interactions potentially hidden states inherently heteroscedastic reward observations. BID20 recently demonstrated even simpler bandit setting classical approaches UCB TS fail efficiently account heteroscedastic noise.In work propose use Information-Directed Sampling IDS BID31 BID20 efficient exploration RL. IDS framework can be used design exploration-exploitation strategies balance estimated instantaneous regret expected information gain. Importantly choice appropriate information-gain function IDS is able account parametric uncertainty heteroscedastic observation noise exploration.As main contribution propose novel tractable RL algorithm based IDS principle. combine recent advances distributional RL BID4 BID12 approximate parameter uncertainty methods order develop homoscedastic heteroscedastic variants agent is similar DQN BID25 uses informationdirected exploration. evaluation Atari 2600 games shows importance accounting heteroscedastic noise indicates approach can substantially outperform alternative state-of-the-art algorithms focus modeling either epistemic aleatoric uncertainty. best knowledge are the first develop tractable IDS algorithm RL large state spaces. extended idea frequentist Information-Directed Sampling practical RL exploration algorithm can account heteroscedastic noise. best knowledge are the first propose tractable IDS algorithm RL large state spaces. method suggests new way use return distribution combination parametric uncertainty efficient deep exploration demonstrates substantial gains Atari games. also identified several sources heteroscedasticity RL demonstrated importance accounting heteroscedastic noise efficient exploration. Additionally evaluation results demonstrated similarly bandit setting IDS has the potential outperform alternative strategies TS RL.There remain promising directions future work. preliminary results show is similar improvements can be observed when IDS is combined continuous control RL methods Deep Deterministic Policy Gradient DDPG BID23. Developing computationally efficient approximation randomized IDS version which minimizes regret-information ratio set stochastic policies is another idea investigate. Additionally indicated BID31 IDS should be seen design principle rather specific algorithm thus alternative information gain functions are an important direction future research.,953,663,290,0.009,1.437,2025/11/05 17:19:07,0.0,1.455,0.3333333333333333,297.614
"We address the problem of learning structured policies for continuous control. In traditional reinforcement learning, policies of agents are learned by MLPs which take the concatenation of all observations from the environment as input for predicting actions. In this work, we propose NerveNet to explicitly model the structure of an agent, which naturally takes the form of a graph. Specifically, serving as the agent's policy network, NerveNet first propagates information over the structure of the agent and then predict actions for different parts of the agent. In the experiments, we first show that our NerveNet is comparable to state-of-the-art methods on standard MuJoCo environments. We further propose our customized reinforcement learning environments for benchmarking two types of structure transfer learning tasks, i.e., size and disability transfer. We demonstrate that policies learned by NerveNet are significantly better than policies learned by other models and are able to transfer even in a zero-shot setting.
 Deep reinforcement learning (RL) has received increasing attention over the past few years, with the recent success of applications such as playing Atari Games, Mnih et al. (2015) , and Go, BID26 . Significant advances have also been made in robotics using the latest RL techniques, e.g., BID1 ; BID19 .Many RL problems feature agents with multiple dependent controllers. For example, humanoid robots consist of multiple physically linked joints. Action to be taken by each joint or the body should thus not only depend on its own observations but also on actions of other joints.Previous approaches in RL typically use MLP to learn the agent's policy. In particular , MLP takes the concatenation of observations from the environment as input, which may be measurements like positions, velocities of body and joints in the current time instance. The MLP policy then predicts actions to be taken by every joint and body. Thus the task of the MLP policy is to discover the latent relationships between observations. This typically leads to longer training times, requiring more exposure of the agent to the environment. In our work, we aim to exploit the body structure of an agent, and physical dependencies that naturally exist in such agents.We rely on the fact that bodies of most robots and animals have a discrete graph structure. Nodes of the graph may represent the joints, and edges represent the (physical) dependencies between them. In particular, we define the agent's policy using a Graph Neural Network, Scarselli et al. (2009) , which is a neural network that operates over graph structures. We refer to our model as NerveNet due to the resemblance of the neural nervous system to a graph. NerveNet propagates information between different parts of the body based on the underlying graph structure before outputting the action for each part. By doing so, NerveNet can leverage the structure information encoded by the agent's body which is advantageous in learning the correct inductive bias, and thus is less prone to Figure 1: Visualization of the graph structure of CentipedeEight in our environment. We use this agent for testing the ability of transfer learning of our model. Since for this agent, each body node is paired with at least one joint node, we omit the body nodes and fill up the position with the corresponding joint nodes. By omitting the body nodes, a more compact graph is constructed, the details of which are illustrated in the experimental section.overfitting. Moreover, NerveNet is naturally suitable for structure transferring tasks as most of the model weights are shared across the nodes and edges, respectively.We first evaluate our NerveNet on standard RL benchmarks such as the OpenAI Gym, BID5 which stem from MuJoCo. We show that our model achieves comparable results to state-of-the-art MLP based methods. To verify our claim regarding the structure transfer , we further introduce our customized RL environments which are based on the ones of Gym. Two types of structure transfer tasks are designed, size transfer and disability transfer. In particular, size transfer focuses on the scenario in which policies are learned for small-sized agents (simpler body structure) and applied directly to large-sized agents which are composed by some repetitive components shared with the small-sized agent. Secondly, disability transfer investigates scenarios in which policies are learned for one agent and applied to the same agent with some components disabled. Our experiments demonstrate that for structure transfer tasks our NerveNet is significantly better than all other competitors, and can even achieve zero-shot learning for some agents. For the multi-task learning tasks, NerveNet is also able to learn policies that are more robust with better efficiency.The main contribution of this paper is the following: We explore the problem of learning transferable and generalized features by incorporating a prior on the structure via graph neural networks. NerveNet permits powerful transfer learning from one structure to another, which goes well beyond the ability of previous models. NerveNet is also more robust and has more potential in performing multi-task learning. The demo and code for this project are released, under the project page of http://www.cs.toronto.edu/˜tingwuwang/nervenet.html. In this paper, we aimed to exploit the body structure of Reinforcement Learning agents in the form of graphs. We introduced a novel model called NerveNet which uses a Graph Neural Network to represent the agent's policy. At each time instance of the environment, NerveNet takes observations for each of the body joints, and propagates information between them using non-linear messages computed with a neural network. Propagation is done through the edges which represent natural dependencies between joints, such as physical connectivity. We experimentally showed that our NerveNet achieves comparable performance to state-of-the-art methods on standard MuJoCo environments. We further propose our customized reinforcement learning environments for benchmarking two types of structure transfer learning tasks, i.e., size and disability transfer. We demonstrate that policies learned by NerveNet are significantly better than policies learned by other models and are able to transfer even in a zero-shot setting.",address problem learning structured policies continuous control. traditional reinforcement learning policies agents are learned MLPs which take concatenation observations environment input predicting actions. work propose NerveNet explicitly model structure agent which naturally takes form graph. Specifically serving agent's policy network NerveNet first propagates information structure agent predict actions different parts agent. experiments first show NerveNet is comparable state-of-the-art methods standard MuJoCo environments. propose customized reinforcement learning environments benchmarking two types structure transfer learning tasks.e size disability transfer. demonstrate policies learned NerveNet are significantly better policies learned models are able transfer even zero-shot setting. Deep reinforcement learning RL has received increasing attention past years recent success applications playing Atari Games Mnihetal. 2015 Go BID26. Significant advances have also made robotics using latest RL techniques e.g BID1;BID19.Many RL problems feature agents multiple dependent controllers. example humanoid robots consist multiple physically linked joints. Action taken joint body should thus depend observations also actions joints.Previous approaches RL typically use MLP learn agent's policy. particular MLP takes concatenation observations environment input may measurements like positions velocities body joints current time instance. MLP policy predicts actions taken every joint body. Thus task MLP policy is to discover latent relationships observations. typically leads longer training times requiring exposure agent environment. work aim exploit body structure agent physical dependencies naturally exist agents.We rely fact bodies robots animals have a discrete graph structure. Nodes graph may represent joints edges represent physical dependencies them. particular define agent's policy using Graph Neural Network Scarsellietal. 2009 whichis neural network operates graph structures. refer model NerveNet due resemblance neural nervous system graph. NerveNet propagates information different parts body based underlying graph structure outputting action part. NerveNet can leverage structure information encoded agent's body which is advantageous learning correct inductive bias thus is less prone Figure1:Visualization graph structure CentipedeEight environment. use agent testing ability transfer learning model. Since agent body node is paired least one joint node omit body nodes fill position corresponding joint nodes. omitting body nodes compact graph is constructed details which are illustrated experimental section.overfitting. Moreover NerveNet is naturally suitable structure transferring tasks model weights are shared across nodes edges respectively.We first evaluate NerveNet standard RL benchmarks OpenAI Gym BID5 which stem MuJoCo. show model achieves comparable results state-of-the-art MLP based methods. verify claim regarding structure transfer introduce customized RL environments which are based ones Gym. Two types structure transfer tasks are designed size transfer disability transfer. particular size transfer focuses scenario which policies are learned small-sized agents simpler body structure applied directly large-sized agents which are composed repetitive components shared small-sized agent. Secondly disability transfer investigates scenarios which policies are learned one agent applied agent components disabled. experiments demonstrate structure transfer tasks NerveNet is significantly better competitors can even achieve zero-shot learning agents. multi-task learning tasks NerveNet is also able learn policies are more robust better efficiency.The main contribution paper is the following:explore problem learning transferable generalized features incorporating prior structure via graph neural networks. NerveNet permits powerful transfer learning one structure another which goes well beyond ability previous models. NerveNet is also robust has more potential performing multi-task learning. demo code project are released project page http://www.cs.toronto.edu/˜tingwuwang/nervenet.html. paper aimed exploit body structure Reinforcement Learning agents form graphs. introduced novel model called NerveNet which uses Graph Neural Network represent agent's policy. time instance environment NerveNet takes observations body joints propagates information using non-linear messages computed neural network. Propagation is done edges which represent natural dependencies joints physical connectivity. experimentally showed NerveNet achieves comparable performance state-of-the-art methods standard MuJoCo environments. propose customized reinforcement learning environments benchmarking two types structure transfer learning tasks.e size disability transfer. demonstrate policies learned NerveNet are significantly better policies learned models are able transfer even zero-shot setting.,1203,793,410,0.013,1.517,2025/11/05 17:19:07,0.01,1.278,0.5825545171339559,378.294
"Real-world tasks are often highly structured. Hierarchical reinforcement learning (HRL) has attracted research interest as an approach for leveraging the hierarchical structure of a given task in reinforcement learning (RL). However, identifying the hierarchical policy structure that enhances the performance of RL is not a trivial task. In this paper, we propose an HRL method that learns a latent variable of a hierarchical policy using mutual information maximization. Our approach can be interpreted as a way to learn a discrete and latent representation of the state-action space. To learn option policies that correspond to modes of the advantage function, we introduce advantage-weighted importance sampling.  
 In our HRL method, the gating policy learns to select option policies based on an option-value function, and these option policies are optimized based on the deterministic policy gradient method. This framework is derived by leveraging the analogy between a monolithic policy in standard RL and a hierarchical policy in HRL by using a deterministic option policy.   Experimental results indicate that our HRL approach can learn a diversity of options and that it can enhance the performance of RL in continuous control tasks. Reinforcement learning (RL) has been successfully applied to a variety of tasks, including board games BID13 , robotic manipulation tasks (Levine et al., 2016) , and video games (Mnih et al., 2015) . Hierarchical reinforcement learning (HRL) is a type of RL that leverages the hierarchical structure of a given task by learning a hierarchical policy BID15 Dietterich, 2000) . Past studies in this field have shown that HRL can solve challenging tasks in the video game domain BID18 BID0 and robotic manipulation BID3 BID9 . In HRL, lower-level policies, which are often referred to as option policies, learn different behavior/control patterns, and the upper-level policy, which is often referred to as the gating policy, learns to select option policies. Recent studies have developed HRL methods using deep learning (Goodfellow et al., 2016) and have shown that HRL can yield impressive performance for complex tasks BID0 Frans et al., 2018; BID18 Haarnoja et al., 2018a) . However, identifying the hierarchical policy structure that yields efficient learning is not a trivial task, since the problem involves learning a sufficient variety of types of behavior to solve a given task.In this study, we present an HRL method via the mutual information (MI) maximization with advantage-weighted importance, which we refer to as adInfoHRL. We formulate the problem of learning a latent variable in a hierarchical policy as one of learning discrete and interpretable repre-sentations of states and actions. Ideally, each option policy should be located at separate modes of the advantage function. To estimate the latent variable that corresponds to modes of the advantage function, we introduce advantage-weighted importance weights. Our approach can be considered to divide the state-action space based on an information maximization criterion, and it learns option policies corresponding to each region of the state-action space. We derive adInfoHRL as an HRL method based on deterministic option policies that are trained based on an extension of the deterministic policy gradient BID12 Fujimoto et al., 2018) . The contributions of this paper are twofold:1. We propose the learning of a latent variable of a hierarchical policy as a discrete and hidden representation of the state-action space. To learn option policies that correspond to the modes of the advantage function, we introduce advantage-weighted importance. 2. We propose an HRL method, where the option policies are optimized based on the deterministic policy gradient and the gating policy selects the option that maximizes the expected return. The experimental results show that our proposed method adInfoHRL can learn a diversity of options on continuous control tasks. Moreover, our approach can improve the performance of TD3 on such tasks as the Walker2d and Ant tasks in OpenAI Gym with MuJoco simulator. We proposed a novel HRL method, hierarchical reinforcement learning via advantage-weighted information maximization. In our framework, the latent variable of a hierarchical policy is learned as a discrete latent representation of the state-action space. Our HRL framework is derived by considering deterministic option policies and by leveraging the analogy between the gating policy for HRL and a monolithic policy for the standard RL. The results of the experiments indicate that adInfoHRL can learn diverse options on continuous control tasks. Our results also suggested that our approach can improve the performance of TD3 in certain problem domains.",Real-world tasks are often highly structured. Hierarchical reinforcement learning HRL has attracted research interest approach leveraging hierarchical structure given task reinforcement learning RL However identifying hierarchical policy structure enhances performance RL is not a trivial task. paper propose HRL method learns latent variable hierarchical policy using mutual information maximization. approach can be interpreted way learn discrete latent representation state-action space. learn option policies correspond modes advantage function introduce advantage-weighted importance sampling. HRL method gating policy learns select option policies based option-value function where the option policies are optimized based deterministic policy gradient method. framework is derived leveraging analogy monolithic policy standardRL hierarchical policy HRL using deterministic option policy. Experimental results indicate HRL approach can learn diversity options can enhance performance RL continuous control tasks. Reinforcement learning RL has been successfully applied variety tasks including board games BID13 robotic manipulation tasks Levineetal. 2016 video games Mnihetal. 2015 Hierarchical reinforcement learning HRL is a type RL leverages hierarchical structure given task learning hierarchical policy BID15 Dietterich 2000 Past studies field have shown HRL can solve challenging tasks video game domain BID18 BID0 robotic manipulation BID3 BID9. HRL lower-level policies which are which is often referred option policies learn different behavior/control patterns upper-level policy which are which is often referred gating policy learns select option policies. Recent studies have developed HRL methods using deep learning Goodfellowetal. 2016 have shown HRL can yield impressive performance complex tasks BID0 Frans etal. 2018;BID18 Haarnojaetal. 2018a However identifying hierarchical policy structure yields efficient learning is not a trivial task since problem involves learning sufficient variety types behavior solve given task.In study present HRL method via mutual information MI maximization advantage-weighted importance which we refer adInfoHRL. formulate problem learning latent variable hierarchical policy one learning discrete interpretable repre-sentations states actions. Ideally where the option policy should be located separate modes advantage function. estimate latent variable corresponds modes advantage function introduce advantage-weighted importance weights. approach can be considered divide state-action space based information maximization criterion learns option policies corresponding region state-action space. derive adInfoHRL HRL method based deterministic option policies are trained based extension deterministic policy gradient BID12 Fujimotoetal. 2018 contributions paper are twofold:1 twofold:1 propose learning latent variable hierarchical policy discrete hidden representation state-action space. learn option policies correspond modes advantage function introduce advantage-weighted importance. 2. propose HRL method where the option policies are optimized based deterministic policy gradient gating policy selects option maximizes expected return. experimental results show proposed method adInfoHRL can learn diversity options continuous control tasks. Moreover approach can improve performance TD3 tasks Walker2d Ant tasks OpenAI Gym MuJoco simulator. proposed novel HRL method hierarchical reinforcement learning via advantage-weighted information maximization. framework latent variable hierarchical policy is learned discrete latent representation state-action space. HRL framework is derived considering deterministic option policies leveraging analogy gating policy HRL monolithic policy standardRL. results experiments indicate adInfoHRL can learn diverse options continuous control tasks. results also suggested approach can improve performance TD3 certain problem domains.,915,640,275,0.009,1.43,2025/11/05 17:19:07,0.0,1.48,0.3115264797507784,289.349
"Deep neural networks (DNNs) have achieved impressive predictive performance due to their ability to learn complex, non-linear relationships between variables. However, the inability to effectively visualize these relationships has led to DNNs being characterized as black boxes and consequently limited their applications. To ameliorate this problem, we introduce the use of hierarchical interpretations to explain DNN predictions through our proposed method: agglomerative contextual decomposition (ACD). Given a prediction from a trained DNN, ACD produces a hierarchical clustering of the input features, along with the contribution of each cluster to the final prediction. This hierarchy is optimized to identify clusters of features that the DNN learned are predictive. We introduce ACD using examples from Stanford Sentiment Treebank and ImageNet, in order to diagnose incorrect predictions, identify dataset bias, and extract polarizing phrases of varying lengths. Through human experiments, we demonstrate that ACD enables users both to identify the more accurate of two DNNs and to better trust a DNN's outputs. We also find that ACD's hierarchy is largely robust to adversarial perturbations, implying that it captures fundamental aspects of the input and ignores spurious noise. Deep neural networks (DNNs) have recently demonstrated impressive predictive performance due to their ability to learn complex, non-linear, relationships between variables. However, the inability to effectively visualize these relationships has led DNNs to be characterized as black boxes. Consequently, their use has been limited in fields such as medicine (e.g. medical image classification BID19 ), policy-making (e.g. classification aiding public policy makers BID6 ), and science (e.g. interpreting the contribution of a stimulus to a biological measurement BID2 ). Moreover, the use of black-box models like DNNs in industrial settings has come under increasing scrutiny as they struggle with issues such as fairness BID8 and regulatory pressure BID13 .To ameliorate these problems, we introduce the use of hierarchical interpretations to explain DNN predictions. Our proposed method, agglomerative contextual decomposition (ACD) 1 , is a general technique that can be applied to a wide range of DNN architectures and data types. Given a prediction from a trained DNN, ACD produces a hierarchical clustering of the input features, along with the contribution of each cluster to the final prediction. This hierarchy is optimized to identify clusters of features that the DNN learned are predictive (see FIG0 .The development of ACD consists of two novel contributions. First, importance scores for groups of features are obtained by generalizing contextual decomposition (CD), a previous method for obtaining importance scores for LSTMs BID23 . This work extends CD to arbitrary DNN architectures, including convolutional neural networks (CNNs). Second, most importantly , we introduce the idea of hierarchical saliency, where a group-level importance measure, in this case CD, is used as a joining metric in an agglomerative clustering procedure. While we focus on DNNs and use CD as our importance measure, this concept is general, and could be readily applied to any model with a suitable measure for computing importances of groups of variables.We demonstrate the utility of ACD on both long short term memory networks (LSTMs) BID15 trained on the Stanford Sentiment Treebank (SST) (Socher et al., 2013) and CNNs trained on MNIST BID17 and ImageNet (Russakovsky et al., 2015) . Through human experiments , we show that ACD produces intuitive visualizations that enable users to better reason about and trust DNNs. In particular, given two DNN models, we show that users can use the output of ACD to select the model with higher predictive accuracy, and that overall they rank ACD as more trustworthy than prior interpretation methods. In addition, we demonstrate that ACD's hierarchy is robust to adversarial perturbations (Szegedy et al., 2013) in CNNs. : ACD illustrated through the toy example of predicting the phrase ""not very good"" as negative. Given the network and prediction , ACD constructs a hierarchy of meaningful phrases and provides importance scores for each identified phrase. In this example, ACD identifies that ""very"" modifies ""good"" to become the very positive phrase ""very good"", which is subsequently negated by ""not"" to produce the negative phrase ""not very good"". Best viewed in color. In this work, we introduce agglomerative contextual decomposition (ACD), a novel hierarchical interpretation algorithm. ACD is the first method to use a hierarchy to interpret individual neural network predictions. Doing so enables ACD to automatically detect and display non-linear contributions to individual DNN predictions, something prior interpretation methods are unable to do. The benefits of capturing the non-linearities inherent in DNNs are demonstrated through human experiments and examples of diagnosing incorrect predictions and dataset bias. We also demonstrate that ACD's hierarchy is robust to adversarial perturbations in CNNs, implying that it captures fundamental aspects of the input and ignores spurious noise.ACD SUPPLEMENT S1 CD SCORE COMPARISONS FIG0 : Intuition for CD run on a corner-shaped blob compared to build-up and occlusion. CD decomposes a DNN's feedforward pass into a part from the blob of interest (top row) and everything else (second row). Left column shows original image with overlaid blob. Other columns show DNN activations summed over the filter dimension. Top and third rows are on same color scale. Second and bottom rows are on same color scale. FIG1 : Comparing unit-level CD scores for the correct class to scores from baseline methods. In each case, the model correctly predicts the label, shown on the y axis. Blue is positive, white is neutral, and red is negative. Best viewed in color. FIG0 gives intuition for CD on the VGG-16 ImageNet model described in Sec 4. CD keeps track of the contributions of the blob and non-blob throughout the network. This is intuitively similar to the occlusion and build-up methods, shown in the bottom two rows. The build-up method sets everything but the patch of interest to a references value (often zero). These rows compare the CD decomposition to perturbing the input as in the occlusion and build-up methods. They are similar in early layers, but differences become apparent in later layers.",Deep neural networks DNNs have achieved impressive predictive performance due ability learn complex non-linear relationships variables. However inability effectively visualize relationships has led DNNs characterized black boxes consequently limited applications. ameliorate problem introduce use hierarchical interpretations explain DNN predictions proposed method:agglomerative contextual decomposition ACD Given prediction trained DNN ACD produces hierarchical clustering input features along contribution cluster final prediction. hierarchy is optimized identify clusters features DNN learned are predictive. introduce ACD using examples Stanford Sentiment Treebank ImageNet order diagnose incorrect predictions identify dataset bias extract polarizing phrases varying lengths. human experiments demonstrate ACD enables users identify accurate two DNNs better trust DNN's outputs. also find ACD's hierarchy is largely robust adversarial perturbations implying captures fundamental aspects input ignores spurious noise. Deep neural networks DNNs have recently demonstrated impressive predictive performance due ability learn complex non-linear relationships variables. However inability effectively visualize relationships has led DNNs characterized black boxes. Consequently use has been limited fields medicine e.g medical image classification BID19 policy-making e.g classification aiding public policy makers BID6 science e.g interpreting contribution stimulus biological measurement BID2 Moreover use black-box models like DNNs industrial settings has come increasing scrutiny struggle issues fairness BID8 regulatory pressure BID13.To ameliorate problems introduce use hierarchical interpretations explain DNN predictions. proposed method agglomerative contextual decomposition ACD 1 is a general technique can be applied wide range DNN architectures data types. Given prediction trained DNN ACD produces hierarchical clustering input features along contribution cluster final prediction. hierarchy is optimized identify clusters features DNN learned are predictive see FIG0.The development ACD consists two novel contributions. First importance scores groups features are obtained generalizing contextual decomposition CD previous method obtaining importance scores LSTMs BID23. work extendsCD arbitrary DNN architectures including convolutional neural networks CNNs Second importantly introduce idea hierarchical saliency where a group-level importance measure caseCD is used joining metric agglomerative clustering procedure. focus DNNs useCD importance measure concept is general could readily applied model suitable measure computing importances groups variables.We demonstrate utility ACD long short term memory networks LSTMs BID15 trained Stanford Sentiment Treebank SST Socheretal. 2013 CNNs trained MNIST BID17 ImageNet Russakovskyetal. 2015 human experiments show ACD produces intuitive visualizations enable users better reason trust DNNs. particular given two DNN models show users can use output ACD select model higher predictive accuracy overall rank ACD trustworthy prior interpretation methods. addition demonstrate ACD's hierarchy is robust adversarial perturbations Szegedyetal. 2013 CNNs. ACD illustrated toy example predicting phrase good negative. Given network prediction ACD constructs hierarchy meaningful phrases provides importance scores identified phrase. example ACD identifies modifies good become positive phrase good which is subsequently negated produce negative phrase good. Best viewed color. work introduce agglomerative contextual decomposition ACD novel hierarchical interpretation algorithm. ACD is the first method use hierarchy interpret individual neural network predictions. enables ACD automatically detect display non-linear contributions individual DNN predictions something prior interpretation methods are unable do. benefits capturing non-linearities inherent DNNs are demonstrated human experiments examples diagnosing incorrect predictions dataset bias. also demonstrate ACD's hierarchy is robust adversarial perturbations CNNs implying captures fundamental aspects input ignores spurious noise.ACD SUPPLEMENT S1 CD SCORE COMPARISONS FIG0:Intuition CD run corner-shaped blob compared build-up occlusion. CD decomposes DNN's feedforward pass part blob interest top row everything else second row Left column shows original image overlaid blob. columns show DNN activations summed filter dimension. Top third rows are on same color scale. Second bottom rows are on same color scale. FIG1:Comparing unit-level CD scores correct class scores baseline methods. case model correctly predicts label shown axis. Blue is positive white is neutral red is negative. Best viewed color. FIG0 gives intuition CD VGG-16 ImageNet model described Sec4. CD keeps track contributions blob non-blob throughout network. is intuitively similar occlusion build-up methods shown bottom two rows. build-up method sets everything patch interest references value often zero rows compare CD decomposition perturbing input occlusion build-up methods. are similar early layers differences become apparent later layers.,1287,866,421,0.013,1.486,2025/11/05 17:19:07,0.01,1.308,0.4859813084112147,410.685
"Principal Filter Analysis (PFA) is an easy to implement, yet effective method for neural network compression. PFA exploits the intrinsic correlation between filter responses within network layers to recommend a smaller network footprint. We propose two compression algorithms: the first allows a user to specify the proportion of the original spectral energy that should be preserved in each layer after compression, while the second is a heuristic that leads to a parameter-free approach that automatically selects the compression used at each layer. Both algorithms are evaluated against several architectures and datasets, and we show considerable compression rates without compromising accuracy, e.g., for VGG-16 on CIFAR-10, CIFAR-100 and ImageNet, PFA achieves a compression rate of 8x, 3x, and 1.4x with an accuracy gain of 0.4%, 1.4% points, and 2.4% respectively. In our tests we also demonstrate that networks compressed with PFA achieve an accuracy that is very close to the empirical upper bound for a given compression ratio. Finally, we show how PFA is an effective tool for simultaneous compression and domain adaptation. Despite decades of research, the design of neural networks is still an empirical process. Practitioners make design choices, such as the number of layers, type of layers, number of filters per layer, etc., based on intuition or brute-force search. Nevertheless, the performance of these algorithms, together with the advances of GPU devices, have led to a growing popularity of these techniques in both academia and industry. Recent advances are unveiling some properties of neural networks. For example, there is a consensus that depth can accelerate learning, and that wider layers help optimization BID2 BID29 . However, in practical applications, the size of these networks is often a limiting factor when deploying on devices with constrained storage, memory, and computation resources.Another known neural network property is that the responses of a layer exhibit considerable correlation BID12 , inspiring the idea of learning decorrelated filters BID8 BID38 . These algorithms propose a modified loss function to encourage decorrelation during training and show that accuracy improves with decorrelated filters. However, such algorithms focus on training and do not address network compression. Our hypothesis is that layers that exhibit high correlation in filter responses could learn equally well using a smaller number of filters.Principal Filter Analysis (PFA) draws from the recent findings that it is easier to start with an overparametrized network and it then exploits intra-layer correlation for guiding network compression. PFA analyzes a trained network and is agnostic to the training methodology and the loss function. Inference is performed on a dataset, and the correlation within the responses of each layer is used to provide a compression recipe. A new smaller architecture based on this recipe can then be retrained.We propose two closed-form algorithms based on spectral energy analysis for suggesting the number of filters to remove in a layer:PFA-En uses Principal Component Analysis (PCA) BID21 to allow a user to specify the proportion of the energy in the original response that should be preserved in each layer; PFA-KL is a heuristic that leads to a parameter-free approach that uses Kullback-Leibler (KL) divergence BID24 to identify the number of redundant filters.Based on the new suggested number of filters per layer identified by PFA, we remove those that are maximally correlated with other filters and fine-tune the network by retraining. Both PFA algorithms are straightforward to implement and, as shown in Sec. 4, they achieve better compression and, in most cases, better accuracy than the state of the art on several datasets and architectures. In Sec. 4 we also show how PFA can be used to perform simulations compression and domain adaptation. Two effective, and yet easy to implement techniques for the compression of neural networks using Principal Filter Analysis were presented: PFA-En and PFA-KL. These techniques exploit the inherent correlation of filter responses within layers to compress networks without compromising accuracy. These techniques can be applied to the output response of any layer with no knowledge of the training procedure or the loss function. While easy to implement, both algorithms surpass state of the art results in terms or compression ratio with the advantage that PFA-KL is parameter free and PFA-En has only a single intuitive parameter: the energy to be preserved in each layer or a desired network characteristic (such as a target footprint or FLOPs).By performing spectral analysis on the responses rather than the weights, PFA allows users to take advantage of transfer learning in order to perform domain adaptation and derive smaller specialized networks that are optimally designed for a specific task, while starting from the same base model.It is interesting to observe that all compression algorithms in the state of art, including PFA-KL, do not converge if applied repeatedly. This is due to the retraining step which alters the weights in order to optimize an objective function that does not take into account compression criteria. In practical applications this is not a limitation since most of the models tend to be over specified and users can apply compression algorithms until the accuracy falls below an acceptable level. However, it is an interesting theoretical limitation that could inspire future work. Specifically for PFA, this could be a strategy that can also suggest expanding layers so that an optimal size could be reached at convergence.",Principal Filter Analysis PFA is an easy implement yet effective method neural network compression. PFA exploits intrinsic correlation filter responses within network layers recommend smaller network footprint. propose two compression algorithms:first allows user specify proportion original spectral energy should be preserved layer compression second is a heuristic leads parameter-free approach automatically selects compression used layer. algorithms are evaluated several architectures datasets show considerable compression rates without compromising accuracy e.g VGG-16 CIFAR-10 CIFAR-100 ImageNet PFA achieves compression rate 8x 3x 1.4x accuracy gain 0.4 1.4 points 2.4 respectively. tests also demonstrate networks compressed PFA achieve accuracy is very close empirical upper bound given compression ratio. Finally show how PFA is an effective tool simultaneous compression domain adaptation. Despite decades research design neural networks is still empirical process. Practitioners make design choices number layers type layers number filters per layer etc. based intuition brute-force search. Nevertheless performance algorithms together advances GPU devices have led growing popularity techniques academia industry. Recent advances are unveiling properties neural networks. example is a consensus depth can accelerate learning wider layers help optimization BID2 BID29. However practical applications size networks is often limiting factor when deploying devices constrained storage memory computation resources.Another known neural network property is that the responses layer exhibit considerable correlation BID12 inspiring idea learning decorrelated filters BID8 BID38. algorithms propose modified loss function encourage decorrelation training show accuracy improves decorrelated filters. However algorithms focus training do not address network compression. hypothesis is that layers exhibit high correlation filter responses could learn equally well using smaller number filters.Principal Filter Analysis PFA draws recent findings is easier start overparametrized network exploits intra-layer correlation guiding network compression. PFA analyzes trained network is agnostic training methodology loss function. Inference is performed dataset correlation within responses layer is used provide compression recipe. new smaller architecture based recipe can then be retrained.We propose two closed-form algorithms based spectral energy analysis suggesting number filters remove layer:PFA-En uses Principal Component Analysis PCA BID21 allow user specify proportion energy original response should be preserved layer;PFA-KL is a heuristic leads parameter-free approach uses Kullback-Leibler KL divergence BID24 identify number redundant filters.Based new suggested number filters per layer identified PFA remove are maximally correlated filters fine-tune network retraining. PFA algorithms are straightforward implement shown Sec. 4 achieve better compression cases better accuracy state art several datasets architectures. Sec. 4 also show how PFA can be used perform simulations compression domain adaptation. Two effective yet easy implement techniques compression neural networks using Principal Filter Analysis were presented:PFA-En PFA-KL techniques exploit inherent correlation filter responses within layers compress networks without compromising accuracy. techniques can be applied output response layer knowledge training procedure loss function. easy implement algorithms surpass state art results terms compression ratio advantage PFA-KL is parameter free PFA-En has only a single intuitive parameter:energy preserved layer desired network characteristic target footprint FLOPs.By performing spectral analysis responses rather weights PFA allows users take advantage transfer learning order perform domain adaptation derive smaller specialized networks are optimally designed specific task starting base model.It is interesting observe compression algorithms state art including PFA-KL do not converge if applied repeatedly. is due retraining step which alters weights order optimize objective function does not take account compression criteria. practical applications is not a limitation since models tend specified users can apply compression algorithms accuracy falls acceptable level. However is an interesting theoretical limitation could inspire future work. Specifically PFA could strategy can also suggest expanding layers optimal size could reached convergence.,1069,713,356,0.011,1.499,2025/11/05 17:19:07,0.01,1.525,0.5264797507788164,339.445
"We propose a method to efficiently learn diverse strategies in reinforcement learning for query reformulation in the tasks of document retrieval and question answering. In the proposed framework an agent consists of multiple specialized sub-agents and a meta-agent that learns to aggregate the answers from sub-agents to produce a final answer. Sub-agents are trained on disjoint partitions of the training data, while the meta-agent is trained on the full training set. Our method makes learning faster, because it is highly parallelizable, and has better generalization performance than strong baselines, such as an ensemble of agents trained on the full data. We show that the improved performance is due to the increased diversity of reformulation strategies. Reinforcement learning has proven effective in several language processing tasks, such as machine translation BID12 Ranzato et al., 2015; BID1 , question-answering BID9 Hu et al., 2017) , and text summarization (Paulus et al., 2017) . In reinforcement learning efficient exploration is key to achieve good performance. The ability to explore in parallel a diverse set of strategies often speeds up training and leads to a better policy (Mnih et al., 2016; Osband et al., 2016) .In this work, we propose a simple method to achieve efficient parallelized exploration of diverse policies, inspired by hierarchical reinforcement learning (Singh, 1992; Lin, 1993; Dietterich, 2000; Dayan & Hinton, 1993) . We structure the agent into multiple sub-agents, which are trained on disjoint subsets of the training data. Sub-agents are co-ordinated by a meta-agent, called aggregator, that groups and scores answers from the sub-agents for each given input. Unlike sub-agents , the aggregator is a generalist since it learns a policy for the entire training set.We argue that it is easier to train multiple sub-agents than a single generalist one since each sub-agent only needs to learn a policy that performs well for a subset of examples. Moreover, specializing agents on different partitions of the data encourages them to learn distinct policies, thus giving the aggregator the possibility to see answers from a population of diverse agents. Learning a single policy that results in an equally diverse strategy is more challenging.Since each sub-agent is trained on a fraction of the data, and there is no communication between them, training can be done faster than training a single agent on the full data. Additionally, it is easier to parallelize than applying existing distributed algorithms such as asynchronous SGD or A3C (Mnih et al., 2016) , as the sub-agents do not need to exchange weights or gradients. After training the sub-agents , only their actions need to be sent to the aggregator.We build upon the works of Nogueira & Cho (2017) and Buck et al. (2018b) . Therefore, we evaluate the proposed method on the same tasks they used: query reformulation for document retrieval and question-answering. We show that it outperforms a strong baseline of an ensemble of agents trained on the full dataset. We also found that performance and reformulation diversity are correlated (Sec. 5.5).Our main contributions are the following:1 Under review as a conference paper at ICLR 2019• A simple method to achieve more diverse strategies and better generalization performance than a model average ensemble.• Training can be easily parallelized in the proposed method.• An interesting finding that contradicts our, perhaps naive, intuition: specializing agents on semantically similar data does not work as well as random partitioning. An explanation is given in Appendix F. We proposed a method to build a better query reformulation system by training multiple sub-agents on partitions of the data using reinforcement learning and an aggregator that learns to combine the answers of the multiple agents given a new query. We showed the effectiveness and efficiency of the proposed approach on the tasks of document retrieval and question answering. One interesting orthogonal extension would be to introduce diversity on the beam search decoder BID8 Li et al., 2016) , thus shedding light on the question of whether the gains come from the increased capacity of the system due to the use of the multiple agents, the diversity of reformulations, or both.",propose method efficiently learn diverse strategies reinforcement learning query reformulation tasks document retrieval question answering. proposed framework agent consists multiple specialized sub-agents meta-agent learns aggregate answers sub-agents produce final answer. Sub-agents are trained disjoint partitions training data meta-agent is trained full training set. method makes learning faster is highly parallelizable has better generalization performance strong baselines ensemble agents trained full data. show improved performance is due increased diversity reformulation strategies. Reinforcement learning has proven effective several language processing tasks machine translation BID12 Ranzato etal. 2015;BID1 question-answering BID9Huet al. 2017 text summarization Paulusetal. 2017 reinforcement learning efficient exploration is key achieve good performance. ability explore parallel diverse set strategies often speeds training leads better policy Mnihetal. 2016;Osbandetal. 2016.In work propose simple method achieve efficient parallelized exploration diverse policies inspired hierarchical reinforcement learning Singh 1992;Lin 1993;Dietterich 2000;Dayan Hinton 1993 structure agent multiple sub-agents which are trained disjoint subsets training data. Sub-agents are co-ordinated meta-agent called aggregator groups scores answers sub-agents given input. Unlike sub-agents aggregator is a generalist since learns policy entire training set.We argue is easier train multiple sub-agents single generalist one since sub-agent needs learn policy performs well subset examples. Moreover specializing agents different partitions data encourages learn distinct policies thus giving aggregator possibility see answers population diverse agents. Learning single policy results equally diverse strategy is more challenging.Since sub-agent is trained fraction data is communication training can be done faster training single agent full data. Additionally is easier parallelize applying existing distributed algorithms asynchronous SGD A3C Mnihetal. 2016 sub-agents do not need exchange weights gradients. training sub-agents actions need sent aggregator.We build upon works Nogueira Cho 2017 Bucketal. 2018b Therefore evaluate proposed method tasks used:query reformulation document retrieval question-answering show outperforms strong baseline ensemble agents trained full dataset. also found performance reformulation diversity are correlated Sec. 5.5.Our main contributions are the following:1 review conference paper ICLR 2019• simple method achieve diverse strategies better generalization performance model average ensemble.• Training can be easily parallelized proposed method.• interesting finding contradicts perhaps naive intuition:specializing agents semantically similar data does not work well random partitioning. explanation is given AppendixF. proposed method build better query reformulation system training multiple sub-agents partitions data using reinforcement learning aggregator learns combine answers multiple agents given new query. showed effectiveness efficiency proposed approach tasks document retrieval question answering. One interesting orthogonal extension would introduce diversity beam search decoder BID8 Lietal. 2016 thus shedding light question whether gains come increased capacity system due use multiple agents diversity reformulations both.,872,587,285,0.008,1.486,2025/11/05 17:19:07,0.0,1.381,0.4859813084112147,284.657
"Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that 'similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if 'similar' means being 'more likely to be connected') or classification (if 'similar' means 'being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes.

 A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create \emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently.

 We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization. Network Embeddings (NEs) map nodes into d-dimensional Euclidean space R d such that an ordinary distance measure allows for meaningful comparisons between nodes. Embeddings directly enable the use of a variety of machine learning methods (classification, clustering, etc.) on networks, explaining their exploding popularity. NE approaches typically have three components (Hamilton et al., 2017) : (1) A measure of similarity between nodes. E.g. nodes can be deemed more similar if they are adjacent, have strongly overlapping neighborhoods, or are otherwise close to each other (link and path-based measures) BID18 BID20 , or if they have similar functional properties (structural measures) BID19 . FORMULA3 A metric in the embedding space. (3) A loss function comparing similarity between node pairs in the network with the proximity of their embeddings. A good NE is then one for which the average loss is small. The literature on NE has so far considered embeddings as tools that are used on their own. Yet, Euclidean embeddings are unable to accurately reflect certain kinds of network topologies, such that this approach is inevitably limited. We proposed the notion of Conditional Network Embeddings (CNEs), which seeks an embedding of a network that maximally adds information with respect to certain given prior knowledge about the network. This prior knowledge can encode information about the network that cannot be represented well by means of an embedding.We implemented this conceptually novel idea in a new algorithm based on a simple probabilistic model for the joint of the data and the network, which scales similarly to state-of-the-art NE approaches. The empirical evaluation of this algorithm confirms our intuition that the combination of structural prior knowledge and a Euclidean embedding is extremely powerful. This is confirmed empirically for both the tasks of link prediction and multi-label classification, where CNE outperforms a range of state-of-the-art baselines on a wide range of networks.In our future work we intend to investigate other models implementing the idea of conditional NEs, alternative and more scalable optimization strategies, as well as the use of other types of structural information as prior knowledge on the network.",Network Embeddings NEs map nodes given network $d $-dimensional Euclidean space $\mathbb R ^d $. Ideally mapping is such that 'similar' nodes are mapped onto nearby points NE can be used purposes link prediction if 'similar' means 'more likely connected' classification if 'similar' means 'being likely have the same label' recent years various methods NE have been introduced following similar strategy:defining notion similarity nodes typically distance measure within network distance measure embedding space loss function penalizes large distances similar nodes small distances dissimilar nodes. difficulty faced existing methods is that certain networks are fundamentally hard embed due structural properties:approximate multipartiteness certain degree distributions assortativity etc. overcome introduce conceptual innovation NE literature propose create \emph Conditional Network Embeddings CNEs embeddings maximally add information respect given structural properties e.g node degrees block densities etc. use simple Bayesian approach achieve propose block stochastic gradient descent algorithm fitting efficiently. demonstrate CNEs are superior link prediction multi-label classification when compared state-of-the-art methods without adding significant mathematical computational complexity. Finally illustrate potential CNE network visualization. Network Embeddings NEs map nodes d-dimensional Euclidean spaceR ordinary distance measure allows meaningful comparisons nodes. Embeddings directly enable use variety machine learning methods classification clustering etc. networks explaining exploding popularity. NE approaches typically have three components Hamiltonetal. 2017 1 measure similarity nodes. E.g nodes can be deemed similar if they are adjacent have strongly overlapping neighborhoods are otherwise close link path-based measures BID18 BID20 if they have similar functional properties structural measures BID19. FORMULA3 metric embedding space. 3 loss function comparing similarity node pairs network proximity embeddings. goodNE is then one which the average loss is small. literature NE has so far considered embeddings tools are used own. Yet Euclidean embeddings are unable accurately reflect certain kinds network topologies approach is inevitably limited. proposed notion Conditional Network Embeddings CNEs which seeks embedding network maximally adds information respect certain given prior knowledge network. prior knowledge can encode information network cannot represented well means embedding.We implemented conceptually novel idea new algorithm based simple probabilistic model joint data network which scales similarly state-of-the-art NE approaches. empirical evaluation algorithm confirms intuition combination structural prior knowledge Euclidean embedding is extremely powerful. is confirmed empirically tasks link prediction multi-label classification where CNE outperforms range state-of-the-art baselines wide range networks.In future work intend investigate models implementing idea conditional NEs alternative scalable optimization strategies well use types structural information prior knowledge network.,745,501,244,0.007,1.487,2025/11/05 17:19:07,0.0,1.467,0.4890965732087229,270.224
"This paper studies a class of adaptive gradient based momentum algorithms that update the  search directions and learning rates simultaneously using past gradients. This class, which we refer to as the ''``Adam-type'', includes the popular algorithms such as Adam, AMSGrad, AdaGrad. Despite their popularity in training deep neural networks (DNNs), the convergence of these algorithms for solving  non-convex problems remains an open question. In this paper, we develop an analysis framework and a set of mild sufficient conditions that guarantee the convergence of the Adam-type methods, with a convergence rate of order   $O(\log{T}/\sqrt{T})$ for non-convex stochastic optimization. Our convergence analysis applies to a new algorithm called AdaFom (AdaGrad with First Order Momentum). We show that the conditions are essential, by identifying concrete examples in which violating the conditions makes an algorithm diverge. Besides providing one of the first comprehensive analysis for Adam-type methods in the non-convex setting, our results can also help the practitioners to easily  monitor the progress of algorithms and determine their convergence behavior. First-order optimization has witnessed tremendous progress in the last decade, especially to solve machine learning problems BID3 . Almost every first-order method obeys the following generic form BID4 ), x t+1 = x t − α t ∆ t , where x t denotes the solution updated at the tth iteration for t = 1, 2, . . . , T , T is the number of iterations, ∆ t is a certain (approximate) descent direction, and α t > 0 is some learning rate. The most well-known first-order algorithms are gradient descent (GD) for deterministic optimization (Nesterov, 2013; BID5 and stochastic gradient descent (SGD) for stochastic optimization (Zinkevich, 2003; Ghadimi & Lan, 2013) , where the former determines ∆ t using the full (batch) gradient of an objective function, and the latter uses a simpler but more computationally-efficient stochastic (unbiased) gradient estimate.Recent works have proposed a variety of accelerated versions of GD and SGD (Nesterov, 2013) . These achievements fall into three categories: a) momentum methods (Nesterov, 1983; Polyak, 1964; BID10 which carefully design the descent direction ∆ t ; b) adaptive learning rate methods BID1 BID9 Zeiler, 2012; BID7 which determine good learning rates α t , and c) adaptive gradient methods that enjoy dual advantages of a) and b). In particular, Adam (Kingma & Ba, 2014) , belonging to the third type of methods, has become extremely popular to solve deep learning problems, e.g., to train deep neural networks. Despite its superior performance in practice, theoretical investigation of Adam-like methods for non-convex optimization is still missing.Very recently, the work (Reddi et al., 2018) pointed out the convergence issues of Adam even in the convex setting, and proposed AMSGrad, a corrected version of Adam. Although AMSGrad has made a positive step towards understanding the theoretical behavior of adaptive gradient methods, the convergence analysis of (Reddi et al., 2018) was still very restrictive because it only works for convex problems, despite the fact that the most successful applications are for non-convex problems. Apparently, there still exists a large gap between theory and practice. To the best of our knowledge,• (Practicality) The sufficient conditions we derive are simple and easy to check in practice. They can be used to either certify the convergence of a given algorithm for a class of problem instances, or to track the progress and behavior of a particular realization of an algorithm.• (Tightness and Insight) We show the conditions are essential and ""tight"", in the sense that violating them can make an algorithm diverge. Importantly , our conditions provide insights on how oscillation of a so-called ""effective stepsize"" (that we define later) can affect the convergence rate of the class of algorithms. We also provide interpretations of the convergence conditions to illustrate why under some circumstances, certain Adam-type algorithms can outperform SGD. Notations We use z = x/y to denote element-wise division if x and y are both vectors of size d; x y is element-wise product, x 2 is element-wise square if x is a vector, √ x is element-wise square root if x is a vector, (x) j denotes jth coordinate of x, x is x 2 if not otherwise specified. We use [N ] to denote the set {1, · · · , N }, and use O(·), o(·), Ω(·), ω(·) as standard asymptotic notations. We provided some mild conditions to ensure convergence of a class of Adam-type algorithms, which includes Adam, AMSGrad, AdaGrad, AdaFom, SGD, SGD with momentum as special cases. Apart from providing general convergence guarantees for algorithms, our conditions can also be checked in practice to monitor empirical convergence. To the best of our knowledge, the convergence of Adam-type algorithm for non-convex problems was unknown before. We also provide insights on how oscillation of effective stepsizes can affect convergence rate for the class of algorithms which could be beneficial for the design of future algorithms. This paper focuses on unconstrained non-convex optimization problems, and one future direction is to study a more general setting of constrained non-convex optimization.",paper studies class adaptive gradient based momentum algorithms update search directions learning rates simultaneously using past gradients. class which we refer Adam-type which includes popular algorithms Adam AMSGrad AdaGrad. Despite popularity training deep neural networks DNNs convergence algorithms solving non-convex problems remains open question. paper develop analysis framework set mild sufficient conditions guarantee convergence Adam-type methods convergence rate order$O \log/\sqrt non-convex stochastic optimization. convergence analysis applies new algorithm called AdaFom AdaGrad First Order Momentum show conditions are essential identifying concrete examples which violating conditions makes algorithm diverge. Besides providing one first comprehensive analysis Adam-type methods non-convex setting results can also help practitioners easily monitor progress algorithms determine convergence behavior. First-order optimization has witnessed tremendous progress last decade especially solve machine learning problems BID3. Almost every first-order method obeys following generic form BID4 x+1 x −α ∆ wherex denotes solution updated tth iteration 1 2 is the number iterations ∆ is a certain approximate descent direction α 0 is some learning rate. well-known first-order algorithms are gradient descent GD deterministic optimization Nesterov 2013;BID5 stochastic gradient descent SGD stochastic optimization Zinkevich 2003;Ghadimi Lan 2013 where the former determines∆ using full batch gradient objective function latter uses simpler computationally-efficient stochastic unbiased gradient estimate.Recent works have proposed variety accelerated versions GD SGD Nesterov 2013 achievements fall three categories:momentum methods Nesterov 1983;Polyak 1964;BID10 which carefully design descent direction∆ t;b adaptive learning rate methods BID1 BID9 Zeiler 2012;BID7 which determine good learning rates α c adaptive gradient methods enjoy dual advantages b particular Adam Kingma Ba 2014 belonging third type methods has become extremely popular solve deep learning problems e.g train deep neural networks. Despite superior performance practice theoretical investigation Adam-like methods non-convex optimization is still missing.Very recently work Reddietal. 2018 pointed convergence issues Adam even convex setting proposed AMSGrad corrected version Adam. Although AMSGrad has made positive step towards understanding theoretical behavior adaptive gradient methods convergence analysis Reddietal. 2018 was still restrictive works convex problems despite fact successful applications are for non-convex problems. Apparently still exists large gap theory practice. best knowledge • Practicality sufficient conditions derive are simple easy check practice. can be used either certify convergence given algorithm class problem instances track progress behavior particular realization algorithm.• Tightness Insight show conditions are essential tight sense violating can make algorithm diverge. Importantly conditions provide insights how oscillation so-called effective stepsize define later can affect convergence rate class algorithms. also provide interpretations convergence conditions illustrate why under some circumstances certain Adam-type algorithms can outperform SGD. Notations usez x/denote element-wise division ifx are both vectors size d;x is element-wise product x2 is element-wise square ifx is a vector √x is element-wise square root ifx is a vector x j denotes jth coordinate x x isx2 if not otherwise specified. use N denote set 1 ··· N use · · Ω · ω · standard asymptotic notations. provided mild conditions ensure convergence class Adam-type algorithms which includes Adam AMSGrad AdaGrad AdaFom SGD SGD momentum special cases. Apart providing general convergence guarantees algorithms conditions can also checked practice monitor empirical convergence. best knowledge convergence Adam-type algorithm non-convex problems was unknown before. also provide insights how oscillation effective stepsizes can affect convergence rate class algorithms could beneficial design future algorithms. paper focuses unconstrained non-convex optimization problems one future direction is to study general setting constrained non-convex optimization.,1131,747,384,0.012,1.514,2025/11/05 17:19:07,0.01,1.351,0.5732087227414329,349.773
"This research paper describes a simplistic architecture named as AANN: Absolute Artificial Neural Network, which can be used to create highly interpretable representations of the input data. These representations are generated by penalizing the learning of the network in such a way that those learned representations correspond to the respective labels present in the labelled dataset used for supervised training; thereby, simultaneously giving the network the ability to classify the input data. The network can be used in the reverse direction to generate data that closely resembles the input by feeding in representation vectors as required. This research paper also explores the use of mathematical abs (absolute valued) functions as activation functions which constitutes the core part of this neural network architecture. Finally the results obtained on the MNIST dataset by using this technique are presented and discussed in brief. In the field of philosophy, there has been a principle known as 'Ockham's Razor' which, in a simplified relevant language states that ""Among the available multiple solutions to the same problem, the simplest one is the best one"". For instance, if there are multiple polynomial functions that fit a given data distribution, the lowest degree one would be preferred BID12 . The technique AANN is driven by this principle. In spite of being elementary in its construction, an AANN is able to classify inputs in the forward direction while being able to generate them back in the reverse direction. It can be visualized to be doing classification in the forward direction whereas performing a regression task in the backward direction.A standalone GAN (Generative Adversarial Network) described in BID2 is able to create representations of the input data by using a novel technique of generating a distribution that contains the original data points as well as data points generated by the Generator part of the network; the distribution is then used by the Discriminator part of the network to classify the data points as genuine or generated. The representations generated by a GAN, although being very effective in creating undistinguishable data points, are however not interpretable and also highly entangled BID1 BID8 . Using an InfoGAN, the problem of entanglement is solved by training in such a way that the network maximises mutual information within small clusters of related latent representations BID1 . Auto-encoder is another technique that uses the concept of encoder-decoder architecture for creating low dimensional representations of the originally very high dimensional input data points. A VAE: Variational Auto-Encoder tries to make the learned representations sparse by using the KL-divergence cost as a regularizer on the final cost of an autoencoder BID5 . Various attempts at combining the two techniques of GAN and VAE have also been made in the unsupervised as well as semi-supervised learning directions BID8 BID7 . However, these techniques kept getting more and more complicated and somewhere in synthesizing these techniques, it is felt that the 'striving for simplicity' principle has been neglected.The Absolute Artificial Neural Network exploits all possible information available in the labelled training datasets to structure the learned representations of the input data. Structurally, an AANN is very similar to a feed forward Neural Network with the distinction that AANN uses the abs function as the activation function of the neurons. Due to this, all the activations produced, including the hidden layer activations, contain positive real number values. Thus, the network runs on the assumption that the input data as well as the label information comes from a positive data distribution. This doesn't create an issue for the computer vision based tasks. However, for those situations, where this is not possible, the feature values in the input dataset can be easily moved 1 into the positive region of the multi-dimensional input data space. The AANN transforms the n-dimensional input data into a space whose number of dimensions are equal to the number of labels used in the training dataset. For instance, presume that, the task is to classify images of cats and dogs and there is a labelled dataset present for achieving this classification. So, the learned representations will contain two dimensions corresponing to each label: cat and dog. The input images are transformed into 2-dimensional vectors by the AANN in such a way that the vectors are as close as possible to their ideal axes. This is achieved by constructing the cost function in a manner that it maximises the cosine value of the angle formed by the vector with its ideal axis. As a result, the representation space generated by this AANN can be visualized as shown in the FIG0 The AANN is constructed by using a 'Bidirectional Neuron' FIG1 ) as the building block for the hidden layers of a preliminary feed forward neural network. This bidirectional neuron uses the abs (mathematical absolute valued) function as the activation function. The computation performed by the neuron is similar in the forward and the backward directions. In the forward direction, the computation is given by: DISPLAYFORM0 Whereas, in the backward direction, the neuron computes: DISPLAYFORM1 The weights of the hidden layers of the AANN in forward direction learn to compute a function for transforming the input data into the representation vectors. While in the reverse direction, the weights constitute a function for constructing data points that closely resemble the data points belonging to the input dataset from the representation vectors. It is highly intriguing, and at the same time enigmatic, that the same set of weights constitute two entirely distinct functions. This research paper put forth an elementary but potent neural network architecture, named as AANN, that has the ability to learn in the forward as well as the backward direction. It also proposed the Abs function as a viable activation function for a neural network architecture. Due to lack of hardware resources, the experimentation had to be limited to the preliminary MNIST dataset, but it is firmly believed that the technique will perform equally well upon tackling other robust datasets, because of the theoretical evidence shown in the performed experiments.The AANN presently encodes the information in real number valued ranges across the the dedicated label axes in the the representation space. Certain regularization functions can be synthesized in order to stretch these ranges so that more information can be incorporated in them. The number of dimensions of the learned representations can be manually controlled by setting certain number of dedicated axes to a single label and by modifiying the forward cost function in such a way that the representation vectors lie inside the space generated by the coordinate axes dedicated to the ideal label. An in depth mathematical study of the Abs activation function could reveal the underlying behaviour of AANN. This forms the future scope for research.This technique also opens up new research opportunities for considering the AANN architectural modifications to certain network architectures like BID10 for semi-supervised learning. Moreover, it would be interesting to note the implications of applying the corresponding modifications to more advanced architectures such as Conv-nets BID6 and Recurrent Nets with LSTM cells BID3 .","research paper describes simplistic architecture named AANN:Absolute Artificial Neural Network which can be used create highly interpretable representations input data. representations are generated penalizing learning network way learned representations correspond respective labels present labelled dataset used supervised training;thereby simultaneously giving network ability classify input data. network can be used reverse direction generate data closely resembles input feeding representation vectors required. research paper also explores use mathematical abs absolute valued functions activation functions which constitutes core part neural network architecture. Finally results obtained MNIST dataset using technique are presented discussed brief. field philosophy has been principle known 'Ockham's Razor' which,in a simplified relevant language states Among available multiple solutions problem simplest one is the best one. instance if there are multiple polynomial functions fit given data distribution lowest degree one would preferred BID12. technique AANN is driven principle. spite elementary construction AANN is able classify inputs forward direction able generate back reverse direction. can be visualized classification forward direction whereas performing regression task backward direction.A standalone GAN Generative Adversarial Network described BID2 is able create representations input data using novel technique generating distribution contains original data points well data points generated Generator part network;distribution is then used Discriminator part network classify data points genuine generated. representations generated GAN although effective creating undistinguishable data points are however interpretable also highly entangled BID1 BID8. Using InfoGAN problem entanglement is solved training way network maximises mutual information within small clusters related latent representations BID1. Auto-encoder is another technique uses concept encoder-decoder architecture creating low dimensional representations originally high dimensional input data points. VAE:Variational Auto-Encoder tries make learned representations sparse using KL-divergence cost regularizer final cost autoencoder BID5. Various attempts combining two techniques GAN VAE have also made unsupervised well semi-supervised learning directions BID8 BID7. However techniques kept getting complicated somewhere synthesizing techniques is felt 'striving simplicity' principle has been neglected.The Absolute Artificial Neural Network exploits possible information available labelled training datasets structure learned representations input data. Structurally AANN is very is similar feed forward Neural Network distinction AANN uses abs function activation function neurons. Due activations produced including hidden layer activations contain positive real number values. Thus network runs assumption input data well label information comes positive data distribution. create issue computer vision based tasks. However situations where thisis possible feature values input dataset can be easily moved1 positive region multi-dimensional input data space. AANN transforms n-dimensional input data space whose number dimensions are equal number labels used training dataset. instance presume task is to classify images cats dogs is a labelled dataset present achieving classification. learned representations will contain two dimensions corresponing label:cat dog. input images are transformed 2-dimensional vectors AANN way vectors are as close possible ideal axes. is achieved constructing cost function manner maximises cosine value angle formed vector ideal axis. result representation space generated AANN can be visualized shown FIG0 AANN is constructed using 'Bidirectional Neuron' FIG1 building block hidden layers preliminary feed forward neural network. bidirectional neuron uses abs mathematical absolute valued function activation function. computation performed neuron is very is similar forward backward directions. forward direction computation is given by:DISPLAYFORM0 Whereas backward direction neuron computes:DISPLAYFORM1 weights hidden layers AANN forward direction learn compute function transforming input data representation vectors. reverse direction weights constitute function constructing data points closely resemble data points belonging input dataset representation vectors. is highly intriguing time enigmatic set weights constitute two entirely distinct functions. research paper put forth elementary potent neural network architecture named AANN has the ability learn forward well backward direction. also proposed Abs function viable activation function neural network architecture. Due lack hardware resources experimentation had to be limited preliminary MNIST dataset is firmly believed technique will perform equally well upon tackling robust datasets theoretical evidence shown performed experiments.The AANN presently encodes information real number valued ranges across dedicated label axes representation space. Certain regularization functions can be synthesized order stretch ranges information can be incorporated them. number dimensions learned representations can be manually controlled setting certain number dedicated axes single label modifiying forward cost function way representation vectors lie inside space generated coordinate axes dedicated ideal label. depth mathematical study Abs activation function could reveal underlying behaviour AANN. forms future scope research.This technique also opens new research opportunities considering AANN architectural modifications certain network architectures like BID10 semi-supervised learning. Moreover would interesting note implications applying corresponding modifications advanced architectures Conv-nets BID6 Recurrent Nets LSTM cells BID3.",1366,891,475,0.017,1.533,2025/11/05 17:19:07,0.01,1.659,0.6323987538940806,450.115
"Current state-of-the-art relation extraction methods typically rely on a set of lexical, syntactic, and semantic features, explicitly computed in a pre-processing step. Training feature extraction models requires additional annotated language resources, which severely restricts the applicability and portability of relation extraction to novel languages. Similarly, pre-processing introduces an additional source of error. To address these limitations, we introduce TRE, a Transformer for Relation Extraction, extending the OpenAI Generative Pre-trained Transformer [Radford et al., 2018]. Unlike previous relation extraction models, TRE uses pre-trained deep language representations instead of explicit linguistic features to inform the relation classification and combines it with the self-attentive Transformer architecture to effectively model long-range dependencies between entity mentions. TRE allows us to learn implicit linguistic features solely from plain text corpora by unsupervised pre-training, before fine-tuning the learned language representations on the relation extraction task. TRE obtains a new state-of-the-art result on the TACRED and SemEval 2010 Task 8 datasets, achieving a test F1 of 67.4 and 87.1, respectively. Furthermore, we observe a significant increase in sample efficiency. With only 20% of the training examples, TRE matches the performance of our baselines and our model trained from scratch on 100% of the TACRED dataset. We open-source our trained models, experiments, and source code. Relation extraction aims to identify the relationship between two nominals, typically in the context of a sentence, making it essential to natural language understanding. Consequently, it is a key component of many natural language processing applications, such as information extraction BID2 , knowledge base population BID6 , and question answering BID26 . Table 1 lists exemplary relation mentions.State-of-the-art relation extraction models, traditional feature-based and current neural methods, typically rely on explicit linguistic features: prefix and morphological features BID11 , syntactic features such as part-of-speech tags BID28 , and semantic features like named entity tags and WordNet hypernyms BID25 . Most recently, BID32 combined dependency parse features with graph convolutional neural networks to considerably increase the performance of relation extraction systems. Table 1 : Relation extraction examples, taken from TACRED (1-3) and SemEval 2010 Task 8 (4-6) . TACRED relation types mostly focus on named entities, whereas SemEval contains semantic relations between concepts.However, relying on explicit linguistic features severely restricts the applicability and portability of relation extraction to novel languages. Explicitly computing such features requires large amounts of annotated, language-specific resources for training; many unavailable in non-English languages. Moreover, each feature extraction step introduces an additional source of error, possibly cascading over multiple steps. Deep language representations, on the other hand, have shown to be a very effective form of unsupervised pre-training, yielding contextualized features that capture linguistic properties and benefit downstream natural language understanding tasks, such as semantic role labeling, coreference resolution, and sentiment analysis BID13 . Similarly, fine-tuning pre-trained language representations on a target task has shown to yield state-of-the-art performance on a variety of tasks, such as semantic textual similarity, textual entailment, and question answering BID14 .In addition, classifying complex relations requires a considerable amount of annotated training examples, which are time-consuming and costly to acquire. BID5 showed language model fine-tuning to be a sample efficient method that requires fewer labeled examples.Besides recurrent (RNN) and convolutional neural networks (CNN), the Transformer BID21 is becoming a popular approach to learn deep language representations. Its self-attentive structure allows it to capture long-range dependencies efficiently; demonstrated by the recent success in machine translation BID21 , text generation , and question answering BID14 .In this paper, we propose TRE: a Transformer based Relation Extraction model. Unlike previous methods, TRE uses deep language representations instead of explicit linguistic features to inform the relation classifier. Since language representations are learned by unsupervised language modeling, pre-training TRE only requires a plain text corpus instead of annotated language-specific resources. Fine-tuning TRE, and its representations, directly to the task minimizes explicit feature extraction, reducing the risk of error accumulation. Furthermore , an increased sample efficiency reduces the need for distant supervision methods BID11 BID15 , allowing for simpler model architectures without task-specific modifications.The contributions of our paper are as follows:• We describe TRE, a Transformer based relation extraction model that, unlike previous methods, relies on deep language representations instead of explicit linguistic features.• We are the first to demonstrate the importance of pre-trained language representations in relation extraction, by outperforming state-of-the-art methods on two supervised datasets, TACRED and SemEval 2010 Task 8.• We report detailed ablations, demonstrating that pre-trained language representations prevent overfitting and achieve better generalization in the presence of complex entity mentions. Similarly, we demonstrate a considerable increase in sample efficiency over baseline methods.• We make our trained models, experiments, and source code available to facilitate wider adoption and further research. We proposed TRE, a Transformer based relation extraction method that replaces explicit linguistic features, required by previous methods, with implicit features captured in pretrained language representations. We showed that our model outperformes the state-ofthe-art on two popular relation extraction datasets, TACRED and SemEval 2010 Task 8. We also found that pre-trained language representations drastically improve the sample efficiency of our approach. In our experiments we observed language representations to capture features very informative to the relation extraction task.While our results are strong, important future work is to further investigate the linguistic features that are captured by TRE. One question of interest is the extent of syntactic structure that is captured in language representations, compared to information provided by dependency parsing. Furthermore, our generic architecture enables us to integrate additional contextual information and background knowledge about entities, which could be used to further improve performance.",Current state-of-the-art relation extraction methods typically rely set lexical syntactic semantic features explicitly computed pre-processing step. Training feature extraction models requires additional annotated language resources which severely restricts applicability portability relation extraction novel languages. Similarly pre-processing introduces additional source error. address limitations introduce TRE Transformer Relation Extraction extending OpenAI Generative Pre-trained Transformer Radfordetal. 2018 Unlike previous relation extraction models TRE uses pre-trained deep language representations instead explicit linguistic features inform relation classification combines self-attentive Transformer architecture effectively model long-range dependencies entity mentions. TRE allowsus learn implicit linguistic features solely plain text corpora unsupervised pre-training fine-tuning learned language representations relation extraction task. TRE obtains new state-of-the-art result TACRED SemEval 2010 Task8 datasets achieving testF1 67.4 87.1 respectively. Furthermore observe significant increase sample efficiency. 20% training examples TRE matches performance baselines model trained scratch 100% TACRED dataset. open-source trained models experiments source code. Relation extraction aims identify relationship two nominals typically context sentence making essential natural language understanding. Consequently is a key component many natural language processing applications information extraction BID2 knowledge base population BID6 question answering BID26. Table 1 lists exemplary relation mentions.State-of-the-art relation extraction models traditional feature-based current neural methods typically rely explicit linguistic features:prefix morphological features BID11 syntactic features part-of-speech tags BID28 semantic features like named entity tags WordNet hypernyms BID25. recently BID32 combined dependency parse features graph convolutional neural networks considerably increase performance relation extraction systems. Table1:Relation extraction examples taken TACRED 1-3 SemEval 2010 Task8 4-6 TACRED relation types mostly focus named entities whereas SemEval contains semantic relations concepts.However relying explicit linguistic features severely restricts applicability portability relation extraction novel languages. Explicitly computing features requires large amounts annotated language-specific resources training;many unavailable non-English languages. Moreover feature extraction step introduces additional source error possibly cascading multiple steps. Deep language representations hand have shown effective form unsupervised pre-training yielding contextualized features capture linguistic properties benefit downstream natural language understanding tasks semantic role labeling coreference resolution sentiment analysis BID13. Similarly fine-tuning pre-trained language representations target task has shown yield state-of-the-art performance variety tasks semantic textual similarity textual entailment question answering BID14.In addition classifying complex relations requires considerable amount annotated training examples which are time-consuming costly acquire. BID5 showed language model fine-tuning sample efficient method requires fewer labeled examples.Besides recurrent RNN convolutional neural networks CNN Transformer BID21 is becoming popular approach learn deep language representations. self-attentive structure allows capture long-range dependencies efficiently;demonstrated recent success machine translation BID21 text generation question answering BID14.In paper propose TRE:Transformer based Relation Extraction model. Unlike previous methods TRE uses deep language representations instead explicit linguistic features inform relation classifier. Since language representations are learned unsupervised language modeling pre-training TRE requires plain text corpus instead annotated language-specific resources. Fine-tuning TRE representations directly task minimizes explicit feature extraction reducing risk error accumulation. Furthermore increased sample efficiency reduces need distant supervision methods BID11 BID15 allowing simpler model architectures without task-specific modifications.The contributions paper are as follows:• describe TRE Transformer based relation extraction model unlike previous methods relies deep language representations instead explicit linguistic features.• are the first demonstrate importance pre-trained language representations relation extraction outperforming state-of-the-art methods two supervised datasets TACRED SemEval 2010 Task8.• report detailed ablations demonstrating pre-trained language representations prevent overfitting achieve better generalization presence complex entity mentions. Similarly demonstrate considerable increase sample efficiency baseline methods.• make trained models experiments source code available facilitate wider adoption research. proposed TRE Transformer based relation extraction method replaces explicit linguistic features required previous methods implicit features captured pretrained language representations. showed model outperformes state-ofthe-art two popular relation extraction datasets TACRED SemEval 2010 Task8. also found pre-trained language representations drastically improve sample efficiency approach. experiments observed language representations capture features informative relation extraction task.While results are strong important future work is to further investigate linguistic features are is captured TRE. One question interest is the extent syntactic structure are is captured language representations compared information provided dependency parsing. Furthermore generic architecture enablesus integrate additional contextual information background knowledge entities could used improve performance.,1186,864,322,0.011,1.373,2025/11/05 17:19:07,0.0,1.5,0.1339563862928346,326.029
"Neural networks have recently had a lot of success for many tasks. However, neural
 network architectures that perform well are still typically designed manually
 by experts in a cumbersome trial-and-error process. We propose a new method
 to automatically search for well-performing CNN architectures based on a simple
 hill climbing procedure whose operators apply network morphisms, followed
 by short optimization runs by cosine annealing. Surprisingly, this simple method
 yields competitive results, despite only requiring resources in the same order of
 magnitude as training a single network. E.g., on CIFAR-10, our method designs
 and trains networks with an error rate below 6% in only 12 hours on a single GPU;
 training for one day reduces this error further, to almost 5%. Neural networks have rapidly gained popularity over the last few years due to their success in a variety of tasks, such as image recognition BID16 , speech recognition and machine translation BID1 . In most cases, these neural networks are still designed by hand, which is an exhausting, time-consuming process. Additionally, the vast amount of possible configurations requires expert knowledge to restrict the search. Therefore, a natural goal is to design optimization algorithms that automate this neural architecture search.However, most classic optimization algorithms do not apply to this problem, since the architecture search space is discrete (e.g., number of layers, layer types) and conditional (e.g., the number of parameters defining a layer depends on the layer type). Thus, methods that rely on, e.g., differentiability or independent parameters are not applicable. This led to a growing interest in using evolutionary algorithms BID22 BID26 and reinforcement learning BID2 BID6 for automatically designing CNN architectures. Unfortunately, most proposed methods are either very costly (requiring hundreds or thousands of GPU days) or yield non-competitive performance.In this work, we aim to dramatically reduce these computational costs while still achieving competitive performance. Specifically, our contributions are as follows:• We propose a baseline method that randomly constructs networks and trains them with SGDR BID20 . We demonstrate that this simple baseline achieves 6%-7% test error on CIFAR-10, which already rivals several existing methods for neural archictecture search. Due to its simplicity, we hope that this baseline provides a valuable starting point for the development of more sophisticated methods in the future.• We formalize and extend the work on network morphisms BID27 BID6 in order to provide popular network building blocks, such as skip connections and batch normalization.• We propose Neural Architecture Search by Hillclimbing (NASH), a simple iterative approach that, at each step, applies a set of alternative network morphisms to the current network, trains the resulting child networks with short optimization runs of cosine annealing BID20 , and moves to the most promising child network. NASH finds and trains competitive architectures at a computational cost of the same order of magnitude as training a single network; e.g., on CIFAR-10, NASH finds and trains CNNs with an error rate below 6 % in roughly 12 hours on a single GPU. After one day the error is reduced to almost 5%. Models from different stages of our algorithm can be combined to achieve an error of 4.7 % within two days on a single GPU. On CIFAR-100 , we achieve an error below 24% in one day and get close to 20% after two days.• Our method is easy to use and easy to extend, so it hopefully can serve as a basis for future work.We first discuss related work in Section 2. Then, we formalize the concept of network morphisms in Section 3 and propose our architecture search methods based on them in Section 4. We evaluate our methods in Section 5 and conclude in Section 6. We proposed NASH, a simple and fast method for automated architecture search based on a hill climbing strategy, network morphisms, and training via SGDR. Experiments on CIFAR-10 and CIFAR-100 showed that our method yields competitive results while requiring considerably less computational resources than most alternative approaches. Our algorithm is easily extendable, e.g., by other network morphisms, evolutionary approaches for generating new models, other methods for cheap performance evaluation (such as, e.g., learning curve prediction BID15 or hypernetworks BID10 BID5 ), or better resource handling strategies (such as Hyperband BID18 ). In this sense, we hope that our approach can serve as a basis for the development of more sophisticated methods that yield further improvements of performance. B SOME MODELS",Neural networks have recently had a lot success many tasks. However neural network architectures perform well are still typically designed manually experts cumbersome trial-and-error process. propose new method automatically search well-performing CNN architectures based simple hill climbing procedure whose operators apply network morphisms followed short optimization runs cosine annealing. Surprisingly simple method yields competitive results despite requiring resources order magnitude training single network. E.g CIFAR-10 method designs trains networks error rate 6% 12 hours single GPU;training one day reduces error almost 5%. Neural networks have rapidly gained popularity last years due success variety tasks image recognition BID16 speech recognition machine translation BID1. cases neural networks are still designed hand which is an exhausting time-consuming process. Additionally vast amount possible configurations requires expert knowledge restrict search. Therefore natural goal is to design optimization algorithms automate neural architecture search.However classic optimization algorithms do not apply problem since architecture search space is discrete e.g number layers layer types conditional e.g number parameters defining layer depends layer type Thus methods rely e.g differentiability independent parameters are not applicable. led growing interest using evolutionary algorithms BID22 BID26 reinforcement learning BID2 BID6 automatically designing CNN architectures. Unfortunately proposed methods are either costly requiring hundreds thousands GPU days yield non-competitive performance.In work aim dramatically reduce computational costs still achieving competitive performance. Specifically contributions are as follows:• propose baseline method randomly constructs networks trains SGDR BID20. demonstrate simple baseline achieves6%-7 test error CIFAR-10 which already rivals several existing methods neural archictecture search. Due simplicity hope baseline provides valuable starting point development sophisticated methods future.• formalize extend work network morphisms BID27 BID6 order provide popular network building blocks skip connections batch normalization.• propose Neural Architecture Search Hillclimbing NASH simple iterative approach step applies set alternative network morphisms current network trains resulting child networks short optimization runs cosine annealing BID20 moves promising child network. NASH finds trains competitive architectures computational cost order magnitude training single network;e.g CIFAR-10 NASH finds trains CNNs error rate 6% roughly 12 hours single GPU. one day error is reduced almost 5%. Models different stages algorithm can be combined achieve error 4.7 within two days single GPU. CIFAR-100 achieve error 24% one day get close 20% two days.• method is easy use easy extend hopefully can serve basis future work.We first discuss related work Section2. formalize concept network morphisms Section3 propose architecture search methods based Section4. evaluate methods Section5 conclude Section6. proposed NASH simple fast method automated architecture search based hill climbing strategy network morphisms training via SGDR. Experiments CIFAR-10 CIFAR-100 showed method yields competitive results requiring considerably less computational resources alternative approaches. algorithm is easily extendable e.g network morphisms evolutionary approaches generating new models methods cheap performance evaluation e.g learning curve prediction BID15 hypernetworks BID10 BID5 better resource handling strategies Hyperband BID18 sense hope approach can serve basis development sophisticated methods yield improvements performance. B MODELS,921,604,317,0.009,1.525,2025/11/05 17:19:07,0.0,1.471,0.6074766355140183,294.916
"We propose GraphGAN - the first implicit generative model for graphs that enables to mimic real-world networks.
 We pose the problem of graph generation as learning the distribution of biased random walks over a single input graph.
 Our model is based on a stochastic neural network that generates discrete output samples, and is trained using the Wasserstein GAN objective. GraphGAN enables us to generate sibling graphs, which have similar properties yet are not exact replicas of the original graph. Moreover, GraphGAN learns a semantic mapping from the latent input space to the generated graph's properties. We discover that sampling from certain regions of the latent space leads to varying properties of the output graphs, with smooth transitions between them. Strong generalization properties of GraphGAN are highlighted by its competitive performance in link prediction as well as promising results on node classification, even though not specifically trained for these tasks. Generative models for graphs have a longstanding history, with applications including data augmentation, anomaly detection and recommendation BID6 . Explicit probabilistic models such as Barabási-Albert or stochastic blockmodels are the de-facto standard in this field BID11 . However, it has also been shown on multiple occasions that our intuitions about structure and behavior of graphs may be misleading. For instance, heavy-tailed degree distributions in real graphs were in stark disagreement with the models existing at the time of their discovery BID2 . More recent works, like BID9 , keep bringing up other surprising characteristics of real-world networks, not accounted for by the models at hand. This leads us to the question: ""How do we define a model that captures all the essential (potentially still unknown) properties of real graphs?"" An increasingly popular way to address this issue in other fields is by switching from explicit (prescribed) models to implicit ones. This transition is especially notable in Computer Vision, where Variational Autoencoder BID23 and Generative Adversarial Networks (GANs) BID13 significantly advanced the state of the art over the classic prescribed approaches like Mixtures of Gaussians BID5 . GANs achieve unparalleled results in scenarios such as image and 3D objects generation (e.g., BID32 BID4 . However, despite their massive success when dealing with real-valued data, adapting GANs to handle discrete objects like graphs or text remains an open research problem BID12 . Indeed, the combinatorial structure of the graph is only one of the obstacles when applying GANs to graphs. Second, large repositories of graphs, which all come from the same distribution, do not exist. This means that in a typical setting one has to learn from a single graph. And last, any model operating on a graph necessarily has to be permutation invariant, as the graphs remain isomorphic under node reordering.In this work we introduce GraphGAN -the first implicit generative model for graphs, that tackles all of the above challenges. We formulate the problem of learning the graph topology as learning the distribution of biased random walks over the graph. Like in the typical GAN setting, the generator G -in our case defined as a stochastic neural network with discrete output samples -learns to generate random walks that are plausible in the real graph, while the discriminator D then has to distinguish them from the true ones that are sampled from the original graph. The objective function of our model is based on the Wasserstein GAN , which allows to learn multimodal distributions and leads to more stable convergence. Our GraphGAN exhibits strong generalization properties, which we study in detail in the experimental section. The example in FIG0 shows that the graphs generated by GraphGAN possess similar properties as the input graph, as shown by the degree distributions in FIG0 . The generated graphs, however, are not simply exact replicas: as the visualized subset of nodes in Figs. 1a and 1b shows, the graphs exhibit similar structure while being not identical; in fact, the two graphs have less than 50% of edges in common. This initial insight is underlined by an extensive comparison of graphs generated by GraphGAN and the respective input networks in the experimental section of this work. And even more, when generating graphs based on specific regions of the latent space learned by GraphGAN, we can smoothly interpolate between graphs with varying properties. Our main contributions are:• We introduce GraphGAN -the first of its kind GAN that generates graphs via random walks. Our model tackles the associated challenges of staying permutation invariant, learning from a single graph and generating discrete output.• We show that our model generalizes, and is able to produce sibling graphs to the given input graph. These graphs posses similar topological characteristics, but are not exact replicas (see FIG0 ). We further demonstrate how latent space interpolation leads to generation of graphs with smoothly changing properties.• We highlight the generalization properties of GraphGAN by its link prediction performance, which is competitive with the state of the art on real-word datasets, although not trained explicitly for this task. Additionally, to give the reader a better insight about the behavior of our model, we analyze the learned weights of our model -that can be viewed as node ""embeddings"" -and by using them in a node classification task we show that they capture meaningful structural information. When evaluating different graph generative models in Sec. 4.1, we observed a major limitation of explicit models. While the prescribed approaches excel at recovering the properties that are directly included in their definition, they perform significantly worse with respect to the rest of the metrics. This phenomenon clearly indicates the need for implicit graph generators, such as GraphGAN. Indeed, we notice that our model is able to consistently capture all the important graph characteristics (see TAB1 ). Moreover, GraphGAN generalizes beyond the input graph, as can be seen by its strong link prediction performance in Sec. 4.2.Still, being the first model of its kind, GraphGAN possesses certain limitations, and a number of related questions could be addressed in follow-up works:Scalability. We have observed in Sec. 4.2 that it takes a large number of generated random walks to get representative transition counts for large graphs. While sampling random walks from GraphGAN is trivially parallelizable, a possible extension of our model is to use a conditional generator, i.e. the generator can be provided a desired starting node, thus ensuring a more even coverage. On the other hand, the sampling procedure itself can be sped up by incorporating a hierarchical softmax output layer -a method commonly used in natural language processing.Evaluation. It is nearly impossible to judge whether a graph is realistic by visually inspecting it (unlike images, for example). In this work we already quantitatively evaluate the performance of GraphGAN on a large number of standard graph statistics. However, developing new measures applicable to (implicit) graph generative models will deepen our understanding of their behavior.Experimental scope. In the current work we focused on the setting of a single connected graph.Other scenarios, such as dealing with a collection of smaller i.i.d. graphs, that frequently occur in other fields (e.g., chemistry, biology), would be an important application area for the proposed model. Studying the influence of the graph topology (e.g., sparsity, diameter) on performance of GraphGAN will shed more light on its properties.Other types of graphs. While plain graphs are ubiquitous, many of real-world applications deal with attributed, k-partite or heterogeneous networks. Adapting the GraphGAN model to handle these other modalities of the data is a promising direction for future research. Especially important would be an adaptation to the dynamic / inductive setting, when new nodes are added over time. GraphGAN is the first work to successfully bridge the worlds of implicit modeling and graphs. Our work enables future researchers to gain better insight into the properties of real networks and opens new and exciting lines of research. We are able to generate realistic graphs by learning to generate (biased) random walks from the same distribution as the random walks from an input graph. We employ the GAN framework to learn our implicit generative model, overcoming key challenges such as permutation invariance, working in the discrete domain and having a single graph as input. Our generator is able to generate sibling graphs that maintain structural similarity with the original graph without being exact replicas. Better yet, using our defined stopping criteria, we can control how close are the generated graphs to the original. We further show that GraphGAN learns a semantic mapping from the latent space to the properties of the generated graph, which is evidenced by the smooth transitions of the output. GraphGAN shows strong generalization properties, as demonstrated by the competitive performance on the link prediction and the promising results on the node classification task, without being explicitly trained with these tasks in mind.",propose GraphGAN first implicit generative model graphs enables mimic real-world networks. pose problem graph generation learning distribution biased random walks single input graph. model is based stochastic neural network generates discrete output samples is trained using Wasserstein GAN objective. GraphGAN enablesus generate sibling graphs which have similar properties yet are not exact replicas original graph. Moreover GraphGAN learns semantic mapping latent input space generated graph's properties. discover sampling certain regions latent space leads varying properties output graphs smooth transitions them. Strong generalization properties GraphGAN are highlighted competitive performance link prediction well promising results node classification even though specifically trained tasks. Generative models graphs have a longstanding history applications including data augmentation anomaly detection recommendation BID6. Explicit probabilistic models Barabási-Albert stochastic blockmodels are the de-facto standard field BID11. However has also shown multiple occasions intuitions structure behavior graphs may misleading. instance heavy-tailed degree distributions real graphs were in stark disagreement models existing time discovery BID2. recent works like BID9 keep bringing surprising characteristics real-world networks accounted models hand. leadsus question:How do we define model captures essential potentially still unknown properties real graphs? increasingly popular way address issue fields is by switching explicit prescribed models implicit ones. transition is especially notable Computer Vision where Variational Autoencoder BID23 Generative Adversarial Networks GANs BID13 significantly advanced state art classic prescribed approaches like Mixtures Gaussians BID5. GANs achieve unparalleled results scenarios image 3D objects generation e.g BID32 BID4. However despite massive success when dealing real-valued data adapting GANs handle discrete objects like graphs text remains open research problem BID12. Indeed combinatorial structure graph is only one obstacles when applying GANs graphs. Second large repositories graphs which all come distribution do not exist. means typical setting one has to learn single graph. last model operating graph necessarily has to be permutation invariant graphs remain isomorphic node reordering.In work introduce GraphGAN -the first implicit generative model graphs tackles challenges. formulate problem learning graph topology learning distribution biased random walks graph. Like typical GAN setting generator G -in case defined stochastic neural network discrete output samples -learns generate random walks are plausible real graph discriminator has to distinguish true ones are sampled original graph. objective function model is based Wasserstein GAN which allows learn multimodal distributions leads stable convergence. GraphGAN exhibits strong generalization properties which we study detail experimental section. example FIG0 shows graphs generated GraphGAN possess similar properties input graph shown degree distributions FIG0. generated graphs however are not simply exact replicas:visualized subset nodes Figs. 1a 1b shows graphs exhibit similar structure identical;fact two graphs have less 50% edges common. initial insight is underlined extensive comparison graphs generated GraphGAN respective input networks experimental section work. even when generating graphs based specific regions latent space learned GraphGAN can smoothly interpolate graphs varying properties. main contributions are:• introduce GraphGAN -the first kind GAN generates graphs via random walks. model tackles associated challenges staying permutation invariant learning single graph generating discrete output.• show model generalizes is able produce sibling graphs given input graph. graphs posses similar topological characteristics are not exact replicas see FIG0 demonstrate how latent space interpolation leads generation graphs smoothly changing properties.• highlight generalization properties GraphGAN link prediction performance which is competitive state art real-word datasets although trained explicitly task. Additionally give reader better insight behavior model analyze learned weights model -that can be viewed node embeddings -and using node classification task show capture meaningful structural information. When evaluating different graph generative models Sec. 4.1 observed major limitation explicit models. prescribed approaches excel recovering properties are directly included definition perform significantly worse respect rest metrics. phenomenon clearly indicates need implicit graph generators GraphGAN. Indeed notice model is able consistently capture important graph characteristics see TAB1 Moreover GraphGAN generalizes beyond input graph can be seen strong link prediction performance Sec. 4. 2.Still first model kind GraphGAN possesses certain limitations number related questions could addressed follow-up works:Scalability. have observed Sec. 4.2 takes large number generated random walks get representative transition counts large graphs. sampling random walks GraphGAN is trivially parallelizable possible extension model is to use conditional generator.e generator can be provided desired starting node thus ensuring even coverage. hand sampling procedure can be sped incorporating hierarchical softmax output layer -a method commonly used natural language processing.Evaluation. is nearly impossible judge whether graph is realistic visually inspecting unlike images example work already quantitatively evaluate performance GraphGAN large number standard graph statistics. However developing new measures applicable implicit graph generative models will deepen understanding behavior.Experimental scope. current work focused setting single connected graph.Other scenarios dealing collection smaller.i.d graphs frequently occur fields e.g chemistry biology would important application area proposed model. Studying influence graph topology e.g sparsity diameter performance GraphGAN will shed light properties.Other types graphs. plain graphs are ubiquitous many real-world applications deal attributed k-partite heterogeneous networks. Adapting GraphGAN model handle modalities data is a promising direction future research. Especially important would adaptation dynamic/inductive setting when new nodes are added time. GraphGAN is the first work successfully bridge worlds implicit modeling graphs. work enables future researchers gain better insight properties real networks opens new exciting lines research. are able generate realistic graphs learning generate biased random walks distribution random walks input graph. employ GAN framework learn implicit generative model overcoming key challenges permutation invariance working discrete domain single graph input. generator is able generate sibling graphs maintain structural similarity original graph without exact replicas. Better yet using defined stopping criteria can control how close are the generated graphs original. show GraphGAN learns semantic mapping latent space properties generated graph which is evidenced smooth transitions output. GraphGAN shows strong generalization properties demonstrated competitive performance link prediction promising results node classification task without explicitly trained tasks mind.,1750,1153,597,0.022,1.518,2025/11/05 17:19:07,0.01,1.483,0.585669781931464,557.903
"The ability of a classifier to recognize unknown inputs is important for many classification-based systems. We discuss the problem of simultaneous classification and novelty detection, i.e. determining whether an input is from the known set of classes and from which specific class, or from an unknown domain and does not belong to any of the known classes. We propose a method based on the Generative Adversarial Networks (GAN) framework. We show that a multi-class discriminator trained with a generator that generates samples from a mixture of nominal and novel data distributions is the optimal novelty detector. We approximate that generator with a mixture generator trained with the Feature Matching loss and empirically show that the proposed method outperforms conventional methods for novelty detection. Our findings demonstrate a simple, yet powerful new application of the GAN framework for the task of novelty detection. In recent years we have witnessed incredible progress in AI, largely due to the success of Deep Learning, and more specifically Supervised Deep Learning. One of the basic requirements from a good supervised learning algorithm is generalization -the ability to classify input that is reasonably similar to the training data. However, usually there are no requirements whatsoever on how the classifier should behave for new types of input that differ substantially from the data that are available during training. In fact for such novel input the algorithm will produce erroneous output and classify it as one of the classes that were available to it during training. Ideally, we would like that the classifier, in addition to its generalization ability, be able to detect novel inputs, or in other words, we would like the classifier to say, ""I don't know."" Novelty detection can be defined as the task of recognizing that test data differs in some manner from the data that was available during training. The problem of novelty detection arises in many fields and is closely related, but not identical, to the problems of anomaly detection (also outlier detection), where the goal is to recognize anomalous examples in a dataset BID2 . Novelty detection is a hard problem that has received relatively little attention in the ML literature. Nevertheless, in our opinion novelty detection should be a central part of every recognition system. For a comprehensive in-depth review of the topic of novelty detection, we refer the reader to BID18 . Popular conventional novelty detection methods such as Probabilistic methods BID18 , which perform density estimation of the examples from a nominal class, or Domainbased methods BID23 ; BID27 , which re-formulate novelty detection as a ""one-class classification"" problem and define a boundary around the nominal class, do not scale well to large high-dimensional datasets. Another class of novelty detection methods is distance-based methods, which assume that the nominal data are tightly clustered, while novel data occur far from their nearest neighbors. These methods require computationally expensive clustering or nearest neighbors search. One of the major drawbacks of conventional novelty detection methods is that at test time, they are separated from the classification algorithm and therefore increase the overall computational and design complexity of the system. Furthermore, combining novelty detection with a multi-class classifier into a single algorithm may leverage important intra and inter-class information in the training data which can benefit both tasks.In this paper we are interested in methods for simultaneous classification and novelty detection. A popular heuristic approach to simultaneous classification and novelty detection is thresholding the maximum of estimated class probability BID9 , or alternatively, to threshold the entropy of the estimated probability distribution. Another practical approach is to collect ""backgroundclass"" samples, that is, samples that are not from the nominal set and hopefully represent novel data. In this case, novelty detection can be reduced to a supervised learning problem. Unfortunately, this solution requires collecting a large set of background inputs -a time-consuming task and moreover, it is very difficult to sample a large enough background class that will represent all possible novel examples.We embrace the ""background-class"" sampling idea and ask is it possible to generate novel data? To the best of our knowledge, no method for novelty detection is based on generating novel examples. In this paper we examine whether Generative Adversarial Networks (GAN), a popular generative framework that can be used to generate novel examples. The GAN framework was proposed by BID8 , as a generative modeling method, mostly used for generating realistic samples of natural images. More specifically, GAN is an approach to generative modeling where two models are trained simultaneously: a generator and a discriminator. The task of the discriminator is to classify an input as either the output of the generator (""fake"" data), or actual samples from the underlying data distribution (""real"" data). The goal of the generator is to produce outputs that are classified by the discriminator as ""real"", or as coming from the underlying data distribution.In some formulations of GANs Odena (2016); BID25 , the discriminator is trained to classify data not only into two classes ""real"" and ""fake"", but rather into multiple classes. If the ""real"" data consists of K classes, then the output of the discriminator is K + 1 class probabilities where K probabilities corresponds to K known classes, and the K + 1 probability correspond to the ""fake"" class.In this paper, we propose to use a multi-class GAN framework for simultaneous classification and novelty detection. If during training the generator generates a mixture of nominal data and novel data, the multi-class discriminator learns to discriminate novel data from nominal data and essentially became a novelty detector. At test time, when the discriminator classifies a real example to the K + 1 th class, i.e., class which represented ""fake examples"" during training, this the example is most likely a novel example and not from one of the K nominal classes. In fact, we prove that in this case the discriminator become an optimal novelty detector (for a given false positive rate). We approximate such a mixture generator with a generator trained with specifically designed loss functions. In Section 2 we provide background and a theoretical justification to our proposed method and its connection to existing novelty detection methods. We validate the proposed method by a set of experiments in Section 3. The ability to identify novelties or say ""I don't know"" is an important tool for many classificationbased systems. In this work, we propose to solve a problem of simultaneous classification and novelty detection within the GAN framework. We propose to use a GAN with a mixture generator to turn this problem into a supervised learning problem without collecting ""background-class"" data.In the case where a mixture generator generates samples from a mixture of nominal data distribution and novel data distribution, we showed that the GAN's discriminator is an optimal novelty detector. We approximate that generator with a mixture generator trained with the Feature Matching loss. This mixture generator generates samples scattered around and in the low-density areas of the data manifold, and this makes a multi-class discriminator a powerful novelty detector. We empirically validate that the performance of the proposed solution is comparable to several popular novelty detection methods, and sometimes outperforms them.Clearly, evaluation of the proposed framework on more challenging datasets is required. As a future research direction we would like to search for new loss functions for mixture generators that will enrich the generator distribution and will improve novelty detection. Classification with asymmetric label noise problem BID24 is closely related to semi-supervised novelty detection, and it will be interesting to see whether the GAN framework can be used to solve this problem. Finally, it is interesting to see if the suggested framework can be applied to detecting the adversarial examples.",ability classifier recognize unknown inputs is is an important many classification-based systems. discuss problem simultaneous classification novelty detection.e determining whether input is from the known set classes which specific class unknown domain does not belong known classes. propose method based Generative Adversarial Networks GAN framework. show multi-class discriminator trained generator generates samples mixture nominal novel data distributions is the is an optimal novelty detector. approximate generator mixture generator trained Feature Matching loss empirically show proposed method outperforms conventional methods novelty detection. findings demonstrate simple yet powerful new application GAN framework task novelty detection. recent years have witnessed incredible progress AI largely due success Deep Learning specifically Supervised Deep Learning. One basic requirements good supervised learning algorithm is generalization -the ability classify input is reasonably similar training data. However usually are no requirements whatsoever how the classifier should behave new types input differ substantially data are were was available training. fact novel input algorithm will produce erroneous output classify one classes are were was available training. Ideally would like classifier addition generalization ability able detect novel inputs words would like classifier say know. Novelty detection can be defined task recognizing test data differs manner data are were was available training. problem novelty detection arises many fields is closely related identical problems anomaly detection also outlier detection where the goal is to recognize anomalous examples dataset BID2. Novelty detection is a hard problem has received relatively little attention ML literature. Nevertheless opinion novelty detection should be a central part every recognition system. comprehensive in-depth review topic novelty detection refer reader BID18. Popular conventional novelty detection methods Probabilistic methods BID18 which perform density estimation examples nominal class Domainbased methods BID23;BID27 which re-formulate novelty detection one-class classification problem define boundary around nominal class do not scale well large high-dimensional datasets. Another class novelty detection methods is distance-based methods which assume are not from nominal data are tightly clustered novel data occur far nearest neighbors. methods require computationally expensive clustering nearest neighbors search. One major drawbacks conventional novelty detection methods is that at test time are separated classification algorithm therefore increase overall computational design complexity system. Furthermore combining novelty detection multi-class classifier single algorithm may leverage important intra inter-class information training data which can benefit tasks.In paper are interested methods simultaneous classification novelty detection. popular heuristic approach simultaneous classification novelty detection is thresholding maximum estimated class probability BID9 alternatively threshold entropy estimated probability distribution. Another practical approach is to collect backgroundclass samples samples are not from nominal set hopefully represent novel data. case novelty detection can be reduced supervised learning problem. Unfortunately solution requires collecting large set background inputs -a time-consuming task moreover is very difficult sample large enough background class will represent possible novel examples.We embrace background-class sampling idea ask is it possible generate novel data? best knowledge method novelty detection is based generating novel examples. paper examine whether Generative Adversarial Networks GAN popular generative framework can be used generate novel examples. GAN framework was proposed BID8 generative modeling method mostly used generating realistic samples natural images. specifically GAN is an approach generative modeling where two models are trained simultaneously:generator discriminator. task discriminator is to classify input either output generator fake data actual samples underlying data distribution real data where the goal generator is to produce outputs are classified discriminator real coming underlying data distribution.In formulations GANs Odena 2016 BID25 when the discriminator is trained classify data two classes real fake rather multiple classes. If the real data consists K classes output discriminator is K+1 class probabilities where K probabilities corresponds K known classes K+1 probability correspond fake class.In paper propose use multi-class GAN framework simultaneous classification novelty detection. If during training generator generates mixture nominal data novel data multi-class discriminator learns discriminate novel data nominal data essentially became novelty detector. test time when the discriminator classifies real example K+1th class.e class which represented fake examples training example is most likely novel example one K nominal classes. fact prove case discriminator become optimal novelty detector given false positive rate approximate mixture generator generator trained specifically designed loss functions. Section2 provide background theoretical justification proposed method connection existing novelty detection methods. validate proposed method set experiments Section3. ability identify novelties say know is is an important tool many classificationbased systems. work propose solve problem simultaneous classification novelty detection within GAN framework. propose use GAN mixture generator turn problem supervised learning problem without collecting background-class data.In case where a mixture generator generates samples mixture nominal data distribution novel data distribution showed GAN's discriminator is the is an optimal novelty detector. approximate generator mixture generator trained Feature Matching loss. mixture generator generates samples scattered around low-density areas data manifold makes multi-class discriminator powerful novelty detector. empirically validate performance proposed solution is comparable several popular novelty detection methods sometimes outperforms them.Clearly evaluation proposed framework challenging datasets is required. future research direction would like search new loss functions mixture generators will enrich generator distribution will improve novelty detection. Classification asymmetric label noise problem BID24 is closely related semi-supervised novelty detection willis interesting see whether GAN framework can be used solve problem. Finally will is interesting see if the suggested framework can be applied detecting adversarial examples.,1492,996,496,0.019,1.498,2025/11/05 17:19:07,0.01,1.522,0.5233644859813082,482.88
"  Verifying a person's identity based on their voice is a challenging, real-world problem in biometric security. A crucial requirement of such speaker verification systems is to be domain robust. Performance should not degrade even if speakers are talking in languages not seen during training. To this end, we present a flexible and interpretable framework for learning domain invariant speaker embeddings using Generative Adversarial Networks. We combine adversarial training with an angular margin loss function, which encourages the speaker embedding model to be discriminative by directly optimizing for cosine similarity between classes. We are able to beat a strong baseline system using a cosine distance classifier and a simple score-averaging strategy. Our results also show that models with adversarial adaptation perform significantly better than unadapted models. In an attempt to better understand this behavior, we quantitatively measure the degree of invariance induced by our proposed methods using Maximum Mean Discrepancy and Frechet distances. Our analysis shows that our proposed adversarial speaker embedding models significantly reduce the distance between source and target data distributions, while performing similarly on the former and better on the latter.",Verifying person's identity based voice is a challenging real-world problem biometric security. crucial requirement speaker verification systems is to be domain robust. Performance should not degrade even if speakers are talking languages seen training. end present flexible interpretable framework learning domain invariant speaker embeddings using Generative Adversarial Networks. combine adversarial training angular margin loss function which encourages speaker embedding model discriminative directly optimizing cosine similarity classes. are able beat strong baseline system using cosine distance classifier simple score-averaging strategy. results also show models adversarial adaptation perform significantly better unadapted models. attempt better understand behavior quantitatively measure degree invariance induced proposed methods using Maximum Mean Discrepancy Frechet distances. analysis shows proposed adversarial speaker embedding models significantly reduce distance source target data distributions performing similarly former better latter.,219,156,63,0.002,1.404,2025/11/05 17:19:07,0.0,1.571,0.2305295950155758,81.948
"Learning disentangling representations of the independent factors of variations that explain the data in an unsupervised setting is still a major challenge. In the following paper we address the task of disentanglement and introduce a new state-of-the-art approach called Non-synergistic variational Autoencoder (Non-Syn VAE). Our model draws inspiration from population coding, where the notion of synergy arises when we describe the encoded information by neurons in the form of responses from the stimuli. If those responses convey more information together than separate as independent sources of encoding information, they are acting synergetically. By penalizing the synergistic mutual information within the latents we encourage information independence and by doing that disentangle the latent factors. Notably, our approach could be added to the VAE framework easily, where the new ELBO function is still a lower bound on the log likelihood. In addition, we qualitatively compare our model with Factor VAE and show that this one implicitly minimises the synergy of the latents. Our world is hierarchical and compositional, humans can generalise better since we use primitive concepts that allow us to create complex representations BID11 ). Towards the creation of truly intelligent systems, they should learn in a similar way resulting in an increase of their performance since they would capture the underlying factors of variation of the data BID2 ; ; ). In addition, good representations improve the performance for tasks involving transfer learning and multi-task learning; since it will capture the explanatory factors.According to BID18 , a compositional representation should create new elements from the combination of primitive concepts resulting in a infinite number of new representations. For example if our model is trained with images of white wall and then is presented a boy with a white shirt, it should identify the color white as a primitive element. Intuitively, our model will be able to construct different and multiple representations from the primitives.Furthermore, a disentangled representation has been interpreted in different ways, for instance BID2 define it as one where single latent variables are sensitive to changes in generative factors, while being invariant to changes in other factors. In addition, we agree with BID12 , which mentions that a disentangle representation should be factorised and interpretable. Intuitevely, the model could learn generative factors such as position, scale or colour; if it is disentangle it should be able to traverse along the position variable without changing the scale or the colour. It's worth noting that disentangled representations have been useful for a variety of downstream tasks such as domain adaptation by training a Reinforcement Learning agent that uses a disentangled representation of its environment BID13 ; or for learning disentangled primitives grounded in the visual domain discovered in an unsupervised manner BID14 .",Learning disentangling representations independent factors variations explain data unsupervised setting is still major challenge. following paper address task disentanglement introduce new state-of-the-art approach called Non-synergistic variational Autoencoder Non-Syn VAE model draws inspiration population coding where the notion synergy arises when we describe encoded information neurons form responses stimuli. If those responses convey information together separate independent sources encoding information are acting synergetically. penalizing synergistic mutual information within latents encourage information independence disentangle latent factors. Notably approach could added VAE framework easily where the new ELBO function is still lower bound log likelihood. addition qualitatively compare model Factor VAE show one implicitly minimises synergy latents. world is hierarchical compositional humans can generalise better since use primitive concepts allowus create complex representations BID11 Towards creation truly intelligent systems should learn similar way resulting increase performance since would capture underlying factors variation data BID2;addition good representations improve performance tasks involving transfer learning multi-task learning;since will capture explanatory factors.According BID18 compositional representation should create new elements combination primitive concepts resulting infinite number new representations. example if our model is trained images white wall is presented boy white shirt should identify color white primitive element. Intuitively model will be able construct different multiple representations primitives.Furthermore disentangled representation has been interpreted different ways instance BID2 define one where single latent variables are sensitive changes generative factors invariant changes factors. addition agree BID12 which mentions disentangle representation should be factorised interpretable. Intuitevely model could learn generative factors position scale colour;if it is disentangle should be able traverse along position variable without changing scale colour. worth noting disentangled representations have been useful variety downstream tasks domain adaptation training Reinforcement Learning agent uses disentangled representation environment BID13;learning disentangled primitives grounded visual domain discovered unsupervised manner BID14.,550,373,177,0.005,1.475,2025/11/05 17:19:07,0.0,1.5,0.4517133956386294,193.711
"   Metric embeddings are   immensely useful representations of associations between entities   (images, users, search queries, words, and more).   Embeddings are learned by  optimizing a loss objective of the general form of a sum over example associations. Typically, the optimization uses stochastic gradient updates over minibatches of examples that are arranged  independently at random. In this work, we propose the use of {\em structured arrangements} through randomized {\em microbatches} of examples that are more likely to include similar ones. We make a principled argument for the properties of our arrangements  that accelerate the training and present efficient algorithms to generate microbatches that respect the marginal  distribution of training examples.   Finally, we observe experimentally that our structured arrangements accelerate training by 3-20\%. Structured arrangements emerge as a powerful and novel performance knob for SGD that is independent and complementary to other SGD  hyperparameters and thus is a candidate for wide deployment. Metric embeddings of entities that are trained to capture example associations are common representations that also allow for inference of associations not present in the data. Embeddings are used in complex learning tasks or directly applied for similarity and recommendations tasks. Example usage domains includes embeddings of text document from occurrences of words BID2 ; BID9 ; BID7 , users and videos from watch or ratings BID15 , words from co-occurrence frequencies in a corpus BID16 , and nodes in a graph from co-occurrence in short random walks BID19 . The example associations may involve entities of the same type (word co-occurrences, video co-watch, social) or different types (such as users and products) and often are distilled by reweighing frequencies of raw interactions Salton & Buckley (1988) ; BID7 ; BID16 ; BID18 .Embeddings are computed by minimizing a loss objective of the form of a sum over example associations. The optimization starts with random initialization followed by gradient updates. In modern applications , the objective can have billions of terms or more, and the de facto method at such scale is stochastic gradient descent (SGD) Robbins & Siegmund (1971) ; BID14 ; Salakhutdinov et al. (2007) ; BID11 ; BID16 . The terms (examples) are randomly grouped into minibatches. Gradient updates, that are equal in expectation to the full gradient, are then computed sequentially for each minibatch. SGD is much more efficient than working with full gradients and the minibatch size determines the amount of concurrency. There are numerous tunable parameters and methods aimed to improve quality and speed of convergence. Some notable recent work includes per-parameter tuning of the learning rate BID8 and altering the distribution of training examples by gradient magnitude BID1 , negatives selection with triplet loss Schroff et al. (2015) , clustering BID10 and diversity criteria BID10 .In this work we introduce principled schemes that control the arrangement of examples into minibatches. Note that arrangement tuning is separate and orthogonal to optimizations knobs that alter the distribution of training examples, learning rate, or minibatch size. The baseline practice of independent arrangements places examples into minibatches independently at random. This practice is supported by classic SGD convergence analysis and has the upside of controlling the variance of the stochastic gradients. We make a novel case here for an antithesis of independent arrangements which we term coordinated arrangements. Coordinated arrangements are much more likely to place corresponding associations in the same minibatch. We show that coordination offers different upsides: At the micro level , updates are more effective in pulling vectors of similar entities closer. At a macro level, the examples in small fractions of epochs encode (in expectation) the similarity structure in the full set of example associations whereas independent arrangement disperse that information. This ""self similarity"" of the training sequence effectively allows a single epoch to act as multiple passes.We specify coordinated arrangements through a distribution on randomized subsets of associations which we refer to as microbatches. Basic coordinated microbatches co-place corresponding associations to the maximum extent possible while adhering to the marginal distribution of training examples. Locality Sensitive Hashing (LSH) maps allow for refining our microbatches so that corresponding associations are more likely to be co-placed when the overall similarity of the entities is higher. The LSH maps we apply leverage some available coarse proxy of entity similarity. A readily available first-order proxy is the similarity of the sparse association vectors. Another proxy is an embedding obtained by a weaker model. We present efficient generators of basic and refined microbatches for both LSH functions. Finally, microbatches are independently grouped into minibatches of desired size, which allows us to retain the traditional advantages of independent arrangements at the microbatch level. This design enables us to tune the microbatches to the problem and even the stage of training. We compare the effectiveness of different arrangements through experiments on synthetic stochastic block matrices and on recommendation data sets. The stochastic block data, with its simplicity and symmetry, allows us to factor out the potential effect of other optimizations. We learn that basic coordination is always beneficial earlier in training whereas LSH refinements are more effective later on. We obtain consistent 3%-30% reduction in training with respect to the independent arrangements baseline that holds across other training hyperparameters.The paper is organized as follows. Section 2 presents necessary background on the loss objective we use in our experiments and working with minibatches with one-sided gradient updates. In Section 3 we define LSH microbatches and coordinated minibatch arrangements. In We report our experiment results comparing different arrangement methods on stochastic blocks and on recommendation data sets in Section 4. In Section 5 we examine properties of coordinated arrangements that are helpful for faster convergence. We conclude in Section 6. We consider embedding computations with stochastic gradients and establish that the arrangement of training examples into minibatches can be a powerful performance knob. In particular, we introduced coordinated arrangements as a principled method to accelerate SGD training of embedding vectors. Our experiments focused on the popular SGNS loss and our methods were designed for pairwise associations. In future we hope to explore the use of coordinated arrangement with other loss objectives, deeper networks, and more complex association structures. . We observe that the training gain of coordinated arrangements over the baseline IND increases with minibatch size. The methods that cap the microbatch size by the minibatch size (Jaccard* and Angular*) perform much better with larger minibatches, as larger minibatches allow for a higher recall of helpful co-placements. In particular we can see that in early training on small minibatches (b = 4) these methods are outperformed by COO (which produces our largest (and unrefined) microbatches).0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Training ( We quantify the gains of different methods over the baseline IND arrangements in the following tables. Results for precision at k = 10 are reported in TAB2 for Jaccard LSH MIX, in Table 3 for (pure) Jaccard*, and in TAB6 for angular* LSH MIX(where angular LSH is applied with respect to a d = 3 embedding). Results for cosine gap are reported in Table 5 for Jaccard LSH MIX and in Table 6 for angular* LSH MIX.The tables report results for different minibatch sizes b and block sizes B. In each table we list the peak quality (cosine gap or precision) of the respective coordinated method and the amount of training used by IND to reach 0.75, 0.95, or 0.99 of that peak. We also show the reduction in training 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Training ( that is gained by using the respective coordinated method instead of IND. Overall, we can see that the coordinated methods consistently had training gains of 5-30%. The gain is larger with smaller blocks and also with larger minibatches. The emphasized numbers in the Jaccard MIX and Jaccard* correspond to the method that provided the higher gain. We can see that Jaccard* performed better than Jaccard MIX for larger minibatch sizes.",Metric embeddings are immensely useful representations associations entities images users search queries words Embeddings are learned optimizing loss objective general form sum example associations. Typically optimization uses stochastic gradient updates minibatches examples are arranged independently random. work propose use \em structured arrangements randomized \em microbatches examples are more likely include similar ones. make principled argument properties arrangements accelerate training present efficient algorithms generate microbatches respect marginal distribution training examples. Finally observe experimentally structured arrangements accelerate training 3-20\ %. Structured arrangements emerge powerful novel performance knob SGD is independent complementary SGD hyperparameters thus is a candidate wide deployment. Metric embeddings entities are trained capture example associations are common representations also allow inference associations present data. Embeddings are used complex learning tasks directly applied similarity recommendations tasks. Example usage domains includes embeddings text document occurrences words BID2;BID9;BID7 users videos watch ratings BID15 words co-occurrence frequencies corpus BID16 nodes graph co-occurrence short random walks BID19. example associations may involve entities type word co-occurrences video co-watch social different types users products often are distilled reweighing frequencies raw interactions Salton Buckley 1988 BID7;BID16;BID18.Embeddings are computed minimizing loss objective form sum example associations. optimization starts random initialization followed gradient updates. modern applications objective can have billions terms de facto method scale is stochastic gradient descent SGD Robbins Siegmund 1971 BID14;Salakhutdinovetal. 2007 BID11;BID16. terms examples are randomly grouped minibatches. Gradient updates are equal expectation full gradient are then computed sequentially minibatch. SGD is much efficient working full gradients minibatch size determines amount concurrency. are numerous tunable parameters methods aimed improve quality speed convergence. notable recent work includes per-parameter tuning learning rate BID8 altering distribution training examples gradient magnitude BID1 negatives selection triplet loss Schroffet al. 2015 clustering BID10 diversity criteria BID10.In work introduce principled schemes control arrangement examples minibatches. Note arrangement tuning is separate orthogonal optimizations knobs alter distribution training examples learning rate minibatch size. baseline practice independent arrangements places examples minibatches independently random. practice is supported classic SGD convergence analysis has the upside controlling variance stochastic gradients. make novel case antithesis independent arrangements which we term coordinated arrangements. Coordinated arrangements are much likely place corresponding associations minibatch. show coordination offers different upsides:micro level updates are more effective pulling vectors similar entities closer. macro level examples small fractions epochs encode expectation similarity structure full set example associations whereas independent arrangement disperse information. self similarity training sequence effectively allows single epoch act multiple passes.We specify coordinated arrangements distribution randomized subsets associations which we refer microbatches. Basic coordinated microbatches co-place corresponding associations maximum extent possible adhering marginal distribution training examples. Locality Sensitive Hashing LSH maps allow refining microbatches corresponding associations are more likely co-placed when the overall similarity entities is higher. LSH maps apply leverage available coarse proxy entity similarity. readily available first-order proxy is the similarity sparse association vectors. Another proxy is an embedding obtained weaker model. present efficient generators basic refined microbatches LSH functions. Finally microbatches are independently grouped minibatches desired size which allowsus retain traditional advantages independent arrangements microbatch level. design enablesus tune microbatches problem even stage training. compare effectiveness different arrangements experiments synthetic stochastic block matrices recommendation data sets. stochastic block data simplicity symmetry which allowsus factor potential effect optimizations. learn basic coordination is always beneficial earlier training whereas LSH refinements are more effective later on. obtain consistent 3%-30 reduction training respect independent arrangements baseline holds across training hyperparameters.The paper is organized follows. Section 2 presents necessary background loss objective use experiments working minibatches one-sided gradient updates. Section3 define LSH microbatches coordinated minibatch arrangements. report experiment results comparing different arrangement methods stochastic blocks recommendation data sets Section4. Section5 examine properties coordinated arrangements are helpful faster convergence. conclude Section6. consider embedding computations stochastic gradients establish arrangement training examples minibatches can be a powerful performance knob. particular introduced coordinated arrangements principled method accelerate SGD training embedding vectors. experiments focused popular SGNS loss methods were designed pairwise associations. future hope explore use coordinated arrangement loss objectives deeper networks complex association structures. observe training gain coordinated arrangements baseline IND increases minibatch size. methods cap microbatch size minibatch size Jaccard* Angular* perform much better larger minibatches larger minibatches allow higher recall helpful co-placements particular can see early training small minibatches b 4 methods are outperformed COO which produces largest unrefined microbatches .0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Training quantify gains different methods baseline IND arrangements following tables. Results precision k 10 are reported TAB2 Jaccard LSH MIX Table3 pure Jaccard* TAB6 angular * LSH MIX where angular LSH is applied respect 3 embedding Results cosine gap are reported Table5 Jaccard LSH MIX Table6 angular * LSH MIX.The tables report results different minibatch sizesb block sizesB. table list peak quality cosine gap precision respective coordinated method amount training used IND reach 0.75 0.95 0.99 peak. also show reduction training 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Training is gained using respective coordinated method instead IND. Overall can see coordinated methods consistently had training gains 5-30%. gain is larger smaller blocks also larger minibatches. emphasized numbers Jaccard MIX Jaccard * correspond method provided higher gain. can see Jaccard * performed better Jaccard MIX larger minibatch sizes.,1688,1171,517,0.017,1.442,2025/11/05 17:19:07,0.01,1.292,0.3489096573208719,506.918
"Ubuntu dialogue corpus is the largest public available dialogue corpus to make it feasible to build end-to-end
deep neural network models directly from the conversation data. One challenge of Ubuntu dialogue corpus is 
the large number of out-of-vocabulary words. In this paper we proposed an algorithm which combines the general pre-trained word embedding vectors with those  generated on the task-specific training set to address this issue.   We integrated character embedding into Chen et al's Enhanced LSTM method (ESIM) and used it to evaluate the effectiveness of our proposed method. For the task of next utterance selection, the proposed method has demonstrated a significant performance improvement against original ESIM and the new model has achieved state-of-the-art results on both Ubuntu dialogue corpus and Douban conversation corpus. In addition, we investigated the performance impact of end-of-utterance and end-of-turn token tags. The ability for a machine to converse with human in a natural and coherent manner is one of challenging goals in AI and natural language understanding. One problem in chat-oriented humanmachine dialog system is to reply a message within conversation contexts. Existing methods can be divided into two categories: retrieval-based methods BID31 BID8 BID36 and generation based methods BID28 . The former is to rank a list of candidates and select a good response. For the latter, encoder-decoder framework BID28 or statistical translation method BID19 are usually used to generate a response. It is not easy to main the fluency of the generated texts.Ubuntu dialogue corpus BID13 is the public largest unstructured multi-turns dialogue corpus which consists of about one-million two-person conversations. The size of the corpus makes it attractive for the exploration of deep neural network modeling in the context of dialogue systems. Most deep neural networks use word embedding as the first layer. They either use fixed pre-trained word embedding vectors generated on a large text corpus or learn word embedding for the specific task. The former is lack of flexibility of domain adaptation. The latter requires a very large training corpus and significantly increases model training time. Word out-of-vocabulary issue occurs for both cases. Ubuntu dialogue corpus also contains many technical words (e.g. ""ctrl+alt+f1"", ""/dev/sdb1""). The ubuntu corpus (V2) contains 823057 unique tokens whereas only 22% tokens occur in the pre-built GloVe word vectors 1 . Although character-level representation which models sub-word morphologies can alleviate this problem to some extent BID7 BID3 BID11 , character-level representation still have limitations: learn only morphological and orthographic similarity, other than semantic similarity (e.g. 'car' and 'bmw') and it cannot be applied to Asian languages (e.g. Chinese characters).In this paper, we generate word embedding vectors on the training corpus based on word2vec BID16 . Then we propose an algorithm to combine the generated one with the pre-trained word embedding vectors on a large general text corpus based on vector concatenation. The new word representation maintains information learned from both general text corpus and taskdomain. The nice property of the algorithm is simplicity and little extra computational cost will be added. It can address word out-of-vocabulary issue effectively. This method can be applied to most NLP deep neural network models and is language-independent. We integrated our methods with ESIM(baseline model) . The experimental results have shown that the proposed method has significantly improved the performance of original ESIM model and obtained state-ofthe-art results on both Ubuntu Dialogue Corpus and Douban Conversation Corpus BID34 . On Ubuntu Dialogue Corpus (V2), the improvement to the previous best baseline model (single) on R 10 @1 is 3.8% and our ensemble model on R 10 @1 is 75.9%. On Douban Conversation Corpus, the improvement to the previous best model (single) on P @1 is 3.6%.Our contributions in this paper are summarized below:1. We propose an algorithm to combine pre-trained word embedding vectors with those generated on the training corpus to address out-of-vocabulary word issues and experimental results have shown that it is very effective.2. ESIM with our method has achieved the state-of-the-art results on both Ubuntu Dialogue corpus and Douban conversation corpus.3. We investigate performance impact of two special tags on Ubuntu Dialogue Corpus: endof-utterance and end-of-turn.The rest paper is organized as follows. In Section 2, we review the related work. In Section 3 we provide an overview of ESIM (baseline) model and describe our methods to address out-ofvocabulary issues. In Section 4, we conduct extensive experiments to show the effectiveness of the proposed method. Finally we conclude with remarks and summarize our findings and outline future research directions. We propose an algorithm to combine pre-trained word embedding vectors with those generated on training set as new word representation to address out-of-vocabulary word issues. The experimental results have shown that the proposed method is effective to solve out-of-vocabulary issue and improves the performance of ESIM, achieving the state-of-the-art results on Ubuntu Dialogue Corpus and Douban conversation corpus. In addition, we investigate the performance impact of two special tags: end-of-utterance and end-of-turn. In the future, we may design a better neural architecture to leverage utterance structure in multi-turn conversations.",Ubuntu dialogue corpus is the largest public available dialogue corpus make feasible build end-to-end deep neural network models directly conversation data. One challenge Ubuntu dialogue corpus is the large number out-of-vocabulary words. paper proposed algorithm which combines general pre-trained word embedding vectors generated task-specific training set address issue. integrated character embedding Chen et al's Enhanced LSTM method ESIM used evaluate effectiveness proposed method. task next utterance selection proposed method has demonstrated significant performance improvement original ESIM new model has achieved state-of-the-art results Ubuntu dialogue corpus Douban conversation corpus. addition investigated performance impact end-of-utterance end-of-turn token tags. ability machine converse human natural coherent manner is one challenging goals AI natural language understanding. One problem chat-oriented humanmachine dialog system is to reply message within conversation contexts. Existing methods can be divided two categories:retrieval-based methods BID31 BID8 BID36 generation based methods BID28. former is to rank list candidates select good response. latter encoder-decoder framework BID28 statistical translation method BID19 are usually used generate response. is not easy main fluency generated texts.Ubuntu dialogue corpus BID13 is the public largest unstructured multi-turns dialogue corpus which consists one-million two-person conversations. size corpus makes attractive exploration deep neural network modeling context dialogue systems. deep neural networks use word embedding first layer. either use fixed pre-trained word embedding vectors generated large text corpus learn word embedding specific task. former is lack flexibility domain adaptation. latter requires large training corpus significantly increases model training time. Word out-of-vocabulary issue occurs cases. Ubuntu dialogue corpus also contains many technical words e.g ctrl+alt+f1/dev/sdb1 ubuntu corpus V2 contains 823057 unique tokens whereas 22% tokens occur pre-built GloVe word vectors 1. Although character-level representation which models sub-word morphologies can alleviate problem extent BID7 BID3 BID11 character-level representation still have limitations:learn morphological orthographic similarity semantic similarity e.g 'car' 'bmw' cannot applied Asian languages e.g Chinese characters.In paper generate word embedding vectors training corpus based word2vec BID16. propose algorithm combine generated one pre-trained word embedding vectors large general text corpus based vector concatenation. new word representation maintains information learned general text corpus taskdomain. nice property algorithm is simplicity little extra computational cost will be added. can address word out-of-vocabulary issue effectively. method can be applied NLP deep neural network models is language-independent language-independent integrated methods ESIM baseline model experimental results have shown proposed method has significantly improved performance original ESIM model obtained state-ofthe-art results Ubuntu Dialogue Corpus Douban Conversation Corpus BID34. Ubuntu Dialogue Corpus V2 improvement previous best baseline model single R10@1 is 3.8 3.8 ensemble model R10@1 is 75.9%. Douban Conversation Corpus improvement previous best model single P@1 is 3.6%.Our contributions paper are summarized summarized below:1 propose algorithm combine pre-trained word embedding vectors generated training corpus address out-of-vocabulary word issues experimental results have shown is very effective.2 ESIM method has achieved state-of-the-art results Ubuntu Dialogue corpus Douban conversation corpus.3 investigate performance impact two special tags Ubuntu Dialogue Corpus:endof-utterance end-of-turn.The rest paper is organized follows. Section2 review related work. Section3 provide overview ESIM baseline model describe methods address out-ofvocabulary issues. Section4 conduct extensive experiments show effectiveness proposed method. Finally conclude remarks summarize findings outline future research directions. propose algorithm combine pre-trained word embedding vectors generated training set new word representation address out-of-vocabulary word issues. experimental results have shown proposed method is effective solve out-of-vocabulary issue improves performance ESIM achieving state-of-the-art results Ubuntu Dialogue Corpus Douban conversation corpus. addition investigate performance impact two special tags:end-of-utterance end-of-turn future may design better neural architecture leverage utterance structure multi-turn conversations.,1078,785,293,0.009,1.373,2025/11/05 17:19:07,0.0,1.419,0.1339563862928346,314.163
"Deep learning has shown that learned functions can dramatically outperform hand-designed functions on perceptual tasks. Analogously, this suggests that learned update functions may similarly outperform current hand-designed optimizers, especially for specific tasks. However, learned optimizers are notoriously difficult to train and have yet to demonstrate wall-clock speedups over hand-designed optimizers, and thus are rarely used in practice. Typically, learned optimizers are trained by truncated backpropagation through an unrolled optimization process. The resulting gradients are either strongly biased (for short truncations) or have exploding norm (for long truncations). In this work we propose a training scheme which overcomes both of these difficulties, by dynamically weighting two unbiased gradient estimators for a variational loss on optimizer performance. This allows us to train neural networks to perform optimization faster than well tuned first-order methods. Moreover, by training the optimizer against validation loss, as opposed to training loss, we are able to use it to train models which generalize better than those trained by first order methods. We demonstrate these results on problems where our learned optimizer trains convolutional networks in a fifth of the wall-clock time compared to tuned first-order methods, and with an improvement Gradient based optimization is a cornerstone of modern machine learning. Improvements in optimization have been critical to recent successes on a wide variety of problems. In practice, this typically involves analysis and development of hand-designed optimization algorithms BID22 BID7 BID34 BID15 . These algorithms generally work well on a wide variety of tasks, and are tuned to specific problems via hyperparameter search. On the other hand, a complementary approach is to learn the optimization algorithm BID5 BID30 BID13 BID0 BID36 BID19 BID2 . That is, to learn a function to perform optimization, targeted to particular problems of interest. In this way, the algorithm may learn task specific structure, enabling dramatic performance improvements over more general optimizers.However, training learned optimizers is notoriously difficult. Existing work in this vein can be classified into two broad categories. On one hand are black-box methods such as evolution BID11 BID3 , random search BID6 , reinforcement learning BID2 BID18 BID40 , or Bayesian optimization BID31 . However, these methods scale poorly with the number of optimizer parameters. The other approach is to use first-order methods, by computing the gradient of some measure of optimizer effectiveness with respect to the optimizer parameters. Computing these gradients is costly as we need to iteratively apply the learned update rule, and then backpropagate through these applications, a technique commonly referred to as ""unrolled optimization"" BID4 BID21 . To address the problem of backpropagation through many optimization steps (analogous to many timesteps in recurrent neural networks), many works make use of truncated backpropagation though time (TBPTT) to partition the long unrolled computational graph into separate pieces BID35 BID33 . This yields computational savings, but at the cost of increased bias BID33 and/or exploding gradients due to many iterated update steps BID26 BID25 . Existing methods address the bias at the cost of increased variance or computa-tional complexity BID38 BID24 BID33 . Previous techniques for training RNNs via TBPTT have thus far not been effective for training optimizers.In this paper, we analytically and experimentally explore the debilitating role of bias and exploding gradients on training optimizers ( §2.3). We then show how these pathologies can be remedied by optimizing the parameters of a distribution over the optimizer parameters, known as variational optimization BID32 ) ( §3). We define two unbiased gradient estimators for this objective: a reparameterization based gradient, and evolutionary strategies BID27 BID23 . By dynamically reweighting the contribution of these two gradient estimators, we are able to avoid strongly biased or exploding gradients, and thus stably and efficiently train learned optimizers.We demonstrate the utility of this approach by training a learned optimizer to target optimization of convolutional networks on image classification ( §4). On the targeted task distribution, this learned optimizer achieves better validation loss, and is five times faster in wall-clock time, compared to well tuned hand-designed optimizers such as SGD+Momentum, RMSProp, and ADAM ( FIG0 ). While not the explicit focus of this work, we also find that the learned optimizer demonstrates promising generalization ability on out of distribution tasks ( Figure 6 ). Training and validation curves for a three layer CNN, trained on a subset of 32x32 imagenet classes not seen during outer-training of the optimizer. Dashed lines indicate the best achieved performance over an additional 130 seconds. We show two learned optimizers -one trained to minimize training loss, and the other trained to minimize validation loss on the inner-problem. We compare against Adam, RMSProp, and SGD+Momentum, individually tuned for the train and validation loss (Panel (a) and (b), respectively). On training loss (a), our learned optimizer approaches zero training loss, and achieves it's smallest loss values in less than one quarter the wall-clock time.On validation loss (b), our learned optimizer achieves a lower minimum, in roughly one third the wall-clock time. Shaded regions correspond to 25 and 75 percentile over five random initializations of the CNN. For plots showing performance in terms of step count rather than wall clock (where we achieve even more dramatic speedups), and for more task instances, see Appendix D. (c) Distribution of the performance difference between the learned optimizers and a tuned baseline of either Adam, RMSProp, or Momentum (loss improvement). Positive values indicate performance better than baseline. We show training and validation losses for the outer-testing task distribution. On the majority of tasks, the learned optimizers outperform the baseline. In this work we demonstrate two difficulties when training learned optimizers: ""exploding"" gradients, and a bias introduced by truncated backpropagation through time. To combat this, we construct a variational bound of the outer-objective and minimize this via a combination of reparameterization and ES style gradient estimators. By using our combined estimator and a curriculum over truncation step we are able to train learned optimizers that achieve more than five times speedup on wallclock time as compared to existing optimizers.In this work, we focused on applying optimizers to a restricted family of tasks. While useful on its own right (e.g. rapid retraining of models on new data), future work will explore the limits of ""no free lunch"" BID39 to understand how and when learned optimizers generalize across tasks. We are also interested in using these methods to better understand what problem structure our learned optimizers exploit. By analyzing the trained optimizer, we hope to develop insights that may transfer back to hand-designed optimizers. Outside of meta-learning, we believe the gradient estimator presented here can be used to train other long time dependence recurrent problems such as neural turning machines BID12 , or neural GPUs BID14 .Much in the same way deep learning has replaced feature design for perceptual tasks, we see metalearning as a tool capable of learning new and interesting algorithms, especially for domains with unexploited problem-specific structure. With better outer-training stability, we hope to improve our ability to learn interesting algorithms, both for optimizers and beyond.","Deep learning has shown learned functions can dramatically outperform hand-designed functions perceptual tasks. Analogously suggests learned update functions may similarly outperform current hand-designed optimizers especially specific tasks. However learned optimizers are notoriously difficult train have yet demonstrate wall-clock speedups hand-designed optimizers thus are rarely used practice. Typically learned optimizers are trained truncated backpropagation unrolled optimization process. resulting gradients are either strongly biased short truncations have exploding norm long truncations work propose training scheme which overcomes difficulties dynamically weighting two unbiased gradient estimators variational loss optimizer performance. allowsus train neural networks perform optimization faster well tuned first-order methods. Moreover training optimizer validation loss opposed training loss are able use train models which generalize better trained first order methods. demonstrate results problems where our learned optimizer trains convolutional networks fifth wall-clock time compared tuned first-order methods improvement Gradient based optimization is a cornerstone modern machine learning. Improvements optimization have been critical recent successes wide variety problems. practice typically involves analysis development hand-designed optimization algorithms BID22 BID7 BID34 BID15. algorithms generally work well wide variety tasks are tuned specific problems via hyperparameter search. hand complementary approach is to learn optimization algorithm BID5 BID30 BID13 BID0 BID36 BID19 BID2. is,to learn function perform optimization targeted particular problems interest. way algorithm may learn task specific structure enabling dramatic performance improvements general optimizers.However training learned optimizers is notoriously difficult. Existing work vein can be classified two broad categories. one hand are black-box methods evolution BID11 BID3 random search BID6 reinforcement learning BID2 BID18 BID40 Bayesian optimization BID31. However methods scale poorly number optimizer parameters. approach is to use first-order methods computing gradient measure optimizer effectiveness respect optimizer parameters. Computing gradients is costly need iteratively apply learned update rule backpropagate applications technique commonly referred unrolled optimization BID4 BID21. address problem backpropagation many optimization steps analogous many timesteps recurrent neural networks many works make use truncated backpropagation though time TBPTT partition long unrolled computational graph separate pieces BID35 BID33. yields computational savings cost increased bias BID33/exploding gradients due many iterated update steps BID26 BID25. Existing methods address bias cost increased variance computa-tional complexity BID38 BID24 BID33. Previous techniques training RNNs via TBPTT have thus far effective training optimizers.In paper analytically experimentally explore debilitating role bias exploding gradients training optimizers §2.3 show how these pathologies can be remedied optimizing parameters distribution optimizer parameters known variational optimization BID32 §3 define two unbiased gradient estimators objective:reparameterization based gradient evolutionary strategies BID27 BID23. dynamically reweighting contribution two gradient estimators are able avoid strongly biased exploding gradients thus stably efficiently train learned optimizers.We demonstrate utility approach training learned optimizer target optimization convolutional networks image classification §4 targeted task distribution learned optimizer achieves better validation loss is five times faster wall-clock time compared well tuned hand-designed optimizers SGD+Momentum RMSProp ADAM FIG0 explicit focus work also find learned optimizer demonstrates promising generalization ability distribution tasks Figure6 Training validation curves three layer CNN trained subset 32x32 imagenet classes seen outer-training optimizer. Dashed lines indicate best achieved performance additional 130 seconds. show two learned optimizers -one trained minimize training loss trained minimize validation loss inner-problem compare Adam RMSProp SGD+Momentum individually tuned train validation loss Panel b respectively training loss learned optimizer approaches zero training loss achieves smallest loss values less one quarter wall-clock time.On validation loss b learned optimizer achieves lower minimum roughly one third wall-clock time. Shaded regions correspond 25 75 percentile five random initializations CNN. plots showing performance terms step count rather wall clock where we achieve even dramatic speedups task instances see Appendix D. c Distribution performance difference learned optimizers tuned baseline either Adam RMSProp Momentum loss improvement Positive values indicate performance better baseline. show training validation losses outer-testing task distribution. majority tasks learned optimizers outperform baseline. work demonstrate two difficulties when training learned optimizers:exploding gradients bias introduced truncated backpropagation time. combat construct variational bound outer-objective minimize via combination reparameterization ES style gradient estimators. using combined estimator curriculum truncation step are able train learned optimizers achieve five times speedup wallclock time compared existing optimizers.In work focused applying optimizers restricted family tasks. useful right e.g rapid retraining models new data future work will explore limits free lunch BID39 understand how and when learned optimizers generalize across tasks. are also interested using methods better understand what problem structure learned optimizers exploit. analyzing trained optimizer hope develop insights may transfer back hand-designed optimizers. Outside meta-learning believe gradient estimator presented can be used train long time dependence recurrent problems neural turning machines BID12 neural GPUs BID14.Much way deep learning has replaced feature design perceptual tasks see metalearning tool capable learning new interesting algorithms especially domains unexploited problem-specific structure. better outer-training stability hope improve ability learn interesting algorithms optimizers beyond.",1465,999,466,0.015,1.466,2025/11/05 17:19:07,0.01,1.4,0.4236760124610589,448.188
"Asynchronous distributed gradient descent algorithms for training of deep neural
 networks are usually considered as inefficient, mainly because of the Gradient delay
 problem. In this paper, we propose a novel asynchronous distributed algorithm
 that tackles this limitation by well-thought-out averaging of model updates, computed
 by workers. The algorithm allows computing gradients along the process
 of gradient merge, thus, reducing or even completely eliminating worker idle time
 due to communication overhead, which is a pitfall of existing asynchronous methods.
 We provide theoretical analysis of the proposed asynchronous algorithm,
 and show its regret bounds. According to our analysis, the crucial parameter for
 keeping high convergence rate is the maximal discrepancy between local parameter
 vectors of any pair of workers. As long as it is kept relatively small, the
 convergence rate of the algorithm is shown to be the same as the one of a sequential
 online learning. Furthermore, in our algorithm, this discrepancy is bounded
 by an expression that involves the staleness parameter of the algorithm, and is
 independent on the number of workers. This is the main differentiator between
 our approach and other solutions, such as Elastic Asynchronous SGD or Downpour
 SGD, in which that maximal discrepancy is bounded by an expression that
 depends on the number of workers, due to gradient delay problem. To demonstrate
 effectiveness of our approach, we conduct a series of experiments on image
 classification task on a cluster with 4 machines, equipped with a commodity communication
 switch and with a single GPU card per machine. Our experiments
 show a linear scaling on 4-machine cluster without sacrificing the test accuracy,
 while eliminating almost completely worker idle time. Since our method allows
 using commodity communication switch, it paves a way for large scale distributed
 training performed on commodity clusters. Distributed training of deep learning models is devised to reduce training time of the models. Synchronous distributed SGD methods, such as BID0 and BID7 , perform training using mini-batch size of several dozens of thousands of images. However, they either require expensive communication switch for fast gradient sharing between workers or, otherwise, introduce a high communication overhead during gradient merge, where workers are idle waiting for communicating gradients over communication switch.Distributed asynchronous SGD methods reduce the communication overhead on one hand, but usually introduce gradient delay problem on the other hand, as described in BID0 . Indeed, usually in an asynchronous distributed approach, a worker w obtains a copy of the central model, computes a gradient on this model and merges this gradient back into the central model. Note, however, that since the worker obtained the copy of the central model till it merges its gradient back into the central model, other workers could have merged their gradients into the central model. Thus, when the worker w merges its gradient into a central model, that model may have been updated and, thus, the gradient of the worker w is delayed, leading to gradient delay problem. We will refer to algorithms that suffer from gradient delay problem as gradient delay algorithms, e.g. Downpour SGD BID1 .As our analysis reveals in Section 3, the quantity that controls the convergence rate of an asynchronous distributed algorithm, is maximal pairwise distance -the maximal distance between local models of any pair of workers at any iteration. Usually gradient delay algorithms do not limit this distance and it may depend on the number of asynchronous workers, which may be large in large clusters. This may explain their poor scalability, convergence rate and struggle to reach as high test accuracy as in synchronous SGD algorithms, as experimentally shown in BID0 .While Elastic Averaging SGD Zhang et al. (2015) is also a gradient delay algorithm, it introduces a penalty for workers, whose models diverge too far from the central model. This, in turn , helps to reduce the maximal pairwise distance between local models of workers and, thus, leads to better scalability and convergence rate. In contrast, our analysis introduces staleness parameter that directly controls the maximal pair distance of the asynchronous workers.Our analysis builds on the work of BID10 , who studied convergence rate of gradient delay algorithms, when the maximum delay is bounded. They provided analysis for Lipschitz continuous losses, strongly convex and smooth losses. While they show that bounding staleness can improve convergence rate of a gradient delay algorithm, in their algorithm each worker computes exactly one gradient and is idle, waiting to merge the gradient with PS model and download the updated PS model back to the worker.The main contributions of this paper are the following. We present and analyze a new asynchronous distributed SGD method that both reduces idle time and eliminates gradient delay problem. Our main theoretic result shows that an asynchronous distributed SGD algorithm can achieve convergence rate as good as in sequential online learning. We support this theoretic result by conducting experiments that show that on a cluster with up to 4 machines, with a single GPU per machine and a commodity communication switch, our asynchronous method achieves linear scalability without degradation of the test accuracy. We presented a new asynchronous distributed SGD method. We show empirically that it reduces both idle time and gradient delay. We analyze the synchronous part of the algorithm, and show theoretical regret bounds.The proposed method shows promising results on distributed training of deep neural networks. We show that our method eliminates waiting times, which allows significant improvements in run time, compared to fully synchronous setup. The very fact of efficient hiding of communication overhead opens opportunity for distributed training over commodity clusters. Furthermore, the experiments show linear scaling of training time from 1 to 4 GPU's without compromising the final test accuracy.Proof. We start with RHS of (8) DISPLAYFORM0 By the definition of average parameter vector (1), the first summand in RHS of (29) equals x iβ+t , while the last two summands cancel each other.Proof of Lemma 3.3.Proof. At iteration (i − 1)β after reset operation FORMULA7 , workers w and w start updating their local parameter vectors for β iterations, so that at the end of the cycle before the reset operation (7), DISPLAYFORM1 The reset operation FORMULA7 at iteration iβ adds the updates of workers w and w , computed at iterations (i − 1)β + 1, . . . , iβ, to the common copy of PS model, so that x (i−1)β,w − x (i−1)β,w = 0. Thus, after the reset operation DISPLAYFORM2 Finally, from (31), our assumption on the size of the gradient ∇f t (x) and from decreasing learning rate, during this cycle that started at iteration (i − 1)β, the distance between workers w and w grows at most by DISPLAYFORM3 Proof of Lemma 3.4.Proof. We decompose our progress as follows DISPLAYFORM4 To prove (33) from (32), we used (12) Dividing both sides by η iτ +t and moving < x iτ +t − x * ,g iτ +t > to the LHS completes the proof.Proof of Theorem 3.5.Proof. First we state a useful inequality: For n vectors a i , i = 1, . . . , n (by induction on n): DISPLAYFORM5 Also we will use the following sum bounds: DISPLAYFORM6 and DISPLAYFORM7 We start with summing (13) along iterations: DISPLAYFORM8 Next, we borrow the derivation of expressions (38) and (39) from the proof of Theorem 2, BID9 . Note, however, that we added a new term to (37) -the last term that is specific to Algorithm 2. This term does not appear in the proof of Theorem 2, BID9 . By the Lipschitz property of gradients and the definition of η t , we can bound the first summand of the above regret expression via DISPLAYFORM9 Also DISPLAYFORM10 We omit the negative factor − DISPLAYFORM11 . Now we start the analysis of the last term in (37), which is new and specific to Algorithm 2. Using (34), we bound the last summand of (37) DISPLAYFORM12 Substituting FORMULA3 , FORMULA3 and FORMULA4 into FORMULA3 , we get DISPLAYFORM13 We use (14) in the above expression DISPLAYFORM14 Now, note that the last summand in (50) corresponds to the summand in (18) for k = j − 1. This completes the proof.Proof of Lemma 3.7.Proof. First note that from (19) it follows that η t βH ≤ 0.1 .Since η i shrinks down, as i grows up, and η t H + 1 > 1, (18) yields ||x iβ+j,w − x iβ+j,w || ≤ (η iβ H + 1) β · ||x iβ,w − x iβ,w || + η iβ β−1 k=0 ||e iβ+k,w − e iβ+k,w || .After the expansion of (η iβ H + 1) β in (52) into Taylor sequence and applying a simple algebra DISPLAYFORM15 From FORMULA1 we can bound DISPLAYFORM16 Assigning FORMULA4 into FORMULA2 , ||x iβ+j,w − x iβ+j,w || ≤ 1.2 · ||x iβ,w − x iβ,w || + 1.2 · η iβ β−1 k=0 ||e iβ+k,w − e iβ+k,w || .Since e iτ +k,w and e iτ +k,w are i.i.d. with mean 0, E||e iβ+k,w − e iβ+k,w || = var(e iβ+k,w − e iβ+k,w ) = 2var(e iβ+k,w ) .Taking expectation of the both sides of (55), substituting (56) into the resulting inequality and using the assumption on variance of random variables e t,w , we complete the proof.Proof of Lemma 3.8.Proof. From Lemma 3.3, ||x i0β,w − x i0β,w || ≤ 2Lτ η (i0−1)β .From FORMULA2 , each cycle j after iteration i 0 β, reduces the distance between w and w by factor of 0.2, while adding to the distance the value of 1.2 · η iβ+j τ s. This means that after the number of cycles j 0 j 0 = log 1.2 · η i0β τ s 2Lτ η (i0−1)β = log s L , for any i ≥ i 0 + j 0 , the first summand in (22) gets bounded by 0.8 · η iβ τ s.Proof of Theorem 3.9.Proof. To prove this theorem , we follow the proof of Theorem 3.5 and develop an alternative bound on ||x t,w − x t || in (42).We will split the sum in (40) into two ranges of t: t < t 0 + j 0 β and t ≥ t 0 + j 0 β for t 0 , j 0 , defined in FORMULA1 and FORMULA2 respectively. To simplify notation, from (23), we can assume that j 0 is a constant and we can assume that t 0 + j 0 ≤ 2t 0 . For t < 2t 0 , we use (48) to show 2t0−1 t=1 ||x t − x * || · ||g t −g t || ≤ 2τ F LH(2τ + 2σ DISPLAYFORM17 For t ≥ 2t 0 , we first observe DISPLAYFORM18 Next we use (24) to bound the above expression.E||x t,w − x t || ≤ 2η t−τ τ s .Substituting this bound into (42), we get E||g t −g t || ≤ 2Hη t−τ τ s .Using FORMULA1 Combining FORMULA5 and FORMULA2 in FORMULA4 and using the definition (19) of t 0 DISPLAYFORM19 Using the assumption (25), and substituting into (41) we prove (26). Finally we use value σ = F L to prove (27).",Asynchronous distributed gradient descent algorithms training deep neural networks are usually considered inefficient mainly Gradient delay problem. paper propose novel asynchronous distributed algorithm tackles limitation well-thought-out averaging model updates computed workers. algorithm allows computing gradients along process gradient merge thus reducing even completely eliminating worker idle time due communication overhead which is a pitfall existing asynchronous methods. provide theoretical analysis proposed asynchronous algorithm show regret bounds. According analysis crucial parameter keeping high convergence rate is the maximal discrepancy local parameter vectors pair workers. long is kept relatively small convergence rate algorithm is shown one sequential online learning. Furthermore algorithm discrepancy is bounded expression involves staleness parameter algorithm is independent number workers. is the main differentiator approach solutions Elastic Asynchronous SGD Downpour SGD which that is maximal discrepancy is bounded expression depends number workers due gradient delay problem. demonstrate effectiveness approach conduct series experiments image classification task cluster 4 machines equipped commodity communication switch single GPU card per machine. experiments show linear scaling 4-machine cluster without sacrificing test accuracy eliminating almost completely worker idle time. Since method allows using commodity communication switch paves way large scale distributed training performed commodity clusters. Distributed training deep learning models is devised reduce training time models. Synchronous distributed SGD methods BID0 BID7 perform training using mini-batch size several dozens thousands images. However either require expensive communication switch fast gradient sharing workers otherwise introduce high communication overhead gradient merge where workers are idle waiting communicating gradients communication switch.Distributed asynchronous SGD methods reduce communication overhead one hand usually introduce gradient delay problem hand described BID0. Indeed usually asynchronous distributed approach when the worker w obtains copy central model computes gradient model merges gradient back central model. Note however since worker obtained copy central model till merges gradient back central model where workers could have merged gradients central model. Thus when the worker w merges gradient central model model may have been updated thus gradient workerw is delayed leading gradient delay problem. will refer algorithms suffer gradient delay problem gradient delay algorithms e.g Downpour SGD BID1.As analysis reveals Section3 quantity controls convergence rate asynchronous distributed algorithm which that is maximal pairwise distance -the maximal distance local models pair workers iteration. Usually gradient delay algorithms do not limit distance may depend number asynchronous workers may large large clusters. may explain poor scalability convergence rate struggle reach high test accuracy synchronous SGD algorithms experimentally shown BID0.While Elastic Averaging SGD Zhangetal. 2015 is also gradient delay algorithm introduces penalty workers whose models diverge far central model. turn helps reduce maximal pairwise distance local models workers thus leads better scalability convergence rate. contrast analysis introduces staleness parameter directly controls maximal pair distance asynchronous workers.Our analysis builds work BID10 who studied convergence rate gradient delay algorithms when the maximum delay is bounded. provided analysis Lipschitz continuous losses strongly convex smooth losses. show bounding staleness can improve convergence rate gradient delay algorithm algorithm worker computes exactly one gradient is idle waiting merge gradient PS model download updated PS model back worker.The main contributions paper are the following. present analyze new asynchronous distributed SGD method reduces idle time eliminates gradient delay problem. main theoretic result shows asynchronous distributed SGD algorithm can achieve convergence rate good sequential online learning. support theoretic result conducting experiments show cluster 4 machines single GPU per machine commodity communication switch asynchronous method achieves linear scalability without degradation test accuracy. presented new asynchronous distributed SGD method. show empirically reduces idle time gradient delay. analyze synchronous part algorithm show theoretical regret bounds.The proposed method shows promising results distributed training deep neural networks. show method eliminates waiting times which allows significant improvements run time compared fully synchronous setup. fact efficient hiding communication overhead opens opportunity distributed training commodity clusters. Furthermore experiments show linear scaling training time 1 4 GPU's without compromising final test accuracy.Proof. start RHS 8 DISPLAYFORM0 definition average parameter vector 1 first summand RHS 29 equalsxiβ+last two summands cancel other.Proof Lemma3. 3.Proof. iteration −1 β reset operation FORMULA7 where workersw w start updating local parameter vectors β iterations end cycle reset operation 7 DISPLAYFORM1 reset operation FORMULA7 iteration iβ adds updates workersw w computed iterations −1 β+1 iβ common copy PS model x i−1 β w−x i−1 β w 0. Thus reset operation DISPLAYFORM2 Finally 31 assumption size gradient∇f x decreasing learning rate cycle started iteration −1 β distance workersw w grows DISPLAYFORM3 Proof Lemma3. 4.Proof. decompose progress follows DISPLAYFORM4 prove 33 32 used 12 Dividing sides ηiτ+moving xiτ+−x* giτ+LHS completes proof.Proof Theorem3. 5.Proof. First state useful inequality:n vectors 1 n induction n DISPLAYFORM5 Also will use following sum bounds:DISPLAYFORM6 DISPLAYFORM7 start summing 13 along iterations:DISPLAYFORM8 Next borrow derivation expressions 38 39 proof Theorem2 BID9. Note however added new term 37 -the last term is specific Algorithm2. term does not appear proof Theorem2 BID9. Lipschitz property gradients definition η can bound first summand regret expression via DISPLAYFORM9 Also DISPLAYFORM10 omit negative factor − DISPLAYFORM11. start analysis last term 37 which is new specific Algorithm2. Using 34 bound last summand 37 DISPLAYFORM12 Substituting FORMULA3 FORMULA3 FORMULA4 FORMULA3 get DISPLAYFORM13 use 14 expression DISPLAYFORM14 note last summand 50 corresponds summand 18 k j−1. completes proof.Proof Lemma3. 7.Proof. First note 19 follows η βH ≤ 0.1.Since η shrinks grows η H+1 1 18 yields ||xiβ+j w−xiβ+j w||≤ ηiβH+1 β · ||xiβ w−xiβ w||+η iβ β−1 k=0 ||e iβ+k w−eiβ+k w || .After expansion ηiβH+1 β 52 Taylor sequence applying simple algebra DISPLAYFORM15 FORMULA1 can bound DISPLAYFORM16 Assigning FORMULA4 FORMULA2 ||xiβ+j w−xiβ+j w || ≤ 1.2 · ||xiβ w−xiβ w ||+1.2 · η iβ β−1 k=0 ||eiβ+k w−eiβ+k w || .Sincee iτ+k w eiτ+k w arei.i.i.d mean0 E||eiβ+k w−eiβ+k w|| var eiβ+k w−eiβ+k w 2var eiβ+k w.Taking expectation sides 55 substituting 56 resulting inequality using assumption variance random variablese w complete proof.Proof Lemma3. 8.Proof. Lemma 3.3 ||x i0β w − x i0β w || ≤ 2Lτ η i0−1 β.From FORMULA2 cyclej iteration 0β reduces distance w w factor 0.2 adding distance value 1.2·ηiβ+jτ s. means number cyclesj0j 0 log 1.2·η i0βτ 2Lτη i0−1 β log L ≥ 0+j0 first summand 22 gets bounded 0.8·ηiβ τ s.Proof Theorem3. 9.Proof. prove theorem follow proof Theorem 3.5 develop alternative bound ||x w−x || 42.We will split sum 40 two ranges t:0+j0 β ≥ 0+j0 β 0 j0 defined FORMULA1 FORMULA2 respectively. simplify notation 23 can assume j0 is a constant can assume 0+j0 ≤2t0. 2t0 use 48 show 2t0−1 t=1 ||x −x*|| · ||g −g ||≤2τF LH 2τ+2σ DISPLAYFORM17 ≥2t0 first observe DISPLAYFORM18 Next will use 24 bound expression.E||x w−x || ≤ 2η t−τ τ.Substituting bound 42 get E||g −g || ≤ 2Hη t−τ τ.Using FORMULA1 Combining FORMULA5 FORMULA2 FORMULA4 using definition 19 0 DISPLAYFORM19 Using assumption 25 substituting 41 prove 26 Finally will use valueσ FL prove 27,2551,1702,849,0.044,1.499,2025/11/05 17:19:07,0.01,1.395,0.5264797507788164,810.05
"Neural network quantization is becoming an industry standard to efficiently deploy deep learning models on hardware platforms, such as CPU, GPU, TPU, and FPGAs. However, we observe that the conventional quantization approaches are vulnerable to adversarial attacks. This paper aims to raise people's awareness about the security of the quantized models, and we designed a novel quantization methodology to jointly optimize the efficiency and robustness of deep learning models. We first conduct an empirical study to show that vanilla quantization suffers more from adversarial attacks. We observe that the inferior robustness comes from the error amplification effect, where the quantization operation further enlarges the distance caused by amplified noise. Then we propose a novel Defensive Quantization (DQ) method by controlling the Lipschitz constant of the network during quantization, such that the magnitude of the adversarial noise remains non-expansive during inference. Extensive experiments on CIFAR-10 and SVHN datasets demonstrate that our new quantization method can defend neural networks against adversarial examples, and even achieves superior robustness than their full-precision counterparts, while maintaining the same hardware efficiency as vanilla quantization approaches. As a by-product, DQ can also improve the accuracy of quantized models without adversarial attack. Neural network quantization BID10 BID34 BID12 ) is a widely used technique to reduce the computation and memory costs of neural networks, facilitating efficient deployment. It has become an industry standard for deep learning hardware. However, we find that the widely used vanilla quantization approaches suffer from unexpected issues -the quantized model is more vulnerable to adversarial attacks ( FIG1 ). Adversarial attack is consist of subtle perturbations on the input images that causes the deep learning models to give incorrect labels BID28 . Such perturbations are hardly detectable by human eyes but can easily fool neural networks. Since quantized neural networks are widely deployed in many safety-critical scenarios, e.g., autonomous driving BID1 , the potential security risks cannot be neglected. The efficiency and latency in such applications are also important, so we need to jointly optimize them.The fact that quantization leads to inferior adversarial robustness is counter intuitive, as small perturbations should be denoised with low-bit representations. Recent work BID31 ) also demonstrates that quantization on input image space , i.e. color bit depth reduction, is quite effective to defend adversarial examples. A natural question then rises, why the quantization operator is yet effective when applied to intermediate DNN layers ? We analyze that such issue is caused by the error amplification effect of adversarial perturbation BID15 -although the magnitude of perturbation on the image is small, it is amplified significantly when passing through deep neural network (see FIG4 . The deeper the layers are, the more significant such side effect is. Such amplification pushes values into a different quantization bucket, which is undesirable. We conducted empirical experiments to analyze how quantization influences the activation error between clean and adversarial samples FIG4 ): when the magnitude of the noise is small, activation quantization is capable of reducing the errors by eliminating small perturbations; However, when the magnitude of perturbation is larger than certain threshold, quantization instead amplify the errors, which causes the quantized model to make mistakes. We argue that this is the main reason causing the inferior robustness of the quantized models.In this paper, we propose Defensive Quantization (DQ) that not only fixes the robustness issue of quantized models, but also turns activation quantization into a defense method that further boosts adversarial robustness. We are inspired by the success of image quantization in improving robustness. Intuitively, it will be possible to defend the attacks with quantization operations if we can keep the magnitude of the perturbation small. However, due to the error amplification effect of gradient based adversarial samples, it is non-trivial to keep the noise at a small scale during inference. Recent works BID5 BID21 have attempted to make the network non-expansive by controlling the Lipschitz constant of the network to be smaller than 1, which has smaller variation change in its output than its input. In such case, the input noise will not propagate through the intermediate layers and impact the output, but attenuated. Our method is built on the theory. Defensive quantization not only quantizes feature maps into low-bit representations, but also controls the Lipschitz constant of the network, such that the noise is kept within a small magnitude for all hidden layers. In such case, we keep the noise small, as in the left zone of FIG4 , quantization can reduce the perturbation error. The produced model with our method enjoys better security and efficiency at the same time.Experiments show that Defensive Quantization (DQ) offers three unique advantages. First, DQ provides an effective way to boost the robustness of deep learning models while maintains the efficiency. Second, DQ is a generic building block of adversarial defense, which can be combined with other adversarial defense techniques to advance state-of-the-art robustness. Third, our method makes quantization itself easier thanks to the constrained dynamic range. In this work, we aim to raise people's awareness about the security of the quantized neural networks, which is widely deployed in GPU/TPU/FPGAs, and pave a possible direction to bridge two important areas in deep learning: efficiency and robustness. We connect these two domains by designing a novel Defensive Quantization (DQ) module to defend adversarial attacks while maintain the efficiency. Experimental results on two datasets validate that the new quantization method can make the deep learning models be safely deployed on mobile devices. BID16 . To make a comparison, we also trained a full precision model and a ReLU6 quantized model following same setting. All the quantized models use bit=2. We tested the trained model using PGD attack by BID16 under both white-box and black-box setting. We use a VGG-16 model separately trained with PGD adversarial training as the black-box attacker. The results are provided in TAB8 . Our white-box result is consistent with BID22 , where Tanh based quantizaion with PGD training gives much higher white-box accuracy compared to the full precision model. However, we can see that the black-box robustness decreases. Worse still, the black-box attack successful rate is even lower than white-box, which is abnormal since black-box attack is generally weaker than white-box. This phenomenon indicates severe gradient masking problem BID19 BID2 , which gives a false sense of security. As a comparison, we also trained a ReLU6 quantized model. With ReLU6 quantization, there is no sign of gradient masking, nor improvement in robustness, indicating that gradient masking problem majorly comes from Tanh activation function. Actually, ReLU6 quantized model has slightly worse robustness.","Neural network quantization is becoming industry standard efficiently deploy deep learning models hardware platforms CPU GPU TPU FPGAs. However observe conventional quantization approaches are vulnerable adversarial attacks. paper aims raise people's awareness security quantized models designed novel quantization methodology jointly optimize efficiency robustness deep learning models. first conduct empirical study show vanilla quantization suffers adversarial attacks. observe inferior robustness comes error amplification effect where the why the quantization operation enlarges distance caused amplified noise. propose novel Defensive Quantization DQ method controlling Lipschitz constant network quantization when the magnitude adversarial noise remains non-expansive inference. Extensive experiments CIFAR-10 SVHN datasets demonstrate new quantization method can defend neural networks adversarial examples even achieves superior robustness full-precision counterparts maintaining hardware efficiency vanilla quantization approaches. by-product DQ can also improve accuracy quantized models without adversarial attack. Neural network quantization BID10 BID34 BID12 is a widely used technique reduce computation memory costs neural networks facilitating efficient deployment. has become industry standard deep learning hardware. However find widely used vanilla quantization approaches suffer unexpected issues -the quantized model is more vulnerable adversarial attacks FIG1 Adversarial attack is consist subtle perturbations input images causes deep learning models give incorrect labels BID28. perturbations are hardly detectable human eyes can easily fool neural networks. Since quantized neural networks are widely deployed many safety-critical scenarios e.g autonomous driving BID1 potential security risks cannot neglected. efficiency latency applications are also important need jointly optimize them.The fact quantization leads inferior adversarial robustness is counter intuitive small perturbations should be denoised low-bit representations. Recent work BID31 also demonstrates quantization input image space.e color bit depth reduction is quite effective defend adversarial examples. natural question rises where the why the quantization operator is yet effective when applied intermediate DNN layers? analyze issue is caused error amplification effect adversarial perturbation BID15 -although magnitude perturbation image is small is amplified significantly when passing deep neural network see FIG4. deeper layers are,the more significant side effect is. amplification pushes values different quantization bucket which is undesirable. conducted empirical experiments analyze how quantization influences activation error clean adversarial samples FIG4 when the magnitude noise is small activation quantization is capable reducing errors eliminating small perturbations;However when the magnitude perturbation is larger certain threshold where the why the quantization instead amplify errors which causes quantized model make mistakes. argue is the main reason causing inferior robustness quantized models.In paper propose Defensive Quantization DQ fixes robustness issue quantized models also turns activation quantization defense method boosts adversarial robustness. are inspired success image quantization improving robustness. Intuitively will be possible defend attacks quantization operations if we can keep magnitude perturbation small. However due error amplification effect gradient based adversarial samples is non-trivial keep noise small scale inference. Recent works BID5 BID21 have attempted make network non-expansive controlling Lipschitz constant network smaller 1 which has smaller variation change output input. case input noise will not propagate intermediate layers impact output attenuated. method is built theory. Defensive quantization quantizes feature maps low-bit representations also controls Lipschitz constant network noise is kept within small magnitude hidden layers. case keep noise small left zone FIG4 where the why the quantization can reduce perturbation error. produced model method enjoys better security efficiency time.Experiments show Defensive Quantization DQ offers three unique advantages. First DQ provides effective way boost robustness deep learning models maintains efficiency. Second DQ is a generic building block adversarial defense which can be combined adversarial defense techniques advance state-of-the-art robustness. Third method makes quantization easier thanks constrained dynamic range. work aim raise people's awareness security quantized neural networks which is widely deployed GPU/TPU/FPGAs pave possible direction bridge two important areas deep learning:efficiency robustness. connect two domains designing novel Defensive Quantization DQ module defend adversarial attacks maintain efficiency. Experimental results two datasets validate new quantization method can make deep learning models safely deployed mobile devices. BID16. make comparison also trained full precision model ReLU6 quantized model following setting. quantized models use bit=2 tested trained model using PGD attack BID16 white-box black-box setting. use VGG-16 model separately trained PGD adversarial training black-box attacker. results are provided TAB8. white-box result is consistent BID22 where Tanh based quantizaion PGD training gives much higher white-box accuracy compared full precision model. However can see black-box robustness decreases. Worse still black-box attack successful rate is even lower white-box which is abnormal since black-box attack is generally weaker white-box phenomenon indicates severe gradient masking problem BID19 BID2 which gives false sense security. comparison also trained ReLU6 quantized model. ReLU6 quantization is no sign gradient masking improvement robustness indicating gradient masking problem majorly comes Tanh activation function. Actually ReLU6 quantized model has slightly worse robustness.",1373,993,380,0.013,1.383,2025/11/05 17:19:07,0.01,1.411,0.1651090342679126,426.977
"Recurrent Neural Networks (RNNs) continue to show  outstanding performance in sequence modeling tasks. However, training RNNs on long sequences often face challenges like slow inference, vanishing gradients and difficulty in capturing long term dependencies. In backpropagation through time settings, these issues are tightly coupled with the large, sequential computational graph resulting from unfolding the RNN in time. We introduce the Skip RNN model which extends existing RNN models by learning to skip state updates and shortens the effective size of the computational graph. This model can also be encouraged to perform fewer state updates through a budget constraint. We evaluate the proposed model on various tasks and show how it can reduce the number of required RNN updates while preserving, and sometimes even improving, the performance of the baseline RNN models. Source code is publicly available at https://imatge-upc.github.io/skiprnn-2017-telecombcn/. Recurrent Neural Networks (RNNs) have become the standard approach for practitioners when addressing machine learning tasks involving sequential data. Such success has been enabled by the appearance of larger datasets, more powerful computing resources and improved architectures and training algorithms. Gated units, such as the Long Short-Term Memory (Hochreiter & Schmidhuber, 1997 ) (LSTM) and the Gated Recurrent Unit (Cho et al., 2014 ) (GRU), were designed to deal with the vanishing gradients problem commonly found in RNNs (Bengio et al., 1994) . These architectures have been popularized, in part, due to their impressive results on a variety of tasks in machine translation (Bahdanau et al., 2015) , language modeling BID17 and speech recognition (Graves et al., 2013) .Some of the main challenges of RNNs are in their training and deployment when dealing with long sequences, due to their inherently sequential behaviour. These challenges include throughput degradation, slower convergence during training and memory leakage, even for gated architectures (Neil et al., 2016) . Sequence shortening techniques, which can be seen as a sort of conditional computation (Bengio et al., 2013; Bengio, 2013; Davis & Arel, 2013) in time, can alleviate these issues. The most common approaches, such as cropping discrete signals or reducing the sampling rate in continuous signals, are based on heuristics and can be suboptimal. In contrast , we propose a model that is able to learn which samples (i.e., elements in the input sequence) need to be used in order to solve the target task. Consider a video understanding task as an example: scenes with large motion may benefit from high frame rates, whereas only a few frames are needed to capture the semantics of a mostly static scene.The main contribution of this work is a novel modification for existing RNN architectures that allows them to skip state updates, decreasing the number of sequential operations performed, without requiring any additional supervision signal. This model , called Skip RNN, adaptively determines whether the state needs to be updated or copied to the next time step. We show how the network can be encouraged to perform fewer state updates by adding a penalization term during training, allowing us to train models under different computation budgets. The proposed modification can generally be integrated with any RNN and we show, in this paper, implementations with well-known RNNs, namely LSTM and GRU. The resulting models show promising results on a series of sequence modeling tasks. In particular , we evaluate the proposed Skip RNN architecture on six sequence learning problems: an adding task, sine wave frequency discrimination, digit classification, sentiment analysis in movie reviews, action classification in video, and temporal action localization in video 1 . We presented Skip RNNs as an extension to existing recurrent architectures enabling them to skip state updates thereby reducing the number of sequential operations in the computation graph. Unlike other approaches, all parameters in Skip RNN are trained with backpropagation. Experiments conducted with LSTMs and GRUs showed that Skip RNNs can match or in some cases even outperform the baseline models while relaxing their computational requirements. Skip RNNs provide faster and more stable training for long sequences and complex models, owing to gradients being backpropagated through fewer time steps resulting in a simpler optimization task. Moreover, the introduced computational savings are better suited for modern hardware than those methods that reduce the amount of computation required at each time step (Koutnik et al., 2014; Neil et al., 2016; Chung et al., 2017) .A ADDITIONAL EXPERIMENTS",Recurrent Neural Networks RNNs continue show outstanding performance sequence modeling tasks. However training RNNs long sequences often face challenges like slow inference vanishing gradients difficulty capturing long term dependencies. backpropagation time settings issues are tightly coupled large sequential computational graph resulting unfolding RNN time. introduce Skip RNN model which extends existing RNN models learning skip state updates shortens effective size computational graph. model can also encouraged perform fewer state updates budget constraint. evaluate proposed model various tasks show how it can reduce number required RNN updates preserving sometimes even improving performance baseline RNN models. Source code is publicly available https://imatge-upc.github.io/skiprnn-2017-telecombcn/. Recurrent Neural Networks RNNs have become standard approach practitioners when addressing machine learning tasks involving sequential data. success has been enabled appearance larger datasets powerful computing resources improved architectures training algorithms. Gated units Long Short-Term Memory Hochreiter Schmidhuber 1997 LSTM Gated Recurrent Unit Choetal. 2014 GRU were designed deal vanishing gradients problem commonly found RNNs Bengioetal. 1994 architectures have been popularized part due impressive results variety tasks machine translation Bahdanauetal. 2015 language modeling BID17 speech recognition Gravesetal. 2013.Some main challenges RNNs are in their training deployment when dealing long sequences due inherently sequential behaviour. challenges include throughput degradation slower convergence training memory leakage even gated architectures Neiletal. 2016 Sequence shortening techniques which can be seen sort conditional computation Bengioetal. 2013;Bengio 2013;Davis Arel 2013 time can alleviate issues. common approaches cropping discrete signals reducing sampling rate continuous signals are based heuristics can be suboptimal. contrast propose model is able learn which samples.e elements input sequence need used order solve target task. Consider video understanding task example:scenes large motion may benefit high frame rates whereas frames are needed capture semantics mostly static scene.The main contribution work is a novel modification existing RNN architectures allows skip state updates decreasing number sequential operations performed without requiring additional supervision signal. model called Skip RNN adaptively determines whether state needs updated copied next time step. show how the network can be encouraged perform fewer state updates adding penalization term training allowingus train models different computation budgets. proposed modification can generally integrated RNN show paper implementations well-known RNNs namely LSTM GRU. resulting models show promising results series sequence modeling tasks. particular evaluate proposed Skip RNN architecture six sequence learning problems:adding task sine wave frequency discrimination digit classification sentiment analysis movie reviews action classification video temporal action localization video1. presented Skip RNNs extension existing recurrent architectures enabling skip state updates thereby reducing number sequential operations computation graph. Unlike approaches parameters Skip RNN are trained backpropagation. Experiments conducted LSTMs GRUs showed Skip RNNs can match cases even outperform baseline models relaxing computational requirements. Skip RNNs provide faster stable training long sequences complex models owing gradients backpropagated fewer time steps resulting simpler optimization task. Moreover introduced computational savings are better suited modern hardware methods reduce amount computation required time step Koutniketal. 2014;Neiletal. 2016;Chungetal. 2017.A ADDITIONAL EXPERIMENTS,943,660,283,0.009,1.429,2025/11/05 17:19:07,0.0,1.462,0.308411214953271,293.598
"We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation operations per iteration, which has a computational cost comparable to two standard forward passes and is easy to implement. Our method addresses long-standing issues with current second-order solvers, which invert an approximate Hessian matrix every iteration exactly or by conjugate-gradient methods, procedures that are much slower than a SGD step. Instead, we propose to keep a single estimate of the gradient projected by the inverse Hessian matrix, and update it once per iteration with just two passes over the network. This estimate has the same size and is similar to the momentum variable that is commonly used in SGD. No estimate of the Hessian is maintained.
 We first validate our method, called CurveBall, on small problems with known solutions (noisy Rosenbrock function and degenerate 2-layer linear networks), where current deep learning solvers struggle. We then train several large models on CIFAR and ImageNet, including ResNet and VGG-f networks, where we demonstrate faster convergence with no hyperparameter tuning. We also show our optimiser's generality by testing on a large set of randomly-generated architectures. Stochastic Gradient Descent (SGD) and back-propagation BID16 are the algorithmic backbone of current deep network training. The success of deep learning demonstrates the power of this combination, which has been successfully applied on various tasks with large datasets and very deep networks BID11 ).Yet , while SGD has many advantages, speed of convergence (in terms of number of iterations) is not necessarily one of them. While individual SGD iterations are very quick to compute and lead to rapid progress at the beginning of the optimisation, it soon reaches a slower phase where further improvements are achieved slowly. This can be attributed to entering regions of the parameter space where the objective function is poorly scaled. In such cases, rapid progress would require vastly different step sizes for different directions in parameter space, which SGD cannot deliver.Second-order methods, such as Newton's method and its variants, eliminate this issue by rescaling the gradient according to the local curvature of the objective function. For a scalar loss in R, this rescaling takes the form H −1 J where H is the Hessian matrix (second-order derivatives) or an approximation of the local curvature in the objective space, and J is the gradient of the objective. They can in fact achieve local scale-invariance (Wright & Nocedal, 1999, p. 27) , and make provably better progress in the regions where gradient descent stalls. While they are unmatched in other domains, there are several obstacles to their application to deep models. First, it is impractical to invert or even store the Hessian, since it grows quadratically with the number of parameters, and there are typically millions of them. Second, any Hessian estimate is necessarily noisy and ill-conditioned due to stochastic sampling, to which classic inversion methods such as conjugate-gradient are not robust.In this paper, we propose a new algorithm that can overcome these difficulties and make second order optimisation practical for deep learning. We show in particular how to avoid the storage of any estimate of the Hessian matrix or its inverse. Instead, we treat the computation of the Newton update, H −1 J, as solving a linear system that itself can be solved via gradient descent. The cost of solving this system is amortized over time by interleaving its steps with the parameter update steps. Our proposed method adds little overhead, since a Hessian-vector product can be implemented for modern networks with just two steps of automatic differentiation. Interestingly , we show that our method is equivalent to momentum SGD (also known as the heavy-ball method) with a single additional term, accounting for curvature. For this reason we named our method CURVEBALL. Unlike other proposals , the total memory footprint is as small as that of momentum SGD. This paper is structured as follows. We introduce relevant technical background in sec. 2, and present our method in sec. 3. We evaluate our method and show experimental results in sec. 4. Related work is discussed in sec. 5. Finally we summarise our findings in sec. 6. In this work, we have proposed a practical second-order solver that has been specifically tailored for deep-learning-scale stochastic optimisation problems. We showed that our optimiser can be applied to a large range of datasets and reach better training error than first order method with the same number of iterations, with essentially no hyper-parameters tuning. In future work, we intend to bring more improvements to the wall-clock time of our method by engineering the FMAD operation to the same standard as back-propagation, and study optimal trust-region strategies to obtain λ in closed-form.We now perform a change of variables to diagonalize the Hessian, H = Qdiag(h)Q T , with Q orthogonal and h the vector of eigenvalues. Let w * = arg min w f (w) = H −1 b be the optimal solution of the minimization. Then, replacing w t = Qx t + w * in eq. 30: DISPLAYFORM0 Then, expanding H with its eigendecomposition, DISPLAYFORM1 Left-multiplying by Q T ,and canceling out Q due to orthogonality, DISPLAYFORM2 Similarly for eq. 29, replacing z t = Qy t yields DISPLAYFORM3 Note that each pair formed by the corresponding element of y t and x t is an independent system with only 2 variables, since the pairs do not interact (eq. 33 and 34 only contain element-wise operations).From now on, we will be working on the ith element of each vector.We can thus write eq. 33 and 34 (for a single element i of each) as a vector equation: DISPLAYFORM4 The matrix on the left is necessary to express the fact that the y t+1 factor in eq. 34 must be moved to the left-hand side, which corresponds to iteration t + 1 (x t+1 − y t+1 = x t ). Left-multiplying eq. 35 by the inverse, DISPLAYFORM5 This is the transition matrix R i that characterizes the iteration, and taking its power models multiple iterations in closed-form: DISPLAYFORM6 The two eigenvalues of R i are given in closed-form by: DISPLAYFORM7 The series in eq. 37 converges when |eig (R i )| < 1 simultaneously for both eigenvalues, which is equivalent to: DISPLAYFORM8 with ρ > 0 and βh i > 0. Note that when using the Gauss-Newton approximation of the Hessian, h i > 0 and thus the last condition simplifies to β > 0.Since eq. 39 has to be satisfied for every eigenvalue, we have 3 2 βh max − 1 < ρ < 1 + βh min ,with h min and h max the smallest and largest eigenvalues of the Hessian H, respectively, proving the result.The rate of convergence is the largest of the two values |eig (R i )|. When the argument of the square root in eq. 38 is non-negative, it does not admit an easy interpretation; however, when it is negative, eq. 38 simplifies to: The convergence rate for a single eigenvalue is illustrated in FIG3 . Graphically, the regions of convergence for different eigenvalues will differ only by a scale factor along the βh i axis (horizontal stretching of FIG3 ). Moreover, the largest possible range of βh i values is obtained when ρ = 1, and that range is 0 < βh i < 4 3 . We can infer that the intersection of the regions of convergence for several eigenvalues will be maximized with ρ = 1, for any fixed β. DISPLAYFORM9",propose fast second-order method can be used drop-in replacement current deep learning solvers. Compared stochastic gradient descent SGD requires two additional forward-mode automatic differentiation operations per iteration which has a computational cost comparable two standard forward passes is easy implement. method addresses long-standing issues current second-order solvers which invert approximate Hessian matrix every iteration exactly conjugate-gradient methods procedures are much slower SGD step. Instead propose keep single estimate gradient projected inverse Hessian matrix update per iteration two passes network. estimate has the same size is similar momentum variable is commonly used SGD. estimate Hessian is maintained. first validate method called CurveBall small problems known solutions noisy Rosenbrock function degenerate 2-layer linear networks where current deep learning solvers struggle. train several large models CIFAR ImageNet including ResNet VGG-f networks where we demonstrate faster convergence hyperparameter tuning. also show optimiser's generality testing large set randomly-generated architectures. Stochastic Gradient Descent SGD back-propagation BID16 are the algorithmic backbone current deep network training. success deep learning demonstrates power combination which has been successfully applied various tasks large datasets deep networks BID11.Yet which SGD has many advantages speed convergence terms number iterations is not necessarily one them. individual SGD iterations are very quick compute lead rapid progress beginning optimisation soon reaches slower phase where further improvements are achieved slowly. can be attributed entering regions parameter space where the objective function is poorly scaled. cases rapid progress would require vastly different step sizes different directions parameter space which SGD cannot deliver.Second-order methods Newton's method variants eliminate issue rescaling gradient according local curvature objective function. scalar loss R rescaling takes formH−1J whereH is the Hessian matrix second-order derivatives approximation local curvature objective space J is the gradient objective. can in fact achieve local scale-invariance Wright Nocedal 1999 p. 27 make provably better progress regions where gradient descent stalls. are unmatched domains are several obstacles application deep models. First is impractical invert even store Hessian since grows quadratically number parameters are typically millions them. Second Hessian estimate is necessarily noisy ill-conditioned due stochastic sampling which classic inversion methods conjugate-gradient are not robust.In paper propose new algorithm can overcome difficulties make second order optimisation practical deep learning. show particular how to avoid storage estimate Hessian matrix inverse. Instead treat computation Newton update H−1J solving linear system can be solved via gradient descent. cost solving system is amortized time interleaving steps parameter update steps. proposed method adds little overhead since Hessian-vector product can be implemented modern networks two steps automatic differentiation. Interestingly show method is equivalent momentum SGD also known heavy-ball method single additional term accounting curvature. reason named method CURVEBALL. Unlike proposals total memory footprint is as small momentum SGD. paper is structured follows. introduce relevant technical background sec. 2 present method sec. 3. evaluate method show experimental results sec. 4. Related work is discussed sec. 5. Finally summarise findings sec. 6. work have proposed practical second-order solver has been specifically tailored deep-learning-scale stochastic optimisation problems. showed optimiser can be applied large range datasets reach better training error first order method number iterations essentially hyper-parameters tuning. future work intend bring improvements wall-clock time method engineering FMAD operation standard back-propagation study optimal trust-region strategies obtainλ closed-form.We perform change variables diagonalize Hessian H Qdiag h Q Q orthogonal h vector eigenvalues. Letw* arg minwf w H−1b optimal solution minimization. replacingw Qx+w* eq. 30:DISPLAYFORM0 expandingH eigendecomposition DISPLAYFORM1 Left-multiplying Q canceling Q due orthogonality DISPLAYFORM2 Similarly eq. 29 replacingz Qy yields DISPLAYFORM3 Note pair formed corresponding element x is an independent system 2 variables since pairs do not interact eq. 33 34 contain element-wise operations.From willbe working ith element vector.We can thus writeeq. 33 34 single element vector equation:DISPLAYFORM4 matrix left is necessary express fact+1 factor eq. 34 must moved left-hand side which corresponds iteration+1 x+1−+1 x Left-multiplyingeq. 35 inverse DISPLAYFORM5 is the transition matrixR characterizes iteration taking power models multiple iterations closed-form DISPLAYFORM6 two eigenvalues R are given closed-form by:DISPLAYFORM7 series eq. 37 converges when |eig R 1 simultaneously eigenvalues which is equivalent to:DISPLAYFORM8 ρ 0 βh 0. Note when using Gauss-Newton approximation Hessian h 0 thus last condition simplifies β 0.Sinceeq. 39 has to be satisfied every eigenvalue have 3 2 βh max −1 ρ 1+βh min h min h max smallest largest eigenvalues HessianH respectively proving result.The rate convergence is the largest two values |eig R |. When the argument square root eq. 38 is non-negative does not admit easy interpretation;however when it is negative eq. 38 simplifies to:convergence rate single eigenvalue is illustrated FIG3. Graphically regions convergence different eigenvalues will differ scale factor along βh axis horizontal stretching FIG3 Moreover largest possible range βh values is obtained whenρ 1 range is0 βh 43. can infer intersection regions convergence several eigenvalues will be maximized ρ 1 fixedβ. DISPLAYFORM9,1626,1090,536,0.019,1.492,2025/11/05 17:19:07,0.01,1.521,0.5046728971962615,526.236
"The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms. Imagine yourself travelling to a scientific conference. The field is popular, and surely you do not want to miss out on anything. You have selected several posters you want to visit, and naturally you must return to the place where you are now: the coffee corner. In which order should you visit the posters, to minimize your time walking around? This is the Travelling Scientist Problem (TSP).You realize that your problem is equivalent to the Travelling Salesman Problem (conveniently also TSP). This seems discouraging as you know the problem is (NP-)hard (Garey & Johnson, 1979) . Fortunately , complexity theory analyzes the worst case, and your Bayesian view considers this unlikely. In particular , you have a strong prior: the posters will probably be laid out regularly. You want a special algorithm that solves not any, but this type of problem instance. You have some months left to prepare. As a machine learner , you wonder whether your algorithm can be learned?Motivation Machine learning algorithms have replaced humans as the engineers of algorithms to solve various tasks. A decade ago, computer vision algorithms used hand-crafted features but today they are learned end-to-end by Deep Neural Networks (DNNs). DNNs have outperformed classic approaches in speech recognition, machine translation, image captioning and other problems, by learning from data (LeCun et al., 2015) . While DNNs are mainly used to make predictions, Reinforcement Learning (RL) has enabled algorithms to learn to make decisions, either by interacting with an environment, e.g. to learn to play Atari games (Mnih et al., 2015) , or by inducing knowledge through look-ahead search: this was used to master the game of Go (Silver et al., 2017) .The world is not a game, and we desire to train models that make decisions to solve real problems. These models must learn to select good solutions for a problem from a combinatorially large set of potential solutions. Classically, approaches to this problem of combinatorial optimization can be divided into exact methods, that guarantee finding optimal solutions, and heuristics, that trade off optimality for computational cost, although exact methods can use heuristics internally and vice versa. Heuristics are typically expressed in the form of rules, which can be interpreted as policies to make decisions. We believe that these policies can be parameterized using DNNs, and be trained to obtain new and stronger algorithms for many different combinatorial optimization problems, similar to the way DNNs have boosted performance in the applications mentioned before. In this paper, we focus on routing problems: an important class of practical combinatorial optimization problems.The promising idea to learn heuristics has been tested on TSP BID4 . In order to push this idea, we need better models and better ways of training. Therefore, we propose to use a powerful model based on attention and we propose to train this model using REINFORCE with a simple but effective greedy rollout baseline. The goal of our method is not to outperform a nonlearned, specialized TSP algorithm such as Concorde BID0 . Rather, we show the flexibility of our approach on multiple (routing) problems of reasonable size, with a single set of hyperparameters. This is important progress towards the situation where we can learn strong heuristics to solve a wide range of different practical problems for which no good heuristics exist. In this work we have introduced a model and training method which both contribute to significantly improved results on learned heuristics for TSP and additionally learned strong (single construction) heuristics for multiple routing problems, which are traditionally solved by problem-specific approaches. We believe that our method is a powerful starting point for learning heuristics for other combinatorial optimization problems defined on graphs, if their solutions can be described as sequential decisions. In practice, operational constraints often lead to many variants of problems for which no good (human-designed) heuristics are available such that the ability to learn heuristics could be of great practical value.Compared to previous works, by using attention instead of recurrence (LSTMs) we introduce invariance to the input order of the nodes, increasing learning efficiency. Also this enables parallelization, for increased computational efficiency. The multi-head attention mechanism can be seen as a message passing algorithm that allows nodes to communicate relevant information over different channels, such that the node embeddings from the encoder can learn to include valuable information about the node in the context of the graph. This information is important in our setting where decisions relate directly to the nodes in a graph. Being a graph based method, our model has increased scaling potential (compared to LSTMs) as it can be applied on a sparse graph and operate locally.Scaling to larger problem instances is an important direction for future research, where we think we have made an important first step by using a graph based method, which can be sparsified for improved computational efficiency. Another challenge is that many problems of practical importance have feasibility constraints that cannot be satisfied by a simple masking procedure, and we think it is promising to investigate if these problems can be addressed by a combination of heuristic learning and backtracking. This would unleash the potential of our method, already highly competitive to the popular Google OR Tools project, to an even larger class of difficult practical problems. A ATTENTION MODEL DETAILS FIG4 : Illustration of weighted message passing using a dot-attention mechanism. Only computation of messages received by node 1 are shown for clarity. Best viewed in color.Attention mechanism We interpret the attention mechanism by Vaswani et al. FORMULA9 as a weighted message passing algorithm between nodes in a graph. The weight of the message value that a node receives from a neighbor depends on the compatibility of its query with the key of the neighbor, as illustrated in FIG4 . Formally, we define dimensions d k and d v and compute the key k i ∈ R dk , value v i ∈ R dv and query q i ∈ R dk for each node by projecting the embedding h i : DISPLAYFORM0 From the queries and keys, we compute the compatibility u ij ∈ R of the query q i of node i with the key k j of node j as the (scaled, see Vaswani et al. FORMULA9 ) dot-product: DISPLAYFORM1 In a general graph, defining the compatibility of non-adjacent nodes as −∞ prevents message passing between these nodes. From the compatibilities u ij , we compute the attention weights a ij ∈ [0, 1] using a softmax: DISPLAYFORM2 Finally, the vector h i that is received by node i is the convex combination of messages v j : DISPLAYFORM3 Multi-head attention As was noted by Vaswani et al. (2017) and Velickovic et al. (2018) , it is beneficial to have multiple attention heads. This allows nodes to receive different types of messages from different neighbors. Especially, we compute the value in equation 13 M = 8 times with different parameters, using DISPLAYFORM4 We denote the result vectors by h im for m ∈ 1, . . . , M . These are projected back to a single d h -dimensional vector using DISPLAYFORM5 The final multi-head attention value for node i is a function of h 1 , . . . , h n through h im : DISPLAYFORM6 Feed-forward sublayer The feed-forward sublayer computes node-wise projections using a hidden (sub)sublayer with dimension d ff = 512 and a ReLu activation: DISPLAYFORM7 Batch normalization We use batch normalization with learnable d h -dimensional affine parameters w bn and b bn : DISPLAYFORM8 Here denotes the element-wise product and BN refers to batch normalization without affine transformation.",recently presented idea learn heuristics combinatorial optimization problems is promising can save costly development. However push idea towards practical implementation need better models better ways training. contribute directions:propose model based attention layers benefits Pointer Network show how to train model using REINFORCE simple baseline based deterministic greedy rollout which we find is more efficient using value function. significantly improve recent learned heuristics Travelling Salesman Problem TSP getting close optimal results problems 100 nodes. hyperparameters learn strong heuristics two variants Vehicle Routing Problem VRP Orienteering Problem OP stochastic variant Prize Collecting TSP PCTSP outperforming wide range baselines getting results close highly optimized specialized algorithms. Imagine travelling scientific conference. field is popular surely do not want miss anything. have selected several posters do not want visit naturally must return place where you are now:coffee corner. which order should you visit posters minimize time walking around? is the Travelling Scientist Problem TSP.You realize problem is equivalent Travelling Salesman Problem conveniently also TSP seems discouraging know problem is(NP- hard Garey Johnson 1979 Fortunately complexity theory analyzes worst case Bayesian view considers unlikely. particular have a strong prior:posters will probably laid regularly. want special algorithm solves type problem instance. have some months left prepare. machine learner wonder whether algorithm can be learned? Motivation Machine learning algorithms have replaced humans engineers algorithms solve various tasks. decade ago computer vision algorithms used hand-crafted features today are learned end-to-end Deep Neural Networks DNNs DNNs have outperformed classic approaches speech recognition machine translation image captioning problems learning data LeCunetal. 2015 DNNs are mainly used make predictions Reinforcement Learning RL has enabled algorithms learn make decisions either interacting environment e.g learn play Atari games Mnihetal. 2015 inducing knowledge look-ahead search:was used master game Go Silveretal. 2017.The world is not a game desire train models make decisions solve real problems. models must learn select good solutions problem combinatorially large set potential solutions. Classically approaches problem combinatorial optimization can be divided exact methods guarantee finding optimal solutions heuristics trade optimality computational cost although exact methods can use heuristics internally vice versa. Heuristics are typically expressed form rules which can be interpreted policies make decisions. believe policies can be parameterized using DNNs trained obtain new stronger algorithms many different combinatorial optimization problems similar way DNNs have boosted performance applications mentioned before. paper focus routing problems:important class practical combinatorial optimization problems.The promising idea learn heuristics has been tested TSP BID4. which order push idea need better models better ways training. Therefore propose use powerful model based attention propose train model using REINFORCE simple effective greedy rollout baseline. goal method is not to outperform nonlearned specialized TSP algorithm Concorde BID0. Rather show flexibility approach multiple routing problems reasonable size single set hyperparameters. is important progress towards situation where we can learn strong heuristics solve wide range different practical problems which no good heuristics exist. work have introduced model training method which both contribute significantly improved results learned heuristics TSP additionally learned strong single construction heuristics multiple routing problems which are traditionally solved problem-specific approaches. believe method is a powerful starting point learning heuristics combinatorial optimization problems defined graphs if their solutions can be described sequential decisions. practice operational constraints often lead many variants problems which no good human-designed heuristics are available ability learn heuristics could great practical value.Compared previous works using attention instead recurrence LSTMs introduce invariance input order nodes increasing learning efficiency. Also enables parallelization increased computational efficiency. multi-head attention mechanism can be seen message passing algorithm allows nodes communicate relevant information different channels node embeddings encoder can learn include valuable information node context graph. information is is an important setting where decisions relate directly nodes graph. graph based method model has increased scaling potential compared LSTMs can applied sparse graph operate locally.Scaling larger problem instances is is an important direction future research where we think have made important first step using graph based method which can be sparsified improved computational efficiency. Another challenge is that many problems practical importance have feasibility constraints cannot satisfied simple masking procedure where we think is promising investigate if these problems can be addressed combination heuristic learning backtracking. would unleash potential method already highly competitive popular Google Tools project even larger class difficult practical problems. ATTENTION MODEL DETAILS FIG4:Illustration weighted message passing using dot-attention mechanism. computation messages received node1 are shown clarity. Best viewed color.Attention mechanism interpret attention mechanism Vaswanietal. FORMULA9 weighted message passing algorithm nodes graph. weight message value node receives neighbor depends compatibility query key neighbor illustrated FIG4. Formally define dimensions k v compute keyk ∈Rdk valuev ∈Rdv queryq ∈Rdk node projecting embeddingh i:DISPLAYFORM0 queries keys compute compatibilityuij∈ R queryq node keykj nodej scaled see Vaswanietal. FORMULA9 dot-product DISPLAYFORM1 general graph defining compatibility non-adjacent nodes −∞ prevents message passing nodes. compatibilitiesuij compute attention weights ij∈ 0 1 using softmax:DISPLAYFORM2 Finally vectorh is received node is the convex combination messagesvj:DISPLAYFORM3 Multi-head attention was noted Vaswanietal. 2017 Velickovicetal. 2018 is beneficial have multiple attention heads. allows nodes receive different types messages different neighbors. Especially compute value equation13 8 times different parameters using DISPLAYFORM4 denote result vectors him ∈1 M. are projected back single h -dimensional vector using DISPLAYFORM5 final multi-head attention value node is a function h1 hn him:DISPLAYFORM6 Feed-forward sublayer feed-forward sublayer computes node-wise projections using hidden sub sublayer dimension ff 512 ReLu activation:DISPLAYFORM7 Batch normalization use batch normalization learnable h -dimensional affine parameters wbn bbn:DISPLAYFORM8 denotes element-wise product BN refers batch normalization without affine transformation.,1773,1198,575,0.021,1.48,2025/11/05 17:19:07,0.01,1.591,0.467289719626168,557.034
"We propose an efficient online hyperparameter optimization method which uses a joint dynamical system to evaluate the gradient with respect to the hyperparameters. While similar methods are usually limited to hyperparameters with a smooth impact on the model, we show how to apply it to the probability of dropout in neural networks. Finally, we show its effectiveness on two distinct tasks. With the growing size and complexity of both datasets and models, training times keep increasing and it is not uncommon to train a model for several days or weeks. This effect is compounded by the number of hyperparameters a practitioner has to search through. Even though search through hyperparameter space has improved beyond grid search, this task is still often computationally intensive, mainly because these techniques are offline, in that they need to perform a full learning before trying a new value. Recently, several authors proposed online hyperparameter optimization techniques, where the hyperparameters are tuned alongside the parameters of the model themselves by running short runs of training and updating the hyperparameter after each such run. By casting the joint learning of parameters and hyperparameters as a dynamical system, we show that these approaches are unstable and need to be stopped using an external process, like early stopping, to achieve a good performance. We then modify these techniques such that the joint optimization procedure is stable as well as efficient by changing the hyperparameter at every time step. Further, while existing techniques are limited in the type of hyperparameters they can optimize, we extend the process to dropout probability optimization, a popular regularization technique in deep learning.",propose efficient online hyperparameter optimization method which uses joint dynamical system evaluate gradient respect hyperparameters. similar methods are usually limited hyperparameters smooth impact model show how to apply probability dropout neural networks. Finally show effectiveness two distinct tasks. growing size complexity datasets models training times keep increasing is not uncommon train model several days weeks. effect is compounded number hyperparameters practitioner has to search through. Even though search hyperparameter space has improved beyond grid search task is still often computationally intensive mainly techniques are offline need perform full learning trying new value. Recently several authors proposed online hyperparameter optimization techniques where the hyperparameters are tuned alongside parameters model running short runs training updating hyperparameter run. casting joint learning parameters hyperparameters dynamical system show approaches are unstable need stopped using external process like early stopping achieve good performance. modify techniques joint optimization procedure is stable well efficient changing hyperparameter every time step. existing techniques are limited type hyperparameters can optimize extend process dropout probability optimization popular regularization technique deep learning.,307,195,112,0.003,1.574,2025/11/05 17:19:07,0.0,1.267,0.7601246105919004,124.216
"Ongoing innovations in recurrent neural network architectures have provided a steady influx of apparently state-of-the-art results on language modelling benchmarks. However, these have been evaluated using differing codebases and limited computational resources, which represent uncontrolled sources of experimental variation. We reevaluate several popular architectures and regularisation methods with large-scale automatic black-box hyperparameter tuning and arrive at the somewhat surprising conclusion that standard LSTM architectures, when properly regularised, outperform more recent models. We establish a new state of the art on the Penn Treebank and Wikitext-2 corpora, as well as strong baselines on the Hutter Prize dataset.
 The scientific process by which the deep learning research community operates is guided by empirical studies that evaluate the relative quality of models. Complicating matters, the measured performance of a model depends not only on its architecture (and data), but it can strongly depend on hyperparameter values that affect learning, regularisation, and capacity. This hyperparameter dependence is an often inadequately controlled source of variation in experiments, which creates a risk that empirically unsound claims will be reported.In this paper, we use a black-box hyperparameter optimisation technique to control for hyperparameter effects while comparing the relative performance of language modelling architectures based on LSTMs, Recurrent Highway Networks BID26 and NAS BID27 . We specify flexible, parameterised model families with the ability to adjust embedding and recurrent cell sizes for a given parameter budget and with fine grain control over regularisation and learning hyperparameters.Once hyperparameters have been properly controlled for, we find that LSTMs outperform the more recent models, contra the published claims. Our result is therefore a demonstration that replication failures can happen due to poorly controlled hyperparameter variation, and this paper joins other recent papers in warning of the under-acknowledged existence of replication failure in deep learning BID7 BID21 . However, we do show that careful controls are possible, albeit at considerable computational cost.Several remarks can be made in light of these results. First, as (conditional) language models serve as the central building block of many tasks, including machine translation, there is little reason to expect that the problem of unreliable evaluation is unique to the tasks discussed here. However, in machine translation, carefully controlling for hyperparameter effects would be substantially more expensive because standard datasets are much larger. Second, the research community should strive for more consensus about appropriate experimental methodology that balances costs of careful experimentation with the risks associated with false claims. Finally, more attention should be paid to hyperparameter sensitivity. Models that introduce many new hyperparameters or which perform well only in narrow ranges of hyperparameter settings should be identified as such as part of standard publication practice. During the transitional period when deep neural language models began to supplant their shallower predecessors, effect sizes tended to be large, and robust conclusions about the value of the modelling innovations could be made, even in the presence of poorly controlled ""hyperparameter noise."" However, now that the neural revolution is in full swing, researchers must often compare competing deep architectures. In this regime, effect sizes tend to be much smaller, and more methodological care is required to produce reliable results. Furthermore, with so much work carried out in parallel by a growing research community, the costs of faulty conclusions are increased.Although we can draw attention to this problem, this paper does not offer a practical methodological solution beyond establishing reliable baselines that can be the benchmarks for subsequent work. Still, we demonstrate how, with a huge amount of computation, noise levels of various origins can be carefully estimated and models meaningfully compared. This apparent tradeoff between the amount of computation and the reliability of results seems to lie at the heart of the matter. Solutions to the methodological challenges must therefore make model evaluation cheaper by, for instance, reducing the number of hyperparameters and the sensitivity of models to them, employing better hyperparameter optimisation strategies, or by defining ""leagues"" with predefined computational budgets for a single model representing different points on the tradeoff curve.","Ongoing innovations recurrent neural network architectures have provided steady influx apparently state-of-the-art results language modelling benchmarks. However have been evaluated using differing codebases limited computational resources which represent uncontrolled sources experimental variation. reevaluate several popular architectures regularisation methods large-scale automatic black-box hyperparameter tuning arrive somewhat surprising conclusion standard LSTM architectures when properly regularised outperform recent models. establish new state art Penn Treebank Wikitext-2 corpora well strong baselines Hutter Prize dataset. scientific process which the deep learning research community operates is guided empirical studies evaluate relative quality models. Complicating matters measured performance model depends architecture data can strongly depend hyperparameter values affect learning regularisation capacity. hyperparameter dependence is an often inadequately controlled source variation experiments which creates risk empirically unsound claims will be reported.In paper use black-box hyperparameter optimisation technique control hyperparameter effects comparing relative performance language modelling architectures based LSTMs Recurrent Highway Networks BID26 NAS BID27. specify flexible parameterised model families ability adjust embedding recurrent cell sizes given parameter budget fine grain control regularisation learning hyperparameters.Once hyperparameters have been properly controlled find LSTMs outperform recent models contra published claims. result is therefore demonstration replication failures can happen due poorly controlled hyperparameter variation paper joins recent papers warning under-acknowledged existence replication failure deep learning BID7 BID21. However do show careful controls are possible albeit considerable computational cost.Several remarks can be made light results. First conditional language models serve central building block many tasks including machine translation is little reason expect problem unreliable evaluation is unique tasks discussed here. However machine translation carefully controlling hyperparameter effects would substantially expensive standard datasets are much larger. Second research community should strive consensus appropriate experimental methodology balances costs careful experimentation risks associated false claims. Finally attention should be paid hyperparameter sensitivity. Models introduce many new hyperparameters which perform well narrow ranges hyperparameter settings should be identified part standard publication practice. transitional period when deep neural language models began supplant shallower predecessors effect sizes tended large robust conclusions value modelling innovations could made even presence poorly controlled hyperparameter noise. However neural revolution is in full swing researchers must often compare competing deep architectures. regime effect sizes tend much smaller methodological care is required produce reliable results. Furthermore much work carried parallel growing research community costs faulty conclusions are increased.Although can draw attention problem paper does not offer practical methodological solution beyond establishing reliable baselines can be the benchmarks subsequent work. Still demonstrate how,with a huge amount computation noise levels various origins can be carefully estimated models meaningfully compared. apparent tradeoff amount computation reliability results seems lie heart matter. Solutions methodological challenges must therefore make model evaluation cheaper instance reducing number hyperparameters sensitivity models employing better hyperparameter optimisation strategies defining leagues predefined computational budgets single model representing different points tradeoff curve.",800,547,253,0.008,1.463,2025/11/05 17:19:07,0.0,1.5,0.4143302180685358,266.05
"  Residual and skip connections play an important role in many current
  generative models. Although their theoretical and numerical advantages
  are understood, their role in speech enhancement systems has not been
  investigated so far. When performing spectral speech enhancement,
  residual connections are very similar in nature to spectral subtraction,
  which is the one of the most commonly employed speech enhancement approaches.
   Highway networks, on the other hand, can be seen as a combination of spectral
  masking and spectral subtraction. However, when using deep neural networks, such operations would
  normally happen in a transformed spectral domain, as opposed to traditional speech
  enhancement where all operations are often done directly on the spectrum.
   In this paper, we aim to investigate the role of residual and highway
  connections in deep neural networks for speech enhancement, and verify whether
  or not they operate similarly to their traditional, digital signal processing
  counterparts. We visualize the outputs of such connections, projected back to
  the spectral domain, in models trained for speech denoising, and show that while
  skip connections do not necessarily improve performance with regards to the
  number of parameters, they make speech enhancement models more interpretable. Highway BID7 and residual networks BID1 have been proposed with the objective of improving activation and gradient flow in the training of deep neural networks. On the other hand, in tasks like image reconstruction or speech enhancement, the use of such skip connections serves a different purpose: if we model a corrupted signal x = y + n as the addition of noise n to a clean signal y and x is the input to a neural network, we know that the task at hand is to predict n. In other words, to predict y, we have to alter the input x by subtracting n.In speech enhancement, the two more commonly used approaches are spectral subtraction and spectral masking. In the first, a statistical model of n is used to predict its magnitude spectrum N , which is then subtracted from the input spectrum X to yield a clean magnitude spectrum estimateŶ . In spectral masking, instead of performing subtraction, we find a multiplicative mask M which aims at either blocking time-frequency cells dominated by noise (in the case of binary masks) or scaling down energies in such time-frequency cells to make them match that of the original clean signal. Recent work in speech enhancement has explored skip connections as a way of performing masking BID4 and spectral estimation BID6 . Time domain approaches, such as SEGAN BID5 , use a UNet-style network which employs multiple skip connections as well. Other works, such as BID12 , perform spectral masking but Figure 1: Diagrams for highway, residual, and masking blocks used in this paper learn how to estimate an ideal mask instead of having the masking mechanism embedded in the neural network as a skip connection.For better understanding of such models, we would like to understand whether there are any parallels between such connections and two traditional DSP approaches to speech enhancement, namely spectral subtraction and spectral masking. We also want to understand whether models using skip connections perform better for enhancement when such connections appear only once (resembling their DSP counterparts) or repeated as multiple blocks (like in highway and residual networks). This paper shows early results of our investigation on the role of skip connections in speech enhancement models. Our preliminary experiments show that, although they have no significant impact in the performance of the models, such connections might help making the models more interpretable, as we can identify the contribution of each individual layer to the task. In the future, we intend to investigate more complex models, such as models based on the UNet architecture, as well as models that employ a temporal context window at the input instead of a single frame (such as the work in BID6 ), since those are more in line with state-of-the-art models in the literature.",Residual skip connections play important role many current generative models. Although theoretical numerical advantages are understood role speech enhancement systems has not been investigated far. When performing spectral speech enhancement residual connections are very similar nature spectral subtraction which is the one commonly employed speech enhancement approaches. Highway networks hand can be seen combination spectral masking spectral subtraction. However when using deep neural networks operations would normally happen transformed spectral domain opposed traditional speech enhancement where all operations are often done directly spectrum. paper aim investigate role residual highway connections deep neural networks speech enhancement verify whether operate similarly traditional digital signal processing counterparts. visualize outputs connections projected back spectral domain models trained speech denoising show skip connections do not necessarily improve performance regards number parameters make speech enhancement models interpretable. Highway BID7 residual networks BID1 have been proposed objective improving activation gradient flow training deep neural networks. hand tasks like image reconstruction speech enhancement use skip connections serves different purpose:if we model corrupted signalx+n addition noisen clean signal x is the input neural network know task hand is to predictn. words predict have alter inputx subtracting n.In speech enhancement two commonly used approaches are spectral subtraction spectral masking. first statistical model n is used predict magnitude spectrumN which is then subtracted input spectrumX yield clean magnitude spectrum estimateŶ. spectral masking instead performing subtraction find multiplicative mask which aims either blocking time-frequency cells dominated noise case binary masks scaling energies time-frequency cells make match original clean signal. Recent work speech enhancement has explored skip connections way performing masking BID4 spectral estimation BID6. Time domain approaches SEGAN BID5 use UNet-style network which employs multiple skip connections well. works BID12 perform spectral masking Figure1:Diagrams highway residual masking blocks used paper learn how to estimate ideal mask instead masking mechanism embedded neural network skip connection.For better understanding models would like understand whether are any parallels connections two traditional DSP approaches speech enhancement namely spectral subtraction spectral masking. also want understand whether models using skip connections perform better enhancement when such connections appear resembling DSP counterparts repeated multiple blocks like highway residual networks paper shows early results investigation role skip connections speech enhancement models. preliminary experiments show although have no significant impact performance models connections might help making models interpretable can identify contribution individual layer task. future intend investigate complex models models based UNet architecture well models employ temporal context window input instead single frame work BID6 since are more in line state-of-the-art models literature.,776,470,306,0.008,1.651,2025/11/05 17:19:07,0.0,1.741,1.0,264.386
"Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally efficient. With wide recognition of potential advantages, why is it that variational Bayes has seen very limited practical use for BNNs in real applications? We argue that variational inference in neural networks is fragile: successful implementations require careful initialization and tuning of prior variances, as well as controlling the variance of Monte Carlo gradient estimates. We provide two innovations that aim to turn VB into a robust inference tool for Bayesian neural networks: first, we introduce a novel deterministic method to approximate moments in neural networks, eliminating gradient variance; second, we introduce a hierarchical prior for parameters and a novel Empirical Bayes procedure for automatically selecting prior variances. Combining these two innovations, the resulting method is highly efficient and robust. On the application of heteroscedastic regression we demonstrate good predictive performance over alternative approaches. Bayesian approaches to neural network training marry the representational flexibility of deep neural networks with principled parameter estimation in probabilistic models. Compared to ""standard"" parameter estimation by maximum likelihood, the Bayesian framework promises to bring key advantages such as better uncertainty estimates on predictions and automatic model regularization (MacKay, 1992; Graves, 2011) . These features are often crucial for informing downstream decision tasks and reducing overfitting, particularly on small datasets. However, despite potential advantages, such Bayesian neural networks (BNNs) are often overlooked due to two limitations: First, posterior inference in deep neural networks is analytically intractable and approximate inference with Monte Carlo (MC) techniques can suffer from crippling variance given only a reasonable computation budget (Kingma et al., 2015; Molchanov et al., 2017; Miller et al., 2017; BID8 . Second, performance of the Bayesian approach is sensitive to the choice of prior BID1 , and although we may have a priori knowledge concerning the function represented by a neural network, it is generally difficult to translate this into a meaningful prior on neural network weights. Sensitivity to priors and initialization makes BNNs non-robust and thus often irrelevant in practice.In this paper, we describe a novel approach for inference in feed-forward BNNs that is simple to implement and aims to solve these two limitations. We adopt the paradigm of variational Bayes (VB) for BNNs (Hinton & van Camp, 1993; MacKay, 1995c) which is normally deployed using Monte Carlo variational inference (MCVI) (Graves, 2011; Blundell et al., 2015) . Within this paradigm we address the two shortcomings of current practice outlined above: First, we address the issue of high variance in MCVI, by reducing this variance to zero through novel deterministic approximations to variational inference in neural networks. Second, we derive a general and robust Empirical Bayes (EB) approach to prior choice using hierarchical priors. By exploiting conjugacy we derive data-adaptive closed-form variance priors for neural network weights, which we experimentally demonstrate to be remarkably effective.Combining these two novel ingredients gives us a performant and robust BNN inference scheme that we refer to as ""deterministic variational inference"" (DVI). We demonstrate robustness and improved predictive performance in the context of non-linear regression models, deriving novel closed-form results for expected log-likelihoods in homoscedastic and heteroscedastic regression (similar derivations for classification can be found in the appendix).Experiments on standard regression datasets from the UCI repository, (Dheeru & Karra Taniskidou, 2017) , show that for identical models DVI converges to local optima with better predictive loglikelihoods than existing methods based on MCVI. In direct comparisons , we show that our Empirical Bayes formulation automatically provides better or comparable test performance than manual tuning of the prior and that heteroscedastic models consistently outperform the homoscedastic models.Concretely, our contributions are:• Development of a deterministic procedure for propagating uncertain activations through neural networks with uncertain weights and ReLU or Heaviside activation functions.• Development of an EB method for principled tuning of weight priors during BNN training.• Experimental results showing the accuracy and efficiency of our method and applicability to heteroscedastic and homoscedastic regression on real datasets. We introduced two innovations to make variational inference for neural networks more robust: 1. an effective deterministic approximation to the moments of activations of a neural networks; and 2. a simple empirical Bayes hyperparameter update. We demonstrate that together these innovations make variational Bayes a competitive method for Bayesian inference in neural heteroscedastic regression models.Bayesian neural networks have been shown to substantially improve upon standard networks in these settings where calibrated predictive uncertainty estimates, sequential decision making, or continual learning without catastrophic forgetting are required (see e.g. BID3 Gal et al. (2017) ; Nguyen et al. FORMULA0 ). In future work, the new innovations proposed in this paper can be applied to these areas. In the sequential decision making and continual learning applications, approximate Bayesian inference must be run as an inner loop of a larger algorithm. This requires a robust and automated version of BNN training: this is precisely where we believe the innovations in this paper will have large impact since they pave the way to automated and robust deployment of BBNs that do not involve an expert in-the-loop.",Bayesian neural networks BNNs hold great promise flexible principled solution deal uncertainty when learning finite data. Among approaches realize probabilistic inference deep neural networks why is it variational Bayes VB is theoretically grounded is generally applicable computationally efficient. wide recognition potential advantages whyisit variational Bayes has seen limited practical use BNNs real applications? argue variational inference neural networks is fragile:successful implementations require careful initialization tuning prior variances well controlling variance Monte Carlo gradient estimates. provide two innovations aim turnVB robust inference tool Bayesian neural networks:first introduce novel deterministic method approximate moments neural networks eliminating gradient variance;second introduce hierarchical prior parameters novel Empirical Bayes procedure automatically selecting prior variances. Combining two innovations resulting method is highly efficient robust. application heteroscedastic regression demonstrate good predictive performance alternative approaches. Bayesian approaches neural network training marry representational flexibility deep neural networks principled parameter estimation probabilistic models. Compared standard parameter estimation maximum likelihood Bayesian framework promises bring key advantages better uncertainty estimates predictions automatic model regularization MacKay 1992;Graves 2011 features are often crucial informing downstream decision tasks reducing overfitting particularly small datasets. However despite potential advantages Bayesian neural networks BNNs are often overlooked due two limitations:First posterior inference deep neural networks is analytically intractable approximate inference Monte Carlo MC techniques can suffer crippling variance given reasonable computation budget Kingmaetal. 2015;Molchanovetal. 2017;Milleretal. 2017;BID8. Second performance Bayesian approach is sensitive choice prior BID1 although may have a priori knowledge concerning function represented neural network is generally difficult translate meaningful prior neural network weights. Sensitivity priors initialization makes BNNs non-robust thus often irrelevant practice.In paper describe novel approach inference feed-forward BNNs is simple implement aims solve two limitations. adopt paradigm variational Bayes VB BNNs Hinton van Camp 1993;MacKay 1995c which is normally deployed using Monte Carlo variational inference MCVI Graves 2011;Blundelletal. 2015 Within paradigm address two shortcomings current practice outlined above:First address issue high variance MCVI reducing variance zero novel deterministic approximations variational inference neural networks. Second derive general robust Empirical Bayes EB approach prior choice using hierarchical priors. exploiting conjugacy derive data-adaptive closed-form variance priors neural network weights which we experimentally demonstrate remarkably effective.Combining two novel ingredients gives us performant robust BNN inference scheme refer deterministic variational inference DVI demonstrate robustness improved predictive performance context non-linear regression models deriving novel closed-form results expected log-likelihoods homoscedastic heteroscedastic regression similar derivations classification can be found appendix.Experiments standard regression datasets UCI repository Dheeru Karra Taniskidou 2017 show identical models DVI converges local optima better predictive loglikelihoods existing methods based MCVI. direct comparisons show Empirical Bayes formulation automatically provides better comparable test performance manual tuning prior heteroscedastic models consistently outperform homoscedastic models.Concretely contributions are:• Development deterministic procedure propagating uncertain activations neural networks uncertain weights ReLU Heaviside activation functions.• Development EB method principled tuning weight priors BNN training.• Experimental results showing accuracy efficiency method applicability heteroscedastic homoscedastic regression real datasets. introduced two innovations make variational inference neural networks robust:1. effective deterministic approximation moments activations neural networks;2. simple empirical Bayes hyperparameter update. demonstrate together innovations make variational Bayes competitive method Bayesian inference neural heteroscedastic regression models.Bayesian neural networks have been shown substantially improve upon standard networks settings where calibrated predictive uncertainty estimates sequential decision making continual learning without catastrophic forgetting are required see e.g BID3 Galetal. 2017 Nguyenetal. FORMULA0 future work new innovations proposed paper can be applied areas. sequential decision making continual learning applications approximate Bayesian inference must run inner loop larger algorithm. requires robust automated version BNN training:is precisely where we believe innovations paper will have large impact since pave way automated robust deployment BBNs do not involve expert in-the-loop,1153,831,322,0.011,1.387,2025/11/05 17:19:07,0.0,1.44,0.1775700934579437,332.898
"Skills learned through (deep) reinforcement learning often generalizes poorly
 across tasks and re-training is necessary when presented with a new task. We
 present a framework that combines techniques in formal methods with reinforcement
 learning (RL) that allows for the convenient specification of complex temporal
 dependent tasks with logical expressions and construction of new skills from existing
 ones with no additional exploration. We provide theoretical results for our
 composition technique and evaluate on a simple grid world simulation as well as
 a robotic manipulation task. Policies learned using reinforcement learning aim to maximize the given reward function and are often difficult to transfer to other problem domains. Skill composition is the process of constructing new skills out of existing ones (policies) with little to no additional learning. In stochastic optimal control, this idea has been adopted by BID20 and BID9 to construct provably optimal control laws based on linearly solvable Markov decision processes.Temporal logic (TL) is a formal language commonly used in software and digital circuit verification BID7 as well as formal synthesis BID8 . It allows for convenient expression of complex behaviors and causal relationships. TL has been used by BID19 , BID11 , BID10 to synthesize provably correct control policies. BID6 have also combined TL with Q-learning to learn satisfiable policies in discrete state and action spaces.We make the distinction between skill composition and multi-task learning/meta-learning where the latter often requires a predefined set of tasks/task distributions to learn and generalize from, whereas the focus of the former is to construct new policies from a library of already learned policies that achieve new tasks (often some combination of the constituent tasks) with little to no additional constraints on task distribution at learning time. In this work, we focus on skill composition with policies learned using automata guided reinforcement learning BID15 . We adopt the syntactically co-safe truncated linear temporal logic (scTLTL) as the task specification language. Compared to most heuristic reward structures used in the RL literature, formal specification language has the advantage of semantic rigor and interpretability.In our framework, skill composition is accomplished by taking the product of finite state automata (FSA). Instead of interpolating/extrapolating among learned skills/latent features, our method is based on graph manipulation of the FSA. Therefore, the outcome is much more transparent. Compared with previous work on skill composition, we impose no constraints on the policy representation or the problem class. We validate our framework in simulation (discrete state and action spaces) and experimentally on a Baxter robot (continuous state and action spaces). In FIG6 (left), we report the discounted return as a function of policy update steps for task φ ∧ . 5 evaluation episodes are collected after each set policy updates to calculate the performance statistics. As comparison, we learn the same task using SQL with FSA augmented MDP. We can see that our composition method takes less update steps to reach a policy that achieves higher returns with lower variance than the policy obtained from learning. FIG6 (right) shows the episode length as a function of policy update (upper bound clipped at 100 steps). As mentioned in the previous section, a shorter episode length indicates faster accomplishment of the task. It can be observed that both the composition and learning method result in high variances likely due to the randomized task configuration (some plate/joint/hand configurations make the task easier to accomplish than others). However, the policy obtained from composition achieves a noticeable decrease in the average episode length.It is important to note that the wall time for learning a policy is significantly longer than that from composition. For robotic tasks with relatively simple policy representations (feed-forward neural networks), learning time is dominated by the time used to collect experiences and the average episode length (recall that we update the policy 100 times with each 5 episodes of exploration). Since skill composition uses already collected experience, obtaining a policy can be much faster. TAB1 shows the mean training time and standard deviation (over 5 random seeds) for each task (tasks φ traverse , φ interrupt and φ ∧ (learned) are trained for 80K policy updates. φ ∧ (composed) is trained for 40K policy updates). In general, training time is shorter for tasks with higher episodic success rate and shorter episode length. We also show the task success rate evaluated on the real robot over 20 evaluation trials. Task success is evaluated by calculating the robustness of the trajectories resulting from executing each policy. A robustness of greater than 0 evaluates to success and vice versa. π φ∧ (learned) fails to complete the task even though a convergence is reached during training. This is likely due to the large FSA of φ ∧ with complex per-step reward (D q φ in Equation FORMULA15 ) which makes learning difficult. FIG5 shows an evaluation run of the composed policy for task φ ∧ . We provide a technique that takes advantage of the product of finite state automata to perform deterministic skill composition. Our method is able to synthesize optimal composite policies for −AN D− and −OR− tasks. We provide theoretical results on our method and show its effectiveness on a grid world simulation and a real world robotic task. For future work, we will adapt our method to the more general case of task-space transfer -given a library of optimal policies (Qfunctions) that each satisfies its own specification, construct a policy that satisfies a specification that's an arbitrary (temporal) logical combination of the constituent specifications.",Skills learned deep reinforcement learning often generalizes poorly across tasks re-training is necessary when presented new task. present framework combines techniques formal methods reinforcement learning RL allows convenient specification complex temporal dependent tasks logical expressions construction new skills existing ones additional exploration. provide theoretical results composition technique evaluate simple grid world simulation well robotic manipulation task. Policies learned using reinforcement learning aim maximize given reward function are often difficult transfer problem domains. Skill composition is the process constructing new skills existing ones policies little additional learning. stochastic optimal control idea has been adopted BID20 BID9 construct provably optimal control laws based linearly solvable Markov decision processes.Temporal logic TL is a formal language commonly used software digital circuit verification BID7 well formal synthesis BID8. allows convenient expression complex behaviors causal relationships. TL has been used BID19 BID11 BID10 synthesize provably correct control policies. BID6 have also combinedTL Q-learning learn satisfiable policies discrete state action spaces.We make distinction skill composition multi-task learning/meta-learning where the latter often requires predefined set tasks/task distributions learn generalize whereas focus former is to construct new policies library already learned policies achieve new tasks often combination constituent tasks little additional constraints task distribution learning time. work focus skill composition policies learned using automata guided reinforcement learning BID15. adopt syntactically co-safe truncated linear temporal logic scTLTL task specification language. Compared heuristic reward structures used RL literature formal specification language has the advantage semantic rigor interpretability.In framework skill composition is accomplished taking product finite state automata FSA Instead interpolating/extrapolating among learned skills/latent features method is based graph manipulation FSA. Therefore outcome is much transparent. Compared previous work skill composition impose constraints policy representation problem class. validate framework simulation discrete state action spaces experimentally Baxter robot continuous state action spaces FIG6 left report discounted return function policy update steps taskφ∧5 evaluation episodes are collected set policy updates calculate performance statistics. comparison learn task using SQL FSA augmented MDP. can see composition method takes less update steps reach policy achieves higher returns lower variance policy obtained learning. FIG6 right shows episode length function policy update upper bound clipped 100 steps mentioned previous section shorter episode length indicates faster accomplishment task. can be observed composition learning method result high variances likely due randomized task configuration plate/joint/hand configurations make task easier accomplish others However policy obtained composition achieves noticeable decrease average episode length.It is important note wall time learning policy is significantly longer composition. robotic tasks relatively simple policy representations feed-forward neural networks learning time is dominated time used collect experiences average episode length recall update policy 100 times 5 episodes exploration Since skill composition uses already collected experience obtaining policy can be much faster. TAB1 shows mean training time standard deviation 5 random seeds task tasks φ traverse φ interrupt φ∧ learned are is trained 80K policy updates. φ∧ composed are is trained 40K policy updates general training time is shorter tasks higher episodic success rate shorter episode length. also show task success rate evaluated real robot 20 evaluation trials. Task success is evaluated calculating robustness trajectories resulting executing policy. robustness greater 0 evaluates success vice versa. πφ∧ learned fails complete task even though convergence is reached training. is likely due large FSA φ∧ complex per-step reward qφ Equation FORMULA15 which makes learning difficult. FIG5 shows evaluation run composed policy taskφ∧ provide technique takes advantage product finite state automata perform deterministic skill composition. method is able synthesize optimal composite policies −AND− −OR− tasks. provide theoretical results method show effectiveness grid world simulation real world robotic task. future work will adapt method general case task-space transfer -given library optimal policies Qfunctions satisfies specification construct policy satisfies specification that's arbitrary temporal logical combination constituent specifications.,1104,741,363,0.011,1.49,2025/11/05 17:19:07,0.01,1.3,0.4984423676012459,342.052
"The application of multi-modal generative models by means of a Variational Auto Encoder (VAE) is an upcoming research topic for sensor fusion and bi-directional modality exchange.
 This contribution gives insights into the learned joint latent representation and shows that expressiveness and coherence are decisive properties for multi-modal datasets.
 Furthermore, we propose a multi-modal VAE derived from the full joint marginal log-likelihood that is able to learn the most meaningful representation for ambiguous observations.
 Since the properties of multi-modal sensor setups are essential for our approach but hardly available, we also propose a technique to generate correlated datasets from uni-modal ones.
 Auto Encoder (AE), Variational Auto Encoder (VAE), and more recently Disentangled Variational Auto Encoder (β-VAE) have a considerable impact on the field of data-driven leaning of generative models. Furthermore, recent investigations have shown the fruitful applicability to deep reinforcement learning (DRL) as well as bi-directionally exchange of multi-modal data. VAEs tend to encode the data into latent space features that are (ideally) linearly separable as shown by BID4 . They also allow the discovery of generative joint models (e.g. BID17 ), as well as zero-shot domain transfer in DRL as shown by BID5 .However , a good generative model should not just generate good data and achieve a good quantitative score, but also gives a coherent and expressive latent space representation. This property is decisive for multi-modal approaches if the data shows correlation, as it is the case for every sensor setup designed for sensor fusion. With this contribution , we investigate the characteristic of the latent space as well as the quantitative features for existing multi-modal VAEs. Furthermore, we propose a novel approach to build and train a novel multi-modal VAE (M 2 VAE) which comprises the complete marginal joint log-likelihood without simplifying assumptions. As our objective is the consideration of raw multi-modal sensor data, we also propose an approach to generate correlated multi-modal datasets from available uni-modal ones. Lastly, we draw connections to in-place sensor fusion and epistemic (ambiguity-resolving) active-sensing.Section 2 comprises the related work on multi-modal VAEs. Our comprehensive approach (i.e. M 2 VAE) is given in Sec. 3. Furthermore, we describe multi-modal datasets as well as the generation of correlated sets in Sec. 4 which are evaluated in Sec. 5. Finally, we conclude our work in Sec. 6. This work presents a novel multi-modal Variational Auto Encoder which is derived from the complete marginal joint log-likelihood. We showed that this expression can jointly be trained on an Mixture-of-Gaussian dataset with ambiguous observations, as well as on a complex dataset derived from MNIST and fashion-MNIST. Furthermore, we formulated requirements and characteristics for multi-modal data for sensor fusion and derived a technique to learn new datasets, namely the proposed entangled-MNIST, which suffice these requirements. Lastly, we developed the idea of in-place sensor fusion in distributed, active sensing scenarios and formulated the requirements, by means of auto re-encoding, to VAEs. This revealed the properties of VAEs, that they tend to denoise the observable data which leads to an attractor behavior in latent space. However, we performed all qualitative evaluations of the latent space with the premise in mind, that a good generative model should not just generate good data but also gives a good latent representation. This does also correlate with the quantitative behaviors, as our proposed model achieved the highest ELBO values. Future work will concentrate on the integration of the ambiguous resolving characteristics to an epistemic-exploration scenario.",application multi-modal generative models means Variational Auto Encoder VAE is an upcoming research topic sensor fusion bi-directional modality exchange. contribution gives insights learned joint latent representation shows expressiveness coherence are decisive properties multi-modal datasets. Furthermore propose multi-modal VAE derived full joint marginal log-likelihood is able learn meaningful representation ambiguous observations. Since properties multi-modal sensor setups are essential approach hardly available also propose technique generate correlated datasets uni-modal ones. Auto Encoder AE Variational Auto Encoder VAE recently Disentangled Variational Auto Encoder β-VAE have a considerable impact field data-driven leaning generative models. Furthermore recent investigations have shown fruitful applicability deep reinforcement learning DRL well bi-directionally exchange multi-modal data. VAEs tend encode data latent space features are(ideally linearly separable shown BID4. also allow discovery generative joint models e.g BID17 well zero-shot domain transfer DRL shown BID5.However good generative model should not just generate good data achieve good quantitative score also gives coherent expressive latent space representation. property is decisive multi-modal approaches if the data shows correlation is case every sensor setup designed sensor fusion. contribution investigate characteristic latent space well quantitative features existing multi-modal VAEs. Furthermore propose novel approach build train novel multi-modal VAE 2 VAE which comprises complete marginal joint log-likelihood without simplifying assumptions. objective is the consideration raw multi-modal sensor data also propose approach generate correlated multi-modal datasets available uni-modal ones. Lastly draw connections in-place sensor fusion epistemic ambiguity-resolving active-sensing.Section 2 comprises related work multi-modal VAEs. comprehensive approach.e 2 VAE is given Sec. 3. Furthermore describe multi-modal datasets well generation correlated sets Sec. 4 which are evaluated Sec. 5. Finally conclude work Sec. 6. work presents novel multi-modal Variational Auto Encoder which is derived complete marginal joint log-likelihood showed expression can jointly trained Mixture-of-Gaussian dataset ambiguous observations well complex dataset derived MNIST fashion-MNIST Furthermore formulated requirements characteristics multi-modal data sensor fusion derived technique learn new datasets namely proposed entangled-MNIST which suffice requirements. Lastly developed idea in-place sensor fusion distributed active sensing scenarios formulated requirements means auto re-encoding VAEs. revealed properties VAEs tend denoise observable data which leads attractor behavior latent space. However performed qualitative evaluations latent space premise mind good generative model should not just generate good data also gives good latent representation. does also correlate quantitative behaviors proposed model achieved highest ELBO values. Future work will concentrate integration ambiguous resolving characteristics epistemic-exploration scenario.,743,514,229,0.007,1.446,2025/11/05 17:19:07,0.0,1.429,0.3613707165109031,263.51
"We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies on the efficiency of sequential Monte Carlo (SMC) for performing inference in structured probabilistic models and the flexibility of deep neural networks to model complex conditional probability distributions. We develop additional theoretical insights and introduce a new training procedure which improves both model and proposal learning. We demonstrate that our approach provides a fast, easy-to-implement and scalable means for simultaneous model learning and proposal adaptation in deep generative models. We build upon AESMC , a method for model learning that itself builds on variational auto-encoders (VAEs) BID4 BID10 and importance weighted auto-encoders (IWAEs) BID0 . AESMC is similarly based on maximizing a lower bound to the log marginal likelihood, but uses SMC BID3 as the underlying marginal likelihood estimator instead of importance sampling (IS). For a very wide array of models, particularly those with sequential structure, SMC forms a substantially more powerful inference method than IS, typically returning lower variance estimates for the marginal likelihood. Consequently, by using SMC for its marginal likelihood estimation, AESMC often leads to improvements in model learning compared with VAEs and IWAEs. We provide experiments on structured time-series data that show that AESMC based learning was able to learn useful representations of the latent space for both reconstruction and prediction more effectively than the IWAE counterpart.AESMC was introduced in an earlier preprint concurrently with the closely related methods of ; BID7 . In this work we take these ideas further by providing new theoretical insights for the resulting evidence lower bounds (ELBOs), extending these to explore the relative efficiency of different approaches to proposal learning, and using our results to develop a new and improved training procedure. In particular, we introduce a method for expressing the gap between an ELBO and the log marginal likelihood as a Kullback-Leibler (KL) divergence between two distributions on an extended sampling space. Doing so allows us to investigate the behavior of this family of algorithms when the objective is maximized perfectly, which occurs only if the KL divergence becomes zero. In the IWAE case, this implies that the proposal distributions are equal to the posterior distributions under the learned model. In the AESMC case, it has implications for both the proposal distributions and the intermediate set of targets that are learned. We demonstrate that, somewhat counter-intuitively, using lower variance estimates for the marginal likelihood can actually be harmful to proposal learning. Using these insights, we experiment with an adaptation to the AESMC algorithm, which we call alternating ELBOs, that uses different lower bounds for updating the model parameters and proposal parameters. We observe that this adaptation can, in some cases, improve model learning and proposal adaptation. We have developed AESMC-a method for performing model learning using a new ELBO objective which is based on the SMC marginal likelihood estimator. This ELBO objective is optimized using SGA and the reparameterization trick. Our approach utilizes the efficiency of SMC in models with intermediate observations and hence is suitable for highly structured models. We experimentally demonstrated that this objective leads to better generative model training than the IWAE objective for structured problems, due to the superior inference and tighter bound provided by using SMC instead of importance sampling.Additionally, in Claim 1, we provide a simple way to express the bias of objectives induced by log of marginal likelihood estimators as a KL divergence on an extended space. In Propositions 1 and 2, we investigate the implications of these KLs being zero in the case of IWAE and AESMC. In the latter case, we find that we can achieve zero KL only if we are able to learn SMC intermediate target distributions corresponding to marginals of the target distribution. Using our assertion that tighter variational bounds are not necessarily better, we then introduce and test a new method, alternating ELBOs, that addresses some of these issues and observe that, in some cases, this improves both model and proposal learning.","build auto-encoding sequential Monte Carlo AESMC method model proposal learning based maximizing lower bound log marginal likelihood broad family structured probabilistic models. approach relies efficiency sequential Monte Carlo SMC performing inference structured probabilistic models flexibility deep neural networks model complex conditional probability distributions. develop additional theoretical insights introduce new training procedure which improves model proposal learning. demonstrate approach provides fast easy-to-implement scalable means simultaneous model learning proposal adaptation deep generative models. build upon AESMC method model learning builds variational auto-encoders VAEs BID4 BID10 importance weighted auto-encoders IWAEs BID0. AESMC is similarly based maximizing lower bound log marginal likelihood uses SMC BID3 underlying marginal likelihood estimator instead importance sampling IS). wide array models particularly sequential structure SMC forms substantially powerful inference method IS,typically returning lower variance estimates marginal likelihood. Consequently using SMC marginal likelihood estimation AESMC often leads improvements model learning compared VAEs IWAEs. provide experiments structured time-series data show AESMC based learning was able learn useful representations latent space reconstruction prediction effectively IWAE counterpart.AESMC was introduced earlier preprint concurrently closely related methods of;BID7. work take ideas providing new theoretical insights resulting evidence lower bounds ELBOs extending explore relative efficiency different approaches proposal learning using results develop new improved training procedure. particular introduce method expressing gap ELBO log marginal likelihood Kullback-Leibler KL divergence two distributions extended sampling space. allowsus investigate behavior family algorithms when the objective is maximized perfectly which occurs if the KL divergence becomes zero. IWAE case implies proposal distributions are equal posterior distributions learned model. AESMC case has implications proposal distributions intermediate set targets are learned. demonstrate somewhat counter-intuitively using lower variance estimates marginal likelihood can actually harmful proposal learning. Using insights experiment adaptation AESMC algorithm which we call alternating ELBOs uses different lower bounds updating model parameters proposal parameters. observe adaptation can,in some cases improve model learning proposal adaptation. have developed AESMC-a method performing model learning using new ELBO objective which is based SMC marginal likelihood estimator. ELBO objective is optimized using SGA reparameterization trick. approach utilizes efficiency SMC models intermediate observations hence is suitable highly structured models. experimentally demonstrated objective leads better generative model training IWAE objective structured problems due superior inference tighter bound provided using SMC instead importance sampling.Additionally Claim1 provide simple way express bias objectives induced log marginal likelihood estimators KL divergence extended space. Propositions1 2 investigate implications KLs zero case IWAE AESMC. latter case find can achieve zeroKL if we are able learn SMC intermediate target distributions corresponding marginals target distribution. Using assertion tighter variational bounds are not necessarily better introduce test new method alternating ELBOs addresses issues observe cases improves model proposal learning.",832,548,284,0.008,1.518,2025/11/05 17:19:07,0.0,1.565,0.585669781931464,284.825
"A key component for many reinforcement learning agents is to learn a value function, either for policy evaluation or control. Many of the algorithms for learning values, however, are designed for linear function approximation---with a fixed basis or fixed representation. Though there have been a few sound extensions to nonlinear function approximation, such as nonlinear gradient temporal difference learning, these methods have largely not been adopted, eschewed in favour of simpler but not sound methods like temporal difference learning and Q-learning. In this work, we provide a two-timescale network (TTN) architecture that enables linear methods to be used to learn values, with a nonlinear representation learned at a slower timescale. The approach facilitates the use of algorithms developed for the linear setting, such as data-efficient least-squares methods, eligibility traces and the myriad of recently developed linear policy evaluation algorithms, to provide nonlinear value estimates. We prove convergence for TTNs, with particular care given to ensure convergence of the fast linear component under potentially dependent features provided by the learned representation. We empirically demonstrate the benefits of TTNs, compared to other nonlinear value function approximation algorithms, both for policy evaluation and control.     Value function approximation-estimating the expected returns from states for a policy-is heavily reliant on the quality of the representation of state. One strategy has been to design a basis-such as radial basis functions (Sutton and Barto, 1998) or a Fourier basis BID17 )-for use with a linear function approximator and temporal difference (TD) learning (Sutton, 1988) . For low-dimensional observation vectors, this approach has been effective, but can be onerous to extend to high-dimensional observations, potentially requiring significant domain expertise. Another strategy has been to learn the representation, such as with basis adaptation or neural networks. Though there is still the need to specify the parametric form, learning these representations alleviates the burden of expert specification. Further, it is more feasible to scale to high-dimensional observations, such as images, with neural networks (Mnih et al., 2015; BID16 . Learning representations necessitates algorithms for nonlinear function approximation.Despite the deficiencies in specification for fixed bases, linear function approximation for estimating value functions has several benefits over nonlinear estimators. They enable least-squares methods, which can be much more data-efficient for policy evaluation BID5 Szepesvari, 2010; van Seijen and Sutton, 2015) , as well as robust to meta-parameters (Pan et al., 2017) . Linear algorithms can also make use of eligibility traces, which can significantly speed learning (Sutton, 1988; BID9 White and White, 2016 ), but have not been able to be extended to nonlinear value function approximation. Additionally, there have been a variety of algorithms derived for the linear setting, both for on-policy and off-policy learning (Sutton et al., 2009; BID23 van Seijen and Sutton, 2014; van Hasselt et al., 2014; Mahadevan et al., 2014; Sutton et al., 2016; Mahmood et al., 2017) . These linear methods have also been well-explored theoretically (Tsitsiklis and Van Roy, 1997; BID23 Mahmood and Sutton, 2015; Yu, 2015) and empirically BID9 White and White, 2016) , with some insights into improvements from gradient methods (Sutton et al., 2009 ), true-online traces (van Seijen and Sutton, 2014) and emphatic weightings (Sutton et al., 2016) . These algorithms are easy to implement, with relatively simple objectives. Objectives for nonlinear value function approximation, on the other hand, can be quite complex (Maei et al., 2009) , resulting in more complex algorithms (Menache et al., 2005; BID10 BID2 or requiring a primal-dual formulation as has been done for control BID8 .In this work, we pursue a simple strategy to take advantage of the benefits of linear methods, while still learning the representation. The main idea is to run two learning processes in parallel: the first learns nonlinear features using a surrogate loss and the second estimates the value function as a linear function of those features. We show that these Two-timescale Networks (TTNs) converge, because the features change on a sufficiently slow scale, so that they are effectively fixed for the fast linear value function estimator. Similar ideas have previously been explored for basis adaptation, but without this key aspect of TTNs-namely the separation of the loss for the representation and value function. This separation is critical because it enables simpler objectives-for which the gradient can be easily sampled-to drive the representation, but still enables use of the mean squared projected Bellman error (MSPBE)-on which all the above linear algorithms are based. This separation avoids the complexity of the nonlinear MSPBE, but maintains the useful properties of the (linear) MSPBE. A variety of basis adaptation approaches have used a two-timescale approach, but with the same objective for the representation and the values (Menache et al., 2005; BID10 BID2 . Yu and Bertsekas ( 2009) provided algorithms for basis adaptation using other losses, such as Bellman error using Monte carlo samples, taking derivatives through fixed point solutions for the value function. BID21 periodically compute a closed form least-squares solution for the last layer of neural network, with a Bayesian update to prevent too much change. Because these methods did not separate the value learn and basis adaptation, the resulting algorithms are more complex. The strategy of using two different heads-one to drive the representation and one to learn the values-has yet to be systematically explored.We show that TTNs are a promising direction for nonlinear function approximation, allowing us to leverage linear algorithms while retaining the flexibility of nonlinear function approximators. We first discuss a variety of possible surrogate losses, and their potential for learning a useful representation. We then show that TTNs converge , despite the fact that a linear algorithm is used with a changing representation. This proof is similar to previous convergence proofs for policy evaluation, but with a relaxation on the requirement that features be independent, which is unlikely for learned features. We then show empirically that TTNs are effective compared to other nonlinear value function approximations and that they can exploit several benefits of linear value approximations algorithms. In particular, for both low-dimensional and high-dimensional (image-based) observations, we show (a) the utility of least-squares (or batch ) methods, (b) advantages from eligibility traces and (c) gains from being able to select amongst different linear policy evaluation algorithms. We demonstrate that TTNs can be effective for control with neural networks, enabling use of fitted Q-iteration within TTNs as an alternative to target networks. In this work, we proposed Two-timescale Networks as a new strategy for policy evaluation with nonlinear function approximation. As opposed to many other algorithms derived for nonlinear value function approximation, TTNs are intentionally designed to be simple to promote ease-of-use. The algorithm combines a slow learning process for adapting features and a fast process for learning a linear value function, both of which are straightforward to train. By leveraging these two timescales, we are able to prove convergence guarantees for a broad class of choices for both the fast and slow learning components. We highlighted several cases where the decoupled architecture in TTNs can improve learning, particularly enabling the use of linear methods-which facilitates use of least-squares methods and eligibility traces.This work has only begun the investigation into which combinations for surrogate losses and linear value function approximation algorithms are most effective. We provided some evidence that, when using stochastic approximation algorithms rather than least-squares algorithms, the addition of traces can have a significant effect within TTNs. This contrasts nonlinear TD, where traces were not effective. The ability to use traces is potentially one of the most exciting outcomes for TTNs, since traces have been so effective for linear methods. More generally, TTNs provide the opportunity to investigate the utility of the many linear value function algorithms, in more complex domains with learned representations. For example, emphatic algorithms have improved asymptotic properties (Sutton et al., 2016) , but to the best of our knowledge, have not been used with neural networks.Another promising direction for TTNs is for off-policy learning, where many value functions are learned in parallel. Off-policy learning can suffer from variance due to large magnitude corrections (importance sampling ratios). With a large collection of value functions, it is more likely that some of them will cause large updates, potentially destabilizing learning in the network if trained in an end-to-end fashion. TTNs would not suffer from this problem, because a different objective can be used to drive learning in the network. We provide some preliminary experiments in the appendix supporting this hypothesis (Appendix C.7). θ,w ← GradientDescent on L slow using sample (s, r, s ) DISPLAYFORM0 w ← Update on L value using sample (s, r, s )8: DISPLAYFORM1 end while 10:return learned parameters w, θ,w 11: end procedure B CONVERGENCE PROOF OF TWO-TIMESCALE NETWORKS B.1 DEFINITIONS & NOTATIONS -Let R + denote the set of non-negative real numbers, N = {0, 1, 2, . . . } and · denote the Euclidean norm or any equivalent norm. DISPLAYFORM2 3. h is upper-semicontinuous, i.e., if {x n } n∈N → x and {y n } n∈N → y, where x n ∈ R d , y n ∈ h(x n ), ∀n ∈ N, then y ∈ h(x).-For x 1 , x 2 ∈ R d and D ∈ R k×k a diagonal matrix, we define the inner-product < x 1 , x 2 > D x 1 Dx 2 . We also define the semi-norm DISPLAYFORM3 D . If all the diagonal elements of D are strictly positive, then · D is a norm.-For any set X, letX denote the interior of X and ∂X denote the boundary of X. -For brevity, letθ = (θ,w) and Φθ be the feature matrix corresponding to the feature parameterθ, i.e. DISPLAYFORM4 where x θ (s) is the row-vector corresponding to state s. Further, define the |S| × |S|-matrix P π as follows: P π s,s a∈A π(s, a)P (s, a, s ), s, s ∈ S.-Also, recall that DISPLAYFORM5 is Frechet differentiable at x ∈ U if there exists a bounded linear operator Γ x : R d1 → R d2 such that the limit DISPLAYFORM6 exists and is equal to Γ x (y). We say Γ is Frechet differentiable if Frechet derivative of Γ exists at every point in its domain.",key component many reinforcement learning agents is to learn value function either policy evaluation control. Many algorithms learning values however are designed linear function approximation -with fixed basis fixed representation. Though have beena sound extensions nonlinear function approximation nonlinear gradient temporal difference learning methods have largely adopted eschewed favour simpler sound methods like temporal difference learning Q-learning work provide two-timescale network TTN architecture enables linear methods used learn values nonlinear representation learned slower timescale. approach facilitates use algorithms developed linear setting data-efficient least-squares methods eligibility traces myriad recently developed linear policy evaluation algorithms provide nonlinear value estimates. prove convergence TTNs particular care given ensure convergence fast linear component potentially dependent features provided learned representation. empirically demonstrate benefits TTNs compared nonlinear value function approximation algorithms policy evaluation control. Value function approximation-estimating expected returns states policy-is heavily reliant quality representation state. One strategy has been to design basis-such radial basis functions Sutton Barto 1998 Fourier basis BID17 -for use linear function approximator temporal difference TD learning Sutton 1988 low-dimensional observation vectors approach has been effective can be onerous extend high-dimensional observations potentially requiring significant domain expertise. Another strategy has been to learn representation basis adaptation neural networks. Though is still need specify parametric form learning representations alleviates burden expert specification. is feasible scale high-dimensional observations images neural networks Mnihetal. 2015;BID16. Learning representations necessitates algorithms nonlinear function approximation.Despite deficiencies specification fixed bases linear function approximation estimating value functions has several benefits nonlinear estimators. enable least-squares methods which can be much data-efficient policy evaluation BID5 Szepesvari 2010;van Seijen Sutton 2015 well robust meta-parameters Panetal. 2017 Linear algorithms can also make use eligibility traces which can significantly speed learning Sutton 1988;BID9 White White 2016 have able extended nonlinear value function approximation. Additionally have been variety algorithms derived linear setting on-policy off-policy learning Suttonetal. 2009;BID23 van Seijen Sutton 2014;van Hasseltetal. 2014;Mahadevanetal. 2014;Suttonetal. 2016;Mahmoodetal. 2017 linear methods have also well-explored theoretically Tsitsiklis Van Roy 1997;BID23 Mahmood Sutton 2015;Yu 2015 empirically BID9 White White 2016 insights improvements gradient methods Suttonetal. 2009 true-online traces van Seijen Sutton 2014 emphatic weightings Suttonetal. 2016 algorithms are easy implement relatively simple objectives. Objectives nonlinear value function approximation hand can be quite complex Maeietal. 2009 resulting complex algorithms Menacheetal. 2005;BID10 BID2 requiring primal-dual formulation has been done control BID8.In work pursue simple strategy take advantage benefits linear methods still learning representation. main idea is to run two learning processes parallel:first learns nonlinear features using surrogate loss second estimates value function linear function features. show Two-timescale Networks TTNs converge features change sufficiently slow scale are effectively fixed fast linear value function estimator. Similar ideas have previously explored basis adaptation without key aspect TTNs-namely separation loss representation value function. separation is critical enables simpler objectives-for which the gradient can be easily sampled-to drive representation still enables use mean squared projected Bellman error MSPBE -on which all the above linear algorithms are based. separation avoids complexity nonlinear MSPBE maintains useful properties linear MSPBE. variety basis adaptation approaches have used two-timescale approach objective representation values Menacheetal. 2005;BID10 BID2. Yu Bertsekas 2009 provided algorithms basis adaptation using losses Bellman error using Monte carlo samples taking derivatives fixed point solutions value function. BID21 periodically compute closed form least-squares solution last layer neural network Bayesian update prevent much change. methods did not separate value learn basis adaptation resulting algorithms are more complex. strategy using two different heads-one drive representation one learn values-has yet systematically explored.We show TTNs are a promising direction nonlinear function approximation allowingus leverage linear algorithms retaining flexibility nonlinear function approximators. first discuss variety possible surrogate losses potential learning useful representation. show TTNs converge despite fact linear algorithm is used changing representation. proof is similar previous convergence proofs policy evaluation relaxation requirement features independent which is unlikely learned features. show empirically TTNs are are most effective compared nonlinear value function approximations can exploit several benefits linear value approximations algorithms. particular low-dimensional high-dimensional image-based observations show utility least-squares batch methods b advantages eligibility traces c gains able select amongst different linear policy evaluation algorithms. demonstrate TTNs can be effective control neural networks enabling use fitted Q-iteration within TTNs alternative target networks. work proposed Two-timescale Networks new strategy policy evaluation nonlinear function approximation. opposed many algorithms derived nonlinear value function approximation TTNs are intentionally designed simple promote ease-of-use algorithm combines slow learning process adapting features fast process learning linear value function which are straightforward train. leveraging two timescales are able prove convergence guarantees broad class choices fast slow learning components. highlighted several cases where the decoupled architecture TTNs can improve learning particularly enabling use linear methods-which facilitates use least-squares methods eligibility traces.This work has only begun investigation which combinations surrogate losses linear value function approximation algorithms are are most effective. provided evidence when using stochastic approximation algorithms rather least-squares algorithms addition traces can have a significant effect within TTNs. contrasts nonlinearTD where traces were not effective. ability use traces is potentially one exciting outcomes TTNs since traces have been so effective linear methods. generally TTNs provide opportunity investigate utility many linear value function algorithms complex domains learned representations. example emphatic algorithms have improved asymptotic properties Suttonetal. 2016 best knowledge have not been used neural networks.Another promising direction TTNs is for off-policy learning where many value functions are learned parallel. Off-policy learning can suffer variance due large magnitude corrections importance sampling ratios large collection value functions is more likely will cause large updates potentially destabilizing learning network if trained end-to-end fashion. TTNs would suffer problem different objective can be used drive learning network. provide preliminary experiments appendix supporting hypothesis Appendix C.7 θ w ← GradientDescent L slow using sample r DISPLAYFORM0 w ← Update L value using sample r 8:DISPLAYFORM1 end 10:return learned parametersw θ w11:end procedure B CONVERGENCE PROOF TWO-TIMESCALE NETWORKS B.1 DEFINITIONS NOTATIONS -LetR+denote set non-negative real numbers N 0 1 2 · denote Euclidean norm equivalent norm. DISPLAYFORM23. h is upper-semicontinuous.e if{xn n∈N→x n n∈N→ wherexn∈R n∈h xn ∀n∈N ∈h x.-Forx1 if{x2∈R ∈ R k×k diagonal matrix define inner-product x1 if{x2 x1Dx2. also define semi-norm DISPLAYFORM3 D. If all the diagonal elements are strictly positive · is a norm.-For setX letX denote interior X ∂X denote boundary X. -For brevity letθ θ w Φθ feature matrix corresponding feature parameterθ.e DISPLAYFORM4 wherexθ is row-vector corresponding state s. define |S| × |S|-matrixP π follows:Pπ a∈Aπ P ∈ .-Also recall DISPLAYFORM5 is Frechet differentiable x∈U if there exists bounded linear operatorΓ x:Rd1→R d2 limit DISPLAYFORM6 exists is equal Γx sayΓ is Frechet differentiable if Frechet derivative Γ exists every point domain.,2272,1551,721,0.03,1.465,2025/11/05 17:19:08,0.01,1.587,0.4205607476635514,747.865
"Large-scale Long Short-Term Memory (LSTM) cells are often the building blocks of many state-of-the-art algorithms for tasks in Natural Language Processing (NLP). However, LSTMs are known to be computationally inefficient because the memory capacity of the models depends on the number of parameters, and the inherent recurrence that models the temporal dependency is not parallelizable. In this paper, we propose simple, but effective, low-rank matrix factorization (MF) algorithms to compress network parameters and significantly speed up LSTMs with almost no loss of performance (and sometimes even gain). To show the effectiveness of our method across different tasks, we examine two settings: 1) compressing core LSTM layers in Language Models, 2) compressing biLSTM layers of ELMo~\citep{ELMo} and evaluate in three downstream NLP tasks (Sentiment Analysis, Textual Entailment, and Question Answering). The latter is particularly interesting as embeddings from large pre-trained biLSTM Language Models are often used as contextual word representations. Finally, we discover that matrix factorization performs better in general, additive recurrence is often more important than multiplicative recurrence, and we identify an interesting correlation between matrix norms and compression performance.

 Long Short-Term Memory (LSTM) networks (Hochreiter & Schmidhuber, 1997; BID11 have become the core of many models for tasks that require temporal dependency. They have particularly shown great improvements in many different NLP tasks, such as Language Modeling (Sundermeyer et al., 2012; Mikolov, 2012) , Semantic Role Labeling (He et al., 2017) , Named Entity Recognition (Lee et al., 2017) , Machine Translation BID0 , and Question Answering (Seo et al., 2016) . Recently, a bidirectional LSTM has been used to train deep contextualized Embeddings from Language Models (ELMo) (Peters et al., 2018a) , and has become a main component of state-of-the-art models in many downstream NLP tasks.However, there is an obvious drawback of scalability that accompanies these excellent performances, not only in training time but also during inference time. This shortcoming can be attributed to two factors: the temporal dependency in the computational graph, and the large number of parameters for each weight matrix. The former problem is an intrinsic nature of RNNs that arises while modeling temporal dependency, and the latter is often deemed necessary to achieve better generalizability of the model (Hochreiter & Schmidhuber, 1997; BID11 . On the other hand, despite such belief that the LSTM memory capacity is proportional to model size, several recent results have empirically proven the contrary, claiming that LSTMs are indeed over-parameterized BID4 James Bradbury & Socher, 2017; Merity et al., 2018; Melis et al., 2018; Levy et al., 2018) . Naturally, such results motivate us to search for the most effective compression method for LSTMs in terms of performance, time, and practicality, to cope with the aforementioned issue of scalability. There have been many solutions proposed to compress such large, over-parameterized neural networks including parameter pruning and sharing BID12 Huang et al., 2018) , low-rank Matrix Factorization (MF) (Jaderberg et al., 2014) , and knowledge distillation (Hinton et al., 2015) . However, most of these approaches have been applied to Feed-forward Neural Networks and Convolutional Neural Networks (CNNs), while only a small attention has been given to compressing LSTM architectures (Lu et al., 2016; BID1 , and even less in NLP tasks. Notably, See et al. (2016) applied parameter pruning to standard Seq2Seq (Sutskever et al., 2014) architecture in Neural Machine Translation, which uses LSTMs for both encoder and decoder. Furthermore, in language modeling, BID13 uses Tensor-Train Decomposition (Oseledets, 2011 BID18 uses binarization techniques, and Kuchaiev & Ginsburg (2017) uses an architectural change to approximate low-rank factorization.All of the above mentioned works require some form of training or retraining step. For instance, Kuchaiev & Ginsburg (2017) requires to be trained completely from scratch, as well as distillation based compression techniques (Hinton et al., 2015) . In addition, pruning techniques (See et al., 2016) often accompany selective retraining steps to achieve optimal performance. However, in scenarios involving large pre-trained models, e.g. ELMo (Peters et al., 2018a) , retraining can be very expensive in terms of time and resources. Moreover, compression methods are normally applied to large and over-parameterized networks, but this is not necessarily the case in our paper. We consider strongly tuned and regularized state-of-the-art models in their respective tasks, which often already have very compact representations. These circumstances make the compression much more challenging, but more realistic and practically useful.In this work, we advocate low-rank matrix factorization as an effective post-processing compression method for LSTMs which achieve good performance with guaranteed minimum algorithmic speed compared to other existing techniques. We summarize our contributions as the following:• We thoroughly explore the limits of several different compression methods (matrix factorization and pruning), including fine-tuning after compression, in Language Modeling, Sentiment Analysis, Textual Entailment, and Question Answering.• We consistently achieve an average of 1.5x (50% faster) speedup inference time while losing ∼1 point in evaluation metric across all datasets by compressing additive and/or multiplicative recurrences in the LSTM gates.• In PTB, by further fine-tuning very compressed models (∼98%) obtained with both matrix factorization and pruning, we can achieve ∼2x (200% faster) speedup inference time while even slightly improving the performance of the uncompressed baseline.• We discover that matrix factorization performs better in general, additive recurrence is often more important than multiplicative recurrence, and we identify clear and interesting correlations between matrix norms and compression performance. In conclusion, we exhaustively explored the limits of compressing LSTM gates using low-rank matrix factorization and pruning in four different NLP tasks. Our experiment results and norm analysis show that show that Low-Rank Matrix Factorization works better in general than pruning, but if the matrix is particularly sparse, Pruning works better. We also discover that inherent low-rankness and low nuclear norm correlate well, explaining why compressing multiplicative recurrence works better than compressing additive recurrence. In future works, we plan to factorize all LSTMs in the model, e.g. BiDAF model, and try to combine both Pruning and Matrix Factorization. In this section, we provide the semi-NMF algorithm and we elaborate the optimization and the aim of each step. This algorithm is an extension of NMF, where the data matrix is remained unconstrained BID7 . The original NMF optimization function shows in 8. Semi-NMF ignores the constraint in U as showed in 9. DISPLAYFORM0 Exploring the relationships between matrix factorization and K-means clustering has implications for the interpretability of matrix factors Ding et al. FORMULA0 1. Initialize U and run k-means clustering Hartigan & Wong (1979) . DISPLAYFORM1 The objective function of k-means clustering DISPLAYFORM2 We can relax the range of v ki over the values in (0, 1) or (0, ∞). This restricts V to accept only nonnegative values and allow U to have mixed signs values.2. Update U by fixing V using this constraint. By fixing V, the solution of U can be obtained by calculating the derivative of dJ/dU = −2WV T + 2U VV T = 0. Then we can get the DISPLAYFORM3 The positive and negative parts are computed A DISPLAYFORM4 According to BID7 , this method will reach convergence. By fixing U, the residual ||W − UV T || 2 will decrease monotonically, and after fixing V, we get the optimal solution for the objective function.The algorithm is computed by using an iterative updating algorithm that alternates between the update of U and V BID7 . The steps are very similar to coordinate descent Luo & Tseng (1992) with some modifications. The optimization is convex in U or V, not both.In the latent space derived by the NMF factorization family, each axis captures the centroid of a particular cluster, and each sample is represented as an additive combination of the centroids. The cluster membership of each document can be easily determined by finding the corresponding cluster centroid (the axis) with which the document has the largest projection value. Note in particular that the result of a K-means clustering run can be written as a matrix factorization W = UV , where W ∈ R nm is the data matrix, U ∈ R nr contains the cluster centroids, and V ∈ R rm contains the cluster membership indicators.• Perform the NMF or semi-NMF on W to obtain the two non-negative matrices U and V.• Matrix U contains r n−dimensional cluster centers and matrix V contains membership weight for each of the m samples in each of the r clusters. One can assign data i to the cluster c if c = argmax j V ij . DISPLAYFORM5 The algorithm complexity in terms of time and memory is shown in TAB4 .",Large-scale Long Short-Term Memory LSTM cells are often building blocks many state-of-the-art algorithms tasks Natural Language Processing NLP However LSTMs are known computationally inefficient memory capacity models depends number parameters inherent recurrence models temporal dependency is not parallelizable. paper propose simple effective low-rank matrix factorization MF algorithms compress network parameters significantly speed LSTMs almost loss performance sometimes even gain show effectiveness method across different tasks examine two settings:1 compressing core LSTM layers Language Models 2 compressing biLSTM layers ELMo~\citep ELMo evaluate three downstream NLP tasks Sentiment Analysis Textual Entailment Question Answering latter is particularly interesting embeddings large pre-trained biLSTM Language Models are often used contextual word representations. Finally discover matrix factorization performs better general additive recurrence is often important multiplicative recurrence identify interesting correlation matrix norms compression performance. Long Short-Term Memory LSTM networks Hochreiter Schmidhuber 1997;BID11 have become core many models tasks require temporal dependency. have particularly shown great improvements many different NLP tasks Language Modeling Sundermeyeretal. 2012;Mikolov 2012 Semantic Role Labeling etal. 2017 Named Entity Recognition Leeetal. 2017 Machine Translation BID0 Question Answering Seoetal. 2016 Recently bidirectional LSTM has been used train deep contextualized Embeddings Language Models ELMo Petersetal. 2018a has become main component state-of-the-art models many downstream NLP tasks.However is an obvious drawback scalability accompanies excellent performances training time also inference time. shortcoming can be attributed two factors:temporal dependency computational graph large number parameters weight matrix. former problem is an intrinsic nature RNNs arises modeling temporal dependency latter is often deemed necessary achieve better generalizability model Hochreiter Schmidhuber 1997;BID11. hand despite belief LSTM memory capacity is proportional model size several recent results have empirically proven contrary claiming LSTMs are indeed over-parameterized BID4 James Bradbury Socher 2017;Merityetal. 2018;Melisetal. 2018;Levyetal. 2018 Naturally results motivateus search effective compression method LSTMs terms performance time practicality cope aforementioned issue scalability. have been many solutions proposed compress large over-parameterized neural networks including parameter pruning sharing BID12 Huanget al. 2018 low-rank Matrix Factorization MF Jaderbergetal. 2014 knowledge distillation Hintonetal. 2015 However approaches have been applied Feed-forward Neural Networks Convolutional Neural Networks CNNs small attention has been given compressing LSTM architectures Luetal. 2016;BID1 even less NLP tasks. Notably Seeetal. 2016 applied parameter pruning standard Seq2Seq Sutskeveretal. 2014 architecture Neural Machine Translation which uses LSTMs encoder decoder. Furthermore language modeling BID13 uses Tensor-Train Decomposition Oseledets 2011 BID18 uses binarization techniques Kuchaiev Ginsburg 2017 uses architectural change approximate low-rank factorization.All mentioned works require form training retraining step. instance Kuchaiev Ginsburg 2017 requires trained completely scratch well distillation based compression techniques Hintonetal. 2015 addition pruning techniques Seeetal. 2016 often accompany selective retraining steps achieve optimal performance. However scenarios involving large pre-trained models e.g ELMo Petersetal. 2018a retraining can be very expensive terms time resources. Moreover compression methods are normally applied large over-parameterized networks is necessarily case paper. consider strongly tuned regularized state-of-the-art models respective tasks which often already have very compact representations. circumstances make compression much challenging realistic practically useful.In work advocate low-rank matrix factorization effective post-processing compression method LSTMs which achieve good performance guaranteed minimum algorithmic speed compared existing techniques. summarize contributions following:• thoroughly explore limits several different compression methods matrix factorization pruning including fine-tuning compression Language Modeling Sentiment Analysis Textual Entailment Question Answering.• consistently achieve average 1.5x 50% faster speedup inference time losing ∼1 point evaluation metric across datasets compressing additive/multiplicative recurrences LSTM gates.• PTB fine-tuning compressed models ∼98 obtained matrix factorization pruning can achieve ∼2x 200% faster speedup inference time even slightly improving performance uncompressed baseline.• discover matrix factorization performs better general additive recurrence is often important multiplicative recurrence identify clear interesting correlations matrix norms compression performance. conclusion exhaustively explored limits compressing LSTM gates using low-rank matrix factorization pruning four different NLP tasks. experiment results norm analysis show show Low-Rank Matrix Factorization works better general pruning if the matrix is particularly sparse Pruning works better. also discover inherent low-rankness low nuclear norm correlate well explaining why compressing multiplicative recurrence works better compressing additive recurrence. future works plan factorize LSTMs model e.g BiDAF model try combine Pruning Matrix Factorization. section provide semi-NMF algorithm elaborate optimization aim step. algorithm is an extension NMF where the data matrix is remained unconstrained BID7. original NMF optimization function shows 8. Semi-NMF ignores constraint U showed 9. DISPLAYFORM0 Exploring relationships matrix factorization K-means clustering has implications interpretability matrix factors Dinget al. FORMULA01. InitializeU run k-means clustering Hartigan Wong 1979 DISPLAYFORM1 objective function k-means clustering DISPLAYFORM2 can relax range vki values 0 1 0 ∞ restrictsV accept nonnegative values allowU have mixed mixed signs values.2 Update U fixing V using constraint. fixingV solution U can be obtained calculating derivative dJ/dU −2WV+2UVV 0. can get DISPLAYFORM3 positive negative parts are computed DISPLAYFORM4 According BID7 method will reach convergence. fixingU residual ||W−UV ||2 will decrease monotonically fixingV get optimal solution objective function.The algorithm is computed using iterative updating algorithm alternates update U V BID7. steps are very similar coordinate descent Luo Tseng 1992 modifications. optimization is convex U V both.In latent space derived NMF factorization family axis captures centroid particular cluster sample is represented additive combination centroids. cluster membership document can be easily determined finding corresponding cluster centroid axis which the document has the largest projection value. Note particular result K-means clustering run can be written matrix factorizationW UV whereW∈Rnm is the data matrix U∈Rnr contains cluster centroids V∈Rrm contains cluster membership indicators.• Perform NMF semi-NMF W obtain two non-negative matricesU V.• MatrixU contains r n−dimensional cluster centers matrix V contains membership weight samples r clusters. One can assign data clusterc ifc argmaxjVij. DISPLAYFORM5 algorithm complexity terms time memory is shown TAB4.,1984,1405,579,0.022,1.412,2025/11/05 17:19:08,0.01,1.423,0.2554517133956382,570.352
"Manipulation and re-use of images in scientific publications is a recurring problem, at present lacking a scalable solution.   Existing tools for detecting image duplication are mostly manual or semi-automated, despite the fact that generating data for a learning-based approach is straightforward, as we here illustrate. This paper addresses the problem of determining if, given two images, one is a manipulated version of the other by means of certain geometric and statistical manipulations, e.g. copy, rotation, translation, scale, perspective transform, histogram adjustment, partial erasing, and compression artifacts. We propose a solution based on a 3-branch Siamese Convolutional Neural Network. The ConvNet model is trained to map images into a 128-dimensional space, where the Euclidean distance between duplicate (respectively, unique) images is no greater (respectively, greater) than 1. Our results suggest that such an approach can serve as tool to improve surveillance of the published and in-peer-review literature for image manipulation. We also show that as a byproduct the network learns useful representations for semantic segmentation, with performance comparable to that of domain-specific models. Duplicative data reporting in the biomedical literature is more prevalent than most people realize BID1 ). One common form of data duplication, regardless of intent, is the re-use of scientific images, across multiple publications or even within the same publication. In some cases, images are altered before being re-used BID1 ). Changing orientation, perspective or image statistics, introducing skew or crop, and deleting or inserting data into the original image plane are all ways in which image data may be altered prior to inappropriate introduction, or re-introduction, into the reporting of experimental outcomes BID13 ; BID4 ; BID2 ). While the scientific community has affirmatively recognized the need for preventing the incorporation of duplicative or flawed image data into the scientific record, a consistent approach to screening and identifying problematic image data has yet to be established BID11 BID12 ).Cases of image data duplication and/or manipulation have often been detected by fellow scientists 1 or by editorial staff during the manuscript review process. Efforts to move towards automation include tools developed to isolate regions of manipulation within images already flagged as suspicious BID9 ). However , current methods for identifying duplicative and/or manipulated images largely rely on individual visual identification with accompanying application of qualitative similarity measures 2 . Given the rate at which the scientific literature is expanding, it is not feasible for all cases of potential image manipulation to be detected by human eyes. Thus, there is a continued need for automated tools to detect potential duplications, even in the presence of manipulation, to allow for more focused, thorough evaluation of this smaller errant image candidate pool. Such a tool would be invaluable to scientists and research staff on many levels, from figure screening as a step in improving raw data maintenance and manuscript preparation at the laboratory level BID13 ), to the routine screening by journal editorial staff of submitted manuscripts prior to the peer-review process BID11 BID5 ).The general problem of detecting similar images has been well studied in the field of computer vision (e.g. BID17 ; BID16 ; BID15 ). The one application that stands out is determining if two given faces are of the same person, where recent breakthroughs in deep Convolutional Neural Networks have allowed rapid progress BID14 ).In this paper, we apply modern methods in metric learning to address the problem of detecting image manipulation and re-use in scientific work. Specifically, we train a ConvNet to learn an image embedding such that images with the same original content, albeit altered through a common set of image manipulations, appear close to each other in the embedding space. We train this model on a large corpus of simulated image manipulations, and test on a small set of manipulated images from known instances of image duplication/manipulation 3 . To our knowledge, this is the first application of deep learning to the detection of image re-use in the scientific literature, although there have been works on the area of detecting image manipulation (e.g. BID0 ).We focus on the domain of biological images, since we have easy access to one such dataset, but naturally the model to be described is agnostic to the image domain. We test the learned forensic representation not only on new/unseen synthetic and real data for the problem of duplicate-detection, but also on a somewhat unrelated area: semantic segmentation. We show that the features learned in the convolution layers of the siamese network can be readily plugged into a pixel classifier, yielding results comparable with those of state-of-the art, domain-specific architectures. We have demonstrated that siamese networks have the potential to improve surveillance of the published and in-peer-review literature for duplicated images. This approach may not prove accurate enough to definitively determine image duplication, but rather could serve to narrow down the pool of images which are subjected to further review.We found that most errors in the real-world test set involved histogram/contrast alterations that are difficult to simulate, or scale changes beyond those the network was trained to detect. We will continue to explore synthetic manipulations as a way to improve accuracy of the algorithm.As indicated by the self-similarity matrices in Figure 3 , improvements are needed when different images are from the same category. We will improve the training procedure to sample more of these hard cases.One of the main roadblocks to this research is the lack of a public, large-scale database of image manipulation cases on which to further test the model. The challenge here is not only of generating one such dataset, but also of securing the proper permissions to release the data, given the legal issues involved. We are continually expanding our dataset and will make it available as soon as possible.The application to semantic segmentation was discovered somewhat by chance in an attempt to circumvent issues with the U-Net, mainly the need for a large corpus of annotations and difficulty setting hyperparameters. In contrast, the representation provided by the forensic siamese net is quite easy to deploy in conjunction with a random forest classifier.","Manipulation re-use images scientific publications is a recurring problem present lacking scalable solution. Existing tools detecting image duplication are mostly manual semi-automated despite fact generating data learning-based approach is straightforward illustrate. paper addresses problem determining if,given two images one is a manipulated version means certain geometric statistical manipulations e.g copy rotation translation scale perspective transform histogram adjustment partial erasing compression artifacts. propose solution based 3-branch Siamese Convolutional Neural Network. ConvNet model is trained map images 128-dimensional space where the Euclidean distance duplicate respectively unique images is no greater respectively greater 1. results suggest approach can serve tool improve surveillance published in-peer-review literature image manipulation. also show byproduct network learns useful representations semantic segmentation performance comparable domain-specific models. Duplicative data reporting biomedical literature is more prevalent people realize BID1 One common form data duplication regardless intent is the re-use scientific images across multiple publications even within publication. cases images are altered re-used BID1 Changing orientation perspective image statistics introducing skew crop deleting inserting data original image plane are all ways which image data may altered prior inappropriate introduction re-introduction reporting experimental outcomes BID13;BID4;BID2 scientific community has affirmatively recognized need preventing incorporation duplicative flawed image data scientific record consistent approach screening identifying problematic image data has yet established BID11 BID12.Cases image data duplication/manipulation have often detected fellow scientists1 editorial staff manuscript review process. Efforts move towards automation include tools developed isolate regions manipulation within images already flagged suspicious BID9 However current methods identifying duplicative/manipulated images largely rely individual visual identification accompanying application qualitative similarity measures2. Given rate which the scientific literature is expanding is not feasible cases potential image manipulation detected human eyes. Thus is a continued need automated tools detect potential duplications even presence manipulation allow focused thorough evaluation smaller errant image candidate pool. tool would invaluable scientists research staff many levels figure screening step improving raw data maintenance manuscript preparation laboratory level BID13 routine screening journal editorial staff submitted manuscripts prior peer-review process BID11 BID5.The general problem detecting similar images has been well studied field computer vision e.g BID17;BID16;BID15 one application stands is determining if two given faces are of the same person where recent breakthroughs deep Convolutional Neural Networks have allowed rapid progress BID14.In paper apply modern methods metric learning address problem detecting image manipulation re-use scientific work. Specifically train ConvNet learn image embedding images original content albeit altered common set image manipulations appear close embedding space. train model large corpus simulated image manipulations test small set manipulated images known instances image duplication/manipulation 3. knowledge is the first application deep learning detection image re-use scientific literature although have been works area detecting image manipulation e.g BID0.We focus domain biological images since have easy access one dataset naturally model described is agnostic image domain. test learned forensic representation new/unseen synthetic real data problem duplicate-detection also somewhat unrelated area:semantic segmentation. show features learned convolution layers siamese network can be readily plugged pixel classifier yielding results comparable state-of-the art domain-specific architectures. have demonstrated siamese networks have the potential improve surveillance published in-peer-review literature duplicated images. approach may prove accurate enough definitively determine image duplication rather could serve narrow pool images which are subjected review.We found errors real-world test set involved histogram/contrast alterations are difficult simulate scale changes beyond network was trained detect. will continue explore synthetic manipulations way improve accuracy algorithm.As indicated self-similarity matrices Figure3 improvements are needed when different images are from the same category. will improve training procedure sample hard cases.One main roadblocks research is the lack public large-scale database image manipulation cases which to further test model. challenge is not only generating one dataset also securing proper permissions release data given legal issues involved. are continually expanding dataset will make available soon possible.The application semantic segmentation was discovered somewhat chance attempt circumvent issues U-Net mainly need large corpus annotations difficulty setting hyperparameters. contrast representation provided forensic siamese net is quite easy deploy conjunction random forest classifier.",1201,797,404,0.014,1.507,2025/11/05 17:19:08,0.01,1.571,0.551401869158878,385.75
"Training generative adversarial networks is unstable in high-dimensions as the true data distribution tends to be concentrated in a small fraction of the ambient space. The discriminator is then quickly able to classify nearly all generated samples as fake, leaving the generator without meaningful gradients and causing it to deteriorate after a point in training. In this work, we propose training a single generator simultaneously against an array of discriminators, each of which looks at a different random low-dimensional projection of the data. Individual discriminators, now provided with restricted views of the input, are unable to reject generated samples perfectly and continue to provide meaningful gradients to the generator throughout training.   Meanwhile, the generator learns to produce samples consistent with the full data distribution to satisfy all discriminators simultaneously. We  demonstrate the practical utility of this approach experimentally, and show that it is able to produce image samples with higher quality than traditional training with a single discriminator. Generative adversarial networks (GANs), introduced by BID12 , endow neural networks with the ability to express distributional outputs. The framework includes a generator network that is tasked with producing samples from some target distribution, given as input a (typically low dimensional) noise vector drawn from a simple known distribution, and possibly conditional side information. The generator learns to generate such samples, not by directly looking at the data, but through adversarial training with a discriminator network that seeks to differentiate real data from those generated by the generator. To satisfy the objective of ""fooling"" the discriminator, the generator eventually learns to produce samples with statistics that match those of real data.In regression tasks where the true output is ambiguous, GANs provide a means to simply produce an output that is plausible (with a single sample), or to explicitly model that ambiguity (through multiple samples). In the latter case, they provide an attractive alternative to fitting distributions to parametric forms during training, and employing expensive sampling techniques at the test time. In particular, conditional variants of GANs have shown to be useful for tasks such as in-painting BID7 , and super-resolution BID16 . Recently, BID13 demonstrated that GANs can be used to produce plausible mappings between a variety of domains-including sketches and photographs, maps and aerial views, segmentation masks and images, etc. GANs have also found uses as a means of un-supervised learning, with latent noise vectors and hidden-layer activations of the discriminators proving to be useful features for various tasks BID7 .Despite their success, training GANs to generate high-dimensional data (such as large images) is challenging. Adversarial training between the generator and discriminator involves optimizing a min-max objective. This is typically carried out by gradient-based updates to both networks, and the generator is prone to divergence and mode-collapse as the discriminator begins to successfully distinguish real data from generated samples with high confidence. Researchers have tried to address this instability and train better generators Figure 1 : Overview of our approach. We train a single generator against an array of discriminators, each of which receives lower-dimensional projections-chosen randomly prior to training-as input. Individually, these discriminators are unable to perfectly separate real and generated samples, and thus provide stable gradients to the generator throughout training. In turn, by trying to fool all the discriminators simultaneously, the generator learns to match the true full data distribution. through several techniques . BID8 proposed generating an image by explicitly factorizing the task into a sequence of conditional generations of levels of a Laplacian pyramid, while demonstrated that specific architecture choices and parameter settings led to higher-quality samples. Other techniques include providing additional supervision BID20 , adding noise to the discriminator input BID0 , as well as modifying or adding regularization to the training objective functions BID18 BID1 BID23 .We propose a different approach to address this instability, where the generator is trained against an array of discriminators, each of which looks at a different, randomly-chosen, low-dimensional projection of the data. Each discriminator is unable to perfectly separate real and generated samples since it only gets a partial view of these samples. At the same time, to satisfy its objective of fooling all discriminators, the generator learns to match the true full data distribution. We describe a realization of this approach for training image generators, and discuss the intuition behind why we expect this training to be stable-i.e., the gradients to the generator to be meaningful throughout training-and consistent-i.e., for the generator to learn to match the full real data distribution. Despite its simplicity, we find this approach to be surprisingly effective in practice. We demonstrate this efficacy by using it to train generators on standard image datasets, and find that these produce higher-quality samples than generators trained against a single discriminator. In this paper, we proposed a new framework to training GANs for high-dimensional outputs. Our approach employs multiple discriminators on random low-dimensional projections of the data to stabilize training, with enough projections to ensure that the generator learns the true data distribution. Experimental results demonstrate that this approaches leads to more stable training, with generators continuing to improve for longer to ultimately produce higher-quality samples. Source code and trained models for our implementation is available at the project page [anonymized for review].In our current framework, the number of discriminators is limited by computational cost. In future work, we plan to investigate training with a much larger set of discriminators, employing only a small subset of them at each iteration, or every set of iterations. We are also interested in using multiple discriminators with modified and regularized objectives (e.g., BID18 BID1 BID23 ). Such modifications are complementary to our approach, and deploying them together will likely be beneficial.",Training generative adversarial networks is unstable high-dimensions true data distribution tends concentrated small fraction ambient space. discriminator is then quickly able classify nearly generated samples fake leaving generator without meaningful gradients causing deteriorate point training. work propose training single generator simultaneously array discriminators which looks different random low-dimensional projection data. Individual discriminators provided restricted views input are unable reject generated samples perfectly continue provide meaningful gradients generator throughout training. Meanwhile where the generator learns produce samples consistent full data distribution satisfy discriminators simultaneously. demonstrate practical utility approach experimentally show is able produce image samples higher quality traditional training single discriminator. Generative adversarial networks GANs introduced BID12 endow neural networks ability express distributional outputs. framework includes generator network is tasked producing samples target distribution given input typically low dimensional noise vector drawn simple known distribution possibly conditional side information. generator learns generate samples directly looking data adversarial training discriminator network seeks differentiate real data generated generator. satisfy objective fooling discriminator where the generator eventually learns produce samples statistics match real data.In regression tasks where the true output is ambiguous GANs provide means simply produce output is plausible single sample explicitly model ambiguity multiple samples latter case provide attractive alternative fitting distributions parametric forms training employing expensive sampling techniques test time. particular conditional variants GANs have shown useful tasks in-painting BID7 super-resolution BID16. Recently BID13 demonstrated GANs can be used produce plausible mappings variety domains-including sketches photographs maps aerial views segmentation masks images etc. GANs have also found uses means un-supervised learning latent noise vectors hidden-layer activations discriminators proving useful features various tasks BID7.Despite success training GANs generate high-dimensional data large images is challenging. Adversarial training generator discriminator involves optimizing min-max objective. is typically carried gradient-based updates networks where the generator is prone divergence mode-collapse discriminator begins successfully distinguish real data generated samples high confidence. Researchers have tried address instability train better generators Figure 1:Overview approach. train single generator array discriminators which receives lower-dimensional projections-chosen randomly prior training-as input. Individually discriminators are unable perfectly separate real generated samples thus provide stable gradients generator throughout training. turn trying fool discriminators simultaneously where the generator learns match true full data distribution. several techniques. BID8 proposed generating image explicitly factorizing task sequence conditional generations levels Laplacian pyramid demonstrated specific architecture choices parameter settings led higher-quality samples. techniques include providing additional supervision BID20 adding noise discriminator input BID0 well modifying adding regularization training objective functions BID18 BID1 BID23.We propose different approach address instability where the generator is trained array discriminators which looks different randomly-chosen low-dimensional projection data. discriminator is unable perfectly separate real generated samples since gets partial view samples. time satisfy objective fooling discriminators where the generator learns match true full data distribution. describe realization approach training image generators discuss intuition behind why we expect training stable-i.e gradients generator meaningful throughout training-and consistent-i.e where the generator learn match full real data distribution. Despite simplicity find approach surprisingly effective practice. demonstrate efficacy using train generators standard image datasets find produce higher-quality samples generators trained single discriminator. paper proposed new framework training GANs high-dimensional outputs. approach employs multiple discriminators random low-dimensional projections data stabilize training enough projections ensure generator learns true data distribution. Experimental results demonstrate approaches leads stable training generators continuing improve longer ultimately produce higher-quality samples. Source code trained models implementation is available project page anonymized review.In current framework number discriminators is limited computational cost. future work plan investigate training much larger set discriminators employing small subset iteration every set iterations. are also interested using multiple discriminators modified regularized objectives e.g BID18 BID1 BID23 modifications are complementary approach deploying together will likely beneficial.,1135,729,406,0.012,1.557,2025/11/05 17:19:08,0.01,1.185,0.7071651090342675,358.308
"We present a novel method to precisely impose tree-structured category information onto word-embeddings, resulting in ball embeddings in higher dimensional spaces (N-balls for short). Inclusion relations among N-balls implicitly encode subordinate relations among categories. The similarity measurement in terms of the cosine function is enriched by category information. Using a geometric construction method instead of back-propagation, we create large N-ball embeddings that satisfy two conditions: (1) category trees are precisely imposed onto word embeddings at zero energy cost; (2) pre-trained word embeddings are well preserved. A new benchmark data set is created for validating the category of unknown words. Experiments show that N-ball embeddings, carrying category information, significantly outperform word embeddings in the test of nearest neighborhoods, and demonstrate surprisingly good performance in validating categories of unknown words. Source codes and data-sets are free for public access \url{https://github.com/gnodisnait/nball4tree.git} and \url{https://github.com/gnodisnait/bp94nball.git}. Words in similar contexts have similar semantic and syntactic information. Word embeddings are vector representations of words that reflect this characteristic BID16 BID19 and have been widely used in AI applications such as question-answering BID24 , text classification BID22 , information retrieval BID14 , or even as a building-block for a unified NLP system to process common NLP tasks BID2 . To enhance semantic reasoning, researchers proposed to represent words in terms of regions instead of vectors. For example, BID5 extended a word vector into a region by estimating the log-linear probability of weighted feature distances and found that hyponym regions often do not fall inside of their hypernym regions. By using external hyponym relations, she obtained 95.2% precision and 43.4% recall in hypernym prediction for a small scale data set. Her experiments suggest that regions structured by hyponym relations may not be located within the same dimension as the space of word embeddings. Yet, how to construct strict inclusion relations among regions is still an open problem when representing hypernym relations.In this paper, we restrict regions to be n dimensional balls (N -ball for short) and propose a novel geometrical construction approach to impose tree-structured category information onto word embeddings. This is guided by two criteria: (1) Subordinate relations among categories shall be implicitly and precisely represented by inclusion relations among corresponding N -balls. This way, the energy costs of imposing structure will be zero; (2) Pre-trained word embeddings shall be well-preserved. Our particular contributions are as follows: (1) The proposed novel geometric approach achieves zero energy costs of imposing tree structures onto word-embeddings. (2) By considering category information in terms of the boundary of an N -ball, we propose a new similarity measurement that is We create a large data set of N -ball embeddings using the pre-trained GloVe embeddings and a large category tree of word senses extracted from Word-Net 3.0.The remainder of our presentation is structured as follows: Section 2 presents the structure of N -ball embeddings; Section 3 describes the geometric approach to construct N -ball embeddings; Section 4 presents experiment results; Section 5 briefly reviews related work; Section 6 concludes the presented work, and lists on-going research. FIG0 (a), so they are not RCC regions that can be either open or closed, or even a mixture, thus avoiding a number of problems BID4 BID3 . We proposed a novel geometric method to precisely impose external tree-structured category information onto word embeddings, resulting in region-based (N -ball embeddings) word sense embeddings. They can be viewed as Venn diagrams (Venn, 1880) of the tree structure, if zero energy cost is achieved. Our N -ball method has demonstrated great performance in validating the category of unknown words, the reason for this being under further investigation. Our on-going work also includes multi-lingual region-based knowledge graph embedding where multiple relations on directed acyclic graphs need to be considered. N -balls carry both vector information from deep learning and region information from symbolic structures. Therefore, N -balls establish a harmony between Connectionism and Symbolicism, as discussed by BID15 , and thus may serve as a novel building block for the commonsense representation and reasoning in Artificial Intelligence. N -balls, in particular, contribute a new topic to Qualitative Spatial Reasoning (QSR) that dates back to BID26 .",present novel method precisely impose tree-structured category information onto word-embeddings resulting ball embeddings higher dimensional spaces N-balls short Inclusion relations among N-balls implicitly encode subordinate relations among categories. similarity measurement terms cosine function is enriched category information. Using geometric construction method instead back-propagation create large N-ball embeddings satisfy two conditions:1 category trees are precisely imposed onto word embeddings zero energy cost;2 pre-trained word embeddings are well preserved. new benchmark data set is created validating category unknown words. Experiments show N-ball embeddings carrying category information significantly outperform word embeddings test nearest neighborhoods demonstrate surprisingly good performance validating categories unknown words. Source codes data-sets are free public access \url https://github.com/gnodisnait/nball4tree.git \url https://github.com/gnodisnait/bp94nball.git Words similar contexts have similar semantic syntactic information. Word embeddings are vector representations words reflect characteristic BID16 BID19 have been widely used AI applications question-answering BID24 text classification BID22 information retrieval BID14 even building-block unified NLP system process common NLP tasks BID2. enhance semantic reasoning researchers proposed represent words terms regions instead vectors. example BID5 extended word vector region estimating log-linear probability weighted feature distances found hyponym regions often do not fall inside hypernym regions. using external hyponym relations obtained 95.2 precision 43.4 recall hypernym prediction small scale data set. experiments suggest regions structured hyponym relations may located within dimension space word embeddings. Yet how to construct strict inclusion relations among regions is still open problem when representing hypernym relations.In paper restrict regions n dimensional balls N -ball short propose novel geometrical construction approach impose tree-structured category information onto word embeddings. is guided two criteria:1 Subordinate relations among categories shall implicitly precisely represented inclusion relations among corresponding N -balls way energy costs imposing structure will be zero;2 Pre-trained word embeddings shall well-preserved particular contributions are as follows:1 proposed novel geometric approach achieves zero energy costs imposing tree structures onto word-embeddings 2 considering category information terms boundary N -ball propose new similarity measurement is We create large data set N -ball embeddings using pre-trained GloVe embeddings large category tree word senses extracted Word-Net3. 0.The remainder presentation is structured follows:Section 2 presents structure N -ball embeddings;Section 3 describes geometric approach construct N -ball embeddings;Section 4 presents experiment results;Section 5 briefly reviews related work;Section 6 concludes presented work lists on-going research. FIG0 are not RCC regions can be either open closed even mixture thus avoiding number problems BID4 BID3. proposed novel geometric method precisely impose external tree-structured category information onto word embeddings resulting region-based N -ball embeddings word sense embeddings. can be viewed Venn diagrams Venn 1880 tree structure if zero energy cost is achieved. N -ball method has demonstrated great performance validating category unknown words reason investigation. on-going work also includes multi-lingual region-based knowledge graph embedding where multiple relations directed acyclic graphs need considered. N -balls carry vector information deep learning region information symbolic structures. Therefore N -balls establish harmony Connectionism Symbolicism discussed BID15 thus may serve novel building block commonsense representation reasoning Artificial Intelligence. N -balls particular contribute new topic Qualitative Spatial Reasoning QSR dates back BID26.,906,672,234,0.008,1.348,2025/11/05 17:19:08,0.0,1.375,0.0560747663551402,270.347
"For the challenging semantic image segmentation task the best performing models
 have traditionally combined the structured modelling capabilities of Conditional
 Random Fields (CRFs) with the feature extraction power of CNNs. In more recent
 works however, CRF post-processing has fallen out of favour. We argue that this
 is mainly due to the slow training and inference speeds of CRFs, as well as the
 difficulty of learning the internal CRF parameters. To overcome both issues we
 propose to add the assumption of conditional independence to the framework of
 fully-connected CRFs. This allows us to reformulate the inference in terms of
 convolutions, which can be implemented highly efficiently on GPUs.Doing so
 speeds up inference and training by two orders of magnitude. All parameters of
 the convolutional CRFs can easily be optimized using backpropagation. Towards
 the goal of facilitating further CRF research we have made our implementations
 publicly available. Semantic image segmentation, which aims to produce a categorical label for each pixel in an image, is a very import task for visual perception. Convolutional Neural Networks have been proven to be very strong in tackling semantic segmentation tasks BID23 BID5 BID40 . While simple feed-forward CNNs are extremely powerful in extracting local features and performing good predictions utilizing a small field of view, they lack the capability to utilize context information and cannot model interactions between predictions directly. Thus it has been suggested that such deep neural networks may not be the perfect model for structured predictions tasks such as semantic segmentation BID40 BID20 BID41 . Several authors have successfully combined the effectiveness of CNNs to extract powerful features, with the modelling power of CRFs in order to address the discussed issues BID20 Chandra & Kokkinos, 2016; BID41 . Despite their indisputable success, structured models have fallen out of favour in more recent approaches BID38 BID4 BID40 .We believe that the main reasons for this development are that CRFs are notoriously slow and hard to optimize. Learning the features for the structured component of the CRF is an open research problem BID37 BID20 and many approaches rely on entirely hand-crafted Gaussian features BID41 BID31 BID5 . In addition , CRF inference is typically two orders of magnitude slower than CNN inference. This makes CRF based approaches too slow for many practical applications. The long training times of the current generation of CRFs also make more in-depth research and experiments with such structured models impractical.To solve both of these issues we propose to add the strong and valid assumption of conditional independence to the existing framework of fully-connected CRFs (FullCRFs) introduced by . This allows us to reformulate a large proportion of the inference as convolutions, which can be implemented highly efficiently on GPUs. We call our method convolutional CRFs (ConvCRFs). Backpropagation BID30 can be used to train all parameters of the ConvCRF. Inference in ConvCRFs can be performed in less then 10ms. This is a speed increase of two-orders of magnitude compared to FullCRFs. We believe that those fast train and inference speeds will greatly benefit future research and hope that our results help to revive CRFs as a popular method to solve structured tasks. In this work we proposed Convolutional CRFs, a novel CRF design. Adding the strong and valid assumption of conditional independence enables us to remove the permutohedral lattice approximation. This allows us to implement the message passing highly efficiently on GPUs as convolution operations. This increases training and inference speed by two orders of magnitude. In addition we observe a modest accuracy improvement when computing the message passing exactly. Our method also enables us to easily train the Gaussian features of the CRF using backpropagation.In future work we will investigate the potential of learning Gaussian features further. We are also going to examine more sophisticated CRF architectures, towards the goal of capturing context information even better. Lastly we are particularly interested in exploring the potential of ConvCRFs in other structured applications such as instance segmentation, landmark recognition and weakly supervised learning.",challenging semantic image segmentation task best performing models have traditionally combined structured modelling capabilities Conditional Random Fields CRFs feature extraction power CNNs. recent works however CRF post-processing has fallen favour. argue is mainly due slow training inference speeds CRFs well difficulty learning internal CRF parameters. overcome issues propose add assumption conditional independence framework fully-connected CRFs. allowsus reformulate inference terms convolutions which can be implemented highly efficiently GPUs.Doing speeds inference training two orders magnitude. parameters convolutional CRFs can easily optimized using backpropagation. Towards goal facilitating CRF research have made implementations publicly available. Semantic image segmentation which aims produce categorical label pixel image is a very import task visual perception. Convolutional Neural Networks have been proven strong tackling semantic segmentation tasks BID23 BID5 BID40. simple feed-forward CNNs are extremely powerful extracting local features performing good predictions utilizing small field view lack capability utilize context information cannot model interactions predictions directly. Thus has been suggested deep neural networks may perfect model structured predictions tasks semantic segmentation BID40 BID20 BID41. Several authors have successfully combined effectiveness CNNs extract powerful features modelling power CRFs order address discussed issues BID20 Chandra Kokkinos 2016;BID41. Despite indisputable success structured models have fallen favour recent approaches BID38 BID4 BID40.We believe main reasons development are that CRFs are notoriously slow hard optimize. Learning features structured component CRF is an open research problem BID37 BID20 many approaches rely entirely hand-crafted Gaussian features BID41 BID31 BID5. addition CRF inference is typically two orders magnitude slower CNN inference. makes CRF based approaches slow many practical applications. long training times current generation CRFs also make in-depth research experiments structured models impractical.To solve issues propose add strong valid assumption conditional independence existing framework fully-connected CRFs FullCRFs introduced by. allowsus reformulate large proportion inference convolutions which can be implemented highly efficiently GPUs. call method convolutional CRFs ConvCRFs Backpropagation BID30 can be used train parameters ConvCRF. Inference ConvCRFs can be performed less 10ms. is a speed increase two-orders magnitude compared FullCRFs. believe fast train inference speeds will greatly benefit future research hope results help revive CRFs popular method solve structured tasks. work proposed Convolutional CRFs novel CRF design. Adding strong valid assumption conditional independence enablesus remove permutohedral lattice approximation. allowsus implement message passing highly efficiently GPUs convolution operations. increases training inference speed two orders magnitude. addition observe modest accuracy improvement when computing message passing exactly. method also enablesus easily train Gaussian features CRF using backpropagation.In future work will investigate potential learning Gaussian features further. are also going examine sophisticated CRF architectures towards goal capturing context information even better. Lastly are particularly interested exploring potential ConvCRFs structured applications instance segmentation landmark recognition weakly supervised learning.,811,569,242,0.007,1.425,2025/11/05 17:19:08,0.0,1.44,0.2959501557632398,275.683
"Deep Learning NLP domain lacks procedures for the analysis of model robustness. In this paper we propose a framework which validates robustness of any Question Answering model through model explainers. We propose that output of a robust model should be invariant to alterations that do not change its semantics. We test this property by manipulating question in two ways: swapping important question word for 1) its semantically correct synonym and 2) for word vector that is close in embedding space. We estimate importance of words in asked questions with Locally Interpretable Model Agnostic Explanations method (LIME). With these two steps we compare state-of-the-art Q&A models. We show that although accuracy of state-of-the-art models is high, they are very fragile to changes in the input. We can choose architecture that is more immune to attacks and thus more robust and stable in production environment. Morevoer, we propose 2 adversarial training scenarios which raise model sensitivity to true synonyms by up to 7% accuracy measure. Our findings help to understand which models are more stable and how they can be improved. In addition, we have created and published a new dataset that may be used for validation of robustness of a Q&A model. Up-to-date advancements in natural language processing show that it is possible to achieve high accuracy on tasks that from human point of view require language understanding. However, recent research on adversarial examples revealed shortcomings of neural network models, despite their great performance on selected datasets BID10 . Most adversarial examples studies in Question Answering (Q&A) task focus on designing sophisticated attacks that prove overstability understood as an inability of the model to distinguish sentences that answer the question from sentences that have words in common with the question BID3 . BID5 and BID2 also show that the whole question itself is not crucial to get the right answer. Despite growing research in the area of adversarial attacks, little is still known about the source of lacking robustness of Q&A models and effective ways of overcoming this problem. In order to come up with a solution it is crucial to understand the inner workings of task specific architectures and benchmark their performance on adversarial attacks.In this work we propose a model agnostic framework that checks stability of three state-of-the-art Q&A architectures in terms of their ability to respond to semantically similar questions. We formulate two aspects which are subject to tests: semantic input stability (relying on true semantics) and numerical input stability (purely induced by similarity between word embeddings). These terms are explained later on in the article. We state that a robust and reliable Q&A model should be invariant to changes in the input until they induce semantic changes. Having said that, we state that a stable model must display higher semantic input stability measure than numerical input stability measure. We claim that a robust Q&A model should possess high sensitivity to true semantics, as opposed to closeness between word embeddings. Otherwise, attacks based on commonly accessible sets of embeddings become possible, including antonymous questions, as antonyms are often close in embedding space.We make the following contributions:• We investigate robustness of the model in the face of semantic and numerical changes to the input.• We use output of Locally Interpretable Model Agnostic Explanations BID9 to create attacks.• We offer 2 approaches to adversarial training which increase model sensitivity to true semantic differences by a maximum of 7% in accuracy.• We release a collection of 1500 semantically coherent questions from SQuAD dataset BID8 preprocessed by LIME and human annotators, that we used in this study, as a reference dataset for further works on this problem.In section 2 we explain measures and tools that we used in the study. In section 3 we conduct experiments on three popular Q&A architectures, then we introduce two modifications to one of the models in order to increase ability to answer semantically similar questions and finally we refer to related work and conclude. In our study we focused on one particular aspect of model robustness -ability to answer semantically coherent questions. We show that performance of all tested models decreases once we change important question words indicated by LIME. However, we observe that models have higher performance once we swap tokens in questions for words close in their embedding space defined by word vectors they were trained on, in comparison to accuracy obtained by asking semantically correct questions. We manage to increase ability of the model to answer this kind of questions but it does not mean that they understand semantics -it is reflected in increased accuracy of questions with GloVe embeddings once we test our newly trained models on num-Dataset.We show that the reason behind the success of some adversarial examples lies in the way input words are represented. Popular embeddings do not include knowledge about real meaning of the words, but rather incorporate knowledge about their context. Our work serves as a starting point for future research on more semantically-conscious representation of words.",Deep Learning NLP domain lacks procedures analysis model robustness. paper propose framework which validates robustness Question Answering model model explainers. propose output robust model should be invariant alterations do not change semantics. test property manipulating question two ways:swapping important question word 1 semantically correct synonym 2 word vector is close embedding space. estimate importance words asked questions Locally Interpretable Model Agnostic Explanations method LIME two steps compare state-of-the-artQ models. show although accuracy state-of-the-art models is high are very fragile changes input. can choose architecture is more immune attacks thus robust stable production environment. Morevoer propose 2 adversarial training scenarios which raise model sensitivity true synonyms 7% accuracy measure. findings help understand which models are more stable how they can improved. addition have created published new dataset may used validation robustness Q model. Up-to-date advancements natural language processing show is possible achieve high accuracy tasks human point view require language understanding. However recent research adversarial examples revealed shortcomings neural network models despite great performance selected datasets BID10. adversarial examples studies Question Answering Q task focus designing sophisticated attacks prove overstability understood inability model distinguish sentences answer question sentences have words common question BID3. BID5 BID2 also show whole question is not crucial get right answer. Despite growing research area adversarial attacks little is still known source lacking robustness Q models effective ways overcoming problem. order come solution is crucial understand inner workings task specific architectures benchmark performance adversarial attacks.In work propose model agnostic framework checks stability three state-of-the-artQ architectures terms ability respond semantically similar questions. formulate two aspects which are subject tests:semantic input stability relying true semantics numerical input stability purely induced similarity word embeddings terms are explained later article. state robust reliableQ model should be invariant changes input induce semantic changes. said state stable model must display higher semantic input stability measure numerical input stability measure. claim robustQ model should possess high sensitivity true semantics opposed closeness word embeddings. Otherwise attacks based commonly accessible sets embeddings become possible including antonymous questions antonyms are often close embedding space.We make following contributions:• investigate robustness model face semantic numerical changes input.• use output Locally Interpretable Model Agnostic Explanations BID9 create attacks.• offer 2 approaches adversarial training which increase model sensitivity true semantic differences maximum 7% accuracy.• release collection 1500 semantically coherent questions SQuAD dataset BID8 preprocessed LIME human annotators used study reference dataset works problem.In section2 explain measures tools used study. section3 conduct experiments three popularQ architectures introduce two modifications one models order increase ability answer semantically similar questions finally refer related work conclude. study focused one particular aspect model robustness -ability answer semantically coherent questions. show performance tested models decreases change important question words indicated LIME. However observe models have higher performance swap tokens questions words close embedding space defined word vectors were trained comparison accuracy obtained asking semantically correct questions. manage increase ability model answer kind questions does not mean understand semantics -it is reflected increased accuracy questions GloVe embeddings test newly trained models num-Dataset.We show reason behind success adversarial examples lies way input words are represented. Popular embeddings do not include knowledge real meaning words rather incorporate knowledge context. work serves starting point future research semantically-conscious representation words.,984,655,329,0.01,1.502,2025/11/05 17:19:08,0.0,1.379,0.5358255451713394,321.08
"In this paper, we propose a mix-generator generative adversarial networks (PGAN) model that works in parallel by mixing multiple disjoint generators to approximate a complex real distribution. In our model, we propose an adjustment component that collects all the generated data points from the generators, learns the boundary between each pair of generators, and provides error to separate the support of each of the generated distributions. To overcome the instability in a multiplayer game, a shrinkage adjustment component method is introduced to gradually reduce the boundary between generators during the training procedure. To address the linearly growing training time problem in a multiple generators model, we propose a method to train the generators in parallel. This means that our work can be scaled up to large parallel computation frameworks. We present an efficient loss function for the discriminator, an effective adjustment component, and a suitable generator. We also show how to introduce the decay factor to stabilize the training procedure. We have performed extensive experiments on synthetic datasets, MNIST, and CIFAR-10. These experiments reveal that the error provided by the adjustment component could successfully separate the generated distributions and each of the generators can stably learn a part of the real distribution even if only a few modes are contained in the real distribution. Generative Adversarial Networks were proposed by BID7 , where two neural networks, generator and discriminator, are trained to play a minimax game. The generator is trained to fool the discriminator while the discriminator is trained to distinguish fake data (generated data) from real data. When Nash Equilibrium is reached, generated distribution P G will be equal to the real distribution P real . Unlike Restricted Boltzmann Machine (RBM, BID20 or Variational Auto-encoder (VAE, BID11 ), that explicitly approximate data distribution, the approximation of GAN is implicit. Due to this property, training GAN is challenging. It has been reported that GAN suffers from the mode collapse problem BID6 , BID14 ). Many methods have been proposed to solve this problem BID21 , BID22 , BID8 , ). In this paper, we propose a new model to solve this problem.Similar to the work of BID18 ), we use a set of generators to replace the single, complex generator. Each generator only captures a part of the real distribution, while the distance between the mix-generated distribution and the real distribution should be minimized. An adjustment component is added to achieve separation between each pair of generators, and a penalty will be passed to the generator if an overlap is detected. Moreover, we propose a shrinkage adjustment component method to gradually reduce the effect of the penalty, since the strict boundary will lead to a nonconvergence problem. Practically, forcing each generated distribution to be totally disjoint will cause potential problems. More specifically, we observe two problems in practice: (1) competition: multiple generators try to capture one mode, but are hampered by a strict boundary. This happens when the total number of generators K is greater than the actual number of modes of P real . (2) One beats all: One or a few of the generators are strong enough to capture all the modes, while the other generators are blocked outside and capture nothing. To solve these problems, we propose the following approach: (1) use reverse KL divergence instead of JS Divergence as the generator loss, to reduce the generator's ability to capture all the modes, and (2) introduce a shrinkage adjustment method to gradually reduce the weight of the adjustment component C based on the training time and the difference between each generator loss. We will discuss the details in part 3. Benefiting from such design, there is no need to pre-define the number of generators, and stable convergence can be obtained when the new component shrinks to zero. Finally, our model can allow parallelized training among generators, with synchronized or asynchronized updated for the discriminator, which reduces the training time.To highlight, our main contributions are:1. In Sections 3.1 and 2, we propose a multi-generator model where each generator captures different parts of the real data distribution while the mixing distribution captures all the data.2. We introduce an adjustment component to separate between generated distributions. The adjustment can work with any discriminator.3. In Section 3.3, we propose a shrinkage component method which reduces the penalty to guarantee convergence. If the penalty shrinks to zero, we will minimize DISPLAYFORM0 We organize the shared memory to allow for parallel training to reduce the training time.Our algorithm scales well even on large parallel platforms.5. In Section 4, we use synthetic and real data to illustrate the effectiveness of our design. In this paper, we propose a mixed generator method to solve the mode collapse problem of GAN, and our algorithm is parallelizable, and can be scaled to large platforms. To conquer the competition and one-beat all problems in the mix generator model, we have designed the reverse KL divergence loss function, and an adjustment component decay to produce a stable, converging, and fast training method. The results show we can handle the situation when the generators compete for the same mode even when the number of generators is greater than the number of modes. The shrinkage method which gradually reduced extra component to zero will eliminate the adjustment player and reduce to multi-generator vs discriminator game.More works need to be done in this multi-player game. First, the shrinkage method can also be improved if we can have a better heuristic for β. Or we can train to learn β, to achieve balance between competition and convergence. Second, the weight for each generator can also be dynamic. The generator learns more should have higher weight. Finally, new parallelization algorithm with less communication cost could be investigate to accelerate the multi-generator model since currently the run time is far from optimal.",paper propose mix-generator generative adversarial networks PGAN model works parallel mixing multiple disjoint generators approximate complex real distribution. model propose adjustment component collects generated data points generators learns boundary pair generators provides error separate support generated distributions. overcome instability multiplayer game shrinkage adjustment component method is introduced gradually reduce boundary generators training procedure. address linearly growing training time problem multiple generators model propose method train generators parallel. means work can be scaled large parallel computation frameworks. present efficient loss function discriminator effective adjustment component suitable generator. also show how to introduce decay factor stabilize training procedure. have performed extensive experiments synthetic datasets MNIST CIFAR-10 experiments reveal error provided adjustment component could successfully separate generated distributions generators can stably learn part real distribution even if only a few modes are contained real distribution. Generative Adversarial Networks were proposed BID7 where two neural networks generator discriminator are trained play minimax game. generator is trained fool discriminator discriminator is trained distinguish fake data generated data real data. When Nash Equilibrium is reached generated distributionPG will be equal real distribution P real. Unlike Restricted Boltzmann Machine RBM BID20 Variational Auto-encoder VAE BID11 explicitly approximate data distribution approximation GAN is implicit. Due property training GAN is challenging. has been reported GAN suffers mode collapse problem BID6 BID14 Many methods have been proposed solve problem BID21 BID22 BID8 paper propose new model solve problem.Similar work BID18 use set generators replace single complex generator. generator captures part real distribution distance mix-generated distribution real distribution should be minimized. adjustment component is added achieve separation pair generators penalty will be passed generator if an overlap is detected. Moreover propose shrinkage adjustment component method gradually reduce effect penalty since strict boundary will lead nonconvergence problem. Practically forcing generated distribution totally disjoint will cause potential problems. specifically observe two problems practice:1 competition:multiple generators try capture one mode are hampered strict boundary. happens when the total number generatorsK is greater actual number modes P real. 2 One beats all:One generators are strong enough capture modes generators are blocked outside capture nothing. solve problems propose following approach:1 use reverse KL divergence instead JS Divergence generator loss reduce generator's ability capture modes 2 introduce shrinkage adjustment method gradually reduce weight adjustment component C based training time difference generator loss. will discuss details part3. Benefiting design is no need pre-define number generators stable convergence can be obtained when the new component shrinks zero. Finally model can allow parallelized training among generators synchronized asynchronized updated discriminator which reduces training time.To highlight main contributions are:1 Sections 3.1 2 propose multi-generator model where each generator captures different parts real data distribution mixing distribution captures data.2 introduce adjustment component separate generated distributions. adjustment can work discriminator.3 Section 3.3 propose shrinkage component method which reduces penalty guarantee convergence. If the penalty shrinks zero will minimize DISPLAYFORM0 organize shared memory allow parallel training reduce training time.Our algorithm scales well even large parallel platforms.5 Section4 use synthetic real data illustrate effectiveness design. paper propose mixed generator method solve mode collapse problem GAN algorithm is parallelizable can be scaled large platforms. conquer competition one-beat problems mix generator model have designed reverse KL divergence loss function adjustment component decay produce stable converging fast training method. results show can handle situation when the generators compete mode even when the number generators is greater number modes. shrinkage method which gradually reduced extra component zero will eliminate adjustment player reduce multi-generator vs discriminator game.More works need done multi-player game. First shrinkage method can also improved if we can have better heuristic β. can train learnβ achieve balance competition convergence. Second weight generator can also dynamic. generator learns should have higher weight. Finally new parallelization algorithm less communication cost could investigate accelerate multi-generator model since currently run time is far optimal.,1162,759,403,0.014,1.531,2025/11/05 17:19:08,0.01,1.444,0.626168224299065,412.272
"We capitalize on the natural compositional structure of images in order to learn object segmentation with weakly labeled images. The intuition behind our approach is that removing objects from images will yield natural images, however removing random patches will yield unnatural images. We leverage this signal to develop a generative model that decomposes an image into layers, and when all layers are combined, it reconstructs the input image. However, when a layer is removed, the model learns to produce a different image that still looks natural to an adversary, which is possible by removing objects. Experiments and visualizations suggest that this model automatically learns object segmentation on images labeled only by scene better than baselines. Visual recognition models demand large amounts of annotated data that is expensive to collect, and this cost is amplified for tasks that require densely labeled data, such as semantic segmentation. In this paper, we develop an approach where object segmentation emerges automatically for images only labeled by scene category.We capitalize on the natural compositional structure of images to learn object segmentation through counterfactual images. An image is counterfactual if it shows a real scene, except part of it has been removed or changed. To learn to segment, we train a model to generate counterfactual images such that they are perceptually realistic, a task the model can solve by removing objects and filling in the holes. For example, if you fully remove the bed from the scene in Figure 1 , the image is still realistic. However, if you only partially remove the bed, the image is not realistic anymore. We use this intuition to automatically learn object segmentation.We develop a stochastic layered model that decomposes an input image into several layers. We train this model so that when all layers are combined together in some order, it reconstructs the input image. However, we also train the model so that if we randomly permute the layers and remove a layer, the combination still appears perceptually real to an adversary. Consequently, the model learns a layered image decomposition that allows parts of the image to be removed. We show that the model automatically learns to isolate objects in different layers in order to make the output image still appear realistic, a signal we capitalize on for learning to segment.We present three main experiments to analyze this approach. Firstly, experiments show that our model learns to automatically segment images into objects for some scene categories, with only weakly labeled training data, and our approach outperforms several baselines. Secondly, we show that we use a small amount of densely labeled data with our approach to further improve performance. Finally, visualizations suggest that the model can generate the scene behind objects that it learns to segment, enabling us to remove pictures from a wall or take off the bed sheets.Our main contribution is to introduce a novel method for object segmentation on data only labeled by scene by capitalizing on natural compositional structures in images. While the focus of this paper is on images, the method is general and could be applied to other signals, such as audio. The remainder of this paper describes this contribution. Section 2 reviews related work. Section 3 present our method to auto-encode images with a layered decomposition, and shows how removing image regions is a useful signal for segmentation. Section 4 shows several experiments for semantic segmentation, and section 5 offers concluding remarks. We plan to release all code, data, and models.",capitalize natural compositional structure images order learn object segmentation weakly labeled images. intuition behind approach is that removing objects images will yield natural images however removing random patches will yield unnatural images. leverage signal develop generative model decomposes image layers when all layers are combined reconstructs input image. However when a layer is removed model learns produce different image still looks natural adversary which is possible removing objects. Experiments visualizations suggest model automatically learns object segmentation images labeled scene better baselines. Visual recognition models demand large amounts annotated data is expensive collect cost is amplified tasks require densely labeled data semantic segmentation. paper develop approach where object segmentation emerges automatically images labeled scene category.We capitalize natural compositional structure images learn object segmentation counterfactual images. image is counterfactual if it shows real scene except part has been removed changed. learn segment train model generate counterfactual images are perceptually realistic task model can solve removing objects filling holes. example if you fully remove bed scene Figure1 image is still realistic. However if you only partially remove bed image is not realistic anymore. use intuition automatically learn object segmentation.We develop stochastic layered model decomposes input image several layers. train model when all layers are combined together order reconstructs input image. However also train model if we randomly permute layers remove layer combination still appears perceptually real adversary. Consequently model learns layered image decomposition allows parts image removed. show model automatically learns isolate objects different layers order make output image still appear realistic signal capitalize learning segment.We present three main experiments analyze approach. Firstly experiments show model learns automatically segment images objects scene categories weakly labeled training data approach outperforms several baselines. Secondly show use small amount densely labeled data approach improve performance. Finally visualizations suggest model can generate scene behind objects learns segment enablingus remove pictures wall take bed sheets.Our main contribution is to introduce novel method object segmentation data labeled scene capitalizing natural compositional structures images. focus paper is on images method is general could applied signals audio. remainder paper describes contribution. Section 2 reviews related work. Section 3 present method auto-encode images layered decomposition shows how removing image regions is a useful signal segmentation. Section 4 shows several experiments semantic segmentation section 5 offers concluding remarks. plan release code data models.,675,446,229,0.007,1.513,2025/11/05 17:19:08,0.0,1.556,0.5700934579439247,250.932
"Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. We propose a geometric framework, drawing on tools from the manifold reconstruction literature, to analyze the high-dimensional geometry of adversarial examples. In particular, we highlight the importance of codimension: for low-dimensional data manifolds embedded in high-dimensional space there are many directions off the manifold in which to construct adversarial examples. Adversarial examples are a natural consequence of learning a decision boundary that classifies the low-dimensional data manifold well, but classifies points near the manifold incorrectly. Using our geometric framework we prove (1) a tradeoff between robustness under different norms, (2) that adversarial training in balls around the data is sample inefficient, and (3) sufficient sampling conditions under which nearest neighbor classifiers and ball-based adversarial training are robust. Deep learning at scale has led to breakthroughs on important problems in computer vision (Krizhevsky et al. (2012) ), natural language processing (Wu et al. (2016) ), and robotics (Levine et al. (2015) ). Shortly thereafter, the interesting phenomena of adversarial examples was observed. A seemingly ubiquitous property of machine learning models where perturbations of the input that are imperceptible to humans reliably lead to confident incorrect classifications (Szegedy et al. (2013) ; BID21 ). What has ensued is a standard story from the security literature: a game of cat and mouse where defenses are proposed only to be quickly defeated by stronger attacks BID3 ). This has led researchers to develop methods which are provably robust under specific attack models (Madry et al. (2018) ; Wong & Kolter (2018) ; Sinha et al. (2018) ; Raghunathan et al. (2018) ). As machine learning proliferates into society, including security-critical settings like health care BID18 ) or autonomous vehicles BID10 ), it is crucial to develop methods that allow us to understand the vulnerability of our models and design appropriate counter-measures.In this paper, we propose a geometric framework for analyzing the phenomenon of adversarial examples. We leverage the observation that datasets encountered in practice exhibit low-dimensional structure despite being embedded in very high-dimensional input spaces. This property is colloquially referred to as the ""Manifold Hypothesis"": the idea that low-dimensional structure of 'real' data leads to tractable learning. We model data as being sampled from class-specific low-dimensional manifolds embedded in a high-dimensional space. We consider a threat model where an adversary may choose any point on the data manifold to perturb by in order to fool a classifier. In order to be robust to such an adversary, a classifier must be correct everywhere in an -tube around the data manifold. Observe that, even though the data manifold is a low-dimensional object, this tube has the same dimension as the entire space the manifold is embedded in. Our analysis argues that adversarial examples are a natural consequence of learning a decision boundary that classifies all points on a low-dimensional data manifold correctly, but classifies many points near the manifold incorrectly. The high codimension, the difference between the dimension of the data manifold and the dimension of the embedding space, is a key source of the pervasiveness of adversarial examples.Our paper makes the following contributions. First, we develop a geometric framework, inspired by the manifold reconstruction literature, that formalizes the manifold hypothesis described above and our attack model. Second, we highlight the role codimension plays in vulnerability to adversarial DISPLAYFORM0 rch 2 ⇤ 2 rch 2 ⇤ 2 rch 2 ⇤ 2 rch 2 ⇤ 2 rch 2 ⇤ 2 rch 2 ⇤ 2 Figure 1 : Examples of the decision axis Λ 2 , shown here in green, for different data manifolds. Intuitively, the decision axis captures an optimal decision boundary between the data manifolds. It's optimal in the sense that each point on the decision axis is as far away from each data manifold as possible. Notice that in the first example, the decision axis coincides with the maximum margin line.examples. As the codimension increases, there are an increasing number of directions off the data manifold in which to construct adversarial perturbations. Prior work has attributed vulnerability to adversarial examples to input dimension BID20 ). This is the first work that investigates the role of codimension in adversarial examples. Interestingly, we find that different classification algorithms are less sensitive to changes in codimension. Third, we apply this framework to prove the following results: (1) we show that the choice of norm to restrict an adversary is important in that there exists a tradeoff between being robust to different norms: we present a classification problem where improving robustness under the · ∞ norm requires a loss of Ω(1−1/ √ d) in robustness to the · 2 norm; (2) we show that a common approach, training against adversarial examples drawn from balls around the training set, is insufficient to learn robust decision boundaries with realistic amounts of data; and (3) we show that nearest neighbor classifiers do not suffer from this insufficiency, due to geometric properties of their decision boundary away from data, and thus represent a potentially robust classification algorithm. Finally we provide experimental evidence on synthetic datasets and MNIST that support our theoretical results. We have presented a geometric framework for proving robustness guarantees for learning algorithms. Our framework is general and can be used to describe the robustness of any classifier. We have shown that no single model can be simultaneously robust to attacks under all norms and that nearest neighbor classifiers are theoretically more sample efficient than adversarial training. Most importantly, we have highlighted the role of codimension in contributing to adversarial examples and verified our theoretical contributions with experimental results.We believe that a geometric understanding of the decision boundaries learned by deep networks will lead to both new geometrically inspired attacks and defenses. In Appendix C we provide a novel gradient-free geometric attack in support of this claim. Finally we believe future work into the geometric properties of decision boundaries learned by various optimization procedures will provide new techniques for black-box attacks.",Adversarial examples are a pervasive phenomenon machine learning models where seemingly imperceptible perturbations input lead misclassifications otherwise statistically accurate models. propose geometric framework drawing tools manifold reconstruction literature analyze high-dimensional geometry adversarial examples. particular highlight importance codimension:low-dimensional data manifolds embedded high-dimensional space are many directions manifold which to construct adversarial examples. Adversarial examples are a natural consequence learning decision boundary classifies low-dimensional data manifold well classifies points near manifold incorrectly. Using geometric framework prove 1 tradeoff robustness different norms 2 adversarial training balls around data is sample inefficient 3 sufficient sampling conditions which nearest neighbor classifiers ball-based adversarial training are robust. Deep learning scale has led breakthroughs important problems computer vision Krizhevskyetal. 2012 natural language processing Wuetal. 2016 robotics Levineetal. 2015 Shortly thereafter interesting phenomena adversarial examples was observed. seemingly ubiquitous property machine learning models where perturbations input are imperceptible humans reliably lead confident incorrect classifications Szegedyetal. 2013 BID21 What has ensued is a standard story security literature:game cat mouse where defenses are proposed quickly defeated stronger attacks BID3 has led researchers develop methods which are provably robust specific attack models Madryetal. 2018 Wong Kolter 2018 Sinhaetal. 2018 Raghunathanetal. 2018 machine learning proliferates society including security-critical settings like health care BID18 autonomous vehicles BID10 is crucial develop methods allowus understand vulnerability models design appropriate counter-measures.In paper propose geometric framework analyzing phenomenon adversarial examples. leverage observation datasets encountered practice exhibit low-dimensional structure despite embedded high-dimensional input spaces. property is colloquially referred Manifold Hypothesis:idea low-dimensional structure 'real' data leads tractable learning. model data sampled class-specific low-dimensional manifolds embedded high-dimensional space. consider threat model where an adversary may choose point data manifold perturb order fool classifier. order robust adversary classifier must correct everywhere -tube around data manifold. Observe even though data manifold is a low-dimensional object tube has the same dimension entire space manifold is embedded in. analysis argues adversarial examples are a natural consequence learning decision boundary classifies points low-dimensional data manifold correctly classifies many points near manifold incorrectly. high codimension difference dimension data manifold dimension embedding space is a key source pervasiveness adversarial examples.Our paper makes following contributions. First develop geometric framework inspired manifold reconstruction literature formalizes manifold hypothesis described attack model. Second highlight role codimension plays vulnerability adversarial DISPLAYFORM0 rch2 ⇤ 2 rch2 ⇤ 2 rch2 ⇤ 2 rch2 ⇤ 2 rch2 ⇤ 2 rch2 ⇤ 2 Figure1:Examples decision axisΛ2 shown green different data manifolds. Intuitively decision axis captures optimal decision boundary data manifolds. optimal sense point decision axis is as far away data manifold possible. Notice first example decision axis coincides maximum margin line.examples. codimension increases are an increasing number directions data manifold which to construct adversarial perturbations. Prior work has attributed vulnerability adversarial examples input dimension BID20 is first work investigates role codimension adversarial examples. Interestingly find different classification algorithms are less sensitive changes codimension. Third apply framework prove following results:1 show choice norm restrict adversary is important exists tradeoff robust different norms:present classification problem where improving robustness · ∞ norm requires loss Ω 1−1/√ robustness · 2 norm;2 show common approach training adversarial examples drawn balls around training set is insufficient learn robust decision boundaries realistic amounts data;3 show nearest neighbor classifiers do not suffer insufficiency due geometric properties decision boundary away data thus represent potentially robust classification algorithm. Finally provide experimental evidence synthetic datasets MNIST support theoretical results. have presented geometric framework proving robustness guarantees learning algorithms. framework is general can be used describe robustness classifier. have shown single model can be simultaneously robust attacks norms nearest neighbor classifiers are theoretically sample efficient adversarial training. importantly have highlighted role codimension contributing adversarial examples verified theoretical contributions experimental results.We believe geometric understanding decision boundaries learned deep networks will lead new geometrically inspired attacks defenses. AppendixC provide novel gradient-free geometric attack support claim. Finally believe future work geometric properties decision boundaries learned various optimization procedures will provide new techniques black-box attacks.,1266,868,398,0.013,1.459,2025/11/05 17:19:08,0.01,1.372,0.4018691588785047,373.458
"Character-based neural machine translation (NMT) models alleviate out-of-vocabulary issues, learn morphology, and move us closer to completely end-to-end translation systems.   Unfortunately, they are also very brittle and easily falter when presented with noisy data. In this paper, we confront NMT models with synthetic and natural sources of noise. We find that state-of-the-art models fail to translate even moderately noisy texts that humans have no trouble comprehending. We explore two approaches to increase model robustness: structure-invariant word representations and robust training on noisy texts. We find that a model based on a character convolutional neural network is able to simultaneously learn representations robust to multiple kinds of noise. Humans have surprisingly robust language processing systems that can easily overcome typos, misspellings, and the complete omission of letters when reading BID34 . A particularly extreme and comical exploitation of our robustness came years ago in the form of a popular meme: ""Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae."" A person's ability to read this text comes as no surprise to the psychology literature. BID38 found that this robustness extends to audio as well. They experimented with playing parts of audio transcripts backwards and found that it did not affect comprehension. BID35 found that in noisier settings reading comprehension only slowed by 11%. BID27 found that the common case of swapping letters could often go unnoticed by the reader. The exact mechanisms and limitations of our understanding system are unknown. There is some evidence that we rely on word shape BID26 , that we can switch between whole word recognition and piecing together words from letters BID36 BID33 , and there appears to be no evidence that the first and last letter positions are required to stay constant for comprehension. 1 In stark contrast, neural machine translation (NMT) systems, despite their pervasive use, are immensely brittle. For instance, Google Translate produces the following unintelligible translation for a German version of the above meme: 2 ""After being stubbornly defiant, it is clear to kenie Rlloe in which Reiehnfogle is advancing the boulders in a Wrot that is integral to Sahce, as the utterance and the lukewarm boorstbaen stmimt.""While typos and noise are not new to NLP, our systems are rarely trained to explicitly address them, as we instead hope that the relevant noise will occur in the training data.Despite these weaknesses, the move to character-based NMT is important. It helps us tackle the long tailed distribution of out-of-vocabulary words in natural language, as well as reduce computation load of dealing with large word embedding matrices. NMT models based on characters and other sub-word units are able to extract stem and morphological information to generalize to unseen words and conjugations. They perform very well in practice on a range of languages BID44 BID53 . In many cases, these models actually discover an impressive amount of morphological information about a language BID2 . Unfortunately, training (and testing) on clean data makes models brittle and, arguably, unfit for broad deployment. Figure 1 shows how the performance of two state-of-the-art NMT systems degrades when translating German to English as a function of the percent of German words modified. Here we show three types of noise: 1) Random permutation of the word, 2) Swapping a pair of adjacent letters, and 3) Natural human errors. We discuss these types of noise and others in depth in section 4.2. The important thing to note is that even small amounts of noise lead to substantial drops in performance. Figure 1: Degradation of Nematus and char2char BID21 performance as noise increases.To address these trends and investigate the effects of noise on NMT, we explore two simple strategies for increasing model robustness: using structure-invariant representations and robust training on noisy data, a form of adversarial training BID49 BID14 . We find that a character CNN representation trained on an ensemble of noise types is robust to all kinds of noise. We shed some light on the model ability to learn robust representations to multiple types of noise, and point to remaining difficulties in handling natural noise. Our goal is two fold: 1) initiate a conversation on robust training and modeling techniques in NMT, and 2) promote the creation of better and more linguistically accurate artificial noise to be applied to new languages and tasks.","Character-based neural machine translation NMT models alleviate out-of-vocabulary issues learn morphology move us closer completely end-to-end translation systems. Unfortunately are also brittle easily falter when presented noisy data. paper confront NMT models synthetic natural sources noise. find state-of-the-art models fail translate even moderately noisy texts humans have no trouble comprehending. explore two approaches increase model robustness:structure-invariant word representations robust training noisy texts. find model based character convolutional neural network is able simultaneously learn representations robust multiple kinds noise. Humans have surprisingly robust language processing systems can easily overcome typos misspellings complete omission letters when reading BID34. particularly extreme comical exploitation robustness came years ago form popular meme:Aoccdrnig rscheearch Cmabrigde Uinervtisy deosn't mttaer waht oredr ltteers wrod are,the olny iprmoetnt tihng is taht frist lsat ltteer rghit pclae. person's ability read text comes surprise psychology literature. BID38 found robustness extends audio well. experimented playing parts audio transcripts backwards found did not affect comprehension. BID35 found noisier settings reading comprehension slowed 11%. BID27 found common case swapping letters could often go unnoticed reader. exact mechanisms limitations understanding system are unknown. is some evidence rely word shape BID26 can switch whole word recognition piecing together words letters BID36 BID33 appears evidence first last letter positions are required stay constant comprehension. 1 stark contrast neural machine translation NMT systems despite pervasive use are immensely brittle. instance Google Translate produces following unintelligible translation German version meme:2 stubbornly defiant is clear kenie Rlloe which Reiehnfogle is advancing boulders Wrot is integral Sahce utterance lukewarm boorstbaen stmimt.While typos noise are not new NLP systems are rarely trained explicitly address instead hope relevant noise will occur training data.Despite weaknesses move character-based NMT is important. helps us tackle long tailed distribution out-of-vocabulary words natural language well reduce computation load dealing large word embedding matrices. NMT models based characters sub-word units are able extract stem morphological information generalize unseen words conjugations. perform well practice range languages BID44 BID53. many cases models actually discover impressive amount morphological information language BID2. Unfortunately training testing clean data makes models brittle arguably unfit broad deployment. Figure 1 shows how the performance two state-of-the-art NMT systems degrades when translating German English function percent German words modified. show three types noise:1 Random permutation word 2 Swapping pair adjacent letters 3 Natural human errors. discuss types noise others depth section 4.2 important thing note is that even small amounts noise lead substantial drops performance. Figure1:Degradation Nematus char2char BID21 performance noise increases.To address trends investigate effects noise NMT explore two simple strategies increasing model robustness:using structure-invariant representations robust training noisy data form adversarial training BID49 BID14. find character CNN representation trained ensemble noise types is robust kinds noise. shed light model ability learn robust representations multiple types noise point remaining difficulties handling natural noise. goal is two fold:1 initiate conversation robust training modeling techniques NMT 2 promote creation better linguistically accurate artificial noise applied new languages tasks.",952,658,294,0.009,1.447,2025/11/05 17:19:08,0.0,1.276,0.3644859813084112,292.868
"As neural networks grow deeper and wider, learning networks with hard-threshold activations is becoming increasingly important, both for network quantization, which can drastically reduce time and energy requirements, and for creating large integrated systems of deep networks, which may have non-differentiable components and must avoid vanishing and exploding gradients for effective learning. However, since gradient descent is not applicable to hard-threshold functions, it is not clear how to learn them in a principled way. We address this problem by observing that setting targets for hard-threshold hidden units in order to minimize loss is a discrete optimization problem, and can be solved as such. The discrete optimization goal is to find a set of targets such that each unit, including the output, has a linearly separable problem to solve. Given these targets, the network decomposes into individual perceptrons, which can then be learned with standard convex approaches. Based on this, we develop a recursive mini-batch algorithm for learning deep hard-threshold networks that includes the popular but poorly justified straight-through estimator as a special case. Empirically, we show that our algorithm improves classification accuracy in a number of settings, including for AlexNet and ResNet-18 on ImageNet, when compared to the straight-through estimator.",neural networks grow deeper wider learning networks hard-threshold activations is becoming increasingly important network quantization which can drastically reduce time energy requirements creating large integrated systems deep networks may have non-differentiable components must avoid vanishing exploding gradients effective learning. However since gradient descent is not applicable hard-threshold functions is not clear how to learn principled way. address problem observing setting targets hard-threshold hidden units order minimize loss is a discrete optimization problem can be solved such. discrete optimization goal is to find set targets unit including output has a linearly separable problem solve. Given targets network decomposes individual perceptrons which can then learned standard convex approaches. Based develop recursive mini-batch algorithm learning deep hard-threshold networks includes popular poorly justified straight-through estimator special case. Empirically show algorithm improves classification accuracy number settings including AlexNet ResNet-18 ImageNet when compared straight-through estimator.,255,179,76,0.003,1.425,2025/11/05 17:19:08,0.0,1.833,0.2959501557632398,93.035
"The robust and efficient recognition of visual relations in images is a hallmark of biological vision. Here, we argue that, despite recent progress in visual recognition, modern machine vision algorithms are severely limited in their ability to learn visual relations. Through controlled experiments, we demonstrate that visual-relation problems strain convolutional neural networks (CNNs). The networks eventually break altogether when rote memorization becomes impossible such as when the intra-class variability exceeds their capacity. We further show that another type of feedforward network, called a relational network (RN), which was shown to successfully solve seemingly difficult visual question answering (VQA) problems on the CLEVR datasets, suffers similar limitations. Motivated by the comparable success of biological vision, we argue that feedback mechanisms including working memory and attention are the key computational components underlying abstract visual reasoning. Consider the two images in Fig. 1 . The image on the left was correctly classified as a flute by a deep convolutional neural network (CNN) BID13 . This is quite a remarkable feat for such a complicated image, which includes distractors that partially occlude the object of interest. After the network was trained on millions of photographs, this and many other images were accurately categorized into one thousand natural object categories, surpassing, for the first time, the accuracy of a human observer on the ImageNet classification challenge. Now, consider the image on the right. On its face, it is quite simple compared to the image on the left. It is just a binary image containing two curves. Further, it has a rather distinguishing property, at least to the human eye: both curves are the same. The relation between the two items in this simple scene is rather intuitive and immediately obvious to a human observer. Yet, the CNN failed to learn this relation even after seeing millions of training examples.Why is it that a CNN can accurately detect the flute in Fig. 1a while struggling to recognize the simple relation depicted in Fig. 1b? (a) (b) Figure 1: Two images: The image in panel (a) can be classified with high confidence as containing a flute by contemporary computer vision algorithms. However, these same algorithms struggle to learn the concept of ""sameness"" as exemplified by the image with the two curves shown in panel (b) . The image in panel (b) is sampled from the SVRT challenge BID6 .That such task is difficult, and even sometimes impossible for contemporary computer vision algorithms including CNNs, is known BID6 BID12 BID4 BID26 but has, so far, been overlooked. To make matters worse, the issue has been overshadowed by the recent success of a novel class of neural networks called relational networks (RNs) on seemingly challenging visual question answering (VQA) benchmarks. However , RNs have so far only been tested using toy datasets like the sort-of-CLEVR dataset which depicts combinations of items of only a handful of colors and shapes BID22 . As we will show, RNs suffer the same limitations as CNNs for a same-different task such as the one shown in Fig. 1b .This failure of modern computer vision algorithms is all the more striking given the widespread ability to recognize visual relations across the animal kingdom, from human and non-human primates BID3 BID15 to rodents BID28 , birds BID2 BID18 and even insects BID10 . Examining the failures of existing models is a critical step on the path to understanding the computational principles underlying visual reasoning. Yet, to our knowledge , there has not been any systematic exploration of the limits of contemporary machine learning algorithms on relational reasoning problems.Previous work by BID6 showed that black-box classifiers fail on most tasks from the synthetic visual reasoning test (SVRT), a battery of twenty-three visual-relation problems, despite massive amounts of training data. More recent work by BID4 and BID26 each showed how two different CNN architectures could only solve a handful of the twentythree SVRT problems. Similarly, BID12 , after showing how CNNs fail to learn a same-different task with simple binary ""sprite"" items, only managed to train a multi-layer perceptron on this task by providing carefully engineered training schedules. However, these results of BID4 , BID12 and BID26 were inconclusive: does the inability of feedforward neural networks to solve various visual-relation problems reflect a poor choice of hyperparameters for their particular implementation or rather a systematic failure of the entire class of feedforward models?Here, we propose to systematically probe the limits of CNNs and other state-of-the-art visual reasoning networks (RNs) on visual-relation tasks. Through a series of controlled experiments , we demonstrate that visual-relation tasks strain CNNs and that these limitations are not alleviated in RNs, which were specifically designed to tackle visual-relation problems. A brief review of the biological vision literature suggests that two key brain mechanisms, working memory and attention, underlie primates' ability to reason about visual relations. We argue that these mechanisms and possibly other feedback mechanisms are needed to extend current computer vision models to efficiently learn to solve complex visual reasoning tasks.Our contributions are threefold: (i) We perform the first systematic performance analysis of CNN architectures on each of the twenty-three SVRT problems. This yields a dichotomy of visual-relation problems, hard same-different problems vs. easy spatial-relation problems.(ii) We describe a novel, controlled, visual-relation challenge which convincingly shows that CNNs solve same-different tasks via rote memorization. (iii) We show that a simple modification of the sort-of-CLEVR challenge similarly breaks state-of-the-art relational network architectures.Overall, we wish to motivate the computer vision community to reconsider existing visual question answering challenges and turn to neuroscience and cognitive science for inspiration to help with the design of visual reasoning architectures. Our results indicate that visual-relation problems can quickly exceed the representational capacity of CNNs. While learning templates for individual objects appears to be quite tractable for today's deep networks, learning templates for arrangements of objects become rapidly intractable because of the combinatorial explosion in the number of templates needed. That stimuli with a combinatorial structure are difficult to represent with feedforward networks has been long acknowledged by cognitive scientists at least as early as BID7 . However, this limitation seems to have been somehow overlooked by current computer vision scientists.Compared to the feedforward networks in this study, biological visual systems excel at detecting relations. BID6 found that humans are capable of learning rather complicated visual rules and generalizing them to new instances from just a few SVRT training examples. For instance, their participants could learn the rule underlying the hardest SVRT problem for CNNs in our Experiment 1, problem 20, from an average of about 6 examples. Moreover, problem 20 is rather complicated, involving two shapes such that ""one shape can be obtained from the other by reflection around the perpendicular bisector of the line joining their centers."" In contrast, the best performing network for this problem in our high-throughput search could not get significantly above chance after a million training examples.Visual reasoning ability is not just found in humans. For example, birds and primates can be trained to recognize same-different relations and then transfer this knowledge to novel objects BID29 . A recent, striking example of same-different learning in animals comes from BID18 who essentially showed that ducklings can perform a one-shot version of our Experiment 3 from birth. During a training phase, newly hatched ducklings were exposed to a single pair of simple 3D objects that were either the same or different. Later, they demonstrated a preference for novel objects obeying the relationship observed in the training phase. This result suggests that these animals can either rapidly learn the abstract concepts of same and different from a single example or they simply possess these concepts innately. Contrast the behavior of these ducklings with the CNN+RN of Experiment 3, which demonstrated no ability to transfer the concept of same-different to novel objects FIG2 even after hundreds of thousands of training examples. For a recent review of similar literature (including additional evidence for abstract relational reasoning in pigeons and nutcrackers), see BID30 .There is substantial evidence that the neural substrate of visual-relation detection may depend on reentrant/feedback signals beyond feedforward, pre-attentive processes. It is relatively well accepted that, despite the widespread presence of feedback connections in our visual cortex, certain visual recognition tasks, including the detection of natural object categories, are possible in the near absence of cortical feedback -based primarily on a single feedforward sweep of activity through our visual cortex BID23 . However , psychophysical evidence suggests that this feedforward sweep is too spatially coarse to localize objects even when they can be recognized BID5 . The implication is that object localization in clutter requires attention BID31 .It is difficult to imagine how one could recognize the spatial relation between two objects without spatial information. Indeed, converging neuroscience evidence BID17 BID19 BID21 BID14 BID8 BID27 suggests that the processing of spatial relations between pairs of objects in a cluttered scene requires attention, even when participants are able to detect the presence of the individual objects pre-attentively, presumably in a single feedforward sweep.Another brain mechanism that has been implicated in our ability to process visual relations is working memory BID16 BID11 BID1 BID0 . In particular, imaging studies BID16 BID11 have highlighted the role of working memory in prefrontal and premotor cortices when participants solve Raven's progressive matrices which require both spatial and same-different reasoning.What is the computational role of attention and working memory in the detection of visual relations? One assumption BID8 is that these two mechanisms allow flexible representations of relations to be constructed dynamically at run-time via a sequence of attention shifts rather than statically by storing visual-relation templates in synaptic weights (as done in feedforward neural networks). Such representations built ""on-the-fly"" circumvent the combinatorial explosion associated with the storage of templates for all possible relations, helping to prevent the capacity overload associated with feedforward neural networks.Humans can easily detect when two objects are the same up to some transformation BID24 or when objects exist in a given spatial relation BID6 BID8 . More generally, humans can effortlessly construct an unbounded set of structured descriptions about the visual world around them BID9 . Given the vast superiority of humans over modern computers in their ability to detect visual relations, we see the exploration of attentional and mnemonic mechanisms as an important step in our computational understanding of visual reasoning.","robust efficient recognition visual relations images is a hallmark biological vision. argue despite recent progress visual recognition modern machine vision algorithms are severely limited ability learn visual relations. controlled experiments demonstrate visual-relation problems strain convolutional neural networks CNNs networks eventually break altogether when rote memorization becomes impossible when the intra-class variability exceeds capacity. show another type feedforward network called relational network RN which was shown successfully solve seemingly difficult visual question answering VQA problems CLEVR datasets suffers similar limitations. Motivated comparable success biological vision argue feedback mechanisms including working memory attention are the key computational components underlying abstract visual reasoning. Consider two images Fig. 1. image left was correctly classified flute deep convolutional neural network CNN BID13. is quite remarkable feat complicated image which includes distractors partially occlude object interest. network was trained millions photographs many images were accurately categorized one thousand natural object categories surpassing first time accuracy human observer ImageNet classification challenge. consider image right. face is quite simple compared image left. is just a binary image containing two curves. has rather distinguishing property least human eye:curves are the same. relation two items simple scene is rather intuitive immediately obvious human observer. Yet CNN failed learn relation even seeing millions training examples.Why is it that a CNN can accurately detect flute Fig. 1a struggling recognize simple relation depicted Fig. 1b? b Figure1:Two images:image panel can classified high confidence containing flute contemporary computer vision algorithms. However algorithms struggle learn concept sameness exemplified image two curves shown panel b image panel b is sampled SVRT challenge BID6.That task is difficult even sometimes impossible contemporary computer vision algorithms including CNNs is known BID6 BID12 BID4 BID26 has,so far overlooked. make matters worse issue has been overshadowed recent success novel class neural networks called relational networks RNs seemingly challenging visual question answering VQA benchmarks. However RNs have so far tested using toy datasets like sort-of-CLEVR dataset which depicts combinations items handful colors shapes BID22. will show RNs suffer limitations CNNs same-different task one shown Fig. 1b.This failure modern computer vision algorithms is all the more striking given widespread ability recognize visual relations across animal kingdom human non-human primates BID3 BID15 rodents BID28 birds BID2 BID18 even insects BID10. Examining failures existing models is a critical step path understanding computational principles underlying visual reasoning. Yet knowledge has not systematic exploration limits contemporary machine learning algorithms relational reasoning problems.Previous work BID6 showed black-box classifiers fail tasks synthetic visual reasoning test SVRT battery twenty-three visual-relation problems despite massive amounts training data. recent work BID4 BID26 showed how two different CNN architectures could solve handful twentythree SVRT problems. Similarly BID12 showing how CNNs fail learn same-different task simple binary sprite items managed train multi-layer perceptron task providing carefully engineered training schedules. However results BID4 BID12 BID26 were inconclusive:does the inability feedforward neural networks solve various visual-relation problems reflect poor choice hyperparameters particular implementation rather systematic failure entire class feedforward models? propose systematically probe limits CNNs state-of-the-art visual reasoning networks RNs visual-relation tasks. series controlled experiments demonstrate visual-relation tasks strain CNNs limitations are not alleviated RNs which were specifically designed tackle visual-relation problems. brief review biological vision literature suggests two key brain mechanisms working memory attention underlie primates' ability reason visual relations. argue mechanisms possibly feedback mechanisms are needed extend current computer vision models efficiently learn solve complex visual reasoning tasks.Our contributions are threefold:perform first systematic performance analysis CNN architectures twenty-three SVRT problems. yields dichotomy visual-relation problems hard same-different problemsvs. easy spatial-relation problems. ii describe novel controlled visual-relation challenge which convincingly shows CNNs solve same-different tasks via rote memorization. iii show simple modification sort-of-CLEVR challenge similarly breaks state-of-the-art relational network architectures.Overall wish motivate computer vision community reconsider existing visual question answering challenges turn neuroscience cognitive science inspiration help design visual reasoning architectures. results indicate visual-relation problems can quickly exceed representational capacity CNNs. learning templates individual objects appears quite tractable today's deep networks learning templates arrangements objects become rapidly intractable combinatorial explosion number templates needed. stimuli combinatorial structure are difficult represent feedforward networks has been long acknowledged cognitive scientists least early BID7. However limitation seems have been somehow overlooked current computer vision scientists.Compared feedforward networks study biological visual systems excel detecting relations. BID6 found humans are capable learning rather complicated visual rules generalizing new instances SVRT training examples. instance participants could learn rule underlying hardest SVRT problem CNNs Experiment1 problem20 average 6 examples. Moreover problem20 is rather complicated involving two shapes one shape can be obtained reflection around perpendicular bisector line joining centers. contrast best performing network problem high-throughput search could get significantly chance million training examples.Visual reasoning ability is not just found humans. example birds primates can be trained recognize same-different relations transfer knowledge novel objects BID29. recent striking example same-different learning animals comes BID18 who essentially showed ducklings can perform one-shot version Experiment3 birth. training phase newly hatched ducklings were exposed single pair simple 3D objects were either different. Later which demonstrated preference novel objects obeying relationship observed training phase. result suggests animals can either rapidly learn abstract concepts different single example simply possess concepts innately. Contrast behavior ducklings CNN+RN Experiment3 which demonstrated ability transfer concept same-different novel objects FIG2 even hundreds thousands training examples. recent review similar literature including additional evidence abstract relational reasoning pigeons nutcrackers see BID30.There is substantial evidence neural substrate visual-relation detection may depend reentrant/feedback signals beyond feedforward pre-attentive processes. is relatively well accepted despite widespread presence feedback connections visual cortex certain visual recognition tasks including detection natural object categories are possible near absence cortical feedback -based primarily single feedforward sweep activity visual cortex BID23. However psychophysical evidence suggests feedforward sweep is too spatially coarse localize objects even when they can be recognized BID5. implication is that object localization clutter requires attention BID31.It is difficult imagine how one could recognize spatial relation two objects without spatial information. Indeed converging neuroscience evidence BID17 BID19 BID21 BID14 BID8 BID27 suggests processing spatial relations pairs objects cluttered scene requires attention even when participants are able detect presence individual objects pre-attentively presumably single feedforward sweep.Another brain mechanism has been implicated ability process visual relations is working memory BID16 BID11 BID1 BID0. particular imaging studies BID16 BID11 have highlighted role working memory prefrontal premotor cortices when participants solve Raven's progressive matrices which require spatial same-different reasoning.What is the computational role attention working memory detection visual relations? One assumption BID8 is that these two mechanisms allow flexible representations relations constructed dynamically run-time via sequence attention shifts rather statically storing visual-relation templates synaptic weights done feedforward neural networks representations built on-the-fly circumvent combinatorial explosion associated storage templates possible relations helping prevent capacity overload associated feedforward neural networks.Humans can easily detect when two objects are the sameup transformation BID24 when objects exist given spatial relation BID6 BID8. generally humans can effortlessly construct unbounded set structured descriptions visual world around BID9. Given vast superiority humans modern computers ability detect visual relations see exploration attentional mnemonic mechanisms important step computational understanding visual reasoning.",2135,1483,652,0.025,1.44,2025/11/05 17:19:08,0.01,1.548,0.3426791277258563,727.052
"Visual Active Tracking (VAT) aims at following a target object by autonomously controlling the motion system of a tracker given visual observations. Previous work has shown that the tracker can be trained in a simulator via reinforcement learning and deployed in real-world scenarios. However, during training, such a method requires manually specifying the moving path of the target object to be tracked, which cannot ensure the tracker’s generalization on the unseen object moving patterns. To learn a robust tracker for VAT, in this paper, we propose a novel adversarial RL method which adopts an Asymmetric Dueling mechanism, referred to as AD-VAT. In AD-VAT, both the tracker and the target are approximated by end-to-end neural networks, and are trained via RL in a dueling/competitive manner: i.e., the tracker intends to lockup the target, while the target tries to escape from the tracker. They are asymmetric in that the target is aware of the tracker, but not vice versa. Specifically, besides its own observation, the target is fed with the tracker’s observation and action, and learns to predict the tracker’s reward as an auxiliary task. We show that such an asymmetric dueling mechanism produces a stronger target, which in turn induces a more robust tracker. To stabilize the training, we also propose a novel partial zero-sum reward for the tracker/target. The experimental results, in both 2D and 3D environments, demonstrate that the proposed method leads to a faster convergence in training and yields more robust tracking behaviors in different testing scenarios. For supplementary videos, see: https://www.youtube.com/playlist?list=PL9rZj4Mea7wOZkdajK1TsprRg8iUf51BS 
 The code is available at https://github.com/zfw1226/active_tracking_rl Visual Active Tracking (VAT) aims at following a target object by autonomously controlling the motion system of a tracker given visual observations. VAT is demanded in many real-world applications such as autonomous vehicle fleet (e.g., a slave-vehicle should follow a master-vehicle ahead), service robots and drones (e.g., a drone is required to follow a person when recording a video). To accomplish the VAT task, one typically needs to perform a sequence of tasks such as recognition, localization, motion prediction, and camera control. However, conventional visual tracking BID0 BID29 BID24 BID11 BID3 BID13 aims to solely propose a 2D bounding box of the target frame by frame, and does not actively take into consideration the control of camera. Thus, compared to the problem of ""passive"" tracking, VAT is more practical and challenging.With the advancement of deep reinforcement learning BID35 BID25 BID26 , training an end-to-end deep neural network via reinforcement learning for VAT is shown to be feasible BID21 BID20 . The authors learn a policy that maps raw-pixel observation to control signal straightly with a Conv-LSTM network. Such an end-to-end approach could save the effort of tuning an extra camera controller. Meanwhile, it also outperforms the conventional methods where the passive tracker is equipped with a hand-engineered camera controller. However, the performance of the deep reinforcement learning based tracker is still limited by the training methods. Due to the ""trial-and-error"" nature of reinforcement learning, it is infeasible to directly train the tracker in the real world. Alternatively, virtual environments are always utilized to generate sufficient data for training without tedious human labeling. Nevertheless, to deploy the trained tracker in the real world, one has to overcome the virtual-to-real gap. One solution can be building numbers of high-fidelity environments . However, it is expensive and tedious to build such environments for VAT. Both the visual rendering (illumination, texture, etc.) and the physical properties should be carefully designed to emulate the real world. Suppose we carry out VAT where the target is a pedestrian. To build the environment, one has to not only model the human's appearance, but also design physical rules and the pedestrian's trajectory so that it moves naturally like a human beings. Recently, BID21 tried to overcome the virtual-to-real gap by applying the so-called environment augmentation technique. They diversify the visual appearance by changing the placement of the background objects and by flipping left-right the screen frame. However, they neglect another important factor, that is, the motion of the target for VAT task. Intuitively, the complexity and diversity of the target motion in training will impact the generalization of the data-driven tracker. For example, if the target only moves forward during training, the tracker may over fit to move straightly and fail to track other motion patterns, like a sharp turn. In this paper, we have proposed an asymmetric dueling mechanism for visual active tracking (AD-VAT). Within AD-VAT, agents of tracker and target are learned in an adversarial manner. With the design of the partial zero-sum reward structure and tracker-aware model, the reinforced active tracker outperforms baseline methods. Experiments including ablation study in both 2D and 3D environments verify the effectiveness of the proposed mechanism.As future work, we would like to: 1) investigate the theoretical justification of applying modern Multi-Agent RL methods BID18 BID32 to solving Partially Observable Markov Game and finding Nash Equilibrium. 2) further develop the mechanism/model for active tracking in more complex environment (e.g., environments with a number of obstacles and moving distractors); 3) adapt the mechanism to other tasks (e.g., learning to grab a moving object).","Visual Active Tracking VAT aims following target object autonomously controlling motion system tracker given visual observations. Previous work has shown tracker can be trained simulator via reinforcement learning deployed real-world scenarios. However training method requires manually specifying moving path target object tracked which cannot ensure trackers generalization unseen object moving patterns. learn robust tracker VAT paper propose novel adversarial RL method which adopts Asymmetric Dueling mechanism referred AD-VAT AD-VAT tracker target are approximated end-to-end neural networks are trained viaRL dueling/competitive manner:.e tracker intends lockup target if the target tries escape tracker. are asymmetric target is aware tracker vice versa. Specifically besides observation if the target is fed trackers observation action learns predict trackers reward auxiliary task. show asymmetric dueling mechanism produces stronger target which in turn induces robust tracker. stabilize training also propose novel partial zero-sum reward tracker/target. experimental results 2D 3D environments demonstrate proposed method leads faster convergence training yields robust tracking behaviors different testing scenarios. supplementary videos see:https://www.youtube.com/playlist?list=PL9rZj4Mea7wOZkdajK1TsprRg8iUf51BS code is available https://github.com/zfw1226/active_tracking_rl Visual Active Tracking VAT aims following target object autonomously controlling motion system tracker given visual observations. VAT is demanded many real-world applications autonomous vehicle fleet e.g slave-vehicle should follow master-vehicle ahead service robots drones e.g drone is required follow person when recording video accomplish VAT task one typically needs perform sequence tasks recognition localization is,motion prediction camera control. However conventional visual tracking BID0 BID29 BID24 BID11 BID3 BID13 aims solely propose 2D bounding box target frame frame does not actively take consideration control camera. Thus compared problem passive tracking VAT is more practical challenging.With advancement deep reinforcement learning BID35 BID25 BID26 training end-to-end deep neural network via reinforcement learning VAT is shown feasible BID21 BID20. authors learn policy maps raw-pixel observation control signal straightly Conv-LSTM network. end-to-end approach could save effort tuning extra camera controller. Meanwhile also outperforms conventional methods where the passive tracker is equipped hand-engineered camera controller. However performance deep reinforcement learning based tracker is still limited training methods. Due trial-and-error nature reinforcement learning is infeasible directly train tracker real world. Alternatively virtual environments are always utilized generate sufficient data training without tedious human labeling. Nevertheless deploy trained tracker real world one has to overcome virtual-to-real gap. One solution can be building numbers high-fidelity environments. However is expensive tedious build environments VAT. visual rendering illumination texture etc. physical properties should be carefully designed emulate real world. Suppose carry VAT where the target is a pedestrian. build environment one has to not only model human's appearance also design physical rules pedestrian's trajectory moves naturally like human beings. Recently BID21 tried overcome virtual-to-real gap applying so-called environment augmentation technique. diversify visual appearance changing placement background objects flipping left-right screen frame. However neglect another important factor is,motion target VAT task. Intuitively complexity diversity target motion training will impact generalization data-driven tracker. example if the target moves forward training tracker may fit move straightly fail track motion patterns like sharp turn. paper have proposed asymmetric dueling mechanism visual active tracking AD-VAT Within AD-VAT agents tracker target are learned adversarial manner. design partial zero-sum reward structure tracker-aware model reinforced active tracker outperforms baseline methods. Experiments including ablation study 2D 3D environments verify effectiveness proposed mechanism.As future work would like to:1 investigate theoretical justification applying modern Multi-AgentRL methods BID18 BID32 solving Partially Observable Markov Game finding Nash Equilibrium. 2 develop mechanism/model active tracking complex environment e.g environments number obstacles moving distractors 3 adapt mechanism tasks e.g learning grab moving object",1124,768,356,0.011,1.464,2025/11/05 17:19:08,0.01,1.429,0.4174454828660433,338.961
"Identifying the hypernym relations that hold between words is a fundamental task in NLP. Word embedding methods have recently shown some capability to encode hypernymy. However, such methods tend not to explicitly encode the hypernym hierarchy that exists between words. In this paper, we propose a method to learn a hierarchical word embedding in a specific order to capture the hypernymy. To learn the word embeddings, the proposed method considers not only the hypernym relations that exists between words on a taxonomy, but also their contextual information in a large text corpus. The experimental results on a supervised hypernymy detection and a newly-proposed hierarchical path completion tasks show the ability of the proposed method to encode the hierarchy. Moreover, the proposed method outperforms previously proposed methods for learning word and hypernym-specific word embeddings on multiple benchmarks. Hypernymy relation is an essential component for many Natural Language Processing (NLP) tasks. It represents an asymmetric relation between name of a class (hypernym) and a particular instance of it (hyponym). For example, given the hypernymy pair (bird, vertebrate), the hyponym word bird is a particular instance of the hypernym word vertebrate, and one can simply say ""a bird is a vertebrate"". Hypernymy identification plays a major role in various NLP tasks such as question answering BID14 , taxonomy construction BID25 , textual entailment BID8 and text generation BID5 , to name a few.The task of identifying hypernymy has been long addressed by relying on either the lexicalsyntactic patterns where a particular textual pattern suggests the existence of a hypernymy relation, or the distributional representation of a given pair of words. In a pattern-based approach, from a sentence like ""a bird such as a falcon"" we can identify a hypernymy relation between bird and fal-con. Despite its simplicity and efficiency, pattern-based approaches suffer from a low precision and coverage issue BID44 . For example, let us consider the sentence ""some birds recorded in Africa such as Gadwall"", a typical lexical-pattern based approach may incorrectly detect (Gadwall, Africa) as hypernymy.In contrast to the requirement of the pattern-based approaches to have the hypernym and hyponym words occurring in the same sentence, the distributional family of approaches rely on the words co-occurrence statistics in a large text corpus to represent the words and then deduce the hold of hypernymy. It works on the assumption that taxonomically related words tend to occur in a similar context. In particular, a hypernym word has a broader context than its hypernym, and therefore the contextual features of the hyponym word are usually a subset of that of its hypernym. However, such approaches commonly struggle from discriminating the hypernym relations from other lexico-semantic relations BID34 .Lately , distributed word representations (a.k.a word embeddings) BID22 BID29 have shown some capability to encode hypernymy. Such methods typically embed the words into dense, low-dimensional, real-valued vectors, using the co-occurrence statistics obtained from a text corpora, and then used in a supervised settings to detect hypernymy. However , typical word embeddings models rely only on co-occurrence based similarity, and therefore are insufficient to encode taxonomic relations in the learnt word embeddings BID2 .Several recent studies have proposed methods for learning hypernymy-specific word embeddings BID44 BID2 BID26 . BID44 design a neural network to learn word embeddings that perceive hypernymy, purely relying on extracted pairwise training data from a web corpus. Moreover, Anh et al. [2016] proposed a similar approach, but further utilise the contextual information of the pre-extracted pairwise hypernymy. Similarly, Nguyen et al. [2017] introduce the HyperVec model that use the Skip-gram with Negative Sampling (SGNS) BID22 objective to learn the word embeddings from a corpus subject to pairwise hypernymy constraints extracted from a taxonomy. Moreover, BID27 proposed a new model that embed symbolic data into hyperbolic space, particularly into Poincaré ball, to learn hierarchical embeddings. Another model that is recently proposed is the LEAR model of BID39 . LEAR is a post-processing model that takes any word vectors and then adjust the input vectors to emphasis the hypernym relations. The aforementioned methods merely consider pairwise hypernymy relations rather than the hierarchical hypernymy path connecting a word to the root in a taxonomy.In this paper, we propose a method that jointly learns hierarchical word embeddings (HWE) from a corpus and a taxonomy. The proposed method begins by embedding the words into random low-dimensional real-valued vectors, and subsequently updates the embeddings to encode the hierarchical structure available in the taxonomy. To train the proposed method, we use a taxonomy to extract the hierarchical hypernymy paths for the hyponym words, and use the global vector BID29 as a context-aware objective between the hypernym and hyponym words. As such, the proposed model benefits from both the contextual information as well as the taxonomic relations to learn the embeddings.In our experiments, we evaluate our hierarchical word embeddings on the standard supervised hypernymy task on various benchmarks, graded lexical entailment prediction and a newly-proposed hierarchical path completion task. On the supervised hypernymy identification , the proposed method reports an improvement over several previously proposed methods, showing the benefit of considering the full hierarchical hypernymy paths instead of only pairwise relations. Moreover, a quantitative and qualitative analysis on the newly-proposed hierarchical path completion task further illustrate the ability of the proposed method to encode hypernymy in the learn embeddings. We presented a method to learn a Hierarchical Word Embedding (HWE) for identifying the hypernymy relations between words. For this purpose, we introduced a joint objective that make use of both a taxonomy and a large text corpus to learn hierarchical word embeddings. We evaluated HWE on the standard supervised hypernymy identification and a newly-proposed hierarchical hypernymy path completion tasks. The experiments conducted in this paper on the above mentioned two tasks demonstrate that HWE was able to encode the hypernymy relations between words into the learnt embeddings, and reports an improvement over several previously proposed methods that learn either general word embeddings or hypernymy-specific word embeddings.",Identifying hypernym relations hold words is a fundamental task NLP. Word embedding methods have recently shown capability encode hypernymy. However methods tend explicitly encode hypernym hierarchy exists words. paper propose method learn hierarchical word embedding specific order capture hypernymy. learn word embeddings proposed method considers hypernym relations exists words taxonomy also contextual information large text corpus. experimental results supervised hypernymy detection newly-proposed hierarchical path completion tasks show ability proposed method encode hierarchy. Moreover proposed method outperforms previously proposed methods learning word hypernym-specific word embeddings multiple benchmarks. Hypernymy relation is an essential component many Natural Language Processing NLP tasks. represents asymmetric relation name class hypernym particular instance hyponym example given hypernymy pair bird vertebrate hyponym word bird is a particular instance hypernym word vertebrate one can simply say bird is a vertebrate. Hypernymy identification plays major role various NLP tasks question answering BID14 taxonomy construction BID25 textual entailment BID8 text generation BID5 name few.The task identifying hypernymy has been long addressed relying either lexicalsyntactic patterns where a particular textual pattern suggests existence hypernymy relation distributional representation given pair words. pattern-based approach sentence like bird falcon can identify hypernymy relation bird fal-con Despite simplicity efficiency pattern-based approaches suffer low precision coverage issue BID44. example let us consider sentence birds recorded Africa Gadwall typical lexical-pattern based approach may incorrectly detect Gadwall Africa hypernymy.In contrast requirement pattern-based approaches have the hypernym hyponym words occurring sentence distributional family approaches rely words co-occurrence statistics large text corpus represent words deduce hold hypernymy. works assumption taxonomically related words tend occur similar context. particular hypernym word has a broader context hypernym therefore contextual features hyponym word are usually subset hypernym. However approaches commonly struggle discriminating hypernym relations lexico-semantic relations BID34.Lately distributed word representations.k.a word embeddings BID22 BID29 have shown capability encode hypernymy. methods typically embed words dense low-dimensional real-valued vectors using co-occurrence statistics obtained text corpora used supervised settings detect hypernymy. However typical word embeddings models rely co-occurrence based similarity therefore are insufficient encode taxonomic relations learnt word embeddings BID2.Several recent studies have proposed methods learning hypernymy-specific word embeddings BID44 BID2 BID26. BID44 design neural network learn word embeddings perceive hypernymy purely relying extracted pairwise training data web corpus. Moreover Anhetal. 2016 proposed similar approach utilise contextual information pre-extracted pairwise hypernymy. Similarly Nguyenetal. 2017 introduce HyperVec model use Skip-gram Negative Sampling SGNS BID22 objective learn word embeddings corpus subject pairwise hypernymy constraints extracted taxonomy. Moreover BID27 proposed new model embed symbolic data hyperbolic space particularly Poincaré ball learn hierarchical embeddings. Another model is recently proposed is the LEAR model BID39. LEAR is a post-processing model takes word vectors adjust input vectors emphasis hypernym relations. aforementioned methods merely consider pairwise hypernymy relations rather hierarchical hypernymy path connecting word root taxonomy.In paper propose method jointly learns hierarchical word embeddings HWE corpus taxonomy. proposed method begins embedding words random low-dimensional real-valued vectors subsequently updates embeddings encode hierarchical structure available taxonomy. train proposed method use taxonomy extract hierarchical hypernymy paths hyponym words use global vector BID29 context-aware objective hypernym hyponym words. proposed model benefits contextual information well taxonomic relations learn embeddings.In experiments evaluate hierarchical word embeddings standard supervised hypernymy task various benchmarks graded lexical entailment prediction newly-proposed hierarchical path completion task. supervised hypernymy identification proposed method reports improvement several previously proposed methods showing benefit considering full hierarchical hypernymy paths instead pairwise relations. Moreover quantitative qualitative analysis newly-proposed hierarchical path completion task illustrate ability proposed method encode hypernymy learn embeddings. presented method learn Hierarchical Word Embedding HWE identifying hypernymy relations words. purpose introduced joint objective make use taxonomy large text corpus learn hierarchical word embeddings. evaluated HWE standard supervised hypernymy identification newly-proposed hierarchical hypernymy path completion tasks. experiments conducted paper mentioned two tasks demonstrate HWE was able encode hypernymy relations words learnt embeddings reports improvement several previously proposed methods learn either general word embeddings hypernymy-specific word embeddings.,1282,871,411,0.013,1.472,2025/11/05 17:19:08,0.01,1.526,0.4423676012461057,355.971
"While self-organizing principles have motivated much of early learning models, such principles have rarely been included in deep learning architectures. Indeed, from a supervised learning perspective it seems that topographic constraints are rather decremental to optimal performance. Here we study a network model that incorporates self-organizing maps into a supervised network and show how gradient learning results in a form of a self-organizing learning rule. Moreover, we show that such a model is robust in the sense of its application to a variety of  areas, which is believed to be a hallmark of biological learning systems. Machine learning has made significant improvements, specifically with deep neural network models BID13 , BID0 , BID4 . Deep learning was made possible by much faster computer technology such as GPUs, and with algorithmic advancement such as BID17 BID3 BID10 , BID2 . Learning tasks that, due to their complexity or data volume, were impossible to execute a decade ago, now can be run in reasonable time scale. The improvements allow the applications of Deep Learning to many real world problems.Learning good internal representations is a key aspect of deep learning. Indeed, it is interesting to recall that the first breakthrough in deep learning came from an application of unsupervised pretraining with gradient-based fine tuning BID7 . Restricted Boltzmann Machines (RBMs) BID6 and Autoencoders BID1 BID8 are utilized for constructing the hidden layers of early models such as Deep Belief Networks (DBN) and Deep Boltzmann Machine (DBM), , BID16 . While much research of deep learning research focuses on learning efficiency and running performances, there is much less research into the understanding of the formation of internal representation in hierarchical neural networks. Moreover, while self-organizing maps have been and integral part of biologically motivated learning theories since the 1970s BID19 , BID12 the role of such self-organizing mechansims are less understood in modern deep learning theories. Topographical self-organization is often observed in biological neural networks BID11 , BID15 and thus may give new insights in understanding learning and self-organization in artificial neural networks.Here, we propose a network that combines aspects of self-organization into a supervised network model for classification. More specifically, in this study we modify the previously proposed Restricted Radial Basis Function Networks (rRBF) BID5 with a softmax output layer that is trained on a crossentropic cost function. This is more consistent with a probabilistic interpretation of the class membership output function than the previous implementation which allows a more clear derivation of the emergence of the self-organizing learning aspects of this network. We call this modified network the Softmax Restricted Radial Basis Function Networks (S-rRBF). Through this network we argue that it is possible to build a learning model in which unsupervised self-organization and supervised learning are just different aspect of a single learning mechanism. We show that the network achieves compatible performance with other deep network architectures while having the added feature of robustness in the sense that it compares favorable with the best performers in the studied examples, while the best performer changes for different applications. While the results are consistent with BID20 'No free lunch theorem', they also highlight that robustness against variation of applications and not the best performance is an important part in flexible learner, which is thought to be of importance when understanding biological learning systems.We highlight our ideas here with well understood applications examples of moderate complexity. However, the proposed architecture can also be scaled to deeper layers and hence applied to deeper learning problems. The main contribution here is showing algebraically the emergence of the selforganizing structures from supervised gradient learning. We believe that this research opens new insights into the relation between unsupervised and supervised learning. Also, we illustrate on some examples the internal representation in the competitive layer and compare it to a standard selforganizing map (SOM) BID12 and to t-Stochastic Neighborhood Embedding (t-SNE) BID18 ) that represents a deeper transformation of the feature space. In this research we showed that it is possible to build a hierarchical neural network that self-organizes with context-relevant topographical internal representation. More specifically, we showed that topographical self-organization can emerge as an implication of the supervised learning. Thus, the two learning processes of self-organization and supervised learning, which are often considered to be unrelated, are can be viewed as two different aspects of a single learning mechanism. The two learning processes are only distinguished by the layers where they occurs. The internal self-organization in this network is not fully unsupervised. However, the direction of the self-organization process in a hidden neuron is only decided by the relative value of the connection weight leading from the neuron to the output neuron relevant to the true label of the input and thus not dependent on the supervised error.The experiments show that the classification performance of the proposed model is comparable to that of standard supervised networks. While the proposed model does not always outperform existing conventional models, we found that the performance was comparable to the best performer for most of the diverse benchmark applications. Specific machine learning methods often perform well on datasets for which they have been designed, but it is well acknowledged that sufficient performance in a variety of tasks is useful in many applications such as robotics and probably to understand better human abilities. Another advantage of our system is its 2-dimensional internal layer offers auxiliary visual information on its learning representations. The S-rRBFcan can readily expanded into deep networks. As layered networks transfer transform inputs (physical stimuli) into labels (concepts) in a layer by layer manner, the visualization of internal layers in multi-layered S-rRBF can be considered as concept-forming visualization. The visualization can potentially offer new insights for machine learning.",self-organizing principles have motivated much early learning models principles have rarely included deep learning architectures. Indeed supervised learning perspective seems topographic constraints are rather decremental optimal performance. study network model incorporates self-organizing maps supervised network show how gradient learning results form self-organizing learning rule. Moreover show model is robust sense application variety areas which is believed hallmark biological learning systems. Machine learning has made significant improvements specifically deep neural network models BID13 BID0 BID4. Deep learning was made possible much faster computer technology GPUs algorithmic advancement BID17 BID3 BID10 BID2. Learning tasks due complexity data volume were impossible execute decade ago can be run reasonable time scale. improvements allow applications Deep Learning many real world problems.Learning good internal representations is a key aspect deep learning. Indeed is interesting recall first breakthrough deep learning came application unsupervised pretraining gradient-based fine tuning BID7. Restricted Boltzmann Machines RBMs BID6 Autoencoders BID1 BID8 are utilized constructing hidden layers early models Deep Belief Networks DBN Deep Boltzmann Machine DBM BID16. much research deep learning research focuses learning efficiency running performances is much less research understanding formation internal representation hierarchical neural networks. Moreover self-organizing maps have been and integral part biologically motivated learning theories since 1970s BID19 BID12 role self-organizing mechansims are less understood modern deep learning theories. Topographical self-organization is often observed biological neural networks BID11 BID15 thus may give new insights understanding learning self-organization artificial neural networks.Here propose network combines aspects self-organization supervised network model classification. specifically study modify previously proposed Restricted Radial Basis Function Networks rRBF BID5 softmax output layer is trained crossentropic cost function. is more consistent probabilistic interpretation class membership output function previous implementation which allows clear derivation emergence self-organizing learning aspects network. call modified network Softmax Restricted Radial Basis Function Networks S-rRBF network argue is possible build learning model which unsupervised self-organization supervised learning are just different aspect single learning mechanism. show network achieves compatible performance deep network architectures added feature robustness sense compares favorable best performers studied examples best performer changes different applications. results are consistent BID20 'No free lunch theorem' also highlight robustness variation applications best performance is an important part flexible learner which is thought importance when understanding biological learning systems.We highlight ideas well understood applications examples moderate complexity. However proposed architecture can also scaled deeper layers hence applied deeper learning problems. main contribution is showing algebraically emergence selforganizing structures supervised gradient learning. believe research opens new insights relation unsupervised supervised learning. Also illustrate examples internal representation competitive layer compare standard selforganizing map SOM BID12 t-Stochastic Neighborhood Embedding t-SNE BID18 represents deeper transformation feature space. research showed is possible build hierarchical neural network self-organizes context-relevant topographical internal representation. specifically showed topographical self-organization can emerge implication supervised learning. Thus two learning processes self-organization supervised learning which are often considered unrelated are can be viewed two different aspects single learning mechanism. two learning processes are only distinguished layers where they occurs. internal self-organization network is not fully unsupervised. However direction self-organization process hidden neuron is only decided relative value connection weight leading neuron output neuron relevant true label input thus dependent supervised error.The experiments show classification performance proposed model is comparable standard supervised networks. proposed model does not always outperform existing conventional models found performance was comparable best performer diverse benchmark applications. Specific machine learning methods often perform well datasets which they have designed is well acknowledged sufficient performance variety tasks is useful many applications robotics probably understand better human abilities. Another advantage system is its 2-dimensional internal layer offers auxiliary visual information learning representations. S-rRBFcan can readily expanded deep networks. layered networks transfer transform inputs physical stimuli labels concepts layer layer manner visualization internal layers multi-layered S-rRBF can be considered concept-forming visualization. visualization can potentially offer new insights machine learning.,1152,784,368,0.012,1.469,2025/11/05 17:19:08,0.01,1.457,0.4330218068535826,344.508
"Quantization of a neural network has an inherent problem called accumulated quantization error, which is the key obstacle towards ultra-low precision, e.g., 2- or 3-bit precision. To resolve this problem, we propose precision highway, which forms an end-to-end high-precision information flow while performing the ultra-low-precision computation. First, we describe how the precision highway reduce the accumulated quantization error in both convolutional and recurrent neural networks. We also provide the quantitative analysis of the benefit of precision highway and evaluate the overhead on the state-of-the-art hardware accelerator. In the experiments, our proposed method outperforms the best existing quantization methods while offering 3-bit weight/activation quantization with no accuracy loss and 2-bit quantization with a 2.45 % top-1 accuracy loss in ResNet-50. We also report that the proposed method significantly outperforms the existing method in the 2-bit quantization of an LSTM for language modeling. Energy-efficient inference of neural networks is becoming increasingly important in both servers and mobile devices (e.g., smartphones, AR/VR devices, and drones). Recently, there have been active studies on ultra-low-precision inference using 1 to 4 bits BID21 BID9 BID27 BID25 BID28 BID2 BID15 BID1 and their implementations on CPU and GPU BID23 , and dedicated hardware BID19 BID22 . However, as will be explained in section 5.2, the existing quantization methods suffer from a problem called accumulated quantization error where large quantization errors get accumulated across layers, making it difficult to enable ultra-low precision in deep neural networks.In order to address this problem, we propose a novel concept called precision highway where an end-to-end path of high-precision information reduces the accumulated quantization error thereby enabling ultra-low-precision computation. Our proposed work is similar to recent studies BID15 BID2 which propose utilizing pre-activation residual networks, where skip connections are kept in full precision while the residual path performs low-precision computation. Compared with these works, our proposed method offers a generalized concept of high-precision information flow, namely, precision highway, which can be applied to not only the pre-activation convolutional networks but also both the post-activation convolutional and recurrent neural networks. Our contributions are as follows.• We propose a novel idea of network-level approach to quantization, called precision highway and quantitatively analyze its benefits in terms of the propagation of quantization errors and the difficulty of convergence in training based on the shape of loss surface.• We provide the detailed analysis of the energy and memory overhead of precision highway based on the state-of-the-art hardware accelerator model. According to our experiments, the overhead is negligible while offering significant improvements in accuracy.• We apply precision highway to both convolution and recurrent networks. We report a 3-bit quantization of ResNet-50 without accuracy loss and a 2-bit quantization with a very small accuracy loss. We also provide the sub 4-bit quantization results of long short-term memory (LSTM) for language modeling.2 RELATED WORK BID16 presented an int8 quantization method that selects an activation truncation threshold to minimize the Kullback-Leibler divergence between the distributions of the original and quantized data. BID12 proposed a quantization scheme that enables integer-arithmetic only matrix multiplications (practically, 8-bit quantization for neural networks). These methods are implemented on existing CPUs or GPUs BID11 ACL) . BID9 presented a binarization method and demonstrated the performance benefit on a GPU. BID21 proposed a binary network called XNOR-Net in which a weight-binarized AlexNet gives the same accuracy as a full-precision one. BID25 presented DoReFa-Net, which applies tanh-based weight quantization and bounded activation. BID26 proposed a balanced quantization that attempts to balance the population of values on quantization levels. BID7 proposed utilizing full precision for internal cell states in the LSTM because of their wide value distributions. This work is similar to ours in that high-precision data are selectively utilized to improve the quantized network. Our difference is proposing a network-level end-to-end flow of high-precision activation. Recently, BID28 presented 4-bit quantization with ResNet-50 . They adopt Dorefa-net style weight quantization with static bounded activation, and improve accuracy by adopting multi-step quantization and knowledge distillation during fine-tuning. proposed a trade-off between the number of channels and precision . Clustering-based methods have the potential to further reduce the precision BID5 . However, they require a lookup table and full-precision computation , which makes them less hardware-friendly.Recently, BID2 a) and BID15 proposed utilizing full-precision on the skip connections in pre-activation residual networks 1 . Compared with those works, our proposed idea has a salient difference in that it offers a network-level solution and demonstrates that the end-to-end flow of high-precision information is crucial. In addition, our method is not limited to pre-activation residual networks , but general enough to be applied to both post-activation convolutional and recurrent neural networks. In this paper, we proposed the concept of end-to-end precision highway which can be applied to both feedforward and feedback networks and enable ultra-low precision in deep neural networks. The proposed precision highway reduces quantization errors by keeping high-precision activation from the input to output of the network with small computation costs. We described how it reduces the accumulated quantization error and presented quantitative analyses in terms of accuracy and hardware cost as well as training characteristics. Our experiments showed that the proposed method outperforms the state-of-the-art methods in the 3-and 2-bit quantizations of ResNet-18/50 and 2-bit quantization of an LSTM model. We believe that our work will serve as a step toward mixed precision networks for computational efficiency.",Quantization neural network has an inherent problem called accumulated quantization error which is the key obstacle towards ultra-low precision e.g 2- 3-bit precision. resolve problem propose precision highway which forms end-to-end high-precision information flow performing ultra-low-precision computation. First describe how the precision highway reduce accumulated quantization error convolutional recurrent neural networks. also provide quantitative analysis benefit precision highway evaluate overhead state-of-the-art hardware accelerator. experiments proposed method outperforms best existing quantization methods offering 3-bit weight/activation quantization accuracy loss 2-bit quantization 2.45 top-1 accuracy loss ResNet-50 also report proposed method significantly outperforms existing method 2-bit quantization LSTM language modeling. Energy-efficient inference neural networks is becoming increasingly important servers mobile devices e.g smartphones AR/VR devices drones Recently have been active studies ultra-low-precision inference using1 4 bits BID21 BID9 BID27 BID25 BID28 BID2 BID15 BID1 implementations CPU GPU BID23 dedicated hardware BID19 BID22. However will be explained section 5.2 existing quantization methods suffer problem called accumulated quantization error where large quantization errors get accumulated across layers making difficult enable ultra-low precision deep neural networks.In order address problem propose novel concept called precision highway where an end-to-end path high-precision information reduces accumulated quantization error thereby enabling ultra-low-precision computation. proposed work is similar recent studies BID15 BID2 which propose utilizing pre-activation residual networks where skip connections are kept full precision residual path performs low-precision computation. Compared works proposed method offers generalized concept high-precision information flow namely precision highway which can be applied pre-activation convolutional networks also post-activation convolutional recurrent neural networks. contributions are as follows.• propose novel idea network-level approach quantization called precision highway quantitatively analyze benefits terms propagation quantization errors difficulty convergence training based shape loss surface.• provide detailed analysis energy memory overhead precision highway based state-of-the-art hardware accelerator model. According experiments overhead is negligible offering significant improvements accuracy.• apply precision highway convolution recurrent networks. report 3-bit quantization ResNet-50 without accuracy loss 2-bit quantization small accuracy loss. also provide sub 4-bit quantization results long short-term memory LSTM language modeling.2 RELATED WORK BID16 presented int8 quantization method selects activation truncation threshold minimize Kullback-Leibler divergence distributions original quantized data. BID12 proposed quantization scheme enables integer-arithmetic matrix multiplications practically 8-bit quantization neural networks methods are implemented existing CPUs GPUs BID11 ACL BID9 presented binarization method demonstrated performance benefit GPU. BID21 proposed binary network called XNOR-Net which a weight-binarized AlexNet gives accuracy full-precision one. BID25 presented DoReFa-Net which applies tanh-based weight quantization bounded activation. BID26 proposed balanced quantization attempts balance population values quantization levels. BID7 proposed utilizing full precision internal cell states LSTM wide value distributions. work is similar high-precision data are selectively utilized improve quantized network. difference is proposing network-level end-to-end flow high-precision activation. Recently BID28 presented 4-bit quantization ResNet-50 adopt Dorefa-net style weight quantization static bounded activation improve accuracy adopting multi-step quantization knowledge distillation fine-tuning proposed trade-off number channels precision. Clustering-based methods have the potential reduce precision BID5. However require lookup table full-precision computation which makes less hardware-friendly.Recently BID2 BID15 proposed utilizing full-precision skip connections pre-activation residual networks1. Compared works proposed idea has a salient difference offers network-level solution demonstrates end-to-end flow high-precision information is crucial. addition method is not limited pre-activation residual networks general enough applied post-activation convolutional recurrent neural networks. paper proposed concept end-to-end precision highway which can be applied feedforward feedback networks enable ultra-low precision deep neural networks. proposed precision highway reduces quantization errors keeping high-precision activation input output network small computation costs. described how it reduces accumulated quantization error presented quantitative analyses terms accuracy hardware cost well training characteristics. experiments showed proposed method outperforms state-of-the-art methods 3-and 2-bit quantizations ResNet-18/50 2-bit quantization LSTM model. believe work will serve step toward mixed precision networks computational efficiency.,1197,874,323,0.01,1.37,2025/11/05 17:19:08,0.0,1.586,0.1246105919003116,324.261
"The vast majority of natural sensory data is temporally redundant. For instance, video frames or audio samples which are sampled at nearby points in time tend to have similar values.   Typically, deep learning algorithms take no advantage of this redundancy to reduce computations.   This can be an obscene waste of energy.   We present a variant on backpropagation for neural networks in which computation scales with the rate of change of the data - not the rate at which we process the data.   We do this by implementing a form of Predictive Coding wherein neurons communicate a combination of their state, and their temporal change in state, and quantize this signal using Sigma-Delta modulation.   Intriguingly, this simple communication rule give rise to units that resemble biologically-inspired leaky integrate-and-fire neurons, and to a spike-timing-dependent weight-update similar to Spike-Timing Dependent Plasticity (STDP), a synaptic learning rule observed in the brain.   We demonstrate that on MNIST, on a temporal variant of MNIST, and on Youtube-BB, a dataset with videos in the wild, our algorithm performs about as well as a standard deep network trained with backpropagation, despite only communicating discrete values between layers.   Currently, most algorithms used in Machine Learning work under the assumption that data points are independent and identically distributed, as this assumption provides good statistical guarantees for convergence. This is very different from the way data enters our brains. Our eyes receive a single, never-ending stream of temporally correlated data. We get to use this data once, and then it's gone. Moreover, most sensors produce sequential, temporally redundant streams of data. This can be both a blessing and a curse. From a statistical learning point of view this redundancy may lead to biased estimators when used to train models which assume independent and identically distributed input data. However, the temporal redundancy also implies that intuitively not all computations are necessary.Online Learning is the study of how to learn in this domain -where data becomes available in sequential order and is given to the model only once. Given the enormous amount of sequential data, mainly videos, that are being produced nowadays, it seems desirable to develop learning systems that simply consume data on-the-fly as it is being generated, rather than collect it into datasets for offline-training. There is, however a problem of efficiency, which we hope to illustrate with two examples:1. CCTV feeds. CCTV Cameras collect an enormous amount of data from mostly-static scenes.The amount of new information in a frame, given the previous frame, tends to be low, i.e. the data tends to be temporally redundant. If we want to train a model from of this data (for example a pedestrian detector), we need to process a large amount of mostly-static frames. If the frame rate doubles, so does the amount of computation. Intuitively, it feels that this should not be necessary. It would be nice to still be able to use all this data, but have the amount of computation scale with the amount of new information in each frame, not just the number of frames and dimensions of the data.2. Robot perception. Robots have no choice but to learn online -their future input data (e.g. camera frames) are dependent on their previous predictions (i.e. motor actions). Not only does their data come in nonstationary temporal streams, but it typically comes from several sensors running at different rates. The camera may produce 1MB images at 30 frames/s, while the gyroscope might produce 1-byte readings at 1000 frames/s. It is not obvious, using current methods in deep learning, how we can integrate asynchronous sensory signals into a unified, trainable, latent representation, without undergoing the inefficient process of recomputing the function of the network every time a new signal arrives.These examples point to the need for a training method where the amount of computation required to update the model scales with the amount of new information in the data, and not just the dimensionality of the data.There has been a lot of work on increasing the computational efficiency of neural networks by quantizing neural weights or activations (see Section 4), but comparatively little work on exploiting redundancies in the data to reduce the amount of computation. BID12 , set out to exploit the temporal redundancy in video by having neurons only send their quantized changes in activation to downstream neurons, and having the downstream neurons integrate these changes over time. This approach (take the temporal difference, multiply by weights, temporally integrate) works for efficiently approximating the function of the network, but fails for training. The reason for this failure is that when the weights are functions of time, we no longer reconstruct the correct activation for the next layer. In other words, given a sequence of inputs x 0 ...x t with x 0 = 0 and weights w 1 ...w t :t τ =1 (x τ − x τ −1 ) · w τ = x t · w t unless w t = w 0 ∀t. FIG0 describes the problem visually.In this paper, we correct for this problem by encoding a mixture of two components of the layers activation x t : the proportional component k p x t , and the derivative component k d (x t − x t−1 ). When we invert this encoding scheme, we get a decoding scheme which corresponds to taking an exponentially decaying temporal average of past inputs. Interestingly, the resulting neurons begin to resemble models of biological spiking neurons, whose membrane potentials can approximately be modeled as an exponentially decaying temporal average of past inputs.In this work, we present a scheme wherein the temporal redundancy of input data is used to reduce the computation required to train a neural network. We demonstrate this on the MNIST and Youtube-BB datasets. To our knowledge we are the first to create a neural network training algorithm which uses less computation as data becomes more temporally redundant. We set out with the objective of reducing the computation in deep networks by taking advantage of temporal redundancy in data. We described a simple rule (Equation 4) for sparsifying the communication between layers of a neural network by having our neurons communicate a combination of their temporal change in activation, and the current value of their activation. We show that it follows from this scheme that neurons should behave as leaky integrators (Equation 5 ). When we quantize our neural activations with Sigma-Delta modulation, a common quantization scheme in signal processing, we get something resembling a leaky integrate-and-fire neuron. We derive efficient update rules for the weights of our network, and show these to be related to STDP -a learning rule first observed in neuroscience. Finally, we train our network, verify that it does indeed compute more efficiently on temporal data, and show that it performs about as well as a traditional deep network of the same architecture, but with significantly reduced computation. Finally, we show that our network can train on real video data.The efficiency of our approach hinges on the temporal redundancy of our input data and neural activations. There is an interesting synergy here with the concept of slow-features BID17 . Slow-Feature learning aims to discover latent objects that persist over time. If the hidden units were to specifically learn to respond to slowly-varying features of the input, the layers in a spiking implementation of such a network would have to communicate less often. In such a network, the tasks of feature-learning and reducing inter-layer communication may be one and the same.Code is available at github.com/petered/pdnn.","vast majority natural sensory data is temporally redundant. instance video frames audio samples which are sampled nearby points time tend have similar values. Typically deep learning algorithms take advantage redundancy reduce computations. can be an obscene waste energy. present variant backpropagation neural networks which computation scales rate change data rate which we process data. do this by implementing form Predictive Coding wherein neurons communicate combination state temporal change state quantize signal using Sigma-Delta modulation. Intriguingly simple communication rule give rise units resemble biologically-inspired leaky integrate-and-fire neurons spike-timing-dependent weight-update similar Spike-Timing Dependent Plasticity STDP synaptic learning rule observed brain. demonstrate MNIST temporal variant MNIST Youtube-BB dataset videos wild algorithm performs well standard deep network trained backpropagation despite communicating discrete values layers. Currently algorithms used Machine Learning work assumption data points are independent identically distributed assumption provides good statistical guarantees convergence. is very different way data enters brains. eyes receive single never-ending stream temporally correlated data. get use data gone. Moreover sensors produce sequential temporally redundant streams data. can be both blessing curse. statistical learning point view redundancy may lead biased estimators when used train models which assume independent identically distributed input data. However temporal redundancy also implies intuitively computations are necessary.Online Learning is the study how to learn domain -where data becomes available sequential order is given model once. Given enormous amount sequential data mainly videos are being produced nowadays seems desirable develop learning systems simply consume data on-the-fly is being generated rather collect datasets offline-training is,however problem efficiency which we hope illustrate two examples:1 CCTV feeds. CCTV Cameras collect enormous amount data mostly-static scenes.The amount new information frame given previous frame tends low.e data tends temporally redundant. If we want train model data example pedestrian detector need process large amount mostly-static frames. If the frame rate doubles does the have the amount computation. Intuitively feels should not necessary. would nice still able use data does the have the amount computation scale amount new information frame number frames dimensions data.2 Robot perception. Robots have no choice learn online -their future input data e.g camera frames are dependent previous predictions.e motor actions does their data come nonstationary temporal streams typically comes several sensors running different rates. camera may produce 1MB images 30 frames/gyroscope might produce 1-byte readings 1000 frames/s. is not obvious using current methods deep learning how we can integrate asynchronous sensory signals unified trainable latent representation without undergoing inefficient process recomputing function network every time new signal arrives.These examples point need training method where the amount computation required update model scales amount new information data dimensionality data.There has been a lot work increasing computational efficiency neural networks quantizing neural weights activations see Section4 comparatively little work exploiting redundancies data reduce amount computation. BID12 set exploit temporal redundancy video neurons send quantized changes activation downstream neurons downstream neurons integrate changes time. approach take temporal difference multiply weights temporally integrate works efficiently approximating function network fails training. reason failure is that when the weights are functions time longer reconstruct correct activation next layer. words given sequence inputs x 0... x x0 0 weights w 1... w t:τ=1 xτ−x τ−1 ·wτ x ·w unlessw w 0 ∀t FIG0 describes problem visually.In paper correct problem encoding mixture two components layers activationx t:proportional componentkp x derivative componentk x − x t−1 When we invert encoding scheme get decoding scheme which corresponds taking exponentially decaying temporal average past inputs. Interestingly resulting neurons begin resemble models biological spiking neurons whose membrane potentials can approximately modeled exponentially decaying temporal average past inputs.In work present scheme wherein temporal redundancy input data is used reduce computation required train neural network. demonstrate MNIST Youtube-BB datasets. knowledge are the first create neural network training algorithm which uses less computation data becomes temporally redundant. set objective reducing computation deep networks taking advantage temporal redundancy data. described simple rule Equation4 sparsifying communication layers neural network neurons communicate combination temporal change activation current value activation. show follows scheme neurons should behave leaky integrators Equation5 When we quantize neural activations Sigma-Delta modulation common quantization scheme signal processing get something resembling leaky integrate-and-fire neuron. derive efficient update rules weights network show related STDP -a learning rule first observed neuroscience. Finally train network verify does indeed compute efficiently temporal data show performs well traditional deep network architecture significantly reduced computation. Finally show network can train real video data.The efficiency approach hinges temporal redundancy input data neural activations. is an interesting synergy concept slow-features BID17. Slow-Feature learning aims discover latent objects persist time. If the hidden units were to specifically learn respond slowly-varying features input layers spiking implementation network would have to communicate less often. network tasks feature-learning reducing inter-layer communication may one same.Code is available github.com/petered/pdnn.",1528,984,544,0.018,1.553,2025/11/05 17:19:08,0.01,1.776,0.6947040498442364,494.008
"Information bottleneck (IB) is a method for extracting information from one random variable X that is relevant for predicting another random variable Y. To do so, IB identifies an intermediate ""bottleneck"" variable T that has low mutual information I(X;T) and high mutual information I(Y;T). The ""IB curve"" characterizes the set of bottleneck variables that achieve maximal I(Y;T) for a given I(X;T), and is typically explored by maximizing the ""IB Lagrangian"", I(Y;T) - βI(X;T). In some cases, Y is a deterministic function of X, including many classification problems in supervised learning where the output class Y is a deterministic function of the input X. We demonstrate three caveats when using IB in any situation where Y is a deterministic function of X: (1) the IB curve cannot be recovered by maximizing the IB Lagrangian for different values of β; (2) there are ""uninteresting"" trivial solutions at all points of the IB curve; and (3) for multi-layer classifiers that achieve low prediction error, different layers cannot exhibit a strict trade-off between compression and prediction, contrary to a recent proposal. We also show that when Y is a small perturbation away from being a deterministic function of X, these three caveats arise in an approximate way. To address problem (1), we propose a functional that, unlike the IB Lagrangian, can recover the IB curve in all cases. We demonstrate the three caveats on the MNIST dataset. The information bottleneck (IB) method BID29 provides a principled way to extract information that is present in one variable that is relevant for predicting another variable. Given two random variables X and Y , IB posits a ""bottleneck"" variable T that obeys the Markov condition Y − X − T . By the data processing inequality (DPI) BID9 , this Markov condition implies that I(X; T ) ≥ I(Y ; T ), meaning that the bottleneck variable cannot contain more information about Y than it does about X. In fact, any particular choice of the bottleneck variable T can be quantified by two terms: the mutual information I(X; T ), which reflects how much T compresses X, and the mutual information I(Y ; T ), which reflects how well T predicts Y . In IB, bottleneck variables are chosen to maximize prediction given a constraint on compression BID32 BID1 BID13 , where ∆ is the set of random variables T obeying the Markov condition Y − X − T . The values of F (r) for different r specify the IB curve. In order to explore the IB curve, one must find optimal T for different values of r. It is known that the IB curve is concave in r but may not be strictly concave. This seemingly minor issue of non-strict concavity will play a central role in our analysis.In practice, the IB curve is almost always explored not via the constrained optimization problem of Eq.(1), but rather by maximizing the so-called IB Lagrangian, Several recent papers have drawn connections between IB and supervised learning, in particular classification using neural networks. In this context, X represents input vectors, Y represents the output classes, and T represents intermediate representations used by the network architecture, such as the activity of hidden layer(s ) BID30 . Some of these papers modify neural network training algorithms so as to optimize the IB Lagrangian BID2 BID7 , thereby permitting the use of IB with high-dimensional, continuousvalued random variables. Some papers have also suggested that by controlling the amount of compression, one can tune desired characteristics of trained models such as generalization error BID23 BID30 BID31 , robustness to adversarial inputs BID2 , and detection of out-of-distribution data BID3 . Other research (ShwartzZiv & Tishby, 2017) has suggested -somewhat controversially BID22 -that stochastic gradient descent (SGD) training dynamics may implicitly favor hidden layer mappings that balances compression and prediction, with earlier hidden layers favoring prediction over compression and latter hidden layers favoring compression over prediction. Finally , there is the general notion that intermediate representations that are optimal in the IB sense correspond to ""interesting"" or ""useful"" compressions of input vectors BID4 .There are also numerous application domains of IB beyond supervised learning, including clustering BID25 , coding theory and quantization BID6 BID34 BID8 , and cognitive science BID33 . In most of these applications, it is of central interest to explore solutions at different points on the IB curve, for example to control the number of detected clusters, or to adapt codes to available channel capacity.In some scenarios, Y may be a deterministic function of X, i.e., Y = f (X) for some single-valued function f . For example , in many classification problems, it is assumed that any given input belongs to a single class, which implies a deterministic relationship between X and Y . In this paper , we demonstrate three caveats for IB that appear whenever Y is a deterministic function of X: 1. There is no one-to-one mapping between different points on the IB curve and maximizers of the IB Lagrangian L β IB for different β, thus the IB curve cannot be explored by maximizing L β IB while varying β. This occurs because when Y = f (X), the IB curve has a piecewise linear shape and is therefore not strictly concave. The dependence of the IB Lagrangian on the strict concavity of F (r) has been previously noted BID13 BID24 , but the implications and pervasiveness of this problem (e.g., in many classification scenarios) has not been fully recognized. We analyze this issue and propose a solution in the form of an alternative objective function, which can be used to explore the IB curve even when Y = f (X). 2. All points on the IB curve contain uninteresting trivial solutions (in particular, stochastic mixtures of two very simple solutions). This suggests that IB-optimality is not sufficient for an intermediate representation to be an interesting or useful compression of input data. 3. For a neural network with several hidden layers that achieves a low probability of error, the hidden layers cannot display a strict trade-off between compression and prediction (in particular, different layers can only differ in the amount of compression, not prediction). In Appendix B, we show that the above three caveats also apply to the recently proposed deterministic IB variant of IB BID26 , in which the compression term is quantified using the entropy H(T ) rather than the mutual information I(X; T ). In that Appendix, we propose an alternative objective function that can be used to resolve the first problem for dIB.We also show, in Appendix C, that our results apply when Y is not exactly a deterministic function of X, but -close to one. In this case: (1) it is hard to explore the IB curve by optimizing the IB Lagrangian, because all optimizers will fall within O(− log ) of a single ""corner"" point on the information plane; (2) along all points on the IB curve, there are ""uninteresting"" trivial solutions that are no more than O(− log ) away from being optimal; (3) different layers of a neural networks can trade-off at most O(− log ) amount of prediction.A recent paper BID4 ) also discusses several difficulties in using IB to analyze intermediate representations in supervised learning. That paper does not consider the particular 1 Note that optimizing L β IB is still a constrained problem in that p(t|x) must be a valid conditional probability. However, this constraint is usually easier to handle, e.g., by using an appropriate parameterization.issues that arise when Y is a deterministic function of X, and its arguments are complementary to ours. BID24 [Sec. 2.4 ] discuss another caveat for IB in deterministic settings, concerning the relationship between sufficient statistics and the complexity of the inputoutput mapping, which is orthogonal to the three caveats analyzed here. Finally, BID22 and BID4 observed that when T is continuous-valued and a deterministic function of a continuous-valued X, I(X; T ) can be unbounded, making the application of the IB framework problematic. We emphasize that the caveats discussed in this paper are unrelated to that problem.Note that our results are based on analytically-provable properties of the IB curve, i.e., global optima of Eq. (1), and do not concern practical issues of optimization (which may be important in realworld scenarios). Our theoretical results are also independent of the practical issue of estimating MI between neural network layers, an active area of recent research BID5 BID14 BID10 BID12 , though our empirical experiments in Section 7 rely on the estimator proposed in . Finally, our results are also independent of issues related to the relationship between IB, finite data sampling, and generalization error BID23 BID30 BID31 .In the next section, we review some of the connections between supervised learning and IB. In Section 3, we show that when Y = f (X), the IB curve has a piecewise linear (not strictly concave) shape. In Sections 4, 5 and 6, we discuss the three caveats mentioned above. In Section 7, we demonstrate the caveats using a neural-network implementation of IB on the MNIST dataset. The information bottleneck principle has attracted a great deal of attention in various fields, including information theory, cognitive science, and machine learning, particularly in the context of classification using neural networks. In this work, we showed that in any scenario where Y is a deterministic function of X -which includes many classification problems -IB demonstrates behavior that is qualitatively different from when the mapping from X to Y is stochastic. In particular, in such cases: (1) the IB curve cannot be recovered by maximizing the IB Lagrangian I(Y ; T ) − βI(X; T ) while varying β; (2) all points on the IB curve contain ""uninteresting"" representations of inputs; (3) multi-layer classifiers that achieve zero probability of error cannot have a strict trade-off between prediction and compression among successive layers, contrary to a recent proposal.Our results should not be taken to mean that the application of IB to supervised learning is without merit. First, they do not apply to various non-deterministic classification problems where the output is stochastic. Second, even for deterministic scenarios, one may still wish to control the amount of compression during training, e.g., to improve generalization or robustness to adversarial inputs. In this case, however, our work shows that to achieve varying rates of compression, one should use a different objective function than the IB Lagrangian.","Information bottleneck IB is a method extracting information one random variableX is relevant predicting another random variable Y. do so,IB identifies intermediate bottleneck variable has low mutual information X;high mutual information Y;IB curve characterizes set bottleneck variables achieve maximal Y;given X;is typically explored maximizing IB Lagrangian Y;-βI X;cases is a deterministic function X including many classification problems supervised learning where the output class is a deterministic function inputX. demonstrate three caveats when usingIB situation where Y is a deterministic function X:1 IB curve cannot recovered maximizing IB Lagrangian different values β;2 are uninteresting trivial solutions points IB curve;3 multi-layer classifiers achieve low prediction error different layers cannot exhibit strict trade-off compression prediction contrary recent proposal. also show whenYis small perturbation away deterministic function X three caveats arise approximate way. address problem 1 propose functional unlike IB Lagrangian can recover IB curve cases. demonstrate three caveats MNIST dataset. information bottleneck IB is a method BID29 provides principled way extract information is present one variable is relevant predicting another variable. Given two random variables X IB posits bottleneck variable obeys Markov condition −X− T. data processing inequality DPI BID9 Markov condition implies X;≥ Y;meaning bottleneck variable cannot contain information does about X. fact particular choice bottleneck variable can be quantified two terms:mutual information X;which reflects how much compressesX mutual information Y;which reflects how well predicts Y. IB bottleneck variables are chosen maximize prediction given constraint compression BID32 BID1 BID13 where∆ is the set random variables obeying Markov condition −X− T. values F r different r specify IB curve. order explore IB curve one must find optimal different values r. is known IB curve is concave r may strictly concave. seemingly minor issue non-strict concavity will play central role analysis.In practice IB curve is almost always explored via constrained optimization problem Eq. 1 rather maximizing so-called IB Lagrangian Several recent papers have drawn connections IB supervised learning particular classification using neural networks. context X represents input vectors represents output classes represents intermediate representations used network architecture activity hidden layer BID30. papers modify neural network training algorithms optimize IB Lagrangian BID2 BID7 thereby permitting use IB high-dimensional continuousvalued random variables. papers have also suggested controlling amount compression one can tune desired characteristics trained models generalization error BID23 BID30 BID31 robustness adversarial inputs BID2 detection out-of-distribution data BID3. research ShwartzZiv Tishby 2017 has suggested -somewhat controversially BID22 -that stochastic gradient descent SGD training dynamics may implicitly favor hidden layer mappings balances compression prediction earlier hidden layers favoring prediction compression latter hidden layers favoring compression prediction. Finally is the general notion intermediate representations are optimal IB sense correspond interesting useful compressions input vectors BID4.There are also numerous application domains IB beyond supervised learning including clustering BID25 coding theory quantization BID6 BID34 BID8 cognitive science BID33. applications is of central interest explore solutions different points IB curve example control number detected clusters adapt codes available channel capacity.In scenarios may deterministic function X.e f X single-valued functionf. example many classification problems is assumed given input belongs single class which implies deterministic relationship X Y. paper demonstrate three caveats IB appear whenever is a deterministic function X:1. is no one-to-one mapping different points IB curve maximizers IB LagrangianLβ IB differentβ thus IB curve cannot explored maximizingLβIB varyingβ. occurs whenY=f X IB curve has a piecewise linear shape is therefore strictly concave. dependence IB Lagrangian strict concavity F r has been previously noted BID13 BID24 implications pervasiveness problem e.g many classification scenarios has not been fully recognized. analyze issue propose solution form alternative objective function which can be used explore IB curve even whenY=f X 2. points IB curve contain uninteresting trivial solutions particular stochastic mixtures two simple solutions suggests IB-optimality is not sufficient intermediate representation interesting useful compression input data. 3. neural network several hidden layers achieves low probability error hidden layers cannot display strict trade-off compression prediction particular different layers can only differ amount compression prediction AppendixB show three caveats also apply recently proposed deterministicIB variant IB BID26 which the compression term is quantified using entropyH rather mutual information X;Appendix propose alternative objective function can be used resolve first problem dIB.We also show AppendixC results apply when Y is not exactly deterministic function X -close one. case:1 is hard explore IB curve optimizing IB Lagrangian optimizers will fall within − log single corner point information plane;2 along points IB curve are uninteresting trivial solutions are no more − log away optimal;3 different layers neural networks can trade-off − log amount prediction.A recent paper BID4 also discusses several difficulties usingIB analyze intermediate representations supervised learning. paper does not consider particular 1 Note optimizingLβIB is still constrained problem p t|x must valid conditional probability. However constraint is usually easier handle e.g using appropriate parameterization.issues arise when Y is a deterministic function X arguments are complementary ours. BID24 Sec. 2.4 discuss another caveat IB deterministic settings concerning relationship sufficient statistics complexity inputoutput mapping which is orthogonal three caveats analyzed here. Finally BID22 BID4 observed when T is continuous-valued deterministic function continuous-valuedX X;can be unbounded making application IB framework problematic. emphasize caveats discussed paper are unrelated problem.Note results are based analytically-provable properties IB curve.e global optima Eq. 1 do concern practical issues optimization may important realworld scenarios theoretical results are also independent practical issue estimatingMI neural network layers active area recent research BID5 BID14 BID10 BID12 though empirical experiments Section 7 rely estimator proposed in. Finally results are also independent issues related relationship IB finite data sampling generalization error BID23 BID30 BID31.In next section review connections supervised learning IB. Section3 show whenY=f X IB curve has a piecewise linear strictly concave shape. Sections4 5 6 discuss three caveats mentioned above. Section7 demonstrate caveats using neural-network implementation IB MNIST dataset. information bottleneck principle has attracted great deal attention various fields including information theory cognitive science machine learning particularly context classification using neural networks. work showed scenario where Y is a deterministic function X -which includes many classification problems -IB demonstrates behavior is qualitatively different when the mapping X is stochastic. particular cases:1 IB curve cannot recovered maximizing IB Lagrangian Y;−βI X;varyingβ;2 points IB curve contain uninteresting representations inputs;3 multi-layer classifiers achieve zero probability error cannot have a strict trade-off prediction compression among successive layers contrary recent proposal.Our results should not be taken mean application IB supervised learning is without merit. First do not apply various non-deterministic classification problems where the output is stochastic. Second even deterministic scenarios one may still wish control amount compression training e.g improve generalization robustness adversarial inputs. case however work shows achieve varying rates compression one should use different objective function IB Lagrangian.",2193,1434,759,0.035,1.529,2025/11/05 17:19:08,0.01,1.662,0.6199376947040495,766.403
"We prove, under two sufficient conditions, that idealised models can have no adversarial examples. We discuss which idealised models satisfy our conditions, and show that idealised Bayesian neural networks (BNNs) satisfy these. We continue by studying near-idealised BNNs using HMC inference, demonstrating the theoretical ideas in practice. We experiment with HMC on synthetic data derived from MNIST for which we know the ground-truth image density, showing that near-perfect epistemic uncertainty correlates to density under image manifold, and that adversarial images lie off the manifold in our setting. This suggests why MC dropout, which can be seen as performing approximate inference, has been observed to be an effective defence against adversarial examples in practice; We highlight failure-cases of non-idealised BNNs relying on dropout, suggesting a new attack for dropout models and a new defence as well. Lastly, we demonstrate the defence on a cats-vs-dogs image classification task with a VGG13 variant. Adversarial examples, inputs to machine learning models that an adversary designs to manipulate model output, pose a major concern in machine learning applications. Many hypotheses have been suggested in the literature trying to explain the existence of adversarial examples. For example, BID31 hypothesise that these examples lie near the decision boundary, while BID22 hypothesise that these examples lie in low density regions of the input space. However, adversarial examples can lie far from the decision boundary (e.g. ""garbage"" images BID22 ), and using a simple spheres dataset it was shown that adversarial examples can exist in high density regions as well BID9 . In parallel work following BID22 's low-density hypothesis, BID17 empirically modelled input image density on MNIST and successfully detected adversarial examples by thresholding low input density. This puzzling observation, seemingly inconsistent with the spheres experiment in BID9 , suggests that perhaps additional conditions beyond the ability to detect low input density have led to the observed robustness by BID17 .Suggesting two sufficient conditions, here we prove that an idealised model (in a sense defined below) cannot have adversarial examples, neither in low density nor in high density regions of the input space. We concentrate on adversarial examples in discriminative classification models, models which are used in practical applications. To formalise our treatment, and to gain intuition into the results, we use tools such as discriminative Bayesian neural network (BNN) classifiers BID19 BID21 together with their connections to modern techniques in deep learning such as stochastic regularisation techniques BID6 . This pragmatic Bayesian perspective allows us to shed some new light on the phenomenon of adversarial examples. We further discuss which models other than BNNs abide by our conditions. Our hypothesis suggests why MC dropout-based techniques are sensible for adversarial examples identification, and why these have been observed to be consistently effective against a variety of attacks BID18 BID5 BID27 BID0 .We support our hypothesis mathematically and experimentally using HMC and dropout inference. We construct a synthetic dataset derived from MNIST for which we can calculate ground truth input densities, and use this dataset to demonstrate that model uncertainty correlates to input density, and that under our conditions this density is low for adversarial examples. Using our new-found insights we develop a new attack for MC dropout-based models which does not require gradient information, by looking for ""holes"" in the epistemic uncertainty estimation, i.e. imperfections in the uncertainty approximation, and suggest a mitigation technique as well. We give illustrative examples using MNIST BID15 , and experiment with real-world cats-vs-dogs image classification tasks BID3 ) using a VGG13 variant BID28 . Our result gives intuition into why dropout, a technique shown to relate to Bayesian modelling, seems to be effective in identifying adversarial examples. We presented several idealised models which satisfy the conditions we defined for robustness, opening the door for research into how various practical tools can approximate our idealised conditions. We highlighted that the main difficulty with modern BNNs is not coverage, but rather that approximate inference doesn't increase the un-certainty fast enough with practical BNN tools (we show this in figures 7a, demonstrating that we have holes in the dropout uncertainty). In contrast, HMC (which is not scalable for practical applications) does not have such uncertainty holes, suggesting that we must improve practical inference techniques in BNNs to improve robustness.",prove two sufficient conditions idealised models can have no adversarial examples. discuss which idealised models satisfy conditions show idealised Bayesian neural networks BNNs satisfy these. continue studying near-idealised BNNs using HMC inference demonstrating theoretical ideas practice. experiment HMC synthetic data derived MNIST which we know ground-truth image density showing near-perfect epistemic uncertainty correlates density image manifold adversarial images lie manifold setting. suggests why MC dropout which can be seen performing approximate inference has been why these observed effective defence adversarial examples practice;highlight failure-cases non-idealised BNNs relying dropout suggesting new attack dropout models new defence well. Lastly demonstrate defence cats-vs-dogs image classification task VGG13 variant. Adversarial examples inputs machine learning models adversary designs manipulate model output pose major concern machine learning applications. Many hypotheses have been suggested literature trying explain existence adversarial examples. example BID31 hypothesise examples lie near decision boundary BID22 hypothesise examples lie low density regions input space. However adversarial examples can lie far decision boundary e.g garbage images BID22 using simple spheres dataset was shown adversarial examples can exist high density regions well BID9. parallel work following BID22 's low-density hypothesis BID17 empirically modelled input image density MNIST successfully detected adversarial examples thresholding low input density. puzzling observation seemingly inconsistent spheres experiment BID9 suggests perhaps additional conditions beyond ability detect low input density have led observed robustness BID17.Suggesting two sufficient conditions prove idealised model sense defined cannot have adversarial examples neither low density high density regions input space. concentrate adversarial examples discriminative classification models models which are used practical applications. formalise treatment gain intuition results use tools discriminative Bayesian neural network BNN classifiers BID19 BID21 together connections modern techniques deep learning stochastic regularisation techniques BID6. pragmatic Bayesian perspective allows us shed new light phenomenon adversarial examples. discuss which models BNNs abide conditions. hypothesis suggests why MC dropout-based techniques are sensible adversarial examples identification has been why these have been observed consistently effective variety attacks BID18 BID5 BID27 BID0.We support hypothesis mathematically experimentally using HMC dropout inference. construct synthetic dataset derived MNIST which we can calculate ground truth input densities use dataset demonstrate model uncertainty correlates input density conditions density is low adversarial examples. Using new-found insights develop new attack MC dropout-based models which does not require gradient information looking holes epistemic uncertainty estimation.e imperfections uncertainty approximation suggest mitigation technique well. give illustrative examples using MNIST BID15 experiment real-world cats-vs-dogs image classification tasks BID3 using VGG13 variant BID28. result gives intuition why dropout technique shown relate Bayesian modelling seems effective identifying adversarial examples. presented several idealised models which satisfy conditions defined robustness opening door research how various practical tools can approximate idealised conditions. highlighted main difficulty modern BNNs is not coverage rather approximate inference increase un-certainty fast enough practical BNN tools show figures7a demonstrating have holes dropout uncertainty contrast HMC which is not scalable practical applications does not have uncertainty holes suggesting must improve practical inference techniques BNNs improve robustness.,894,624,270,0.008,1.433,2025/11/05 17:19:08,0.0,1.679,0.3208722741433021,291.749
"Deep neural networks are susceptible to adversarial attacks. In computer vision, well-crafted perturbations to images can cause neural networks to make mistakes such as confusing a cat with a computer. Previous adversarial attacks have been designed to degrade performance of models or cause machine learning models to produce specific outputs chosen ahead of time by the attacker. We introduce attacks that instead reprogram the target model to perform a task chosen by the attacker without the attacker needing to specify or compute the desired output for each test-time input. This attack finds a single adversarial perturbation, that can be added to all test-time inputs to a machine learning model in order to cause the model to perform a task chosen by the adversary—even if the model was not trained to do this task. These perturbations can thus be considered a program for the new task. We demonstrate adversarial reprogramming on six ImageNet classification models, repurposing these models to perform a counting task, as well as classification tasks: classification of MNIST and CIFAR-10 examples presented as inputs to the ImageNet model. The study of adversarial examples is often motivated in terms of the danger posed by an attacker whose goal is to cause model prediction errors with a small change to the model's input. Such an attacker could make a self-driving car react to a phantom stop sign BID6 by means of a sticker (a small L 0 perturbation), or cause an insurance company's damage model to overestimate the claim value from the resulting accident by subtly doctoring photos of the damage (a small L ∞ perturbation). With this context, various methods have been proposed both to construct BID40 BID32 BID3 BID24 and defend against BID9 BID17 BID25 BID42 BID14 BID13 this style of adversarial attack. Thus far, the majority of adversarial attacks have consisted of untargeted attacks that aim to degrade the performance of a model without necessarily requiring it to produce a specific output, or targeted attacks in which the attacker designs an adversarial perturbation to produce a specific output for that input. For example, an attack against a classifier might target a specific desired output class for each input image, or an attack against a reinforcement learning agent might induce that agent to enter a specific state BID22 .In practice, there is no requirement that adversarial attacks will adhere to this framework. Thus , it is crucial to proactively anticipate other unexplored adversarial goals in order to make machine learning systems more secure. In this work, we consider a novel and more challenging adversarial goal: reprogramming the model to perform a task chosen by the attacker, without the attacker needing to compute the specific desired output. Consider a model trained to perform some original task: for inputs x it produces outputs f (x). Consider an adversary who wishes to perform an adversarial task:for inputsx (not necessarily in the same domain as x) the adversary wishes to compute a function g(x). We show that an adversary can accomplish this by learning adversarial reprogramming functions h f (·; θ) and h g (·; θ) that map between the two tasks. Here, h f converts inputs from the domain of x into the domain of x (i.e., h f (x; θ) is a valid input to the function f ), while h g maps output of f (h(x; θ)) back to outputs of g (x) . The parameters θ of the adversarial program are then adjusted to achieve h g (f (h f (x))) = g (x).In our work, for simplicity, we definex to be a small image, g a function that processes small images, x a large image, and f a function that processes large images. Our function h f then just consists of drawing x in the center of the large image and θ in the borders (though see Section 4.5 for other schemes), and h g is simply a hard coded mapping between output class labels. However, the idea is more general; h f (h g ) could be any consistent transformation that converts between the input (output) formats for the two tasks and causes the model to perform the adversarial task.We refer to the class of attacks where a model is repurposed to perform a new task as adversarial reprogramming. We refer to θ as an adversarial program. In contrast to most previous adversarial work, the attack does not need to be imperceptible to humans, or even subtle, in order to be considered a success. However, we note that it is still possible to construct reprogramming attacks that are imperceptible. Potential consequences of adversarial reprogramming include theft of computational resources from public facing services, repurposing of AI-driven assistants into spies or spam bots, and abusing machine learning services for tasks violating the ethical principles of system providers. Risks stemming from this type of attack are discussed in more detail in Section 5.2.It may seem unlikely that an additive offset to a neural network's input would be sufficient on its own to repurpose the network to a new task. However, this flexibility stemming only from changes to a network's inputs is consistent with results on the expressive power of deep neural networks. For instance, in BID36 it is shown that, depending on network hyperparameters, the number of unique output patterns achievable by moving along a one-dimensional trajectory in input space increases exponentially with network depth. Further, BID21 shows that networks can often be trained to high accuracy even if parameter updates are restricted to occur only in a low dimensional subspace. An additive offset to a neural network's input is equivalent to a modification of its first layer biases (for a convolutional network with biases shared across space, this operation effectively introduces new parameters because the additive input is not shared across space), and therefore an adversarial program corresponds to an update in a low dimensional parameter subspace.In this paper, we present the first instances of adversarial reprogramming. In Section 2, we discuss related work. In Section 3, we present a training procedure for crafting adversarial programs, which cause a neural network to perform a new task. In Section 4, we experimentally demonstrate adversarial programs that target several convolutional neural networks designed to classify ImageNet data. These adversarial programs alter the network function from ImageNet classification to: counting squares in an image, classifying MNIST digits, and classifying CIFAR-10 images. Next, we examine the susceptibility of trained and untrained networks to adversarial reprogramming. We then demonstrate the possibility of reprograming adversarial tasks with adversarial data that has no resemblance to original data, demonstrating that results from transfer learning do not fully explain adversarial reprogramming. Further, we demonstrate the possibility of concealing adversarial programs and data. Finally, we end in Sections 5 and 6 by discussing and summarizing our results. In this work, we proposed a new class of adversarial attacks that aim to reprogram neural networks to perform novel adversarial tasks. Our results demonstrate for the first time the possibility of such attacks. They are also illustrative of both surprising flexibility and surprising vulnerability in deep neural networks. Future investigation should address the properties and limitations of adversarial reprogramming, and possible ways to mitigate or defend against it.",Deep neural networks are susceptible adversarial attacks. computer vision well-crafted perturbations images can cause neural networks make mistakes confusing cat computer. Previous adversarial attacks have been designed degrade performance models cause machine learning models produce specific outputs chosen ahead time attacker. introduce attacks instead reprogram target model perform task chosen attacker without attacker needing specify compute desired output test-time input. attack finds single adversarial perturbation can be added test-time inputs machine learning model order cause model perform task chosen adversary even if the model was not trained do this task. perturbations can thus considered program new task. demonstrate adversarial reprogramming six ImageNet classification models repurposing models perform counting task well classification tasks:classification MNIST CIFAR-10 examples presented inputs ImageNet model. study adversarial examples is often motivated terms danger posed attacker whose goal is to cause model prediction errors small change model's input. attacker could make self-driving car react phantom stop sign BID6 means sticker small L 0 perturbation cause insurance company's damage model overestimate claim value resulting accident subtly doctoring photos damage small L ∞ perturbation context various methods have been proposed construct BID40 BID32 BID3 BID24 defend BID9 BID17 BID25 BID42 BID14 BID13 style adversarial attack. Thus far majority adversarial attacks have consisted untargeted attacks aim degrade performance model without necessarily requiring produce specific output targeted attacks which the attacker designs adversarial perturbation produce specific output input. example attack classifier might target specific desired output class input image attack reinforcement learning agent might induce agent enter specific state BID22.In practice is no requirement adversarial attacks will adhere framework. Thus is crucial proactively anticipate unexplored adversarial goals order make machine learning systems secure. work consider novel challenging adversarial goal:reprogramming model perform task chosen attacker without attacker needing compute specific desired output. Consider model trained perform original task:inputsx produces outputsf x Consider adversary who wishes perform adversarial task:inputsx necessarily domain x adversary wishes compute functiong x show adversary can accomplish learning adversarial reprogramming functions hf ·θ hg ·θ map two tasks. h f converts inputs domain x domain x.e hf x;θ is a valid input functionf h g maps output f h x;θ back outputs g x parametersθ adversarial program are then adjusted achievehg f hf x g x.In work simplicity definex small image g function processes small images x large image f function processes large images. functionhf consists drawingx center large image θ borders though see Section 4.5 schemes hg is simply hard coded mapping output class labels. However idea is more general;hf hg could consistent transformation converts input output formats two tasks causes model perform adversarial task.We refer class attacks where a model is repurposed perform new task adversarial reprogramming. refer θ adversarial program. contrast previous adversarial work attack does not need imperceptible humans even subtle order considered success. However note is still possible construct reprogramming attacks are imperceptible. Potential consequences adversarial reprogramming include theft computational resources public facing services repurposing AI-driven assistants spies spam bots abusing machine learning services tasks violating ethical principles system providers. Risks stemming type attack are discussed detail Section5. 2.It may seem unlikely additive offset neural network's input would sufficient repurpose network new task. However flexibility stemming changes network's inputs is consistent results expressive power deep neural networks. instance BID36 is shown depending network hyperparameters number unique output patterns achievable moving along one-dimensional trajectory input space increases exponentially network depth. BID21 shows networks can often trained high accuracy even if parameter updates are restricted occur low dimensional subspace. additive offset neural network's input is equivalent modification first layer biases convolutional network biases shared across space operation effectively introduces new parameters additive input is not shared across space therefore adversarial program corresponds update low dimensional parameter subspace.In paper present first instances adversarial reprogramming. Section2 discuss related work. Section3 present training procedure crafting adversarial programs which cause neural network perform new task. Section4 experimentally demonstrate adversarial programs target several convolutional neural networks designed classify ImageNet data. adversarial programs alter network function ImageNet classification to:counting squares image classifying MNIST digits classifying CIFAR-10 images. Next examine susceptibility trained untrained networks adversarial reprogramming. demonstrate possibility reprograming adversarial tasks adversarial data has no resemblance original data demonstrating results transfer learning do not fully explain adversarial reprogramming. demonstrate possibility concealing adversarial programs data. Finally end Sections5 6 discussing summarizing results. work proposed new class adversarial attacks aim reprogram neural networks perform novel adversarial tasks. results demonstrate first time possibility attacks. are also illustrative surprising flexibility surprising vulnerability deep neural networks. Future investigation should address properties limitations adversarial reprogramming possible ways mitigate defend it.,1478,965,513,0.019,1.532,2025/11/05 17:19:08,0.01,1.425,0.6292834890965732,476.369
"As shown in recent research, deep neural networks can perfectly fit randomly labeled data, but with very poor accuracy on held out data. This phenomenon indicates that loss functions such as cross-entropy are not a reliable indicator of generalization. This leads to the crucial question of how generalization gap should be predicted from the training data and network parameters. In this paper, we propose such a measure, and conduct extensive empirical studies on how well it can predict the generalization gap. Our measure is based on the concept of margin distribution, which are the distances of training points to the decision boundary. We find that it is necessary to use margin distributions at multiple layers of a deep network. On the CIFAR-10 and the CIFAR-100 datasets, our proposed measure correlates very strongly with the generalization gap. In addition, we find the following other factors to be of importance: normalizing margin values for scale independence, using characterizations of margin distribution rather than just the margin (closest distance to decision boundary), and working in log space instead of linear space (effectively using a product of margins rather than a sum).
 Our measure can be easily applied to feedforward deep networks with any architecture and may point towards new training loss functions that could enable better generalization. Generalization, the ability of a classifier to perform well on unseen examples, is a desideratum for progress towards real-world deployment of deep neural networks in domains such as autonomous cars and healthcare. Until recently, it was commonly believed that deep networks generalize well to unseen examples. This was based on empirical evidence about performance on held-out dataset. However, new research has started to question this assumption. Adversarial examples cause networks to misclassify even slightly perturbed images at very high rates BID9 BID22 . In addition, deep networks can overfit to arbitrarily corrupted data BID10 , and they are sensitive to small geometric transformations BID2 BID6 . These results have led to the important question about how the generalization gap (difference between train and test accuracy) of a deep network can be predicted using the training data and network parameters. Since in all of the above cases, the training loss is usually very small, it is clear that existing losses such as cross-entropy cannot serve that purpose. It has also been shown (e.g. in BID10 ) that regularizers such as weight decay cannot solve this problem either.Consequently, a number of recent works BID21 BID4 BID23 BID1 have started to address this question, proposing generalization bounds based on analyses of network complexity or noise stability properties. However, a thorough empirical assessment of these bounds in terms of how accurately they can predict the generalization gap across various practical settings is not yet available.In this work, we propose a new quantity for predicting generalization gap of a feedforward neural network. Using the notion of margin in support vector machines (Vapnik, 1995) and extension to deep networks BID5 , we develop a measure that shows a strong correlation with generalization gap and significantly outperforms recently developed theoretical bounds on Test Acc. : 55.2% Test Acc. : 70.6% Test Acc. : 85.1% Figure 1 : (Best seen as PDF) Density plots (top) and box plots (bottom) of normalized margin of three convolutional networks trained with cross-entropy loss on CIFAR-10 with varying test accuracy: left: 55.2%, middle: 70.6%, right: 85.1%. The left network was trained with 20% corrupted labels. Train accuracy of all above networks are close to 100%, and training losses close to zero. The densities and box plots are computed on the training set. Normalized margin distributions are strongly correlated with test accuracy (moving to the right as accuracy increases). This motivates our use of normalized margins at all layers. The (Tukey) box plots show the median and other order statistics (see section 3.2 for details), and motivates their use as features to summarize the distributions. generalization 2 . This is empirically shown by studying a wide range of deep networks trained on the CIFAR-10 and CIFAR-100 datasets. The measure presented in this paper may be useful for a constructing new loss functions with better generalization. Besides improvement in the prediction of the generalization gap, our work is distinct from recently developed bounds and margin definitions in a number of ways:1. These recently developed bounds are typically functions of weight norms (such as the spectral, Frobenius or various mixed norms). Consequently, they cannot capture variations in network topology that are not reflected in the weight norms, e.g. adding residual connections BID10 without careful additional engineering based on the topology changes. Furthermore, some of the bounds require specific treatment for nonlinear activations. Our proposed measure can handle any feedforward deep network. 2. Although some of these bounds involve margin, the margin is only defined and measured at the output layer BID4 BID21 . For a deep network, however, margin can be defined at any layer BID5 . We show that measuring margin at a single layer does not suffice to capture generalization gap. We argue that it is crucial to use margin information across layers and show that this significantly improves generalization gap prediction. 3. The common definition of margin, as used in the recent bounds e.g. BID21 , or as extended to deep networks, is based on the closest distance of the training points to the decision boundary. However, this notion is brittle and sensitive to outliers. In contrast, we adopt margin distribution BID7 BID13 Zhang & Zhou, 2017; by looking at the entire distribution of distances. This is shown to have far better prediction power. 4. We argue that the direct extension of margin definition to deep networks BID5 , although allowing margin to be defined on all layers of the model, is unable to capture generalization gap without proper normalization. We propose a simple normalization scheme that significantly boosts prediction accuracy. We have presented a predictor for generalization gap based on margin distribution in deep networks and conducted extensive experiments to assess it. Our results show that our scheme achieves a high adjusted coefficient of determination (a linear regression predicts generalization gap accurately). Specifically, the predictor uses normalized margin distribution across multiple layers of the network. The best predictor uses quartiles of the distribution combined in multiplicative way (additive in log transform). Compared to the strong baseline of spectral complexity normalized output margin BID4 , our scheme exhibits much higher predictive power and can be applied to any feedforward network (including ResNets, unlike generalization bounds such as BID4 BID21 BID1 ). We also find that using hidden layers is crucial for the predictive power. Our findings could be a stepping stone for studying new generalization theories and We use an architecture very similar to Network in Network BID16 ), but we remove all dropout and max pool from the network.Layer Index Layer Type Output Shape 0 Input 32 × 32 × 3 1 3 × 3 convolution + stride 2 16 × 16 × 192 Residual plots for all explanatory variables, row: h0, h1, h2, h3, column: lower fence, Q 1 , Q 2 , Q 3 , upper fence. lower fence is clipped because distance cannot be smaller than 0. The residual is less evenly distributed as are in other two settings; this fact is well reflected in the cluster along the x axis and in theR 2 ; we speculate that this is due to not having diverse enough generalization gap in the models trained to cover the entire space of the ""model"" unlike in the other two settings. 3.45e-13 3.04e-16 9.21e-9 4.07e-4 6.59e-3 h3 4.14e-13 0.60 0.27 7.14e-3 2.4e-10 Table 6 : F score (top) and p-values (bottom) for all 20 variables. Using p = 0.05, we see that the null hypotheses are not rejected for 4 of the variables. We believe having a more diverse generalization behavior in the study will solve this problem. Residual plots for all explanatory variables, row: h0, h1, h2, h3, column: lower fence, Q 1 , Q 2 , Q 3 , upper fence. lower fence is clipped because distance cannot be smaller than 0. The residual is fairly evenly distributed around 0. There is one outlier in this experimental setting as shown in the plots. 9 APPENDIX: SOME OBSERVATIONS AND CONJECTURES Everythig here uses the full quartile description. DISPLAYFORM0",shown recent research deep neural networks can perfectly fit randomly labeled data poor accuracy held data. phenomenon indicates loss functions cross-entropy are not a reliable indicator how generalization. leads crucial question how generalization gap should be predicted training data network parameters. paper propose measure conduct extensive empirical studies how well can predict generalization gap. measure is based concept margin distribution which are the distances training points decision boundary. find is necessary use margin distributions multiple layers deep network. CIFAR-10 CIFAR-100 datasets proposed measure correlates strongly generalization gap. addition find following factors importance:normalizing margin values scale independence using characterizations margin distribution rather margin closest distance decision boundary working log space instead linear space effectively using product margins rather sum measure can be easily applied feedforward deep networks architecture may point towards new training loss functions could enable better generalization. Generalization ability classifier perform well unseen examples is a desideratum progress towards real-world deployment deep neural networks domains autonomous cars healthcare. recently was commonly believed deep networks generalize well unseen examples. was based empirical evidence performance held-out dataset. However new research has started question assumption. Adversarial examples cause networks misclassify even slightly perturbed images high rates BID9 BID22. addition deep networks can overfit arbitrarily corrupted data BID10 are sensitive small geometric transformations BID2 BID6. results have led important question how the generalization gap difference train test accuracy deep network can be predicted using training data network parameters. Since cases training loss is usually small is clear existing losses cross-entropy cannot serve purpose. has also shown e.g BID10 regularizers weight decay cannot solve problem either.Consequently number recent works BID21 BID4 BID23 BID1 have started address question proposing generalization bounds based analyses network complexity noise stability properties. However thorough empirical assessment bounds terms how accurately can predict generalization gap across various practical settings is not yet available.In work propose new quantity predicting generalization gap feedforward neural network. Using notion margin support vector machines Vapnik 1995 extension deep networks BID5 develop measure shows strong correlation generalization gap significantly outperforms recently developed theoretical bounds Test Acc. 55.2 Test Acc. 70.6 Test Acc. 85.1 Figure1:Best seen PDF Density plots top box plots bottom normalized margin three convolutional networks trained cross-entropy loss CIFAR-10 varying test accuracy:left:55.2 middle:70.6 right:85.1%. left network was trained 20% corrupted labels. Train accuracy networks are close 100% training losses close zero. densities box plots are computed training set. Normalized margin distributions are strongly correlated test accuracy moving right accuracy increases motivates use normalized margins layers. Tukey box plots show median order statistics see section 3.2 details motivates use features summarize distributions. generalization2. is empirically shown studying wide range deep networks trained CIFAR-10 CIFAR-100 datasets. measure presented paper may useful constructing new loss functions better generalization. Besides improvement prediction how generalization gap work is distinct recently developed bounds margin definitions number ways:1 recently developed bounds are typically functions weight norms spectral Frobenius various mixed norms Consequently cannot capture variations network topology are not reflected weight norms e.g adding residual connections BID10 without careful additional engineering based topology changes. Furthermore bounds require specific treatment nonlinear activations. proposed measure can handle feedforward deep network. 2. Although bounds involve margin margin is only defined measured output layer BID4 BID21. deep network however margin can be defined layer BID5. show measuring margin single layer does not suffice capture generalization gap. argue is crucial use margin information across layers show significantly improves generalization gap prediction. 3. common definition margin used recent boundse.g BID21 extended deep networks is based closest distance training points decision boundary. However notion is brittle sensitive outliers. contrast adopt margin distribution BID7 BID13 Zhang Zhou 2017;looking entire distribution distances. is shown have far better prediction power. 4. argue direct extension margin definition deep networks BID5 although allowing margin defined layers model is unable capture generalization gap without proper normalization. propose simple normalization scheme significantly boosts prediction accuracy. have presented predictor generalization gap based margin distribution deep networks conducted extensive experiments assess it. results show scheme achieves high adjusted coefficient determination linear regression predicts generalization gap accurately Specifically predictor uses normalized margin distribution across multiple layers network. best predictor uses quartiles distribution combined multiplicative way additive log transform Compared strong baseline spectral complexity normalized output margin BID4 scheme exhibits much higher predictive power can be applied feedforward network including ResNets unlike generalization bounds BID4 BID21 BID1 also find using hidden layers is crucial predictive power. findings could stepping stone studying new generalization theories use architecture similar Network Network BID16 remove dropout max pool network.Layer Index Layer Type Output Shape 0 Input 32×32× 313× 3 convolution+stride 216×16 × 192 Residual plots explanatory variables row:h0 h1 h2 h3 column:lower fence Q1 Q2 Q3 upper fence. lower fence is clipped distance cannot smaller 0. residual is less evenly distributed are in other two settings;fact is well reflected cluster along x axis theR2;speculate is due diverse enough generalization gap models trained cover entire space model unlike two settings. 3.45e-13 3.04e-16 9.21e-9 4.07e-4 6.59e-3 h3 4.14e-13 0.60 0.27 7.14e-3 2.4e-10 Table 6:F score top p-values bottom 20 variables. Usingp 0.05 see null hypotheses are not rejected 4 variables. believe diverse generalization behavior study will solve problem. Residual plots explanatory variables row:h0 h1 h2 h3 column:lower fence Q1 Q2 Q3 upper fence. lower fence is clipped distance cannot smaller 0. residual is fairly evenly distributed around 0. is one outlier experimental setting shown plots. 9 APPENDIX:OBSERVATIONS CONJECTURES Everythig uses full quartile description. DISPLAYFORM0,1797,1241,556,0.018,1.448,2025/11/05 17:19:08,0.01,1.321,0.3676012461059186,521.689
"We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our algorithm draws ideas from (1) isotonic regression for learning neural networks and (2) landscape analysis of non-convex matrix factorization problems. We believe these findings may inspire further development in designing provable algorithms for learning neural networks and other complex models. While our focus is theoretical, we also present experiments that illustrate our theoretical findings. Giving provably efficient algorithms for learning neural networks is a core challenge in machine learning theory. The case of convolutional architectures has recently attracted much interest due to their many practical applications. Recently BID2 showed that distributionfree learning of one simple non-overlapping convolutional filter is NP-hard. A natural open question is whether we can design provably efficient algorithms to learn convolutional neural networks under mild assumptions.We consider a convolutional neural network of the form f px, w, aq "" k ÿ j""1 a j σ`w J P j x˘(1)where w P R r is a shared convolutional filter, a P R k is the second linear layer and P j "" r 0 lo omo on pj´1qs I lo omo on r 0 lo omo on d´pj´1qs`r s P R rˆd selects the ppj´1qs`1q-th to ppj´1qs`rq-th coordinates of x with stride s and σ p¨q is the activation function. Note here that both w and a are unknown vectors to be learned and there may be overlapping patches because the stride size s may be smaller than the filter size r.Our Contributions We give the first efficient algorithm that can provably learn a convolutional neural network with two unknown layers with commonly used overlapping patches. Our main result is the following theorem. Theorem 1.1 (Main Theorem (Informal)). Suppose s ě t r 2 u`1 and the marginal distribution is symmetric and isotropic. Then the convolutional neural network defined in equation 1 with piecewise linear activation functions is learnable in polynomial time.We refer readers to Theorem 3.1 for the precise statement.Technical Insights Our algorithm is a novel combination of the algorithm for isotonic regression and the landscape analysis of non-convex problems. First, inspired by recent work on isotonic regression, we extend the idea in BID13 to reduce learning a CNN with piecewise linear activation to learning a convolutional neural network with linear activation (c.f. Section 4). Second, we show learning a linear convolutional filter can be reduced to a non-convex matrix factorization problem which admits a provably efficient algorithm based on non-convex geometry BID8 . Third, in analyzing our algorithm, we present a robust analysis of Convotron algorithm proposed by BID13 , in which we draw connections to the spectral properties of Toeplitz matrices. We believe these ideas may inspire further development in designing provable learning algorithms for neural networks and other complex models.Related Work From the point of view of learning theory, it is well known that training is computational infeasible in the worst case BID12 BID2 . Thus distributional assumptions are needed for efficient learning. A line of research has focused on analyzing the dynamics of gradient descent conditioned on the input distribution being standard Gaussian BID29 BID28 BID21 BID32 BID2 BID31 BID5 . Specifically for convolutional nets, existing analyses heavily relied on the analytical formulas which can only be derived if the input is Gaussian and patches are non-overlapping.Recent work has tried to relax the Gaussian input assumption and the non-overlapping structure for learning convolutional filters. BID5 showed if the patches are sufficiently close to each other then stochastic gradient descent can recover the true filter. BID13 proposed a modified iterative algorithm inspired from isotonic regression that gives the first recovery guarantees for learning a filter for commonly used overlapping patches under much weaker assumptions on the distribution. However, these two analyses only work for learning one unknown convoutional filter.Moving away from gradient descent, various works have shown positive results for learning general simple fully connected neural networks in polynomial time and sample complexity under certain assumptions using techniques such as kernel methods BID12 BID30 BID10 BID0 and tensor decomposition BID27 BID18 . The main drawbacks include the shift to improper learning for kernel methods and the knowledge of the probability density function for tensor methods. In contrast to this, our algorithm is proper and does not assume that the input distribution is known.Learning a neural network is often formulated as a non-convex problem. If the objective function satisfies (1) all saddle points and local maxima are strict (i.e., there exists a direction with negative curvature), and (2) all local minima are global (no spurious local minmum), then noise-injected (stochastic) gradient descent BID7 BID19 ) finds a global minimum in polynomial time. Recent work has studied these properties for the landscape of neural networks BID20 BID3 BID15 BID14 BID22 BID6 BID25 Zhou & Feng, 2017; BID23 BID0 BID9 Zhou & Feng, 2017; BID26 BID4 . A crucial step in our algorithm is reducing the convolutional neural network learning problem to matrix factorization and using the geometric properties of matrix factorization. In this paper, we propose the first efficient algorithm for learning a one-hidden-layer convolutional neural network with possibly overlapping patches. Our algorithm draws ideas from isotonic regression, landscape analysis of non-convex problem and spectral analysis of Toeplitz matrices. These findings can inspire further development in this field. Our next step is extend our ideas to design provable algorithms that can learn complicated models consisting of multiple filters. To solve this problem, we believe the recent progress on landscape design BID9 may be useful.",propose new algorithm learn one-hidden-layer convolutional neural network where both the convolutional weights outputs weights are parameters learned. algorithm works general class potentially overlapping patches including commonly used structures computer vision tasks. algorithm draws ideas 1 isotonic regression learning neural networks 2 landscape analysis non-convex matrix factorization problems. believe findings may inspire development designing provable algorithms learning neural networks complex models. focus is theoretical also present experiments illustrate theoretical findings. Giving provably efficient algorithms learning neural networks is a core challenge machine learning theory. case convolutional architectures has recently attracted much interest due many practical applications. Recently BID2 showed distributionfree learning one simple non-overlapping convolutional filter is NP-hard NP-hard natural open question is whether can design provably efficient algorithms learn convolutional neural networks mild assumptions.We consider convolutional neural network formfpx w aqkÿj1 jσwJP jx˘ 1 wherewPRr is a shared convolutional filter PRk is the second linear layer Pjr0 lo omo pj´1qs lo omo r 0 lo omo d´pj´1qsr P R rˆd selects ppj´1qs1q-th ppj´1qsrq-th coordinates x stride σ p¨q is the activation function. Note w are unknown vectors learned may overlapping patches stride size may smaller filter size r.Our Contributions give first efficient algorithm can provably learn convolutional neural network two unknown layers commonly used overlapping patches. main result is the following theorem. Theorem 1.1 Main Theorem Informal Suppose ě r2u1 marginal distribution is symmetric isotropic. convolutional neural network defined equation1 piecewise linear activation functions is learnable polynomial time.We refer readers Theorem 3.1 precise statement.Technical Insights algorithm is a novel combination algorithm isotonic regression landscape analysis non-convex problems. First inspired recent work isotonic regression extend idea BID13 reduce learning CNN piecewise linear activation learning convolutional neural network linear activation c.f Section4 Second show learning linear convolutional filter can be reduced non-convex matrix factorization problem which admits provably efficient algorithm based non-convex geometry BID8. Third analyzing algorithm present robust analysis Convotron algorithm proposed BID13 which we draw connections spectral properties Toeplitz matrices. believe ideas may inspire development designing provable learning algorithms neural networks complex models.Related Work point view learning theory is well known training is computational infeasible worst case BID12 BID2. Thus distributional assumptions are needed efficient learning. line research has focused analyzing dynamics gradient descent conditioned input distribution standard Gaussian BID29 BID28 BID21 BID32 BID2 BID31 BID5. Specifically convolutional nets existing analyses heavily relied analytical formulas which can only be derived if the input is Gaussian patches are non-overlapping.Recent work has tried relax Gaussian input assumption non-overlapping structure learning convolutional filters. BID5 showed if the patches are sufficiently close stochastic gradient descent can recover true filter. BID13 proposed modified iterative algorithm inspired isotonic regression gives first recovery guarantees learning filter commonly used overlapping patches much weaker assumptions distribution. However two analyses work learning one unknown convoutional filter.Moving away gradient descent various works have shown positive results learning general simple fully connected neural networks polynomial time sample complexity certain assumptions using techniques kernel methods BID12 BID30 BID10 BID0 tensor decomposition BID27 BID18. main drawbacks include shift improper learning kernel methods knowledge probability density function tensor methods. contrast algorithm is proper does not assume input distribution is known.Learning neural network is often formulated non-convex problem. If the objective function satisfies 1 saddle points local maxima are strict.e exists direction negative curvature 2 local minima are global spurious local minmum noise-injected stochastic gradient descent BID7 BID19 finds global minimum polynomial time. Recent work has studied properties landscape neural networks BID20 BID3 BID15 BID14 BID22 BID6 BID25 Zhou Feng 2017;BID23 BID0 BID9 Zhou Feng 2017;BID26 BID4. crucial step algorithm is reducing convolutional neural network learning problem matrix factorization using geometric properties matrix factorization. paper propose first efficient algorithm learning one-hidden-layer convolutional neural network possibly overlapping patches. algorithm draws ideas isotonic regression landscape analysis non-convex problem spectral analysis Toeplitz matrices. findings can inspire development field. next step is extend ideas design provable algorithms can learn complicated models consisting multiple filters. solve problem believe recent progress landscape design BID9 may useful.,1211,895,316,0.011,1.353,2025/11/05 17:19:08,0.0,1.391,0.0716510903426788,340.689
"Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a different metric, but thereby introduce a Lipschitz constraint into the optimization problem. A simple way to enforce the Lipschitz constraint on the class of functions, which can be modeled by the neural network, is weight clipping. Augmenting the loss by a regularization term that penalizes the deviation of the gradient norm of the critic (as a function of the network's input) from one, was proposed as an alternative that improves training. We present theoretical arguments why using a weaker regularization term enforcing the Lipschitz constraint is preferable. These arguments are supported by experimental results on several data sets. General adversarial networks (GANs) BID8 are a class of generative models that have recently gained a lot of attention. They are based on the idea of defining a game between two competing neural networks (NNs): a generator and a classifier (or discriminator). While the classifier aims at distinguishing generated from real data, the generator tries to generate samples which the classifier can not distinguish from the ones from the empirical distribution. Realizing the potential behind this new approach to generative models, more recent contributions focused on the stabilization of training, including ensemble methods BID18 , improved network structure BID14 BID15 and theoretical improvements BID13 BID15 that helped to successfully model complex distributions using GANs.It was proposed by to train generator and discriminator networks by minimizing the Wasserstein-1 distance, a distance with properties superior to the Jensen-Shannon distance (used in the original GAN) in terms of convergence. Accordingly, this version of GAN was called Wasserstein GAN (WGAN) . The change of metric introduces a new minimization problem, which requires the discriminator function to lie in the space of 1-Lipschitz functions. In the same paper, the Lipschitz constraint was guaranteed by performing weight clipping, i.e., by constraining the parameters of the discriminator NN to be smaller than a given value in magnitude. An improved training strategy was proposed by BID9 based on results from optimal transport theory (see BID19 . Here, instead of clipping weights, the loss gets augmented by a regularization term that penalizes any deviation of the norm of the gradient of the critic function (with respect to its input) from one.We review these results and present both theoretical considerations and empirical results, leading to the proposal of a less restrictive regularization term for WGANs.1 More precisely, our contributions are as follows:• We review the arguments that the regularization technique proposed by BID9 is based on and make the following two observations: (i) The regularization strategy requires training samples and generated samples to be drawn from a certain joint distribution. In practice, however, samples are drawn independently from their marginals.(ii ) The arguments further assume the discriminator to be differentiable. We explain why both can be harmful for training.• We propose a less restrictive regularization term and present empirical results strongly supporting our theoretical considerations. For stable training of Wasserstein GANs, we propose to use the following penalty term to enforce the Lipschitz constraint that appears in the objective function: DISPLAYFORM0 We presented theoretical and empirical evidence that this gradient penalty performs better than the previously considered approaches of clipping weights and of applying the stronger gradient penalty given by Ex ∼τ [(||∇f (x)|| 2 − 1) 2 ]. In addition to more stable learning behavior, the proposed regularization term leads to lower sensitivity to the value of the penalty weight λ (demonstrating smooth convergence and well-behaved critic scores throughout the whole training process for different values of λ).",Since invention generative adversarial networks GANs have become popular approach learning model distribution real unlabeled data. Convergence problems training are overcome Wasserstein GANs which minimize distance model empirical distribution terms different metric thereby introduce Lipschitz constraint optimization problem. simple way enforce Lipschitz constraint class functions which can be modeled neural network is weight clipping. Augmenting loss regularization term penalizes deviation gradient norm critic function network's input one was proposed alternative improves training. present theoretical arguments why using weaker regularization term enforcing Lipschitz constraint is preferable. arguments are supported experimental results several data sets. General adversarial networks GANs BID8 are a class generative models have recently gained lot attention. are based idea defining game two competing neural networks NNs generator classifier discriminator classifier aims distinguishing generated real data generator tries generate samples which the classifier can not distinguish ones empirical distribution. Realizing potential behind new approach generative models recent contributions focused stabilization training including ensemble methods BID18 improved network structure BID14 BID15 theoretical improvements BID13 BID15 helped successfully model complex distributions using GANs.It was proposed train generator discriminator networks minimizing Wasserstein-1 distance distance properties superior Jensen-Shannon distance used original GAN terms convergence. Accordingly version GAN was called Wasserstein GAN WGAN change metric introduces new minimization problem which requires discriminator function lie space 1-Lipschitz functions. paper Lipschitz constraint was guaranteed performing weight clipping.e constraining parameters discriminatorNN smaller given value magnitude. improved training strategy was proposed BID9 based results optimal transport theory see BID19. instead clipping weights loss gets augmented regularization term penalizes deviation norm gradient critic function respect input one.We review results present theoretical considerations empirical results leading proposal less restrictive regularization term WGANs.1 precisely contributions are as follows:• review arguments regularization technique proposed BID9 is based make following two observations:regularization strategy requires training samples generated samples drawn certain joint distribution. practice however samples are drawn independently marginals. ii arguments assume discriminator differentiable. explain why both can be harmful training.• propose less restrictive regularization term present empirical results strongly supporting theoretical considerations. stable training Wasserstein GANs propose use following penalty term enforce Lipschitz constraint appears objective function:DISPLAYFORM0 presented theoretical empirical evidence gradient penalty performs better previously considered approaches clipping weights applying stronger gradient penalty given Ex∼τ ||∇f x ||2−1 2 addition stable learning behavior was proposed regularization term leads lower sensitivity value penalty weightλ demonstrating smooth convergence well-behaved critic scores throughout whole training process different values λ,780,506,274,0.008,1.542,2025/11/05 17:19:08,0.0,1.409,0.660436137071651,277.697
"We introduce a new method for training GANs by applying the Wasserstein-2 metric proximal on the generators. 
 The approach is based on the gradient operator induced by optimal transport, which connects the geometry of sample space and parameter space in implicit deep generative models. From this theory, we obtain an easy-to-implement regularizer for the parameter updates. Our experiments demonstrate that this method improves the speed and stability in training GANs in terms of wall-clock time and Fr\'echet Inception Distance (FID) learning curves. Generative Adversarial Networks (GANs) BID11 are a powerful approach to learning generative models. Here, a discriminator tries to tell apart the data generated from a real source and the data generated by a generator, whereas the generator tries to fool the discriminator. This adversarial game is formulated as an optimization problem over an implicit generative model for the generator. An implicit generative model is a parametrized family of functions mapping a noise source to sample space. In trying to fool the discriminator, the generator should try to recreate the density distribution from the real source.The problem of matching a target density can be formulated as the minimization of a discrepancy measure. The Kullback-Leibler (KL) divergence is known to be difficult when the distributions have a low dimensional support set, as is commonly the case in applications with structured data and high dimensional sample spaces. An alternative approach to define a discrepancy measure between densities is optimal transport, a.k.a. Wasserstein distance, or Earth Mover's distance. This has been used recently to define the loss function for learning generative models BID30 BID10 . In particular, the Wasserstein GAN BID4 has attracted much interest in recent years.Besides defining the loss function, optimal transport can also be used to introduce structures serving the optimization itself, in terms of the gradient operator. In full probability space, this is known as the Wasserstein steepest descent flow BID15 BID32 . In this paper we derive the Wasserstein steepest descent flow for deep generative models in GANs. We use the Wasserstein-2 metric function, which allows us to obtain a Riemannian structure and a corresponding natural (i.e., Riemannian) gradient. A well known example of a natural gradient is the Fisher-Rao natural gradient, which is induced by the KL divergence. In learning problems, one often finds that the natural gradients can offer advantages compared to the Euclidean gradient BID1 BID2 . In GANs, because of the low dimensional support sets and the associated difficulties with the KL divergence, the Fisher-Rao natural gradient is problematic. Therefore, we propose to use the gradient operator induced by the Wasserstein-2 metric BID21 b) .We compute the proximal operator for the generators of GANs, where the regularization is the squared constrained Wasserstein-2 distance. In practice, the constrained distance can be approximated by a simple neural network. In implicit generative models, the constrained Wasserstein-2 metric exhibits a simple structure. We generalize the metric and introduce the relaxed proximal operator for generators, which allows us to further simplify the computation. The resulting relaxed proximal operator involves only the difference of outputs, so that the proximal computation has very simple parameter updates. The method can be easily implemented and used as a drop-in regularizer for the generator updates. This paper is organized as follows. In Section 2, we briefly introduce the Wasserstein natural gradient. A Wasserstein proximal method is introduced in Algorithm 1. In Section 3, we demonstrate the effectiveness of the proposed methods in experiments with various types of GANs. Section 4 reviews related work. In this work, we apply the constrained Wasserstein gradient and its relaxations on implicit generative models. Whereas much work has focused on regularizing the discriminator, in this work we focus on regularizing the generator. For Wasserstein GAN (with gradient penalty), we compute the Wasserstein-2 gradient flow of Wasserstein-1 distance on parameter space. Experimentally, the proposed method allows us to obtain a better minimizer in the sense of FID, with faster convergence speeds in wall-clock time.",introduce new method training GANs applying Wasserstein-2 metric proximal generators. approach is based gradient operator induced optimal transport which connects geometry sample space parameter space implicit deep generative models. theory obtain easy-to-implement regularizer parameter updates. experiments demonstrate method improves speed stability training GANs terms wall-clock time Fr\'echet Inception Distance FID learning curves. Generative Adversarial Networks GANs BID11 are a powerful approach learning generative models. discriminator tries tell apart data generated real source data generated generator whereas generator tries fool discriminator. adversarial game is formulated optimization problem implicit generative model generator. implicit generative model is a parametrized family functions mapping noise source sample space. trying fool discriminator generator should try recreate density distribution real source.The problem matching target density can be formulated minimization discrepancy measure. Kullback-Leibler KL divergence is known difficult when the distributions have a low dimensional support set is commonly case applications structured data high dimensional sample spaces. alternative approach define discrepancy measure densities is optimal transport.k.a Wasserstein distance Earth Mover's distance. has been used recently define loss function learning generative models BID30 BID10. particular Wasserstein GAN BID4 has attracted much interest recent years.Besides defining loss function optimal transport can also used introduce structures serving optimization terms gradient operator. full probability space is known Wasserstein steepest descent flow BID15 BID32. paper derive Wasserstein steepest descent flow deep generative models GANs. use Wasserstein-2 metric function which allowsus obtain Riemannian structure corresponding natural.e Riemannian gradient. well known example natural gradient is the Fisher-Rao natural gradient which is induced KL divergence. learning problems one often finds natural gradients can offer advantages compared Euclidean gradient BID1 BID2. GANs low dimensional support sets associated difficulties KL divergence Fisher-Rao natural gradient is problematic. Therefore propose use gradient operator induced Wasserstein-2 metric BID21b.We compute proximal operator generators GANs where the regularization is the squared constrained Wasserstein-2 distance. practice constrained distance can be approximated simple neural network. implicit generative models constrained Wasserstein-2 metric exhibits simple structure. generalize metric introduce relaxed proximal operator generators which allowsus simplify computation. resulting relaxed proximal operator involves difference outputs proximal computation has very simple parameter updates. method can be easily implemented used drop-in regularizer generator updates. paper is organized follows. Section2 briefly introduce Wasserstein natural gradient. Wasserstein proximal method is introduced Algorithm1. Section3 demonstrate effectiveness proposed methods experiments various types GANs. Section 4 reviews related work. work apply constrained Wasserstein gradient relaxations implicit generative models. Whereas much work has focused regularizing discriminator work focus regularizing generator. Wasserstein GAN gradient penalty compute Wasserstein-2 gradient flow Wasserstein-1 distance parameter space. Experimentally proposed method allowsus obtain better minimizer sense FID faster convergence speeds wall-clock time.,841,582,259,0.008,1.445,2025/11/05 17:19:08,0.0,1.448,0.3582554517133957,271.051
"Influence diagrams provide a modeling and inference framework for sequential decision problems, representing the probabilistic knowledge by a Bayesian network and the preferences of an agent by utility functions over the random variables and decision variables.
 MDPs and POMDPS, widely used for planning under uncertainty can also be represented by influence diagrams.
 The time and space complexity of computing the maximum expected utility (MEU) and its maximizing policy is exponential in the induced width of the underlying graphical model, which is often prohibitively large due to the growth of the information set under the sequence of decisions.
 In this paper, we develop a weighted mini-bucket approach for bounding the MEU.  These bounds can be used as a stand-alone approximation that can be improved as a function of a controlling i-bound parameter .
They can also be used as heuristic  functions to guide search, especially for planning 
 such as MDPs and POMDPs.
 We evaluate the scheme empirically against state-of-the-art, thus illustrating its potential.
 An influence diagram (ID) BID4 ) is a graphical model for sequential decision-making under uncertainty that compactly captures the local structure of the conditional independence of probability functions and the additivity of utility functions. Its structure is captured by a directed acyclic graph (DAG) over nodes representing the variables (decision and chance variables). The standard query on an ID is finding the maximum expected utility (MEU) and the corresponding optimal policy for each decision, subject to the history of observations and decisions.Computing the MEU is recognized as one of the hardest tasks over graphical models, and hence recent work aims at developing anytime bounding schemes that tighten the bounds if more time and memory is available. Often, the target is to incorporate such bounds as heuristic functions to guide search algorithms. In this paper, we focus on computing the upper bound of MEU for a single agent sequential decision making problem with no-forgetting assumptions. We build on the methodology of weighted mini-bucket with costshifting that was used in the past for bounding probabilistic queries such as the partition function, Maximum A Posteriori (MAP) and Marginal MAP (MMAP) BID0 BID12 BID5 BID14 BID13 ). We presented a new bounding scheme for influence diagrams, called WMBE-ID, which computes upper bounds of the MEU by interleaving variable elimination with optimizing partial decomposition within each variable's bucket. Compared with the previous approaches, our proposed upper bounding scheme produces high quality upper bounds in shorter time bounds. This is instrumental for our plan to Table 2 : The performance of the bounding schemes on individual instances. n is the number of variables, f is the number of functions, k is the maximum domain size, s is the maximum scope size, w is the constrained induced width. We show the (time, upper bound) for various i-bounds and number of iterations for algorithms updating the costs or weights. WMBE-U is the mini-bucket elimination with uniform weights, WMBE-UC preforms cost shifting without optimizing the weight, WMBE-WC optimizes both weights and costs, JGDID is the fully decomposed bound over a join graph that optimizes both weights and costs, MBE is the simple mini-bucket elimination, and MBE-Re is mini-bucket elimination with relaxed variable ordering. MBE, MBE-RE, and WMBE-U do not optimize the bound. The best upper bounds are highlighted. Table 3 : Comparing the ratio of time and quality of upper bounds against JGDID(i=1). WMBE-UC and WMBE-WC were provided with i-bound 10 and 15 with the number of iteration fixed to 5, and JGDID were provided i-bound 1 and 10 with the maximum number iteration limited by 100. All the quantities are normalized by the statistics of JGDID(i=1). DISPLAYFORM0 use such bounds as a heuristic evaluation function for search algorithms for solving influence diagrams.",Influence diagrams provide modeling inference framework sequential decision problems representing probabilistic knowledge Bayesian network preferences agent utility functions random variables decision variables. MDPs POMDPS widely used planning uncertainty can also represented influence diagrams. time space complexity computing maximum expected utility MEU maximizing policy is exponential induced width underlying graphical model which is often prohibitively large due growth information set sequence decisions. paper develop weighted mini-bucket approach bounding MEU. bounds can be used stand-alone approximation can be improved function controlling i-bound parameter. can also used heuristic functions guide search especially planning MDPs POMDPs. evaluate scheme empirically state-of-the-art thus illustrating potential. influence diagram ID BID4 is a graphical model sequential decision-making uncertainty compactly captures local structure conditional independence probability functions additivity utility functions. structure is captured directed acyclic graph DAG nodes representing variables decision chance variables standard query ID is finding maximum expected utility MEU corresponding optimal policy decision subject history observations decisions.Computing MEU is recognized one hardest tasks graphical models hence recent work aims developing anytime bounding schemes tighten bounds if more time memory is available. Often target is to incorporate bounds heuristic functions guide search algorithms. paper focus computing upper bound MEU single agent sequential decision making problem no-forgetting assumptions. build methodology weighted mini-bucket costshifting was used past bounding probabilistic queries partition function Maximum Posteriori MAP Marginal MAP MMAP BID0 BID12 BID5 BID14 BID13 presented new bounding scheme influence diagrams called WMBE-ID which computes upper bounds MEU interleaving variable elimination optimizing partial decomposition within variable's bucket. Compared previous approaches proposed upper bounding scheme produces high quality upper bounds shorter time bounds. is instrumental plan Table2:performance bounding schemes individual instances. n is the number variables f is the number functions k is the maximum domain size is the maximum scope size w is the constrained induced width. show time upper bound various i-bounds number iterations algorithms updating costs weights. WMBE-U is the is mini-bucket elimination uniform weights WMBE-UC preforms cost shifting without optimizing weight WMBE-WC optimizes weights costs JGDID is the fully decomposed bound join graph optimizes weights costs MBE is the simple mini-bucket elimination MBE-Re is the is mini-bucket elimination relaxed variable ordering. MBE MBE-RE WMBE-U do not optimize bound. best upper bounds are highlighted. Table3:Comparing ratio time quality upper bounds JGDID i=1 WMBE-UC WMBE-WC were provided i-bound10 15 number iteration fixed 5 JGDID were provided i-bound1 10 maximum number iteration limited 100. quantities are normalized statistics JGDID i=1 DISPLAYFORM0 use bounds heuristic evaluation function search algorithms solving influence diagrams.,808,557,251,0.008,1.451,2025/11/05 17:19:08,0.0,1.5,0.3769470404984424,276.866
"Probabilistic Neural Networks deal with various sources of stochasticity: input noise, dropout, stochastic neurons, parameter uncertainties modeled as random variables, etc.
 In this paper we revisit a feed-forward propagation approach that allows one to estimate for each neuron its mean and variance w.r.t. all mentioned sources of stochasticity. In contrast, standard NNs propagate only point estimates, discarding the uncertainty.
 Methods propagating also the variance have been proposed by several authors in different context. The view presented here attempts to clarify the assumptions and derivation behind such methods, relate them to classical NNs and broaden their scope of applicability.
 The main technical contributions are new approximations for the distributions of argmax and max-related transforms, which allow for fully analytic uncertainty propagation in networks with softmax and max-pooling layers as well as leaky ReLU activations.
 We evaluate the accuracy of the approximation and suggest a simple calibration. Applying the method to networks with dropout allows for faster training and gives improved test likelihoods without the need of sampling. Despite the massive success of Neural Networks (NNs) considered as deterministic predictors, there are many scenarios where a probabilistic treatment is highly desirable. One of the best known techniques to improve the network generalization is dropout BID29 , which introduces multiplicative Bernoulli noise in the network. At test time, however, it is commonly approximated by substituting the mean value of the noise variables. Computing the expectation more accurately by Monte Carlo (MC) sampling has been shown to improve test likelihood and accuracy BID29 BID5 but is computationally expensive.Another challenging problem in NNs is the sensitivity of the output to perturbations of the input, in particular random and adversarial perturbations BID19 BID3 BID23 . In FIG6 we illustrate the point that the average of the network output under noisy input differs from propagating the clean input. It is therefore desirable to estimate the output uncertainty resulting from the uncertainty of the input. In classification networks, propagating the uncertainty of the input can impact the confidence of the classifier and its robustness BID1 . We would like that a classifier is not overconfident when making errors. However such high confidences of wrong predictions are typically observed in NNs. Similarly, when predicting real values (e.g. in optical flow estimation), it is desirable to estimate also their confidences. Taking into account uncertainties from input or dropout allows to predict output uncertainties better correlated with the test error BID14 BID6 BID26 . Another important problem is overfitting, which may be addressed in a sound way with Bayesian learning. The parameters are considered as random variables and are determined up to an uncertainty implied by the training data. This uncertainty needs then to be propagated to predictions at the test-time.The above scenarios motivate considering NNs with different sources of stochasticity not as deterministic feed-forward networks but as directed probabilistic graphical models. We focus on the We have described uncertainty propagation method for approximate inference in probabilistic neural networks that takes into account all noises analytically. Latent variable models allow a transparent interpretation of standard propagation in NNs as the simplest approximation and facilitate the devel- Table 3 : Results for All-CNN on CIFAR-10 test set: negative log likelihood (NLL) and accuracy. Left: state of the art results for this network BID6 , table 3). Middle: All-CNN trained with standard dropout (our learning schedule and analytic normalization) evaluated using different test-time methods. Observe that ""AP2 calibrated"" well approximates dropout: the test likelihood is better than MC-100. Right: All-CNN trained with analytic dropout (same schedule and normalization). Observe that ""AP2 calibrated"" achieves the best likelihood and accuracy.opment of variance propagating approximations. We proposed new such approximations allowing to handle max, argmax, softmax and log-softmax layers using latent variable models ( § 4 and § A.2).We measured the quality of the approximation of posterior in isolated layers and complete networks. The accuracy is improved compared to standard propagation and is sufficient for several use cases such as estimating statistics over the dataset (normalization) and dropout training, where we report improved test likelihoods. We identified the factorization assumption as the weakest point of the approximation. While modeling of correlations is possible (e.g. BID22 , it is also more expensive. We showed that a calibration of a cheap method can give a significant improvement and thus is a promising direction for further research. Argmax and softmax may occur not only as the final layer but also inside the network, in models such as capsules BID25 or multiple hypothesis BID11 , etc. Further applications of the developed technique may include generative and semi-supervised learning and Bayesian model estimation.",Probabilistic Neural Networks deal various sources stochasticity:input noise dropout stochastic neurons parameter uncertainties modeled random variables etc. paper revisit feed-forward propagation approach allows one estimate neuron mean variancew.r.t mentioned sources stochasticity. contrast standard NNs propagate point estimates discarding uncertainty. Methods propagating also variance have been proposed several authors different context. view presented attempts clarify assumptions derivation behind methods relate classical NNs broaden scope applicability. main technical contributions are new approximations distributions argmax max-related transforms which allow fully analytic uncertainty propagation networks softmax max-pooling layers well leaky ReLU activations. evaluate accuracy approximation suggest simple calibration. Applying method networks dropout allows faster training gives improved test likelihoods without need sampling. Despite massive success Neural Networks NNs considered deterministic predictors are many scenarios where a probabilistic treatment is highly desirable. One best known techniques improve network generalization is dropout BID29 which introduces multiplicative Bernoulli noise network. test time however is commonly approximated substituting mean value noise variables. Computing expectation accurately Monte Carlo MC sampling has been shown improve test likelihood accuracy BID29 BID5 is computationally expensive.Another challenging problem NNs is the sensitivity output perturbations input particular random adversarial perturbations BID19 BID3 BID23. FIG6 illustrate point average network output noisy input differs propagating clean input. is therefore desirable estimate output uncertainty resulting uncertainty input. classification networks propagating uncertainty input can impact confidence classifier robustness BID1. would like classifier is not overconfident when making errors. However high confidences wrong predictions are typically observed NNs. Similarly when predicting real values e.g optical flow estimation is desirable estimate also confidences. Taking account uncertainties input dropout allows predict output uncertainties better correlated test error BID14 BID6 BID26. Another important problem is overfitting may addressed sound way Bayesian learning. parameters are considered random variables are determined uncertainty implied training data. uncertainty needs propagated predictions test-time.The scenarios motivate considering NNs different sources stochasticity deterministic feed-forward networks directed probabilistic graphical models. focus have described uncertainty propagation method approximate inference probabilistic neural networks takes account noises analytically. Latent variable models allow transparent interpretation standard propagation NNs simplest approximation facilitate devel- Table3:Results All-CNN CIFAR-10 test set:negative log likelihood NLL accuracy. Left:state art results network BID6 table3 Middle:All-CNN trained standard dropout learning schedule analytic normalization evaluated using different test-time methods. Observe AP2 calibrated well approximates dropout:test likelihood is better MC-100 Right:All-CNN trained analytic dropout schedule normalization Observe AP2 calibrated achieves best likelihood accuracy.opment variance propagating approximations. proposed new approximations allowing handle max argmax softmax log-softmax layers using latent variable models §4 § A.2.We measured quality approximation posterior isolated layers complete networks. accuracy is improved compared standard propagation is sufficient several use cases estimating statistics dataset normalization dropout training where we report improved test likelihoods. identified factorization assumption weakest point approximation. modeling correlations is possible e.g BID22 is also expensive. showed calibration cheap method can give significant improvement thus is a promising direction research. Argmax softmax may occur final layer also inside network models capsules BID25 multiple hypothesis BID11 etc. applications developed technique may include generative semi-supervised learning Bayesian model estimation.,956,656,300,0.009,1.457,2025/11/05 17:19:08,0.0,1.226,0.3956386292834891,302.753
"Generative Adversarial Networks are one of the leading tools in generative modeling, image editing and content creation. 
 However, they are hard to train as they require a delicate balancing act between two deep networks fighting a never ending duel. Some of the most promising adversarial models today minimize a Wasserstein objective. It is smoother and more stable to optimize. In this paper, we show that the Wasserstein distance is just one out of a large family of objective functions that yield these properties. By making the discriminator of a GAN robust to adversarial attacks we can turn any GAN objective into a smooth and stable loss. We experimentally show that any GAN objective, including Wasserstein GANs, benefit from adversarial robustness both quantitatively and qualitatively. The training additionally becomes more robust to suboptimal choices of hyperparameters, model architectures, or objective functions. Generative adversarial networks (GANs) BID4 are at the forefront of generative modeling. They cast generative modeling as a never ending duel between two networks: a generator network produces synthetic samples from random noise and a discriminator network distinguishes synthetic from real data samples. GANs produce visually appealing samples, but are often hard to train. Much recent work, tries to stabilize GAN training through novel architecture BID25 BID3 or training objectives BID17 BID6 .In this paper, we show that GAN objectives significantly stabilize, if the discriminator is robust to adversarial attacks. Specifically , we show that a robust discriminator leads to a robust minimax objective for the generator irrespective of the training objective used. In addition , any training objective is smooth and Lipschitz as long as the discriminator is Lipschitz. Finally, we show that this robustness does not need to be enforced for every single input of the discriminator, but rather just in expectation over the generated samples. We present two new regularization terms, borrowed from the adversarial training literature. Both terms ensure the robustness of the discriminator. They are easy to optimize and can be added to any existing GAN objective.Our experiments show that adversarial robustness both improves the visual quality of the results, as well as stabilizes the training procedure across a wide range of architectures, hyper-parameters and training objectives. We will publish the code and data used to perform our experiments upon acceptance. In this paper, we established a clear connection between robust discriminators in generative adversarial networks and the overall smoothness of the optimization and the quality of the results. To our knowledge, we are the first to show that a robustness regularization guarantees a smooth and robust loss function for any GAN objective. Finally, our results suggest that robust regularization leads to better training and visual results than standard gradient penalties.",Generative Adversarial Networks are one leading tools generative modeling image editing content creation. However are hard train require delicate balancing act two deep networks fighting never ending duel. promising adversarial models today minimize Wasserstein objective. is smoother stable optimize. paper show Wasserstein distance is just one large family objective functions yield properties. making discriminator GAN robust adversarial attacks can turn GAN objective smooth stable loss. experimentally show GAN objective including Wasserstein GANs benefit adversarial robustness quantitatively qualitatively. training additionally becomes robust suboptimal choices hyperparameters model architectures objective functions. Generative adversarial networks GANs BID4 are at the forefront generative modeling. cast generative modeling never ending duel two networks:generator network produces synthetic samples random noise discriminator network distinguishes synthetic real data samples. GANs produce visually appealing samples are often hard train. Much recent work tries stabilize GAN training novel architecture BID25 BID3 training objectives BID17 BID6.In paper show GAN objectives significantly stabilize if the discriminator is robust adversarial attacks. Specifically show robust discriminator leads robust minimax objective generator irrespective training objective used. addition training objective is smooth Lipschitz long discriminator is Lipschitz. Finally show robustness does not need enforced every single input discriminator rather expectation generated samples. present two new regularization terms borrowed adversarial training literature. terms ensure robustness discriminator. are easy optimize can be added existing GAN objective.Our experiments show adversarial robustness improves visual quality results well stabilizes training procedure across wide range architectures hyper-parameters training objectives. will publish code data used perform experiments upon acceptance. paper established clear connection robust discriminators generative adversarial networks overall smoothness optimization quality results. knowledge are the first show robustness regularization guarantees smooth robust loss function GAN objective. Finally results suggest robust regularization leads better training visual results standard gradient penalties.,537,356,181,0.005,1.508,2025/11/05 17:19:08,0.0,1.438,0.5545171339563861,179.841
"We propose a method to learn stochastic activation functions for use in probabilistic neural networks.
 First, we develop a framework to embed stochastic activation functions based on Gaussian processes in probabilistic neural networks.
 Second, we analytically derive expressions for the propagation of means and covariances in such a network, thus allowing for an efficient implementation and training without the need for sampling.
 Third, we show how to apply variational Bayesian inference to regularize and efficiently train this model.
 The resulting model can deal with uncertain inputs and implicitly provides an estimate of the confidence of its predictions.
 Like a conventional neural network it can scale to datasets of arbitrary size and be extended with convolutional and recurrent connections, if desired. The popularity of deep learning and the implied race for better accuracy and performance has lead to new research of the fundamentals of neural networks. Finding an optimal architecture often focusses on a hyperparameter search over the network architecture, regularization parameters, and one of a few standard activation functions: tanh, ReLU BID5 ), maxout ) . . . Focussing on the latter, looking into activation functions has only taken off since BID12 introduced the rectified linear unit (ReLU), which were shown to produce significantly better results on image recognition tasks BID10 . BID11 then introduced the leaky ReLU, which has a very small, but non-zero, slope for negative values. BID8 proposed the parameterized ReLU, by making the slope of the negative part of the leaky ReLU adaptable. It was trained as an additional parameter for each neuron alongside the weights of the neural network using stochastic gradient descent. Thus, the activation function was not treated as a fixed hyper-parameter anymore but as adaptable to training data. While the parameterized ReLU only has one parameter, this was generalized in BID0 to piecewise linear activation functions that can have an arbitrary (but fixed) number of points where the function changes it slope. This can be interpreted as a different parameterization of a Maxout network ), in which each neuron takes the maximum over a set of different linear combinations of its inputs.Instead of having a fixed parameter for the negative slope of the ReLU, BID18 introduced stochasticity into the activation function by sampling the value for the slope with each training iteration from a fixed uniform distribution. BID3 and BID9 replaced the negative part of ReLUs with a scaled exponential function and showed that, under certain conditions, this leads to automatic renormalization of the inputs to the following layer and thereby simplifies the training of the neural networks, leading to an improvement in accuracy in various tasks.Nearly fully adaptable activation functions have been proposed by BID4 . The authors use a Fourier basis expansion to represent the activation function; thus with enough coefficients any (periodic) activation function can be represented. The coefficients of this expansion are trained as network parameters using stochastic gradient descent or extensions thereof.Promoting a more general approach, BID1 proposed to learn the activation functions alongside the layer weights. Their adaptive piecewise linear units consist of a sum of hinge-shaped functions with parameters to control the hinges and the slopes of the linear segments. However, by construction the derivative of these activation functions is not continuous at the joints between two linear segments, which often leads to non-optimal optimizer performance.To our knowledge, previous research on learning activation functions took place in a fully deterministic setting, i.e. deterministic activation functions were parameterized and included in the optimization of a conventional neural network. Here instead, we explore the setting of probabilistic activation functions embedded in a graphical model of random variables resembling the structure of a neural network. We develop the theory of Gaussian-process neurons and subsequently derive a lower-bound approximation using variational inference, in order to develop a computationally efficient version of the Gaussian Process neuron. We have presented a non-parametric model based on GPs for learning of activation functions in a multi-layer neural network. We then successively applied variational to make fully Bayesian inference feasible and efficient while keeping its probabilistic nature and providing not only best guess predictions but also confidence estimations in our predictions. Although we employ GPs, our parametric approximation allows our model to scale to datasets of unlimited size like conventional neural networks do.We have validated networks of Gaussian Process Neurons in a set of experiments, the details of which we submit in a subsequent publication. In those experiments, our model shows to be significantly less prone to overfitting than a traditional feed-forward network of same size, despite having more parameters.",propose method learn stochastic activation functions use probabilistic neural networks. First develop framework embed stochastic activation functions based Gaussian processes probabilistic neural networks. Second analytically derive expressions propagation means covariances network thus allowing efficient implementation training without need sampling. Third show how to apply variational Bayesian inference regularize efficiently train model. resulting model can deal uncertain inputs implicitly provides estimate confidence predictions. Like conventional neural network can scale datasets arbitrary size extended convolutional recurrent connections if desired. popularity deep learning implied race better accuracy performance has lead new research fundamentals neural networks. Finding optimal architecture often focusses hyperparameter search network architecture regularization parameters one standard activation functions:tanh ReLU BID5 maxout Focussing latter looking activation functions has only taken since BID12 introduced rectified linear unit ReLU which were shown produce significantly better results image recognition tasks BID10. BID11 introduced leaky ReLU which hasa small non-zero slope negative values. BID8 proposed parameterized ReLU making slope negative part leaky ReLU adaptable. was trained additional parameter neuron alongside weights neural network using stochastic gradient descent. Thus activation function was not treated fixed hyper-parameter anymore adaptable training data. parameterized ReLU has one parameter was generalized BID0 piecewise linear activation functions can have an arbitrary fixed number points where the function changes slope. can be interpreted different parameterization Maxout network which neuron takes maximum set different linear combinations inputs.Instead fixed parameter negative slope ReLU BID18 introduced stochasticity activation function sampling value slope training iteration fixed uniform distribution. BID3 BID9 replaced negative part ReLUs scaled exponential function showed certain conditions leads automatic renormalization inputs following layer thereby simplifies training neural networks leading improvement accuracy various tasks.Nearly fully adaptable activation functions have been proposed BID4. authors use Fourier basis expansion represent activation function;thus enough coefficients periodic activation function can be represented. coefficients expansion are trained network parameters using stochastic gradient descent extensions thereof.Promoting general approach BID1 proposed learn activation functions alongside layer weights. adaptive piecewise linear units consist sum hinge-shaped functions parameters control hinges slopes linear segments. However construction derivative activation functions is not continuous joints two linear segments which often leads non-optimal optimizer performance.To knowledge previous research learning activation functions took place fully deterministic setting.e deterministic activation functions were parameterized included optimization conventional neural network. instead explore setting probabilistic activation functions embedded graphical model random variables resembling structure neural network. develop theory Gaussian-process neurons subsequently derive lower-bound approximation using variational inference order develop computationally efficient version Gaussian Process neuron. have presented non-parametric model based GPs learning activation functions multi-layer neural network. successively applied variational make fully Bayesian inference feasible efficient keeping probabilistic nature providing best guess predictions also confidence estimations predictions. Although employ GPs parametric approximation allows model scale datasets unlimited size like conventional neural networks do.We have validated networks Gaussian Process Neurons set experiments details which we submit subsequent publication. experiments model shows significantly less prone overfitting traditional feed-forward network size despite parameters.,902,589,313,0.009,1.531,2025/11/05 17:19:08,0.0,1.56,0.626168224299065,300.383
"Recent results from linear algebra stating that any matrix can be decomposed into products of diagonal and circulant matrices has lead to the design of compact deep neural network architectures that perform well in practice. In this paper, we bridge the gap between these good empirical results 
 and the theoretical approximation capabilities of Deep diagonal-circulant ReLU networks. More precisely, we first demonstrate  that a Deep diagonal-circulant ReLU networks of
 bounded width and small depth can approximate a deep ReLU network in which the dense matrices are
 of low rank. Based on this result, we provide new bounds on the expressive power and universal approximativeness of this type of networks. We support our experimental results with thorough experiments on a large, real world video classification problem. Recent progress in deep neural networks came at the cost of an important increase of model sizes. Nowadays, state-of-the-art architectures for common tasks such as object recognition typically have tens of millions of parameters BID13 ) and up to a billion parameters in some cases BID10 . Best performing (ensemble) models typically combine dozens of such models, and their size can quickly add up to ten or twenty gigabytes. Large models are often more accurate, but training them requires time and large amounts of computational resources. Even when they are trained, they remain difficult to deploy, especially on mobile devices where memory or computational power is limited.In linear algebra, it is common to exploit structural properties of matrices to speedup computations, or reduce memory usage. BID7 have applied this principle in the context of deep neural networks, and proposed a network architecture in which large unstructured weight matrices have been replaced with more compact matrices with a circulant structure. Since any n-by-n circulant matrix can be represented in memory using only a vector of dimension n, the change resulted in a drastic reduction of the model size (from 230MB to 21MB). Furthermore, Cheng et al. have shown empirically that their network architecture can be almost as accurate as the original network. BID23 have proposed a more principled approach leveraging a result by BID16 stating that any matrix A ∈ C n×n can be decomposed into 2n − 1 diagonal and circulant matrices. They use this result to design Deep diagonal-circulant ReLU networks. However their experiments show good results even with a small number of factors (down to 2 factors), suggesting that Deep diagonal-circulant ReLU networks can achieve good approximation error, even with few factors.In this paper, we bridge the gap between the good empirical results observed by BID23 , and the theoretical approximation capabilities of Deep diagonal-circulant ReLU networks. We prove that Deep diagonal-circulant ReLU networks with bounded width and small depth can approximate any dense neural network. We obtain this result by showing that any matrix A can be decomposed into 4k + 1 diagonal and circulant matrices where k is the rank of the matrix A. In practice, this result is more useful than the one by Huhtanen & Perämäki since one can rely on a low rank SVD decomposition of A while controlling the approximation error.In addition to this theoretical contribution, we also conduct thorough experiments on synthetic and real datasets. In accordance with the theory, our experiments demonstrate that we can easily tradeoff accuracy for model size by adjusting the number of factors in the matrix decomposition. Finally we evaluate the applicability of this approach on state-of-the-art neural network architectures trained for video classification on the Youtube-8m Video dataset (over 1TB of training data). This experiment demonstrates that Deep diagonal-circulant ReLU networks can be used to train more compact neural networks on large scale, real world scenarios. In this paper we provided a theoretical study of the properties of Deep diagonal-circulant ReLU networks and demonstrated that they are bounded width universal approximators. The bound on this decomposition allowed us to calculate the error bound on any Deep diagonal-circulant ReLU networks given the depth on the network and the singular values associated with the weight matrices. Our empirical study demonstrate that we can trade-off model size for accuracy in accordance with the theory, and that we can use Deep diagonal-circulant ReLU networks in large scale machine learning applications.",Recent results linear algebra stating matrix can be decomposed products diagonal circulant matrices has lead design compact deep neural network architectures perform well practice. paper bridge gap good empirical results theoretical approximation capabilities Deep diagonal-circulant ReLU networks. precisely first demonstrate Deep diagonal-circulant ReLU networks bounded width small depth can approximate deep ReLU network which the dense matrices are of low rank. Based result provide new bounds expressive power universal approximativeness type networks. support experimental results thorough experiments large real world video classification problem. Recent progress deep neural networks came cost important increase model sizes. Nowadays state-of-the-art architectures common tasks object recognition typically have tens millions parameters BID13 billion parameters cases BID10. Best performing ensemble models typically combine dozens models size can quickly add ten twenty gigabytes. Large models are often accurate training requires time large amounts computational resources. Even when they are trained remain difficult deploy especially mobile devices where memory computational power is limited.In linear algebra is common exploit structural properties matrices speedup computations reduce memory usage. BID7 have applied principle context deep neural networks proposed network architecture which large unstructured weight matrices have been replaced compact matrices circulant structure. Since n-by-n circulant matrix can be represented memory using vector dimensionn change resulted drastic reduction model size 230MB 21MB Furthermore Chengetal. have shown empirically network architecture can be almost accurate original network. BID23 have proposed principled approach leveraging result BID16 stating matrix ∈ C n×n can be decomposed 2n − 1 diagonal circulant matrices. use result design Deep diagonal-circulant ReLU networks. However experiments show good results even small number factors 2 factors suggesting Deep diagonal-circulant ReLU networks can achieve good approximation error even factors.In paper bridge gap good empirical results observed BID23 theoretical approximation capabilities Deep diagonal-circulant ReLU networks. prove Deep diagonal-circulant ReLU networks bounded width small depth can approximate dense neural network. obtain result showing matrix can be decomposed 4k+1 diagonal circulant matrices wherek is the rank matrix A. practice result is more useful one Huhtanen Perämäki since one can rely low rank SVD decomposition controlling approximation error.In addition theoretical contribution also conduct thorough experiments synthetic real datasets. accordance theory experiments demonstrate can easily tradeoff accuracy model size adjusting number factors matrix decomposition. Finally evaluate applicability approach state-of-the-art neural network architectures trained video classification Youtube-8m Video dataset 1TB training data experiment demonstrates Deep diagonal-circulant ReLU networks can be used train compact neural networks large scale real world scenarios. paper provided theoretical study properties Deep diagonal-circulant ReLU networks demonstrated are bounded width universal approximators. bound decomposition allowedus calculate error bound Deep diagonal-circulant ReLU networks given depth network singular values associated weight matrices. empirical study demonstrate can trade-off model size accuracy accordance theory can use Deep diagonal-circulant ReLU networks which large scale machine learning applications.,862,595,267,0.008,1.449,2025/11/05 17:19:08,0.0,1.4,0.3707165109034268,284.817
"Camera drones, a rapidly emerging technology, offer people the ability to remotely inspect an environment with a high degree of mobility and agility. However, manual remote piloting of a drone is prone to errors. In contrast, autopilot systems can require a significant degree of environmental knowledge and are not necessarily designed to support flexible visual inspections. Inspired by camera manipulation techniques in interactive graphics, we designed StarHopper, a novel touch screen interface for efficient object-centric camera drone navigation, in which a user directly specifies the navigation of a drone camera relative to a specified object of interest. The system relies on minimal environmental information and combines both manual and automated control mechanisms to give users the freedom to remotely explore an environment with efficiency and accuracy. A lab study shows that StarHopper offers an efficiency gain of 35.4% over manual piloting, complimented by an overall user preference towards our object-centric navigation system. Researchers in telepresence have long envisioned 'beyond being there' [21] . Replicating all relevant local experiences, while remote, should not be the only goal of telepresence; rather, we should also strive to create telepresence systems which can enable benefits that are not possible when the person is physically present. As such, telepresence goes from replication to augmentation. One particular instance of this vision is enabled by camera drones: our local bodies can only walk on the ground, but our remote bodies can fly. Current commercial remote robotic presence platforms have mostly been designed to replicate face-to-face conversation experiences [38, 55, 56] . Researchers have also explored their usage in a wider range of scenarios, such as shopping in a mall [55] or attending conferences [41] , and noted a number of social and functional issues due to their insufficient mobility [2, 19, 55] . With unmanned micro aerial vehicles (called 'drones' hereafter) becoming more affordable and reliable, they hold the potential for enabling more flexible remote presence and visual inspection experiences [16, 20, 25, 39, 48, 56] for the general population. While drones offer promise for such telepresence applications, they are challenging to manually control remotely, due to numerous factors including high degrees of freedom, narrow camera field-of-views, and network delays [40] . Their control interfaces -virtual or physical joysticks for consumer drones -are also unfamiliar for many users and take extended training time to master [48] . To relieve the burden of manual piloting, autopilot techniques have been applied to drone control. Most existing drone autopilot interfaces are based on specifying a series of planned waypoints in a 2D or 3D global map [10, 13, 48, 58] . However, in a situation where a user wishes to perform a real-time inspection, setting waypoints a priori may not be efficient for producing the viewer's desired viewpoints. For example, the viewer may wish to see something from a closer distance, from a different viewpoint, or view an area they didn't know about when the waypoints were set. Some autonomous systems avoid the use of waypoints and execute higher-level plans [11, 26, 33] , such as following a subject to form canonical shots [26] , but they typically do not offer the flexibility for exploring remote environments. The difficulty of drone piloting poses a significant barrier for the widespread adoption of free-flying robots. The goal of this research is to design a camera drone control interface to support efficient and flexible remote visual inspection for now universally adopted touchscreens. Inspired by recent work in semi-autonomous hybrid systems [33, 40] , we wish to combine the strengths of both manual and automatic piloting into a single hybrid navigation interface. Our work is also inspired by decades of research in interactive graphics, for which many camera navigation techniques have been established [5, 18, 29, 34] . Most relevant, we build upon object-centric techniques, where zooming, panning, and orbiting occurs relative to the location of a 3D object of interest. Existing object-aware drone navigation interfaces, such as DJI ActiveTrack [61] and XPose [33] , have been designed for aerial photography within visual line-of-sight. As such, they lack support for two important requirements of remote navigation and inspection: first, free exploration of a remote environment, which may include objects out of the initial camera field-of-view; and second, flexible inspection from various viewing angles or distances in relation to the objectof-interest. We propose StarHopper, a remote object-centric camera drone navigation interface that is operated through familiar touch interactions and relies on minimal geometric information of the environment (Figure 1 ). The system is designed based on a set of design goals for remote objectcentric drone navigation. It consists of an overhead camera view for context and a 3D-tracked drone's first-person view for focus. New objects of interest can be specified through simple touch gestures on both camera views. We combine automatic and manual control via four navigation mechanisms that can complement each other with unique strengths, to support efficient and flexible visual inspection. The system focuses on indoor environments, representative of tasks such as remote warehouse inspection [48] and museum visits [50, 51] , and where positional tracking technology is more reliable. A remote object inspection study showed that StarHopper was 35.4% faster than a manual baseline interface, for both simple and complex navigation routes. Users expressed general preferences towards object-centric navigation for remote inspection. We conclude by discussing potential design opportunities and future research to further increase the efficiency of remote visual inspection tasks. In this section, we discuss the implications of the results from our study, clarify important considerations and limitations related to our work, and propose future lines of research. To remove the barriers of using drones as free-flying remote inspection platforms, we explored touch-based object-centric navigation for camera drones through our prototype system, StarHopper. An in-lab study showed that users were able to achieve notable efficiency improvement using StarHopper for remote visual inspection, in comparison to a baseline condition using a touchscreen joystick for manual control. A strength of StarHopper comes from its combined use of a suite of automated, semiautomated, and manual control mechanisms to achieve efficiency and flexibility. In future work, we plan to empirically study users' mental models when working with automated camera drones, to understand how to build better human-automation collaboration for remote inspection. We are also interested in extending the usage of StarHopper to larger spaces and outdoor environments with a second drone as the overview camera. Our object-centric navigation techniques took inspiration from classical techniques in interactive graphics. As 3D sensing, reconstruction, object recognition, and other related fields advance, more powerful techniques initially developed for the virtual world may be applicable to telepresence navigation, taking us even closer to the vision of unconstrained 'beyond being there' telepresence.",Camera drones rapidly emerging technology offer people ability remotely inspect environment high degree mobility agility. However manual remote piloting drone is prone errors. contrast autopilot systems can require significant degree environmental knowledge are not necessarily designed support flexible visual inspections. Inspired camera manipulation techniques interactive graphics designed StarHopper novel touch screen interface efficient object-centric camera drone navigation which a user directly specifies navigation drone camera relative specified object interest. system relies minimal environmental information combines manual automated control mechanisms give users freedom remotely explore environment efficiency accuracy. lab study shows StarHopper offers efficiency gain 35.4 manual piloting complimented overall user preference towards object-centric navigation system. Researchers telepresence have long envisioned 'beyond there' 21 Replicating relevant local experiences remote should notbe goal telepresence;rather should also strive create telepresence systems which can enable benefits are not possible when the person is physically present. telepresence goes replication augmentation. One particular instance vision is enabled camera drones:local bodies can only walk ground remote bodies can fly. Current commercial remote robotic presence platforms have mostly designed replicate face-to-face conversation experiences 38 55 56 Researchers have also explored usage wider range scenarios shopping mall 55 attending conferences 41 noted number social functional issues due insufficient mobility 2 19 55 unmanned micro aerial vehicles called 'drones' hereafter becoming affordable reliable hold potential enabling flexible remote presence visual inspection experiences 16 20 25 39 48 56 general population. drones offer promise telepresence applications are challenging manually control remotely due numerous factors including high degrees freedom narrow camera field-of-views network delays 40 control interfaces -virtual physical joysticks consumer drones -are also unfamiliar many users take extended training time master 48 relieve burden manual piloting autopilot techniques have been applied drone control. existing drone autopilot interfaces are based specifying series planned waypoints 2D 3D global map 10 13 48 58 However situation where a user wishes perform real-time inspection setting waypoints priori may efficient producing viewer's desired viewpoints. example viewer may wish see something closer distance different viewpoint view area know when the waypoints were set. autonomous systems avoid use waypoints execute higher-level plans 11 26 33 following subject form canonical shots 26 typically do not offer flexibility exploring remote environments. difficulty drone piloting poses significant barrier widespread adoption free-flying robots. goal research is to design camera drone control interface support efficient flexible remote visual inspection universally adopted touchscreens. Inspired recent work semi-autonomous hybrid systems 33 40 wish combine strengths manual automatic piloting single hybrid navigation interface. work is also inspired decades research interactive graphics which many camera navigation techniques have been established 5 18 29 34 relevant build upon object-centric techniques where zooming panning orbiting occurs relative location 3D object interest. Existing object-aware drone navigation interfaces DJI ActiveTrack 61 XPose 33 have been designed aerial photography within visual line-of-sight lack support two important requirements remote navigation inspection:first free exploration remote environment may include objects initial camera field-of-view second flexible inspection various viewing angles distances relation objectof-interest propose StarHopper remote object-centric camera drone navigation interface is operated familiar touch interactions relies minimal geometric information environment Figure1 system is designed based set design goals remote objectcentric drone navigation. consists overhead camera view context 3D-tracked drone's first-person view focus. New objects interest can be specified simple touch gestures camera views. combine automatic manual control via four navigation mechanisms can complement unique strengths support efficient flexible visual inspection. system focuses indoor environments representative tasks remote warehouse inspection 48 museum visits 50 51 where positional tracking technology is more reliable. remote object inspection study showed StarHopper was 35.4 35.4 faster manual baseline interface simple complex navigation routes. Users expressed general preferences towards object-centric navigation remote inspection. conclude discussing potential design opportunities future research increase efficiency remote visual inspection tasks. section discuss implications results study clarify important considerations limitations related work propose future lines research. remove barriers using drones free-flying remote inspection platforms explored touch-based object-centric navigation camera drones prototype system StarHopper. in-lab study showed users were able achieve notable efficiency improvement using StarHopper remote visual inspection comparison baseline condition using touchscreen joystick manual control. strength StarHopper comes combined use suite automated semiautomated manual control mechanisms achieve efficiency flexibility. future work plan empirically study users' mental models when working automated camera drones understand how to build better human-automation collaboration remote inspection. are also interested extending usage StarHopper larger spaces outdoor environments second drone overview camera. object-centric navigation techniques took inspiration classical techniques interactive graphics. 3D sensing reconstruction object recognition related fields advance powerful techniques initially developed virtual world may applicable telepresence navigation taking us even closer vision unconstrained 'beyond there' telepresence.,1404,956,448,0.015,1.469,2025/11/05 17:19:08,0.01,1.475,0.4330218068535826,449.568
"Recurrent neural networks (RNN), convolutional neural networks (CNN) and self-attention networks (SAN) are commonly used to produce context-aware representations. RNN can capture long-range dependency but is hard to parallelize and not time-efficient. CNN focuses on local dependency but does not perform well on some tasks. SAN can model both such dependencies via highly parallelizable computation, but memory requirement grows rapidly in line with sequence length. In this paper, we propose a model, called ""bi-directional block self-attention network (Bi-BloSAN)"", for RNN/CNN-free sequence encoding. It requires as little memory as RNN but with all the merits of SAN. Bi-BloSAN splits the entire sequence into blocks, and applies an intra-block SAN to each block for modeling local context, then applies an inter-block SAN to the outputs for all blocks to capture long-range dependency. Thus, each SAN only needs to process a short sequence, and only a small amount of memory is required. Additionally, we use feature-level attention to handle the variation of contexts around the same word, and use forward/backward masks to encode temporal order information. On nine benchmark datasets for different NLP tasks, Bi-BloSAN achieves or improves upon state-of-the-art accuracy, and shows better efficiency-memory trade-off than existing RNN/CNN/SAN. Context dependency provides critical information for most natural language processing (NLP) tasks. In deep neural networks (DNN), context dependency is usually modeled by a context fusion module, whose goal is to learn a context-aware representation for each token from the input sequence. Recurrent neural networks (RNN), convolutional neural networks (CNN) and self-attention networks (SAN) are commonly used as context fusion modules. However, each has its own merits and defects, so which network to use is an open problem and mainly depends on the specific task.RNN is broadly used given its capability in capturing long-range dependency through recurrent computation. It has been applied to various NLP tasks, e.g., question answering BID51 , neural machine translation BID0 , sentiment analysis , natural language inference BID29 , etc. However, training the basic RNN encounters the gradient dispersion problem, and is difficult to parallelize. Long short-term memory (LSTM) BID14 effectively avoids the vanishing gradient. Gated recurrent unit (GRU) BID5 and simple recurrent unit (SRU) BID24 improve the efficiency by reducing parameters and removing partial temporal-dependency, respectively. However, they still suffer from expensive time cost, especially when applied to long sequences.CNN becomes popular recently on some NLP tasks because of its the highly parallelizable convolution computation BID7 . Unlike RNN, CNN can simultaneously apply convolutions defined by different kernels to multiple chunks of a sequence BID19 . It is mainly used for sentence-encoding tasks BID25 BID17 . Recently, hierarchical CNNs, e.g. ByteNet BID18 , and ConvS2S BID8 , are proposed to capture relatively long-range dependencies by using stacking CNNs to increase the number of input BID2 . The details of all the models are provided in Section 4.We propose an attention mechanism, called ""bidirectional block self-attention (Bi-BloSA)"", for fast and memory-efficient context fusion. The basic idea is to split a sequence into several length-equal blocks (with padding if necessary), and apply an intra-block SAN to each block independently. The outputs for all the blocks are then processed by an inter-block SAN. The intra-block SAN captures the local dependency within each block, while the inter-block SAN captures the long-range/global dependency. Hence, every SAN only needs to process a short sequence. Compared to a single SAN applied to the whole sequence, such two-layer stacked SAN saves a significant amount of memory. A feature fusion gate combines the outputs of intra-block and inter-block SAN with the original input, to produce the final contextaware representations of all the tokens. Similar to directional self-attention (DiSA) BID42 , BiBloSA uses forward/backward masks to encode the temporal order information, and feature-level attention to handle the variation of contexts around the same word. Further, a RNN/CNN-free sequence encoding model we build based on Bi-BloSA, called ""bi-directional block self-attention network (Bi-BloSAN)"", uses an attention mechanism to compress the output of Bi-BloSA into a vector representation.In experiments 1 , we implement Bi-BloSAN and popular sequence encoding models on several NLP tasks, e.g., language inference, sentiment analysis, semantic relatedness, reading comprehension, question-type classification, etc. The baseline models include Bi-LSTM, Bi-GRU, Bi-SRU, CNNs, multi-head attention and DiSAN. A thorough comparison on nine benchmark datasets demonstrates the advantages of Bi-BloSAN in terms of training speed, inference accuracy and memory consumption. FIG0 shows that Bi-BloSAN obtains the best accuracy by costing similar training time to DiSAN, and as little memory as Bi-LSTM, Bi-GRU and multi-head attention. This shows that Bi-BloSAN achieves a better efficiency-memory trade-off than existing RNN/CNN/SAN models.Our notations follow these conventions: 1) lowercase denotes a vector; 2) bold lowercase denotes a sequence of vectors (stored as a matrix); and 3) uppercase denotes a matrix or a tensor. This paper presents an attention network, called bi-directional block self-attention network (BiBloSAN) , for fast, memory-efficient and RNN/CNN-free sequence modeling. To overcome large memory consumption of existing self-attention networks, Bi-BloSAN splits the sequence into several blocks and employs intra-block and inter-block self-attentions to capture both local and long-range context dependencies, respectively. To encode temporal order information, Bi-BloSAN applies forward and backward masks to the alignment scores between tokens for asymmetric selfattentions.Our experiments on nine benchmark datasets for various different NLP tasks show that Bi-BloSAN can achieve the best or state-of-the-art performance with better efficiency-memory trade-off than existing RNN/CNN/SAN models. Bi-BloSAN is much more time-efficient than the RNN models (e.g., Bi-LSTM, Bi-GRU, etc.), requires much less memory than DiSAN, and significantly outperforms the CNN models and multi-head attention on prediction quality.",Recurrent neural networks RNN convolutional neural networks CNN self-attention networks SAN are commonly used produce context-aware representations. RNN can capture long-range dependency is hard parallelize time-efficient CNN focuses local dependency does not perform well tasks. SAN can model dependencies via highly parallelizable computation memory requirement grows rapidly line sequence length. paper propose model called bi-directional block self-attention network Bi-BloSAN RNN/CNN-free sequence encoding. requires little memory RNN merits SAN. Bi-BloSAN splits entire sequence blocks applies intra-block SAN block modeling local context applies inter-block SAN outputs blocks capture long-range dependency. Thus SAN needs process short sequence small amount memory is required. Additionally use feature-level attention handle variation contexts around word use forward/backward masks encode temporal order information. nine benchmark datasets different NLP tasks Bi-BloSAN achieves improves upon state-of-the-art accuracy shows better efficiency-memory trade-off existing RNN/CNN/SAN. Context dependency provides critical information natural language processing NLP tasks. deep neural networks DNN context dependency is usually modeled context fusion module whose goal is to learn context-aware representation token input sequence. Recurrent neural networks RNN convolutional neural networks CNN self-attention networks SAN are commonly used context fusion modules. However has its merits defects which network use is an open problem mainly depends specific task.RNN is broadly used given capability capturing long-range dependency recurrent computation. has been applied various NLP tasks e.g question answering BID51 neural machine translation BID0 sentiment analysis natural language inference BID29 etc. However training basic RNN encounters gradient dispersion problem is difficult parallelize. Long short-term memory LSTM BID14 effectively avoids vanishing gradient. Gated recurrent unit GRU BID5 simple recurrent unit SRU BID24 improve efficiency reducing parameters removing partial temporal-dependency respectively. However still suffer expensive time cost especially when applied long sequences.CNN becomes popular recently NLP tasks highly parallelizable convolution computation BID7. Unlike RNN CNN can simultaneously apply convolutions defined different kernels multiple chunks sequence BID19. is mainly used sentence-encoding tasks BID25 BID17. Recently hierarchical CNNs e.g ByteNet BID18 ConvS2S BID8 are proposed capture relatively long-range dependencies using stacking CNNs increase number input BID2. details models are provided Section 4.We propose attention mechanism called bidirectional block self-attention Bi-BloSA fast memory-efficient context fusion. basic idea is to split sequence several length-equal blocks padding if necessary apply intra-block SAN block independently. outputs blocks are then processed inter-block SAN. intra-block SAN captures local dependency within block inter-block SAN captures long-range/global dependency. Hence every SAN needs process short sequence. Compared single SAN applied whole sequence two-layer stacked SAN saves significant amount memory. feature fusion gate combines outputs intra-block inter-block SAN original input produce final contextaware representations tokens. Similar directional self-attention DiSA BID42 BiBloSA uses forward/backward masks encode temporal order information feature-level attention handle variation contexts around word. RNN/CNN-free sequence encoding model build based Bi-BloSA called bi-directional block self-attention network Bi-BloSAN uses attention mechanism compress output Bi-BloSA vector representation.In experiments1 implement Bi-BloSAN popular sequence encoding models several NLP tasks e.g language inference sentiment analysis semantic relatedness reading comprehension question-type classification etc. baseline models include Bi-LSTM Bi-GRU Bi-SRU CNNs multi-head attention DiSAN. thorough comparison nine benchmark datasets demonstrates advantages Bi-BloSAN terms training speed inference accuracy memory consumption. FIG0 shows Bi-BloSAN obtains best accuracy costing similar training time DiSAN little memory Bi-LSTM Bi-GRU multi-head attention. shows Bi-BloSAN achieves better efficiency-memory trade-off existing RNN/CNN/SAN models.Our notations follow conventions:1 lowercase denotes vector;2 bold lowercase denotes sequence vectors stored matrix 3 uppercase denotes matrix tensor. paper presents attention network called bi-directional block self-attention network BiBloSAN fast memory-efficient RNN/CNN-free sequence modeling. overcome large memory consumption existing self-attention networks Bi-BloSAN splits sequence several blocks employs intra-block inter-block self-attentions capture local long-range context dependencies respectively. encode temporal order information Bi-BloSAN applies forward backward masks alignment scores tokens asymmetric selfattentions.Our experiments nine benchmark datasets various different NLP tasks show Bi-BloSAN can achieve best state-of-the-art performance better efficiency-memory trade-off existing RNN/CNN/SAN models. Bi-BloSAN is much time-efficient RNN models e.g Bi-LSTM Bi-GRU etc. requires much less memory DiSAN significantly outperforms CNN models multi-head attention prediction quality.,1294,927,367,0.011,1.396,2025/11/05 17:19:09,0.01,1.292,0.2056074766355135,355.34
"End-to-end neural models have made significant progress in question answering, however recent studies show that these models implicitly assume that the answer and evidence appear close together in a single document. In this work, we propose the Coarse-grain Fine-grain Coattention Network (CFC), a new question answering model that combines information from evidence across multiple documents. The CFC consists of a coarse-grain module that interprets documents with respect to the query then finds a relevant answer, and a fine-grain module which scores each candidate answer by comparing its occurrences across all of the documents with the query. We design these modules using hierarchies of coattention and self-attention, which learn to emphasize different parts of the input. On the Qangaroo WikiHop multi-evidence question answering task, the CFC obtains a new state-of-the-art result of 70.6% on the blind test set, outperforming the previous best by 3% accuracy despite not using pretrained contextual encoders. A requirement of scalable and practical question answering (QA) systems is the ability to reason over multiple documents and combine their information to answer questions. Although existing datasets enabled the development of effective end-to-end neural question answering systems, they tend to focus on reasoning over localized sections of a single document (Hermann et al., 2015; Rajpurkar et al., 2016; 2018; Trischler et al., 2017) . For example, Min et al. (2018) find that 90% of the questions in the Stanford Question Answering Dataset are answerable given 1 sentence in a document. In this work, we instead focus on multi-evidence QA, in which answering the question requires aggregating evidence from multiple documents (Welbl et al., 2018; Joshi et al., 2017) .Our multi-evidence QA model, the Coarse-grain Fine-grain Coattention Network (CFC), selects among a set of candidate answers given a set of support documents and a query. The CFC is inspired by coarse-grain reasoning and fine-grain reasoning. In coarse-grain reasoning, the model builds a coarse summary of support documents conditioned on the query without knowing what candidates are available, then scores each candidate. In fine-grain reasoning, the model matches specific finegrain contexts in which the candidate is mentioned with the query in order to gauge the relevance of the candidate. These two strategies of reasoning are respectively modeled by the coarse-grain and fine-grain modules of the CFC. Each module employs a novel hierarchical attention -a hierarchy of coattention and self-attention -to combine information from the support documents conditioned on the query and candidates. FIG0 illustrates the architecture of the CFC.The CFC achieves a new state-of-the-art result on the blind Qangaroo WikiHop test set of 70.6% accuracy, beating previous best by 3% accuracy despite not using pretrained contextual encoders. In addition , on the TriviaQA multi-paragraph question answering task (Joshi et al., 2017) , reranking Most of this work was done while Victor Zhong was at Salesforce Research. outputs from a traditional span extraction model (Clark & Gardner, 2018) using the CFC improves exact match accuracy by 3.1% and F1 by 3.0%.Our analysis shows that components in the attention hierarchies of the coarse and fine-grain modules learn to focus on distinct parts of the input. This enables the CFC to more effectively represent a large collection of long documents. Finally, we outline common types of errors produced by CFC, caused by difficulty in aggregating large quantity of references, noise in distant supervision, and difficult relation types. We presented CFC, a new state-of-the-art model for multi-evidence question answering inspired by coarse-grain reasoning and fine-grain reasoning. On the WikiHop question answering task, the CFC achieves 70.6% test accuracy, outperforming previous methods by 3% accuracy. We showed in our analysis that the complementary coarse-grain and fine-grain modules of the CFC focus on different aspects of the input, and are an effective means to represent large collections of long documents.",End-to-end neural models have made significant progress question answering however recent studies show models implicitly assume answer evidence appear close together single document. work propose Coarse-grain Fine-grain Coattention Network CFC new question answering model combines information evidence across multiple documents. CFC consists coarse-grain module interprets documents respect query finds relevant answer fine-grain module which scores candidate answer comparing occurrences across documents query. design modules using hierarchies coattention self-attention which learn emphasize different parts input. Qangaroo WikiHop multi-evidence question answering task CFC obtains new state-of-the-art result 70.6 blind test set outperforming previous best 3% accuracy despite using pretrained contextual encoders. requirement scalable practical question answering QA systems is the ability reason multiple documents combine information answer questions. Although existing datasets enabled development effective end-to-end neural question answering systems tend focus reasoning localized sections single document Hermannetal. 2015;Rajpurkaretal. 2016;2018;Trischleretal. 2017 example Minetal. 2018 find 90% questions Stanford Question Answering Dataset are answerable given 1 sentence document. work instead focus multi-evidenceQA which answering question requires aggregating evidence multiple documents Welbletal. 2018;Joshietal. 2017.Our multi-evidence QA model Coarse-grain Fine-grain Coattention Network CFC selects among set candidate answers given set support documents query. CFC is inspired coarse-grain reasoning fine-grain reasoning. coarse-grain reasoning model builds coarse summary support documents conditioned query without knowing what candidates are available scores candidate. fine-grain reasoning model matches specific finegrain contexts which the candidate is mentioned query order gauge relevance candidate. two strategies reasoning are respectively modeled coarse-grain fine-grain modules CFC. module employs novel hierarchical attention-a hierarchy coattention self-attention -to combine information support documents conditioned query candidates. FIG0 illustrates architecture CFC.The CFC achieves new state-of-the-art result blind Qangaroo WikiHop test set 70.6 accuracy beating previous best 3% accuracy despite using pretrained contextual encoders. addition TriviaQA multi-paragraph question answering task Joshietal. 2017 reranking work was done Victor Zhong was at Salesforce Research. outputs traditional span extraction model Clark Gardner 2018 using CFC improves exact match accuracy 3.1 F1 3.0%.Our analysis shows components attention hierarchies coarse fine-grain modules learn focus distinct parts input. enables CFC effectively represent large collection long documents. Finally outline common types errors produced CFC caused difficulty aggregating large quantity references noise distant supervision difficult relation types. presented CFC new state-of-the-art model multi-evidence question answering inspired coarse-grain reasoning fine-grain reasoning. WikiHop question answering task CFC achieves 70.6 test accuracy outperforming previous methods 3% accuracy. showed analysis complementary coarse-grain fine-grain modules CFC focus different aspects input are an effective means represent large collections long documents.,860,608,252,0.007,1.414,2025/11/05 17:19:09,0.0,1.267,0.2616822429906538,269.604
"Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We formulate unbalanced OT as a problem of simultaneously learning a transport map and a scaling factor that push a source measure to a target measure in a cost-optimal manner. We provide theoretical justification for this formulation, showing that it is closely related to an existing static formulation by Liero et al. (2018). We then propose an algorithm for solving this problem based on stochastic alternating gradient updates, similar in practice to GANs, and perform numerical experiments demonstrating how this methodology can be applied to population modeling. We consider the problem of unbalanced optimal transport: given two measures, find a cost-optimal way to transform one measure to the other using a combination of mass variation and transport. Such problems arise, for example, when modeling the transformation of a source population into a target population ( Figure 1a ). In this setting, one needs to model mass transport to account for the features that are evolving, as well as local mass variations to allow sub-populations to become more or less prominent in the target population BID34 .Classical optimal transport (OT) considers the problem of pushing a source to a target distribution in a way that is optimal with respect to some transport cost without allowing for mass variations. Modern approaches are based on the Kantorovich formulation BID24 , which seeks the optimal probabilistic coupling between measures and can be solved using linear programming methods for discrete measures. Recently, BID13 showed that regularizing the objective using an entropy term allows the dual problem to be solved more efficiently using the Sinkhorn algorithm. Stochastic methods based on the dual objective have been proposed for the continuous setting BID19 . Optimal transport has been applied to many areas, such as computer graphics BID17 BID36 and domain adaptation (Courty et al., 2014; .In many applications where a transport cost is not available, transport maps can also be learned using generative models such as generative adversarial networks (GANs) BID20 , which push a source distribution to a target distribution by training against an adversary. Numerous transport problems in image translation BID30 BID38 BID37 , natural language translation BID22 , domain adaptation BID5 and biological data integration (Amodio & (a) (b)Figure 1: (a) Illustration of the problem of modeling the transformation of a source population µ to a target population ν. In this example, one sub-population is growing more rapidly than the others. (b) Schematic of Monge-like formulations of unbalanced optimal transport. The objective is to learn a transport map T (for transporting mass) and scaling factor ξ (for mass variation) to push the source µ to the target ν, using a deterministic transport map (top) BID7 or a stochastic transport map (bottom).Krishnaswamy, 2018) have been tackled using variants of GANs, with strategies such as conditioning or cycle-consistency employed to enforce correspondence between original and transported samples. However, all these methods conserve mass between the source and target and therefore cannot handle mass variation.Several formulations have been proposed for extending the theory of OT to the setting where the measures can have unbalanced masses BID7 BID26 BID27 BID18 . In terms of numerical methods, a class of scaling algorithms BID8 ) that generalize the Sinkhorn algorithm for balanced OT have been developed for approximating the solution to optimal entropy-transport problems; this formulation of unbalanced OT by BID27 corresponds to the Kantorovich OT problem in which the hard marginal constraints are relaxed using divergences to allow for mass variation. In practice, these algorithms have been used to approximate unbalanced transport plans between discrete measures for applications such as computer graphics BID8 , tumor growth modeling BID6 and computational biology BID34 . However, while optimal entropy-transport allows mass variation , it cannot explicitly model it, and there are currently no methods that can perform unbalanced OT between continuous measures.Contributions. Inspired by the recent successes of GANs for high-dimensional transport problems, we present a novel framework for unbalanced optimal transport that directly models mass variation in addition to transport. Concretely, our contributions are the following:• We propose to solve a Monge-like formulation of unbalanced OT, in which the goal is to learn a stochastic transport map and scaling factor to push a source to a target measure in a cost-optimal manner. This generalizes the unbalanced Monge OT problem by BID7 .• By relaxing this problem, we obtain an alternative form of the optimal entropy-transport problem by BID27 , which confers desirable theoretical properties.• We develop scalable methodology for solving the relaxed problem . Our derivation uses a convex conjugate representation of divergences , resulting in an alternating gradient descent method similar to GANs BID20 ).• We demonstrate in practice how our methodology can be applied towards population modeling using the MNIST and USPS handwritten digits datasets, the CelebA dataset, and a recent single-cell RNA-seq dataset from zebrafish embrogenesis.In addition to these main contributions, for completeness we also propose a new scalable method (Algorithm 2) in the Appendix for solving the optimal-entropy transport problem by BID27 in the continuous setting. The algorithm extends the work of to unbalanced OT and is a scalable alternative to the algorithm of BID8 for very large or continuous datasets.",Generative adversarial networks GANs are an expressive class neural generative models tremendous success modeling high-dimensional continuous measures. paper present scalable method unbalanced optimal transport OT based generative-adversarial framework. formulate unbalancedOT problem simultaneously learning transport map scaling factor push source measure target measure cost-optimal manner. provide theoretical justification formulation showing is closely related existing static formulation Lieroetal. 2018 propose algorithm solving problem based stochastic alternating gradient updates similar practice GANs perform numerical experiments demonstrating how this how our methodology can be applied population modeling. consider problem unbalanced optimal transport:given two measures find cost-optimal way transform one measure using combination mass variation transport. problems arise example when modeling transformation source population target population Figure1a setting one needs model mass transport account features are evolving well local mass variations allow sub-populations become less prominent target population BID34.Classical optimal transport OT considers problem pushing source target distribution way is optimal respect transport cost without allowing mass variations. Modern approaches are based Kantorovich formulation BID24 which seeks optimal probabilistic coupling measures can be solved using linear programming methods discrete measures. Recently BID13 showed regularizing objective using entropy term allows dual problem solved efficiently using Sinkhorn algorithm. Stochastic methods based dual objective have been proposed continuous setting BID19. Optimal transport has been applied many areas computer graphics BID17 BID36 domain adaptation Courtyetal. 2014;.In many applications where a transport cost is not available transport maps can also learned using generative models generative adversarial networks GANs BID20 which push source distribution target distribution training adversary. Numerous transport problems image translation BID30 BID38 BID37 natural language translation BID22 domain adaptation BID5 biological data integration Amodio b Figure1:Illustration problem modeling transformation source populationµ target populationν. example one sub-population is growing rapidly others. b Schematic Monge-like formulations unbalanced optimal transport. objective is to learn transport map transporting mass scaling factorξ mass variation push sourceµ targetν using deterministic transport map top BID7 stochastic transport map bottom.Krishnaswamy 2018 have been tackled using variants GANs strategies conditioning cycle-consistency employed enforce correspondence original transported samples. However methods conserve mass source target therefore cannot handle mass variation.Several formulations have been proposed extending theory OT setting where the measures can have unbalanced masses BID7 BID26 BID27 BID18. terms numerical methods class scaling algorithms BID8 generalize Sinkhorn algorithm balancedOT have been developed approximating solution optimal entropy-transport problems;formulation unbalancedOT BID27 corresponds Kantorovich OT problem which the hard marginal constraints are relaxed using divergences allow mass variation. practice algorithms have been used approximate unbalanced transport plans discrete measures applications computer graphics BID8 tumor growth modeling BID6 computational biology BID34. However optimal entropy-transport allows mass variation cannot explicitly model are currently methods can perform unbalancedOT continuous measures.Contributions. Inspired recent successes GANs high-dimensional transport problems present novel framework unbalanced optimal transport directly models mass variation addition transport. Concretely contributions are the following:• propose solve Monge-like formulation unbalancedOT which the goal is to learn stochastic transport map scaling factor push source target measure cost-optimal manner. generalizes unbalanced Monge OT problem BID7.• relaxing problem obtain alternative form optimal entropy-transport problem BID27 which confers desirable theoretical properties.• develop scalable methodology solving relaxed problem. derivation uses convex conjugate representation divergences resulting alternating gradient descent method similar GANs BID20.• demonstrate practice how this how our methodology can be applied towards population modeling using MNIST USPS handwritten digits datasets CelebA dataset recent single-cell RNA-seq dataset zebrafish embrogenesis.In addition main contributions completeness also propose new scalable method Algorithm2 Appendix solving optimal-entropy transport problem BID27 continuous setting. algorithm extends work unbalancedOT is a scalable alternative algorithm BID8 large continuous datasets.,1122,773,349,0.011,1.451,2025/11/05 17:19:09,0.01,1.594,0.3769470404984424,339.102
"Extracting saliency maps, which indicate parts of the image important to classification, requires many tricks to achieve satisfactory performance when using classifier-dependent methods. Instead, we propose classifier-agnostic saliency map extraction, which finds all parts of the image that any classifier could use, not just one given in advance. We observe that the proposed approach extracts higher quality saliency maps and outperforms existing weakly-supervised localization techniques, setting the new state of the art result on the ImageNet dataset. The success of deep convolutional networks for large-scale object recognition Krizhevsky et al. (2012) ; Simonyan & Zisserman (2014) ; Szegedy et al. (2015) ; He et al. (2016) has spurred interest in utilizing them to automatically detect and localize objects in natural images. Pioneering this direction, Simonyan et al. (2013) and Springenberg et al. (2014) demonstrated that the gradient of the class-specific score of a given classifier could be used for extracting a saliency map of an image. Such classifier-dependent saliency maps can be utilized to analyze the inner workings of a specific network. However, as only the part of the image that is used by a given model is highlighted, these methods are not identifying all ""evidence"" in a given image. They also tend to be noisy, covering many irrelevant pixels and missing many relevant ones. Therefore, much of the recent work has focused on introducing regularization techniques of correcting such classifier-dependent saliency maps. For instance, Selvaraju et al. (2017) propose averaging multiple saliency maps created for perturbed images to obtain a smooth saliency map. We argue, however, that applying tricks and tweaks on top of methods that were designed to analyze inner workings of a given classifier is not a principled way to get saliency maps that focus on all useful evidence. In this work, we aim to find saliency maps indicating pixels which aid classification, i.e. we want to find pixels in the input image such that if they were masked, it would confuse an unknown classifier. Assuming we were given a classifier, a naive approximate solution would be to train a generative model to output a mask (a saliency map) confusing that classifier. That can be achieved using a simple GAN-like approach (Goodfellow et al., 2014) where the classifier acts as a fixed discriminator. Unfortunately, as we prove experimentally, this solution suffers from the same issues as prior approaches. We argue that the strong dependence on a given classifier lies at the center of the problem. To tackle this directly we propose to train a saliency mapping that is not strongly coupled with any specific classifier. Our approach, a class-agnostic saliency map extraction, can be formulated as a practical algorithm that realizes our goal. Our focus on classifier-agnostic saliency maps is not our objective per se, it is a remedy that resolves the core problem. The proposed approach results in a neural network based saliency mapping that only depends on an input image. We qualitatively find that it extracts higher quality saliency maps compared to classifier-dependent methods, as can be seen in Fig. 2 . Extracted saliency maps show all the evidence without using any symptom-masking methods: difficult to tune regularization penalties (such as total variation), exotic activation functions, complex training procedures or image preprocessing tricks (such as superpixels), etc. We also evaluate our method quantitatively by using the extracted saliency maps for object localization. We observe that the proposed approach outperforms the existing weakly-supervised techniques setting the new state of the art result on the ImageNet dataset and closely approaches the localization performance of a strongly supervised model. Furthermore, we experimentally validate that the proposed approach works reasonably well even for classes unseen during training. Our method has many potential applications, in which being classifier-agnostic is of primary importance. For instance, in medical image analysis, where we are interested not only in class prediction but also in indicating which part of the image is important to classification. Importantly, however, it is criticial to indicate all parts of the image, which can influence diagnosis, not just ones used by a specific classifier. In this paper, we proposed a new framework for classifier-agnostic saliency map extraction which aims at finding a saliency mapping that works for all possible classifiers weighted by their posterior probabilities. We designed a practical algorithm that amounts to simultaneously training a classifier and a saliency mapping using stochastic gradient descent. We qualitatively observed that the proposed approach extracts saliency maps that cover all the relevant pixels in an image and that the masked-out images cannot be easily recovered by inpainting, unlike for classifier-dependent approaches. We further observed that the proposed saliency map extraction procedure outperforms all existing weakly supervised approaches to object localization and can also be used on images containing objects from previously unseen classes, paving a way toward class-agnostic saliency map extraction.",Extracting saliency maps which indicate parts image important classification requires many tricks achieve satisfactory performance when using classifier-dependent methods. Instead propose classifier-agnostic saliency map extraction which finds parts image classifier could use one given advance. observe proposed approach extracts higher quality saliency maps outperforms existing weakly-supervised localization techniques setting new state art result ImageNet dataset. success deep convolutional networks large-scale object recognition Krizhevsky etal. 2012 Simonyan Zisserman 2014 Szegedyetal. 2015 etal. 2016 has spurred interest utilizing automatically detect localize objects natural images. Pioneering direction Simonyanetal. 2013 Springenbergetal. 2014 demonstrated gradient class-specific score given classifier could used extracting saliency map image. classifier-dependent saliency maps can be utilized analyze inner workings specific network. However part image is used given model is highlighted methods are not identifying evidence given image. also tend noisy covering many irrelevant pixels missing many relevant ones. Therefore much recent work has focused introducing regularization techniques correcting classifier-dependent saliency maps. instance Selvarajuetal. 2017 propose averaging multiple saliency maps created perturbed images obtain smooth saliency map. argue however applying tricks tweaks top methods were designed analyze inner workings given classifier is not a principled way get saliency maps focus useful evidence. work aim find saliency maps indicating pixels which aid classification.e want find pixels input image if they were masked would confuse unknown classifier. Assuming were given classifier naive approximate solution would train generative model output mask saliency map confusing classifier. can be achieved using simple GAN-like approach Goodfellowetal. 2014 where the classifier acts fixed discriminator. Unfortunately prove experimentally solution suffers issues prior approaches. argue strong dependence given classifier lies center problem. tackle directly propose train saliency mapping is not strongly coupled specific classifier. approach class-agnostic saliency map extraction can be formulated practical algorithm realizes goal. focus classifier-agnostic saliency maps is not our objective perse is a remedy resolves core problem. proposed approach results neural network based saliency mapping depends input image. qualitatively find extracts higher quality saliency maps compared classifier-dependent methods can be seen Fig. 2. Extracted saliency maps show evidence without using symptom-masking methods:difficult tune regularization penalties total variation exotic activation functions complex training procedures image preprocessing tricks superpixels etc. also evaluate method quantitatively using extracted saliency maps object localization. observe proposed approach outperforms existing weakly-supervised techniques setting new state art result ImageNet dataset closely approaches localization performance strongly supervised model. Furthermore experimentally validate proposed approach works reasonably well even classes unseen training. method has many potential applications which being classifier-agnostic is of primary importance. instance medical image analysis where we are interested class prediction also indicating which part image is important classification. Importantly however is criticial indicate parts image which can influence diagnosis ones used specific classifier. paper proposed new framework classifier-agnostic saliency map extraction which aims finding saliency mapping works possible classifiers weighted posterior probabilities. designed practical algorithm amounts simultaneously training classifier saliency mapping using stochastic gradient descent. qualitatively observed proposed approach extracts saliency maps cover relevant pixels image masked-out images cannot easily recovered inpainting unlike classifier-dependent approaches. observed proposed saliency map extraction procedure outperforms existing weakly supervised approaches object localization can also used images containing objects previously unseen classes paving way toward class-agnostic saliency map extraction.,1015,693,322,0.01,1.465,2025/11/05 17:19:09,0.0,1.562,0.4205607476635514,308.131
"Unsupervised image-to-image translation has gained considerable attention due to the recent impressive progress based on generative adversarial networks (GANs). However, previous methods often fail in challenging cases, in particular, when an image has multiple target instances and a translation task involves significant changes in shape, e.g., translating pants to skirts in fashion images. To tackle the issues, we propose a novel method, coined instance-aware GAN (InstaGAN), that incorporates the instance information (e.g., object segmentation masks) and improves multi-instance transfiguration. The proposed method translates both an image and the corresponding set of instance attributes while maintaining the permutation invariance property of the instances. To this end, we introduce a context preserving loss that encourages the network to learn the identity function outside of target instances. We also propose a sequential mini-batch inference/training technique that handles multiple instances with a limited GPU memory and enhances the network to generalize better for multiple instances. Our comparative evaluation demonstrates the effectiveness of the proposed method on different image datasets, in particular, in the aforementioned challenging cases. Code and results are available in https://github.com/sangwoomo/instagan Cross-domain generation arises in many machine learning tasks, including neural machine translation BID2 BID21 , image synthesis BID33 BID48 , text style transfer BID34 , and video generation BID3 BID39 BID6 . In particular, the unpaired (or unsupervised) image-to-image translation has achieved an impressive progress based on variants of generative adversarial networks (GANs) BID27 BID7 BID0 BID23 , and has also drawn considerable attention due to its practical applications including colorization , super-resolution BID22 , semantic manipulation BID40 , and domain adaptation BID5 BID35 BID15 . Previous methods on this line of research, however, often fail on challenging tasks, in particular, when the translation task involves significant changes in shape of instances or the images to translate contains multiple target instances BID10 . Our goal is to extend image-to-image translation towards such challenging tasks, which can strengthen its applicability up to the next level, e.g., changing pants to skirts in fashion images for a customer to decide which one is better to buy. To this end, we propose a novel method that incorporates the instance information of multiple target objectsin the framework of generative adversarial networks (GAN); hence we called it instance-aware GAN (InstaGAN) . In this work, we use the object segmentation masks for instance information, which may be a good representation for instance shapes, as it contains object boundaries while ignoring other details such as color. Using the information, our method shows impressive results for multi-instance transfiguration tasks, as shown in FIG0 .Our main contribution is three-fold: an instance-augmented neural architecture, a context preserving loss, and a sequential mini-batch inference/training technique. First , we propose a neural network architecture that translates both an image and the corresponding set of instance attributes. Our architecture can translate an arbitrary number of instance attributes conditioned by the input, and is designed to be permutation-invariant to the order of instances. Second , we propose a context preserv- ), and our proposed method, InstaGAN. Our method shows better results for multi-instance transfiguration problems.ing loss that encourages the network to focus on target instances in translation and learn an identity function outside of them. Namely, it aims at preserving the background context while transforming the target instances. Finally, we propose a sequential mini-batch inference/training technique, i.e., translating the mini-batches of instance attributes sequentially, instead of doing the entire set at once. It allows to handle a large number of instance attributes with a limited GPU memory, and thus enhances the network to generalize better for images with many instances. Furthermore, it improves the translation quality of images with even a few instances because it acts as data augmentation during training by producing multiple intermediate samples. All the aforementioned contributions are dedicated to how to incorporates the instance information (e.g., segmentation masks) for image-to-image translation. However, we believe that our approach is applicable to numerous other cross-domain generation tasks where set-structured side information is available.To the best of our knowledge, we are the first to report image-to-image translation results for multiinstance transfiguration tasks. A few number of recent methods BID27 BID10 show some transfiguration results but only for images with a single instance often in a clear background. Unlike the previous results in a simple setting, our focus is on the harmony of instances naturally rendered with the background. On the other hand, CycleGAN show some results for multi-instance cases, but report only a limited performance for transfiguration tasks. At a high level, the significance of our work is also on discovering that the instance information is effective for shape-transforming image-to-image translation, which we think would be influential to other related research in the future. Mask contrast-GAN and Attention-GAN (Mejjati et al., 2018) use segmentation masks or predicted attentions, but only to attach the background to the (translated) cropped instances. They do not allow to transform the shapes of the instances. To the contrary, our method learns how to preserve the background by optimizing the context preserving loss, thus facilitating the shape transformation. We have proposed a novel method incorporating the set of instance attributes for image-to-image translation. The experiments on different datasets have shown successful image-to-image translation on the challenging tasks of multi-instance transfiguration, including new tasks, e.g., translating jeans to skirt in fashion images. We remark that our ideas utilizing the set-structured side information have potential to be applied to other cross-domain generations tasks, e.g., neural machine translation or video generation. Investigating new tasks and new information could be an interesting research direction in the future.",Unsupervised image-to-image translation has gained considerable attention due recent impressive progress based generative adversarial networks GANs However previous methods often fail challenging cases particular when an image has multiple target instances translation task involves significant changes shape e.g translating pants skirts fashion images. tackle issues propose novel method coined instance-aware GAN InstaGAN incorporates instance information e.g object segmentation masks improves multi-instance transfiguration. proposed method translates image corresponding set instance attributes maintaining permutation invariance property instances. end introduce context preserving loss encourages network learn identity function outside target instances. also propose sequential mini-batch inference/training technique handles multiple instances limited GPU memory enhances network generalize better multiple instances. comparative evaluation demonstrates effectiveness proposed method different image datasets particular aforementioned challenging cases. Code results are available https://github.com/sangwoomo/instagan Cross-domain generation arises many machine learning tasks including neural machine translation BID2 BID21 when an image synthesis BID33 BID48 text style transfer BID34 video generation BID3 BID39 BID6. particular unpaired unsupervised image-to-image translation has achieved impressive progress based variants generative adversarial networks GANs BID27 BID7 BID0 BID23 has also drawn considerable attention due practical applications including colorization super-resolution BID22 semantic manipulation BID40 domain adaptation BID5 BID35 BID15. Previous methods line research however often fail challenging tasks particular when the translation task involves significant changes shape instances images translate contains multiple target instances BID10. goal is to extend image-to-image translation towards challenging tasks which can strengthen applicability next level e.g changing pants skirts fashion images customer decide which one is better buy. end propose novel method incorporates instance information multiple target objectsin framework generative adversarial networks GAN hence called instance-aware GAN InstaGAN work use object segmentation masks instance information may good representation instance shapes contains object boundaries ignoring details color. Using information method shows impressive results multi-instance transfiguration tasks shown FIG0.Our main contribution is three-fold three-fold instance-augmented neural architecture context preserving loss sequential mini-batch inference/training technique. First propose neural network architecture translates image corresponding set instance attributes. architecture can translate arbitrary number instance attributes conditioned input is designed permutation-invariant order instances. Second propose context preserv- proposed method InstaGAN. method shows better results multi-instance transfiguration problems.ing loss encourages network focus target instances translation learn identity function outside them. Namely aims preserving background context transforming target instances. Finally propose sequential mini-batch inference/training technique.e translating mini-batches instance attributes sequentially instead entire set once. allows handle large number instance attributes limited GPU memory thus enhances network generalize better images many instances. Furthermore improves translation quality images even instances acts data augmentation training producing multiple intermediate samples. aforementioned contributions are dedicated how to incorporates instance information e.g segmentation masks image-to-image translation. However believe approach is applicable numerous cross-domain generation tasks where set-structured side information is available.To best knowledge are the first report image-to-image translation results multiinstance transfiguration tasks. number recent methods BID27 BID10 show transfiguration results images single instance often clear background. Unlike previous results simple setting focus is on the harmony instances naturally rendered background. hand CycleGAN show results multi-instance cases report limited performance transfiguration tasks. high level significance work is also discovering instance information is effective shape-transforming image-to-image translation which we think would influential related research future. Mask contrast-GAN Attention-GAN Mejjatietal. 2018 use segmentation masks predicted attentions attach background translated cropped instances. do not allow transform shapes instances. contrary method learns how to preserve background optimizing context preserving loss thus facilitating shape transformation. have proposed novel method incorporating set instance attributes image-to-image translation. experiments different datasets have shown successful image-to-image translation challenging tasks multi-instance transfiguration including new tasks e.g translating jeans skirt fashion images. remark ideas utilizing set-structured side information have potential applied cross-domain generations tasks e.g neural machine translation video generation. Investigating new tasks new information could interesting research direction future.,1166,786,380,0.012,1.483,2025/11/05 17:19:09,0.01,1.414,0.4766355140186917,355.037
"Deep neural networks (DNNs) generalize remarkably well without explicit regularization even in the strongly over-parametrized regime  where classical learning theory would instead predict that they would severely overfit.   While many proposals for some kind of implicit regularization have been made to rationalise this success, there is no consensus for the fundamental reason why DNNs do not strongly overfit.   In this paper, we provide a new explanation. By applying a very general probability-complexity bound recently derived from  algorithmic information theory (AIT), we argue that the parameter-function map of many DNNs should be exponentially biased towards simple functions. We then provide clear evidence for this strong simplicity bias in a model DNN for Boolean functions, as well as in much larger fully connected and convolutional networks trained on CIFAR10 and MNIST.
 As the target functions in many real problems are expected to be highly structured, this intrinsic simplicity bias helps explain why deep networks generalize well on real world problems.
 This picture also facilitates a novel PAC-Bayes approach where the prior is taken over the DNN input-output function space, rather than  the more conventional prior over parameter space.   If we assume that the training algorithm samples parameters close to uniformly within the zero-error region then the PAC-Bayes theorem can be used to guarantee good expected generalization for target functions producing high-likelihood training sets.   By exploiting recently discovered connections between DNNs and Gaussian processes to estimate the marginal likelihood,  we produce relatively tight generalization PAC-Bayes error bounds which correlate well with the true error on realistic datasets such as MNIST and CIFAR10 and for architectures including convolutional and fully connected networks. Deep learning is a machine learning paradigm based on very large, expressive and composable models, which most often require similarly large data sets to train. The name comes from the main component in the models: deep neural networks (DNNs) with many layers of representation. These models have been remarkably successful in domains ranging from image recognition and synthesis, to natural language processing, and reinforcement learning (Mnih et al. (2015) ; LeCun et al. (2015) ; BID7 ; BID12 ). There has been work on understanding the expressive power of certain classes of deep networks ), their learning dynamics BID0 ; ), and generalization properties (Kawaguchi et al. (2017) ; BID5 ; BID1 ). However, a full theoretical understanding of many of these properties is still lacking.DNNs are typically overparametrized, with many more parameters than training examples. Classical learning theory suggests that overparamterized models lead to overfitting, and so poorer generalization performance. By contrast, for deep learning there is good evidence that increasing the number of parameters leads to improved generalization (see e.g. BID2 ). For a typical supervised learning scenario, classical learning theory provides bounds on the generalization error (f ) for target function f that typically scale as the complexity of the hypothesis class H. Complexity measures include simply the number of functions in H, the VC dimension, and the Rademacher complexity BID15 ). Since neural networks are highly expressive, typical measures of C(H) will be extremely large, leading to trivial bounds.Many empirical schemes such as dropout BID18 ), weight decay (Krogh & Hertz (1992) ), early stopping (Morgan & Bourlard (1990) ), have been proposed as sources of regularization that effectively lower C(H). However, in an important recent paper BID27 ), it was explicitly demonstrated that these regularization methods are not necessary to obtain good generalization. Moreover, by randomly labelling images in the well known CIFAR10 data set (Krizhevsky & Hinton (2009) ), these authors showed that DNNs are sufficiently expressive to memorize a data set in not much more time than it takes to train on uncorrupted CIFAR10 data. By showing that it is relatively easy to train DNNs to find functions f that do not generalize at all, this work sharpened the question as to why DNNs generalize so well when presented with uncorrupted training data. This study stimulated much recent work, see e.g. (Kawaguchi et al. (2017) ; Arora et al. (2018) ; Morcos et al. (2018) ; BID1 ; Dziugaite & Roy (2017; ; Neyshabur et al. (2017a; ), but there is no consensus as to why DNNs generalize so well.Because DNNs have so many parameters, minimizing the loss function L to find a minimal training set error is a challenging numerical problem. The most popular methods for performing such optimization rely on some version of stochastic gradient descent (SGD). In addition, many authors have also argued that SGD may exploit certain features of the loss-function to find solutions that generalize particularly well BID17 ; BID28 ) However, while SGD is typically superior to other standard minimization methods in terms of optimization performance, there is no consensus in the field on how much of the remarkable generalization performance of DNNs is linked to SGD (Krueger et al. (2017) ). In fact DNNs generalize well when other optimization methods are used (from variants of SGD, like Adam (Kingma & Ba (2014) ), to gradient-free methods )). For example, in recent papers BID23 ; BID29 ; Keskar et al. (2016) simple gradient descent (GD) was shown to lead to differences in generalization with SGD of at most a few percent. Of course in practical applications such small improvements in generalization performance can be important. However, the question we want to address in this paper is the broader one of Why do DNNs generalize at all, given that they are so highly expressive and overparameterized? . While SGD is important for optimization, and may aid generalization, it does not appear to be the fundamental source of generalization in DNNs.Another longstanding family of arguments focuses on the local curvature of a stationary point of the loss function, typically quantified in terms of products of eigenvalues of the local Hessian matrix. Flatter stationary points (often simply called minima) are associated with better generalization performance (Hochreiter & Schmidhuber (1997) ; Hinton & van Camp (1993) ). Part of the intuition is that flatter minima are associated with simpler functions (Hochreiter & Schmidhuber (1997) ; BID23 ), which should generalize better. Recent work (Dinh et al. (2017) ) has pointed out that flat minima can be transformed to sharp minima under suitable re-scaling of parameters, so care must be taken in how flatness is defined. In an important recent paper BID23 ) an attack data set was used to vary the generalization performance of a standard DNN from a few percent error to nearly 100% error. This performance correlates closely with a robust measure of the flatness of the minima (see also BID29 for a similar correlation over a much smaller range, but with evidence that SGD leads to slightly flatter minima than simple GD does). The authors also conjectured that this large difference in local flatness would be reflected in large differences between the volume V good of the basin of attraction for solutions that generalize well and V bad for solutions that generalize badly. If these volumes differ sufficiently, then this may help explain why SGD and other methods such as GD converge to good solutions; these are simply much easier to find than bad ones. Although this line of argument provides a tantalizing suggestion for why DNNs generalize well in spite of being heavily overparameterized, it still begs the fundamental question of Why do solutions vary so much in flatness or associated properties such as basin volume?In this paper we build on recent applications of algorithmic information theory (AIT) (Dingle et al. (2018) ) to suggest that the large observed differences in flatness observed by BID23 ) can be correlated with measures of descriptional complexity. We then apply a connection between Gaussian processes and DNNS to empirically demonstrate for several different standard architectures that the probability of obtaining a function f in DNNs upon a random choice of parameters varies over many orders of magnitude. This bias allows us to apply a classical result from PAC-Bayes theory to help explain why DNNs generalize so well. In this paper, we present an argument that we think offers a first-order explanation of generalization in highly overparameterized DNNs. First, PAC-Bayes shows how priors which are sufficiently biased towards the true distribution can result in generalization in highly expressive models, e.g. even if there are many more parameters than data points. Second, the huge bias towards simple functions in the parameter-function map strongly suggests that neural networks have a similarly biased prior. The number of parameters in a fully expressive DNN does not strongly affect the bias. Third, since real-world problems tend to be far from random, using these same complexity measures, we expect the prior to be biased towards the right class of solutions for real-world datasets and problems. Figure 4: Average probability of finding a function for a variant of SGD, versus average probability of finding a function when using the Gaussian process approximation. This is done for a randomly chosen, but fixed, target Boolean function of Lempel-Ziv complexity 84.0. See Appendix D for details. The Gaussian process parameters are σ w = 10.0, and σ b = 10.0. For advSGD, we have removed functions which only appared once in the whole sample, to avoid finite-size effects. In the captions, ρ refers to the 2-tailed Pearson correlation coefficient, and p to its corresponding p value.To demonstrate the bias in the parameter-function map, we used both direct sampling for a small network and an equivalence with Gaussian processes for larger networks. We also used arguments from AIT to show that functions f that obtain with higher P (f ) are likely to be simple. However, a more complete understanding of this bias is still called for.We also demonstrated how to make this approach quantitative, approximating neural networks as Gaussian processes to calculate PAC-Bayesian bounds on the generalization error.It should be noted that our approach is not yet able to explain the effects that different tricks used in practice have on generalization. However, most of these improvements tend to be of the order of a few percent in the accuracy. The aim of this paper is to explain the bulk of the generalization, which classical learning theory would predict to be poor in this highly overparametrized regime. It is still an open question whether our approach can be extended to explain some of the tricks used in practice, as well as to methods other than neural networks (Belkin et al. (2018) ) that may also have simple parameter-function maps. To stimulate work in improving our bounds, we summarize here the main potential sources of error for our bounds:1. The probability that the training algorithm (like SGD) finds a particular function in the zero-error region can be approximated by the probability that the function obtains upon i.i.d. sampling of parameters.2. Gaussian processes model neural networks with i.i.d.-sampled parameters well even for finite widths.3. Expectation-propagation gives a good approximation of the Gaussian process marginal likelihood.",Deep neural networks DNNs which should generalize remarkably well without explicit regularization even strongly over-parametrized regime where classical learning theory would instead predict would severely overfit. many proposals kind implicit regularization have been made rationalise success is no consensus fundamental reason why DNNs do not strongly overfit. paper provide new explanation. applying general probability-complexity bound recently derived algorithmic information theory AIT argue parameter-function map many DNNs should be exponentially biased towards simple functions. provide clear evidence strong simplicity bias model DNN Boolean functions well much larger fully connected convolutional networks trained CIFAR10 MNIST. target functions many real problems are expected highly structured intrinsic simplicity bias helps explain why deep networks generalize well real world problems. picture also facilitates novel PAC-Bayes approach where the prior is taken DNN input-output function space rather conventional prior parameter space. If we assume training algorithm samples parameters close uniformly within zero-error region PAC-Bayes theorem can be used guarantee good expected generalization target functions producing high-likelihood training sets. exploiting recently discovered connections DNNs Gaussian processes estimate marginal likelihood produce relatively tight generalization PAC-Bayes error bounds which correlate well true error realistic datasets MNIST CIFAR10 architectures including convolutional fully connected networks. Deep learning is a machine learning paradigm based large expressive composable models which most often require similarly large data sets train. name comes main component models:deep neural networks DNNs many layers representation. models have been remarkably successful domains ranging image recognition synthesis natural language processing reinforcement learning Mnihetal. 2015 LeCunetal. 2015 BID7;BID12 has work understanding expressive power certain classes deep networks learning dynamics BID0;generalization properties Kawaguchietal. 2017 BID5;BID1 However full theoretical understanding many properties is still lacking.DNNs are typically overparametrized many parameters training examples. Classical learning theory suggests overparamterized models lead overfitting poorer generalization performance. contrast deep learning is good evidence increasing number parameters leads improved generalization see e.g BID2 typical supervised learning scenario which classical learning theory provides bounds generalization error f target functionf typically scale complexity hypothesis classH. Complexity measures include simply number functions H VC dimension Rademacher complexity BID15 Since neural networks are highly expressive typical measures C H will be extremely large leading trivial bounds.Many empirical schemes dropout BID18 weight decay Krogh Hertz 1992 early stopping Morgan Bourlard 1990 have proposed sources regularization effectively lowerC H However important recent paper BID27 was explicitly demonstrated regularization methods are not necessary obtain good generalization. Moreover randomly labelling images well known CIFAR10 data set Krizhevsky Hinton 2009 authors showed DNNs are sufficiently expressive memorize data set much time takes train uncorrupted CIFAR10 data. showing is relatively easy train DNNs find functionsf do not generalize work sharpened question why DNNs generalize well when presented uncorrupted training data. study stimulated much recent work seee.g Kawaguchietal. 2017 Aroraetal. 2018 Morcosetal. 2018 BID1;Dziugaite Roy 2017;Neyshaburetal. 2017a;isno consensus why DNNs generalize well.Because DNNs have so many parameters minimizing loss functionL find minimal training set error is a challenging numerical problem. popular methods performing optimization rely version stochastic gradient descent SGD addition many authors have also argued SGD may exploit certain features loss-function find solutions do not generalize particularly well BID17;BID28 However SGD is typically superior standard minimization methods terms optimization performance is no consensus field how much remarkable generalization performance Why do DNNs is linked SGD Kruegeretal. 2017 fact DNNs generalize well when other optimization methods are used variants SGD like Adam Kingma Ba 2014 gradient-free methods example recent papers BID23;BID29;Keskaretal. 2016 simple gradient descent GD was shown lead differences generalization SGD percent. course practical applications small improvements generalization performance can be important. However question want address paper is the broader one Why do DNNs generalize given are so highly expressive overparameterized? SGD is important optimization may aid generalization does not appear fundamental source generalization DNNs.Another longstanding family arguments focuses local curvature stationary point loss function typically quantified terms products eigenvalues local Hessian matrix. Flatter stationary points often simply called minima are associated better generalization performance Hochreiter Schmidhuber 1997 Hinton van Camp 1993 Part intuition is that flatter minima are associated simpler functions Hochreiter Schmidhuber 1997 BID23 which should generalize better. Recent work Dinhetal. 2017 has pointed flat minima can be transformed sharp minima suitable re-scaling parameters care must taken how flatness is defined. important recent paper BID23 attack data set was used vary generalization performance standard DNN percent error nearly 100% error. performance correlates closely robust measure flatness minima see also BID29 similar correlation much smaller range evidence SGD leads slightly flatter minima simpleGD does). The authors also conjectured large difference local flatness would reflected large differences volume V good basin attraction solutions do not generalize well V bad solutions do not generalize badly. If these volumes differ sufficiently may help explain why SGD methods GD converge good solutions;are simply much easier find bad ones. Although line argument provides tantalizing suggestion why DNNs generalize well spite heavily overparameterized still begs fundamental question Why do solutions vary much how flatness associated properties basin volume? paper build recent applications algorithmic information theory AIT Dingleetal. 2018 suggest large observed differences how flatness observed BID23 can be correlated measures descriptional complexity. apply connection Gaussian processes DNNS empirically demonstrate several different standard architectures probability obtaining functionf DNNs upon random choice parameters varies many orders magnitude. bias allowsus apply classical result PAC-Bayes theory help explain why DNNs generalize well. paper present argument think offers first-order explanation generalization highly overparameterized DNNs. First PAC-Bayes shows how priors which are sufficiently biased towards true distribution can result generalization highly expressive models e.g even if there are many parameters data points. Second huge bias towards simple functions parameter-function map strongly suggests neural networks have a similarly biased prior. number parameters fully expressive DNN does not strongly affect bias. Third since real-world problems tend far random using complexity measures expect prior biased towards right class Why do solutions real-world datasets problems. Figure4:Average probability finding function variant SGD versus average probability finding function when using Gaussian process approximation. is done randomly chosen fixed target Boolean function Lempel-Ziv complexity 84.0 See Appendix details. Gaussian process parameters areσw 10.0 σb 10.0 advSGD have removed functions which only appared whole sample avoid finite-size effects. captions ρ refers 2-tailed Pearson correlation coefficient p corresponding p value.To demonstrate bias parameter-function map used direct sampling small network equivalence Gaussian processes larger networks. also used arguments AIT show functionsf obtain higherP f are likely simple. However complete understanding bias is still called for.We also demonstrated how to make approach quantitative approximating neural networks Gaussian processes calculate PAC-Bayesian bounds generalization error.It should be noted approach is not yet able explain effects different tricks used practice have on generalization. However improvements tend order percent accuracy. aim paper is to explain bulk generalization which classical learning theory would predict poor highly overparametrized regime. is still open question whether approach can be extended explain tricks used practice well methods neural networks Belkinetal. 2018 may also have simple parameter-function maps. stimulate work improving bounds summarize main potential sources error bounds:1 probability training algorithm like SGD finds particular function zero-error region can be approximated probability function obtains upon.i.d sampling parameters.2 Gaussian processes model neural networks.i.d.-sampled parameters well even finite widths.3 Expectation-propagation gives good approximation Gaussian process marginal likelihood.,2339,1630,709,0.03,1.435,2025/11/05 17:19:09,0.01,1.524,0.3271028037383177,770.501
"We establish a theoretical link between evolutionary algorithms and variational parameter optimization of probabilistic generative models with binary hidden variables.
 While the novel approach is independent of the actual generative model, here we use two such models to investigate its applicability and scalability: a noisy-OR Bayes Net (as a standard example of binary data) and Binary Sparse Coding (as a model for continuous data).

 Learning of probabilistic generative models is first formulated as approximate maximum likelihood optimization using variational expectation maximization (EM).
 We choose truncated posteriors as variational distributions in which discrete latent states serve as variational parameters. In the variational E-step,
 the latent states are then  
optimized according to a tractable free-energy objective . Given a data point, we can show that evolutionary algorithms can be used for the variational optimization loop by (A)~considering the bit-vectors of the latent states as genomes of individuals, and by (B)~defining the fitness of the
 individuals as the (log) joint probabilities given by the used generative model.

 As a proof of concept, we apply the novel evolutionary EM approach to the optimization of the parameters of noisy-OR Bayes nets and binary sparse coding on artificial and real data (natural image patches). Using point mutations and single-point cross-over for the evolutionary algorithm, we find that scalable variational EM algorithms are obtained which efficiently improve the data likelihood. In general we believe that, with the link established here, standard as well as recent results in the field of evolutionary optimization can be leveraged to address the difficult problem of parameter optimization in generative models. Evolutionary algorithms (EA) have been introduced (e.g. BID3 BID23 as a technique for function optimization using methods inspired by biological evolutionary processes such as mutation, recombination, and selection. As such EAs are of interest as tools to solve Machine Learning problems, and they have been frequently applied to a number of tasks such as clustering BID21 BID9 , reinforcement learning BID25 , and hierarchical unsupervised BID16 or deep supervised learning (e.g., BID32 BID32 BID33 BID22 for recent examples). In some of these tasks EAs have been investigated as alternatives to standard procedures BID9 ), but most frequently EAs are used to solve specific sub-problems. For example, for classification with Deep Neural Networks (DNNs LeCun et al., 2015; BID27 , EAs are frequently applied to solve the sub-problem of selecting the best DNN architectures for a given task (e.g. BID32 BID33 or more generally to find the best hyper-parameters of a DNN (e.g. BID12 BID22 .Inspired by these previous contributions, we here ask if EAs and learning algorithms can be linked more tightly. To address this question we make use of the theoretical framework of probabilistic generative models and expectation maximization (EM Dempster et al., 1977) approaches for parameter optimization. The probabilistic approach in combination with EM is appealing as it establishes a very general unifying framework able to encompass diverse algorithms from clustering and dimensionality reduction BID24 BID34 over feature learning and sparse coding BID18 to deep learning approaches BID20 . However, for most generative data models, EM is computationally intractable and requires approximations. Variational EM is a very prominent such approximation and is continuously further developed to become more efficient, more accurate and more autonomously applicable. Variational EM seeks to approximately solve optimization problems of functions with potentially many local optima in potentially very high dimensional spaces. The key observation exploited in this study is that a variational EM algorithm can be formulated such that latent states serve as variational parameters. If the latent states are then considered as genomes of individuals, EAs emerge as a very natural choice for optimization in the variational loop of EM. The training of generative models is a very intensively studied branch of Machine Learning. If EM is applied for training, most non-elementary models require approximations. For this reason, sophisticated and mathematically grounded approaches such as sampling or variational EM have been developed in order to derive sufficiently precise and efficient learning algorithms.Evolutionary algorithms (EAs) have also been applied in conjunction with EM. BID21 , for instance, have used EAs for clustering with Gaussian mixture models (GMMs). However, the GMM parameters are updated by their approach relatively conventionally using EM, while EAs are used to select the best GMM models for the clustering problem (using a min. description length criterion). Such a use of EAs is similar to DNN optimization where EAs optimize DNN hyperparameters in an outer optimization loop BID32 BID12 BID22 Suganuma et al., 2017, etc) , while the DNNs themselves are optimized using standard error-minimization algorithms. Still other approaches have used EAs to directly optimize, e.g., a clustering objective. But in these cases EAs replace EM approaches for optimization (compare Hruschka et al., 2009) . In contrast to all such previous applications, we have here shown that EAs and EM can be combined directly and intimately: Alg. 1 defines EAs as an integral part of EM, and as such EAs address the key optimization problem arising in the training of generative models.We see the main contribution of our study in the establishment of this close theoretical link between EAs and EM. This novel link will make it possible to leverage an extensive body of knowledge and experience from the community of evolutionary approaches for learning algorithms. Our numerical experiments are a proof of concept which shows that EAs are indeed able to train generative models with large hidden spaces and local optima. For this purpose we used very basic EAs with elementary selection, mutation, cross-over operators.EAs more specialized to the specific optimization problems arising in the training of generative models have great potentials in future improvements of accuracy and scalability, we believe. In our experiments, we have only just started to exploit the abilities of EAs for learning algorithms. Still, our results represent, to the knowledge of the authors, the first examples of noisy-OR or sparse coding models trained with EAs (although both models have been studied very extensively before). Most importantly, we have pointed out a novel mathematically grounded way how EAs can be used for generative models with binary latents in general. The approach here established is, moreover, not only very generically formulated using the models' joint probabilities but it is also very straightforward to apply.","establish theoretical link evolutionary algorithms variational parameter optimization probabilistic generative models binary hidden variables. novel approach is independent actual generative model use two models investigate applicability scalability:noisy-OR Bayes Net standard example binary data Binary Sparse Coding model continuous data Learning probabilistic generative models is first formulated approximate maximum likelihood optimization using variational expectation maximization EM choose truncated posteriors variational distributions which discrete latent states serve variational parameters. variational E-step latent states are then optimized according tractable free-energy objective. Given data point can show evolutionary algorithms can be used variational optimization loop ~considering bit-vectors latent states genomes individuals B ~defining fitness individuals log joint probabilities given used generative model. proof concept apply novel evolutionary EM approach optimization parameters noisy-OR Bayes nets binary sparse coding artificial real data natural image patches Using point mutations single-point cross-over evolutionary algorithm find scalable variational EM algorithms are obtained which efficiently improve data likelihood. general believe link established standard well recent results field evolutionary optimization can be leveraged address difficult problem parameter optimization generative models. Evolutionary algorithms EA have been introduced e.g BID3 BID23 technique function optimization using methods inspired biological evolutionary processes mutation recombination selection. EAs are of interest tools solve Machine Learning problems have frequently applied number tasks clustering BID21 BID9 reinforcement learning BID25 hierarchical unsupervised BID16 deep supervised learning e.g BID32 BID32 BID33 BID22 recent examples tasks EAs have been investigated alternatives standard procedures BID9 frequently EAs are used solve specific sub-problems example classification Deep Neural Networks DNNs LeCunetal. 2015;BID27 EAs are frequently applied solve sub-problem selecting best DNN architectures given task e.g BID32 BID33 generally find best hyper-parameters DNN e.g BID12 BID22.Inspired previous contributions ask if EAs learning algorithms can be linked tightly. address question make use theoretical framework probabilistic generative models expectation maximization EM Dempsteretal. 1977 approaches parameter optimization. probabilistic approach combination EM is appealing establishes general unifying framework able encompass diverse algorithms clustering dimensionality reduction BID24 BID34 feature learning sparse coding BID18 deep learning approaches BID20. However generative data models EM is computationally intractable requires approximations. VariationalEM is a very prominent approximation is continuously developed become efficient accurate autonomously applicable. Variational EM seeks approximately solve optimization problems functions potentially many local optima potentially high dimensional spaces. key observation exploited study is that a variational EM algorithm can be formulated latent states serve variational parameters. If the latent states are then considered genomes individuals EAs emerge natural choice optimization variational loop EM. training generative models is a very intensively studied branch Machine Learning. IfEM is applied training non-elementary models require approximations. reason sophisticated mathematically grounded approaches sampling variationalEM have been developed order derive sufficiently precise efficient learning algorithms.Evolutionary algorithms EAs have also applied conjunction EM. BID21 instance have used EAs clustering Gaussian mixture models GMMs However GMM parameters are updated approach relatively conventionally using EM EAs are used select best GMM models clustering problem using min. description length criterion use EAs is similar DNN optimization where EAs optimize DNN hyperparameters outer optimization loop BID32 BID12 BID22 Suganumaet al. 2017 etc DNNs are optimized using standard error-minimization algorithms. Still approaches have used EAs directly optimize e.g clustering objective. cases EAs replaceEM approaches optimization compare Hruschkaetal. 2009 contrast previous applications have here shown EAs EM can be combined directly intimately:Alg. 1 defines EAs integral part EM EAs address key optimization problem arising training generative models.We see main contribution study establishment close theoretical link EAs EM. novel link will make possible leverage extensive body knowledge experience community evolutionary approaches learning algorithms. numerical experiments are a proof concept which shows EAs are indeed able train generative models large hidden spaces local optima. purpose used basic EAs elementary selection mutation cross-over operators.EAs specialized specific optimization problems arising training generative models have great potentials future improvements accuracy scalability believe. experiments have only started exploit abilities EAs learning algorithms. Still results represent knowledge authors first examples noisy-OR sparse coding models trained EAs although models have been studied extensively importantly have pointed novel mathematically grounded way how EAs can be used generative models binary latents general. approach established is,moreover generically formulated using models' joint probabilities is also straightforward apply.",1326,907,419,0.014,1.462,2025/11/05 17:19:09,0.01,1.469,0.4112149532710277,422.032
"While deep neural networks have achieved groundbreaking prediction results in many tasks, there is a class of data where existing architectures are not optimal -- sequences of probability distributions. Performing forward prediction on sequences of distributions has many important applications. However, there are two main challenges in designing a network model for this task. First, neural networks are unable to encode distributions compactly as each node encodes just a real value. A recent work of Distribution Regression Network (DRN) solved this problem with a novel network that encodes an entire distribution in a single node, resulting in improved accuracies while using much fewer parameters than neural networks. However, despite its compact distribution representation, DRN does not address the second challenge, which is the need to model time dependencies in a sequence of distributions. In this paper, we propose our Recurrent Distribution Regression Network (RDRN) which adopts a recurrent architecture for DRN. The combination of compact distribution representation and shared weights architecture across time steps makes RDRN suitable for modeling the time dependencies in a distribution sequence. Compared to neural networks and DRN, RDRN achieves the best prediction performance while keeping the network compact. Deep neural networks have achieved state-of-the-art results in many tasks by designing the network architecture according to the data type. For instance, the convolutional neural network (CNN) uses local filters to capture the features in an image and max pooling to reduce the image representation size. By using a series of convolution and max pooling layers, CNN extracts the semantic meaning of the image. The recurrent architecture of recurrent neural networks (RNN) when unrolled, presents a shared weight structure which is designed to model time dependencies in a data sequence. However, among the major network architectures, the multilayer perceptron, convolutional neural network and recurrent neural network, there is no architecture suitable for representing sequences of probability distributions. Specifically, we address the task of forward prediction on distribution sequences.There are two main challenges in designing a network for sequences of probability distributions. First, conventional neural networks are unable to represent distributions compactly. Since each node encodes only a real value, a distribution has to be decomposed to smaller parts that are represented by separate nodes. When the distribution has been decomposed into separate nodes, the notion of distribution is no longer captured explicitly. Similarly, for image data, the fully-connected multilayer perceptron (MLP), unlike convolutional neural networks, fails to capture the notion of an image. A recently proposed network, Distribution Regression Network (DRN) BID8 , has solved this problem. DRN uses a novel representation of encoding an entire distribution in a single node, allowing DRN to use more compact models while achieving superior performance for distribution regression. It has been shown that DRN can achieve better accuracies with 500 times fewer parameters compared to MLP. However, despite the strengths of DRN, it is a feedforward network and hence it does not address a second problem, which is the need to model time dependencies in a distribution sequence.We address these two challenges and propose a recurrent extension of DRN, named the Recurrent Distribution Regression Network (RDRN). In the hidden states of RDRN, each node represents a distribution, thus containing much richer information while using fewer weights compared to the real-valued hidden states in RNN. This compact representation consequently results in better generalization performance. Compared to DRN, the shared weights in RDRN captures time dependencies better and results in better prediction performance. By having both compact distribution representations and modeling of time dependencies, RDRN is able to achieve superior prediction performance compared to the other methods. Neural network models work well by designing the architecture according to the data type. However, among the conventional neural network architectures, there is none that is designed for time-varying probability distributions. There are two key challenges in learning from distribution sequences. First, we require a suitable representation for probability distributions. Conventional neural networks, however, do not have suitable representations for distributions. As each node encodes only a real value, the distribution has to be split into smaller parts which are then represented by independent nodes. Hence, the neural network is agnostic to the distribution nature of the input data. A recently proposed Distribution Regression Network (DRN) addresses this issue. DRN has a novel network representation where each node encodes a distribution, showing improved accuracies compared to neural networks. However, a second challenge remains, which is to model the time dependencies in the distribution sequence. Both the recurrent neural network (RNN) and the Distribution Regression Network address only either one of the challenges. In this work, we propose our Recurrent Distribution Regression Network (RDRN) which extends DRN with a recurrent architecture. By having an explicit distribution representation in each node and shared weights across time steps, RDRN performs forward prediction on distribution sequences most effectively, achieving better prediction accuracies than RNN, DRN and other regression methods.",deep neural networks have achieved groundbreaking prediction results many tasks is a class data where existing architectures are not optimal sequences probability distributions. Performing forward prediction sequences distributions has many important applications. However are two main challenges designing network model task. First neural networks are unable encode distributions compactly node encodes real value. recent work Distribution Regression Network DRN solved problem novel network encodes entire distribution single node resulting improved accuracies using much fewer parameters neural networks. However despite compact distribution representation DRN does not address second challenge which is the need model time dependencies sequence distributions. paper propose Recurrent Distribution Regression Network RDRN which adopts recurrent architecture DRN. combination compact distribution representation shared weights architecture across time steps makes RDRN suitable modeling time dependencies distribution sequence. Compared neural networks DRN RDRN achieves best prediction performance keeping network compact. Deep neural networks have achieved state-of-the-art results many tasks designing network architecture according data type. instance convolutional neural network CNN uses local filters capture features image max pooling reduce image representation size. using series convolution max pooling layers CNN extracts semantic meaning image. recurrent architecture recurrent neural networks RNN when unrolled presents shared weight structure which is designed model time dependencies data sequence. However among major network architectures multilayer perceptron convolutional neural network recurrent neural network is no architecture suitable representing sequences probability distributions. Specifically address task forward prediction distribution sequences.There are two main challenges designing network sequences probability distributions. First conventional neural networks are unable represent distributions compactly. Since node encodes real value distribution has to be has been decomposed smaller parts are represented separate nodes. When the distribution has to be has been decomposed separate nodes notion distribution is no longer captured explicitly. Similarly image data fully-connected multilayer perceptron MLP unlike convolutional neural networks fails capture notion image. recently proposed network Distribution Regression Network DRN BID8 has solved problem. DRN uses novel representation encoding entire distribution single node allowing DRN use compact models achieving superior performance distribution regression. has been shown DRN can achieve better accuracies 500 times fewer parameters compared MLP. However despite strengths DRN is a feedforward network hence does not address second problem which is the need model time dependencies distribution sequence.We address two challenges propose recurrent extension DRN named Recurrent Distribution Regression Network RDRN hidden states RDRN node represents distribution thus containing much richer information using fewer weights compared real-valued hidden states RNN. compact representation consequently results better generalization performance. Compared DRN shared weights RDRN captures time dependencies better results better prediction performance. compact distribution representations modeling time dependencies RDRN is able achieve superior prediction performance compared methods. Neural network models work well designing architecture according data type. However among conventional neural network architectures is none is designed time-varying probability distributions. are two key challenges learning distribution sequences. First require suitable representation probability distributions. Conventional neural networks however do not have suitable representations distributions. node encodes real value distribution has to be split smaller parts which are then represented independent nodes. Hence neural network is agnostic distribution nature input data. recently proposed Distribution Regression Network DRN addresses issue. DRN has a novel network representation where each node encodes distribution showing improved accuracies compared neural networks. However second challenge remains which is to model time dependencies distribution sequence. recurrent neural network RNN Distribution Regression Network address either one challenges. work propose Recurrent Distribution Regression Network RDRN which extends DRN recurrent architecture. explicit distribution representation node shared weights across time steps RDRN performs forward prediction distribution sequences effectively achieving better prediction accuracies RNN DRN regression methods.,997,709,288,0.01,1.406,2025/11/05 17:19:09,0.0,1.694,0.2367601246105914,321.898
"We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods' features, we enable (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of computationally intensive matrix operation (such as inversion) or depending on knowing the graph structure upfront. In this way, we address several key challenges of spectral-based graph neural networks simultaneously, and make our model readily applicable to inductive as well as transductive problems. Our GAT models have achieved or matched state-of-the-art results across four established transductive and inductive graph benchmarks: the Cora, Citeseer and Pubmed citation network datasets, as well as a protein-protein interaction dataset (wherein test graphs remain unseen during training). Convolutional Neural Networks (CNNs) have been successfully applied to tackle problems such as image classification BID17 , semantic segmentation BID21 or machine translation BID13 , where the underlying data representation has a grid-like structure. These architectures efficiently reuse their local filters, with learnable parameters, by applying them to all the input positions.However, many interesting tasks involve data that can not be represented in a grid-like structure and that instead lies in an irregular domain. This is the case of 3D meshes, social networks, telecommunication networks, biological networks or brain connectomes. Such data can usually be represented in the form of graphs.There have been several attempts in the literature to extend neural networks to deal with arbitrarily structured graphs. Early work used recursive neural networks to process data represented in graph domains as directed acyclic graphs BID12 BID35 . Graph Neural Networks (GNNs) were introduced in BID15 and BID33 as a generalization of recursive neural networks that can directly deal with a more general class of graphs, e.g. cyclic, directed and undirected graphs. GNNs consist of an iterative process, which propagates the node states until equilibrium; followed by a neural network, which produces an output for each node based on its state. This idea was adopted and improved by , which propose to use gated recurrent units BID6 in the propagation step.Nevertheless, there is an increasing interest in generalizing convolutions to the graph domain. Advances in this direction are often categorized as spectral approaches and non-spectral approaches.On one hand, spectral approaches work with a spectral representation of the graphs and have been successfully applied in the context of node classification. In BID4 , the convolution operation is defined in the Fourier domain by computing the eigendecomposition of the graph Laplacian, resulting in potentially intense computations and non-spatially localized filters. These issues were addressed by subsequent works. BID18 introduced a parameterization of the spectral filters with smooth coefficients in order to make them spatially localized. Later, BID8 proposed to approximate the filters by means of a Chebyshev expansion of the graph Laplacian, removing the need to compute the eigenvectors of the Laplacian and yielding spatially localized filters. Finally, BID23 simplified the previous method by restricting the filters to operate in a 1-step neighborhood around each node. However, in all of the aforementioned spectral approaches, the learned filters depend on the Laplacian eigenbasis, which depends on the graph structure. Thus, a model trained on a specific structure can not be directly applied to a graph with a different structure.On the other hand, we have non-spectral approaches BID11 BID1 BID16 , which define convolutions directly on the graph, operating on groups of spatially close neighbors. One of the challenges of these approaches is to define an operator which works with different sized neighborhoods and maintains the weight sharing property of CNNs. In some cases, this requires learning a specific weight matrix for each node degree BID11 , using the powers of a transition matrix to define the neighborhood while learning weights for each input channel and neighborhood degree BID1 , or extracting and normalizing neighborhoods containing a fixed number of nodes BID29 . BID28 presented mixture model CNNs (MoNet), a spatial approach which provides a unified generalization of CNN architectures to graphs. More recently, BID16 introduced GraphSAGE, a method for computing node representations in an inductive manner. This technique operates by sampling a fixed-size neighborhood of each node, and then performing a specific aggregator over it (such as the mean over all the sampled neighbors' feature vectors, or the result of feeding them through a recurrent neural network). This approach has yielded impressive performance across several large-scale inductive benchmarks.Attention mechanisms have become almost a de facto standard in many sequence-based tasks BID2 BID13 . One of the benefits of attention mechanisms is that they allow for dealing with variable sized inputs, focusing on the most relevant parts of the input to make decisions. When an attention mechanism is used to compute a representation of a single sequence, it is commonly referred to as self-attention or intra-attention. Together with Recurrent Neural Networks (RNNs) or convolutions, self-attention has proven to be useful for tasks such as machine reading BID5 and learning sentence representations BID25 . However, BID38 showed that not only self-attention can improve a method based on RNNs or convolutions, but also that it is sufficient for constructing a powerful model obtaining state-of-the-art performance on the machine translation task.Inspired by this recent work, we introduce an attention-based architecture to perform node classification of graph-structured data. The idea is to compute the hidden representations of each node in the graph, by attending over its neighbors, following a self-attention strategy. The attention architecture has several interesting properties: (1) the operation is efficient, since it is parallelizable across nodeneighbor pairs; (2) it can be applied to graph nodes having different degrees by specifying arbitrary weights to the neighbors; and (3) the model is directly applicable to inductive learning problems, including tasks where the model has to generalize to completely unseen graphs. We validate the proposed approach on four challenging benchmarks: Cora, Citeseer and Pubmed citation networks as well as an inductive protein-protein interaction dataset, achieving or matching state-of-the-art results that highlight the potential of attention-based models when dealing with arbitrarily structured graphs.It is worth noting that, as BID23 and BID1 , our work can also be reformulated as a particular instance of MoNet BID28 . Moreover, our approach of sharing a neural network computation across edges is reminiscent of the formulation of relational networks BID32 and VAIN BID20 , wherein relations between objects or agents are aggregated pair-wise, by employing a shared mechanism. Similarly, our proposed attention model can be connected to the works by BID10 and BID9 , which use a neighborhood attention operation to compute attention coefficients between different objects in an environment. Other related approaches include locally linear embedding (LLE) BID31 and memory networks BID40 . LLE selects a fixed number of neighbors around each data point, and learns a weight coefficient for each neighbor to reconstruct each point as a weighted sum of its neighbors. A second optimization step extracts the point's feature embedding. Memory networks also share some connections with our work, in particular, if we interpret the neighborhood of a node as the memory, which is used to compute the node features by attending over its values, and then is updated by storing the new features in the same position. We have presented graph attention networks (GATs), novel convolution-style neural networks that operate on graph-structured data, leveraging masked self-attentional layers. The graph attentional layer utilized throughout these networks is computationally efficient (does not require computationally intensive matrix operations, and is parallelizable across all nodes in the graph), allows for (implicitly) assigning different importances to different nodes within a neighborhood while dealing with different sized neighborhoods, and does not depend on knowing the entire graph structure upfrontthus addressing many of the theoretical issues with previous spectral-based approaches. Our models leveraging attention have successfully achieved or matched state-of-the-art performance across four well-established node classification benchmarks, both transductive and inductive (especially, with completely unseen graphs used for testing).There are several potential improvements and extensions to graph attention networks that could be addressed as future work, such as overcoming the practical problems described in subsection 2.2 to be able to handle larger batch sizes. A particularly interesting research direction would be taking advantage of the attention mechanism to perform a thorough analysis on the model interpretability. Moreover, extending the method to perform graph classification instead of node classification would also be relevant from the application perspective. Finally, extending the model to incorporate edge features (possibly indicating relationship among nodes) would allow us to tackle a larger variety of problems.",present graph attention networks GATs novel neural network architectures operate graph-structured data leveraging masked self-attentional layers address shortcomings prior methods based graph convolutions approximations. stacking layers which nodes are able attend neighborhoods' features enable implicitly specifying different weights different nodes neighborhood without requiring kind computationally intensive matrix operation inversion depending knowing graph structure upfront. way address several key challenges spectral-based graph neural networks simultaneously make model readily applicable inductive well transductive problems. GAT models have achieved matched state-of-the-art results across four established transductive inductive graph benchmarks:Cora Citeseer Pubmed citation network datasets well protein-protein interaction dataset wherein test graphs remain unseen training Convolutional Neural Networks CNNs have been successfully applied tackle problems image classification BID17 semantic segmentation BID21 machine translation BID13 where the underlying data representation has a grid-like structure. architectures efficiently reuse local filters learnable parameters applying input positions.However many interesting tasks involve data can not be represented grid-like structure instead lies irregular domain. is the case 3D meshes social networks telecommunication networks biological networks brain connectomes. data can usually represented form graphs.There have been several attempts literature extend neural networks deal arbitrarily structured graphs. Early work used recursive neural networks process data represented graph domains directed acyclic graphs BID12 BID35. Graph Neural Networks GNNs were introduced BID15 BID33 generalization recursive neural networks can directly deal general class graphs e.g cyclic directed undirected graphs. GNNs consist iterative process which propagates node states equilibrium;followed neural network which produces output node based state. idea was adopted improved which propose use gated recurrent units BID6 propagation step.Nevertheless is an increasing interest generalizing convolutions graph domain. Advances direction are often categorized spectral approaches non-spectral approaches.On one hand spectral approaches work spectral representation graphs have been successfully applied context node classification. BID4 convolution operation is defined Fourier domain computing eigendecomposition graph Laplacian resulting potentially intense computations non-spatially localized filters. issues were addressed subsequent works. BID18 introduced parameterization spectral filters smooth coefficients order make spatially localized. Later BID8 proposed approximate filters means Chebyshev expansion graph Laplacian removing need compute eigenvectors Laplacian yielding spatially localized filters. Finally BID23 simplified previous method restricting filters operate 1-step neighborhood around node. However aforementioned spectral approaches learned filters depend Laplacian eigenbasis which depends graph structure. Thus model trained specific structure can not be directly applied graph different structure.On hand have non-spectral approaches BID11 BID1 BID16 which define convolutions directly graph operating groups spatially close neighbors. One challenges approaches is to define operator which works different sized neighborhoods maintains weight sharing property CNNs. cases requires learning specific weight matrix node degree BID11 using powers transition matrix define neighborhood learning weights input channel neighborhood degree BID1 extracting normalizing neighborhoods containing fixed number nodes BID29. BID28 presented mixture model CNNs MoNet spatial approach which provides unified generalization CNN architectures graphs. recently BID16 introduced GraphSAGE method computing node representations inductive manner. technique operates sampling fixed-size neighborhood node performing specific aggregator mean sampled neighbors' feature vectors result feeding recurrent neural network approach has yielded impressive performance across several large-scale inductive benchmarks.Attention mechanisms have become almost de facto standard many sequence-based tasks BID2 BID13. One benefits attention mechanisms is that they allow dealing variable sized inputs focusing relevant parts input make decisions. When an attention mechanism is used compute representation single sequence is commonly referred self-attention intra-attention Together Recurrent Neural Networks RNNs convolutions self-attention has proven useful tasks machine reading BID5 learning sentence representations BID25. However BID38 showed self-attention can improve method based RNNs convolutions also is sufficient constructing powerful model obtaining state-of-the-art performance machine translation task.Inspired recent work introduce attention-based architecture perform node classification graph-structured data. idea is to compute hidden representations node graph attending neighbors following self-attention strategy. attention architecture has several interesting properties:1 operation is efficient since is parallelizable across nodeneighbor pairs;2 can be applied graph nodes different degrees specifying arbitrary weights neighbors;3 model is directly applicable inductive learning problems including tasks where the model has to generalize completely unseen graphs. validate proposed approach four challenging benchmarks:Cora Citeseer Pubmed citation networks well inductive protein-protein interaction dataset achieving matching state-of-the-art results highlight potential attention-based models when dealing arbitrarily structured graphs.It is worth noting BID23 BID1 work can also reformulated particular instance MoNet BID28. Moreover approach sharing neural network computation across edges is reminiscent formulation relational networks BID32 VAIN BID20 wherein relations objects agents are aggregated pair-wise employing shared mechanism. Similarly proposed attention model can be connected works BID10 BID9 which use neighborhood attention operation compute attention coefficients different objects environment. related approaches include locally linear embedding LLE BID31 memory networks BID40. LLE selects fixed number neighbors around data point learns weight coefficient neighbor reconstruct point weighted sum neighbors. second optimization step extracts point's feature embedding. Memory networks also share connections work particular if we interpret neighborhood node memory which is used compute node features attending values is updated storing new features position. have presented graph attention networks GATs novel convolution-style neural networks operate graph-structured data leveraging masked self-attentional layers. graph attentional layer utilized throughout networks is computationally efficient does not require computationally intensive matrix operations is parallelizable across nodes graph allows implicitly assigning different importances different nodes within neighborhood dealing different sized neighborhoods does not depend knowing entire graph structure upfrontthus addressing many theoretical issues previous spectral-based approaches. models leveraging attention have successfully achieved matched state-of-the-art performance across four well-established node classification benchmarks transductive inductive especially completely unseen graphs used testing.There are several potential improvements extensions graph attention networks could addressed future work overcoming practical problems described subsection 2.2 able handle larger batch sizes. particularly interesting research direction would taking advantage attention mechanism perform thorough analysis model interpretability. Moreover extending method perform graph classification instead node classification would also relevant application perspective. Finally extending model incorporate edge features possibly indicating relationship among nodes would allowus tackle larger variety problems.,1783,1219,564,0.019,1.463,2025/11/05 17:19:09,0.01,1.387,0.4143302180685358,548.04
"While bigger and deeper neural network architectures continue to advance the state-of-the-art for many computer vision tasks, real-world adoption of these networks is impeded by hardware and speed constraints. Conventional model compression methods attempt to address this problem by modifying the architecture manually or using pre-defined heuristics. Since the space of all reduced architectures is very large, modifying the architecture of a deep neural network in this way is a difficult task. In this paper, we tackle this issue by introducing a principled method for learning reduced network architectures in a data-driven way using reinforcement learning. Our approach takes a larger 'teacher' network as input and outputs a compressed 'student' network derived from the 'teacher' network. In the first stage of our method, a recurrent policy network aggressively removes layers from the large 'teacher' model. In the second stage, another  recurrent policy network carefully reduces the size of each remaining layer. The resulting network is then evaluated to obtain a reward -- a score based on the accuracy and compression of the network. Our approach uses this reward signal with policy gradients to train the policies to find a locally optimal student network. Our experiments show that we can achieve compression rates of more than 10x for models such as ResNet-34 while maintaining similar performance to the input 'teacher' network. We also present a valuable transfer learning result which shows that policies which are pre-trained on smaller 'teacher' networks can be used to rapidly speed up training on larger 'teacher' networks. While carefully hand-designed deep convolutional networks continue to increase in size and in performance, they also require significant power, memory and computational resources, often to the point of prohibiting their deployment on smaller devices. As a result, researchers have developed model compression techniques based on Knowledge Distillation to compress a large (teacher) network to a smaller (student) network using various training techniques (e.g., soft output matching, hint layer matching, uncertainty modeling). Unfortunately, state-of-the-art knowledge distillation methods share a common feature: they require carefully hand-designed architectures for the student model. Hand-designing networks is a tedious sequential process, often loosely guided by a sequence of trial-and-error based decisions to identify a smaller network architecture. This process makes it very difficult to know if the resulting network is optimal. Clearly, there is a need to develop more principled methods of identifying optimal student architectures. Towards a more principled approach to network architecture compression, we present a reinforcement learning approach to identify a compressed high-performance architecture (student) given knowledge distilled from a larger high-performing model (teacher). We make a key conceptual assumption that formulates the sequential process of converting a teacher network to a student network as a Markov Decision Process (MDP). Under this model, a state s represents the network architecture. Clearly, the domain of the state S is very large since it contains every possible reduced architecture of the teacher network. A deterministic transition in this state space, T (s |s, a), is determined by selecting the action a, e.g., removing a convolutional filter or reducing the size of a fully connected layer. Each action will transform one architecture s to another architecture s . Under the MDP, the strategy for selecting an action given a certain state is represented by the policy π(a|s), which stochastically maps a state to an action. The process of reinforcement learning is used to learn an optimal policy based on a reward function r(s) defined over the state space. In our work, we define the reward function based on the accuracy and the compression rate of the specified architecture s.A straightforward application of reinforcement learning to this problem can be very slow depending on the definition of the action space. For example, an action could be defined as removing a single filter from every layer of a convolutional neural network. Since the search space is exponential in the size of the action space and sequence length, it certainly does not scale to modern networks that have hundreds of layers.Our proposed approach addresses the problem of scalability in part, by introducing a two-stage action selection mechanism which first selects a macro-scale ""layer removal"" action, followed by a micro-scale ""layer shrinkage"" action. In this way we enable our reinforcement learning process to efficiently explore the space of reduced networks. Each network architecture that is generated by our policy is then trained with Knowledge Distillation BID12 . FIG0 illustrates our proposed approach.To the best of our knowledge, this is the first paper to provide a principled approach to the task of network compression, where the architecture of the student network is obtained via reinforcement learning. To facilitate reinforcement learning, we propose a reward function that encodes both the compression rate and the accuracy of the student model. In particular, we propose a novel formulation of the compression reward term based on a relaxation of a constrained optimization problem, which encodes the hardware-based computational budget items in the form of linear constraints.We demonstrate the effectiveness of our approach over several network architectures and several visual learning tasks of varying difficulty (MNIST, SVHN, CIFAR-10, CIFAR-100, Caltech-256). We also demonstrate that the compression policies exhibit generalization across networks with similar architectures. In particular, we use a policy trained on a ResNet-18 model on a ResNet-34 model and show that it greatly accelerates the reinforcement learning process. We introduced a novel method for compressing neural networks. Our approach employs a two-stage layer removal and layer shrinkage procedure to learn how to compress large neural networks. By leveraging signals for accuracy and compression as supervision, our method efficiently learns to search the space of model architectures. We show that our method performs well over a variety of datasets and architectures. We also observe generalization capabilities of our method through transfer learning, allowing our procedure to be made even more efficient. Our method is also able to incorporate other practical constraints, such as power or inference time, thus showing potential for application in a real world setting.",bigger deeper neural network architectures continue advance state-of-the-art many computer vision tasks real-world adoption networks is impeded hardware speed constraints. Conventional model compression methods attempt address problem modifying architecture manually using pre-defined heuristics. Since space reduced architectures is very large modifying architecture deep neural network way is a difficult task. paper tackle issue introducing principled method learning reduced network architectures data-driven way using reinforcement learning. approach takes larger 'teacher' network input outputs compressed 'student' network derived 'teacher' network. first stage method recurrent policy network aggressively removes layers large 'teacher' model. second stage another recurrent policy network carefully reduces size remaining layer. resulting network is then evaluated obtain reward score based accuracy compression network. approach uses reward signal policy gradients train policies find locally optimal student network. experiments show can achieve compression rates 10x models ResNet-34 maintaining similar performance input 'teacher' network. also present valuable transfer learning result which shows policies which are pre-trained smaller 'teacher' networks can be used rapidly speed training larger 'teacher' networks. carefully hand-designed deep convolutional networks continue increase size performance also require significant power memory computational resources often point prohibiting deployment smaller devices. result researchers have developed model compression techniques based Knowledge Distillation compress large teacher network smaller student network using various training techniques e.g soft output matching hint layer matching uncertainty modeling Unfortunately state-of-the-art knowledge distillation methods share common feature:require carefully hand-designed architectures student model. Hand-designing networks is a tedious sequential process often loosely guided sequence trial-and-error based decisions identify smaller network architecture. process makes difficult know if the resulting network is optimal. Clearly is a need develop principled methods identifying optimal student architectures. Towards principled approach network architecture compression present reinforcement learning approach identify compressed high-performance architecture student given knowledge distilled larger high-performing model teacher make key conceptual assumption formulates sequential process converting teacher network student network Markov Decision Process MDP model state represents network architecture. Clearly domain state is very large since contains every possible reduced architecture teacher network. deterministic transition state space |s is determined selecting action e.g removing convolutional filter reducing size fully connected layer. action will transform one architecture another architecture s. MDP strategy selecting action given certain state is represented policyπ a|s which stochastically maps state action. process reinforcement learning is used learn optimal policy based reward functionr defined state space. work define reward function based accuracy compression rate specified architecture.A straightforward application reinforcement learning problem can be very slow depending definition action space. example action could defined removing single filter every layer convolutional neural network. Since search space is exponential size action space sequence length certainly does not scale modern networks have hundreds layers.Our proposed approach addresses problem scalability part introducing two-stage action selection mechanism which first selects macro-scale layer removal action followed micro-scale layer shrinkage action. way enable reinforcement learning process efficiently explore space reduced networks. network architecture is generated policy is then trained Knowledge Distillation BID12. FIG0 illustrates proposed approach.To best knowledge is the first paper provide principled approach task network compression where the architecture student network is obtained via reinforcement learning. facilitate reinforcement learning propose reward function encodes compression rate accuracy student model. particular propose novel formulation compression reward term based relaxation constrained optimization problem which encodes hardware-based computational budget items form linear constraints.We demonstrate effectiveness approach several network architectures several visual learning tasks varying difficulty MNIST SVHN CIFAR-10 CIFAR-100 Caltech-256 also demonstrate compression policies exhibit generalization across networks similar architectures. particular use policy trained ResNet-18 model ResNet-34 model show greatly accelerates reinforcement learning process. introduced novel method compressing neural networks. approach employs two-stage layer removal layer shrinkage procedure learn how to compress large neural networks. leveraging signals accuracy compression supervision method efficiently learns search space model architectures. show method performs well variety datasets architectures. also observe generalization capabilities method transfer learning allowing procedure made even efficient. method is also able incorporate practical constraints power inference time thus showing potential application real world setting.,1194,789,405,0.013,1.513,2025/11/05 17:19:09,0.01,1.5,0.5700934579439247,365.883
"Recent advances in conditional image generation tasks, such as image-to-image translation and image inpainting, are largely accounted to the success of conditional GAN models, which are often optimized by the joint use of the GAN loss with the reconstruction loss. However, we reveal that this training recipe shared by almost all existing methods causes one critical side effect: lack of diversity in output samples. In order to accomplish both training stability and multimodal output generation, we propose novel training schemes with a new set of losses named moment reconstruction losses that simply replace the reconstruction loss. We show that our approach is applicable to any conditional generation tasks by performing thorough experiments on image-to-image translation, super-resolution and image inpainting using Cityscapes and CelebA dataset. Quantitative evaluations also confirm that our methods achieve a great diversity in outputs while retaining or even improving the visual fidelity of generated samples. Recently, active research has led to a huge progress on conditional image generation, whose typical tasks include image-to-image translation BID11 ), image inpainting BID31 ), super-resolution BID18 ) and video prediction BID27 ). At the core of such advances is the success of conditional GANs BID28 ), which improve GANs by allowing the generator to take an additional code or condition to control the modes of the data being generated. However, training GANs, including conditional GANs, is highly unstable and easy to collapse BID8 ). To mitigate such instability, almost all previous models in conditional image generation exploit the reconstruction loss such as 1 / 2 loss in addition to the GAN loss. Indeed, using these two types of losses is synergetic in that the GAN loss complements the weakness of the reconstruction loss that output samples are blurry and lack high-frequency structure, while the reconstruction loss offers the training stability required for convergence.In spite of its success, we argue that it causes one critical side effect; the reconstruction loss aggravates the mode collapse, one of notorious problems of GANs. In conditional generation tasks, which are to intrinsically learn one-to-many mappings, the model is expected to generate diverse outputs from a single conditional input, depending on some stochastic variables (e.g. many realistic street scene images for a single segmentation map BID11 ). Nevertheless, such stochastic input rarely generates any diversity in the output, and surprisingly many previous methods omit a random noise source in their models. Most papers rarely mention the necessity of random noise, and a few others report that the model completely ignores the noise even if it is fed into the model. For example, BID11 state that the generator simply learns to ignore the noise, and even dropout fails to incur meaningful output variation.The objective of this paper is to propose a new set of losses named moment reconstruction losses that can replace the reconstruction loss with losing neither the visual fidelity nor diversity in output samples. The core idea is to use maximum likelihood estimation (MLE) loss (e.g. 1 / 2 loss) to predict conditional statistics of the real data distribution instead of applying it directly to the generator as done in most existing algorithms. Then, we assist GAN training by enforcing the generated distribution to match its statistics to the statistics of the real distribution.In summary, our major contributions are three-fold. First, we show that there is a significant mismatch between the GAN loss and the reconstruction loss, thereby the model cannot achieve the optimality w.r.t. both losses. Second, we propose two novel loss functions that enable the model to accomplish both training stability and multimodal output generation. Our methods simply replace the reconstruction loss, and thus are applicable to any conditional generation tasks. Finally, we show the effectiveness and generality of our methods through extensive experiments on three generation tasks, including image-to-image translation, super-resolution and image inpainting, where our methods outperform recent strong baselines in terms of realism and diversity. In this work, we pointed out that there is a mismatch between the GAN loss and the conventional reconstruction losses. As alternatives, we proposed a set of novel loss functions named MR loss and proxy MR loss that enable conditional GAN models to accomplish both stability of training and multimodal generation. Empirically, we showed that our loss functions were successfully integrated with multiple state-of-the-art models for image translation, super-resolution and image inpainting tasks, for which our method generated realistic image samples of high visual fidelity and variability on Cityscapes and CelebA dataset.There are numerous possible directions beyond this work. First, there are other conditional generation tasks that we did not cover, such as text-to-image synthesis, text-to-speech synthesis and video prediction, for which our methods can be directly applied to generate diverse, high-quality samples. Second, in terms of statistics matching, our methods can be extended to explore other higher order statistics or covariance. Third, using the statistics of high-level features may capture additional correlations that cannot be represented with pixel-level statistics.",Recent advances conditional image generation tasks image-to-image translation image inpainting are largely accounted success conditional GAN models which are often optimized joint use GAN loss reconstruction loss. However reveal training recipe shared almost existing methods causes one critical side effect:lack diversity output samples. order accomplish training stability multimodal output generation propose novel training schemes new set losses named moment reconstruction losses simply replace reconstruction loss. show approach is applicable conditional generation tasks performing thorough experiments image-to-image translation super-resolution image inpainting using Cityscapes CelebA dataset. Quantitative evaluations also confirm methods achieve great diversity outputs retaining even improving visual fidelity generated samples. Recently active research has led huge progress conditional image generation whose typical tasks include image-to-image translation BID11 image inpainting BID31 super-resolution BID18 video prediction BID27 core advances is the success conditional GANs BID28 which improve GANs allowing generator take additional code condition control modes data generated. However training GANs including conditional GANs is highly unstable easy collapse BID8 mitigate instability almost previous models conditional image generation exploit reconstruction loss 1/2 loss addition GAN loss. Indeed using two types losses is synergetic GAN loss complements weakness reconstruction loss output samples are blurry lack high-frequency structure reconstruction loss offers training stability required convergence.In spite success argue causes one critical side effect;reconstruction loss aggravates mode collapse one notorious problems GANs. conditional generation tasks which are to intrinsically learn one-to-many mappings model is expected generate diverse outputs single conditional input depending stochastic variables e.g many realistic street scene images single segmentation map BID11 Nevertheless stochastic input rarely generates diversity output surprisingly many previous methods omit random noise source models. papers rarely mention necessity random noise others report model completely ignores noise even if it is fed model. example BID11 state generator simply learns ignore noise even dropout fails incur meaningful output variation.The objective paper is to propose new set losses named moment reconstruction losses can replace reconstruction loss losing neither visual fidelity diversity output samples. core idea is to use maximum likelihood estimation MLE loss e.g1/2 loss predict conditional statistics real data distribution instead applying directly generator done existing algorithms. assist GAN training enforcing generated distribution match statistics statistics real distribution.In summary major contributions are three-fold three-fold First show is a significant mismatch GAN loss reconstruction loss thereby model cannot achieve optimalityw.r.t losses. Second propose two novel loss functions enable model accomplish training stability multimodal output generation. methods simply replace reconstruction loss thus are applicable conditional generation tasks. Finally show effectiveness generality methods extensive experiments three generation tasks including image-to-image translation super-resolution image inpainting where our which our methods outperform recent strong baselines terms realism diversity. work pointed is mismatch GAN loss conventional reconstruction losses. alternatives proposed set novel loss functions named MR loss proxy MR loss enable conditional GAN models accomplish stability training multimodal generation. Empirically showed loss functions were successfully integrated multiple state-of-the-art models image translation super-resolution image inpainting tasks which our method generated realistic image samples high visual fidelity variability Cityscapes CelebA dataset.There are numerous possible directions beyond work. First are other conditional generation tasks did not cover text-to-image synthesis text-to-speech synthesis video prediction where our which our methods can be directly applied generate diverse high-quality samples. Second terms statistics matching where our which our methods can be extended explore higher order statistics covariance. Third using statistics high-level features may capture additional correlations cannot represented pixel-level statistics.,973,667,306,0.01,1.459,2025/11/05 17:19:09,0.0,1.607,0.4018691588785047,314.114
"Generative models are important tools to capture and investigate the properties of complex empirical data. Recent developments such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) use two very similar, but \textit{reverse}, deep convolutional architectures, one to generate and one to extract information from data. Does learning the parameters of both architectures obey the same rules? We exploit the causality principle of independence of mechanisms to quantify how the weights of successive layers adapt to each other. Using the recently introduced Spectral Independence Criterion, we quantify the dependencies between the kernels of successive convolutional layers and show that those are more independent for the generative process than for information extraction, in line with results from the field of causal inference. In addition, our experiments on generation of human faces suggest that more independence between successive layers of generators results in improved performance of these architectures.
 Deep generative models have proven powerful in learning to design realistic images in a variety of complex domains (handwritten digits, human faces, interior scenes). In particular, two approaches have recently emerged: Generative Adversarial Networks (GANs) BID8 , which train an image generator by having it fool a discriminator that should tell apart real from artificially generated images; and Variational Autoencoders (VAEs) BID15 BID21 ) that learn both a mapping from latent variables to the data (the decoder) and the converse mapping from the data to the latent variables (the encoder), such that correspondences between latent variables and data features can be easily investigated. Although these architecture have been lately the subject of extensive investigations, understanding why and how they work, and how they can be improved, remains elusive.An interesting feature of GANs and VAEs is that they both involve the learning of two deep subnetworks. These sub-networks have a ""mirrored"" architecture, as they both consist in a hierarchy of convolutional layers, but information flows in opposite ways: generators and decoders map latent variables to the data space, while discriminators and encoders extract information from the same space. Interestingly, this difference could be framed in a causal perspective, with information flowing in the causal direction in the case of generators (from the putative causes of variations in the observed data), while extracting high level properties from the observations (with encoders or discriminators) would operate in the anti-causal direction.Generative models in machine learning are usually not required to be causal, as modeling the data distribution is considered to be the goal to achieve. However, the idea that a generative model able to capture the causal structure of the data by disentangling the contribution of independent factors should perform better has been suggested in the literature BID0 BID17 and evidence supports that this can help the learning procedure BID1 . Although many approaches have been implemented on specific examples, principles and automated ways of learning disentangled representations from data remains largely an open problem both for learning representations (targeting supervised learning applications) and for fitting good generative models. GANs have for example recently been a subject of intensive work in this direction, leading to algorithms disentangling high level properties of the data such as InfoGans BID2 or conditional GANs BID18 . However such models require supervision (e.g. feeding digit labels as additional inputs) to disentangle factors of interest. Unsupervised learning of disentangled representations has been addressed in various frameworks including Restricted Boltzmann Machines BID6 , tensor analyzers BID26 and Lie groups BID4 . A recent attempt to address unsupervised learning in VAEs is β-VAE BID10 which introduces and adjustable parameter β in the VAE objective to strengthen the data compression constraint with respect to reconstruction error.While the above approaches envision the disentangling of representations as finding subsets of latent variables that relate to different properties of the generated data, parameters of the network can be also considered as factors affecting the generated data. Ideally, to ensure modularity of deep generative models, different layers should encode different aspects of the data in their parameters. Intuitively for deep convolutional networks, different layers should encode image features at different scales. The idea that successive layers can be used as modules encoding different levels of details has for example been exploited to build high-resolution generative models by training iteratively a GAN with an increasing number of layers BID14 . Enforcing modularity of trained neural architecture may not only allow to adapt them to the task at hand with minimum additional training, but also to better understand the structure and function of these highly complex black-box systems. However, to the best of our knowledge, assessing how independent (or disentangled) are the properties encoded by the weights distributed across the structure of deep networks has not been addressed quantitatively in the literature.We propose that the coupling between high dimensional parameters can be quantified and exploited in a causal framework to infer whether the layered architecture disentangles different aspects of the data. This hypothesis relies on recent work exploiting the postulate of Independence of Cause and Mechanism stating that Nature chooses independently the properties of a cause and those of the mechanism that generate effects from the cause BID13 . Several methods relying on this principle have been proposed in the literature in association to different model classes BID28 BID5 BID24 BID23 . Among these methods, the Spectral Independence Criterion (SIC) BID24 can be used in the context of linear dynamical systems, which involve a convolution mechanism.In this paper, we show how SIC can be adapted to investigate the coupling between the parameters of successive convolutional layers. Empirical investigation shows that SIC is approximately valid between successive layers of generative models, and suggests SIC violations indicate deficiencies in the learning algorithm or the architecture of the network. Interestingly, and in line with theoretical predictions BID24 , SIC tends to be more satisfied for generative sub-networks (mapping latent variables to data), than for the part of the system that map the anti-causal direction (data to latent variables). In addition, comparison of different generative models indicates that more independence between layers is associated to better performance of the model. Overall, our study suggests that quantifying Independence of Mechanisms in deep architecture can help analyze and design better generative models. In this work, we derived a measure of independence between the weights learned by convolutional layers of deep networks. The results suggest that generative models that map latent variables to data tend to have more independence between successive layers than discriminative or encoding networks. This is in line with theoretical predictions about independence of mechanisms for causal and anti-causal systems. In addition, our results suggest the dependency between successive layers relates to the bad performance of the trained generative models. Moreover, the SDR analysis also indicates which layers should be modified to improve the performance. Enforcing independence during training may thus help diagnose and improve generative models. Finally, we speculate that independence between successive layers, by favoring modularity of the network, may help build architectures that can be easily adapted to new purposes. In particular, separation of spatial scales in such models may help build networks in which one can intervene on one scale without affecting others, with applications such as style transfer BID7 . One specific feature of our approach is that this quantitative measure of the network performance in not statistical and as such requires neither extensive sampling form the fitted generative distribution nor from real datasets to be computed: only the parameters of the model are used. This is in strong contrast with state-ofthe-art approaches such as the Fréchet Inception Distance (FID) BID9 , and makes the approach easy to apply to any neural network equipped with convolutional layers.",Generative models are important tools capture investigate properties complex empirical data. Recent developments Generative Adversarial Networks GANs Variational Auto-Encoders VAEs use two similar \textit reverse deep convolutional architectures one generate one extract information data. Does learning parameters architectures obey rules? exploit causality principle independence mechanisms quantify how the weights successive layers adapt other. Using recently introduced Spectral Independence Criterion quantify dependencies kernels successive convolutional layers show are more independent generative process information extraction line results field causal inference. addition experiments generation human faces suggest independence successive layers generators results improved performance architectures. Deep generative models have proven powerful learning design realistic images variety complex domains handwritten digits human faces interior scenes particular two approaches have recently emerged:Generative Adversarial Networks GANs BID8 which train image generator fool discriminator should tell apart real artificially generated images;Variational Autoencoders VAEs BID15 BID21 learn mapping latent variables data decoder converse mapping data latent variables encoder correspondences latent variables data features can be easily investigated. Although architecture have been lately subject extensive investigations understanding why and how they work how they canbe improved remains elusive.An interesting feature GANs VAEs is that they both involve learning two deep subnetworks. sub-networks have a mirrored architecture consist hierarchy convolutional layers information flows opposite ways:generators decoders map latent variables data space discriminators encoders extract information space. Interestingly difference could framed causal perspective information flowing causal direction case generators putative causes variations observed data extracting high level properties observations encoders discriminators would operate anti-causal direction.Generative models machine learning are usually required causal modeling data distribution is considered goal achieve. However idea generative model able capture causal structure data disentangling contribution independent factors should perform better has been suggested literature BID0 BID17 evidence supports can help learning procedure BID1. Although many approaches have been implemented specific examples principles automated ways learning disentangled representations data remains largely open problem learning representations targeting supervised learning applications fitting good generative models. GANs have for example recently subject intensive work direction leading algorithms disentangling high level properties data InfoGans BID2 conditional GANs BID18. However models require supervision e.g feeding digit labels additional inputs disentangle factors interest. Unsupervised learning disentangled representations has been has not been addressed various frameworks including Restricted Boltzmann Machines BID6 tensor analyzers BID26 Lie groups BID4. recent attempt address unsupervised learning VAEs is β-VAE BID10 which introduces adjustable parameterβ VAE objective strengthen data compression constraint respect reconstruction error.While approaches envision disentangling representations finding subsets latent variables relate different properties generated data parameters network can be also considered factors affecting generated data. Ideally ensure modularity deep generative models different layers should encode different aspects data parameters. Intuitively deep convolutional networks different layers should encode image features different scales. idea successive layers can be used modules encoding different levels details has for example exploited build high-resolution generative models training iteratively GAN increasing number layers BID14. Enforcing modularity trained neural architecture may allow adapt task hand minimum additional training also better understand structure function highly complex black-box systems. However best knowledge assessing how independent disentangled are the properties encoded weights distributed across structure deep networks has been has not been addressed quantitatively literature.We propose coupling high dimensional parameters can be quantified exploited causal framework infer whether layered architecture disentangles different aspects data. hypothesis relies recent work exploiting postulate Independence Cause Mechanism stating Nature chooses independently properties cause mechanism generate effects cause BID13. Several methods relying principle have been proposed literature association different model classes BID28 BID5 BID24 BID23. Among methods Spectral Independence Criterion SIC BID24 can be used context linear dynamical systems which involve convolution mechanism.In paper show how SIC can be adapted investigate coupling parameters successive convolutional layers. Empirical investigation shows SIC is approximately valid successive layers generative models suggests SIC violations indicate deficiencies learning algorithm architecture network. Interestingly line theoretical predictions BID24 SIC tends satisfied generative sub-networks mapping latent variables data part system map anti-causal direction data latent variables addition comparison different generative models indicates independence layers is associated better performance model. Overall study suggests quantifying Independence Mechanisms deep architecture can help analyze design better generative models. work derived measure independence weights learned convolutional layers deep networks. results suggest generative models map latent variables data tend have more independence successive layers discriminative encoding networks. is in line theoretical predictions independence mechanisms causal anti-causal systems. addition results suggest dependency successive layers relates bad performance trained generative models. Moreover SDR analysis also indicates which layers should be modified improve performance. Enforcing independence training may thus help diagnose improve generative models. Finally speculate independence successive layers favoring modularity network may help build architectures can be easily adapted new purposes. particular separation spatial scales models may help build networks which one can intervene one scale without affecting others applications style transfer BID7. One specific feature approach is that this quantitative measure network performance statistical requires neither extensive sampling form fitted generative distribution real datasets computed:parameters model are used. is in strong contrast state-ofthe-art approaches Fréchet Inception Distance FID BID9 makes approach easy apply neural network equipped convolutional layers.,1529,1025,504,0.018,1.492,2025/11/05 17:19:09,0.01,1.66,0.5046728971962615,497.947
"Many deep reinforcement learning approaches use graphical state representations,
 this means visually distinct games that share the same underlying structure cannot
 effectively share knowledge. This paper outlines a new approach for learning
 underlying game state embeddings irrespective of the visual rendering of the game
 state. We utilise approaches from multi-task learning and domain adaption in
 order to place visually distinct game states on a shared embedding manifold. We
 present our results in the context of deep reinforcement learning agents. Games have often been used in order to experiment with new approaches with Artificial Intelligence (AI) research. Games provide flexibility to simulate a range of problems such as fully observable vs partially observable, stochastic vs discrete and noisy vs noise free environments. This first started with digital versions of board games being used such as backgammon and chess. More recently video games have begun to provide a plethora of digital environments and tasks for benchmarking AI systems. These new systems use neural networks and are usually trained using the raw pixel values of game frames, meaning the networks have to interpret these pixels into game states that can then be used to learn an optimal policy for play. Due to the fact that they use these raw pixel values they are sensitive to changes in the visuals of the game used, this results in very little knowledge transfer between visually distinct games BID25 resulting in the networks learning each game individually without any representation overlap. Games are usually very visually distinct as concepts are often abstract, especially for puzzle games. Early video games were often like this because it is very computationally expensive to create games that accurately imitate the real world, whereas more modern games may take a more abstract representation due to the financial expense.Learning representations has long been an important area of AI research. It has led to many new approaches to producing representations for many applications, such as word embeddings BID1 and style transfer BID6 . In the case of word embeddings networks can be used to solve various tasks such as predicting the context within which each word appears, the outputs of one of the hidden layers can then be used in order represent that word. This then results in word embeddings that place words that appear in similar contexts within close proximity to each other in the embedding space BID1 ). These resulting embeddings can then be used in order to solve more complex tasks without the system having to train from raw input. This could be seen as a form of knowledge transfer as the knowledge of the meaning of words has been encoded into its embedding and can then be used with new networks working on new tasks without the need to learn this mapping between words and their context again BID27 .In our work we improve knowledge representation across tasks that have underlying similarities but are represented in a visually distinct way. The architecture we propose in this paper learns representations that are independent of the visual differences of the games. This will result in the strategic elements of the game playing network to share knowledge between visually distinct games.In order to achieve this we use and extend work that has been done around domain adaption. Domain adaption seeks to produce shared representation between two separate domains a source domain and a target, such as high resolution product photos and images taken with a low resolution webcam BID5 . We present a method for using similar techniques in the domain of reinforcement learning allowing an agent to learn domain independent representations for a group of similar games that are visually distinct. This paper will first ground our work in the context of both learning representations and reinforcement learning. We will then outline the environment that the networks were trained in along with the desired outcomes. We will finally present the resulting representations and outline future work to extend this approach.2 RELATED WORK 2.1 AI AND GAMES Games provide a good benchmark for AI as they require high level reasoning and planning BID32 BID18 . This means that they have often been used to signify advances in the state of the art such as with Deep Blue the chess playing AI that beat Gary Kasparov BID2 and AlphaGo the go playing agent that beat Lee Sedol . Games also provide a nice interface for agents to be able to either look into the internal state of the games, as needed for methods such as Monte carlo tree search (MCTS) , or can provide visual representations of state that can be used by agents . Games also allow agents to process experiences much faster than would be possible in the real world. This means data hungry methods are still able to learn in a relatively short period of time BID13 ).There has also been a significant amount of research into other areas of game playing, such as competitions aimed at agents passing a form of Turing Test in order to rank agents based on their ability to mimic human play BID9 ). Most of these systems have revolved around using data from human play in order to achieve this goal BID24 BID14 . There have also been competitions organised in order to assess agents ability to generalise across a variety of games, the General Game Playing Competition BID7 focusing on playing multiple board games, and the General Video Game Playing Competition that assess agents performance across a broad range of video games. Other work has also started that uses modified versions of game engines in order to provide environments to teach AI, these include Project Malmo that uses the popular Minecraft Game in order to provide an experimentation platform for AI agents BID11 , and OpenArena, a modified version of the ID Tech 3 engine used by Quake 3, in order to train and benchmark AI at a range of tasks including path finding in a Labyrinth and laser tag BID10 ).There has also been some work in using neural evolution to evolve a network to control an agent in an first-person shooter (FPS) environment BID22 . Others have investigated the use of hierarchical approaches in the design of AI agents for FPS games BID28 that use networks in a hierarchical fashion to deconstruct the tasks into sub-skills. As our results show it is possible for our system to separate game states from raw pixel values despite the renderings of the game being so distinct. It also effectively separates out states that require a different task to be completed, with the game states that contain pickups being in a distinct but related space to the states that require the player to now head towards the goal. This shows that the learned embeddings are capturing a lot about how the game is played irrespective of how the frame is rendered. We show that this is possible in the context of deep reinforcement learning for domain adaptions to be successfully achieved using adversarial networks. Our network also manages to deal with more visually diverse inputs than was possible with a network that fully shares its parameters. As the results have shown the single shared convolutional layers did not have the capacity to deal with the differences between the visual representations of the game. We have shown that it is possible to use adversarial networks along with separate convolutional layers in order to produce shared embedding spaces for visually distinct inputs.",Many deep reinforcement learning approaches use graphical state representations means visually distinct games share underlying structure cannot effectively share knowledge. paper outlines new approach learning underlying game state embeddings irrespective visual rendering game state. utilise approaches multi-task learning domain adaption order place visually distinct game states shared embedding manifold. present results context deep reinforcement learning agents. Games have often used order experiment new approaches Artificial Intelligence AI research. Games provide flexibility simulate range problems fully observable vs partially observable stochastic vs discrete noisy vs noise free environments. first started digital versions board games used backgammon chess. recently video games have begun provide plethora digital environments tasks benchmarking AI systems. new systems use neural networks are usually trained using raw pixel values game frames meaning networks have to interpret pixels game states can then be can be used learn optimal policy play. Due fact use raw pixel values are sensitive changes visuals game used results little knowledge transfer visually distinct games BID25 resulting networks learning game individually without representation overlap. Games are usually visually distinct concepts are often abstract especially puzzle games. Early video games were often like is computationally expensive create games accurately imitate real world whereas modern games may take abstract representation due financial expense.Learning representations has long important area AI research. has led many new approaches producing representations many applications word embeddings BID1 style transfer BID6. case word embeddings networks can be can then be used solve various tasks predicting context within which each word appears outputs one hidden layers can be can then be used order represent word. results word embeddings place words appear similar contexts within close proximity embedding space BID1 resulting embeddings can be can then be used order solve complex tasks without system train raw input. could seen form knowledge transfer knowledge meaning words has been encoded embedding can then be used new networks working new tasks without need learn mapping words context BID27.In work improve knowledge representation across tasks have underlying similarities are represented visually distinct way. architecture propose paper learns representations are independent visual differences games. will result strategic elements game playing network share knowledge visually distinct games.In order achieve use extend work has been done around domain adaption. Domain adaption seeks produce shared representation two separate domains source domain target high resolution product photos images taken low resolution webcam BID5. present method using similar techniques domain reinforcement learning allowing agent learn domain independent representations group similar games are visually distinct. paper will first ground work context learning representations reinforcement learning. will then outline environment networks were trained along desired outcomes. will finally present resulting representations outline future work extend approach.2 RELATED WORK 2.1 AI GAMES Games provide good benchmark AI require high level reasoning planning BID32 BID18. means have often used signify advances state art Deep Blue chess playingAI beat Gary Kasparov BID2 AlphaGo go playing agent beat Lee Sedol. Games also provide nice interface agents able either look internal state games needed methods Monte carlo tree search MCTS can provide visual representations state can then be can be used agents. Games also allow agents process experiences much faster would possible real world. means data hungry methods are still able learn relatively short period time BID13.There has also significant amount research areas game playing competitions aimed agents passing form Turing Test order rank agents based ability mimic human play BID9 systems have revolved around using data human play order achieve goal BID24 BID14. have also competitions organised order assess agents ability generalise across variety games General Game Playing Competition BID7 focusing playing multiple board games General Video Game Playing Competition assess agents performance across broad range video games. work has also started uses modified versions game engines order provide environments teachAI include Project Malmo uses popular Minecraft Game order provide experimentation platform AI agents BID11 OpenArena modified version ID Tech 3 engine used Quake3 order train benchmarkAI range tasks including path finding Labyrinth laser tag BID10.There has also work using neural evolution evolve network control agent first-person shooter FPS environment BID22. Others have investigated use hierarchical approaches design AI agents FPS games BID28 use networks hierarchical fashion deconstruct tasks sub-skills results show is possible system separate game states raw pixel values despite renderings game distinct. also effectively separates states require different task completed game states contain pickups distinct related space states require player head towards goal. shows learned embeddings are capturing lot how the game is played irrespective how the frame is rendered. show is is possible context deep reinforcement learning domain adaptions successfully achieved using adversarial networks. network also manages deal visually diverse inputs was possible network fully shares parameters. results have shown single shared convolutional layers did not have the capacity deal differences visual representations game. have shown is is possible use adversarial networks along separate convolutional layers order produce shared embedding spaces visually distinct inputs.,1364,908,456,0.016,1.502,2025/11/05 17:19:09,0.01,1.383,0.5358255451713394,470.171
"We study discrete time dynamical systems governed by the state equation $h_{t+1}=ϕ(Ah_t+Bu_t)$. Here A,B are weight matrices, ϕ is an activation function, and $u_t$ is the input data. This relation is the backbone of recurrent neural networks (e.g. LSTMs) which have broad applications in sequential learning tasks. We utilize stochastic gradient descent to learn the weight matrices from a finite input/state trajectory $(u_t,h_t)_{t=0}^N$. We prove that SGD estimate linearly converges to the ground truth weights while using near-optimal sample size. Our results apply to increasing activations whose derivatives are bounded away from zero. The analysis is based on i) an SGD convergence result with nonlinear activations and ii) careful statistical characterization of the state vector. Numerical experiments verify the fast convergence of SGD on ReLU and leaky ReLU in consistence with our theory. A wide range of problems involve sequential data with a natural temporal ordering. Examples include natural language processing, time series prediction, system identification, and control design, among others. State-of-the-art algorithms for sequential problems often stem from dynamical systems theory and are tailored to learn from temporally dependent data. Linear models and algorithms; such as Kalman filter, PID controller, and linear dynamical systems, have a long history and are utilized in control theory since 1960's with great success (Brown et al. (1992) ; Ho & Kalman (1966) ; Åström & Hägglund (1995) ). More recently, nonlinear models such as recurrent neural networks (RNN) found applications in complex tasks such as machine translation and speech recognition (Bahdanau et al. (2014) ; Graves et al. (2013) ; Hochreiter & Schmidhuber (1997) ). Unlike feedforward neural networks, RNNs are dynamical systems that use their internal state to process inputs. The goal of this work is to shed light on the inner workings of RNNs from a theoretical point of view. In particular, we focus on the RNN state equation which is characterized by a nonlinear activation function φ, state weight matrix A, and input weight matrix B as follows h t+1 = φ(Ah t + Bu t ),(1.1)Here h t is the state vector and u t is the input data at timestamp t. This equation is the source of dynamic behavior of RNNs and distinguishes RNN from feedforward networks. The weight matrices A and B govern the dynamics of the state equation and are inferred from data. We will explore the statistical and computational efficiency of stochastic gradient descent (SGD) for learning these weight matrices.Contributions: Suppose we are given a finite trajectory of input/state pairs (u t , h t ) N t=0 generated from the state equation (1.1). We consider a least-squares regression obtained from N equations; with inputs (u t , h t ) N t=1 and outputs (h t+1 ) N t=1 . For a class of activation functions including leaky ReLU and for stable systems 1 , we show that SGD linearly converges to the ground truth weight matrices while requiring near-optimal trajectory length N . In particular, the required sample size is O(n + p) where n and p are the dimensions of the state and input vectors respectively. The results are extended to unstable systems when the samples are collected from multiple independent RNN trajectories rather than a single trajectory. Our theory applies to increasing activation functions whose derivatives are bounded away from zero, which includes leaky ReLU, and Gaussian input data. Numerical experiments on ReLU and leaky ReLU corroborate our theory and demonstrate that SGD converges faster as the activation slope increases. To obtain our results, we i) characterize the statistical properties of the state vector (e.g. well-conditioned covariance) and ii) derive a novel SGD convergence result with nonlinear activations; which may be of independent interest. As a whole, this paper provides a step towards foundational understanding of RNN training via SGD. This work showed that SGD can learn the nonlinear dynamical system (1.1); which is characterized by weight matrices and an activation function. This problem is of interest for recurrent neural networks as well as nonlinear system identification. We showed that efficient learning is possible with optimal sample complexity and good computational performance. Our results apply to strictly increasing activations such as Leaky ReLU. We empirically showed that Leaky ReLU converges faster than ReLU and requires less samples; in consistence with our theory. We list a few unanswered problems that would provide further insights into recurrent neural networks.• Covariance of the state-vector: Our results depend on the covariance of the state-vector and requires it to be positive definite. One might be able to improve the current bounds on the condition number and relax the assumptions on the activation function. Deriving similar performance bounds for ReLU is particularly interesting.• Hidden state: For RNNs, the state vector is hidden and is observed through an additional equation (2.1); which further complicates the optimization landscape. Even for linear dynamical systems, learning the (A, B, C, D) system ((1.1), (2.1)) is a non-trivial task Ho & Kalman (1966); Hardt et al. (2016) . What can be said when we add the nonlinear activations?• Classification task: In this work, we used normally distributed input and least-squares regression for our theoretical guarantees. More realistic input distributions might provide better insight into contemporary problems, such as natural language processing; where the goal is closer to classification (e.g. finding the best translation from another language).",study discrete time dynamical systems governed state equation $h_+1 =ϕ Ah_t+Bu_t $. B are weight matrices ϕ is an activation function $u_t is the input data. relation is the backbone recurrent neural networks e.g LSTMs which have broad applications sequential learning tasks. utilize stochastic gradient descent learn weight matrices finite input/state trajectory$ u_t h_t t=0 ^N$. prove SGD estimate linearly converges ground truth weights using near-optimal sample size. results apply increasing activations whose derivatives are bounded away zero. analysis is based SGD convergence result nonlinear activations ii careful statistical characterization state vector. Numerical experiments verify fast convergence SGD ReLU leaky ReLU consistence theory. wide range problems involve sequential data natural temporal ordering. Examples include natural language processing time series prediction system identification control design among others. State-of-the-art algorithms sequential problems often stem dynamical systems theory are tailored learn temporally dependent data. Linear models algorithms;Kalman filter PID controller linear dynamical systems have a long history are utilized control theory since 1960's great success Brownetal. 1992 Ho Kalman 1966 Åström Hägglund 1995 recently nonlinear models recurrent neural networks RNN found applications complex tasks machine translation speech recognition Bahdanauetal. 2014 Gravesetal. 2013 Hochreiter Schmidhuber 1997 Unlike feedforward neural networks RNNs are dynamical systems use internal state process inputs. goal work is to shed light inner workings RNNs theoretical point view. particular focus RNN state equation which is characterized nonlinear activation functionφ state weight matrix input weight matrixB followsh+1 φ Ah+Bu 1.1 h is the state vector u is the input data timestamp t. equation is the source dynamic behavior RNNs distinguishes RNN feedforward networks. weight matrices B govern dynamics state equation are inferred data. will explore statistical computational efficiency stochastic gradient descent SGD learning weight matrices.Contributions:Suppose are given finite trajectory input/state pairs u h N t=0 generated state equation 1.1 consider least-squares regression obtained N equations;inputs u h N t=1 outputs h+1 N t=1 class activation functions including leaky ReLU stable systems1 show SGD linearly converges ground truth weight matrices requiring near-optimal trajectory length N. particular required sample size isO(n+p wheren p are the dimensions state input vectors respectively. results are extended unstable systems when the samples are collected multiple independent RNN trajectories rather single trajectory. theory applies increasing activation functions whose derivatives are bounded away zero which includes leaky ReLU Gaussian input data. Numerical experiments ReLU leaky ReLU corroborate theory demonstrate SGD converges faster activation slope increases. obtain results characterize statistical properties state vector e.g well-conditioned covariance ii derive novel SGD convergence result nonlinear activations;may independent interest. whole paper provides step towards foundational understanding RNN training via SGD. work showed SGD can learn nonlinear dynamical system 1.1 which is characterized weight matrices activation function. problem is of interest recurrent neural networks well nonlinear system identification. showed efficient learning is possible optimal sample complexity good computational performance. results apply strictly increasing activations Leaky ReLU. empirically showed Leaky ReLU converges faster ReLU requires less samples;consistence theory. list unanswered problems would provide insights recurrent neural networks.• Covariance state-vector results depend covariance state-vector requires positive definite. One might able improve current bounds condition number relax assumptions activation function. Deriving similar performance bounds ReLU is particularly interesting.• Hidden state:RNNs state vector is hidden is observed additional equation 2.1 which further complicates optimization landscape. Even linear dynamical systems learning B C system 1.1 2.1 is a non-trivial taskHo Kalman 1966 Hardtetal. 2016 What can said when we add nonlinear activations? • Classification task:work used normally distributed input least-squares regression theoretical guarantees. realistic input distributions might provide better insight contemporary problems natural language processing;where the goal is closer classification e.g finding best translation another language,1178,827,351,0.012,1.424,2025/11/05 17:19:09,0.01,1.538,0.2928348909657317,347.161
"Although deep neural networks show their extraordinary power in various tasks, they are not feasible for deploying such large models on embedded systems due to high computational cost and storage space limitation. The recent work knowledge distillation (KD) aims at transferring model knowledge from a well-trained teacher model to a small and fast student model which can significantly help extending the usage of large deep neural networks on portable platform. In this paper, we show that, by properly defining the neuron manifold of deep neuron network (DNN), we can significantly improve the performance of student DNN networks through approximating neuron manifold of powerful teacher network. To make this, we propose several novel methods for learning neuron manifold from DNN model. Empowered with neuron manifold knowledge, our experiments show the great improvement across a variety of DNN architectures and training data. Compared with other KD methods, our Neuron Manifold Transfer (NMT) has best transfer ability of the learned features. In recent years, deep neural networks become more and more popular in computer vision and neural language processing. A well-trained learning model shows its power on tasks such as image classification, object detection, pattern recognizing, live stream analyzing, etc. We also have the promise that given enough data, deeper and wider neural networks can achieve better performance than the shallow networks BID0 ). However, these larger but well-trained networks also bring in high computational cost, and leave large amount of memory footprints which make these models very hard to travel and reproduce BID7 ). Due to this drawback, a massive amount of trainable data gathered by small devices such as mobiles, cameras, smart sensors, etc. is unable to be utilized in the local environment which can cause time-sensitive prediction delay and other impractical issues.To address the above issues, recently, there are extensive works proposed to mitigate the problem of model compression to reduce the computational burden on embedded system. Back to the date 2006, Buciluǎ et al. first proposed to train a neural network to mimic the output of a complex and large ensemble. This method uses ensemble to label the unlabeled data and trains the neural network with the data labeled by the ensemble, thus mimicking the function which learned by the ensemble and achieves similar accuracy. Based on the idea of (Buciluǎ,Geoffrey et al.) originally introduced a student-teacher paradigm in transferring the knowledge from a deeper and wider network (teacher) to a shallow network (student). They call this student-teacher paradigm as knowledge distillation (KD). By properly defining the knowledge of teacher as softened softmax (soft target), the student learns to mimic soft target distribution for each class. Thanks to Hinton's pioneer work, a series of subsequent works have sprung up by utilizing different forms of knowledge. BID22 regard the spatial attention maps of a convolution neural network as network knowledge. However, an implicit assumption that they make is that the absolute value of a hidden neuron activation can be used as an indication about the importance of that neuron w.r.t. the specific input which limited their application only fit for image classification tasks. Another assumption that has been widely used is from BID0 that deeper networks always learn better representation. Based on that, FitNets BID13 ) tries to learn a thin deep network using a shallow one with more parameters. They believe that the convolution regressor is the network knowledge which can inherit from the teacher to its student. In 2017, researcher from TuSimple ( TuSimple et al. (2015) , using softmax as knowledge, the student network mimics teacher's softmax and minimize the loss on soft target. Middle one, mentioned in BID22 , named as attention transfer, an additional regularizer has been applied known as attention map, student needs to learn the attention map and soft target. The right part is our neuron manifold transfer, where we take neuron manifold as knowledge, and it reduces the computational and space cost.(2015 )) introduces two new definitions of network knowledge, BID8 takes the advantage of Maximum Mean Discrepancy (MMD) to minimize the distance metric in probability distributions, and they regard network knowledge as class distribution. BID4 propose to transfer the cross sample similarities between the student and teacher to improve the performance of transferred networks. We notice that in the DarkRank the network knowledge is defined as cross sample similarities.By reviewing extensive KD works, we notice that the key point in knowledge transfer is how we define the network knowledge, and in fact, a well-defined network knowledge can greatly improve the performance of the distilled network. Moreover, in our perspective, a perfect knowledge transfer method must allow us to transfer one neural network architecture into another, while preserving other generalization. A perfect transfer method, however, would use little observations to train, optimally use the limited samples at its disposal. Unfortunately , to our best knowledge, due to the complexity of large DNN, simply mimicking the teacher logit or a part of teacher features properties is far away to be benefited. Therefore, if we look back and consider the essence of DNN training, we notice that, another point of view to look at the distribution of neuron features is the shape of that feature. Here, the shape of neuron features include the actual value and the relative distance between two features. That is, during the process of knowledge transfer, student network not only learns the numerical information but also inherits the geometric properties. Therefore, in order to track the change of large DNN feature knowledge, a manifold approximation technique is vying for our attention. Manifold learning has been widely used in Topological Data Analysis (TDA) BID3 ), and this technique can project the high dimensional data to a lower dimensional manifold and preserving both numerical feature properties and geometric properties. In previous works, feature mapping causes computational resource waste, and class distribution matching is limited the usage. However, using the neuron manifold information, we not only collect as much as possible feature properties which can greatly represent feature, but also preserve inter-neuron characteristics (spatial relation). Since manifold projection can greatly reduce the dimension of teacher feature, we compress the teacher model and make student model more reliable. To summarize, the contributions of this paper are three folds:• We introduce a new type of knowledge that is the d-dimensional smooth sub-manifold of teacher feature maps called neuron manifold.• We formalize manifold space in feature map, and implement in details.• We test our proposed method on various metric learning tasks. Our method can significantly improve the performance of student networks. And it can be applied jointly with existing methods for a better transferring performance.We test our method on MNIST, CIFAR-10, and CIFAR-100 datasets and show that our Neuron Manifold Transfer (NMT) improves the students performance notably. In this paper, we propose a novel method for knowledge transfer and we define a new type network knowledge named neuron manifold. By utilizing the state of art technique in Topological Data Analysis, we extract the DNN's feature properties and its geometric properties. We test our NMT on various dataset and the results are quite promising, thus further confirming that our knowledge transfer method could indeed learn better feature representations. They can be successfully transferred to high level vision task in the future. We believe that our novel view will facilitate the further design of knowledge transfer methods. In our future work, we plan to explore more applications of our NMT methods, especially in various regression problems, such as super resolution and optical flow prediction, etc.","Although deep neural networks show extraordinary power various tasks are not feasible deploying large models embedded systems due high computational cost storage space limitation. recent work knowledge distillation KD aims transferring model knowledge well-trained teacher model small fast student model which can significantly help extending usage large deep neural networks portable platform. paper show properly defining neuron manifold deep neuron network DNN can significantly improve performance student DNN networks approximating neuron manifold powerful teacher network. make propose several novel methods learning neuron manifold DNN model. Empowered neuron manifold knowledge experiments show great improvement across variety DNN architectures training data. Compared KD methods Neuron Manifold Transfer NMT has best transfer ability learned features. recent years deep neural networks become popular computer vision neural language processing. well-trained learning model shows power tasks image classification object detection pattern recognizing live stream analyzing etc. also have the promise given enough data deeper wider neural networks can achieve better performance shallow networks BID0 However larger well-trained networks also bring high computational cost leave large amount memory footprints which make models hard travel reproduce BID7 Due drawback massive amount trainable data gathered small devices mobiles cameras smart sensors etc. is unable utilized local environment which can cause time-sensitive prediction delay impractical issues.To address issues recently are extensive works proposed mitigate problem model compression reduce computational burden embedded system. Back date 2006 Buciluǎetal. first proposed train neural network mimic output complex large ensemble. method uses ensemble label unlabeled data trains neural network data labeled ensemble thus mimicking function which learned ensemble achieves similar accuracy. Based idea Buciluǎ Geoffreyetal. originally introduced student-teacher paradigm transferring knowledge deeper wider network teacher shallow network student call student-teacher paradigm knowledge distillation KD properly defining knowledge teacher softened softmax soft target student learns mimic soft target distribution class. Thanks Hinton's pioneer work series subsequent works have sprung utilizing different forms knowledge. BID22 regard spatial attention maps convolution neural network network knowledge. However implicit assumption make is that the absolute value hidden neuron activation can be used indication importance neuronw.r.t specific input which limited application fit image classification tasks. Another assumption has been widely used is from BID0 deeper networks always learn better representation. Based FitNets BID13 tries learn thin deep network using shallow one parameters. believe convolution regressor is the network knowledge which can inherit teacher student. 2017 researcher TuSimple TuSimpleetal. 2015 using softmax knowledge student network mimics teacher's softmax minimize loss soft target. Middle one mentioned BID22 named attention transfer additional regularizer has been applied known attention map student needs learn attention map soft target. right part is our neuron manifold transfer where we take neuron manifold knowledge reduces computational space cost. 2015 introduces two new definitions network knowledge BID8 takes advantage Maximum Mean Discrepancy MMD minimize distance metric probability distributions regard network knowledge class distribution. BID4 propose transfer cross sample similarities student teacher improve performance transferred networks. notice DarkRank network knowledge is defined cross sample similarities.By reviewing extensive KD works notice key point knowledge transfer is how we define network knowledge fact well-defined network knowledge can greatly improve performance distilled network. Moreover perspective perfect knowledge transfer method must allowus transfer one neural network architecture another preserving generalization. perfect transfer method however would use little observations train optimally use limited samples disposal. Unfortunately best knowledge due complexity large DNN simply mimicking teacher logit part teacher features properties is far away benefited. Therefore if we look back consider essence DNN training notice another point view look distribution neuron features is the shape feature. shape neuron features include actual value relative distance two features. is,during process knowledge transfer student network learns numerical information also inherits geometric properties. Therefore order track change large DNN feature knowledge manifold approximation technique is vying attention. Manifold learning has been widely used Topological Data Analysis TDA BID3 technique can project high dimensional data lower dimensional manifold preserving numerical feature properties geometric properties. previous works feature mapping causes computational resource waste class distribution matching is limited usage. However using neuron manifold information collect much possible feature properties which can greatly represent feature also preserve inter-neuron characteristics spatial relation Since manifold projection can greatly reduce dimension teacher feature compress teacher model make student model reliable. summarize contributions paper are three folds:• introduce new type knowledge is the d-dimensional smooth sub-manifold teacher feature maps called neuron manifold.• formalize manifold space feature map implement details.• test proposed method various metric learning tasks. method can significantly improve performance student networks. can be applied jointly existing methods better transferring performance.We test method MNIST CIFAR-10 CIFAR-100 datasets show Neuron Manifold Transfer NMT improves students performance notably. paper propose novel method knowledge transfer define new type network knowledge named neuron manifold. utilizing state art technique Topological Data Analysis extract DNN's feature properties geometric properties. test NMT various dataset results are quite promising thus confirming knowledge transfer method could indeed learn better feature representations. can be successfully transferred high level vision task future. believe novel view will facilitate design knowledge transfer methods. future work plan explore applications NMT methods especially various regression problems super resolution optical flow prediction etc.",1499,999,500,0.018,1.501,2025/11/05 17:19:09,0.01,1.61,0.5327102803738313,493.592
"We present a simple and general method to train a single neural network executable at different widths (number of channels in a layer), permitting instant and adaptive accuracy-efficiency trade-offs at runtime. Instead of training individual networks with different width configurations, we train a shared network with switchable batch normalization. At runtime, the network can adjust its width on the fly according to on-device benchmarks and resource constraints, rather than downloading and offloading different models. Our trained networks, named slimmable neural networks, achieve similar (and in many cases better) ImageNet classification accuracy than individually trained models of MobileNet v1, MobileNet v2, ShuffleNet and ResNet-50 at different widths respectively. We also demonstrate better performance of slimmable models compared with individual ones across a wide range of applications including COCO bounding-box object detection, instance segmentation and person keypoint detection without tuning hyper-parameters. Lastly we visualize and discuss the learned features of slimmable networks. Code and models are available at: https://github.com/JiahuiYu/slimmable_networks Recently deep neural networks are prevailing in applications on mobile phones, augmented reality devices and autonomous cars. Many of these applications require a short response time. Towards this goal, manually designed lightweight networks BID51 BID50 are proposed with low computational complexities and small memory footprints. Automated neural architecture search methods ) also integrate on-device latency into search objectives by running models on a specific phone. However, at runtime these networks are not re-configurable to adapt across different devices given a same response time budget. For example, there were over 24,000 unique Android devices in 2015 2 . These devices have drastically different runtimes for the same neural network BID19 , as shown in TAB0 . In practice, given the same response time constraint, high-end phones can achieve higher accuracy by running larger models, while low-end phones have to sacrifice accuracy to reduce latency. Although a global hyper-parameter, width multiplier, is provided in lightweight networks BID51 BID50 to trade off between latency and accuracy, it is inflexible and has many constraints. First, models with different width multipliers need to be trained, benchmarked and deployed individually. A big offline table needs to be maintained to document the allocation of different models to different devices, according to time and energy budget. Second, even on a same device, the computational budget varies (for example, excessive consumption of background apps reduces the available computing capacity), and the energy budget varies (for example, a mobile phone may be in low-power or power-saving mode). Third, when switching to a larger or smaller model, the cost of time and data for downloading and offloading models is not negligible. Recently dynamic neural networks are introduced to allow selective inference paths. BID29 introduce controller modules whose outputs control whether to execute other modules. It has low theoretical computational complexity but is nontrivial to optimize and deploy on mobiles since dynamic conditions prohibit layer fusing and memory optimization. adapt early-exits into networks and connect them with dense connectivity. and propose to selectively choose the blocks in a deep residual network to execute during inference. Nevertheless, in contrast to width (number of channels), reducing depth cannot reduce memory footprint in inference, which is commonly constrained on mobiles.The question remains: Given budgets of resources, how to instantly, adaptively and efficiently trade off between accuracy and latency for neural networks at runtime? In this work we introduce slimmable neural networks, a new class of networks executable at different widths, as a general solution to trade off between accuracy and latency on the fly. FIG0 shows an example of a slimmable network that can switch between four model variants with different numbers of active channels. The parameters of all model variants are shared and the active channels in different layers can be adjusted. For brevity, we denote a model variant in a slimmable network as a switch, the number of active channels in a switch as its width. 0.25× represents that the width in all layers are scaled by 0.25 of the full model. In contrast to other solutions above, slimmable networks have several advantages: (1) For different conditions, a single model is trained, benchmarked and deployed. (2) A near-optimal trade-off can be achieved by running the model on a target device and adjusting active channels accordingly. (3) The solution is generally applicable to (normal, group, depthwise-separable, dilated) convolutions, fully-connected layers, pooling layers and many other building blocks of neural networks. It is also generally applicable to different tasks including classification, detection, identification, image restoration and more. (4) In practice, it is straightforward to deploy on mobiles with existing runtime libraries. After switching to a new configuration, the slimmable network becomes a normal network to run without additional runtime and memory cost.However, neural networks naturally run as a whole and usually the number of channels cannot be adjusted dynamically. Empirically training neural networks with multiple switches has an extremely low testing accuracy around 0.1% for 1000-class ImageNet classification. We conjecture it is mainly due to the problem that accumulating different number of channels results in different feature mean and variance. This discrepancy of feature mean and variance across different switches leads to inaccurate statistics of shared Batch Normalization layers BID20 , an important training stabilizer. To this end, we propose a simple and effective approach, switchable batch normalization, that privatizes batch normalization for different switches of a slimmable network. The variables of moving averaged means and variances can independently accumulate feature statistics of each switch. Moreover, Batch Normalization usually comes with two additional learnable scale and bias parameter to ensure same representation space BID20 . These two parameters may able to act as conditional parameters for different switches, since the computation graph of a slimmable network depends on the width configuration. It is noteworthy that the scale and bias can be merged into variables of moving mean and variance after training, thus by default we also use independent scale and bias as they come for free. Importantly, batch normalization layers usually have negligible size (less than 1%) in a model. BID10 BID53 BID22 and BID16 implanted earlyexiting prediction branches to reduce the average execution depth. The computation graph of these methods are conditioned on network input, and lower theoretical computational complexity can be achieved.Conditional Normalization. Many real-world problems require conditional input. Feature-wise transformation BID7 ) is a prevalent approach to integrate different sources of information, where conditional scales and biases are applied across the network. It is commonly implemented in the form of conditional normalization layers, such as batch normalization or layer normalization BID2 . Conditional normalization is widely used in tasks including style transfer BID6 BID25 BID18 BID26 , image recognition BID24 BID45 and many others BID34 a) . We introduced slimmable networks that permit instant and adaptive accuracy-efficiency trade-offs at runtime. Switchable batch normalization is proposed to facilitate robust training of slimmable networks. Compared with individually trained models with same width configurations, slimmable networks have similar or better performances on tasks of classification, object detection, instance segmentation and keypoints detection. The proposed slimmable networks and slimmable training could be further applied to unsupervised learning and reinforcement learning, and may help to related fields such as network pruning and model distillation.end, we mainly conduct COCO experiments based on another detection framework: MMDetection , which has hyper-parameter settings with same pytorch-style ResNet-50. With same hyper-parameter settings (i.e., RCNN R50 FPN 1 ×), we fine-tune both individual ResNet-50 models and slimmable ResNet-50 on tasks of object detection and instance segmentation. Our reproduced results on ResNet-50 1.0× is consistent with official models in MMDetection ). For keypoint detection task, we conduct experiment on Detectron framework by modifying caffe-style ResNet-50 to pytorch-style and training on 4 GPUs without other modification of hyper-parameters. We have released code (training and testing) and pretrained models on both ImageNet classification task and COCO detection tasks.","present simple general method train single neural network executable different widths number channels layer permitting instant adaptive accuracy-efficiency trade-offs runtime. Instead training individual networks different width configurations train shared network switchable batch normalization. runtime network can adjust width fly according on-device benchmarks resource constraints rather downloading offloading different models. trained networks named slimmable neural networks achieve similar many cases better ImageNet classification accuracy individually trained models MobileNetv1 MobileNetv2 ShuffleNet ResNet-50 different widths respectively. also demonstrate better performance slimmable models compared individual ones across wide range applications including COCO bounding-box object detection instance segmentation person keypoint detection without tuning hyper-parameters Lastly visualize discuss learned features slimmable networks. Code models are available at:https://github.com/JiahuiYu/slimmable_networks Recently deep neural networks are prevailing applications mobile phones augmented reality devices autonomous cars. Many applications require short response time. Towards goal manually designed lightweight networks BID51 BID50 are proposed low computational complexities small memory footprints. Automated neural architecture search methods also integrate on-device latency search objectives running models specific phone. However runtime networks are not re-configurable adapt across different devices given response time budget. example were over 24,000 unique Android devices 20152. devices have drastically different runtimes neural network BID19 shown TAB0. practice given response time constraint high-end phones can achieve higher accuracy running larger models low-end phones have to sacrifice accuracy reduce latency. Although global hyper-parameter width multiplier is provided lightweight networks BID51 BID50 trade latency accuracy is inflexible has many constraints. First models different width multipliers need trained benchmarked deployed individually. big offline table needs maintained document allocation different models different devices according time energy budget. Second even device computational budget varies example excessive consumption background apps reduces available computing capacity energy budget varies example mobile phone may low-power power-saving mode Third when switching larger smaller model cost time data downloading offloading models is not negligible. Recently dynamic neural networks are introduced allow selective inference paths. BID29 introduce controller modules whose outputs control whether execute modules. has low theoretical computational complexity is nontrivial optimize deploy mobiles since dynamic conditions prohibit layer fusing memory optimization. adapt early-exits networks connect dense connectivity. propose selectively choose blocks deep residual network execute inference. Nevertheless contrast width number channels reducing depth cannot reduce memory footprint inference which is commonly constrained mobiles.The question remains:Given budgets resources how to instantly adaptively efficiently trade accuracy latency neural networks runtime? work introduce slimmable neural networks new class networks executable different widths general solution trade accuracy latency fly. FIG0 shows example slimmable network can switch four model variants different numbers active channels. parameters model variants are shared active channels different layers can be adjusted. brevity denote model variant slimmable network switch number active channels switch width. 0.25× represents width layers are scaled 0.25 full model. contrast solutions slimmable networks have several advantages:1 different conditions single model is trained benchmarked deployed. 2 near-optimal trade-off can be achieved running model target device adjusting active channels accordingly. 3 solution is generally applicable normal group depthwise-separable dilated convolutions fully-connected layers pooling layers has many building blocks neural networks. is also generally applicable different tasks including classification detection identification image restoration more. 4 practice is straightforward deploy mobiles existing runtime libraries. switching new configuration slimmable network becomes normal network run without additional runtime memory cost.However neural networks naturally run whole usually number channels cannot adjusted dynamically. Empirically training neural networks multiple switches has an extremely low testing accuracy around 0.1 1000-class ImageNet classification. conjecture is mainly due problem accumulating different number channels results different feature mean variance. discrepancy feature mean variance across different switches leads inaccurate statistics shared Batch Normalization layers BID20 important training stabilizer. end propose simple effective approach switchable batch normalization privatizes batch normalization different switches slimmable network. variables moving averaged means variances can independently accumulate feature statistics switch. Moreover Batch Normalization usually comes two additional learnable scale bias parameter ensure representation space BID20. two parameters may able act conditional parameters different switches since computation graph slimmable network depends width configuration. is noteworthy scale bias can be merged variables moving mean variance training thus default also use independent scale bias come free. Importantly batch normalization layers usually have negligible size less 1% model. BID10 BID53 BID22 BID16 implanted earlyexiting prediction branches reduce average execution depth. computation graph methods are conditioned network input lower theoretical computational complexity can be achieved.Conditional Normalization. Many real-world problems require conditional input. Feature-wise transformation BID7 is a prevalent approach integrate different sources information where conditional scales biases are applied across network. is commonly implemented form conditional normalization layers batch normalization layer normalization BID2. Conditional normalization is widely used tasks including style transfer BID6 BID25 BID18 BID26 image recognition BID24 BID45 has many others BID34 introduced slimmable networks permit instant adaptive accuracy-efficiency trade-offs runtime. Switchable batch normalization is proposed facilitate robust training slimmable networks. Compared individually trained models width configurations slimmable networks have similar better performances tasks classification object detection instance segmentation keypoints detection. proposed slimmable networks slimmable training could applied unsupervised learning reinforcement learning may help related fields network pruning model distillation.end mainly conduct COCO experiments based another detection framework:MMDetection which has hyper-parameter settings pytorch-style ResNet-50 hyper-parameter settings.e RCNN R50 FPN1 × fine-tune individual ResNet-50 models slimmable ResNet-50 tasks object detection instance segmentation. reproduced results ResNet-50 1.0× is consistent official models MMDetection keypoint detection task conduct experiment Detectron framework modifying caffe-style ResNet-50 pytorch-style training 4 GPUs without modification hyper-parameters have released code training testing pretrained models ImageNet classification task COCO detection tasks.",1654,1176,478,0.017,1.406,2025/11/05 17:19:09,0.01,1.277,0.2367601246105914,502.84
"Measuring visual (dis)similarity between two or more instances within a data distribution is a fundamental task in many applications, specially in image retrieval. Theoretically, non-metric distances are able to generate a more complex and accurate similarity model than metric distances, provided that the non-linear data distribution is precisely captured by the similarity model. In this work, we analyze a simple approach for deep learning networks to be used as an approximation of non-metric similarity functions and we study how these models generalize across different image retrieval datasets. For humans, deciding whether two images are visually similar or not is, to some extent, a natural task. However, in computer vision, this is a challenging problem and algorithms do not always succeed in matching pictures that contain similar-looking elements. This is mainly because of the well-known semantic gap problem, which refers to the difference or gap between low-level image pixels and high-level semantic concepts. Estimating visual similarity is a fundamental task that seeks to break this semantic gap by accurately evaluating how alike two or more pictures are. Visual similarity is crucial for many computer vision areas including image retrieval, image classification and object recognition, among others.Given a query image, content-based image retrieval systems rank pictures in a dataset according to how similar they are with respect to the input. This can be broken into two fundamental tasks: 1) computing meaningful image representations that capture the most salient visual information from pixels and 2) measuring accurate visual similarity between these image representations to rank images according to a similarity score.In the last years, several methods to represent visual information from raw pixels in images have been proposed, first by designing handcrafted features such as SIFT BID22 , then by compacting these local features into a single global image descriptor using different techniques such as Fisher Vectors BID28 and more recently by extracting deep image representations from neural networks BID1 ). However, once two images are described by feature vectors, visual similarity is commonly measured by computing a standard metric between them. Although regular distance metrics, such as Euclidean distance or cosine similarity, are fast and easy to implement, they do not take into account the possible interdependency within the dataset, which means that even if a strong nonlinear data dependency is occurring in the visual collection, they might not be able to capture it. This suggests that learning a similarity estimation directly from visual data can improve the performance on image retrieval tasks, provided that the likely nonlinearity dependencies within the dataset are precisely learned by the similarity function.Visual similarity learning is closely related to distance metric learning. Traditionally, distance metric learning algorithms were based on linear metrics such as the Mahalanobis distance. However, if the visual data presents any nonlinear interdependency, better results are expected when using nonlinear approaches. According to some studies BID41 , standard metric axioms are not valid for human perception of visual similarity and hence, visual similarity functions should not necessarily satisfy distance metric conditions. Deep learning-based similarity learning methods are mostly focused on learning an optimal mapping from pixels to a linear space in which Euclidean distance can be applied. Instead, we propose a simple approach based on neural networks to learn a non-metric similarity score in the feature space. Figure 1: System overview. The feature extraction block computes visual representations of images whereas the visual similarity block estimates a similarity score using a neural network. Figure 1 shows an overview of the proposed approach. By training a deep learning model, we can estimate a visual similarity function that outperforms methods based on standard metric computations. One convolutional neural network extracts image representations from input images, while a second neural network computes the visual similarity score. The visual similarity neural network is trained using both pairs of similar and dissimilar images in three stages. The output score of the similarity network can be directly applied as a similarity estimation to rank images in an image retrieval task. Experimental results on standard datasets show that our network is able to discriminate when a pair of images is similar or dissimilar and improve standard metrics score on top of that. Four different configurations A-D for the similarity neural network are proposed. We compare the performance of each one during Stage 1, when the network is trained with the standard cosine similarity measurement. If s l is the network score and y l is the cosine similarity of the l-th pair with l = 1.. L, we evaluate each network by computing the mean squared error, MSE, and the correlation coefficient, ρ, as: DISPLAYFORM0 where µ s and σ s are the mean and standard deviation of the vector of network scores s, and µ y and σ y are the mean and standard deviation of the vectors of cosine similarities y.Results are shown in TAB0 . Unsurprisingly, the configuration with bigger number of parameters, C, achieves the best MSE and ρ results, both in training and validation sets. However, the performance of networks B and D is very close to the performance of network C. As network B requires only 21 million parameters and network C requires 76 million parameters, we keep configuration B as our default architecture for the rest of the experiments. We have presented a method for learning visual similarity directly from visual data. Instead of using a rigid metric distance, such as the standard cosine similarity, we propose to train a neural network model to learn a similarity estimation between a pair of visual representations previously extracted from input images. Our method outperforms state-of-the-art approaches based on rigid distances in standard image retrieval collection of images and experimental results showed that learning a nonmetric visual similarity function is beneficial in image retrieval tasks provided that a small subset of images of the same domain are available during training. Standard image retrieval techniques that are commonly applied after cosine similarity computation, such as query expansion or image re-ranking, might also be applied on top of the similarity network. Finally, we end with an open question, which is the subject of planned future work, concerning efficient computation of exact or approximate K-nearest neighbours based on the learned network similarity function.","Measuring visual dis similarity two instances within data distribution is a fundamental task many applications specially image retrieval. Theoretically non-metric distances are able generate complex accurate similarity model metric distances provided non-linear data distribution is precisely captured similarity model. work analyze simple approach deep learning networks used approximation non-metric similarity functions study how these models generalize across different image retrieval datasets. humans deciding whether two images are visually similar is,extent natural task. However computer vision is a challenging problem algorithms do not always succeed matching pictures contain similar-looking elements. is mainly well-known semantic gap problem which refers difference gap low-level image pixels high-level semantic concepts. Estimating visual similarity is a fundamental task seeks break semantic gap accurately evaluating how alike two pictures are. Visual similarity is crucial many computer vision areas including image retrieval image classification object recognition among others.Given query image content-based image retrieval systems rank pictures dataset according how similar are with respect input. can be broken two fundamental tasks:1 computing meaningful image representations capture salient visual information pixels 2 measuring accurate visual similarity image representations rank images according similarity score.In last years several methods represent visual information raw pixels images have been proposed first designing handcrafted features SIFT BID22 compacting local features single global image descriptor using different techniques Fisher Vectors BID28 recently extracting deep image representations neural networks BID1 However two images are described feature vectors if the visual similarity is commonly measured computing standard metric them. Although regular distance metrics Euclidean distance cosine similarity are fast easy implement do not take account possible interdependency within dataset which means even if a strong nonlinear data dependency is occurring visual collection might able capture it. suggests learning similarity estimation directly visual data can improve performance image retrieval tasks provided likely nonlinearity dependencies within dataset are precisely learned similarity function.Visual similarity learning is closely related distance metric learning. Traditionally distance metric learning algorithms were based linear metrics Mahalanobis distance. However if the visual data presents nonlinear interdependency better results are expected when using nonlinear approaches. According studies BID41 standard metric axioms are not valid human perception visual similarity hence if the visual similarity functions should not necessarily satisfy distance metric conditions. Deep learning-based similarity learning methods are mostly focused learning optimal mapping pixels linear space which Euclidean distance can be applied. Instead propose simple approach based neural networks learn non-metric similarity score feature space. Figure1:System overview. feature extraction block computes visual representations images whereas visual similarity block estimates similarity score using neural network. Figure 1 shows overview proposed approach. training deep learning model can estimate visual similarity function outperforms methods based standard metric computations. One convolutional neural network extracts image representations input images second neural network computes visual similarity score. visual similarity neural network is trained using pairs similar dissimilar images three stages. output score similarity network can be directly applied similarity estimation rank images image retrieval task. Experimental results standard datasets show network is able discriminate when a pair images is similar dissimilar improve standard metrics score top that. Four different configurations A-D similarity neural network are proposed. compare performance one Stage1 when the network is trained standard cosine similarity measurement. Ifsl is the network score l is the cosine similarity l-th pair l 1..L evaluate network computing mean squared error MSE correlation coefficient ρ as:DISPLAYFORM0 whereµ σ are the mean standard deviation vector network scores µ σ are the mean standard deviation vectors cosine similarities y.Results are shown TAB0. Unsurprisingly configuration bigger number parameters C achieves best MSE ρ results training validation sets. However performance networksB is very close performance networkC. network B requires 21 million parameters network C requires76 million parameters keep configurationB default architecture rest experiments. have presented method learning visual similarity directly visual data. Instead using rigid metric distance standard cosine similarity propose train neural network model learn similarity estimation pair visual representations previously extracted input images. method outperforms state-of-the-art approaches based rigid distances standard image retrieval collection images experimental results showed learning nonmetric visual similarity function is beneficial image retrieval tasks provided small subset images domain are available training. Standard image retrieval techniques are commonly applied cosine similarity computation query expansion image re-ranking might also applied top similarity network. Finally end open question which is the subject planned future work concerning efficient computation exact approximate K-nearest neighbours based learned network similarity function.",1201,841,360,0.013,1.428,2025/11/05 17:19:09,0.01,1.446,0.3052959501557628,369.15
"Training a model to perform a task typically requires a large amount of data from the domains in which the task will be applied.
 However, it is often the case that data are abundant in some domains but scarce in others. Domain adaptation deals with the challenge of adapting a model trained from a data-rich source domain to perform well in a data-poor target domain. In general, this requires learning plausible mappings between domains. CycleGAN is a powerful framework that efficiently learns to map inputs from one domain to another using adversarial training and a cycle-consistency constraint. However, the conventional approach of enforcing cycle-consistency via reconstruction may be overly restrictive in cases where one or more domains have limited training data. In this paper, we propose an augmented cyclic adversarial learning model that enforces the cycle-consistency constraint via an external task specific model, which encourages the preservation of task-relevant content as opposed to exact reconstruction. We explore digit classification in a low-resource setting in supervised, semi and unsupervised situation, as well as high resource unsupervised. In low-resource supervised setting, the results show that our approach improves absolute performance by 14% and 4% when adapting SVHN to MNIST and vice versa, respectively, which outperforms unsupervised domain adaptation methods that require high-resource unlabeled target domain.   Moreover, using only few unsupervised target data, our approach can still outperforms many high-resource unsupervised models. Our model also outperforms on USPS to MNIST and synthetic digit to SVHN for high resource unsupervised adaptation. In speech domains, we similarly adopt a speech recognition model from each domain as the task specific model. Our approach improves absolute performance of speech recognition by 2% for female speakers in the TIMIT dataset, where the majority of training samples are from male voices. Domain adaptation BID18 BID36 BID1 aims to generalize a model from source domain to a target domain. Typically, the source domain has a large amount of training data, whereas the data are scarce in the target domain. This challenge is typically addressed by learning a mapping between domains, which allows data from the source domain to enrich the available data for training in the target domain. One way of learning such mappings is through Generative Adversarial Networks (GANs BID8 with cycle-consistency constraint (CycleGAN Zhu et al., 2017) , which enforces that mapping of an example from the source to the target and then back to the source domain would result in the same example (and vice versa for a target example). Due to this constraint, CycleGAN learns to preserve the 'content' 1 from the source domain while only transferring the 'style' to match the distribution of the target domain. This is a powerful constraint, and various works BID37 BID12 have demonstrated its effectiveness in learning cross domain mappings.Enforcing cycle-consistency is appealing as a technique for preserving semantic information of the data with respect to a task, but implementing it through reconstruction may be too restrictive when data are imbalanced across domains. This is because the reconstruction error encourages exact match of samples from the reverse mapping, which may in turn encourage the forward-mapping to keep the sample close to the original domain. Normally, the adversarial objectives would counter this effect; however, when data from the target domain are scarce, it is very difficult to learn a powerful discriminator that can capture meaningful properties of the target distribution. Therefore, the resulting mappings learned is likely to be sub-optimal. Importantly, for the learned mapping to be meaningful, it is not necessary to have the exact reconstruction. As long as the 'semantic' information is preserved and the 'style' matches the corresponding distribution, it would be a valid mapping.To address this issue, we propose an augmented cyclic adversarial learning model (ACAL) for domain adaptation. In particular, we replace the reconstruction objective with a task specific model. The model learns to preserve the 'semantic' information from the data samples in a particular domain by minimizing the loss of the mapped samples for the task specific model. On the other hand, the task specific model also serves as an additional source of information for the corresponding domain and hence supplements the discriminator in that domain to facilitate better modeling of the distribution. The task specific model can also be viewed as an implicit way of disentangling the information essential to the task from the 'style' information that relates to the data distribution of different domain. We show that our approach improves the performance by 40% as compared to the baseline on digit domain adaptation. We improve the phoneme error rate by ∼ 5% on TIMIT dataset, when adapting the model trained on one speech from one gender to the other. In this paper, we propose to use augmented cycle-consistency adversarial learning for domain adaptation and introduce a task specific model to facilitate learning domain related mappings. We enforce cycle-consistency using a task specific loss instead of the conventional reconstruction objective. Additionally, we use the task specific model as an additional source of information for the discriminator in the corresponding domain. We demonstrate the effectiveness of our proposed approach by evaluating on two domain adaptation tasks, and in both cases we achieve significant performance improvement as compared to the baseline.By extending the definition of task-specific model to unsupervised learning, such as reconstruction loss using autoencoder, or self-supervision, our proposed method would work on all settings of domain adaptation. Such unsupervised task can be speech modeling using wavenet BID35 , or language modeling using recurrent or transformer networks BID27 .",Training model perform task typically requires large amount data domains which the task will be applied. However is often case data are abundant domains scarce others. Domain adaptation deals challenge adapting model trained data-rich source domain perform well data-poor target domain. general requires learning plausible mappings domains. CycleGAN is a powerful framework efficiently learns map inputs one domain another using adversarial training cycle-consistency constraint. However conventional approach enforcing cycle-consistency via reconstruction may overly restrictive cases where one domains have limited training data. paper propose augmented cyclic adversarial learning model enforces cycle-consistency constraint via external task specific model which encourages preservation task-relevant content opposed have the exact reconstruction. explore digit classification low-resource setting supervised semi unsupervised situation well high resource unsupervised. low-resource supervised setting results show approach improves absolute performance 14% 4% when adapting SVHN MNIST vice versa respectively which outperforms unsupervised domain adaptation methods require high-resource unlabeled target domain. Moreover using unsupervised target data approach can still outperforms many high-resource unsupervised models. model also outperforms USPS MNIST synthetic digit SVHN high resource unsupervised adaptation. speech domains similarly adopt speech recognition model domain task specific model. approach improves absolute performance speech recognition 2% female speakers TIMIT dataset where the majority training samples are from male voices. Domain adaptation BID18 BID36 BID1 aims generalize model source domain target domain. Typically source domain has a large amount training data whereas data are scarce target domain. challenge is typically addressed learning mapping domains which allows data source domain enrich available data training target domain. One way learning mappings is through Generative Adversarial Networks GANs BID8 cycle-consistency constraint CycleGAN Zhuetal. 2017 which enforces mapping example source target back source domain would result example vice versa target example Due constraint CycleGAN learns preserve 'content'1 source domain transferring 'style' match distribution target domain. is a powerful constraint various works BID37 BID12 have demonstrated effectiveness learning cross domain mappings.Enforcing cycle-consistency is appealing technique preserving semantic information data respect task implementing reconstruction may restrictive when data are imbalanced across domains. is because the reconstruction error encourages exact match samples reverse mapping may turn encourage forward-mapping keep sample close original domain. Normally adversarial objectives would counter effect;however when data target domain are scarce is very difficult learn powerful discriminator can capture meaningful properties target distribution. Therefore resulting mappings learned is likely sub-optimal Importantly learned mapping meaningful is not necessary have the exact reconstruction. long 'semantic' information is preserved 'style' matches corresponding distribution would valid mapping.To address issue propose augmented cyclic adversarial learning model ACAL domain adaptation. particular replace reconstruction objective task specific model. model learns preserve 'semantic' information data samples particular domain minimizing loss mapped samples task specific model. hand task specific model also serves additional source information corresponding domain hence supplements discriminator domain facilitate better modeling distribution. task specific model can also viewed implicit way disentangling information essential task 'style' information relates data distribution different domain. show approach improves performance 40% compared baseline digit domain adaptation. improve phoneme error rate ∼5% TIMIT dataset when adapting model trained one speech one gender other. paper propose use augmented cycle-consistency adversarial learning domain adaptation introduce task specific model facilitate learning domain related mappings. enforce cycle-consistency using task specific loss instead conventional reconstruction objective. Additionally use task specific model additional source information discriminator corresponding domain. demonstrate effectiveness proposed approach evaluating two domain adaptation tasks cases achieve significant performance improvement compared baseline.By extending definition task-specific model unsupervised learning reconstruction loss using autoencoder self-supervision proposed method would work settings domain adaptation. unsupervised task can be speech modeling using wavenet BID35 language modeling using recurrent transformer networks BID27.,1116,750,366,0.011,1.488,2025/11/05 17:19:09,0.01,1.4,0.4922118380062303,341.205
"Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can also be used to inform machine learning on graphs. However, learning structural representations of nodes is a challenging unsupervised-learning task, which typically involves manually specifying and tailoring topological features for each node. Here we develop GraphWave, a method that represents each node’s local network neighborhood via a low-dimensional embedding by leveraging spectral graph wavelet diffusion patterns. We prove that nodes with similar local network neighborhoods will have similar GraphWave embeddings even though these nodes may reside in very different parts of the network. Our method scales linearly with the number of edges and does not require any hand-tailoring of topological features. We evaluate performance on both synthetic and real-world datasets, obtaining improvements of up to 71% over state-of-the-art baselines. Structural role discovery in graphs focuses on identifying nodes which have topologically similar local neighborhoods (i.e., similar local structural roles) while residing in potentially distant areas of the network FIG0 ). Such alternative definition of node similarity is very different than more traditional notions BID21 BID7 BID30 BID19 BID15 BID8 BID6 , which all assume some notion of ""smoothness"" over the graph and thus consider nodes residing in close network proximity to be similar. Such structural role information about the nodes can be used for a variety of tasks, including as input to machine learning problems, or even to identify key nodes in a system (principal ""influencers"" in a social network, critical hubs in contagion graphs, etc.).When structural roles of nodes are defined over a discrete space, they correspond to different topologies of local network neighborhoods (e.g., edge of a chain, center of a star, a bridge between two clusters). However , such discrete roles must be pre-defined, requiring domain expertise and manual inspection of the graph structure. A more powerful and robust method for identifying structural similarity involves learning a continuous vector-valued structural signature χ a of each node a in an unsupervised way. This motivates a natural definition of structural similarity in terms of closeness of topological signatures: For any > 0, nodes a and b are defined to be -structurally similar with respect to a given distance if: dist(χ a , χ b ) ≤ . Thus, a robust structural similarity metric must introduce both an appropriate signature and an adequate distance metric.While several methods have been proposed for structural role discovery in graphs, existing approaches are extremely sensitive to small perturbations in the topology and typically lack one or more desirable properties. They often require manually hand-labeling topological features BID12 , rely on non-scalable heuristics BID22 , and/or return a single similarity score instead of a multidimensional structural signature BID13 .Here we address the problem of structure learning on graphs by developing GRAPHWAVE. Building upon techniques from graph signal processing BID4 BID10 BID26 , our approach learns a structural embedding for each node based on the diffusion of a spectral graph wavelet centered at that node. Intuitively, each node propagates a unit of energy over the graph and characterizes its neighboring topology based on the response of the network to While raw spectral graph wavelet signatures/coefficients Ψ of a and b might be very different, we treat them as probability distributions and show that the coefficient distributions are indeed similar.this probe. In contrast to prior work that characterizes the wavelet diffusion as a function of the wavelet scaling parameter, we study how the wavelet diffuses through the network at a given scale as a function of the initial source node. We prove that the coefficients of this wavelet directly relate to graph topological properties. Hence, these coefficients contain all the necessary information to recover structurally similar nodes, without requiring the hand-labeling of features. However, the wavelets are, by design, localized on the graph. Therefore to compare structural signatures for nodes that are far away from each other, typical graph signal processing methods (using metrics like correlation between wavelets or 2 distance) cannot be used without specifying an exact one-to-one mapping between nodes for every pairwise comparison, a computationally intractable task.To overcome this challenge, we propose a novel way of treating the wavelets as probability distributions over the graph. This way the structural information is contained in how the diffusion spreads over the network rather than where it spreads. In order to provide vector-valued signatures which can then be used as input to any machine learning algorithm, we embed these wavelet distributions using the empirical characteristic function BID18 . The advantage of empirical characteristic functions is that they capture all the moments of a given distribution. This allows GRAPHWAVE to be robust to small perturbations in the local edge structure, as we prove mathematically. Computational complexity of GRAPHWAVE is linear in the number of edges, thus allowing it to scale to large (sparse) networks. Finally, we compare GRAPHWAVE to several state-of-the-art baselines on both real and synthetic datasets, obtaining improvements of up to 71% and demonstrating how our approach is a useful tool for characterizing structural signatures in graphs.Summary of contributions. The main contributions of our paper are as follows:• We develop a novel use of spectral graph wavelets by treating them as probability distributions and characterizing the distributions using empirical characteristic functions.• We leverage these insights to develop a scalable method (GRAPHWAVE) for learning node embeddings based on structural similarity in graphs.• We prove that GRAPHWAVE accurately recovers structurally similar nodes.Further related work. Prior work on discovering nodes with similar structural roles has typically relied on explicit featurization of nodes. These methods generate an exhaustive listing of each node's local topological properties (e.g., node degree, number of triangles it participates in, number of k-cliques, its PageRank score) before computing node similarities based on such heuristic representations. A notable example of such approaches is RolX BID12 , which aims to recover a soft-clustering of nodes into a predetermined number of K distinct roles using recursive feature extraction BID11 . Similarly, struc2vec BID22 uses a heuristic to construct a multilayered graph based on topological metrics and simulates random walks on the graph to capture structural information. In contrast, our approach does not rely on heuristics (we mathematically prove its efficacy) and does not require explicit manual feature engineering or hand-tuning of parameters.Another line of related work are graph diffusion kernels BID4 which have been utilized for various graph modeling purposes BID17 BID2 BID24 BID29 . However, to the best of our knowledge, our paper is the first to apply graph diffusion kernels for determining structural roles in graphs. Kernels have been shown to efficiently capture geometrical properties and have been successfully used for shape detection in the image processing community BID28 BID20 BID0 . However, in contrast to shape-matching problems, GRAPHWAVE considers these kernels as probability distributions over real-world graphs. This is because the graphs that we consider are highly irregular (as opposed to the Euclidean and manifold graphs ). Therefore, traditional wavelet methods, which typically analyze node diffusions across specific nodes that occur in regular and predictable patterns, do not apply. Instead, by treating wavelets as distributions, GRAPHWAVE characterizes the shape of the diffusion, rather than the specific nodes where the diffusion occurs. This key insight allows us to uncover structural signatures and to discover structurally similar nodes. We have developed a new method for learning structural signatures in graphs. Our approach, GRAPHWAVE, uses spectral graph wavelets to generate a structural embedding for each node, which we accomplish by treating the wavelets as a distributions and evaluating the resulting characteristic functions. Considering the wavelets as distributions instead of vectors is a key insight needed to capture structural similarity in graphs.Our method provides mathematical guarantees on the optimality of learned structural signatures. Using spectral graph theory, we prove that structurally equivalent/similar nodes have nearidentical/similar structural signatures in GRAPHWAVE. Experiments on real and synthetic networks provide empirical evidence for our analytical results and yield large gains in performance over stateof-the-art baselines. For future work, these signatures could be used for transfer learning, leveraging data from a well-explored region of the graph to infer knowledge about less-explored regions.","Nodes residing different parts graph can have similar structural roles within local network topology. identification roles provides key insight organization networks can also used inform machine learning graphs. However learning structural representations nodes is a challenging unsupervised-learning task which typically involves manually specifying tailoring topological features node. develop GraphWave method represents nodes local network neighborhood via low-dimensional embedding leveraging spectral graph wavelet diffusion patterns. prove nodes similar local network neighborhoods will have similar GraphWave embeddings even though nodes may reside different parts network. method scales linearly number edges does not require hand-tailoring topological features. evaluate performance synthetic real-world datasets obtaining improvements 71% state-of-the-art baselines. Structural role discovery graphs focuses identifying nodes which have topologically similar local neighborhoods.e similar local structural roles residing potentially distant areas network FIG0 alternative definition node similarity is very different traditional notions BID21 BID7 BID30 BID19 BID15 BID8 BID6 which all assume notion smoothness graph thus consider nodes residing close network proximity similar. structural role information nodes can be used variety tasks including input machine learning problems even identify key nodes system principal influencers social network critical hubs contagion graphs etc. .When structural roles nodes are defined discrete space correspond different topologies local network neighborhoods e.g edge chain center star bridge two clusters However discrete roles must pre-defined requiring domain expertise manual inspection graph structure. powerful robust method identifying structural similarity involves learning continuous vector-valued structural signature χ node unsupervised way. motivates natural definition structural similarity terms closeness topological signatures:0 nodes b are defined -structurally similar respect given distance if:dist χ χb ≤ Thus robust structural similarity metric must introduce appropriate signature adequate distance metric.While several methods have been proposed structural role discovery graphs existing approaches are extremely sensitive small perturbations topology typically lack one desirable properties. often require manually hand-labeling topological features BID12 rely non-scalable heuristics BID22/return single similarity score instead multidimensional structural signature BID13.Here address problem structure learning graphs developing GRAPHWAVE. Building upon techniques graph signal processing BID4 BID10 BID26 approach learns structural embedding node based diffusion spectral graph wavelet centered node. Intuitively node propagates unit energy graph characterizes neighboring topology based response network raw spectral graph wavelet signatures/coefficientsΨ b might different treat probability distributions show coefficient distributions are indeed similar.this probe. contrast prior work characterizes wavelet diffusion function wavelet scaling parameter study how the wavelet diffuses network given scale function initial source node. prove coefficients wavelet directly relate graph topological properties. Hence coefficients contain necessary information recover structurally similar nodes without requiring hand-labeling features. However wavelets are,by design localized graph. Therefore compare structural signatures nodes are far away typical graph signal processing methods using metrics like correlation wavelets 2 distance cannot used without specifying exact one-to-one mapping nodes every pairwise comparison computationally intractable task.To overcome challenge propose novel way treating wavelets probability distributions graph. way structural information is contained how the diffusion spreads network rather where it spreads. order provide vector-valued signatures which can then be used input machine learning algorithm embed wavelet distributions using empirical characteristic function BID18. advantage empirical characteristic functions is that they capture moments given distribution. allows GRAPHWAVE robust small perturbations local edge structure prove mathematically. Computational complexity GRAPHWAVE is linear number edges thus allowing scale large sparse networks. Finally compare GRAPHWAVE several state-of-the-art baselines real synthetic datasets obtaining improvements 71% demonstrating how our approach is a useful tool characterizing structural signatures graphs.Summary contributions. main contributions paper are as follows:• develop novel use spectral graph wavelets treating probability distributions characterizing distributions using empirical characteristic functions.• leverage insights develop scalable method GRAPHWAVE learning node embeddings based structural similarity graphs.• prove GRAPHWAVE accurately recovers structurally similar nodes.Further related work. Prior work discovering nodes similar structural roles has typically relied explicit featurization nodes. methods generate exhaustive listing node's local topological properties e.g node degree number triangles participates number k-cliques PageRank score computing node similarities based heuristic representations. notable example approaches is RolX BID12 which aims recover soft-clustering nodes predetermined number K distinct roles using recursive feature extraction BID11. Similarly struc2vec BID22 uses heuristic construct multilayered graph based topological metrics simulates random walks graph capture structural information. contrast approach does not rely heuristics mathematically prove efficacy does not require explicit manual feature engineering hand-tuning parameters.Another line related work are graph diffusion kernels BID4 which have been utilized various graph modeling purposes BID17 BID2 BID24 BID29. However best knowledge paper is the first apply graph diffusion kernels determining structural roles graphs. Kernels have been shown efficiently capture geometrical properties have been successfully used shape detection image processing community BID28 BID20 BID0. However contrast shape-matching problems GRAPHWAVE considers kernels probability distributions real-world graphs. is because the graphs consider are highly irregular opposed Euclidean manifold graphs Therefore traditional wavelet methods which typically analyze node diffusions across specific nodes occur regular predictable patterns do not apply. Instead treating wavelets distributions GRAPHWAVE characterizes shape diffusion rather specific nodes where the diffusion occurs. key insight allowsus uncover structural signatures discover structurally similar nodes. have developed new method learning structural signatures graphs. approach GRAPHWAVE uses spectral graph wavelets generate structural embedding node which we accomplish treating wavelets distributions evaluating resulting characteristic functions. Considering wavelets distributions instead vectors is a key insight needed capture structural similarity graphs.Our method provides mathematical guarantees optimality learned structural signatures. Using spectral graph theory prove structurally equivalent/similar nodes have nearidentical/similar structural signatures GRAPHWAVE. Experiments real synthetic networks provide empirical evidence analytical results yield large gains performance stateof-the-art baselines. future work signatures could used transfer learning leveraging data well-explored region graph infer knowledge less-explored regions.",1694,1172,522,0.019,1.445,2025/11/05 17:19:09,0.01,1.795,0.3582554517133957,514.64
"Driving simulators play an important role in vehicle research. However, existing virtual reality simulators do not give users a true sense of presence. UniNet is our driving simulator, designed to allow users to interact with and visualize simulated traffic in mixed reality. It is powered by SUMO and Unity. UniNet's modular architecture allows us to investigate interdisciplinary research topics such as vehicular ad-hoc networks, human-computer interaction, and traffic management. We accomplish this by giving users the ability to observe and interact with simulated traffic in a high fidelity driving simulator. We present a user study that subjectively measures user's sense of presence in UniNet. Our findings suggest that our novel mixed reality system does increase this sensation. Many driving simulators have been developed, with most of them being used for driver training or research in the field of driver safety [44] . However, these simulators often present limited features in regards to traffic simulation, and user presence [11, 25, 26] . The need for high-quality Virtual Reality (VR) driving simulators with a focus on user presence is long overdue. In addition to this, a driving simulator with traffic simulation is a strong tool for Vehicular Ad-Hoc Network (VANET) research, which is made possible by our choice of traffic generation software. Network simulation is commonly used in networking research, to evaluate the performance of communication protocols and algorithms. Existing simulation tools for vehicular networks focus exclusively on network simulation. A driving simulator that combines network simulation, application prototyping, and testing would be beneficial Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. to VANET researchers. For instance, one could evaluate the performance of a communication protocol or application by using a realistic virtual environment with thousands of vehicles and interacting with them before deploying their research in the real world, which is costly, and at times, unsafe. In addition to a modular simulator with VANET capabilities, we introduce a system for Mixed Reality (MR). Our system introduces the user as their own avatar in a virtual environment, by using stereoscopic cameras and passthrough VR technology. We designed the system to be compatible with existing VR systems, and most VR systems can easily upgrade to our proposed immersion configuration. In this paper, we describe UniNet -a driving simulator that combines realistic vehicle dynamics [42] with a high performance traffic flow simulation platform Simulation of Urban MObility (SUMO) [27] . We discuss the systems we have built within Unity [40] , which connect external applications for a high quality driving experience. In our user study, we followed a within-subjects experimental design, to test if UniNet's MR immersion system improved the user's sense of presence in the virtual environment. We are able to show that the MR configuration is more immersive, however the results are primarily subjective, and come from the questionnaires we chose to include in our study. Our study produced two types of results for each participant. Subjective results, and behavioural results based on reactions to vehicle collision events. Our analysis of the subjective results supported our hypothesis, however we could not draw any conclusions from the behavioural results. Insko writes that, due to presence being a subjective sensation, subjective means of measuring presence have become the most popular [20] . Therefore our inability to corroborate the results from our questionnaires with the behavioural measurements taken, does not disprove our hypothesis. The in-simulator portion of the study contained four trials, designed to compare four configurations of UniNet, and instigate visceral reactions which we measured as reaction times. The reason we chose to compare four configurations, was to compare common existing options for VR simulations, and a non-VR control with our technology. In summary, here is a brief description of why we chose these four immersion configurations. As the market for VR continues to grow, the development of MR technology should grow with it. The reality-virtuality continuum is defined by the mixed-reality area between reality and virtuality, and UniNet was designed to fit within this range. This thesis focused on the effect of user presence in a MR driving simulator, and the construction of a physical product. The user study investigated the effect of our MR immersion configuration, on user presence. The user study hypothesized that our MR configuration would increase the user's sense of presence in the virtual environment, when compared to traditional VR and non-VR configurations. Participants were presented with four trials to complete in UniNet, and each trial finished with a vehicle collision event to create a behavioural response from participants. The subjective results were significant, and in favor of our study's hypothesis. Prior to the study, we designed and tested the hardware and software for UniNet. Unity and SUMO are the primary systems controlling player vehicles and NPC vehicles respectively. Our technology is built to work with the Oculus Rift, using commercially available stereoscopic cameras mounted to the front face of the HMD. Our software creates a passthrough VR experience with this hardware configuration. When combined with the green screen chamber constructed for UniNet, our technology fits on the reality-virtuality continuum as a unique mixed reality experience.",Driving simulators play important role vehicle research. However existing virtual reality simulators do not give users true sense presence. UniNet is our driving simulator designed allow users interact visualize simulated traffic mixed reality. is powered SUMO Unity. UniNet's modular architecture allows us investigate interdisciplinary research topics vehicular ad-hoc networks human-computer interaction traffic management. accomplish giving users ability observe interact simulated traffic high fidelity driving simulator. present user study subjectively measures user's sense presence UniNet. findings suggest novel mixed reality system does increase sensation. Many driving simulators have been developed used driver training research field driver safety 44 However simulators often present limited features regards traffic simulation user presence 11 25 26 need high-quality Virtual Reality VR driving simulators focus user presence is long overdue. addition driving simulator traffic simulation is a strong tool Vehicular Ad-Hoc Network VANET research which is made possible choice traffic generation software. Network simulation is commonly used networking research evaluate performance communication protocols algorithms. Existing simulation tools vehicular networks focus exclusively network simulation. driving simulator combines network simulation application prototyping testing would beneficial Permission make digital hard copies part work personal classroom use is granted without fee provided copies are not made distributed profit commercial advantage copies bear notice full citation first page. Copyrights components work owned others author must honored. Abstracting credit is permitted. copy otherwise republish post servers redistribute lists requires prior specific permission/fee. Request permissions permissions@acm.org. VANET researchers. instance one could evaluate performance communication protocol application using realistic virtual environment thousands vehicles interacting deploying research real world which is costly times unsafe. addition modular simulator VANET capabilities introduce system Mixed Reality MR system introduces user avatar virtual environment using stereoscopic cameras passthrough VR technology. designed system compatible existing VR systems VR systems can easily upgrade proposed immersion configuration. paper describe UniNet -a driving simulator combines realistic vehicle dynamics 42 high performance traffic flow simulation platform Simulation Urban MObility SUMO 27 discuss systems have built within Unity 40 which connect external applications high quality driving experience. user study followed within-subjects experimental design test if UniNet's MR immersion system improved user's sense presence virtual environment. are able show MR configuration is more immersive however results are primarily subjective come questionnaires chose include study. study produced two types results participant. Subjective results behavioural results based reactions vehicle collision events. analysis subjective results supported hypothesis however could draw conclusions behavioural results. Insko writes due presence subjective sensation subjective means measuring presence have become popular 20 Therefore inability corroborate results questionnaires behavioural measurements taken does not disprove hypothesis. in-simulator portion study contained four trials designed compare four configurations UniNet instigate visceral reactions which we measured reaction times. reason chose compare four configurations was to compare common existing options VR simulations non-VR control technology. summary is a brief description why we chose four immersion configurations. market VR continues grow development MR technology should grow it. reality-virtuality continuum is defined mixed-reality area reality virtuality UniNet was designed fit within range. thesis focused effect user presence MR driving simulator construction physical product. user study investigated effect MR immersion configuration user presence. user study hypothesized MR configuration would increase user's sense presence virtual environment when compared traditionalVR non-VR configurations. Participants were presented four trials complete UniNet trial finished vehicle collision event create behavioural response participants. subjective results were significant favor study's hypothesis. Prior study designed tested hardware software UniNet. Unity SUMO are the primary systems controlling player vehicles NPC vehicles respectively. technology is built work Oculus Rift using commercially available stereoscopic cameras mounted front face HMD. software creates passthrough VR experience hardware configuration. When combined green screen chamber constructed UniNet technology fits reality-virtuality continuum unique mixed reality experience.,1129,737,392,0.013,1.532,2025/11/05 17:19:09,0.01,1.4,0.6292834890965732,354.06
"We consider the problem of improving kernel approximation via feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. We propose to use more efficient numerical integration technique to obtain better estimates of the integrals compared to the state-of-the-art methods. Our approach allows to use information about the integrand to enhance approximation and facilitates fast computations. We derive the convergence behavior and conduct an extensive empirical study that supports our hypothesis. Kernel methods proved to be an efficient technique in numerous real-world problems. The core idea of kernel methods is the kernel trick -compute an inner product in a high-dimensional (or even infinite-dimensional) feature space by means of a kernel function k:k(x, y) = ψ(x ), ψ(y ) ,where ψ : X → F is a non-linear feature map transporting elements of input space X into a feature space F. It is a common knowledge that kernel methods incur space and time complexity infeasible to be used with large-scale datasets directly. For example, kernel regression has O(N 3 + N d 2 ) training time, O(N 2 ) memory, O(N d) prediction time complexity for N data points in original d-dimensional space X . One of the most successful techniques to handle this problem BID18 ) introduces a low-dimensional randomized approximation to feature maps: DISPLAYFORM0 This is essentially carried out by using Monte-Carlo sampling to approximate scalar product in (1). A randomized D-dimensional mappingΨ(·) applied to the original data input allows employing standard linear methods, i.e. reverting the kernel trick. In doing so one reduces the complexity to that of linear methods, e.g. D-dimensional approximation admits O(N D 2 ) training time, O(N D) memory and O(N ) prediction time.It is well known that as D → ∞, the inner product in (2) converges to exact kernel k(x, y). Recent research BID22 ; BID9 ; BID4 ) aims to improve the convergence of approximation so that a smaller D can be used to obtain the same quality of approximation.This paper considers kernels that allow the following integral representation k(x, y) = E q(w) g xy (w) ≈ E p(w) f xy (w) = I(f xy ), p(w ) = 1 (2π) d/2 e − w 2 2 ,where q(w) is a density associated with a kernel, e.g. the popular Gaussian kernel has q(w) = p(w), so the exact equality holds with g xy (w) = f xy (w) = φ(w x) φ(w y), where φ(·) = [cos (·), sin( ·)] .The class of kernels admitting the form in (3) covers shift-invariant kernels (e.g. radial basis function (RBF) kernels) and Pointwise Nonlinear Gaussian (PNG) kernels. They are widely used in practice and have interesting connections with neural networks BID3 BID21 ).The main challenge for the construction of low-dimensional feature maps is the approximation of the expectation in (3) which is d-dimensional integral with Gaussian weight. While standard MonteCarlo rule is easy to implement, there are better quadrature rules for such kind of integrals. For example, BID22 apply quasi-Monte Carlo (QMC) rules and obtain better quality kernel matrix approximations compared to random Fourier features of BID18 .Unlike other research studies we refrain from using simple Monte Carlo estimate of the integral, instead, we propose to use specific quadrature rules. We now list our contributions:1. We propose to use advanced quadrature rules to improve kernel approximation accuracy. We also provide an analytical estimate of the error for the used quadrature rules. 2. We note that for kernels with specific integrand f xy (w) in (3) one can improve on its properties. For example , for kernels with even function f xy (w) we derive the reduced quadrature rule which gives twice smaller embedded dimension D with the same accuracy. This applies, for example, to any RBF kernel. 3. We use structured orthogonal matrices (so-called butterfly matrices ) when designing quadrature rule that allow fast matrix by vector multiplications. As a result, we speed up the approximation of the kernel function and reduce memory requirements. 4. We demonstrate our approach on a set of regression and classification problems. Empirical results show that the proposed approach has a better quality of approximation of kernel function as well as better quality of classification and regression when using different kernels. In this work we proposed to apply advanced integration rule that allowed us to achieve higher quality of kernel approximation. Our derivation of the variance of the error implies the dependence of the error on the scale of data, which in case of Gaussian kernel can be interpreted as width of the kernel. However, as we have seen earlier, accuracy on the final task has no direct dependence on the approximation quality, so we can only speculate whether better approximated wide kernels deliver better accuracy compared to the poorer approximated narrow ones. It is interesting to explore this connection in the future work.To speed up the computations we employed butterfly orthogonal matrices yielding the computational complexity O(d log d). Although the procedure we used to generate butterfly matrices claims to produce uniformly random orthogonal matrices, we found that it is not always so. However, the comparison of the method H (uses properly distributed orthogonal matrices) with method B (sometimes fails to do so) did not reveal any differences. We also leave it for the future investigation.Our experimental study confirms that for many kernels on the most datasets the proposed approach delivers better kernel approximation. Additionally, the empirical results showed that the quality of the final task (classification/regression) is also higher than the state-of-the-art baselines. The connection between the final score and the kernel approximation error is to be explored as well.",consider problem improving kernel approximation via feature maps. maps arise Monte Carlo approximation integral representations kernel functions scale kernel methods larger datasets. propose use efficient numerical integration technique obtain better estimates integrals compared state-of-the-art methods. approach allows use information integrand enhance approximation facilitates fast computations. derive convergence behavior conduct extensive empirical study supports hypothesis. Kernel methods proved efficient technique numerous real-world problems. core idea kernel methods is the kernel trick -compute inner product high-dimensional even infinite-dimensional feature space means kernel functionk:k x ψ x ψ where ψ:X→F is a non-linear feature map transporting elements input spaceX feature spaceF. is a common knowledge kernel methods incur space time complexity infeasible used large-scale datasets directly. example kernel regression hasO(N3+N 2 training time N2 memory N prediction time complexity N data points original d-dimensional spaceX. One successful techniques handle problem BID18 introduces low-dimensional randomized approximation feature maps:DISPLAYFORM0 is essentially carried using Monte-Carlo sampling approximate scalar product 1 randomized D-dimensional mappingΨ · applied original data input allows employing standard linear methods.e reverting kernel trick. one reduces complexity linear methods e.g D-dimensional approximation admits N 2 training time N memory N prediction time.It is well known →∞ inner product 2 converges exact kernelk x Recent research BID22;BID9;BID4 aims improve convergence approximation smaller can be used obtain quality approximation.This paper considers kernels allow following integral representationk x Eq w gxy w ≈Ep w fxy w fxy p w 1 2π/2e− w22 whereq w is a density associated kernel e.g popular Gaussian kernel hasq w p w exact equality holds gxy w fxy w φ wx φ w whereφ · cos · sin · .The class kernels admitting form 3 covers shift-invariant kernels e.g radial basis function RBF kernels Pointwise Nonlinear Gaussian PNG kernels. are widely used practice have interesting connections neural networks BID3 BID21.The main challenge construction low-dimensional feature maps is the approximation expectation 3 which is d-dimensional integral Gaussian weight. standard MonteCarlo rule is easy implement are better quadrature rules kind integrals. example BID22 apply quasi-Monte Carlo QMC rules obtain better quality kernel matrix approximations compared random Fourier features BID18.Unlike research studies refrain using simple Monte Carlo estimate integral instead propose use specific quadrature rules. list contributions:1 propose use advanced quadrature rules improve kernel approximation accuracy. also provide analytical estimate error used quadrature rules. 2. note kernels specific integrandfxy w 3 one can improve properties. example kernels even functionfxy w derive reduced quadrature rule which gives twice smaller embedded dimension accuracy. applies example RBF kernel. 3. use structured orthogonal matrices so-called butterfly matrices when designing quadrature rule allow fast matrix vector multiplications. result speed approximation kernel function reduce memory requirements. 4. demonstrate approach set regression classification problems. Empirical results show proposed approach has a better quality approximation kernel function well better quality classification regression when using different kernels. work proposed apply advanced integration rule allowedus achieve higher quality kernel approximation. derivation variance error implies dependence error scale data which in case Gaussian kernel can be interpreted width kernel. However have seen earlier accuracy final task has no direct dependence approximation quality can speculate whether better approximated wide kernels deliver better accuracy compared poorer approximated narrow ones. is interesting explore connection future work.To speed computations employed butterfly orthogonal matrices yielding computational complexity log Although procedure used generate butterfly matrices claims produce uniformly random orthogonal matrices found is not always so. However comparison methodH uses properly distributed orthogonal matrices methodB sometimes fails doso)did not reveal differences. also leave future investigation.Our experimental study confirms many kernels datasets proposed approach delivers better kernel approximation. Additionally empirical results showed quality final task classification/regression is also higher state-of-the-art baselines. connection final score kernel approximation error is to be explored well.,1196,787,409,0.015,1.52,2025/11/05 17:19:09,0.01,1.559,0.5919003115264797,374.665
"Human world knowledge is both structured and flexible. When people see an object, they represent it not as a pixel array but as a meaningful arrangement of semantic parts. Moreover, when people refer to an object, they provide descriptions that are not merely true but also relevant in the current context. Here, we combine these two observations in order to learn fine-grained correspondences between language and contextually relevant geometric properties of 3D objects. To do this, we employed an interactive communication task with human participants to construct a large dataset containing natural utterances referring to 3D objects from ShapeNet in a wide variety of contexts. Using this dataset, we developed neural listener and speaker models with strong capacity for generalization. By performing targeted lesions of visual and linguistic input, we discovered that the neural listener depends heavily on part-related words and associates these words correctly with the corresponding geometric properties of objects, suggesting that it has learned task-relevant structure linking the two input modalities. We further show that a neural speaker that is `listener-aware' --- that plans its utterances according to how an imagined listener would interpret its words in context --- produces more discriminative referring expressions than an `listener-unaware' speaker, as measured by human performance in identifying the correct object. Human world knowledge is both structured and flexible. For example, when people see a chair, they represent it not as a pixel array but as a semantically meaningful combination of parts, such as arms, legs, seat, and back. How to obtain and flexibly deploy such structured knowledge remains an outstanding problem in machine learning (Lake et al., 2017) . One promising approach is to harness the rich conceptual and relational structure latent in language (Andreas et al., 2017) . Natural languages have been optimized across human history to solve the problem of efficiently communicating those aspects of the world most relevant to current goals (Kirby et al., 2015; Gibson et al., 2017) . Consequently, language reflects the structured nature of our world knowledge: we not only conceive of a chair in terms of its semantic parts, but can combine multiple words to refer to its 'curved back' or 'cushioned seat', and provide more informative descriptions if the context requires it, e.g., refer to a different distinguishing part if all the chairs have a cushioned seat.Our goal is to leverage these insights to develop systems that can make fine-grained distinctions between complex object geometries across a wide variety of contexts. Our approach is to leverage natural language produced by people in an interactive communication task to develop neural network models of the speaker and listener roles in this task. We find that the resulting representations learned by these models exhibit structure that is crucial for robust communication: first, they capture taskrelevant correspondences between individual parts of objects and individual tokens of language, and second, they have strong capacity to generalize to novel contexts, objects, utterances, and other related object classes.We make the following contributions:close context far context Figure 1 : Constructing ""close"" and ""far"" contexts by exploiting the latent neighborhood structure of 3D chairs. Orange is a high indegree seed chair, dark gray its selected distractors in each context. Taken together, our results show that natural language, derived from communication in context, provides a strong objective for learning to make fine-grained distinctions between objects with an emphasis on their shared part-structure. An exciting future application of this work would be to leverage these techniques for improving unsupervised part segmentation and 3D shape retrieval, as well as context-aware shape synthesis, providing an advance over existing context-unaware synthesis techniques (Chen et al., 2018) . ACKNOWLEDGMENTS 9 APPENDIX","Human world knowledge is both structured flexible. When people see object represent pixel array meaningful arrangement semantic parts. Moreover when people refer object provide descriptions are not merely true also relevant current context. combine two observations order learn fine-grained correspondences language contextually relevant geometric properties 3D objects. do this,employed interactive communication task human participants construct large dataset containing natural utterances referring 3D objects ShapeNet wide variety contexts. Using dataset developed neural listener speaker models strong capacity generalization. performing targeted lesions visual linguistic input discovered neural listener depends heavily part-related words associates words correctly corresponding geometric properties objects suggesting has learned task-relevant structure linking two input modalities. show neural speaker is listener-aware' plans utterances according how an imagined listener would interpret words context produces discriminative referring expressions listener-unaware' speaker measured human performance identifying correct object. Human world knowledge is both structured flexible. example when people see chair represent pixel array semantically meaningful combination parts arms legs seat back. How to obtain flexibly deploy structured knowledge remains outstanding problem machine learning Lakeetal. 2017 One promising approach is to harness rich conceptual relational structure latent language Andreasetal. 2017 Natural languages have been optimized across human history solve problem efficiently communicating aspects world relevant current goals Kirbyetal. 2015;Gibsonetal. 2017 Consequently language reflects structured nature world knowledge:conceive chair terms semantic parts can combine multiple words refer 'curved back' 'cushioned seat' provide informative descriptions if the context requires e.g refer different distinguishing part if all the chairs have a cushioned seat.Our goal is to leverage insights develop systems can make fine-grained distinctions complex object geometries across wide variety contexts. approach is to leverage natural language produced people interactive communication task develop neural network models speaker listener roles task. find resulting representations learned models exhibit structure is crucial robust communication:first capture taskrelevant correspondences individual parts objects individual tokens language second have strong capacity generalize novel contexts objects utterances related object classes.We make following contributions:close context far context Figure1:Constructing close far contexts exploiting latent neighborhood structure 3D chairs. Orange is a high indegree seed chair dark gray selected distractors context. Taken together results show natural language derived communication context provides strong objective learning make fine-grained distinctions objects emphasis shared part-structure exciting future application work would leverage techniques improving unsupervised part segmentation 3D shape retrieval well context-aware shape synthesis providing advance existing context-unaware synthesis techniques Chenetal. 2018 ACKNOWLEDGMENTS 9 APPENDIX",753,506,247,0.007,1.488,2025/11/05 17:19:09,0.0,1.7,0.4922118380062303,263.927
"Object-based factorizations provide a useful level of abstraction for interacting with the world. Building explicit object representations, however, often requires supervisory signals that are difficult to obtain in practice. We present a paradigm for learning object-centric representations for physical scene understanding without direct supervision of object properties. Our model, Object-Oriented Prediction and Planning (O2P2), jointly learns a perception function to map from image observations to object representations, a pairwise physics interaction function to predict the time evolution of a collection of objects, and a rendering function to map objects back to pixels. For evaluation, we consider not only the accuracy of the physical predictions of the model, but also its utility for downstream tasks that require an actionable representation of intuitive physics. After training our model on an image prediction task, we can use its learned representations to build block towers more complicated than those observed during training. Consider the castle made out of toy blocks in Figure 1a . Can you imagine how each block was placed, one-by-one, to build this structure? Humans possess a natural physical intuition that aids in the performance of everyday tasks. This physical intuition can be acquired, and refined, through experience. Despite being a core focus of the earliest days of artificial intelligence and computer vision research BID19 BID28 , a similar level of physical scene understanding remains elusive for machines.Cognitive scientists argue that humans' ability to interpret the physical world derives from a richly structured apparatus. In particular, the perceptual grouping of the world into objects and their relations constitutes core knowledge in cognition BID24 . While it is appealing to apply such an insight to contemporary machine learning methods, it is not straightforward to do so. A fundamental challenge is the design of an interface between the raw, often high-dimensional observation space and a structured, object-factorized representation. Existing works that have investigated the benefit of using objects have either assumed that an interface to an idealized object space already exists or that supervision is available to learn a mapping between raw inputs and relevant object properties (for instance, category, position, and orientation).Assuming access to training labels for all object properties is prohibitive for at least two reasons. The most apparent concern is that curating supervision for all object properties of interest is difficult to scale for even a modest number of properties. More subtly , a representation based on semantic a) b)Figure 1: (a) A toy block castle. (b) Our method's build of the observed castle, using its learned object representations as a guide during planning. The second uses ground-truth labels of object properties to supervise a learning algorithm that can map to the space of a traditional or learned physics engine. (c) O2P2, like (b), employs an object factorization and the functional structure of a physics engine, but like (a), does not assume access to supervision of object properties. Without object-level supervision, we must jointly learn a perception function to map from images to objects, a physics engine to simulate a collection of objects, and a rendering engine to map a set of objects back to a single composite image prediction. In all three approaches , we highlight the key supervision in orange.attributes can be limiting or even ill-defined. For example, while the size of an object in absolute terms is unambiguous, its orientation must be defined with respect to a canonical, class-specific orientation. Object categorization poses another problem, as treating object identity as a classification problem inherently limits a system to a predefined vocabulary.In this paper, we propose Object-Oriented Prediction and Planning (O2P2), in which we train an object representation suitable for physical interactions without supervision of object attributes. Instead of direct supervision , we demonstrate that segments or proposal regions in video frames, without correspondence between frames, are sufficient supervision to allow a model to reason effectively about intuitive physics. We jointly train a perception module, an object-factorized physics engine, and a neural renderer on a physics prediction task with pixel generation objective. We evaluate our learned model not only on the quality of its predictions, but also on its ability to use the learned representations for tasks that demand a sophisticated physical understanding. We introduced a method of learning object-centric representations suitable for physical interactions. These representations did not assume the usual supervision of object properties in the form of position, orientation, velocity, or shape labels. Instead, we relied only on segment proposals and a factorized structure in a learned physics engine to guide the training of such representations. We demonstrated that this approach is appropriate for a standard physics prediction task. More importantly, we showed that this method gives rise to object representations that can be used for difficult planning problems, in which object configurations differ from those seen during training, without further adaptation. We evaluated our model on a block tower matching task and found that it outperformed object-agnostic approaches that made comparisons in pixel-space directly.",Object-based factorizations provide useful level abstraction interacting world. Building explicit object representations however often requires supervisory signals are difficult obtain practice. present paradigm learning object-centric representations physical scene understanding without direct supervision object properties. model Object-Oriented Prediction Planning O2P2 jointly learns perception function map image observations object representations pairwise physics interaction function predict time evolution collection objects rendering function map objects back pixels. evaluation consider accuracy physical predictions model also utility downstream tasks require actionable representation intuitive physics. training model image prediction task can use learned representations build block towers complicated observed training. Consider castle made toy blocks Figure1a. Can you imagine how each block was placed one-by-one build structure? Humans possess natural physical intuition aids performance everyday tasks. physical intuition can be acquired refined experience. Despite core focus earliest days artificial intelligence computer vision research BID19 BID28 similar level physical scene understanding remains elusive machines.Cognitive scientists argue humans' ability interpret physical world derives richly structured apparatus. particular perceptual grouping world objects relations constitutes core knowledge cognition BID24. is appealing apply insight contemporary machine learning methods is not straightforward doso. fundamental challenge is the design interface raw often high-dimensional observation space structured object-factorized representation. Existing works have investigated benefit using objects have either assumed interface idealized object space already exists supervision is available learn mapping raw inputs relevant object properties instance category position orientation.Assuming access training labels object properties is prohibitive least two reasons. apparent concern is that curating supervision object properties interest is difficult scale even modest number properties. subtly representation based semantic b Figure1:toy block castle. b method's build observed castle using learned object representations guide planning. second uses ground-truth labels object properties supervise learning algorithm can map space traditional learned physics engine. c O2P2 like b employs object factorization functional structure physics engine like does not assume access supervision object properties. Without object-level supervision must jointly learn perception function map images objects physics engine simulate collection objects rendering engine map set objects back single composite image prediction. three approaches highlight key supervision orange.attributes can be limiting even ill-defined example size object absolute terms is unambiguous orientation must defined respect canonical class-specific orientation. Object categorization poses another problem treating object identity classification problem inherently limits system predefined vocabulary.In paper propose Object-Oriented Prediction Planning O2P2 which train object representation suitable physical interactions without supervision object attributes. Instead direct supervision demonstrate segments proposal regions video frames without correspondence frames are sufficient supervision allow model reason effectively intuitive physics. jointly train perception module object-factorized physics engine neural renderer physics prediction task pixel generation objective. evaluate learned model quality predictions also ability use learned representations tasks demand sophisticated physical understanding. introduced method learning object-centric representations suitable physical interactions. representations did not assume usual supervision object properties form position orientation velocity shape labels. Instead relied segment proposals factorized structure learned physics engine guide training representations. demonstrated approach is appropriate standard physics prediction task. importantly showed method gives rise object representations can be used difficult planning problems which object configurations differ seen training without adaptation. evaluated model block tower matching task found outperformed object-agnostic approaches made comparisons pixel-space directly.,972,609,363,0.011,1.596,2025/11/05 17:19:09,0.01,1.385,0.8286604361370717,323.606
"We study the error landscape of deep linear and nonlinear neural networks with the squared error loss. Minimizing the loss of a deep linear neural network is a nonconvex problem, and despite recent progress, our understanding of this loss surface is still incomplete. For deep linear networks, we present necessary and sufficient conditions for a critical point of the risk function to be a global minimum. Surprisingly, our conditions provide an efficiently checkable test for global optimality, while such tests are typically intractable in nonconvex optimization. We further extend these results to deep nonlinear neural networks and prove similar sufficient conditions for global optimality, albeit in a more limited function space setting. Since the advent of AlexNet BID10 , deep neural networks have surged in popularity, and have redefined the state-of-the-art across many application areas of machine learning and artificial intelligence, such as computer vision, speech recognition, and natural language processing. However, a concrete theoretical understanding of why deep neural networks work well in practice remains elusive. From the perspective of optimization, a significant barrier is imposed by the nonconvexity of training neural networks. Moreover, it was proved by BID2 that training even a 3-node neural network to global optimality is NP-Hard in the worst case, so there is little hope that neural networks have properties that make global optimization tractable.Despite the difficulties of optimizing weights in neural networks, the empirical successes suggest that the local minima of their loss surfaces could be close to global minima; and several papers have recently appeared in the literature attempting to provide a theoretical justification for the success of these models. For example, by relating neural networks to spherical spin-glass models from statistical physics, BID3 provided some empirical evidence that the increase of size of neural networks makes local minima close to global minima.Another line of results BID16 BID14 BID15 BID13 provides conditions under which a critical point of the empirical risk is a global minimum. Such results roughly involve proving that if full rank conditions of certain matrices (as well as some additional technical conditions) are satisfied, derivative of the risk being zero implies loss being zero. However, these results are obtained under restrictive assumptions; for example, BID13 require the width of one of the hidden layers to be as large as the number of training examples. BID14 and BID15 require the product of widths of two adjacent layers to be at least as large as the number of training examples, meaning that the number of parameters in the model must grow rapidly as we have more training data available. Another recent paper BID4 provides a sufficient condition for global optimality when the neural network is composed of subnetworks with identical architectures connected in parallel and a regularizer is designed to control the number of parallel architectures.Towards obtaining a more precise characterization of the loss-surfaces, a valuable conceptual simplification of deep nonlinear networks is deep linear neural networks, in which all activation functions are linear and the output of the entire network is a chained product of weight matrices with the input vector. Although at first sight a deep linear model may appear overly simplistic, even its opti-mization is nonconvex, and only recently theoretical results on this problem have started emerging. Interestingly, already in 1989, BID0 showed that some shallow linear neural networks have no local minima. More recently, BID8 extended this result to deep linear networks and proved that any local minimum is also global while any other critical point is a saddle point. Subsequently, BID11 provided a simpler proof that any local minimum is also global, with fewer assumptions than BID8 . Motivated by the success of deep residual networks BID6 b) , BID5 investigated loss surfaces of deep linear residual networks and showed every critical point is a global minimum in a near-identity region; subsequently, Bartlett et al. (2017) extended this result to a nonlinear function space setting.",study error landscape why deep linear nonlinear neural networks squared error loss. Minimizing loss why deep linear neural network is a is nonconvex problem despite recent progress understanding loss surface is still incomplete. deep linear networks present necessary sufficient conditions critical point risk function global minimum. Surprisingly conditions provide efficiently checkable test global optimality tests are typically intractable nonconvex optimization. extend results deep nonlinear neural networks prove similar sufficient conditions global optimality albeit limited function space setting. Since advent AlexNet BID10 deep neural networks have surged popularity have redefined state-of-the-art across many application areas machine learning artificial intelligence computer vision speech recognition natural language processing. However concrete theoretical understanding why deep neural networks work well practice remains elusive. perspective optimization significant barrier is imposed nonconvexity training neural networks. Moreover was proved BID2 training even 3-node neural network global optimality is NP-Hard worst case is little hope neural networks have properties make global optimization tractable.Despite difficulties optimizing weights neural networks empirical successes suggest local minima loss surfaces could close global minima;several papers have recently appeared literature attempting provide theoretical justification success models. example relating neural networks spherical spin-glass models statistical physics BID3 provided empirical evidence increase size neural networks makes local minima close global minima.Another line results BID16 BID14 BID15 BID13 provides conditions which a critical point empirical risk is a global minimum. results roughly involve proving if full rank conditions certain matrices well additional technical conditions are satisfied derivative risk zero implies loss zero. However results are obtained restrictive assumptions;example BID13 require width one hidden layers large number training examples. BID14 BID15 require product widths two adjacent layers least large number training examples meaning number parameters model must grow rapidly have more training data available. Another recent paper BID4 provides sufficient condition global optimality when the neural network is composed subnetworks identical architectures connected parallel regularizer is designed control number parallel architectures.Towards obtaining precise characterization loss-surfaces valuable conceptual simplification why deep nonlinear networks is deep linear neural networks which all activation functions are linear output entire network is a chained product weight matrices input vector. Although first sight deep linear model may appear overly simplistic even opti-mization is a is nonconvex recently theoretical results problem have started emerging. Interestingly already 1989 BID0 showed shallow linear neural networks have no local minima. recently BID8 extended result deep linear networks proved local minimum is also global critical point is a saddle point. Subsequently BID11 provided simpler proof local minimum is also global fewer assumptions BID8. Motivated success why deep residual networks BID6 b BID5 investigated loss surfaces why deep linear residual networks showed every critical point is a global minimum near-identity region;subsequently Bartlettetal. 2017 extended result nonlinear function space setting.,774,546,228,0.008,1.418,2025/11/05 17:19:09,0.0,1.3,0.2741433021806849,271.542
"Recurrent auto-encoder model can summarise sequential data through an encoder structure into a fixed-length vector and then reconstruct into its original sequential form through the decoder structure. The summarised information can be used to represent time series features. In this paper, we propose relaxing the dimensionality of the decoder output so that it performs partial reconstruction. The fixed-length vector can therefore represent features only in the selected dimensions. In addition, we propose using rolling fixed window approach to generate samples. The change of time series features over time can be summarised as a smooth trajectory path. The fixed-length vectors are further analysed through additional visualisation and unsupervised clustering techniques. 

 This proposed method can be applied in large-scale industrial processes for sensors signal analysis purpose where clusters of the vector representations can be used to reflect the operating states of selected aspects of the industrial system. Successive context vectors generated by windowing approach are always highly correlated, thus form a smooth trajectory in high-dimensional space. Additional dimensionality reduction techniques can be applied visualise the change of features as a smooth trajectory. One of the key contributions of this study is that, the context vectors form distinct neighbourhoods which can be identified through unsupervised clustering algorithms such as K-means. The clusters can be optionally labelled manually to identify operating state (e.g. healthy vs. faulty). Alarm can be triggered when the context vector travels beyond the boundary of a predefined neighbourhood. Moreover, this enables us to find the clusters of unlabelled time series data. Clusters of the vector representation can be used by operators and engineers to aid diagnostics and maintenance.Another contribution of this study is that dimensionality of the output sequence can be relaxed, thus allowing the recurrent auto-encoder to perform partial reconstruction. Although it is clearly easier for the model to partially reconstruct the original sequence, such simple improvement allows users to define different sets of sensors of particular interest. By limiting the number of sensors to include in the output dimension, the context vector can be used to reflect the underlying states of specific aspects of the large-scale industrial process. This ultimately generates more actionable insights and enables users to diagnose the induatrial system. We have demonstrated the use of partial reconstruction by through two examples which graphically show the effects of it.This proposed method performs multidimensional time series clustering, which can natively scale up to very high dimensionality as it is based on recurrent auto-encoder model. We have applied the method to an industrial sensor dataset with P = 158 and empirically show that it can summarise multidimensional time series data effectively.The model can be generalised to any multi-sensor multi-state processes for operating state recognition. We also recognise that the cost of collecting labelled time series data can be very expensive. This study established that recurrent auto-encoder model can be used to analyse unlabelled and un-bounded time series data. This opens up further possibilities for analysing IoT and industrial sensors data given that these domains are predominately overwhelmed with unbounded and unlabelled time series data. Nevertheless, the proposed approach has not included any categorical sensor measurements (e.g. open/closed, tripped/healthy, start/stop... etc). Future research can focus on incorporating categorical measurements alongside real-valued measurements.","Recurrent auto-encoder model can summarise sequential data encoder structure fixed-length vector reconstruct original sequential form decoder structure. summarised information can be used represent time series features. paper propose relaxing dimensionality decoder output performs partial reconstruction. fixed-length vector can therefore represent features selected dimensions. addition propose using rolling fixed window approach generate samples. change time series features time can be summarised smooth trajectory path. fixed-length vectors are further analysed additional visualisation unsupervised clustering techniques. proposed method can be applied large-scale industrial processes sensors signal analysis purpose where clusters vector representations can be used reflect operating states selected aspects industrial system. Successive context vectors generated windowing approach are always highly correlated thus form smooth trajectory high-dimensional space. Additional dimensionality reduction techniques can be applied visualise change features smooth trajectory. One key contributions study is that,the context vectors form distinct neighbourhoods which can be identified unsupervised clustering algorithms K-means clusters can be optionally labelled manually identify operating state e.g healthyvs. faulty Alarm can be triggered when the context vector travels beyond boundary predefined neighbourhood. Moreover enablesus find clusters unlabelled time series data. Clusters vector representation can be used operators engineers aid diagnostics maintenance.Another contribution study is that dimensionality output sequence can be relaxed thus allowing recurrent auto-encoder perform partial reconstruction. Although is clearly easier model partially reconstruct original sequence simple improvement allows users define different sets sensors particular interest. limiting number sensors include output dimension context vector can be used reflect underlying states specific aspects large-scale industrial process. ultimately generates actionable insights enables users diagnose induatrial system. have demonstrated use partial reconstruction two examples which graphically show effects it.This proposed method performs multidimensional time series clustering which can natively scale high dimensionality is based recurrent auto-encoder model. have applied method industrial sensor dataset P 158 empirically show can summarise multidimensional time series data effectively.The model can be generalised multi-sensor multi-state processes operating state recognition. also recognise cost collecting labelled time series data can be very expensive. study established recurrent auto-encoder model can be used analyse unlabelled un-bounded time series data. opens possibilities analysing IoT industrial sensors data given domains are predominately overwhelmed unbounded unlabelled time series data. Nevertheless proposed approach has not included categorical sensor measurements e.g open/closed tripped/healthy start/stop... etc Future research can focus incorporating categorical measurements alongside real-valued measurements.",650,478,172,0.006,1.36,2025/11/05 17:19:09,0.0,1.704,0.0934579439252337,204.555
"We view molecule optimization as a graph-to-graph translation problem. The goal is to learn to map from one molecular graph to another with better properties based on an available corpus of paired molecules. Since molecules can be optimized in different ways, there are multiple viable translations for each input graph. A key challenge is therefore to model diverse translation outputs. Our primary contributions include a junction tree encoder-decoder for learning diverse graph translations along with a novel adversarial training method for aligning distributions of molecules. Diverse output distributions in our model are explicitly realized by low-dimensional latent vectors that modulate the translation process. We evaluate our model on multiple molecule optimization tasks and show that our model outperforms previous state-of-the-art baselines by a significant margin. 
 The goal of drug discovery is to design molecules with desirable chemical properties. The task is challenging since the chemical space is vast and often difficult to navigate. One of the prevailing approaches, known as matched molecular pair analysis (MMPA) BID16 BID11 , learns rules for generating ""molecular paraphrases"" that are likely to improve target chemical properties. The setup is analogous to machine translation: MMPA takes as input molecular pairs {(X, Y )}, where Y is a paraphrase of X with better chemical properties. However, current MMPA methods distill the matched pairs into graph transformation rules rather than treating it as a general translation problem over graphs based on parallel data.In this paper, we formulate molecular optimization as graph-to-graph translation. Given a corpus of molecular pairs, our goal is to learn to translate input molecular graphs into better graphs. The proposed translation task involves many challenges. While several methods are available to encode graphs BID12 BID32 , generating graphs as output is more challenging without resorting to a domain-specific graph linearization. In addition, the target molecular paraphrases are diverse since multiple strategies can be applied to improve a molecule. Therefore, our goal is to learn multimodal output distributions over graphs.To this end, we propose junction tree encoder-decoder, a refined graph-to-graph neural architecture that decodes molecular graphs with neural attention. To capture diverse outputs, we introduce stochastic latent codes into the decoding process and guide these codes to capture meaningful molecular variations. The basic learning problem can be cast as a variational autoencoder, where the posterior over the latent codes is inferred from input molecular pair (X, Y ). Further, to avoid invalid translations, we propose a novel adversarial training method to align the distribution of graphs generated from the model using randomly selected latent codes with the observed distribution of valid targets. Specifically, we perform adversarial regularization on the level of the hidden states created as part of the graph generation. We evaluate our model on three molecular optimization tasks, with target properties ranging from drug likeness to biological activity. 1 As baselines, we utilize state-of-the-art graph generation methods BID23 BID47 and MMPA BID9 . We demonstrate that our model excels in discovering molecules with desired properties, outperforming the baselines across 2 RELATED WORK Molecular Generation/Optimization Prior work on molecular optimization approached the graph translation task through generative modeling BID14 BID42 BID28 BID8 BID23 BID39 BID31 and reinforcement learning BID17 BID36 BID37 BID47 . Earlier approaches represented molecules as SMILES strings BID46 , while more recent methods represented them as graphs. Most of these methods coupled a molecule generator with a property predictor and solved the optimization problem through Bayesian optimization or reinforcement learning. In contrast, our model is trained to translate a molecular graph into a better graph through supervised learning, which is more sample efficient.Our approach is closely related to matched molecular pair analysis (MMPA) BID16 BID11 in drug de novo design, where the matched pairs are hard-coded into graph transformation rules. MMPA's main drawback is that large numbers of rules have to be realized (e.g. millions) to cover all the complex transformation patterns. In contrast, our approach uses neural networks to learn such transformations, which does not require the rules to be explicitly realized.Graph Neural Networks Our work is related to graph encoders and decoders. Previous work on graph encoders includes convolutional BID40 BID4 BID20 BID12 BID35 BID10 BID27 and recurrent architectures BID32 BID7 . Graph encoders have been applied to social network analysis BID26 BID19 and chemistry BID24 BID13 BID41 . Recently proposed graph decoders BID44 BID33 BID23 BID48 BID34 focus on learning generative models of graphs. While our model builds on BID23 to generate graphs, we contribute new techniques to learn multimodal graph-to-graph mappings.Image/Text Style Translation Our work is closely related to image-to-image translation BID21 , which was later extended by to learn multimodal mappings. Our adversarial training technique is inspired by recent text style transfer methods BID43 BID49 ) that adversarially regularize the continuous representation of discrete structures to enable end-to-end training. Our technical contribution is a novel adversarial regularization over graphs that constrains their scaffold structures in a continuous manner. In conclusion, we have evaluated various graph-to-graph translation models for molecular optimization. By combining the variational junction tree encoder-decoder with adversarial training, we can generate better and more diverse molecules than the baselines.",view molecule optimization graph-to-graph translation problem. goal is to learn map one molecular graph another better properties based available corpus paired molecules. Since molecules can be optimized different ways are multiple viable translations input graph. key challenge is therefore model diverse translation outputs. primary contributions include junction tree encoder-decoder learning diverse graph translations along novel adversarial training method aligning distributions molecules. Diverse output distributions model are explicitly realized low-dimensional latent vectors modulate translation process. evaluate model multiple molecule optimization tasks show model outperforms previous state-of-the-art baselines significant margin. goal drug discovery is to design molecules desirable chemical properties. task is is more challenging since chemical space is vast often difficult navigate. One prevailing approaches known matched molecular pair analysis MMPA BID16 BID11 learns rules generating molecular paraphrases are likely improve target chemical properties. setup is analogous machine translation:MMPA takes input molecular pairs X whereYis whereYis paraphrase X better chemical properties. However current MMPA methods distill matched pairs graph transformation rules rather treating general translation problem graphs based parallel data.In paper formulate molecular optimization graph-to-graph translation. Given corpus molecular pairs goal is to learn translate input molecular graphs better graphs. proposed translation task involves many challenges. several methods are available encode graphs BID12 BID32 generating graphs output is is more challenging without resorting domain-specific graph linearization. addition target molecular paraphrases are diverse since multiple strategies can be applied improve molecule. Therefore goal is to learn multimodal output distributions graphs.To end propose junction tree encoder-decoder refined graph-to-graph neural architecture decodes molecular graphs neural attention. capture diverse outputs introduce stochastic latent codes decoding process guide codes capture meaningful molecular variations. basic learning problem can be cast variational autoencoder where the posterior latent codes is inferred input molecular pair X avoid invalid translations propose novel adversarial training method align distribution graphs generated model using randomly selected latent codes observed distribution valid targets. Specifically perform adversarial regularization level hidden states created part graph generation. evaluate model three molecular optimization tasks target properties ranging drug likeness biological activity. 1 baselines utilize state-of-the-art graph generation methods BID23 BID47 MMPA BID9. demonstrate model excels discovering molecules desired properties outperforming baselines across 2 RELATED WORK Molecular Generation/Optimization Prior work molecular optimization approached graph translation task generative modeling BID14 BID42 BID28 BID8 BID23 BID39 BID31 reinforcement learning BID17 BID36 BID37 BID47. Earlier approaches represented molecules SMILES strings BID46 recent methods represented graphs. methods coupled molecule generator property predictor solved optimization problem Bayesian optimization reinforcement learning. contrast model is trained translate molecular graph better graph supervised learning which is more sample efficient.Our approach is closely related matched molecular pair analysis MMPA BID16 BID11 drug de novo design where the matched pairs are hard-coded graph transformation rules. MMPA's main drawback is that large numbers rules have to be realized e.g millions cover complex transformation patterns. contrast approach uses neural networks learn transformations which does not require rules explicitly realized.Graph Neural Networks work is related graph encoders decoders. Previous work graph encoders includes convolutional BID40 BID4 BID20 BID12 BID35 BID10 BID27 recurrent architectures BID32 BID7. Graph encoders have been applied social network analysis BID26 BID19 chemistry BID24 BID13 BID41. Recently proposed graph decoders BID44 BID33 BID23 BID48 BID34 focus learning generative models graphs. model builds BID23 generate graphs contribute new techniques learn multimodal graph-to-graph mappings.Image/Text Style Translation work is closely related image-to-image translation BID21 which was later extended learn multimodal mappings. adversarial training technique is inspired recent text style transfer methods BID43 BID49 adversarially regularize continuous representation discrete structures enable end-to-end training. technical contribution is a novel adversarial regularization graphs constrains scaffold structures continuous manner. conclusion have evaluated various graph-to-graph translation models molecular optimization. combining variational junction tree encoder-decoder adversarial training can generate better diverse molecules baselines.,1063,799,264,0.009,1.33,2025/11/05 17:19:09,0.0,1.606,0.0,306.1
"Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be sub-optimal for specific classes of problems. In contrast to existing hand-crafted solutions, we propose an approach to learn a fast iterative solver tailored to a specific domain. We achieve this goal by learning to modify the updates of an existing solver using a deep neural network. Crucially, our approach is proven to preserve strong correctness and convergence guarantees. After training on a single geometry, our model generalizes to a wide variety of geometries and boundary conditions, and achieves 2-3 times speedup compared to state-of-the-art solvers. Partial differential equations (PDEs) are ubiquitous tools for modeling physical phenomena, such as heat, electrostatics, and quantum mechanics. Traditionally, PDEs are solved with hand-crafted approaches that iteratively update and improve a candidate solution until convergence. Decades of research and engineering went into designing update rules with fast convergence properties.The performance of existing solvers varies greatly across application domains, with no method uniformly dominating the others. Generic solvers are typically effective, but could be far from optimal for specific domains. In addition, high performing update rules could be too complex to design by hand. In recent years, we have seen that for many classical problems, complex updates learned from data or experience can out-perform hand-crafted ones. For example, for Markov chain Monte Carlo, learned proposal distributions lead to orders of magnitude speedups compared to handdesigned ones BID20 BID12 . Other domains that benefited significantly include learned optimizers BID1 and learned data structures BID9 . Our goal is to bring similar benefits to PDE solvers.Hand-designed solvers are relatively simple to analyze and are guaranteed to be correct in a large class of problems. The main challenge is how to provide the same guarantees with a potentially much more complex learned solver. To achieve this goal, we build our learned iterator on top of an existing standard iterative solver to inherit its desirable properties. The iterative solver updates the solution at each step, and we learn a parameterized function to modify this update. This function class is chosen so that for any choice of parameters, the fixed point of the original iterator is preserved. This guarantees correctness, and training can be performed to enhance convergence speed. Because of this design, we only train on a single problem instance; our model correctly generalizes to a variety of different geometries and boundary conditions with no observable loss of performance. As a result, our approach provides: (i) theoretical guarantees of convergence to the correct stationary solution, (ii) faster convergence than existing solvers, and (iii) generalizes to geometries and boundary conditions very different from the ones seen at training time. This is in stark contrast with existing deep learning approaches for PDE solving BID21 BID6 that are limited to specific geometries and boundary conditions, and offer no guarantee of correctness.Our approach applies to any PDE with existing linear iterative solvers. As an example application, we solve the 2D Poisson equations. Our method achieves a 2-3× speedup on number of multiplyadd operations when compared to standard iterative solvers, even on domains that are significantly different from our training set. Moreover, compared with state-of-the-art solvers implemented in FEniCS BID13 , our method achieves faster performance in terms of wall clock CPU time. Our method is also simple as opposed to deeply optimized solvers such as our baseline in FEniCS (minimal residual method + algebraic multigrid preconditioner). Finally, since we utilize standard convolutional networks which can be easily parallelized on GPU, our approach leads to an additional 30× speedup when run on GPU. We presented a method to learn an iterative solver for PDEs that improves on an existing standard solver. The correct solution is theoretically guaranteed to be the fixed point of our iterator. We show that our model, trained on simple domains, can generalize to different grid sizes, geometries and boundary conditions. It converges correctly and achieves significant speedups compared to standard solvers, including highly optimized ones implemented in FEniCS.A PROOFS Theorem 1. For a linear iterator Ψ(u) = T u + c, Ψ converges to a unique stable fixed point from any initialization if and only if the spectral radius ρ(T ) < 1.Proof. Suppose ρ(T ) < 1, then (I−T ) −1 must exist because all eigenvalues of I−T must be strictly positive. Let u * = (I − T ) −1 c; this u * is a stationary point of the iterator Ψ, i.e. u * = T u * + c. For DISPLAYFORM0 Since ρ(T ) < 1, we know BID11 , which means the error e k → 0. Therefore, Ψ converges to u * from any u 0 . DISPLAYFORM1 Now suppose ρ(T ) ≥ 1. Let λ 1 be the largest absolute eigenvalue where ρ(T ) = |λ 1 | ≥ 1, and v 1 be its corresponding eigenvector. We select initialization u 0 = u * + v 1 , then e 0 = v 1 . Because |λ 1 | ≥ 1, we have |λ k 1 | ≥ 1, then T k e 0 = λ k 1 v 1 → k→∞ 0 However we know that under a different initializationû 0 = u * , we haveê 0 = 0, so T kê0 = 0. Therefore the iteration cannot converge to the same fixed point from different initializations u 0 and u 0 .Proposition 1 If M is a full rank diagonal matrix, and u * ∈ R n 2 ×n 2 satisfies Eq. (7) , then u * satisfies Eq. (4).Proof of Proposition 1. Let u * be a fixed point of Eq. (7) then The latter equation is equivalent to GM −1 (Au * − f ) = 0. If M is a full rank diagonal matrix, this implies G(Au * − f ) = 0, which is GAu * = Gf . Therefore, u * satisfies Eq.(4).Theorem 2. For fixed G, f, b, n, the spectral norm of Φ H (u; G, f, b, n) is a convex function of H, and the set of H such that the spectral norm of Φ H (u; G, f, b, n) < 1 is a convex open set.Proof. As before, denote Ψ(u) = T u + c. Observe that Φ H (u; G, f, b, n) = T u + c + GH(T u + c − u) = (T + GHT − GH)u + GHc + cThe spectral norm · 2 is convex with respect to its argument, and (T + GHT − GH) is linear in H. Thus, T + GHT − GH 2 is convex in H as well. Thus, under the condition that T + GHT − GH 2 < 1, the set of H must be convex because it is a sub-level set of the convex function T + GHT − GH 2 .To prove that it is open, observe that · 2 is a continuous function, so T + GHT − GH 2 is a continuous map from H to the spectral radius of Φ H . If we consider the set of H such that T + GHT − GH 2 < 1, this set is the preimage of (− , 1) for any > 0. As (− , 1) is open, its preimage must be open. Proposition 2. For fixed A, G, n and fixed H, if for some f 0 , b 0 , Φ H (u; G, f 0 , b 0 , n) is valid for the PDE problem (A, G, f 0 , b 0 , n), then for all f and b, the iterator Φ H (u; G, f, b, n) is valid for the PDE problem (A, G, f, b, n).Proof. From Theorem 1 and Lemma 1, our iterator is valid if and only if ρ(T + GHT − GH) < 1. The iterator T + GHT − GH only depends on A, G, and is independent of the constant c in Eq. (18). Thus, the validity of the iterator is independent with f and b. Thus, if the iterator is valid for some f 0 and b 0 , then it is valid for any choice of f and b.",Partial differential equations PDEs are widely used across physical computational sciences. Decades research engineering went designing fast iterative solution methods. Existing solvers are general purpose may sub-optimal specific classes problems. contrast existing hand-crafted solutions propose approach learn fast iterative solver tailored specific domain. achieve goal learning modify updates existing solver using deep neural network. Crucially approach is proven preserve strong correctness convergence guarantees. training single geometry model generalizes wide variety geometries boundary conditions achieves 2-3 times speedup compared state-of-the-art solvers. Partial differential equations PDEs are ubiquitous tools modeling physical phenomena heat electrostatics quantum mechanics. Traditionally PDEs are solved hand-crafted approaches iteratively update improve candidate solution convergence. Decades research engineering went designing update rules fast convergence properties.The performance existing solvers varies greatly across application domains method uniformly dominating others. Generic solvers are typically effective could far optimal specific domains. addition high performing update rules could complex design hand. recent years have seen many classical problems complex updates learned data experience can out-perform hand-crafted ones. example Markov chain Monte Carlo learned proposal distributions lead orders magnitude speedups compared handdesigned ones BID20 BID12. domains benefited significantly include learned optimizers BID1 learned data structures BID9. goal is to bring similar benefits PDE solvers.Hand-designed solvers are relatively simple analyze are guaranteed correct large class problems. main challenge is how to provide guarantees potentially much complex learned solver. achieve goal build learned iterator top existing standard iterative solver inherit desirable properties. iterative solver updates solution step learn parameterized function modify update. function class is chosen choice parameters fixed point original iterator is preserved. guarantees correctness training can be performed enhance convergence speed. design train single problem instance;model correctly generalizes variety different geometries boundary conditions observable loss performance. result approach provides:theoretical guarantees convergence correct stationary solution ii faster convergence existing solvers iii generalizes geometries boundary conditions different ones seen training time. is in stark contrast existing deep learning approaches PDE solving BID21 BID6 are limited specific geometries boundary conditions offer guarantee correctness.Our approach applies PDE existing linear iterative solvers. example application solve 2D Poisson equations. method achieves 2-3× speedup number multiplyadd operations when compared standard iterative solvers even domains are significantly different training set. Moreover compared state-of-the-art solvers implemented FEniCS BID13 method achieves faster performance terms wall clock CPU time. method is also simple opposed deeply optimized solvers baseline FEniCS minimal residual method+algebraic multigrid preconditioner Finally since utilize standard convolutional networks which can be easily parallelized GPU approach leads additional 30× speedup when run GPU. presented method learn iterative solver PDEs improves existing standard solver. correct solution is theoretically guaranteed fixed point iterator. show model trained simple domains can generalize different grid sizes geometries boundary conditions. converges correctly achieves significant speedups compared standard solvers including highly optimized ones implemented FEniCS.A PROOFS Theorem 1. linear iteratorΨ u u+c Ψ converges unique stable fixed point initialization if and onlyif spectral radiusρ 1.Proof. Supposeρ 1 I−T −1 must exist eigenvalues I−T must strictly positive. Letu* − −1c;u* is a stationary point iteratorΨ.eu* u*+c. DISPLAYFORM0 Sinceρ 1 know BID11 which means errorek→ 0. Therefore Ψ converges u* u0. DISPLAYFORM1 supposeρ ≥1. Letλ1 largest absolute eigenvalue whereρ |λ1 ≥1 v1 corresponding eigenvector. select initializationu0 u*+v 1 e0 v1. |λ1 ≥1 have|λk1 ≥1 ke0 λk1v 1 → k→∞0 However know different initializationû0 u* haveê0 0 kê0 0. Therefore iteration cannot converge fixed point different initializationsu0 u 0.Proposition1 If M is a full rank diagonal matrix u*∈R n2×n2 satisfiesEq. 7 u * satisfiesEq. 4.Proof Proposition1. Letu* fixed point Eq. 7 latter equation is equivalent GM−1 Au*−f 0. If M is a full rank diagonal matrix impliesG Au*−f 0 which is GAu* Gf. Therefore u * satisfiesEq. 4.Theorem2. fixedG if for somef b n spectral norm ΦH u;G if for somef b n is a convex function H set H spectral norm ΦH u;G if for somef b n 1 is a is convex open set.Proof. denoteΨ u u+c. Observe ΦH u;G if for somef b n u+c+GH u+c− u+GHT−GH u+GHc+cThe spectral norm· 2 is a is convex respect argument+GHT−GH is linear H. Thus+GHT−GH 2 is a is convex H well. Thus condition+GHT−GH 2 1 set H must convex is a sub-level set convex function+GHT−GH 2.To prove is open observe ·2 is a continuous function+GHT−GH 2 is a continuous map H spectral radius ΦH. If we consider set H+GHT−GH 2 1 set is the preimage − 1 0. − 1 is open preimage must open. Proposition2. fixed G n fixedH if for somef0 b0 ΦH u;G if for somef0 b0 n is valid PDE problem G if for somef0 b0 n f b if the iteratorΦH u;G if for somef b n is valid PDE problem G if for somef b n.Proof Theorem1 Lemma1 if the iterator is valid if and onlyifρ+GHT−GH 1. iterator+GHT−GH depends G is independent constantc Eq. 18 Thus validity iterator is independent f b. Thus if the iterator is valid f0 b0 is valid choice f b.,1835,1241,594,0.022,1.479,2025/11/05 17:19:09,0.01,1.54,0.4641744548286605,531.525
"Variational Bayesian neural networks (BNN) perform variational inference over weights, but it is difficult to specify meaningful priors and approximating posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defined directly on stochastic processes, i.e. distributions over functions. We prove that the KL divergence between stochastic processes is equal to the supremum of marginal KL divergences over all finite sets of inputs. Based on this, we introduce a practical training objective which approximates the functional ELBO using finite measurement sets and the spectral Stein gradient estimator. With fBNNs, we can specify priors which entail rich structure, including Gaussian processes and implicit stochastic processes. Empirically, we find that fBNNs extrapolate well using various structured priors, provide reliable uncertainty estimates, and can scale to large datasets. Bayesian neural networks (BNNs) BID22 BID40 have the potential to combine the scalability, flexibility, and predictive performance of neural networks with principled Bayesian uncertainty modelling. However, the practical effectiveness of BNNs is limited by our ability to specify meaningful prior distributions and by the intractability of posterior inference. Choosing a meaningful prior distribution over network weights is difficult because the weights have a complicated relationship to the function computed by the network. Stochastic variational inference is appealing because the update rules resemble ordinary backprop BID15 BID4 , but fitting accurate posterior distributions is difficult due to strong and complicated posterior dependencies BID34 BID51 .In a classic result, BID40 showed that under certain assumptions, as the width of a shallow BNN was increased, the limiting distribution is a Gaussian process (GP). BID31 recently extended this result to deep BNNs. Deep Gaussian Processes (DGP) BID5 BID49 have close connections to BNNs due to similar deep structures. However , the relationship of finite BNNs to GPs is unclear, and practical variational BNN approximations fail to match the predictions of the corresponding GP. Furthermore , because the previous analyses related specific BNN architectures to specific GP kernels, it's not clear how to design BNN architectures for a given kernel. Given the rich variety of structural assumptions that GP kernels can represent BID45 BID33 , there remains a significant gap in expressive power between BNNs and GPs (not to mention stochastic processes more broadly).In this paper , we perform variational inference directly on the distribution of functions. Specifically , we introduce functional variational BNNs (fBNNs), where a BNN is trained to produce a distribution of functions with small KL divergence to the true posterior over functions. We prove that the KL divergence between stochastic processes can be expressed as the supremum of marginal KL divergences at finite sets of points. Based on this , we present functional ELBO (fELBO) training objective. Then we introduce a GAN-like minimax formulation and a sampling-based approximation for functional variational inference. To approximate the marginal KL divergence gradients, we adopt the recently proposed spectral Stein gradient estimator (SSGE) BID52 . Here a × b represents a hidden layers of b units. Red dots are 20 training points. The blue curve is the mean of final prediction, and the shaded areas represent standard derivations. We compare fBNNs and Bayes-by-Backprop (BBB). For BBB, which performs weight-space inference , varying the network size leads to drastically different predictions. For fBNNs, which perform functionspace inference , we observe consistent predictions for the larger networks. Note that the 1 × 100 factorized Gaussian fBNNs network is not expressive enough to generate diverse predictions.Our fBNNs make it possible to specify stochastic process priors which encode richly structured dependencies between function values. This includes stochastic processes with explicit densities, such as GPs which can model various structures like smoothness and periodicity BID33 . We can also use stochastic processes with implicit densities, such as distributions over piecewise linear or piecewise constant functions. Furthermore, in contrast with GPs, fBNNs efficiently yield explicit posterior samples of the function. This enables fBNNs to be used in settings that require explicit minimization of sampled functions, such as Thompson sampling BID57 BID48 or predictive entropy search BID21 BID59 .One desideratum of Bayesian models is that they behave gracefully as their capacity is increased BID44 . Unfortunately, ordinary BNNs don't meet this basic requirement : unless the asymptotic regime is chosen very carefully (e.g. BID40 ), BNN priors may have undesirable behaviors as more units or layers are added. Furthermore, larger BNNs entail more difficult posterior inference and larger description length for the posterior, causing degeneracy for large networks, as shown in FIG0 . In contrast, the prior of fBNNs is defined directly over the space of functions, thus the BNN can be made arbitrarily large without changing the functional variational inference problem. Hence, the predictions behave well as the capacity increases.Empirically , we demonstrate that fBNNs generate sensible extrapolations for both explicit periodic priors and implicit piecewise priors. We show fBNNs outperform competing approaches on both small scale and large scale regression datasets. fBNNs' reliable uncertainty estimates enable state-of-art performance on the contextual bandits benchmark of BID46 . In this paper we investigated variational inference between stochastic processes. We proved that the KL divergence between stochastic processes equals the supremum of KL divergence for marginal distributions over all finite measurement sets. Then we presented two practical functional variational inference approaches: adversarial and sampling-based. Adopting BNNs as the variational posterior yields our functional variational Bayesian neural networks. Empirically, we demonstrated that fBNNs extrapolate well over various structures, estimate reliable uncertainties, and scale to large datasets.",Variational Bayesian neural networks BNN perform variational inference weights is difficult specify meaningful priors approximating posteriors high-dimensional weight space. introduce functional variational Bayesian neural networks fBNNs which maximize Evidence Lower BOund ELBO defined directly stochastic processes.e distributions functions. prove KL divergence stochastic processes is equal supremum marginal KL divergences finite sets inputs. Based introduce practical training objective which approximates functional ELBO using finite measurement sets spectral Stein gradient estimator. fBNNs can specify priors which entail rich structure including Gaussian processes implicit stochastic processes. Empirically find fBNNs extrapolate well using various structured priors provide reliable uncertainty estimates can scale large datasets. Bayesian neural networks BNNs BID22 BID40 have the potential combine scalability flexibility predictive performance neural networks principled Bayesian uncertainty modelling. However practical effectiveness BNNs is limited ability specify meaningful prior distributions intractability posterior inference. Choosing meaningful prior distribution network weights is difficult weights have a complicated relationship function computed network. Stochastic variational inference is appealing update rules resemble ordinary backprop BID15 BID4 fitting accurate posterior distributions is difficult due strong complicated posterior dependencies BID34 BID51.In classic result BID40 showed certain assumptions width shallow BNN was increased limiting distribution is a Gaussian process GP BID31 recently extended result deep BNNs. Deep Gaussian Processes DGP BID5 BID49 have close connections BNNs due similar deep structures. However relationship finite BNNs GPs is unclear practical variational BNN approximations fail match predictions correspondingGP. Furthermore previous analyses related specific BNN architectures specific GP kernels clear how to design BNN architectures given kernel. Given rich variety structural assumptions GP kernels can represent BID45 BID33 remains significant gap expressive power BNNs GPs mention stochastic processes broadly.In paper which perform variational inference directly distribution functions. Specifically introduce functional variational BNNs fBNNs where a BNN is trained produce distribution functions small KL divergence true posterior functions. prove KL divergence stochastic processes can be expressed supremum marginal KL divergences finite sets points. Based present functional ELBO fELBO training objective. introduce GAN-like minimax formulation sampling-based approximation functional variational inference. approximate marginal KL divergence gradients adopt recently proposed spectral Stein gradient estimator SSGE BID52. × b represents hidden layers b units. Red dots are 20 training points. blue curve is the mean final prediction shaded areas represent standard derivations. compare fBNNs Bayes-by-Backprop BBB BBB which performs weight-space inference varying network size leads drastically different predictions. fBNNs which perform functionspace inference observe consistent predictions larger networks. Note 1 × 100 factorized Gaussian fBNNs network is not expressive enough generate diverse predictions.Our fBNNs make possible specify stochastic process priors which encode richly structured dependencies function values. includes stochastic processes explicit densities GPs which can model various structures like smoothness periodicity BID33. can also use stochastic processes implicit densities distributions piecewise linear piecewise constant functions. Furthermore contrast GPs fBNNs efficiently yield explicit posterior samples function. enables fBNNs used settings require explicit minimization sampled functions Thompson sampling BID57 BID48 predictive entropy search BID21 BID59.One desideratum Bayesian models is that they behave gracefully capacity is increased BID44. Unfortunately ordinary BNNs meet basic requirement:unless asymptotic regime is chosen carefully e.g BID40 where a BNN priors may have undesirable behaviors units layers are added. Furthermore larger BNNs entail difficult posterior inference larger description length posterior causing degeneracy large networks shown FIG0. contrast prior fBNNs is defined directly space functions thus BNN can be made arbitrarily large without changing functional variational inference problem. Hence predictions behave well capacity increases.Empirically demonstrate fBNNs generate sensible extrapolations explicit periodic priors implicit piecewise priors. show fBNNs outperform competing approaches small scale large scale regression datasets. fBNNs' reliable uncertainty estimates enable state-of-art performance contextual bandits benchmark BID46. paper investigated variational inference stochastic processes. proved KL divergence stochastic processes equals supremum KL divergence marginal distributions finite measurement sets. presented two practical functional variational inference approaches:adversarial sampling-based Adopting BNNs variational posterior yields functional variational Bayesian neural networks. Empirically demonstrated fBNNs extrapolate well various structures estimate reliable uncertainties can scale large datasets.,1182,868,314,0.01,1.362,2025/11/05 17:19:09,0.0,1.333,0.0996884735202493,331.606
"Words are not created equal. In fact, they form an aristocratic graph with a latent hierarchical structure that the next generation of unsupervised learned word embeddings should reveal. In this paper, justified by the notion of delta-hyperbolicity or tree-likeliness of a space, we propose to embed words in a Cartesian product of hyperbolic spaces which we theoretically connect to the Gaussian word embeddings and their Fisher geometry. This connection allows us to introduce a novel principled hypernymy score for word embeddings. Moreover, we adapt the well-known Glove algorithm to learn unsupervised word embeddings in this type of Riemannian manifolds. We further explain how to solve the analogy task using the Riemannian parallel transport that generalizes vector arithmetics to this new type of geometry. Empirically, based on extensive experiments, we prove that our embeddings, trained unsupervised, are the first to simultaneously outperform strong and popular baselines on the tasks of similarity, analogy and hypernymy detection. In particular, for word hypernymy, we obtain new state-of-the-art on fully unsupervised WBLESS classification accuracy. Word embeddings are ubiquitous nowadays as first layers in neural network and deep learning models for natural language processing. They are essential in order to move from the discrete word space to the continuous space where differentiable loss functions can be optimized. The popular models of Glove BID31 , Word2Vec BID25 or FastText BID6 , provide efficient ways to learn word vectors fully unsupervised from raw text corpora, solely based on word co-occurrence statistics. These models are then successfully applied to word similarity and other downstream tasks and, surprisingly (or not BID1 ), exhibit a linear algebraic structure that is also useful to solve word analogy.However, unsupervised word embeddings still largely suffer from revealing asymmetric word relations including the latent hierarchical structure of words. This is currently one of the key limitations in automatic text understanding, e.g. for tasks such as textual entailment BID9 . To address this issue, BID36 BID27 propose to move from point embeddings to probability density functions, the simplest being Gaussian or Elliptical distributions. Their intuition is that the variance of such a distribution should encode the generality/specificity of the respective word. However, this method results in losing the arithmetic properties of point embeddings (e.g. for analogy reasoning) and becomes unclear how to properly use them in downstream tasks. To this end, we propose to take the best from both worlds: we embed words as points in a Cartesian product of hyperbolic spaces and, additionally, explain how they are bijectively mapped to Gaussian embeddings with diagonal covariance matrices, where the hyperbolic distance between two points becomes the Fisher distance between the corresponding probability distribution functions (PDFs). This allows us to derive a novel principled is-a score on top of word embeddings that can be leveraged for hypernymy detection. We learn these word embeddings unsupervised from raw text by generalizing the Glove method. Moreover, the linear arithmetic property used for solving word analogy has a mathematical grounded correspondence in this new space based on the established notion of parallel transport in Riemannian manifolds. In addition, these hyperbolic embeddings outperform Euclidean Glove on word similarity benchmarks. We thus describe, to our knowledge, the first word embedding model that competitively addresses the above three tasks simultaneously. Finally, these word vectors can also be used in downstream tasks as explained by BID17 .We provide additional reasons for choosing the hyperbolic geometry to embed words. We explain the notion of average δ-hyperbolicity of a graph, a geometric quantity that measures its ""democracy"" BID8 . A small hyperbolicity constant implies ""aristocracy"", namely the existence of a small set of nodes that ""influence"" most of the paths in the graph. It is known that real-world graphs are mainly complex networks (e.g. scale-free exhibiting power-law node degree distributions) which in turn are better embedded in a tree-like space, i.e. hyperbolic BID20 . Since , intuitively, words form an ""aristocratic"" community (few generic ones from different topics and many more specific ones) and since a significant subset of them exhibits a hierarchical structure (e.g. WordNet BID26 ), it is naturally to learn hyperbolic word embeddings. Moreover , we empirically measure very low average δ-hyperbolicity constants of some variants of the word log-co-occurrence graph (used by the Glove method), providing additional quantitative reasons for why spaces of negative curvature (i.e. hyperbolic) are better suited for word representations. We propose to adapt the GloVe algorithm to hyperbolic spaces and to leverage a connection between statistical manifolds of Gaussian distributions and hyperbolic geometry, in order to better interpret entailment relations between hyperbolic embeddings. We justify the choice of products of hyperbolic spaces via this connection to Gaussian distributions and via computations of the hyperbolicity of the symbolic data upon which GloVe is based. Empirically we present the first model that can simultaneously obtain state-of-the-art results or close on the three tasks of word similarity, analogy and hypernymy detection.",Words are not created equal. fact form aristocratic graph latent hierarchical structure next generation unsupervised learned word embeddings should reveal. paper justified notion delta-hyperbolicity tree-likeliness space propose embed words Cartesian product hyperbolic spaces which we theoretically connect Gaussian word embeddings Fisher geometry. connection allowsus introduce novel principled hypernymy score word embeddings. Moreover adapt well-known Glove algorithm learn unsupervised word embeddings type Riemannian manifolds. explain how to solve analogy task using Riemannian parallel transport generalizes vector arithmetics new type geometry. Empirically based extensive experiments prove embeddings trained unsupervised are the first simultaneously outperform strong popular baselines tasks similarity analogy hypernymy detection. particular word hypernymy obtain new state-of-the-art fully unsupervised WBLESS classification accuracy. Word embeddings are ubiquitous nowadays first layers neural network deep learning models natural language processing. are essential order move discrete word space continuous space where differentiable loss functions can be optimized. popular models Glove BID31 Word2Vec BID25 FastText BID6 provide efficient ways learn word vectors fully unsupervised raw text corpora solely based word co-occurrence statistics. models are then successfully applied word similarity downstream tasks surprisingly BID1 exhibit linear algebraic structure is also useful solve word analogy.However unsupervised word embeddings still largely suffer revealing asymmetric word relations including latent hierarchical structure words. is currently one key limitations automatic text understanding e.g tasks textual entailment BID9. address issue BID36 BID27 propose move point embeddings probability density functions simplest Gaussian Elliptical distributions. intuition is that the variance distribution should encode generality/specificity respective word. However method results losing arithmetic properties point embeddings e.g analogy reasoning becomes unclear how to properly use downstream tasks. end propose take best worlds:embed words points Cartesian product hyperbolic spaces additionally explain how they are bijectively mapped Gaussian embeddings diagonal covariance matrices where the hyperbolic distance two points becomes Fisher distance corresponding probability distribution functions PDFs allowsus derive novel principled is-a score top word embeddings can be leveraged hypernymy detection. learn word embeddings unsupervised raw text generalizing Glove method. Moreover linear arithmetic property used solving word analogy has a mathematical grounded correspondence new space based established notion parallel transport Riemannian manifolds. addition where the hyperbolic embeddings outperform Euclidean Glove word similarity benchmarks. thus describe knowledge are the first word embedding model competitively addresses three tasks simultaneously. Finally word vectors can also used downstream tasks explained BID17.We provide additional reasons choosing hyperbolic geometry embed words. explain notion average δ-hyperbolicity graph geometric quantity measures democracy BID8. small hyperbolicity constant implies aristocracy namely existence small set nodes influence paths graph. is known real-world graphs are mainly complex networks e.g scale-free exhibiting power-law node degree distributions which in turn are better embedded tree-like space.e hyperbolic BID20. Since intuitively words form aristocratic community generic ones different topics many specific ones since significant subset exhibits hierarchical structure e.g WordNet BID26 is naturally learn hyperbolic word embeddings. Moreover empirically measure low average δ-hyperbolicity constants variants word log-co-occurrence graph used Glove method providing additional quantitative reasons why spaces negative curvature.e hyperbolic are better suited word representations. propose adapt GloVe algorithm hyperbolic spaces leverage connection statistical manifolds Gaussian distributions hyperbolic geometry order better interpret entailment relations hyperbolic embeddings. justify choice products hyperbolic spaces via connection Gaussian distributions via computations hyperbolicity symbolic data upon which GloVe is based. Empirically present first model can simultaneously obtain state-of-the-art results close three tasks word similarity analogy hypernymy detection.,1064,742,322,0.01,1.434,2025/11/05 17:19:09,0.0,1.5,0.3239875389408096,314.611
"Answering questions about a text frequently requires aggregating information from multiple places in that text. End-to-end neural network models, the dominant approach in the current literature, can theoretically learn how to distill and manipulate representations of the text without explicit supervision about how to do so. We investigate a canonical architecture for this task, the memory network, and analyze how effective it really is in the context of three multi-hop reasoning settings. In a simple synthetic setting, the path-finding task of the bAbI dataset, the model fails to learn the correct reasoning without additional supervision of its attention mechanism. However, with this supervision, it can perform well. On a real text dataset, WikiHop, the memory network gives nearly state-of-the-art performance, but does so without using its multi-hop capabilities. A tougher anonymized version of the WikiHop dataset is qualitatively similar to bAbI: the model fails to perform well unless it has additional supervision. We hypothesize that many ""multi-hop"" architectures do not truly learn this reasoning as advertised, though they could learn this reasoning if appropriately supervised. Question answering from text is a key challenge problem for NLP that tests whether models can extract information based on a query. Recent new datasets BID22 BID9 BID8 BID21 and new models BID24 BID25 have dramatically advanced the state-of-the-art in this area. However, some QA tasks, such as SQuAD, only simple pattern matching to solve BID29 . One thread of recent work has emphasized multi-hop reasoning in particular BID13 BID11 BID30 , particularly work on memory networks BID28 BID13 . Memory networks define a generic model class that attends to a text passage using the question and a memory cell iteratively to gather information in the different parts of the passage. Many existing reading comprehension models use memory net-like structures and iterative attention over the document, showing improvement in a variety of tasks and settings BID8 BID17 BID27 BID4 BID25 BID20 .We tackle two main questions in this paper. First , are memory networks effective? Second , do they behave as advertised (selecting a sequence of relevant passage excerpts through their computation)? We examine the behavior of memory network-like models across three different tasks. These include one purely synthetic setting, the bAbI path-finding task , and two forms of a more realistic multi-hop reasoning dataset constructed from Wikipedia BID30 . In each case, we apply memory networks to the problem, and can observe their performance and behavior. Exploiting the properties of these particular datasets, we can use heuristics capturing how humans might solve this problem to derive a pseudogold ""reasoning chain."" We then compare the model's reasoning chain with this pseudogold to see whether the model is following a similar chain of reasoning.Our results show that memory networks generally do not learn to do reasoning in the right way, but can do well when using additional supervision to guide how they reason. On bAbI and in a Figure 1 : Computation flow of our hierarchical memory network on an example from WikiHop BID30 . The question is encoded to produce a query q 1 , which produces sentencelevel attention α and word-level attention β for each sentence. This attention computes a passage representation m 1 from which we form the query q 2 for the next step of inference.""masked"" form of the WikiHop task (where entities are anonymized), the memory network performs badly when applied in the standard way. However, when we explicitly supervise the model with pseudogold chains, the model can perform dramatically better with no other changes to its structure or parameterization. On the standard WikHop dataset, our memory network model can achieve nearly state-of-the-art performance, but we show that this is not due to multi-hop reasoning: it barely outperforms a baseline that does not make use of the text at all, calling into question what is being learned. However, additional supervision on the attention can still yield improvement, making our final system close in performance to much more sophisticated state-of-the-art models.Our observations can be summarized as follows:• In both synthetic and more realistic settings, memory networks fail to learn multi-hop reasoning from task supervision alone. This is true even though there exist settings of the parameters that do fit the data, as we can see by their success when more heavily supervised.• When the attention of memory networks is additionally supervised during training, they can do well at text question answering. This supervision qualitatively changes the model's performance with respect to multi-hop reasoning.• When memory networks and related models perform well on multi-hop reasoning tasks, they may be doing so through other means and not actually performing multi-hop reasoning, as we see on the standard WikiHop setting. In this paper, we explore how the memory network behaves on the task of multi-hop reasoning. Experimental results on bAbI and WikiHop show that additional supervision beyond the downstream answers to the questions is needed to learn generalizable multi-hop reasoning. However, when incorporating this supervision, our memory network model can learn to do this and achieves strong results on the WikiHop dataset.",Answering questions text frequently requires aggregating information multiple places text. End-to-end neural network models dominant approach current literature can theoretically learn how to distill manipulate representations text without explicit supervision howtodoso. investigate canonical architecture task are memory network analyze how effective really is in the context three multi-hop reasoning settings. simple synthetic setting path-finding task bAbI dataset model fails learn correct reasoning without additional supervision attention mechanism. However supervision can perform well. real text dataset WikiHop are memory network gives nearly state-of-the-art performance does so without using multi-hop capabilities. tougher anonymized version WikiHop dataset is qualitatively similar bAbI:model fails perform well unless has additional supervision. hypothesize many multi-hop architectures do not truly learn reasoning advertised though could learn reasoning if appropriately supervised. Question answering text is a key challenge problem NLP tests whether models can extract information based query. Recent new datasets BID22 BID9 BID8 BID21 new models BID24 BID25 have dramatically advanced state-of-the-art area. However QA tasks SQuAD simple pattern matching solve BID29. One thread recent work has emphasized multi-hop reasoning particular BID13 BID11 BID30 particularly work memory networks BID28 BID13. Memory networks define generic model class attends text passage using question memory cell iteratively gather information different parts passage. Many existing reading comprehension models use memory net-like structures iterative attention document showing improvement variety tasks settings BID8 BID17 BID27 BID4 BID25 BID20.We tackle two main questions paper. First are memory networks effective? Second do they behave advertised selecting sequence relevant passage excerpts computation examine behavior memory network-like models across three different tasks. include one purely synthetic setting bAbI path-finding task two forms realistic multi-hop reasoning dataset constructed Wikipedia BID30. case apply memory networks problem can observe performance behavior. Exploiting properties particular datasets can use heuristics capturing how humans might solve problem derive pseudogold reasoning chain. compare model's reasoning chain pseudogold see whether model is following similar chain reasoning.Our results show memory networks generally do not learn do reasoning right way can do can do well when using additional supervision guide how they reason. bAbI Figure1:Computation flow hierarchical memory network example WikiHop BID30. question is encoded produce queryq1 which produces sentencelevel attentionα word-level attentionβ sentence. attention computes passage representation 1 which we form queryq2 next step inference.masked form WikiHop task where entities are anonymized memory network performs badly when applied standard way. However when we explicitly supervise model pseudogold chains model can perform dramatically better changes structure parameterization. standard WikHop dataset are memory network model can achieve nearly state-of-the-art performance show is not due multi-hop reasoning:barely outperforms baseline does not make use text calling question what is being learned. However additional supervision attention can still yield improvement making final system close performance much sophisticated state-of-the-art models.Our observations can be summarized follows:• synthetic realistic settings are memory networks fail learn multi-hop reasoning task supervision alone. is true even though exist settings parameters do fit data can see success when more heavily supervised.• When the attention memory networks is additionally supervised training can do can do well text question answering. supervision qualitatively changes model's performance respect multi-hop reasoning.• When memory networks related models perform well multi-hop reasoning tasks may means actually performing multi-hop reasoning can see standard WikiHop setting. paper explore how the memory network behaves task multi-hop reasoning. Experimental results bAbI WikiHop show additional supervision beyond downstream answers questions is needed learn generalizable multi-hop reasoning. However when incorporating supervision are memory network model can learn do this and achieves strong results WikiHop dataset.,1024,728,296,0.01,1.407,2025/11/05 17:19:09,0.0,1.472,0.2398753894080995,311.994
"Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be optimized with a discriminator or an encoder. The embedding is Lipschitz continuous to deformations so that generators transform linear interpolations between input white noise vectors into deformations between output images. This embedding is computed with a wavelet Scattering transform. Numerical experiments demonstrate that the resulting Scattering generators have similar properties as GANs or VAEs, without learning a discriminative network or an encoder. Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) allow training generative networks to synthesize images of remarkable quality and complexity from Gaussian white noise. This work shows that one can train generative networks having similar properties to those obtained with GANs or VAEs without learning a discriminator or an encoder. The generator is a deep convolutional network that inverts a predefined embedding operator. To reproduce relevant properties of GAN image synthesis the embedding operator is chosen to be Lipschitz continuous to deformations, and it is implemented with a wavelet Scattering transform. Defining image generators as the solution of an inverse problem provides a mathematical framework, which is closer to standard probabilistic models such as Gaussian autoregressive models.GANs were introduced by BID6 as an unsupervised learning framework to estimate implicit generative models of complex data (such as natural images) by training a generative model (the generator) and a discriminative model (the discriminator) simultaneously. An implicit generative model of the random vector X consists in an operator G which transforms a Gaussian white noise random vector Z into a model X = G(Z) of X. The operator G is called a generative network or generator when it is a deep convolutional network. BID17 introduced deep convolutional architectures for the generator and the discriminator, which result in high-quality image synthesis. They also showed that linearly modifying the vector z results in a progressive deformation of the imagex = G(z). BID6 and BID0 argue that GANs select the generator G by minimizing the Jensen-Shannon divergence or the Wasserstein distance calculated from empirical estimations of these distances with generated and training images. However, BID1 prove that this explanation fails to pass the curse of dimensionality since estimates of Jensen-Shannon or Wasserstein distances do not generalize with a number of training examples which is polynomial on the dimension of the images. Therefore, the reason behind the generalization capacities of generative networks remains an open problem.VAEs, introduced by BID8 , provide an alternative approach to GANs, by optimizing G together with its inverse on the training samples, instead of using a discriminator. The inverse Φ is an embedding operator (the encoder) that is trained to transform X into a Gaussian white noise Z. Therefore, the loss function to train a VAE is based on probabilistic distances which also suffer from the same dimensionality curse shown in BID1 . Furthermore, a significant disadvantage of VAEs is that the resulting generative models produce blurred images compared with GANs.Generative Latent Optimization (GLO) was introduced in BID2 to eliminate the need for a GAN discriminator while restoring sharper images than VAEs. GLO still uses an autoencoder computational structure, where the latent space variables z are optimized together with the generator G. Despite good results, linear variations of the embedding space variables are not mapped as clearly into image deformations as in GANs, which reduces the quality of generated images.GANs and VAEs raise many questions. Where are the deformation properties coming from? What are the characteristics of the embedding operator Φ? Why do these algorithms seem to generalize despite the curse of dimensionality? Learning a stable embedding which maps X into a Gaussian white noise is intractable without strong prior information BID1 . This paper shows that this prior information is available for image generation and that one can predefine the embedding up to a linear operator. The embedding must be Lipschitz continuous to translations and deformations so that modifications of the input noise result in deformations of X. Lipschitz continuity to deformations requires separating the signal variations at different scales, which leads to the use of wavelet transforms. We concentrate on wavelet Scattering transforms BID12 , which linearize translations and provide appropriate Gaussianization. We then define the generative model as an inversion of the Scattering embedding on training data, with a deep convolutional network. The inversion is regularized by the architecture of the generative network, which is the same as the generator of a DCGAN BID17 . Experiments in Section 4 show that these generative Scattering networks have similar properties as GAN generators, and the synthesized images have the same quality as the ones obtained with VAEs or GLOs. This paper shows that most properties of GANs and VAEs can be reproduced with an embedding computed with a Scattering transform, which avoids using a discriminator as in GANs or learning the embedding as in VAEs or GLOs. It also provides a mathematical framework to analyze the statistical properties of these generators through the resolution of an inverse problem, regularized by the convolutional network architecture and the sparsity of the obtained activations. Because the embedding function is known, numerical results can be evaluated on training as well as test samples.We report preliminary numerical results with no hyperparameter optimization. The architecture of the convolutional generator may be adapted to the properties of the Scattering operator S j as j increases. Also, the paper uses a ""plain"" Scattering transform which does not take into account interactions between angle and scale variables, which may also improve the representation as explained in BID15 .",Generative Adversarial Nets GANs Variational Auto-Encoders VAEs provide impressive image generations Gaussian white noise underlying mathematics are not well understood. compute deep convolutional network generators inverting fixed embedding operator. Therefore do not require optimized discriminator encoder. embedding is Lipschitz continuous deformations generators transform linear interpolations input white noise vectors deformations output images. embedding is computed wavelet Scattering transform. Numerical experiments demonstrate resulting Scattering generators have similar properties GANs VAEs without learning discriminative network encoder. Generative Adversarial Networks GANs Variational Auto-Encoders VAEs allow training generative networks synthesize images remarkable quality complexity Gaussian white noise. work shows one can train generative networks similar properties obtained GANs VAEs without learning discriminator encoder. generator is a deep convolutional network inverts predefined embedding operator. reproduce relevant properties GAN image synthesis embedding operator is chosen Lipschitz continuous deformations is implemented wavelet Scattering transform. Defining image generators solution inverse problem provides mathematical framework which is closer standard probabilistic models Gaussian autoregressive models.GANs were introduced BID6 unsupervised learning framework estimate implicit generative models complex data natural images training generative model generator discriminative model discriminator simultaneously. implicit generative model random vector X consists operatorG which transforms Gaussian white noise random vectorZ modelX G Z X. operatorG is called generative network generator when it is a deep convolutional network. BID17 introduced deep convolutional architectures generator discriminator which result high-quality image synthesis. also showed linearly modifying vector z results progressive deformation imagex G z BID6 BID0 argue GANs select generatorG minimizing Jensen-Shannon divergence Wasserstein distance calculated empirical estimations distances generated training images. However BID1 prove explanation fails pass curse dimensionality since estimates Jensen-Shannon Wasserstein distances do not generalize number training examples which is polynomial dimension images. Therefore reason behind generalization capacities generative networks remains open problem.VAEs introduced BID8 provide alternative approach GANs optimizing G together inverse training samples instead using discriminator. inverseΦ is an embedding operator encoder is trained transformX Gaussian white noiseZ. Therefore loss function train VAE is based probabilistic distances which also suffer dimensionality curse shown BID1. Furthermore significant disadvantage VAEs is that the resulting generative models produce blurred images compared GANs.Generative Latent Optimization GLO was introduced BID2 eliminate need GAN discriminator restoring sharper images VAEs. GLO still uses autoencoder computational structure where the latent space variablesz are optimized together generatorG. Despite good results linear variations embedding space variables are not mapped clearly image deformations GANs which reduces quality generated images.GANs VAEs raise many questions. Where are the deformation properties coming from? What are the characteristics embedding operatorΦ? Why do these algorithms seem generalize despite curse dimensionality? Learning stable embedding which mapsX Gaussian white noise is intractable without strong prior information BID1. paper shows prior information is available image generation one can predefine embedding linear operator. embedding must Lipschitz continuous translations deformations modifications input noise result deformations X. Lipschitz continuity deformations requires separating signal variations different scales which leads use wavelet transforms. concentrate wavelet Scattering transforms BID12 which linearize translations provide appropriate Gaussianization. define generative model inversion Scattering embedding training data deep convolutional network. inversion is regularized architecture generative network which is the generator DCGAN BID17. Experiments Section 4 show generative Scattering networks have similar properties GAN generators synthesized images have the same quality ones obtained VAEs GLOs. paper shows properties GANs VAEs can be reproduced embedding computed Scattering transform which avoids using discriminator GANs learning embedding VAEs GLOs. also provides mathematical framework analyze statistical properties generators resolution inverse problem regularized convolutional network architecture sparsity obtained activations. embedding function is known numerical results can be evaluated training well test samples.We report preliminary numerical results hyperparameter optimization. architecture convolutional generator may adapted properties Scattering operator j j increases. Also paper uses plain Scattering transform which does not take account interactions angle scale variables may also improve representation explained BID15.,1180,823,357,0.012,1.434,2025/11/05 17:19:10,0.01,1.636,0.3239875389408096,352.137
"Recurrent neural networks (RNNs) can model natural language by sequentially ''reading'' input tokens and outputting a distributed representation of each token. Due to the sequential nature of RNNs, inference time is linearly dependent on the input length, and all inputs are read regardless of their importance. Efforts to speed up this inference, known as ''neural speed reading'', either ignore or skim over part of the input. We present Structural-Jump-LSTM: the first neural speed reading model to both skip and jump text during inference. The model consists of a standard LSTM and two agents: one capable of skipping single words when reading, and one capable of exploiting punctuation structure (sub-sentence separators (,:), sentence end symbols (.!?), or end of text markers) to jump ahead after reading a word.
 A comprehensive experimental evaluation of our model against all five state-of-the-art neural reading models shows that 
 Structural-Jump-LSTM achieves the best overall floating point operations (FLOP) reduction (hence is faster), while keeping the same accuracy or even improving it compared to a vanilla LSTM that reads the whole text. Recurrent neural networks (RNNs) are a popular model for processing sequential data. The Gated Recurrent Unit (GRU) BID4 and Long Short Term Memory (LSTM) BID7 are RNN units developed for learning long term dependencies by reducing the problem of vanishing gradients during training. However, both GRU and LSTM incur fairly expensive computational costs, with e.g. LSTM requiring the computation of 4 fully connected layers for each input it reads, independently of the input's importance for the overall task.Based on the idea that not all inputs are equally important, and that relevant information can be spread throughout the input sequence, attention mechanisms were developed BID0 to help the network focus on important parts of the input. With soft attention, all inputs are read, but the attention mechanism is fully differentiable. In comparison, hard attention completely ignores part of the input sequence. Hard attention mechanisms have been considered in many areas, ranging from computer vision BID14 BID1 where the model learns what parts of the image it should focus on, to natural language processing (NLP), such as text classification and question answering BID22 BID1 BID23 , where the model learns which part of a document it can ignore. With hard attention, the RNN has fewer state updates, and therefore fewer floating point operations (FLOPs) are needed for inference. This is often denoted as speed reading: obtaining the same accuracy while using (far) fewer FLOPs BID22 BID19 BID8 BID5 . Prior work on speed reading processes text as chunks of either individual words or blocks of contiguous words. If the chunk being read is important enough, a full state update is performed; if not, the chunk is either ignored or a very limited amount of computations are done. This is followed by an action aiming to speed up the reading, e.g. skipping or jumping forward in text.Inspired by human speed reading, we contribute an RNN speed reading model that ignores unimportant words in important sections, while also being able to jump past unimportant sections of the text. Our model, called Structural-Jump-LSTM 1 , both skips and jumps over dynamically defined chunks of text as follows: (a) it can skip individual words, after reading them, but before updating the RNN state; (b) it uses the punctuation structure of the text to define dynamically spaced jumps to the next sub-sentence separator (,;), end of sentence symbol (.!?), or the end of the text.An extensive experimental evaluation against all state-of-the-art speed reading models BID19 BID22 BID5 BID8 , shows that our Structural-Jump-LSTM of dynamically spaced jumps and word level skipping leads to large FLOP reductions while maintaining the same or better reading accuracy than a vanilla LSTM that reads the full text. We presented Structural-Jump-LSTM, a recurrent neural network for speed reading. StructuralJump-LSTM is inspired by human speed reading, and can skip irrelevant words in important sections, while also jumping past unimportant parts of a text. It uses the dynamically spaced punctuation structure of text to determine whether to jump to the next word, the next sub-sentence separator (,;), next end of sentence (.!?), or to the end of the text. In addition, it allows skipping a word after observing it without updating the state of the RNN. Through an extensive experimental evaluation against all five state-of-the-art baselines, Structural-Jump-LSTM obtains the overall largest reduction in floating point operations, while maintaining the same accuracy or even improving it over a vanilla LSTM model that reads the full text. We contribute the first ever neural speed reading model that both skips and jumps over dynamically defined chunks of text without loss of effectiveness and with notable gains in efficiency. Future work includes investigating other reward functions, where most of the reward is not awarded in the end, and whether this would improve agent training by having a stronger signal spread throughout the text.","Recurrent neural networks RNNs can model natural language sequentially reading input tokens outputting distributed representation token. Due sequential nature RNNs inference time is linearly dependent input length inputs are read regardless importance. Efforts speed inference known neural speed reading either ignore skim part input. present Structural-Jump-LSTM first neural speed reading model skip jump text inference. model consists standard LSTM two agents:one capable skipping single words when reading one capable exploiting punctuation structure sub-sentence separators sentence end symbols end text markers jump ahead reading word. comprehensive experimental evaluation model five state-of-the-art neural reading models shows Structural-Jump-LSTM achieves best overall floating point operations FLOP reduction hence is faster keeping accuracy even improving compared vanilla LSTM reads whole text. Recurrent neural networks RNNs are a popular model processing sequential data. Gated Recurrent Unit GRU BID4 Long Short Term Memory LSTM BID7 are RNN units developed learning long term dependencies reducing problem vanishing gradients training. However GRU LSTM incur fairly expensive computational costs e.g LSTM requiring computation 4 fully connected layers input reads independently input's importance overall task.Based idea inputs are equally important relevant information can be spread throughout input sequence attention mechanisms were developed BID0 help network focus important parts input. soft attention inputs are read attention mechanism is fully differentiable. comparison hard attention completely ignores part input sequence. Hard attention mechanisms have been considered many areas ranging computer vision BID14 BID1 where the model learns what parts image should focus natural language processing NLP text classification question answering BID22 BID1 BID23 where the model learns which part document can ignore. hard attention RNN has fewer state updates therefore fewer floating point operations FLOPs are needed inference. is often denoted speed reading:obtaining accuracy using far fewer FLOPs BID22 BID19 BID8 BID5. Prior work speed reading processes text chunks either individual words blocks contiguous words. If the chunk read is important enough full state update is performed;if not,the chunk is either ignored limited amount computations are done. is followed action aiming speed reading e.g skipping jumping forward text.Inspired human speed reading contribute RNN speed reading model ignores unimportant words important sections also able jump past unimportant sections text. model called Structural-Jump-LSTM1 skips jumps dynamically defined chunks text follows:can skip individual words reading updating RNN state;b uses punctuation structure text define dynamically spaced jumps next sub-sentence separator end sentence symbol end text.An extensive experimental evaluation state-of-the-art speed reading models BID19 BID22 BID5 BID8 shows Structural-Jump-LSTM dynamically spaced jumps word level skipping leads large FLOP reductions maintaining better reading accuracy vanilla LSTM reads full text. presented Structural-Jump-LSTM recurrent neural network speed reading. StructuralJump-LSTM is inspired human speed reading can skip irrelevant words important sections also jumping past unimportant parts text. uses dynamically spaced punctuation structure text determine whether jump next word next sub-sentence separator next end sentence end text. addition allows skipping word observing without updating state RNN. extensive experimental evaluation five state-of-the-art baselines Structural-Jump-LSTM obtains overall largest reduction floating point operations maintaining accuracy even improving vanilla LSTM model reads full text. contribute first ever neural speed reading model skips jumps dynamically defined chunks text without loss effectiveness notable gains efficiency. Future work includes investigating reward functions where mostof reward is not awarded end whether would improve agent training stronger signal spread throughout text.",1027,681,346,0.01,1.508,2025/11/05 17:19:10,0.01,1.364,0.5545171339563861,319.063
"One of the key challenges of session-based recommender systems is to enhance users’ purchase intentions. In this paper, we formulate the sequential interactions between user sessions and a recommender agent as a Markov Decision Process (MDP). In practice, the purchase reward is delayed and sparse, and may be buried by clicks, making it an impoverished signal for policy learning. Inspired by the prediction error minimization (PEM) and embodied cognition, we propose a simple architecture to augment reward, namely Imagination Reconstruction Network (IRN). Specifically, IRN enables the agent to explore its environment and learn predictive representations via three key components. The imagination core generates predicted trajectories, i.e., imagined items that users may purchase. The trajectory manager controls the granularity of imagined trajectories using the planning strategies, which balances the long-term rewards and short-term rewards. To optimize the action policy, the imagination-augmented executor minimizes the intrinsic imagination error of simulated trajectories by self-supervised reconstruction, while maximizing the extrinsic reward using model-free algorithms. Empirically, IRN promotes quicker adaptation to user interest, and shows improved robustness to the cold-start scenario and ultimately higher purchase performance compared to several baselines. Somewhat surprisingly, IRN using only the purchase reward achieves excellent next-click prediction performance, demonstrating that the agent can ""guess what you like"" via internal planning. A good recommender system can enhance both satisfaction for users and profit for content providers BID7 . In many real-world scenarios, the recommender systems make recommendations based only on the current browsing session, given the absence of user profiles (because the user is new or not tracked or not logged in, till the final purchase step). A session is a group of sequential interactions between a user and the system within a short period of time. To model this phenomenon, Recurrent Neural Networks (RNNs) were recently employed as session-based recommenders BID9 BID12 . For instance, GRU4Rec BID9 utilizes the session-parallel mini-batch training to handle the variable lengths of sessions, and predicts the next action given the sequence of items in the current session. However, these approaches primarily focus on next-click prediction and model the session data via sequential classification, and thus cannot distinguish the different effects of user clicks and purchases.In this paper, we consider the session-based recommendation as a Markov Decision Process (MDP), which can take into account both the click reward and the purchase reward (see FIG0 , and leverage Reinforcement Learning (RL) to learn the recommendation strategy. In practice, several challenges need to be addressed. First, the recommender systems involve large numbers of discrete actions (i.e., items), making current RL algorithms difficult to apply . This requires the agent to explore its environment for action feature learning and develop an ability to generalize over unseen actions. Second, we found it difficult to specify the click reward and the purchase reward; the policy may be biased by long sessions that contain many user clicks, as RL algorithms maximize the accumulated reward. Besides, real-world recommender systems require quick adaptation to user interest and robustness to the cold-start scenario (i.e., enhancing the purchase performance of short sessions). Therefore, we will be particularly interested in a case where only the purchase is used as reward (click sequences are used as inputs of the imagination core for Under review as a conference paper at ICLR 2019 exploration). 1 However, the purchase reward is delayed and sparse (one session may contain only one purchase), making it a difficult signal for policy learning.To augment reward and encourage exploration, we present the Imagination Reconstruction Network (IRN), which is inspired by the prediction error minimization (PEM) BID10 BID5 BID14 and embodied cognition BID2 BID1 BID23 BID3 from the neuroscience literature. The PEM is an increasingly influential theory that stresses the importance of brain-body-world interactions in cognitive processes, involving perception, action and learning. In particular, IRN can be regarded as a proof-of-concept for the PEM from the recommendation perspective, following the ideas in BID1 and BID23 -the brain utilizes active sensorimotor predictions (or counterfactual predictions) to represent states of affairs in the world in an action-oriented manner. Specifically, the imagination core of IRN that predicts the future trajectories (i.e., a set of imagined items that user may purchase) conditioned on actions sampled from the imagination policy, can be considered as the generative model of the brain that simulates sensorimotor predictions. To update the action policy, the imagination-augmented executor minimizes the intrinsic imagination error of predicted trajectories by self-supervised reconstruction, while maximizing the extrinsic reward using RL, with shared input state or output action representations for predictive learning. This simulates the active perception (a key aspect of embodied cognition) of the body under the PEM framework, which adapts the agent to possible changes that arise from the ongoing exploratory action. Note that the imagination policy imitates the action policy through distillation or a delayed target network, and thus IRN constructs a loop between brain and body, encouraging the agent to perform actions that can reduce the error in the agent's ability to predict the future events BID20 . IRN equips the agent with a planning module, trajectory manager, that controls the granularity of imagined trajectories using the planning strategies (e.g., breadth-n and depth-m). Besides, IRN is a combination of model-based planning and self-supervised RL, as the imagined trajectories provide dense training signals for auxiliary task learning (see section 2).The key contributions of this paper are summarized as follows:• We formulate the session-based recommendation as a MDP, and leverage deep RL to learn the optimal recommendation policy, and also discuss several challenges when RL is applied.• We consider a special case where only the purchase is used as reward, and then propose the IRN architecture to optimize the sparser but more business-critical purchase signals, which draws inspiration from the theories of cognition science.• We present a self-supervised reconstruction method for predictive learning, which minimizes the imagination error of simulated trajectories over time. IRN achieves excellent click and purchase performance even without any external reward (predictive perception BID23 ).• We conduct a comprehensive set of experiments to demonstrate the effectiveness of IRN. Compared to several baselines, IRN improves data efficiency, promotes quicker adaptation to user interest, and shows improved robustness to the cold-start scenario and ultimately higher purchase performance. These are highly valuable properties in an industrial context.",One key challenges session-based recommender systems is to enhance users purchase intentions. paper formulate sequential interactions user sessions recommender agent Markov Decision Process MDP practice purchase reward is delayed sparse may buried clicks making impoverished signal policy learning. Inspired prediction error minimization PEM embodied cognition propose simple architecture augment reward namely Imagination Reconstruction Network IRN Specifically IRN enables agent explore environment learn predictive representations via three key components. imagination core generates predicted trajectories.e imagined items users may purchase. trajectory manager controls granularity imagined trajectories using planning strategies which balances long-term rewards short-term rewards. optimize action policy imagination-augmented executor minimizes intrinsic imagination error simulated trajectories self-supervised reconstruction maximizing extrinsic reward using model-free algorithms. Empirically IRN promotes quicker adaptation user interest shows improved robustness cold-start scenario ultimately higher purchase performance compared several baselines. Somewhat surprisingly IRN using purchase reward achieves excellent next-click prediction performance demonstrating agent can guess what you like via internal planning. good recommender system can enhance satisfaction users profit content providers BID7. many real-world scenarios recommender systems make recommendations based current browsing session given absence user profiles user is new tracked logged till final purchase step session is a group sequential interactions user system within short period time. model phenomenon Recurrent Neural Networks RNNs were recently employed session-based recommenders BID9 BID12. instance GRU4Rec BID9 utilizes session-parallel mini-batch training handle variable lengths sessions predicts next action given sequence items current session. However approaches primarily focus next-click prediction model session data via sequential classification thus cannot distinguish different effects user clicks purchases.In paper consider session-based recommendation Markov Decision Process MDP which can take account click reward purchase reward see FIG0 leverage Reinforcement Learning RL learn recommendation strategy. practice several challenges need addressed. First recommender systems involve large numbers discrete actions.e items making current RL algorithms difficult apply. requires agent explore environment action feature learning develop ability generalize unseen actions. Second found difficult specify click reward purchase reward;policy may biased long sessions contain many user clicks RL algorithms maximize accumulated reward. Besides real-world recommender systems require quick adaptation user interest robustness cold-start scenario.e enhancing purchase performance short sessions Therefore will be particularly interested case where only the purchase is used reward click sequences are used inputs imagination core review conference paper ICLR 2019 exploration 1 However purchase reward is delayed sparse one session may contain one purchase making difficult signal policy learning.To augment reward encourage exploration present Imagination Reconstruction Network IRN which is inspired prediction error minimization PEM BID10 BID5 BID14 embodied cognition BID2 BID1 BID23 BID3 neuroscience literature. PEM is an increasingly influential theory stresses importance brain-body-world interactions cognitive processes involving perception action learning. particular IRN can be regarded proof-of-concept PEM recommendation perspective following ideas BID1 BID23 -the brain utilizes active sensorimotor predictions counterfactual predictions represent states affairs world action-oriented manner. Specifically imagination core IRN predicts future trajectories.e set imagined items user may purchase conditioned actions sampled imagination policy can be considered generative model brain simulates sensorimotor predictions. update action policy imagination-augmented executor minimizes intrinsic imagination error predicted trajectories self-supervised reconstruction maximizing extrinsic reward usingRL shared input state output action representations predictive learning. simulates active perception key aspect embodied cognition body PEM framework which adapts agent possible changes arise ongoing exploratory action. Note imagination policy imitates action policy distillation delayed target network thus IRN constructs loop brain body encouraging agent perform actions can reduce error agent's ability predict future events BID20. IRN equips agent planning module trajectory manager controls granularity imagined trajectories using planning strategies e.g breadth-n depth-m Besides IRN is a combination model-based planning self-supervisedRL imagined trajectories provide dense training signals auxiliary task learning see section2.The key contributions paper are summarized follows:• formulate session-based recommendation MDP leverage deepRL learn optimal recommendation policy also discuss several challenges whenRL is applied.• consider special case where only the purchase is used reward propose IRN architecture optimize sparser business-critical purchase signals which draws inspiration theories cognition science.• present self-supervised reconstruction method predictive learning which minimizes imagination error simulated trajectories time. IRN achieves excellent click purchase performance even without external reward predictive perception BID23.• conduct comprehensive set experiments demonstrate effectiveness IRN. Compared several baselines IRN improves data efficiency promotes quicker adaptation user interest shows improved robustness cold-start scenario ultimately higher purchase performance. are highly valuable properties industrial context.,1311,880,431,0.014,1.49,2025/11/05 17:19:10,0.01,1.444,0.4984423676012459,435.377
"The question why deep learning algorithms generalize so well has attracted increasing
 research interest. However, most of the well-established approaches,
 such as hypothesis capacity, stability or sparseness, have not provided complete
 explanations (Zhang et al., 2016; Kawaguchi et al., 2017). In this work, we focus
 on the robustness approach (Xu & Mannor, 2012), i.e., if the error of a hypothesis
 will not change much due to perturbations of its training examples, then it
 will also generalize well. As most deep learning algorithms are stochastic (e.g.,
 Stochastic Gradient Descent, Dropout, and Bayes-by-backprop), we revisit the robustness
 arguments of Xu & Mannor, and introduce a new approach – ensemble
 robustness – that concerns the robustness of a population of hypotheses. Through
 the lens of ensemble robustness, we reveal that a stochastic learning algorithm can
 generalize well as long as its sensitiveness to adversarial perturbations is bounded
 in average over training examples. Moreover, an algorithm may be sensitive to
 some adversarial examples (Goodfellow et al., 2015) but still generalize well. To
 support our claims, we provide extensive simulations for different deep learning
 algorithms and different network architectures exhibiting a strong correlation between
 ensemble robustness and the ability to generalize. Deep Neural Networks (DNNs) have been successfully applied in many artificial intelligence tasks, providing state-of-the-art performance and a remarkably small generalization error. On the other hand, DNNs often have far more trainable model parameters than the number of samples they are trained on and were shown to have a large enough capacity to memorize the training data BID26 . The findings of Zhang et al. suggest that classical explanations for generalization cannot be applied directly to DNNs and motivated researchers to look for new complexity measures and explanations for the generalization deep neural networks BID2 BID16 BID0 BID13 . However, in this work, we focus on a different approach to study generalization of DNNs, i.e., the connection between the robustness of a deep learning algorithm and its generalization performance. Xu & Mannor have shown that if an algorithm is robust (i.e., its empirical loss does not change dramatically for perturbed samples), its generalization performance can also be guaranteed. However, in the context of DNNs, practitioners observe contradicting evidence between these two attributes. On the one hand, DNNs generalize well, and on the other, they are fragile to adversarial perturbation on the inputs BID21 BID8 . Nevertheless, algorithms that try to improve the robustness of learning algorithms have been shown to improve the generalization of deep neural networks. Two examples are adversarial training, i.e., generating adversarial examples and training on them BID21 BID8 BID18 , and Parseval regularization BID5 , i.e., minimizing the Lifshitz constant of the network to guarantee low robustness. While these meth-ods minimize the robustness implicitly, their empirical success Indicates a connection between the robustness of an algorithm and its ability to generalize.To solve this contradiction, we revisit the robustness argument in BID23 and present ensemble robustness, to characterize the generalization performance of deep learning algorithms. Our proposed approach is not intended to give tight bounds for general deep learning algorithms, but rather to pave the way for addressing the question: how can deep learning perform so well while being fragile to adversarial examples? Answering this question is difficult, yet we present evidence in both theory and simulation suggesting that ensemble robustness explains the generalization performance of deep learning algorithms.Ensemble robustness concerns the fact that a randomized algorithm (e.g., Stochastic Gradient Descent (SGD), Dropout BID19 , Bayes-by-backprop BID3 , etc. ) produces a distribution of hypotheses instead of a deterministic one. Therefore, ensemble robustness takes into consideration robustness of the population of the hypotheses: even though some hypotheses may be sensitive to perturbation on inputs, an algorithm can still generalize well as long as most of the hypotheses sampled from the distribution are robust on average. BID13 took a different approach and claimed that deep neural networks could generalize well despite nonrobustness. However, our definition of ensemble robustness together with our empirical findings suggest that deep learning methods are typically robust although being fragile to adversarial examples.Through ensemble robustness, we prove that the following holds with a high probability: randomized learning algorithms can generalize well as long as its output hypothesis has bounded sensitiveness to perturbation in average (see Theorem 1). Specified for deep learning algorithms, we reveal that if hypotheses from different runs of a deep learning method perform consistently well in terms of robustness, the performance of such deep learning method can be confidently expected. Moreover, each hypothesis may be sensitive to some adversarial examples as long as it is robust on average.Although ensemble robustness may be difficult to compute analytically, we demonstrate an empirical estimate of ensemble robustness and investigate the role of ensemble robustness via extensive simulations. The results provide supporting evidence for our claim: ensemble robustness consistently explains the generalization performance of deep neural networks. Furthermore, ensemble robustness is measured solely on training data, potentially allowing one to use the testing examples for training and selecting the best model based on its ensemble robustness. BID23 proposed to consider model robustness for estimating generalization performance for deterministic algorithms, such as for SVM BID25 and Lasso BID24 . They suggest using robust optimization to construct learning algorithms, i.e., minimizing the empirical loss concerning the adversarial perturbed training examples. In this paper, we investigated the generalization ability of stochastic deep learning algorithm based on their ensemble robustness; i.e., the property that if a testing sample is similar to a training sample, then its loss is close to the training error. We established both theoretically and experimentally evidence that ensemble robustness of an algorithm, measured on the training set, indicates its generalization performance well. Moreover, our theory and experiments suggest that DNNs may be robust (and generalize) while being fragile to specific adversarial examples. Measuring ensemble robustness of stochastic deep learning algorithms may be computationally prohibitive as one needs to sample several output hypotheses of the algorithm. Thus, we demonstrated that by learning the probability distribution of the weights of a neural network explicitly, e.g., via variational methods such as Bayes-by-backprop, we can still observe a positive correlation between robustness and generalization while using fewer computations, making ensemble robustness feasible to measure.As a direct consequence, one can potentially measure the generalization error of an algorithm without using testing examples. In future work, we plan to further investigate if ensemble robustness can be used for model selection instead of cross-validation (and hence, increasing the training set size), in particular in problems that have a small training set. A different direction is to study the resilience of deep learning methods to adversarial attacks BID17 . BID20 recently showed that ensemble methods are useful as a mean to defense against adversarial attacks. However, they only considered implicit ensemble methods which are computationally prohibitive. As our simulations show that explicit ensembles are robust as well, we believe that they are likely to be a useful defense strategy while reducing computational cost. Finally, Theorem 2 suggests that a randomized algorithm can tolerate the non-robustness of some hypotheses to certain samples; this may help to explain Proposition 1 in BID13 : ""For any dataset, there exist arbitrarily unstable non-robust algorithms such that has a small generalization gap"". We leave this intuition for future work.",question why deep learning algorithms generalize well has attracted increasing research interest. However well-established approaches hypothesis capacity stability sparseness have not provided complete explanations Zhangetal. 2016;Kawaguchietal. 2017 work focus robustness approach Xu Mannor 2012.e if the error hypothesis will not change much due perturbations training examples will also generalize well. deep learning algorithms are stochastic e.g Stochastic Gradient Descent Dropout Bayes-by-backprop revisit robustness arguments Xu Mannor introduce new approach – ensemble robustness– concerns robustness population hypotheses. lens ensemble robustness reveal stochastic learning algorithm can generalize well long sensitiveness adversarial perturbations is bounded average training examples. Moreover algorithm may sensitive adversarial examples Goodfellowetal. 2015 still generalize well. support claims provide extensive simulations different deep learning algorithms different network architectures exhibiting strong correlation ensemble robustness ability generalize. Deep Neural Networks DNNs have been successfully applied many artificial intelligence tasks providing state-of-the-art performance remarkably small generalization error. hand DNNs often have far trainable model parameters number samples are trained were shown have a large enough capacity memorize training data BID26. findings Zhangetal. suggest classical explanations generalization cannot applied directly DNNs motivated researchers look new complexity measures explanations generalization deep neural networks BID2 BID16 BID0 BID13. However work focus different approach study generalization DNNs.e connection robustness deep learning algorithm generalization performance. Xu Mannor have have been shown if an algorithm is robust.e empirical loss does not change dramatically perturbed samples generalization performance can also guaranteed. However context DNNs practitioners observe contradicting evidence two attributes. one hand DNNs generalize well are fragile adversarial perturbation inputs BID21 BID8. Nevertheless algorithms try improve robustness learning algorithms have have been shown improve generalization deep neural networks. Two examples are adversarial training.e generating adversarial examples training BID21 BID8 BID18 Parseval regularization BID5.e minimizing Lifshitz constant network guarantee low robustness. meth-ods minimize robustness implicitly empirical success Indicates connection robustness algorithm ability generalize.To solve contradiction revisit robustness argument BID23 present ensemble robustness characterize generalization performance deep learning algorithms. proposed approach is not intended give tight bounds general deep learning algorithms rather pave way addressing question:how can deep learning perform well fragile adversarial examples? Answering question is difficult yet present evidence theory simulation suggesting ensemble robustness explains generalization performance deep learning algorithms.Ensemble robustness concerns fact randomized algorithm e.g Stochastic Gradient Descent SGD Dropout BID19 Bayes-by-backprop BID3 etc. produces distribution hypotheses instead deterministic one. Therefore ensemble robustness takes consideration robustness population hypotheses:even though hypotheses may sensitive perturbation inputs algorithm can still generalize well long hypotheses sampled distribution are robust average. BID13 took different approach claimed deep neural networks could generalize well despite nonrobustness. However definition ensemble robustness together empirical findings suggest deep learning methods are typically robust although fragile adversarial examples.Through ensemble robustness prove following holds high probability:randomized learning algorithms can generalize well long output hypothesis has bounded sensitiveness perturbation average see Theorem1 Specified deep learning algorithms reveal if hypotheses different runs deep learning method perform consistently well terms robustness performance deep learning method can be confidently expected. Moreover hypothesis may sensitive adversarial examples long is robust average.Although ensemble robustness may difficult compute analytically demonstrate empirical estimate ensemble robustness investigate role ensemble robustness via extensive simulations. results provide supporting evidence claim:ensemble robustness consistently explains generalization performance deep neural networks. Furthermore ensemble robustness is measured solely training data potentially allowing one use testing examples training selecting best model based ensemble robustness. BID23 proposed consider model robustness estimating generalization performance deterministic algorithms SVM BID25 Lasso BID24. suggest using robust optimization construct learning algorithms.e minimizing empirical loss concerning adversarial perturbed training examples. paper investigated generalization ability stochastic deep learning algorithm based ensemble robustness;.e property if a testing sample is similar training sample loss is close training error. established theoretically experimentally evidence ensemble robustness algorithm measured training set indicates generalization performance well. Moreover theory experiments suggest DNNs may robust generalize fragile specific adversarial examples. Measuring ensemble robustness stochastic deep learning algorithms may computationally prohibitive one needs sample several output hypotheses algorithm. Thus demonstrated learning probability distribution weights neural network explicitly e.g via variational methods Bayes-by-backprop can still observe positive correlation robustness generalization using fewer computations making ensemble robustness feasible measure.As direct consequence one can potentially measure generalization error algorithm without using testing examples. future work plan investigate if ensemble robustness can be used model selection instead cross-validation hence increasing training set size particular problems have a small training set. different direction is to study resilience deep learning methods adversarial attacks BID17. BID20 recently showed ensemble methods are useful mean defense adversarial attacks. However considered implicit ensemble methods which are computationally prohibitive. simulations show explicit ensembles are robust well believe are likely useful defense strategy reducing computational cost. Finally Theorem 2 suggests randomized algorithm can tolerate non-robustness hypotheses certain samples;may help explain Proposition1 BID13:dataset exist arbitrarily unstable non-robust algorithms has a small generalization gap. leave intuition future work.,1533,1031,502,0.016,1.487,2025/11/05 17:19:10,0.01,1.362,0.4890965732087229,478.385
"Deep autoregressive models have shown state-of-the-art performance in density estimation for natural images on large-scale datasets such as ImageNet.   However, such models require many thousands of gradient-based weight updates and unique image examples for training. Ideally, the models would rapidly learn visual concepts from only a handful of examples, similar to the manner in which humans learns across many vision tasks.   In this paper, we show how 1) neural attention and 2) meta learning techniques can be used in combination with autoregressive models to enable effective few-shot density estimation. Our proposed modifications to PixelCNN result in state-of-the art few-shot density estimation on the Omniglot dataset.   Furthermore, we visualize the learned attention policy and find that it learns intuitive algorithms for simple tasks such as image mirroring on ImageNet and handwriting on Omniglot without supervision. Finally, we extend the model to natural images and demonstrate few-shot image generation on the Stanford Online Products dataset. Contemporary machine learning systems are still far behind humans in their ability to rapidly learn new visual concepts from only a few examples BID14 . This setting, called few-shot learning, has been studied using deep neural networks and many other approaches in the context of discriminative models, for example ; BID21 . However, comparatively little attention has been devoted to the task of few-shot image density estimation; that is, the problem of learning a model of a probability distribution from a small number of examples. Below we motivate our study of few-shot autoregressive models, their connection to meta-learning, and provide a comparison of multiple approaches to conditioning in neural density models. In this paper we adapted PixelCNN to the task of few-shot density estimation. Comparing to several strong baselines, we showed that Attention PixelCNN achieves state-of-the-art results on Omniglot and also promising results on natural images. The model is very simple and fast to train. By looking at the attention weights, we see that it learns sensible algorithms for generation tasks such as image mirroring and handwritten character drawing. In the Meta PixelCNN model, we also showed that recently proposed methods for gradient-based meta learning can also be used for few-shot density estimation, and also achieve state-of-the-art results in terms of likelihood on Omniglot.","Deep autoregressive models have shown state-of-the-art performance density estimation natural images large-scale datasets ImageNet. However models require many thousands gradient-based weight updates unique image examples training. Ideally models would rapidly learn visual concepts handful examples similar manner which humans learns across many vision tasks. paper show how1 neural attention 2 meta learning techniques can be used combination autoregressive models enable effective few-shot density estimation. proposed modifications PixelCNN result state-of-the art few-shot density estimation Omniglot dataset. Furthermore visualize learned attention policy find learns intuitive algorithms simple tasks image mirroring ImageNet handwriting Omniglot without supervision. Finally extend model natural images demonstrate few-shot image generation Stanford Online Products dataset. Contemporary machine learning systems are still far behind humans ability rapidly learn new visual concepts examples BID14. setting called few-shot learning has been studied using deep neural networks many approaches context discriminative models example;BID21. However comparatively little attention has been devoted task few-shot image density estimation;is,the problem learning model probability distribution small number examples. motivate study few-shot autoregressive models connection meta-learning provide comparison multiple approaches conditioning neural density models. paper adapted PixelCNN task few-shot density estimation. Comparing several strong baselines showed Attention PixelCNN achieves state-of-the-art results Omniglot also promising results natural images. model is very simple fast train. looking attention weights see learns sensible algorithms generation tasks image mirroring handwritten character drawing. Meta PixelCNN model also showed recently proposed methods gradient-based meta learning can also used few-shot density estimation also achieve state-of-the-art results terms likelihood Omniglot.",456,316,140,0.004,1.443,2025/11/05 17:19:10,0.0,1.6,0.35202492211838,130.338
"Neural networks exhibit good generalization behavior in the
 over-parameterized regime, where the number of network parameters
 exceeds the number of observations. Nonetheless,
 current generalization bounds for neural networks fail to explain this
 phenomenon. In an attempt to bridge this gap, we study the problem of
 learning a two-layer over-parameterized neural network, when the data is generated by a linearly separable function. In the case where the network has Leaky
 ReLU activations, we provide both optimization and generalization guarantees for over-parameterized networks.
 Specifically, we prove convergence rates of SGD to a global
 minimum and provide generalization guarantees for this global minimum
 that are independent of the network size. 
 Therefore, our result clearly shows that the use of SGD for optimization both finds a global minimum, and avoids overfitting despite the high capacity of the model. This is the first theoretical demonstration that SGD can avoid overfitting, when learning over-specified neural network classifiers. Neural networks have achieved remarkable performance in many machine learning tasks. Although recently there have been numerous theoretical contributions to understand their success, it is still largely unexplained and remains a mystery. In particular, it is not known why in the overparameterized setting, in which there are far more parameters than training points, stochastic gradient descent (SGD) can learn networks that generalize well, as been observed in practice BID15 BID26 .In such over-parameterized settings, the loss function can contain multiple global minima that generalize poorly. Therefore , learning can in principle lead to models with low training error, but high test error. However, as often observed in practice, SGD is in fact able to find models with low training error and good generalization performance. This suggests that the optimization procedure, which depends on the optimization method (SGD) and the training data, introduces some form of inductive bias which directs it towards a low complexity solution. Thus, in order to explain the success of neural networks, it is crucial to characterize this inductive bias and understand what are the guarantees for generalization of over-parameterized neural networks.In this work, we address these problems in a binary classification setting where SGD optimizes a two-layer over-parameterized network with the goal of learning a linearly separable function. We study a relatively simple case of SGD where the weights of the second layer are fixed throughout the training process, and only the weights of the first layer are updated. Clearly, an over-parameterized network is not necessary for classifying linearly separable data, since this is possible with linear classifiers (e.g., with the Perceptron algorithm) which also have good generalization guarantees BID20 . But, the key question which we address here is whether a large network will overfit in such a case or not. As we shall see, it turns out that although the networks we consider are rich enough to considerably overfit the data, this does not happen when SGD is used for optimization. In other words, SGD introduces an inductive bias which allows it to learn over-parameterized networks that can generalize well. Therefore, this setting serves as a good test bed for studying the effect of over-paramaterization. Understanding the performance of over-parameterized neural networks is essential for explaining the success of deep learning models in practice. Despite a plethora of theoretical results for generalization of neural networks, none of them give guarantees for over-parameterized networks. In this work, we give the first provable guarantees for the generalization performance of over-parameterized networks, in a setting where the data is linearly separable and the network has Leaky ReLU activations. We show that SGD compresses its output when learning over-parameterized networks, and thus exhibits good generalization performance.The analysis for networks with Leaky ReLU activations does not hold for networks with ReLU activations, since in this case the loss contains spurious local minima. However, due to the success of over-parameterized networks with ReLU activations in practice, it is likely that similar results hold here as well. It would be very interesting to provide convergence guarantees and generalization bounds for this case. Another direction for future work is to show that similar results hold under different assumptions on the data.",Neural networks exhibit good generalization behavior over-parameterized regime where the number network parameters exceeds number observations. Nonetheless current generalization bounds neural networks fail explain phenomenon. attempt bridge gap study problem learning two-layer over-parameterized neural network when the data is generated linearly separable function. case where the network has Leaky ReLU activations provide optimization generalization guarantees over-parameterized networks. Specifically prove convergence rates SGD global minimum provide generalization guarantees global minimum are independent network size. Therefore result clearly shows use SGD optimization finds global minimum avoids overfitting despite high capacity model. is the first theoretical demonstration SGD can avoid overfitting when learning over-specified neural network classifiers. Neural networks have achieved remarkable performance many machine learning tasks. Although recently have been numerous theoretical contributions understand success is still largely unexplained remains mystery. particular is not known why in the overparameterized setting which there are far parameters training points stochastic gradient descent SGD can learn networks can generalize well observed practice BID15 BID26.In over-parameterized settings loss function can contain multiple global minima can generalize poorly. Therefore when learning can in principle lead models low training error high test error. However often observed practice SGD is in fact able find models low training error good generalization performance. suggests optimization procedure which depends optimization method SGD training data introduces form inductive bias which directs towards low complexity solution. Thus order explain success neural networks is crucial characterize inductive bias understand what are the guarantees generalization over-parameterized neural networks.In work address problems binary classification setting where SGD optimizes two-layer over-parameterized network goal learning linearly separable function. study relatively simple case SGD where the weights second layer are fixed throughout training process weights first layer are updated. Clearly over-parameterized network is not necessary classifying linearly separable data since is possible linear classifiers e.g Perceptron algorithm which also have good generalization guarantees BID20. key question which we address is whether large network will overfit case not. shall see turns although networks consider are rich enough considerably overfit data does not happen when SGD is used optimization. words SGD introduces inductive bias which allows learn over-parameterized networks can generalize well. Therefore setting serves good test bed studying effect over-paramaterization Understanding performance over-parameterized neural networks is essential explaining success deep learning models practice. Despite plethora theoretical results generalization neural networks none give guarantees over-parameterized networks. work give first provable guarantees generalization performance over-parameterized networks setting where the data is linearly separable network has Leaky ReLU activations. show SGD compresses output when learning over-parameterized networks thus exhibits good generalization performance.The analysis networks Leaky ReLU activations does not hold networks ReLU activations since case loss contains spurious local minima. However due success over-parameterized networks ReLU activations practice is likely similar results hold well. would interesting provide convergence guarantees generalization bounds case. Another direction future work is to show similar results hold different assumptions data.,870,606,264,0.009,1.436,2025/11/05 17:19:10,0.0,1.417,0.3302180685358252,296.213
"A central challenge in reinforcement learning is discovering effective policies for tasks where rewards are sparsely distributed. We postulate that in the absence of useful reward signals, an effective exploration strategy should seek out {\it decision states}. These states lie at critical junctions in the state space from where the agent can transition to new, potentially unexplored regions. We propose to learn about decision states from prior experience. By training a goal-conditioned model with an information bottleneck, we can identify decision states by examining where the model accesses the goal state through the bottleneck. We find that this simple mechanism effectively identifies decision states, even in partially observed settings. In effect, the model learns the sensory cues that correlate with potential subgoals. In new environments, this model can then identify novel subgoals for further exploration, guiding the agent through a sequence of potential decision  states and through new regions of the state space.",central challenge reinforcement learning is discovering effective policies tasks where rewards are sparsely distributed. postulate absence useful reward signals effective exploration strategy should seek \it decision states states lie critical junctions state space where the agent can transition new potentially unexplored regions. propose learn decision states prior experience. training goal-conditioned model information bottleneck can identify decision states examining where the model accesses goal state bottleneck. find simple mechanism effectively identifies decision states even partially observed settings. effect model learns sensory cues correlate potential subgoals. new environments model can then identify novel subgoals exploration guiding agent sequence potential decision states new regions state space.,181,122,59,0.002,1.484,2025/11/05 17:19:10,0.0,1.333,0.4797507788161991,78.552
"Many applications in machine learning require optimizing a function whose true gradient is unknown, but where surrogate gradient information (directions that may be correlated with, but not necessarily identical to, the true gradient) is available instead. This arises when an approximate gradient is easier to compute than the full gradient (e.g. in meta-learning or unrolled optimization), or when a true gradient is intractable and is replaced with a surrogate (e.g. in certain reinforcement learning applications or training networks with discrete variables). We propose Guided Evolutionary Strategies, a method for optimally using surrogate gradient directions along with random search. We define a search distribution for evolutionary strategies that is elongated along a subspace spanned by the surrogate gradients. This allows us to estimate a descent direction which can then be passed to a first-order optimizer. We analytically and numerically characterize the tradeoffs that result from tuning how strongly the search distribution is stretched along the guiding subspace, and use this to derive a setting of the hyperparameters that works well across problems. Finally, we apply our method to example problems including truncated unrolled optimization and training neural networks with discrete variables, demonstrating improvement over both standard evolutionary strategies and first-order methods (that directly follow the surrogate gradient). We provide a demo of Guided ES at: redacted URL Optimization in machine learning often involves minimizing a cost function where the gradient of the cost with respect to model parameters is known. When gradient information is available, firstorder methods such as gradient descent are popular due to their ease of implementation, memory efficiency, and convergence guarantees (Sra et al., 2012) . When gradient information is not available, however, we turn to zeroth-order optimization methods, including random search methods such as evolutionary strategies (Rechenberg, 1973; Nesterov & Spokoiny, 2011; Salimans et al., 2017) .However , what if only partial gradient information is available? That is , what if one has access to surrogate gradients that are correlated with the true gradient, but may be biased in some unknown fashion? Naïvely , there are two extremal approaches to optimization with surrogate gradients. On one hand, you could ignore the surrogate gradient information entirely and perform zeroth-order optimization, using methods such as evolutionary strategies to estimate a descent direction. These methods exhibit poor convergence properties when the parameter dimension is large BID5 . On the other hand, you could directly feed the surrogate gradients to a first-order optimization algorithm. However , bias in the surrogate gradients will interfere with optimizing the target problem (Tucker et al., 2017) . Ideally , we would like a method that combines the complementary strengths of these two approaches: we would like to combine the unbiased descent direction estimated with evolutionary strategies with the low-variance estimate given by the surrogate gradient. In this work, we propose a method for doing this called guided evolutionary strategies (Guided ES).The critical assumption underlying Guided ES is that we have access to surrogate gradient information, but not the true gradient. This scenario arises in a wide variety of machine learning problems, which typically fall into two categories: cases where the true gradient is unknown or not defined, and cases where the true gradient is hard or expensive to compute. Examples of the former include: models with discrete stochastic variables (where straight through estimators (Bengio et al., Figure 1: (a) Schematic of guided evolutionary strategies. We perform a random search using a distribution (white contours) elongated along a subspace (white arrow) which we are given instead of the true gradient (blue arrow). (b) Comparison of different algorithms on a quadratic loss, where a bias is explicitly added to the gradient to mimic situations where the true gradient is unknown. The loss (left) and correlation between surrogate and true gradient (right) are shown during optimization. See §4.1 for experimental details.2013 ; van den Oord et al., 2017) or Concrete/Gumble-Softmax methods (Maddison et al., 2016; BID12 are commonly used) and learned models in reinforcement learning (e.g. for Q functions (Watkins & Dayan, 1992; Mnih et al., 2013; or value estimation (Mnih et al., 2016) ). For the latter, examples include optimization using truncated backprop through time (Rumelhart et al., 1985; Williams & Peng, 1990; Wu et al., 2018) . Surrogate gradients also arise in situations where the gradients are explicitly modified during training, as in feedback alignment BID17 and related methods (Nøkland, 2016; BID6 .The key idea in Guided ES is to keep track of a low-dimensional subspace, defined by the recent history of surrogate gradients during optimization, which we call the guiding subspace. We then perform a finite difference random search (as in evolutionary strategies) preferentially within this subspace. By concentrating our search samples in a low-dimensional subspace where the true gradient has non-negative support, we dramatically reduce the variance of the search direction.Our contributions in this work are:• a new method for combining surrogate gradient information with random search,• an analysis of the bias-variance tradeoff underlying the technique ( §3.3),• a scheme for choosing optimal hyperparameters for the method ( §3.4), and• applications to example problems ( §4). We have introduced guided evolutionary strategies (Guided ES), an optimization algorithm which combines the benefits of first-order methods and random search, when we have access to surrogate gradients that are correlated with the true gradient. We analyzed the bias-variance tradeoff inherent in our method analytically, and demonstrated the generality of the technique by applying it to unrolled optimization, synthetic gradients, and training neural networks with discrete variables.","Many applications machine learning require optimizing function whose true gradient is unknown where surrogate gradient information directions may correlated necessarily identical true gradient is available instead. arises when an approximate gradient is easier compute full gradient e.g meta-learning unrolled optimization when true gradient is intractable is replaced surrogate e.g certain reinforcement learning applications training networks discrete variables propose Guided Evolutionary Strategies method optimally using surrogate gradient directions along random search. define search distribution evolutionary strategies is elongated along subspace spanned surrogate gradients. allowsus estimate descent direction which can then be passed first-order optimizer. analytically numerically characterize tradeoffs result tuning how strongly search distribution is stretched along guiding subspace use derive setting hyperparameters works well across problems. Finally apply method example problems including truncated unrolled optimization training neural networks discrete variables demonstrating improvement standard evolutionary strategies first-order methods directly follow surrogate gradient provide demo GuidedES at:redacted URL Optimization machine learning often involves minimizing cost function where the gradient cost respect model parameters is known. When gradient information is is not available firstorder methods gradient descent are popular due ease implementation memory efficiency convergence guarantees Sraetal. 2012 When gradient information is is not available however turn zeroth-order optimization methods including random search methods evolutionary strategies Rechenberg 1973;Nesterov Spokoiny 2011;Salimansetal. 2017.However what if only partial gradient information is is not available? is,what if one has access surrogate gradients are correlated true gradient may biased unknown fashion? Naïvely are two extremal approaches optimization surrogate gradients. one hand could ignore surrogate gradient information entirely perform zeroth-order optimization using methods evolutionary strategies estimate descent direction. methods exhibit poor convergence properties when the parameter dimension is large BID5. hand could directly feed surrogate gradients first-order optimization algorithm. However where a bias surrogate gradients will interfere optimizing target problem Tuckeretal. 2017 Ideally would like method combines complementary strengths two approaches:would like combine unbiased descent direction estimated evolutionary strategies low-variance estimate given surrogate gradient. work propose method called guided evolutionary strategies GuidedES.The critical assumption underlying GuidedES is that we have access surrogate gradient information true gradient. scenario arises wide variety machine learning problems which typically fall two categories:cases where the true gradient is unknown defined cases where the true gradient is hard expensive compute. Examples former include:models discrete stochastic variables where straight estimators Bengioetal. Figure1:Schematic guided evolutionary strategies. perform random search using distribution white contours elongated along subspace white arrow which we are given instead true gradient blue arrow b Comparison different algorithms quadratic loss where a bias is explicitly added gradient mimic situations where the true gradient is unknown. loss left correlation surrogate true gradient right are shown optimization. See §4.1 experimental details.2013 van den Oordetal. 2017 Concrete/Gumble-Softmax methods Maddisonetal. 2016;BID12 are commonly used learned models reinforcement learning e.g Q functions Watkins Dayan 1992;Mnihetal. 2013;value estimation Mnihetal. 2016 latter examples include optimization using truncated backprop time Rumelhartetal. 1985;Williams Peng 1990;Wuetal. 2018 Surrogate gradients also arise situations where the gradients are explicitly modified training feedback alignment BID17 related methods Nøkland 2016;BID6.The key idea GuidedES is to keep track low-dimensional subspace defined recent history surrogate gradients optimization which we call guiding subspace. perform finite difference random search evolutionary strategies preferentially within subspace. concentrating search samples low-dimensional subspace where the true gradient has non-negative support dramatically reduce variance search direction.Our contributions work are:• new method combining surrogate gradient information random search • analysis bias-variance tradeoff underlying technique §3.3 • scheme choosing optimal hyperparameters method §3.4 and• applications example problems §4 have introduced guided evolutionary strategies GuidedES optimization algorithm which combines benefits first-order methods random search when we have access surrogate gradients are correlated true gradient. analyzed bias-variance tradeoff inherent method analytically demonstrated generality technique applying unrolled optimization synthetic gradients training neural networks discrete variables.",1185,826,359,0.012,1.435,2025/11/05 17:19:10,0.01,1.5,0.3271028037383177,363.537
"Point clouds are an important type of geometric data and have widespread use in computer graphics and vision. However, learning representations for point clouds is particularly challenging due to their nature as being an unordered collection of points irregularly distributed in 3D space. Graph convolution, a generalization of the convolution operation for data defined over graphs, has been recently shown to be very successful at extracting localized features from point clouds in supervised or semi-supervised tasks such as classification or segmentation. This paper studies the unsupervised problem of a generative model exploiting graph convolution. We focus on the generator of a GAN and define methods for graph convolution when the graph is not known in advance as it is the very output of the generator. The proposed architecture learns to generate localized features that approximate graph embeddings of the output geometry. We also study the problem of defining an upsampling layer in the graph-convolutional generator, such that it learns to exploit a self-similarity prior on the data distribution to sample more effectively. Convolutional neural networks are at the core of highly successful models in image generation and understanding. This success is due to the ability of the convolution operation to exploit the principles of locality, stationarity and compositionality that hold true for many data of interest. In particular, feature locality and weight sharing across the data domain greatly reduce the number of parameters in the model, simplifying training and countering overfitting. However, while images are defined on an underlying regular grid structure, several other types of data naturally lie on irregular or nonEuclidean domains . Examples include problems in 3D models BID3 BID17 , computational biology BID1 BID7 or social network graphs BID14 . Defining convolutional architectures on these domains is key to exploit useful priors on the data to obtain more powerful representations.Graph convolution is emerging as one of the most successful approaches to deal with data where the irregular domain can be represented as a graph. In this case, the data are defined as vectors on the nodes of a graph. Defining a convolution-like operation for this kind of data is not trivial, as even simple notions such as shifts are undefined. The literature has identified two main approaches to define graph convolution, namely spectral or spatial. In the former case BID13 BID6 BID14 , the convolution operator is defined in the spectral domain through the graph Fourier transform BID24 . Fast polynomial approximations BID6 exist that allow an efficient implementation of the operation. This spectral approach has been successfully used in semi-supervised classification BID14 and link prediction BID23 . However, the main drawback of these techniques is that the structure of the graph is supposed to be fixed and it is not clear how to handle the case where the graph structure varies. The latter class of methods BID25 BID26 defines the convolution operator using a spatial approach by means of local aggregations, i.e., weighted combinations of the vectors restricted to a neighborhood. Since this kind of convolution is defined at a neighborhood level, the operation remains well defined even when the graph varies.Point clouds are a challenging data type due to the irregular positioning of the points and the fact that a point cloud is an unordered set of points, and therefore any permutation of its members, while changing the representation, does not change its semantic meaning. Some works have addressed supervised problems on point clouds such as classification or segmentation, either through voxelization BID19 BID27 , where the irregular point structure is approximated with a regular 3D grid, or by networks like PointNet BID21 b) that address the problem of permutation invariance by processing each point identically and independently before applying a globally symmetric operation. The most recent approaches BID25 BID26 build graphs in the Euclidean space of the point cloud and use graph convolution operations. This approach has shown multiple advantages in i) reducing the degrees of freedom in the learned models by enforcing some kind of weight sharing, ii) extracting localized features that successfully capture dependencies among neighboring points. Generative models are powerful tools in unsupervised learning aiming at capturing the data distribution. However, so far little work has been done on generative models for point clouds. Generative models of point clouds can be useful for many tasks that range from data augmentation to shape completion or inpainting partial data thanks to the features learned by the model. Generative Adversarial Networks (GANs) have been shown on images to provide better approximations of the data distribution than variational autoencoders (VAEs) BID15 , being able to generate sharper images and to capture semantic properties in their latent space. For this reason, it is interesting to study them for unordered point sets. In the first work on the topic, BID0 studied some GAN architectures to generate point clouds. Such architectures use the PointNet approach to deal with the permutation problem at the discriminator and employ a dense generator. However, this means that they are unable to learn localized features or exploit weight sharing. This paper studies a generative model for point clouds based on graph convolution. In particular, we focus on the GAN generator which is not well explored by the graph convolution literature. This poses a unique challenge: how can one apply a localized operation (the graph convolution) without knowing the domain (the graph) in advance because it is the very output of the generator? We show that the proposed architecture learns domain and features simultaneously and promotes the features to be graph embeddings, i.e. representations in a vector space of the local dependencies between a point and its neighbors. Such localized features learned by the generator provide a flexible and descriptive model. Moreover, we address the problem of upsampling at the generator. While downsampling based on graph coarsening is a staple in (semi-)supervised problems using graph convolution, it is not obvious how to properly upsample the intermediate layers of a graph-convolutional GAN generator. We propose a method exploiting non-local self-similarities in the data distribution. We presented a GAN using graph convolutional layers to generate 3D point clouds. In particular, we showed how constructing nearest neighbor graphs from generator features to implement the graph convolution operation promotes the features to be localized and to approximate a graph embedding of the output geometry. We also proposed an upsampling scheme for the generator that exploits self-similarities in the samples to be generated. The main drawback of the current method is the rather high complexity of the graph convolution operation. Future work will focus on reducing the overall complexity, e.g., in the graph construction operation, and study new upsampling schemes.",Point clouds are an important type geometric data have widespread use computer graphics vision. However learning representations point clouds is particularly challenging due nature unordered collection points irregularly distributed 3D space. Graph convolution generalization convolution operation data defined graphs has been recently shown successful extracting localized features point clouds supervised semi-supervised tasks classification segmentation. paper studies unsupervised problem generative model exploiting graph convolution. focus generator GAN define methods graph convolution when the graph is not known advance is the output generator. proposed architecture learns generate localized features approximate graph embeddings output geometry. also study problem defining upsampling layer graph-convolutional generator learns exploit self-similarity prior data distribution sample effectively. Convolutional neural networks are at the core highly successful models image generation understanding. success is due ability convolution operation exploit principles locality stationarity compositionality hold true many data interest. particular feature locality weight sharing across data domain greatly reduce number parameters model simplifying training countering overfitting. However images are defined underlying regular grid structure several types data naturally lie irregular nonEuclidean domains. Examples include problems 3D models BID3 BID17 computational biology BID1 BID7 social network graphs BID14. Defining convolutional architectures domains is key exploit useful priors data obtain powerful representations.Graph convolution is emerging one successful approaches deal data where the irregular domain can be represented graph. case data are defined vectors nodes graph. Defining convolution-like operation kind data is not trivial even simple notions shifts are undefined. literature has identified two main approaches define graph convolution namely spectral spatial. former case BID13 BID6 BID14 convolution operator is defined spectral domain graph Fourier transform BID24. Fast polynomial approximations BID6 exist allow efficient implementation operation. spectral approach has been successfully used semi-supervised classification BID14 link prediction BID23. However main drawback techniques is that the structure graph is supposed fixed is not clear how to handle case where the graph structure varies. latter class methods BID25 BID26 defines convolution operator using spatial approach means local aggregations.e weighted combinations vectors restricted neighborhood. Since kind convolution is defined neighborhood level operation remains well defined even when the graph varies.Point clouds are a challenging data type due irregular positioning points fact point cloud is an unordered set points therefore permutation members changing representation does not change semantic meaning. works have addressed supervised problems point clouds classification segmentation either voxelization BID19 BID27 where the irregular point structure is approximated regular 3D grid networks like PointNet BID21 b address problem permutation invariance processing point identically independently applying globally symmetric operation. recent approaches BID25 BID26 build graphs Euclidean space point cloud use graph convolution operations. approach has shown multiple advantages reducing degrees freedom learned models enforcing kind weight sharing ii extracting localized features successfully capture dependencies among neighboring points. Generative models are powerful tools unsupervised learning aiming capturing data distribution. However far little work has been done generative models point clouds. Generative models point clouds can be useful many tasks range data augmentation shape completion inpainting partial data thanks features learned model. Generative Adversarial Networks GANs have been shown images provide better approximations data distribution variational autoencoders VAEs BID15 able generate sharper images capture semantic properties latent space. reason is interesting study unordered point sets. first work topic BID0 studied GAN architectures generate point clouds. architectures use PointNet approach deal permutation problem discriminator employ dense generator. However means are unable learn localized features exploit weight sharing. paper studies generative model point clouds based graph convolution. particular focus GAN generator which is not well explored graph convolution literature. poses unique challenge:how can one apply localized operation graph convolution without knowing domain graph advance is the output generator? show proposed architecture learns domain features simultaneously promotes features graph embeddings.e representations vector space local dependencies point neighbors. localized features learned generator provide flexible descriptive model. Moreover address problem upsampling generator. downsampling based graph coarsening is a staple semi- supervised problems using graph convolution is not obvious how to properly upsample intermediate layers graph-convolutional GAN generator. propose method exploiting non-local self-similarities data distribution. presented GAN using graph convolutional layers generate 3D point clouds. particular showed how constructing nearest neighbor graphs generator features implement graph convolution operation promotes features localized approximate graph embedding output geometry. also proposed upsampling scheme generator exploits self-similarities samples generated. main drawback current method is the rather high complexity graph convolution operation. Future work will focus reducing overall complexity e.g graph construction operation study new upsampling schemes.,1305,884,421,0.013,1.476,2025/11/05 17:19:10,0.01,1.674,0.4548286604361368,427.928
"Memorization in over-parameterized neural networks can severely hurt generalization in the presence of mislabeled examples. However, mislabeled examples are to hard avoid in extremely large datasets. We address this problem using the implicit regularization effect of stochastic gradient descent with large learning rates, which we find to be able to separate clean and mislabeled examples with remarkable success using loss statistics. We leverage this to identify and on-the-fly discard mislabeled examples using a threshold on their losses. This leads to On-the-fly Data Denoising (ODD), a simple yet effective algorithm that is robust to mislabeled examples, while introducing almost zero computational overhead. Empirical results demonstrate the effectiveness of ODD on several datasets containing artificial and real-world mislabeled examples. Over-parametrized deep neural networks have remarkable generalization properties while achieving near-zero training error (Zhang et al., 2016) . However, the ability to fit the entire training set is highly undesirable, as a small portion of mislabeled examples in the dataset could severely hurt generalization (Zhang et al., 2016; BID0 . Meanwhile, an exponential growth in training data size is required to linearly improve generalization in vision tasks BID31 ; this progress could be hindered if there are mislabeled examples within the dataset.Mislabeled examples are to be expected in large datasets that contain millions of examples. Webbased supervision produces noisy labels BID17 BID21 ; whereas human labeled datasets sacrifice accuracy for scalability BID16 . Therefore, algorithms that are robust to various levels of mislabeled examples are warranted in order to further improve generalization for very large labeled datasets.In this paper, we propose On-the-fly Data Denoising (ODD), a simple and robust method for training with noisy examples based on the implicit regularization effect of stochastic gradient descent. First, we train residual networks with large learning rate schedules and use the resulting losses to separate clean examples from mislabeled ones. This is done by identifying examples whose losses exceed a certain threshold. Reasonable thresholds can be derived from the loss distribution for uniform label noise which does not depend on the amount of mislabeled examples in the dataset. Finally, we remove these examples from the dataset and continue training until convergence. Empirically, ODD performs significantly better than previous methods in datasets containing artificial noise (Sections 4.1 and 4.2) or real-world mislabeled examples (Section 4.3), while achieving equal or better accuracy than the state-of-the-art on clean datasets (Sections 4.1 and 4.2). We further conduct ablation studies to demonstrate that ODD is robust w.r.t hyperparameters and artificial noise levels (Section 4.4). Our method is also able to detect mislabeled examples in the CIFAR-100 dataset without any additional supervision ( FIG0 ). We have proposed ODD, a straightforward method for robust training with mislabeled examples. ODD utilizes the implicit regularization effect of stochastic gradient descent to prune examples that potentially harm generalization. Empirical results demonstrate that ODD is able to significantly outperform related methods on a wide range of datasets with artificial and real-world mislabeled examples, maintain competitiveness with ERM on clean datasets, as well as detecting mislabeled examples automatically in CIFAR-100.The implicit regularization of stochastic gradient descent opens up other research directions for implementing robust algorithms. For example, we could consider using a smaller network to remove examples, removing examples not only once but multiple times, retraining from scratch with the denoised dataset, or other data-augmentation approaches such as mixup (Zhang et al., 2017) . Moreover, it would be interesting to understand the implicit regularization over mislabeled examples from a theoretical viewpoint. A ADDITIONAL EXPERIMENTAL RESULTS",Memorization over-parameterized neural networks can severely hurt generalization presence mislabeled examples. However mislabeled examples are to hard avoid extremely large datasets. address problem using implicit regularization effect stochastic gradient descent large learning rates which we find able separate clean mislabeled examples remarkable success using loss statistics. leverage identify on-the-fly discard mislabeled examples using threshold losses. leads On-the-fly Data Denoising ODD simple yet effective algorithm is are robust mislabeled examples introducing almost zero computational overhead. Empirical results demonstrate effectiveness ODD several datasets containing artificial real-world mislabeled examples. Over-parametrized deep neural networks have remarkable generalization properties achieving near-zero training error Zhangetal. 2016 However ability fit entire training set is highly undesirable small portion mislabeled examples dataset could severely hurt generalization Zhangetal. 2016;BID0. Meanwhile exponential growth training data size is required linearly improve generalization vision tasks BID31;progress could hindered if there are mislabeled examples within dataset.Mislabeled examples are to be expected large datasets contain millions examples. Webbased supervision produces noisy labels BID17 BID21;whereas human labeled datasets sacrifice accuracy scalability BID16. Therefore algorithms is are robust various levels mislabeled examples are warranted order improve generalization large labeled datasets.In paper propose On-the-fly Data Denoising ODD simple robust method training noisy examples based implicit regularization effect stochastic gradient descent. First train residual networks large learning rate schedules use resulting losses separate clean examples mislabeled ones. is done identifying examples whose losses exceed certain threshold. Reasonable thresholds can be derived loss distribution uniform label noise which does not depend amount mislabeled examples dataset. Finally remove examples dataset continue training convergence. Empirically ODD performs significantly better previous methods datasets containing artificial noise Sections 4.1 4.2 real-world mislabeled examples Section 4.3 achieving equal better accuracy state-of-the-art clean datasets Sections 4.1 4.2 conduct ablation studies demonstrate ODD is robustw.r.t hyperparameters artificial noise levels Section 4.4 method is also able detect mislabeled examples CIFAR-100 dataset without additional supervision FIG0 have proposed ODD straightforward method robust training mislabeled examples. ODD utilizes implicit regularization effect stochastic gradient descent prune examples potentially harm generalization. Empirical results demonstrate ODD is able significantly outperform related methods wide range datasets artificial real-world mislabeled examples maintain competitiveness ERM clean datasets well detecting mislabeled examples automatically CIFAR-100.The implicit regularization stochastic gradient descent opens research directions implementing robust algorithms. example could consider using smaller network remove examples removing examples multiple times retraining scratch denoised dataset data-augmentation approaches mixup Zhangetal. 2017 Moreover would interesting understand implicit regularization mislabeled examples theoretical viewpoint. ADDITIONAL EXPERIMENTAL RESULTS,766,565,201,0.007,1.356,2025/11/05 17:19:10,0.0,1.5,0.0809968847352025,234.219
"Binarized Neural Networks (BNNs) have recently attracted significant interest due to their computational efficiency. Concurrently, it has been shown that neural networks may be overly sensitive to ``attacks"" -- tiny adversarial changes in the input -- which may be detrimental to their use in safety-critical domains. Designing attack algorithms that effectively fool trained models is a key step towards learning robust neural networks.
 The discrete, non-differentiable nature of BNNs, which distinguishes them from their full-precision counterparts, poses a challenge to gradient-based attacks. In this work, we study the problem of attacking a BNN through the lens of combinatorial and integer optimization. We propose a Mixed Integer Linear Programming (MILP) formulation of the problem. While exact and flexible, the MILP quickly becomes intractable as the network and perturbation space grow. To address this issue, we propose IProp, a decomposition-based algorithm that solves a sequence of much smaller MILP problems. Experimentally, we evaluate both proposed methods against the standard gradient-based attack (PGD) on MNIST and Fashion-MNIST, and show that IProp performs favorably compared to PGD, while scaling beyond the limits of the MILP. The success of neural networks in vision, text and speech tasks has led to their widespread deployment in commercial systems and devices. However, these models can often be fooled by minimal perturbations to their inputs, posing serious security and safety threats BID13 . A great deal of current research addresses the ""robustification"" of neural networks using adversarially generated examples BID19 BID22 , a variant of standard gradient-based training that uses adversarial training examples to defend against possible attacks. Recent work has also formulated the problem of ""adversarial learning"" as a robust optimization problem BID22 BID17 BID29 , where one seeks the best model parameters with respect to the loss function as measured on the worst-case adversarial perturbation of each point in the training dataset. Attack algorithms may thus be used to augment the training dataset with adversarial examples during training, resulting in more robust models BID19 . These new advances further motivate the need to develop effective methods for generating adversarial examples for neural networks.In this work, we focus on designing effective attacks against Binarized Neural Networks (BNNs) BID8 . BNNs are neural networks with weights in {−1, +1} and the sign function non-linearity, and are especially pertinent in low-power or hardware-constrained settings, where they have the potential to be used at an unprecedented scale if deployed to smartphones and other edge devices. This makes attacking, and consequently robustifying BNNs, a task of major importance. However, the discrete, non-differentiable structure of a BNN renders less effective the typical attack algorithms that rely on gradient information. As strong attacks are crucial to effective adversarial training, we are motivated to address this problem in the hope of generating better attacks.The goal of adversarial attacks is to modify an input slightly, so that the neural network predicts a different class than what it would have predicted for the original input. More formally, the task of generating an optimal adversarial example is the following: Given:-A (clean) data point x ∈ R n ;-A trained BNN model with parameters w, that outputs a value f c (x; w) for a class c ∈ C; -prediction, the class predicted for data point x, arg max c∈C f c (x; w); -target, the class we would like to predict for a slightly perturbed version of x; -, the maximum amount of perturbation allowed in any of the n dimensions of the input x. We developed combinatorial search methods for generating adversarial examples that fool trained Binarized Neural Networks, based on a Mixed Integer Linear Programming (MILP) model and a target propagation-driven iterative algorithm IProp. To our knowledge, this is the first such integer optimization-based attack for BNNs, a type of neural networks that is inherently discrete. Our MILP model results show that standard (PGD) attack methods often are suboptimal in generating good adversarial examples when the perturbation budget is limited. The ultimate goal is to ""attack to protect"", i.e. to generate perturbations that can be used during adversarial training, resulting in BNNs that are robust to a class of perturbation. Unfortunately, our MILP model cannot be solved quickly enough to be incorporated into adversarial training. On the other hand, through extensive experiments we have shown that our iterative algorithm IProp is able to scale-up this solving process while maintaining good performance compared to the PGD attack. With these contributions, we believe we have laid the foundations for improved attacks and potentially robust training of BNNs. This work is a good example of successful cross fertilization of ideas and methods from discrete optimization and machine learning, a growing synergistic area of research, both in terms of using discrete optimization for ML as was done here BID11 BID2 , as well as using ML in discrete optimization tasks BID14 BID28 BID16 BID18 BID9 . We believe that target propagation ideas such as in IProp can be potentially extended for the problem of training BNNs, a challenging task to this day. The same can be said about hard-threshold networks, as hinted to by BID11 . We implemented the method of ""simultaneous perturbation stochastic approximation"" (SPSA) BID30 , which was recently used in BID33 as an example of a gradient-free attack. Our implementation of SPSA follows BID33 and uses the Adam optimization method with learning rate 0.01, a stochastic sample of perturbations (referred to as ""batch size"" in BID33 ) of size 100, and an iteration limit of 100. As with PGD, SPSA is run with random restarts every 100 iterations until the time limit of 180 seconds is reached. FIG10 shows the flip prediction rates for IProp (same as in FIG3 in the main text) and SPSA. Generally, SPSA performs worse than IProp and PGD.",Binarized Neural Networks BNNs have recently attracted significant interest due computational efficiency. Concurrently has been shown neural networks may overly sensitive attacks tiny adversarial changes input may detrimental use safety-critical domains. Designing attack algorithms effectively fool trained models is a key step towards learning robust neural networks. discrete non-differentiable nature BNNs which distinguishes full-precision counterparts poses challenge gradient-based attacks. work study problem attacking BNN lens combinatorial integer optimization. propose Mixed Integer Linear Programming MILP formulation problem. exact flexible MILP quickly becomes intractable network perturbation space grow. address issue propose IProp decomposition-based algorithm solves sequence much smaller MILP problems. Experimentally evaluate proposed methods standard gradient-based attack PGD MNIST Fashion-MNIST show IProp performs favorably compared PGD scaling beyond limits MILP. success neural networks vision text speech tasks has led widespread deployment commercial systems devices. However models can often fooled minimal perturbations inputs posing serious security safety threats BID13. great deal current research addresses robustification neural networks using adversarially generated examples BID19 BID22 variant standard gradient-based training uses adversarial training examples defend possible attacks. Recent work has also formulated problem adversarial learning robust optimization problem BID22 BID17 BID29 where one seeks best model parameters respect loss function measured worst-case adversarial perturbation point training dataset. Attack algorithms may thus used augment training dataset adversarial examples training resulting robust models BID19. new advances motivate need develop effective methods generating adversarial examples neural networks.In work focus designing effective attacks Binarized Neural Networks BNNs BID8. BNNs are neural networks weights −1+1 sign function non-linearity are especially pertinent low-power hardware-constrained settings where they have potential used unprecedented scale if deployed smartphones edge devices. makes attacking consequently robustifying BNNs task major importance. However discrete non-differentiable structure BNN renders less effective typical attack algorithms rely gradient information. strong attacks are crucial effective adversarial training are motivated address problem hope generating better attacks.The goal adversarial attacks is to modify input slightly neural network predicts different class would have predicted original input. formally task generating optimal adversarial example is the following:Given:-A clean data pointx∈ Rn;-A trained BNN model parametersw outputs valuefc x;w classc∈C;-prediction class predicted data pointx arg max c∈Cf c x;w -target class would like predict slightly perturbed version x;- maximum amount perturbation allowed n dimensions inputx. developed combinatorial search methods generating adversarial examples fool trained Binarized Neural Networks based Mixed Integer Linear Programming MILP model target propagation-driven iterative algorithm IProp. knowledge is the first integer optimization-based attack BNNs type neural networks is inherently discrete. MILP model results show standard PGD attack methods often are suboptimal generating good adversarial examples when the perturbation budget is limited. ultimate goal is to attack protect.e generate perturbations can be used adversarial training resulting BNNs are robust class perturbation. Unfortunately MILP model cannot solved quickly enough incorporated adversarial training. hand extensive experiments have shown iterative algorithm IProp is able scale-up solving process maintaining good performance compared PGD attack. contributions believe have laid foundations improved attacks potentially robust training BNNs. work is a good example successful cross fertilization ideas methods discrete optimization machine learning growing synergistic area research terms using discrete optimization ML was done BID11 BID2 well usingML discrete optimization tasks BID14 BID28 BID16 BID18 BID9. believe target propagation ideas IProp can be potentially extended problem training BNNs challenging task day. can be said hard-threshold networks hinted BID11. implemented method simultaneous perturbation stochastic approximation SPSA BID30 which was recently used BID33 example gradient-free attack. implementation SPSA follows BID33 uses Adam optimization method learning rate 0.01 stochastic sample perturbations referred batch size BID33 size 100 iteration limit 100. PGD SPSA is run random restarts every 100 iterations time limit 180 seconds is reached. FIG10 shows flip prediction rates IProp FIG3 main text SPSA. Generally SPSA performs worse IProp PGD.,1244,834,410,0.012,1.492,2025/11/05 17:19:10,0.01,1.4,0.5046728971962615,351.969
"Highly regularized LSTMs achieve impressive results on several benchmark datasets in language modeling. We propose a new regularization method based on decoding the last token in the context using the predicted distribution of the next token. This biases the model towards retaining more contextual information, in turn improving its ability to predict the next token. With negligible overhead in the number of parameters and training time, our Past Decode Regularization (PDR) method achieves a word level perplexity of 55.6 on the Penn Treebank and 63.5 on the WikiText-2 datasets using a single softmax. We also show gains by using PDR in combination with a mixture-of-softmaxes, achieving a word level perplexity of 53.8 and 60.5 on these datasets. In addition, our method achieves 1.169 bits-per-character on the Penn Treebank Character dataset for character level language modeling. These results constitute a new state-of-the-art in their respective settings. Language modeling is a fundamental task in natural language processing. Given a sequence of tokens, its joint probability distribution can be modeled using the auto-regressive conditional factorization. This leads to a convenient formulation where a language model has to predict the next token given a sequence of tokens as context. Recurrent neural networks are an effective way to compute distributed representations of the context by sequentially operating on the embeddings of the tokens. These representations can then be used to predict the next token as a probability distribution over a fixed vocabulary using a linear decoder followed by Softmax.Starting from the work of BID16 , there has been a long list of works that seek to improve language modeling performance using more sophisticated recurrent neural networks (RNNs) BID26 ; BID27 ; BID28 ; BID17 ). However, in more recent work vanilla LSTMs BID7 ) with relatively large number of parameters have been shown to achieve state-of-the-art performance on several standard benchmark datasets both in word-level and character-level perplexity BID14 b) ; BID12 ; BID25 ). A key component in these models is the use of several forms of regularization e.g. variational dropout on the token embeddings BID3 ), dropout on the hidden-to-hidden weights in the LSTM BID24 ), norm regularization on the outputs of the LSTM and classical dropout BID23 ). By carefully tuning the hyperparameters associated with these regularizers combined with optimization algorithms like NT-ASGD (a variant of the Averaged SGD), it is possible to achieve very good performance. Each of these regularizations address different parts of the LSTM model and are general techniques that could be applied to any other sequence modeling problem.In this paper, we propose a regularization technique that is specific to language modeling. One unique aspect of language modeling using LSTMs (or any RNN) is that at each time step t, the model takes as input a particular token x t from a vocabulary W and using the hidden state of the LSTM (which encodes the context till x t ) predicts a probability distribution w t+1 on the next token x t+1 over the same vocabulary as output. Since x t can be mapped to a trivial probability distribution over W , this operation can be interpreted as transforming distributions over W BID9 ). Clearly, the output distribution is dependent on and is a function of x t and the context further in the past and encodes information about it. We ask the following question -How much information is it possible to decode about the input distribution (and hence x t ) from the output distribution w t+1 ? In general, it is impossible to decode x t unambiguously. Even if the language model is perfect and correctly predicts x t+1 with probability 1, there could be many tokens preceding it. However, in this case the number of possibilities for x t will be limited, as dictated by the bigram statistics of the corpus and the language in general. We argue that biasing the language model such that it is possible to decode more information about the past tokens from the predicted next token distribution is beneficial. We incorporate this intuition into a regularization term in the loss function of the language model.The symmetry in the inputs and outputs of the language model at each step lends itself to a simple decoding operation. It can be cast as a (pseudo) language modeling problem in ""reverse"", where the future prediction w t+1 acts as the input and the last token x t acts as the target of prediction. The token embedding matrix and weights of the linear decoder of the main language model can be reused in the past decoding operation. We only need a few extra parameters to model the nonlinear transformation performed by the LSTM, which we do by using a simple stateless layer. We compute the cross-entropy loss between the decoded distribution for the past token and x t and add it to the main loss function after suitable weighting. The extra parameters used in the past decoding are discarded during inference time. We call our method Past Decode Regularization or PDR for short.We conduct extensive experiments on four benchmark datasets for word level and character level language modeling by combining PDR with existing LSTM based language models and achieve new state-of-the-art performance on three of them.",Highly regularized LSTMs achieve impressive results several benchmark datasets language modeling. propose new regularization method based decoding last token context using predicted distribution next token. biases model towards retaining contextual information turn improving ability predict next token. negligible overhead number parameters training time Past Decode Regularization PDR method achieves word level perplexity 55.6 Penn Treebank 63.5 WikiText-2 datasets using single softmax. also show gains using PDR combination mixture-of-softmaxes achieving word level perplexity 53.8 60.5 datasets. addition method achieves 1.169 bits-per-character Penn Treebank Character dataset character level language modeling. results constitute new state-of-the-art respective settings. Language modeling is a fundamental task natural language processing. Given sequence tokens joint probability distribution can be modeled using auto-regressive conditional factorization. leads convenient formulation where a language model has to predict next token given sequence tokens context. Recurrent neural networks are an effective way compute distributed representations context sequentially operating embeddings tokens. representations can then be used predict next token probability distribution fixed vocabulary using linear decoder followed Softmax.Starting work BID16 has been long list works seek improve language modeling performance using sophisticated recurrent neural networks RNNs BID26;BID27;BID28;BID17 However recent work vanilla LSTMs BID7 relatively large number parameters have been shown achieve state-of-the-art performance several standard benchmark datasets word-level character-level perplexity BID14b BID12;BID25 key component models is the use several forms regularization e.g variational dropout token embeddings BID3 dropout hidden-to-hidden weights LSTM BID24 norm regularization outputs LSTM classical dropout BID23 carefully tuning hyperparameters associated regularizers combined optimization algorithms like NT-ASGD variant Averaged SGD is possible achieve good performance. regularizations address different parts LSTM model are general techniques could applied sequence modeling problem.In paper propose regularization technique is specific language modeling. One unique aspect language modeling using LSTMs RNN is thatat time step model takes input particular tokenx vocabularyW using hidden state LSTM which encodes context tillx predicts probability distributionw+1 next tokenx+1 vocabulary output. Sincex can be mapped trivial probability distribution W operation can be interpreted transforming distributions W BID9 Clearly output distribution is dependent is a function x context past encodes information it. ask following question -How much information is it possible decode input distribution hencex output distributionw+1? general is impossible decodex unambiguously. Even if the language model is perfect correctly predictsx+1 probability1 could many tokens preceding it. However case number possibilities x will be limited dictated bigram statistics corpus language general. argue biasing language model is possible decode information past tokens predicted next token distribution is beneficial. incorporate intuition regularization term loss function language model.The symmetry inputs outputs language model step lends simple decoding operation. can be cast pseudo language modeling problem reverse where the future predictionw+1 acts input last tokenx acts target prediction. token embedding matrix weights linear decoder main language model can be reused past decoding operation. need extra parameters model nonlinear transformation performed LSTM whichwedo using simple stateless layer. compute cross-entropy loss decoded distribution past token x add main loss function suitable weighting. extra parameters used past decoding are discarded inference time. call method Past Decode Regularization PDR short.We conduct extensive experiments four benchmark datasets word level character level language modeling combining PDR existing LSTM based language models achieve new state-of-the-art performance three them.,1049,702,347,0.01,1.494,2025/11/05 17:19:10,0.01,1.767,0.5109034267912771,318.499
"The assumption that data samples are independently identically distributed is the backbone of many learning algorithms. Nevertheless, datasets often exhibit rich structures in practice, and we argue that there exist some unknown orders within the data instances. Aiming to find such orders, we introduce a novel Generative Markov Network (GMN) which we use to extract the order of data instances automatically. Specifically, we assume that the instances are sampled from a Markov chain. Our goal is to learn the transitional operator of the chain as well as the generation order by maximizing the generation probability under all possible data permutations. One of our key ideas is to use neural networks as a soft lookup table for approximating the possibly huge, but discrete transition matrix. This strategy allows us to amortize the space complexity with a single model and make the transitional operator generalizable to unseen instances. To ensure the learned Markov chain is ergodic, we propose a greedy batch-wise permutation scheme that allows fast training.   Empirically, we evaluate the learned Markov chain by showing that GMNs are able to discover orders among data instances and also perform comparably well to state-of-the-art methods on the one-shot recognition benchmark task. Recent advances in deep neural networks offer great potentials for machines to learn automatically without humans interventions. For instance, Convolutional Neural Networks (CNNs) BID16 provided an automated way for learning image feature representations. Compared to hand-crafted ones such as SIFT and SURF, these hierarchical deep features demonstrate superior performance in recognition BID35 and transfer learning BID7 problems. Another example would be learning to learn for automatic parameter estimation. BID0 proposed to update model parameters without any pre-defined update rule such as stochastic gradient descent (SGD) or ADAM . Surprisingly, this update-rule-free framework showed better performance and faster convergence on both object recognition and image style transformation tasks. In our paper, we investigate the following novel question: given an unordered dataset where instances may be exhibiting some implicit order, can we order a dataset automatically according to this order?We argue that such order often exists even when we are dealing with the data that are naturally thought of as being i.i.d. sampled from a common though complex distribution. For example, let's consider a dataset consisting of the joint locations on the body of the same person taken on different days. The data i.i.d. assumption is justified since postures of a person took on different days are likely unrelated. However , we can arrange the data instances such that the joints follow an articulated motion or a set of motions in a way that makes each pose highly predictable given the previous ones. Although this arrangement depends on the person as ballerinas' poses might obey different dynamics than the poses of tennis players, the simultaneous inference on the pose dynamics can lead to a robust model that explains the correlations among joints. To put it differently, if we reshuffle the frames of a video clip, the data can now be modeled by an i.i.d. model. Nevertheless , reconstructing the order leads to an alternative model where transitions between the frames are easier to fit the links between the latent structures and observations. The ballerina 's dancing, if sampled very sparsely, can be thought of as a reshuffled video sequence that needs to be reordered such that a temporal model can generate it.One naive and obvious way to find the order in a dataset is to perform sorting based on a predefined distance metric; e.g., the Euclidean distance between image pixel values. However, the distance metrics have to be predefined differently and empirically according to distinct types/characteristics of the datasets at hand. A proper distance metric for one domain may not be a good one for other domains. For instance, p distance is a good measure for DNA/RNA sequences BID23 while it does not characterize the semantic distances between images. We argue that the key component of the ordering problem lies in the discovery of proper distance metric in an automatic and adaptive way.To approach this problem, we propose to learn a distance-metric-free model to discover the ordering in the dataset. More specifically, we model the data by treating them as if they were generated from a Markov chain. We propose to simultaneously train the transitional operator and find the best order by a joint optimization over the parameter space as well as all possible permutations. We term our model Generative Markov Networks (GMNs). One of the key ideas in the design of GMNs is to use neural networks as a soft lookup table to approximate the possibly huge but discrete transition matrix. This strategy allows GMNs to amortize the space complexity using a unified model. Furthermore, due to the differentiable property of neural networks, the transitional operator of GMNs can also generalize on unseen but similar data instances. As an additional contribution, to ensure the Markov chain learned by GMNs is ergodic, we propose a greedy batch-wise permutation scheme that allows fast training.One related task is one-shot recognition which has only one labeled data per category in the target domain. Most of the work in this area considered learning a specific distance metric BID15 BID33 BID28 or category-separation metric BID24 for the data. During the inference phase, they computed either the smallest distance or highest class prediction score between the support and query instances. Alternatively, from a generative modeling perspective, we can first generate the Markov chain for the support instances, then we fit the query instances into the Markov chain and decide the labels with the highest log-likelihood.Empirically, we evaluate the learned Markov chain by showing that GMNs are able to discover implicit orders among data instances and also perform comparably well to state-of-the-art methods on the benchmark one-shot recognition task. In this section we give a detailed description on how to implement the transitional operator where the state can be both discrete or continuous. At the first step, to prevent our GMNs from simply memorizing all the training data and their transitions, we introduce stochastic latent variables z 2 R z via Variational Bayes Inference BID34 . The evidence lower bound (ELBO) of the log likelihood for the transitional operator (i.e., log T (s 0 |s; ✓)) becomes: DISPLAYFORM0 where T (s 0 |s; ✓) has been replaced by a distribution P(s 0 |s, z; ) parametrized by , which allows us to make the dependence of s on z. Moreover, KL is the KL-divergence, Q(z|s; ) is an encoder function parametrized by that encodes latent code z given current state s, and P(z) is a fixed prior which we take its form as Gaussian distribution N (0, I). We use reparametrized trick to draw Q(z|s; ) from Gaussian N µ Q, (s), 2 Q, (s)I where µ Q, (s) and Q, (s) are learnable functions.Next, we consider two types of distribution family for P(s 0 |s, z; ✓): Bernoulli and Gaussian. If s 2 {0, 1} p (i.e., a binary image), we define log P(s 0 |s, z; ) as: DISPLAYFORM1 where is element-wise multiplication and g (s, z) : DISPLAYFORM2 If s 2 R p (i.e., a real-valued feature vector), we choose P(s 0 |s, z; ) to be fixed variance factored DISPLAYFORM3 ⌘ , where µ P, (s, z) : R p+z ! R p and P is a fixed variance. We simply choose P in all the experiments. log P(s 0 |s, z; ✓) can thus be defined as DISPLAYFORM4 where const. is not related to the optimization of .For simplicity, we specify ✓ = { [ }. Therefore , the model parameters update for ✓ in (2) refers to the updates for and . In this paper, we argue that data i.i.d. assumption is not always the case in most of the datasets. Often, data instances are exhibiting some implicit orders which may benefit our understanding and analysis of the dataset. To observe the implicit orders, we propose a novel Generative Markov Network which considers a Markov chain data generation scheme. Specifically, we simultaneously learn the transitional operator as a generative model in the Markov chain as well as find the optimal orders of the data under all possible permutations. In lots of experiments, we show that our model is able to observe implicit orders from unordered datasets and also perform well on the one-shot recognition task.",assumption data samples are independently identically distributed is the backbone many learning algorithms. Nevertheless datasets often exhibit rich structures practice argue exist unknown orders within data instances. Aiming find orders introduce novel Generative Markov Network GMN which we use extract order data instances automatically. Specifically assume instances are sampled Markov chain. goal is to learn transitional operator chain well generation order maximizing generation probability possible data permutations. One key ideas is to use neural networks soft lookup table approximating possibly huge discrete transition matrix. strategy allowsus amortize space complexity single model make transitional operator generalizable unseen instances. ensure learned Markov chain is ergodic propose greedy batch-wise permutation scheme allows fast training. Empirically evaluate learned Markov chain showing GMNs are able discover orders among data instances also perform comparably well state-of-the-art methods one-shot recognition benchmark task. Recent advances deep neural networks offer great potentials machines learn automatically without humans interventions. instance Convolutional Neural Networks CNNs BID16 provided automated way learning image feature representations. Compared hand-crafted ones SIFT SURF hierarchical deep features demonstrate superior performance recognition BID35 transfer learning BID7 problems. Another example would learning learn automatic parameter estimation. BID0 proposed update model parameters without pre-defined update rule stochastic gradient descent SGD ADAM. Surprisingly update-rule-free framework showed better performance faster convergence object recognition image style transformation tasks. paper investigate following novel question:given unordered dataset where instances may exhibiting implicit order can we order dataset automatically according order? argue order often exists even when we are dealing data are naturally thought.i.d sampled common though complex distribution. example let's consider dataset consisting joint locations body person taken different days. data.i.d assumption is justified since postures person took different days are likely unrelated. However can arrange data instances joints follow articulated motion set motions way makes pose highly predictable given previous ones. Although arrangement depends person ballerinas' poses might obey different dynamics poses tennis players simultaneous inference pose dynamics can lead robust model explains correlations among joints. put differently if we reshuffle frames video clip data can now be modeled.i.d model. Nevertheless reconstructing order leads alternative model where transitions frames are easier fit links latent structures observations. ballerina 's dancing if sampled sparsely can be thought reshuffled video sequence needs reordered temporal model can generate it.One naive obvious way find order dataset is to perform sorting based predefined distance metric;e.g Euclidean distance image pixel values. However distance metrics have to be predefined differently empirically according distinct types/characteristics datasets hand. proper distance metric one domain may good one domains. instance p distance is a good measure DNA/RNA sequences BID23 does not characterize semantic distances images. argue key component ordering problem lies discovery proper distance metric automatic adaptive way.To approach problem propose learn distance-metric-free model discover ordering dataset. specifically model data treating if they were generated Markov chain. propose simultaneously train transitional operator find best order joint optimization parameter space well possible permutations. term model Generative Markov Networks GMNs One key ideas design GMNs is to use neural networks soft lookup table approximate possibly huge discrete transition matrix. strategy allows GMNs amortize space complexity using unified model. Furthermore due differentiable property neural networks transitional operator GMNs can also generalize unseen similar data instances. additional contribution ensure Markov chain learned GMNs is ergodic propose greedy batch-wise permutation scheme allows fast training.One related task is one-shot recognition which has only one labeled data per category target domain. work area considered learning specific distance metric BID15 BID33 BID28 category-separation metric BID24 data. inference phase computed either smallest distance highest class prediction score support query instances. Alternatively generative modeling perspective can first generate Markov chain support instances fit query instances Markov chain decide labels highest log-likelihood.Empirically evaluate learned Markov chain showing GMNs are able discover implicit orders among data instances also perform comparably well state-of-the-art methods benchmark one-shot recognition task. section give detailed description how to implement transitional operator where the state can be both discrete continuous. first step prevent GMNs simply memorizing training data transitions introduce stochastic latent variables z2Rz via Variational Bayes Inference BID34. evidence lower bound ELBO log likelihood transitional operator.e log 0|s✓ becomes:DISPLAYFORM0 whereT(s 0|s✓ has been replaced distributionP 0|s z;parametrized which allowsus make dependence z. Moreover KL is the KL-divergence Q z|s is an encoder function parametrized encodes latent codez given current state P z is a fixed prior which we take form Gaussian distributionN 0 use reparametrized trick drawQ z|s GaussianNµQ 2Q where where µQ Q are learnable functions.Next consider two types distribution family P 0|s z;✓ Bernoulli Gaussian. Ifs2 0 1 p.e binary image define logP 0|s z;as:DISPLAYFORM1 where is element-wise multiplication g z DISPLAYFORM2 Ifs2Rp.e real-valued feature vector chooseP 0|s z;is a fixed variance factored DISPLAYFORM3 ⌘ whereµP z Rp+z! Rp P is a fixed variance. simply chooseP experiments. logP 0|s z;✓ can thus defined DISPLAYFORM4 where const. is not related optimization.For simplicity specify✓ Therefore model parameters update ✓ 2 refers updates and. paper argue data.i.d assumption is not always case datasets. Often data instances are exhibiting implicit orders may benefit understanding analysis dataset. observe implicit orders propose novel Generative Markov Network which considers Markov chain data generation scheme. Specifically simultaneously learn transitional operator generative model Markov chain well find optimal orders data possible permutations. lots experiments show model is able observe implicit orders unordered datasets also perform well one-shot recognition task.,1743,1162,581,0.022,1.5,2025/11/05 17:19:10,0.01,1.643,0.5295950155763238,547.296
"We present a Neural Program Search, an algorithm to generate programs from natural language description and a small number of input / output examples. The algorithm combines methods from Deep Learning and Program Synthesis fields by designing rich domain-specific language (DSL) and defining efficient search algorithm guided by a Seq2Tree model on it. To evaluate the quality of the approach we also present a semi-synthetic dataset of descriptions with test examples and corresponding programs. We show that our algorithm significantly outperforms sequence-to-sequence model with attention baseline. The ability to synthesize a program from user intent (specification) is considered as one of the central problems in artificial intelligence BID9 ). Significant progress has been made recently in both program synthesis from examples (e.g. BID1 , BID22 , BID6 ) and program synthesis from descriptions (e.g. BID4 , BID28 , BID17 , BID18 ).Programming by example techniques such as Flash Fill BID11 ) and BlinkFill BID25 ) were developed to help users perform data transformation tasks using examples instead of writing programs. These methods rely on a small domain-specific language (DSL) and then develop algorithms to efficiently search the space of programs. Two shortcomings of these approaches are that DSL limits types of programs that can be synthesized, and that large engineering effort is needed to fine-tune such systems.Program synthesis from description has not been applied widely in practice yet. One of the challenges is that the natural language is very ambiguous, yet there are very strict requirements for the synthesized programs (see BID27 and BID23 for some discussion). In this paper we present Neural Program Search that learns from both description and examples and has high accuracy and speed to be applicable in practice.We specifically consider a problem of synthesizing programs from a short description and several input / output pairs. By combining description and sample tests we address both limitations of programming by example and natural language program inference. We propose LISP-inspired DSL that is capable of representing solutions to many simple problems similar to those given as data transformation homework assignments, but is rather concise, making it more tractable to search in the space of programs in this DSL.We propose a combination of two techniques -search in the programs space that is guided by a deep learning model. This way we can use the latest advances in natural language understanding with the precision of the search techniques. We use a Seq2Tree model BID0 ) that consists of a sequence encoder that reads the problem statement and a tree decoder augmented with attention that computes probabilities of each symbol in an AST tree node one node at a time. We then run a tree beam search that uses those probabilities to compute a number of most likely trees, and chooses one that is consistent with the given input/output pairs.To evaluate the proposed model we have created a partially synthetic dataset AlgoLISP consisting of problem statements, solutions in our DSL and tests. We show that search guided by deep learning models achieves significantly better results than either of the two techniques separately. We have presented an algorithm for program synthesis from textual specification and a sample of input / output pairs, that combines deep learning network for understanding language and general programming patterns with conventional search technique that allows to find correct program in discrete space which neural models struggle with. We presented a semi-synthetic dataset to empirically evaluate learning of program composition and usage of programing constructs. Our empirical results show improvement using combination of structured tree decoding and search over attentional sequence to sequence model.There remain some limitations, however. Our training data currently is semi-generated and contains only limited set of types of problems. It is prohibitively expensive to collect a human annotated set with large quantity of tasks per each problem type, so finding a way to learn from few examples per problem type is crucial. Additionally, in many practical use cases there will be no input / output examples, requiring interaction with the user to resolve ambiguity and improved techniques for structural output decoding in neural networks.",present Neural Program Search algorithm generate programs natural language description small number input/output examples. algorithm combines methods Deep Learning Program Synthesis fields designing rich domain-specific language DSL defining efficient search algorithm guided Seq2Tree model it. evaluate quality approach also present semi-synthetic dataset descriptions test examples corresponding programs. show algorithm significantly outperforms sequence-to-sequence model attention baseline. ability synthesize program user intent specification is considered one central problems artificial intelligence BID9 Significant progress has been made recently program synthesis examples e.g BID1 BID22 BID6 program synthesis descriptions e.g BID4 BID28 BID17 BID18.Programming example techniques Flash Fill BID11 BlinkFill BID25 were developed help users perform data transformation tasks using examples instead writing programs. methods rely small domain-specific language DSL develop algorithms efficiently search space programs. Two shortcomings approaches are that DSL limits types programs can be synthesized large engineering effort is needed fine-tune systems.Program synthesis description has not been applied widely practice yet. One challenges is that the natural language is very ambiguous yet are very strict requirements synthesized programs see BID27 BID23 discussion paper present Neural Program Search learns description examples has high accuracy speed applicable practice.We specifically consider problem synthesizing programs short description several input/output pairs. combining description sample tests address limitations programming example natural language program inference. propose LISP-inspired DSL is capable representing solutions many simple problems similar given data transformation homework assignments is rather concise making tractable search space programs DSL.We propose combination two techniques -search programs space is guided deep learning model. way can use latest advances natural language understanding precision search techniques. use Seq2Tree model BID0 consists sequence encoder reads problem statement tree decoder augmented attention computes probabilities symbol AST tree node one node time. run tree beam search uses probabilities compute number likely trees chooses one is consistent given input/output pairs.To evaluate proposed model have created partially synthetic dataset AlgoLISP consisting problem statements solutions DSL tests. show search guided deep learning models achieves significantly better results either two techniques separately. have presented algorithm program synthesis textual specification sample input/output pairs combines deep learning network understanding language general programming patterns conventional search technique allows find correct program discrete space which neural models struggle with. have presented semi-synthetic dataset empirically evaluate learning program composition usage programing constructs. empirical results show improvement using combination structured tree decoding search attentional sequence sequence model.There remain limitations however. training data currently is semi-generated contains limited set types problems. is prohibitively expensive collect human annotated set large quantity tasks per problem type finding way learn examples per problem type is crucial. Additionally many practical use cases will be no input/output examples requiring interaction user resolve ambiguity improved techniques structural output decoding neural networks.,779,519,260,0.008,1.501,2025/11/05 17:19:10,0.0,1.478,0.5327102803738313,277.573
"Generative adversarial training can be generally understood as minimizing certain moment matching loss defined by a set of discriminator functions, typically  neural networks. The discriminator set should be large enough to be able to uniquely identify the true distribution (discriminative), and also be small enough to go beyond memorizing samples (generalizable). In this paper, we show that a discriminator set is guaranteed to be discriminative whenever its linear span is dense in the set of bounded continuous functions. This is a very mild condition satisfied even by neural networks with a single neuron. Further, we develop generalization bounds between the learned distribution and true distribution under different evaluation metrics. When evaluated with neural distance, our bounds show that generalization is guaranteed as long as the discriminator set is small enough, regardless of the size of the generator or hypothesis set. When evaluated with KL divergence, our bound provides an explanation on the counter-intuitive behaviors of testing likelihood in GAN training. Our analysis sheds lights on understanding the practical performance of GANs. Generative adversarial networks (GANs) BID14 and their variants can be generally understood as minimizing certain moment matching loss defined by a set of discriminator functions. Mathematically, GANs minimize the integral probability metric (IPM) BID31 , that is, DISPLAYFORM0 whereμ m is the empirical measure of the observed data, and F and G are the sets of discriminators and generators, respectively.1. Wasserstain GAN (W-GAN) BID1 . F = Lip 1 (X) := {f : ||f || Lip ≤ 1}, corresponding to the Wasserstain-1 distance. 2. MMD-GAN BID27 BID13 BID25 . F is taken as the unit ball in a Reproducing Kernel Hilbert Space (RKHS), corresponding to the Maximum Mean Discrepency (MMD). 3. Energy-based GANs BID45 . F is taken as the set of continuous functions bounded between 0 and M for some constant M > 0, corresponding to the total variation distance BID1 .4. When the KL divergence is used as the evaluation metric, our bound (Corollary 3.5) suggests that the generator and discriminator sets have to be compatible in that the log density ratios of the generators and the true distributions should exist and be included inside the linear span of the discriminator set. The strong condition that log-density ratio should exist partially explains the counter-intuitive behavior of testing likelihood in flow GANs (e.g., BID11 BID15 . 5. We extend our analysis to study neural f -divergences that are the learning objective of f -GANs, and establish similar results on the discrimination and generalization properties of neural fdivergences; see Appedix B. Different from neural distance, a neural f -divergence is discriminative if linear span of its discriminators without the output activation function is dense in the bounded continuous function space. We studied the discrimination and generalization properties of GANs with parameterized discriminator class such as neural networks. A neural distance is guaranteed to be discriminative whenever the linear span of its discriminator set is dense in the bounded continuous function space. On the other hand, a neural divergence is discriminative whenever the linear span of features defined by the last linear layer of its discriminators is dense in the bounded continuous function space. We also provided generalization bounds for GANs in different evaluation metrics. In terms of neural distance, our bounds show that generalization is guaranteed as long as the discriminator set is small enough, regardless of the size of the generator or hypothesis set. This raises an interesting discriminationgeneralization balance in GANs. Fortunately, several GAN methods in practice already choose their discriminator set at the sweet point, where both the discrimination and generalization hold. Finally, our generalization bound in KL divergence provides an explanation on the counter-intuitive behaviors of testing likelihood in GAN training.There are several directions that we would like to explore in the future. First of all, in this paper, we do not talk about methods to compute the neural distance/divergence. This is typically a non-concave maximization problem and is extremely difficult to solve. Many methods have been proposed to solve this kind of minimax problems, but both stable training methods and theoretical analysis of these algorithms are still missing. Secondly, our generalization bound depends purely on the discriminator set. It is possible to obtain sharper bounds by incorporating structural information from the generator set. Finally, we would like to extend our analysis to conditional GANs (see, e.g., BID30",Generative adversarial training can be generally understood minimizing certain moment matching loss defined set discriminator functions typically neural networks. discriminator set should be large enough able uniquely identify true distribution discriminative also small enough go beyond memorizing samples generalizable paper show discriminator set is guaranteed discriminative whenever linear span is dense set bounded continuous functions. is a very mild condition satisfied even neural networks single neuron. develop generalization bounds learned distribution true distribution different evaluation metrics. When evaluated neural distance bounds show generalization is guaranteed long discriminator set is small enough regardless size generator hypothesis set. When evaluated KL divergence bound provides explanation counter-intuitive behaviors testing likelihood GAN training. analysis sheds lights understanding practical performance GANs. Generative adversarial networks GANs BID14 variants can be generally understood minimizing certain moment matching loss defined set discriminator functions. Mathematically GANs minimize integral probability metric IPM BID31 DISPLAYFORM0 whereμ is the empirical measure observed data F G are the sets discriminators generators respectively.1 Wasserstain GAN W-GAN BID1. F Lip1 X f:||f || Lip≤ 1 corresponding Wasserstain-1 distance. 2. MMD-GAN BID27 BID13 BID25. F is taken unit ball Reproducing Kernel Hilbert Space RKHS corresponding Maximum Mean Discrepency MMD 3. Energy-based GANs BID45. F is taken set continuous functions bounded 0 constant 0 corresponding total variation distance BID1 .4 When the KL divergence is used evaluation metric bound Corollary 3.5 suggests generator discriminator sets have to be compatible log density ratios generators true distributions should exist included inside linear span discriminator set. strong condition log-density ratio should exist partially explains counter-intuitive behavior testing likelihood flow GANs e.g BID11 BID15. 5. extend analysis study neural f -divergences are the learning objective f -GANs establish similar results discrimination generalization properties neural fdivergences;see AppedixB. Different neural distance neural f -divergence is discriminative if linear span discriminators without output activation function is dense bounded continuous function space. studied discrimination generalization properties GANs parameterized discriminator class neural networks. neural distance is guaranteed discriminative whenever linear span discriminator set is dense bounded continuous function space. hand neural divergence is discriminative whenever linear span features defined last linear layer discriminators is dense bounded continuous function space. also provided generalization bounds GANs different evaluation metrics. terms neural distance bounds show generalization is guaranteed long discriminator set is small enough regardless size generator hypothesis set. raises interesting discriminationgeneralization balance GANs. Fortunately several GAN methods practice already choose discriminator set sweet point where both the discrimination generalization hold. Finally generalization bound KL divergence provides explanation counter-intuitive behaviors testing likelihood GAN training.There are several directions would like explore future. First paper do not talk methods compute neural distance/divergence. is typically non-concave maximization problem is extremely difficult solve. Many methods have been proposed solve kind minimax problems stable training methods theoretical analysis algorithms are still missing. Secondly generalization bound depends purely discriminator set. is possible obtain sharper bounds incorporating structural information generator set. Finally would like extend analysis conditional GANs see e.g BID30,925,642,283,0.009,1.441,2025/11/05 17:19:10,0.0,1.56,0.3457943925233644,295.205
"Normalization layers are a staple in state-of-the-art deep neural network architectures. They are widely believed to stabilize training, enable higher learning rate, accelerate convergence and improve generalization, though the reason for their effectiveness is still an active research topic. In this work, we challenge the commonly-held beliefs by showing that none of the perceived benefits is unique to normalization. Specifically, we propose fixed-update initialization (Fixup), an initialization motivated by solving the exploding and vanishing gradient problem at the beginning of training via properly rescaling a standard initialization. We find training residual networks with Fixup to be as stable as training with normalization -- even for networks with 10,000 layers. Furthermore, with proper regularization, Fixup enables residual networks without normalization to achieve state-of-the-art performance in image classification and machine translation. Artificial intelligence applications have witnessed major advances in recent years. At the core of this revolution is the development of novel neural network models and their training techniques. For example, since the landmark work of BID13 , most of the state-of-the-art image recognition systems are built upon a deep stack of network blocks consisting of convolutional layers and additive skip connections, with some normalization mechanism (e.g., batch normalization BID16 ) to facilitate training and generalization. Besides image classification, various normalization techniques (Ulyanov et al., 2016; BID0 BID26 Wu & He, 2018) have been found essential to achieving good performance on other tasks, such as machine translation (Vaswani et al., 2017) and generative modeling (Zhu et al., 2017) . They are widely believed to have multiple benefits for training very deep neural networks, including stabilizing learning, enabling higher learning rate, accelerating convergence, and improving generalization.• Training without normalization. We propose Fixup, a method that rescales the standard initialization of residual branches by adjusting for the network architecture. Fixup enables training very deep residual networks stably at maximal learning rate without normalization. In the remaining of this paper, we first analyze the exploding gradient problem of residual networks at initialization in Section 2. To solve this problem, we develop Fixup in Section 3. In Section 4 we quantify the properties of Fixup and compare it against state-of-the-art normalization methods on real world benchmarks. A comparison with related work is presented in Section 5. In this work, we study how to train a deep residual network reliably without normalization. Our theory in Section 2 suggests that the exploding gradient problem at initialization in a positively homogeneous network such as ResNet is directly linked to the blowup of logits. In Section 3 we develop Fixup initialization to ensure the whole network as well as each residual branch gets updates of proper scale, based on a top-down analysis. Extensive experiments on real world datasets demonstrate that Fixup matches normalization techniques in training deep residual networks, and achieves state-of-the-art test performance with proper regularization.Our work opens up new possibilities for both theory and applications. Can we analyze the training dynamics of Fixup, which may potentially be simpler than analyzing models with batch normalization is? Could we apply or extend the initialization scheme to other applications of deep learning? It would also be very interesting to understand the regularization benefits of various normalization methods, and to develop better regularizers to further improve the test performance of Fixup. Proof of Theorem 1. We use f i→j to denote the composition DISPLAYFORM0 . Note that z is p.h. with respect to the input of each network block, i.e. f i→L ((1 + )x i−1 ) = (1 + )f i→L (x i−1 ) for > −1. This allows us to compute the gradient of the cross-entropy loss with respect to the scaling factor at = 0 as DISPLAYFORM1 Since the gradient L 2 norm ∂ /∂xi−1 must be greater than the directional derivative DISPLAYFORM2 xi−1 ), y), defining = t / xi−1 we have DISPLAYFORM3","Normalization layers are a staple state-of-the-art deep neural network architectures. are widely believed stabilize training enable higher learning rate accelerate convergence improve generalization though reason effectiveness is still active research topic. work challenge commonly-held beliefs showing none perceived benefits is unique normalization. Specifically propose fixed-update initialization Fixup initialization motivated solving exploding vanishing gradient problem beginning training via properly rescaling standard initialization. find training residual networks Fixup stable training normalization even networks 10,000 layers. Furthermore proper regularization Fixup enables residual networks without normalization achieve state-of-the-art performance image classification machine translation. Artificial intelligence applications have witnessed major advances recent years. core revolution is the development novel neural network models training techniques. example since landmark work BID13 state-of-the-art image recognition systems are built upon deep stack network blocks consisting convolutional layers additive skip connections normalization mechanism e.g batch normalization BID16 facilitate training generalization. Besides image classification various normalization techniques Ulyanovetal. 2016;BID0 BID26Wu 2018 have been found essential achieving good performance tasks machine translation Vaswanietal. 2017 generative modeling Zhuetal. 2017 are widely believed have multiple benefits training deep neural networks including stabilizing learning enabling higher learning rate accelerating convergence improving generalization.• Training without normalization. propose Fixup method rescales standard initialization residual branches adjusting network architecture. Fixup enables training deep residual networks stably maximal learning rate without normalization. remaining paper first analyze exploding gradient problem residual networks initialization Section2. solve problem develop Fixup Section3. Section4 quantify properties Fixup compare state-of-the-art normalization methods real world benchmarks. comparison related work is presented Section5. work study how to train deep residual network reliably without normalization. theory Section 2 suggests exploding gradient problem initialization positively homogeneous network ResNet is directly linked blowup logits. Section3 develop Fixup initialization ensure whole network well residual branch gets updates proper scale based top-down analysis. Extensive experiments real world datasets demonstrate Fixup matches normalization techniques training deep residual networks achieves state-of-the-art test performance proper regularization.Our work opens new possibilities theory applications. Can we analyze training dynamics Fixup may potentially simpler analyzing models batch normalization is? Could apply extend initialization scheme applications deep learning? would also interesting understand regularization benefits various normalization methods develop better regularizers improve test performance Fixup. Proof Theorem1. use f i→j denote composition DISPLAYFORM0. Note z ispp.h respect input network block.e f i→L 1+x i−1 1+f i→L x i−1 −1 allowsus compute gradient cross-entropy loss respect scaling factor 0 DISPLAYFORM1 Since gradient L 2 norm ∂/∂xi−1 must greater directional derivative DISPLAYFORM2 xi−1 defining/xi−1 have DISPLAYFORM3",819,560,259,0.008,1.462,2025/11/05 17:19:10,0.0,1.375,0.4112149532710277,271.846
"Designing a metric manually for unsupervised sequence generation tasks, such as text generation, is essentially difficult. In a such situation, learning a metric of a sequence from data is one possible solution. The previous study, SeqGAN, proposed the framework for unsupervised sequence generation, in which a metric is learned from data, and a generator is optimized with regard to the learned metric with policy gradient, inspired by generative adversarial nets (GANs) and reinforcement learning. In this paper, we make two proposals to learn better metric than SeqGAN's: partial reward function and expert-based reward function training. The partial reward function is a reward function for a partial sequence of a certain length. SeqGAN employs a reward function for completed sequence only. By combining long-scale and short-scale partial reward functions, we expect a learned metric to be able to evaluate a partial correctness as well as a coherence of a sequence, as a whole. In expert-based reward function training, a reward function is trained to discriminate between an expert (or true) sequence and a fake sequence that is produced by editing an expert sequence. Expert-based reward function training is not a kind of GAN frameworks. This makes the optimization of the generator easier. We examine the effect of the partial reward function and expert-based reward function training on synthetic data and real text data, and show improvements over SeqGAN and the model trained with MLE. Specifically, whereas SeqGAN gains 0.42 improvement of NLL over MLE on synthetic data, our best model gains 3.02 improvement, and whereas SeqGAN gains 0.029 improvement of BLEU over MLE, our best model gains 0.250 improvement. Generating sequential data is one of the main areas of research in machine learning. Recently, sequential generative model with recurrent neural networks (RNNs) have shown great success in several sequence generation tasks BID7 BID20 . The most common training method of RNNs is maximum log likelihood estimation (MLE). Although MLE provides stable training, a trained RNN generator suffers from the discrepancy of training mode and inference mode, called exposure bias BID3 . Exposure bias occurs because, at the inference, the generator predicts the next token given the tokens that the generator itself has generated so far, though the generator is trained to predict the next token given previous true tokens. To alleviate exposure bias, sequence training methods with reinforcement learning (RL) have been proposed BID17 . By using the methods of RL, the RNN generator can be optimized w.r.t. a task specific metric such as BLEU BID16 , rather than the log likelihood. The application of RL methods to sequence generation tasks is increasing importance recently BID23 BID14 . Throughout this paper, we use the term ""metric"" as a total reward for a sequence.If we have a good metric of a sequence, we can expect that a good sequence generator would be obtained by using a method of RL. However, as BID0 pointed out, it is generally difficult to manually specify a task specific metric for RL. It is especially difficult to manually design a proper metric for unsupervised sequence generation tasks, such as text generation or music generation (imagine how hard it is to manually design the metric of the naturalness of a sentence, or the beauty of music). One of the solutions for designing a metric for those tasks is to learn a metric from data. BID24 proposed SeqGAN, which a metric of sequence is learned from data, and a generator is optimized w.r.t. the metric. Inspired by generative adversarial nets (GANs) BID6 and RL, SeqGAN employs a discriminator which is trained to discriminate between a true sequence and a generated sequence, and a generator is trained with policy gradient BID21 by treating the discriminator as the reward function. Because SeqGAN learns a metric from data and optimizes a generator in RL manner, we can see SeqGAN as the study of inverse reinforcement learning (IRL).In this study, we also consider unsupervised sequence generation as a task of IRL, and we aim to learn the better metric than SeqGAN's. We state two proposals for this purpose: partial reward function and expert-based reward function training.The partial reward function is the reward function for a partial sequence of a certain length. SeqGAN only uses a reward function for completed sequence. As a background of its proposal, we have an assumption that it is too much of a burden on a reward function employed in SeqGAN to evaluate a coherence of sequence as well as a partial correctness comprehensively. By employing the partial reward function, we aim to make a metric that can evaluate both a coherence and a partial correctness of a sequence. Empirically, we show that the partial reward function can correctly evaluate a partial mistake of a sequence which a reward function for a completed sequence can not evaluate.In expert-based reward function training, we train the reward function without the generator's samples. The reward function is trained to discriminate between an expert sequence and a fake sequence that is produced by editing expert one. Unlike SeqGAN, expert-based reward function is not a kind of GAN frameworks. Although GAN framework has an advantage that a reward function is simultaneously trained with a generator's performance, the training of the generator frequently fails because of an instability of the GAN framework. Expert-based reward function training prioritizes executing stable training of the generator over taking an advantage of GAN framework.We conducted experiments based on synthetic data and real text data to investigate the effectiveness of partial reward function and expert-based reward function training. As an evaluation method, we employ oracle negative log likelihood (NLL) in synthetic data, and BLEU BID16 in text data. We show that the models with our proposals outperform SeqGAN in both experiments. Specifically, whereas SeqGAN gains 0.42 improvement of NLL over MLE on synthetic data, our best model gains 3.02 improvement, and whereas SeqGAN gains 0.029 improvement of BLEU over MLE, our best model gains 0.250 improvement. We stated two proposals for a learning better metric: partial reward function and expert-based reward function training. We showed that the partial reward function returns an accurate reward for a partial sequence, and benefits sequence generation training. By using partial functions of different scales, one can compose a reward function that can evaluate both coherence and the partial correctness of a sequence. We also showed that expert-based reward function training is effective compared to adversarial training. We demonstrated that a generator is well optimized w.r.t. the metric that is trained with expert-based reward function training.The balance of short-term reward and long-term reward is a difficult problem. When prioritizing short-term reward too much, the generator produces a sequence that is partially correct but not coherent, and vice versa. In our study, this balance is tuned by the hyperparameter α Di . Unfortunately, the tuning of α Di is difficult. Even validating the goodness of selected α Di is difficult because there is usually no true metric for the generated sequence (except for the special case such as oracle test). Therefore, we have to validate the selected α Di by seeing the generated sentences. This is a fundamental problem of IRL. IRL learns a reward from expert, but a goodness of a learned reward function can be evaluated by a behavior of policy, and an evaluation of a learned policy is done by a human (with a bias), or a surrogate manually designed metric. One practical strategy to balance a partial correctness and a coherence is to separate a generation process into two stages. We first produce a coherent sequence by using the generator learned with only long-term reward, and then use a short-term reward function to make a modification to partial mistakes of the produced sequence.As the generator is improving, it is desirable to update the reward function to a more strict one. A GAN framework is a good method in this sense, but as experimental results showed, it is difficult to train. One idea to update the reward function is to decrease a probability to change a token of expert in expert-based reward function training. If we decrease a probability, the reward function would become more strict. By decreasing a probability as the generator is improving, the generator might generate a more sophisticated sequence.We believe that our proposals in this paper can be applied to GAN-based sequence generation. The partial reward function can be applied to GAN-based text generator directly. In fact, BID18 used similar technique in the image generation with GAN. Expert-based reward function might make GAN training stable. The edited expert sequences have a lot of variety. There is a technique that uses the past generator's samples to ensure the variety of the samples for the training of the discriminator to stabilize GAN training, as we can see in BID18 , and the edited expert can be also applied for this purpose.A GENERATED SENTENCES Model name Generated sentence MLE us light sweet crude futures to enter the [crossover] segment ,"" said nick ross , daimlerchrysler and damaged property finance the reserve chairman united said the us sought bankruptcy protection in the us on monday , kill bill: volume 2 his previous two companies holes has been picking up in the past year . ""we are bringing a small third but the uk has been on hold of many of users to get their hands at least . icstis , ""if you work i were struggling . ""people's spending offer have to bring across the uk opened a 5bn) earlier "" the intel researchers have leveraged the company's ""most affordable media use , reaching the firm , the operating system unless voluntary fit will fund the animation prices , should remain also in novel ways that p2p is a human according to the stability pact to rises and confirm that thrives in succession . tourism said this tactic of creating vedomosti newspaper said mr irish and mark all the caribbean said the ability of the $2 , amid allegations of the virus-fighting program , updated monthly or just also brings me that had been compressed into recession -are a PG L(SeqGAN) these are pooled in london , draw about its future while it is the richest part of the digital images identity theft are being people to jump in sound to the neat business which can walk along at the show a apple of financial mail messages that has already has got given the chicago data , or or their semi-conductor after leaving weather , video games in over the third . stuff has telling parliament: level time checking for gadget there are combining automatic syncing worldwide , and you will give people the state pension age of of large and just been wiped out . the federal reserve is struggling with treasury and organisations have said you play online in a hydroelectric-power generator the airline said in the election , you would then its broadcasting attraction ,"" said research , a number of stagnation and more than 1 million copies of the personal firewalls ,"" he said . ""it is us lawyers claimed that the mac mini and is being piloted by the royal national hi-tech crime unit yuganskneftegas (yugansk) ""it will be disruptive to music , employment for mobile firm , almost three-quarters of job creation , the airline PG L exp ""a literate and qualified turkish population ,"" insisted the year to meet he has been security to be . however the game on be done in the us in the us -it will play games on the net , the success is set to the company's and court ,"" he said , it plans the market by the uk an ex-chief financial advice , that is the biggest category said a problem in europe was not enough . people yukos claims that it would the banning of a market . it will make up of work recently about security there were originally had to be seen in the way . it were also falling demand at 20% of the however , which will continue to make 50gb of high-quality data , which is one of its investment can come the game maker you can be done in the year . ""skype's success at spreading on the launch of sony's russian newspapers has been done -its own fuelled by lower prices than up to 100% . ""we will be mr ghosn will devote 40% of the directive will put up to google's funds . but on the network is PG S exp they would retaliate by seeking injunctions in the company , said they had been seen as they will be used they will be able to add to be used to spot in the world's largest car maker , said they they will be able to be recycled at 1 . 4% in october . 3bn . however , he said however , prices fell as part of the service . they need to invest in the cost of more than however , he said he would be to raise awareness of the 14 . but it is part of the this is likely to be seen in the us government , you go from the deal . but he said however , the company , which is part of the euro last week after new york times on the mobile they will be able to prevent conflicts to take their office . but they are looking for bargains , which more than 1 . 4% in the company , which is part of the industry will be able to invest the deal has been seen as they will be able to prevent conflicts . but they had been sidelined in PG SL exp (α S = 0.3) at a mere £20 , metal slug 3 is as cheap , but it is not the second time when the global entertainment industry was more than two to the uk exported , according to the uk-based journal screen that it is not the firm of england is expected to go on a broadband connection , with a single threat according to figures to come to meet , it said it would also reduce its customers , according to prevail if the end of the year , microsoft , which is expected by to $4 . 35bn , said it two of the most important costs . "" spanish , it would be failed to do a new record for it is expected to make an advisor to work , said it would allow broadband connections by the trading national users navigated around the dollar of 572 ,900 points to build the risks , and it is so far , it is not about stealing to the growing efforts in new york in the south following an apple ipod , ""it's for the most important for us crude oil company in early february , according to the report . at PG SL exp (α S = 1.0) according to the report , the company has not been being announced it will go from the decision to discuss one of the two companies will be able to go with other digital entertainment , with other companies like the it will be able to be part of its efforts . ""we're on the outlook for its core businesses , ""we want to go on the technology ,"" he said . ""we're in december , in a europe -on yukos has been made in december to graphics out of its efforts in 2005 , and paramount will go for their aim is to launch a new rental subscription service , this proves , the company will be able to more than 50% of the economy is part of its efforts to transfer files as a threat of the russian meanwhile , the decision for bt is available in december , the largest us giant earned $630m (£481 . 5m) the company announced it will see the study of the decision for digital images and technology from two companies , people will have to think of the report that it has been working with other carmakers . 5bn in january","Designing metric manually unsupervised sequence generation tasks text generation is essentially difficult. situation learning metric sequence data is one possible solution. previous study SeqGAN proposed framework unsupervised sequence generation which a which a metric is learned data generator is optimized is optimized regard learned metric policy gradient inspired generative adversarial nets GANs reinforcement learning. paper make two proposals learn better metric SeqGAN's partial reward function expert-based reward function training. partial reward function is a is the reward function partial sequence certain length. SeqGAN employs reward function completed sequence only. combining long-scale short-scale partial reward functions can expect learned metric able evaluate partial correctness well coherence sequence whole. expert-based reward function training reward function is trained discriminate expert true sequence fake sequence is produced editing expert sequence. Expert-based reward function training is not a kind GAN frameworks. makes optimization generator easier. examine effect partial reward function expert-based reward function training synthetic data real text data show improvements SeqGAN model trained MLE. Specifically whereas SeqGAN gains 0.42 improvement NLL MLE synthetic data best model gains 3.02 improvement whereas SeqGAN gains 0.029 improvement BLEU MLE best model gains 0.250 improvement. Generating sequential data is one main areas research machine learning. Recently sequential generative model recurrent neural networks RNNs have shown great success several sequence generation tasks BID7 BID20. common training method RNNs is maximum log likelihood estimation MLE Although MLE provides stable training trained RNN generator suffers discrepancy training mode inference mode called exposure bias BID3. Exposure bias occurs inference generator predicts next token given tokens generator has generated far though generator is trained predict next token given previous true tokens. alleviate exposure bias sequence training methods reinforcement learning RL have been proposed BID17. using methods RL RNN generator can be optimized optimizedw.r.t task specific metric BLEU BID16 rather log likelihood. application RL methods sequence generation tasks is increasing importance recently BID23 BID14. Throughout paper use term metric total reward sequence.If have a good metric sequence can expect good sequence generator would obtained using method RL. However BID0 pointed is generally difficult manually specify task specific metric RL. is especially difficult manually design proper metric unsupervised sequence generation tasks text generation music generation imagine how hard is to manually design metric naturalness sentence beauty music One solutions designing metric tasks is to learn metric data. BID24 proposed SeqGAN which a which a metric sequence is learned data generator is optimized is optimizedw.r.t metric. Inspired generative adversarial nets GANs BID6 RL SeqGAN employs discriminator which is trained discriminate true sequence generated sequence generator is trained policy gradient BID21 treating discriminator reward function. SeqGAN learns metric data optimizes generator RL manner can can see SeqGAN study inverse reinforcement learning IRL.In study also consider unsupervised sequence generation task IRL aim learn better metric SeqGAN's state two proposals purpose:partial reward function expert-based reward function training.The partial reward function is a is the reward function partial sequence certain length. SeqGAN uses reward function completed sequence. background proposal have an assumption is too much burden reward function employed SeqGAN evaluate coherence sequence well partial correctness comprehensively. employing partial reward function aim make metric can evaluate coherence partial correctness sequence. Empirically show partial reward function can correctly evaluate partial mistake sequence which a reward function completed sequence can not evaluate.In expert-based reward function training train reward function without generator's samples. reward function is trained discriminate expert sequence fake sequence is produced editing expert one. Unlike SeqGAN expert-based reward function is not a kind GAN frameworks. Although GAN framework has an advantage reward function is simultaneously trained generator's performance training generator frequently fails instability GAN framework. Expert-based reward function training prioritizes executing stable training generator taking advantage GAN framework.We conducted experiments based synthetic data real text data investigate effectiveness partial reward function expert-based reward function training. evaluation method employ oracle negative log likelihood NLL synthetic data BLEU BID16 text data. show models proposals outperform SeqGAN experiments. Specifically whereas SeqGAN gains 0.42 improvement NLL MLE synthetic data best model gains 3.02 improvement whereas SeqGAN gains 0.029 improvement BLEU MLE best model gains 0.250 improvement. stated two proposals learning better metric:partial reward function expert-based reward function training. showed partial reward function returns accurate reward partial sequence benefits sequence generation training. using partial functions different scales which is one can compose reward function can evaluate coherence partial correctness sequence. also showed expert-based reward function training is effective compared adversarial training. demonstrated generator is well optimizedw.r.t metric is trained expert-based reward function training.The balance short-term reward long-term reward is a is difficult problem. When prioritizing short-term reward much generator produces sequence is partially correct coherent vice versa. study balance is tuned hyperparameterαDi. Unfortunately tuning αDi is a is difficult. Even validating goodness selectedαDi is a is difficult is usually true metric generated sequence except special case oracle test Therefore have to validate selectedαDi seeing generated sentences. is a fundamental problem IRL. IRL learns reward expert goodness learned reward function can be evaluated behavior policy evaluation learned policy is done human bias surrogate manually designed metric. One practical strategy balance partial correctness coherence is to separate generation process two stages. first produce coherent sequence using generator learned long-term reward use short-term reward function make modification partial mistakes produced sequence.As generator is improving is desirable update reward function strict one. GAN framework is a good method sense experimental results showed is difficult train. One idea update reward function is to decrease probability change token expert expert-based reward function training. If we decrease probability reward function would become strict. decreasing probability generator is improving generator might generate sophisticated sequence.We believe proposals paper can be applied GAN-based sequence generation. partial reward function can be applied GAN-based text generator directly. fact BID18 used similar technique image generation GAN. Expert-based reward function might make GAN training stable. edited expert sequences have a lot variety. is a technique uses past generator's samples ensure variety samples training discriminator stabilize GAN training can can see BID18 edited expert can be also applied purpose.A GENERATED SENTENCES Model name Generated sentence MLE us light sweet crude futures enter crossover segment said nick ross daimlerchrysler damaged property finance reserve chairman united said us sought bankruptcy protection us monday kill bill:volume2 previous two companies holes has been picking past year. are bringing small third uk has been on hold many users get hands least. icstis if you work were struggling. people's spending offer have to bring across uk opened 5bn earlier intel researchers have leveraged company's affordable media use reaching firm operating system unless voluntary fit will fund animation prices should remain also novel ways p2p is a human according stability pact rises confirm thrives succession. tourism said tactic creating vedomosti newspaper said mr irish mark caribbean said ability $2 amid allegations virus-fighting program updated monthly also brings had been compressed recession -are PGL SeqGAN are pooled london draw future is the richest part digital images identity theft are being people jump sound neat business which can walk along show apple financial mail messages has already has got given chicago data semi-conductor leaving weather video games third. stuff has telling parliament:level time checking gadget are combining automatic syncing worldwide will give people state pension age large wiped out. federal reserve is struggling treasury organisations have said play online hydroelectric-power generator airline said election would broadcasting attraction said research number stagnation 1 million copies personal firewalls said. is us lawyers claimed mac mini is being piloted royal national hi-tech crime unit yuganskneftegas yugansk will be disruptive music employment mobile firm almost three-quarters job creation airline PG L exp literate qualified turkish population insisted year meet has been security be. however game done us us -it will play games net success is set company's court said plans market uk ex-chief financial advice is the biggest category said problem europe was not enough. people yukos claims would banning market. will make work recently security were originally had to be seen way. were also falling demand 20% however which will continue make 50gb high-quality data which is one investment can come game maker can be done year. skype's success spreading launch sony's russian newspapers has been done -its fuelled lower prices 100% will be mr ghosn will devote40% directive will put google's funds. network isPG exp would retaliate seeking injunctions company said had been seen will be used will be will be able add used spot world's largest car maker said will be will be able recycled 1. 4% october. 3bn. however said however prices fell part service. need invest cost however said would raise awareness 14. is part is likely seen us government go deal. said however company which is part euro last week new york times mobile will be will be able prevent conflicts take office. are looking bargains which more than1. 4% company which is part industry will be able invest deal has been seen will be able prevent conflicts. had been sidelined PG SL exp α 0.3 mere £20 metal slug3 is as cheap is second time when the global entertainment industry was more than two uk exported according uk-based journal screen is not firm england is expected go broadband connection single threat according figures come meet said would also reduce customers according prevail if the end year microsoft which is expected $4 35bn said two important costs. spanish would failed do a new record is expected make advisor work said would allow broadband connections trading national users navigated around dollar 572,900 points build risks is far is not stealing growing efforts new york south following apple ipod important us crude oil company early february according report. PG SL exp α 1.0 according report company has not been being announced willgo decision discuss one two companies will be able go digital entertainment companies like will be able part efforts. outlook core businesses want go technology said. december europe -on yukos has been made december graphics efforts 2005 paramount willgo aim is to launch new rental subscription service proves company will be able 50% economy is part efforts transfer files threat russian meanwhile decision bt is available december largest us giant earned $630m £4815m company announced will see study decision digital images technology two companies people will have to think report has been working carmakers. 5bn january",3129,2055,1074,0.062,1.523,2025/11/05 17:19:10,0.02,1.586,0.6012461059190026,1081.711
"One of the most successful techniques in generative models has been decomposing a complicated generation task into a series of simpler generation tasks.   For example, generating an image at a low resolution and then learning to refine that into a high resolution image often improves results substantially.   Here we explore a novel strategy for decomposing generation for complicated objects in which we first generate latent variables which describe a subset of the observed variables, and then map from these latent variables to the observed space.   We show that this allows us to achieve decoupled training of complicated generative models and present both theoretical and experimental results supporting the benefit of such an approach.   Learning useful intermediate representations in a hierarchical manner has been a driving factor in the recent success of deep learning BID11 . When ample amounts of labelled data are available, supervised learning methods are successful in learning useful intermediate representations BID20 BID14 ). However, the task is significantly more challenging in the context of unsupervised learning. One such approach to unsupervised learning is to learn a generative model of high-dimensional observed variables with low-dimensional latent variables, such that the latent variables capture the salient features of the data, which could then be used for other upstream tasks.Recent work by BID22 argues why hierarchical latent variables models are often not able to take advantage of the hierarchy, and only the lowest-level latent variables learn any useful representations. We posit that this is possibly because the vanilla hierarchical latent variable structure by itself only adds a very weak prior (that of devoting more processing to higher-level latent variables). When parameterizing the conditional distributions with powerful deep neural networks, this could admit a local optima in which all factors of variation are sub-optimally explained by the lowest-level latent variable. Notably, this phenomenon was also common in supervised training of deep neural networks, before BID6 introduced batch normalization, which successfully disentangles the learning dynamics at each layer, as if each layer has an independent objective function.For example, the resolution-based hierarchy is well suited to images because lower resolution images capture some factors of variation (such as objects) but discards other factors of variation (such as texture and details), giving the low and high level models distinct responsibilities. However, this decomposition is a strong prior and may not work well or apply to other types of data (for example, it is not clear how it would apply to language or video). This motivates the need for an unsupervised method for learning hierarchical latent variables with a requisite but general prior to facilitate disentangled learning dynamics in each level.Our proposed approach, which we call Locally Disentangled Factors (LDF), has the following desired features:• Decoupled level-wise training objectives which significantly accelerate training.• A graphical model based on spatial locality which aids in credit assignment, and can be thought of as a generalization to resolution-based hierarchies.• Vastly reduced memory consumption which allows training generative models on large objects, such as videos, where this is known to be a prohibitive limitation.• Applicable to variable-length objects, such as videos and text.2 PROPOSED APPROACH We have proposed Locally Disentangled Factors (LDF), a powerful new approach to decomposing the training of generative models. We have shown that LDF is able to successfully generate joint distributions over complicated objects, even though the discriminators and gradient flow are entirely local within the hierarchy. We have also shown that this allows for decoupled training and improved ability to learn from small amounts of data from the joint distribution. While our method assumes a more general prior than resolution-hierarchy style approaches, it still leaves the decision of what the local factors would be on the practitioner. Finding methods that enjoy the same computational and sample-complexity benefits with fewer assumptions about the data is an interesting research direction.",One successful techniques generative models has been decomposing complicated generation task series simpler generation tasks. example generating image low resolution learning refine high resolution image often improves results substantially. explore novel strategy decomposing generation complicated objects which we first generate latent variables which describe subset observed variables map latent variables observed space. show allowsus achieve decoupled training complicated generative models present theoretical experimental results supporting benefit approach. Learning useful intermediate representations hierarchical manner has been a driving factor recent success deep learning BID11. When ample amounts labelled data are available supervised learning methods are successful learning useful intermediate representations BID20 BID14 However task is significantly challenging context unsupervised learning. One approach unsupervised learning is to learn generative model high-dimensional observed variables low-dimensional latent variables latent variables capture salient features data could used upstream tasks.Recent work BID22 argues why hierarchical latent variables models are often able take advantage hierarchy lowest-level latent variables learn useful representations. posit is possibly vanilla hierarchical latent variable structure adds weak prior devoting processing higher-level latent variables When parameterizing conditional distributions powerful deep neural networks could admit local optima which all factors variation are sub-optimally explained lowest-level latent variable. Notably phenomenon was also common supervised training deep neural networks BID6 introduced batch normalization which successfully disentangles learning dynamics layer if each layer has an independent objective function.For example resolution-based hierarchy is well suited images lower resolution images capture factors variation objects discards factors variation texture details giving low high level models distinct responsibilities. However decomposition is a strong prior may work well apply types data example is not clear would apply language video motivates need unsupervised method learning hierarchical latent variables requisite general prior facilitate disentangled learning dynamics level.Our proposed approach which we call Locally Disentangled Factors LDF has the following desired features:• Decoupled level-wise training objectives which significantly accelerate training.• graphical model based spatial locality which aids credit assignment can be thought generalization resolution-based hierarchies.• Vastly reduced memory consumption which allows training generative models large objects videos where this is known prohibitive limitation.• Applicable variable-length objects videos text.2 PROPOSED APPROACH have proposed Locally Disentangled Factors LDF powerful new approach decomposing training generative models. have shown LDF is able successfully generate joint distributions complicated objects even though discriminators gradient flow are entirely local within hierarchy. have also shown allows decoupled training improved ability learn small amounts data joint distribution. method assumes general prior resolution-hierarchy style approaches still leaves decision what the local factors would practitioner. Finding methods enjoy computational sample-complexity benefits fewer assumptions data is an interesting research direction.,763,515,248,0.008,1.482,2025/11/05 17:19:10,0.0,1.472,0.4735202492211836,271.323
"Visual grounding of language is an active research field aiming at enriching text-based representations with visual information. In this paper, we propose a new way to leverage visual knowledge for sentence representations. Our approach transfers the structure of a visual representation space to the textual space by using two complementary sources of information: (1) the cluster information: the implicit knowledge that two sentences associated with the same visual content describe the same underlying reality and (2) the perceptual information contained within the structure of the visual space. We use a joint approach to encourage beneficial interactions during training between textual, perceptual, and cluster information. We demonstrate the quality of the learned representations on semantic relatedness, classification, and cross-modal retrieval tasks. Building linguistic vectors that represent semantics is a long-standing issue in Artificial Intelligence. Distributional Semantic Models BID36 BID41 are well-known recent efforts in this direction, making use of the distributional hypothesis BID16 on text corpora to learn word embeddings. At another granularity level, having high-quality general-purpose sentence representations is crucial for all models that encode sentences into semantic vectors, such as the ones used in machine translation BID0 or question answering BID42 . Moreover, encoding semantics of sentences is paramount because sentences describe relationships between objects and thus convey complex and high-level knowledge better than individual words, which mostly refer to a single concept BID38 .Relying only on text can lead to biased representations and unrealistic predictions (e.g., text-based models could predict that ""the sky is green"" BID1 ). Besides , it has been shown that human understanding of language is grounded in physical reality and perceptual experience (FincherKiefer, 2001 ). To overcome this limitation, one emerging approach is the visual grounding of language, which consists of leveraging visual information, usually from images, to enhance word representations. Two methods showing substantial improvements have emerged: (1) the sequential technique combines textual and visual representations that were separately learned BID3 BID44 , and (2) the joint method learns a common multimodal representation from multiple sources simultaneously BID29 . In the case of words, the latter has proven to produce representations that perform better on intrinsic and downstream tasks.While there exist numerous approaches to learning sentence representations from text corpora only, and to learning multimodal word embeddings, the problem of the visual grounding of sentences is quite new to the research community. To the best of our knowledge, the only work in the field is BID26 . The authors propose a sequential model: linguistic vectors, learned from a purely textual corpus, are concatenated with grounded vectors, which were independently learned from a captioning dataset. However, the two sources are considered separately, which might prevent beneficial interactions between textual and visual modalities during training.We propose a joint model to learn multimodal sentence representations, based on the assumption that the meaning of a sentence is simultaneously grounded in its textual and visual contexts. In our case, the textual context of a sentence consists of adjacent sentences in a text corpus. Within a distinct dataset, the visual context is learned from a paired video and its associated captions. Indeed, we propose to use videos instead of images because of their temporal aspect, since sentences often describe actions grounded in time. The key challenge is to capture visual information. Usually, to transfer information from the visual space to the textual one, one space is projected onto the other BID26 BID29 . However, as pointed out by BID9 , projections are not sufficient to transfer neighborhood structure between modalities. In our work, we rather propose to exploit the visual space by preserving the overall structure, i.e. conserving the similarities between related elements across spaces. More precisely, we take visual context into account by distinguishing two types of complementary information sources. First, the cluster information , which consists in the implicit knowledge that sentences associated with the same video refer to the same underlying reality. Second, the perceptual information , which is the high-level information extracted from a video using a pre-trained CNN.Regarding these considerations, we formulate three Research Questions (RQ):• RQ1: Is perceptual information useful to improve sentence representations?• RQ2: Are cluster and perceptual information complementary, and does their combination compete with previous models based on projections between visual and textual spaces?• RQ3: Is a joint approach better suited than a sequential one regarding the multimodal acquisition of textual and visual knowledge?Our contribution is threefold: (1) We propose a joint multimodal framework for learning grounded sentence representations; (2) We show that cluster and perceptual information are complementary sources of information; (3) To the best of our knowledge, obtained results achieve state-of-the-art performances on multimodal sentence representations. In this paper, we proposed a joint multimodal model to learn sentence representations and our learned grounded sentence embeddings show state-of-the-art performances. Besides, our main findings are the following: (1) Both perceptual and cluster information are useful to learn sentence representations, in a complementary way. (2) Preserving the structure of the visual space, by modeling textual similarities on visual ones, outperforms a strategy based on projecting one space into the other. (3) A joint approach is more appropriate than a sequential method to learn multimodal representation for sentences. As future work, we would investigate the contribution of the temporal knowledge contained in videos for sentence grounding.",Visual grounding language is an active research field aiming enriching text-based representations visual information. paper propose new way leverage visual knowledge sentence representations. approach transfers structure visual representation space textual space using two complementary sources information:1 cluster information:implicit knowledge two sentences associated visual content describe underlying reality 2 perceptual information contained within structure visual space. use joint approach encourage beneficial interactions training textual perceptual cluster information. demonstrate quality learned representations semantic relatedness classification cross-modal retrieval tasks. Building linguistic vectors represent semantics is a long-standing issue Artificial Intelligence. Distributional Semantic Models BID36 BID41 are well-known recent efforts direction making use distributional hypothesis BID16 text corpora learn word embeddings. another granularity level high-quality general-purpose sentence representations is crucial models encode sentences semantic vectors ones used machine translation BID0 question answering BID42. Moreover encoding semantics sentences is paramount sentences describe relationships objects thus convey complex high-level knowledge better individual words which mostly refer single concept BID38.Relying text can lead biased representations unrealistic predictions e.g text-based models could predict sky is green BID1 Besides has been shown human understanding language is grounded physical reality perceptual experience FincherKiefer 2001 overcome limitation one emerging approach is the visual grounding language which consists leveraging visual information usually images enhance word representations. Two methods showing substantial improvements have emerged:1 sequential technique combines textual visual representations were separately learned BID3 BID44 2 joint method learns common multimodal representation multiple sources simultaneously BID29. case words latter has proven produce representations perform better intrinsic downstream tasks.While exist numerous approaches learning sentence representations text corpora learning multimodal word embeddings problem visual grounding sentences is quite new research community. best knowledge work field is BID26. authors propose sequential model:linguistic vectors learned purely textual corpus are concatenated grounded vectors which were independently learned captioning dataset. However two sources are considered separately might prevent beneficial interactions textual visual modalities training.We propose joint model learn multimodal sentence representations based assumption meaning sentence is simultaneously grounded textual visual contexts. case textual context sentence consists adjacent sentences text corpus. Within distinct dataset visual context is learned paired video associated captions. Indeed propose use videos instead images temporal aspect since sentences often describe actions grounded time. key challenge is to capture visual information. Usually transfer information visual space textual one one space is projected onto BID26 BID29. However pointed BID9 projections are not sufficient transfer neighborhood structure modalities. work rather propose exploit visual space preserving overall structure.e conserving similarities related elements across spaces. precisely take visual context account distinguishing two types complementary information sources. First cluster information which consists implicit knowledge sentences associated video refer underlying reality. Second perceptual information which is the high-level information extracted video using pre-trained CNN.Regarding considerations formulate three Research Questions RQ • RQ1:Is perceptual information useful improve sentence representations? • RQ2:Are cluster perceptual information complementary does their combination compete previous models based projections visual textual spaces? • RQ3:Is a joint approach better suited sequential one regarding multimodal acquisition textual visual knowledge? contribution is threefold:1 propose joint multimodal framework learning grounded sentence representations;2 show cluster perceptual information are complementary sources information;3 best knowledge obtained results achieve state-of-the-art performances multimodal sentence representations. paper proposed joint multimodal model learn sentence representations learned grounded sentence embeddings show state-of-the-art performances. Besides main findings are the following:1 perceptual cluster information are useful learn sentence representations complementary way. 2 Preserving structure visual space modeling textual similarities visual ones outperforms strategy based projecting one space other. 3 joint approach is more appropriate sequential method learn multimodal representation sentences. future work would investigate contribution temporal knowledge contained videos sentence grounding.,1070,725,345,0.011,1.476,2025/11/05 17:19:10,0.01,1.371,0.4548286604361368,334.268